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Space groups and packing types

General tools for symmetry

This website gives LATT and SYMM lines for any space group:

http://cci.lbl.gov/cctbx/shelx.html

Packing types and symmetry reduction

The table blow gives that packing types from MOLPAK and the corresponding space groups and symmetry operations. It also gives some of the symmetry reductions that are possible. For more general information on all space groups, try reading the International Tables of Crystallography.

Key

Chiral Space Groups (aa, ae, af, ah, ap, aq, az, ba, bb, bc, db)

From Mercury

Polar Space Groups (aa, ac, ad, ae, af, ag, ah, ar, as, at, au, av, aw, ax, ay, bd, be, bf, bg, bh, bi, bj, da, db)

  

Both Chiral and Polar (aa, ae, af, ah, db)

  

Equivalent unknown space groups

From International Tables
                           

From CPOSS website

MOLPAK Packing Types

Packing type

LATT

SYMM

Space Group

SG number

Symmetry operations

Removed representation

Resulting SG

AA

LATT -1

 

P1

1

None

 

AB

LATT 1

 

P-1

2

Inversion

 

AC

LATT -1

SYMM +X , -Y , +Z

Pm

6

Mirror Plane

1

P1 (1)

AD

LATT -1

SYMM +X , -Y , +Z +1/2

Pc

7

Glide Plane

1

P1 (1)

AE

LATT -1

SYMM -X , +Y , -Z

P2

3

2-fold rotation axis

1

P1 (1)

AF

LATT -1

SYMM -X , +Y +1/2, -Z

P21

4

2-fold screw axis

1

P1 (1)

AG

LATT -1

SYMM +X +1/2, -Y , +Z +1/2

Pn

7

Glide Plane

1

P1 (1)

AH

LATT -1

SYMM -X , +Y +1/2, -Z

P21

4

2-fold screw axis

1

P1 (1)

AI

LATT 1

SYMM -X , +Y +1/2, -Z +1/2

P21/c

14

Inversion
2-fold screw axis
Glide Plane

1

P21 (4)

2

Pc (7)

3

P-1 (2)

AJ

LATT 1

SYMM -X , +Y , -Z +1/2

P2/c

13

Inversion
2-fold rotation axis
Glide Plane

1

Unknown P2 (3)

2

Pc (7)

3

P-1 (2)

 

LATT -1

SYMM -X , +Y , -Z +1/2

Unknown P2 (3)

3

2-fold rotation axis

 

AK

LATT 1

SYMM -X , +Y +1/2, -Z +1/2

P21/c

14

Inversion
2-fold screw axis
Glide Plane

1

P21 (4)

2

Pc (7)

3

P-1 (2)

AL

LATT 1

SYMM -X , +Y , -Z +1/2

P2/c

13

Inversion
2-fold rotation axis
Glide Plane

1

Unknown P2 (3)

2

Pc (7)

3

P-1 (2)

AM

LATT 1

SYMM -X +1/2, +Y +1/2, -Z +1/2

P21/n

14

Inversion
2-fold screw axis
Glide Plane

1

P21 (4)

2

Pn (7)

3

P-1 (2)

AN

LATT 1

SYMM -X , +Y +1/2, -Z

P21/m

11

Inversion
2-fold screw axis
Mirror Plane

1

P21 (4)

2

Pm (6)

3

P-1 (2)

AO

LATT 1

SYMM -X , +Y , -Z

P2/m

10

Inversion
2-fold rotation axis
Mirror Plane

1

P2 (3)

2

Pm (6)

3

P-1 (2)

AP

LATT -1

SYMM +X +1/2, -Y +1/2, -Z
SYMM -X , +Y +1/2, -Z
SYMM -X +1/2, -Y , +Z

P21212

18

2-fold rotation axis
2-fold screw axis
2-fold screw axis

1

P2111 (4)

2

Unknown P112 (3)

3

P21 (4)

 

LATT -1

SYMM +X +1/2, -Y +1/2, -Z

P2111

4

2-fold screw axis

 

 

LATT -1

SYMM -X +1/2, -Y , +Z

Unknown P112 (3)

3

2-fold rotation axis

 

AQ

LATT -1

SYMM +X +1/2, -Y +1/2, -Z
SYMM -X , +Y +1/2, -Z +1/2
SYMM -X +1/2, -Y , +Z +1/2

P212121

19

2-fold screw axis
2-fold screw axis
2-fold screw axis

1

P2111 (4)

2

P1121 (4)

3

P21 (4)

AR

LATT -1

SYMM -X , -Y , +Z
SYMM -X +1/2, +Y +1/2, +Z +1/2
SYMM +X +1/2, -Y +1/2, +Z +1/2

Pnn2

34

2-fold rotation axis
Glide Plane
Glide Plane

1

P112 (3)

2

Pn (7)

3

Unknown Pn11 (7)

 

LATT -1

SYMM -X , -Y , +Z

P112

3

2-fold rotation axis

 

 

LATT -1

SYMM -X +1/2, +Y +1/2, +Z +1/2

Unknown Pn11 (7)

7

Glide Plane

 

AS

LATT -1

SYMM -X , -Y , +Z +1/2
SYMM +X +1/2, -Y +1/2, +Z
SYMM -X +1/2, +Y +1/2, +Z +1/2

Pna21

33

2-fold screw axis
Glide Plane
Glide Plane

1

P1121 (4)

2

Unknown Pn11 (7)

3

Pa (7)

 

LATT -1

SYMM -X , -Y , +Z +1/2

P1121

4

2-fold screw axis

 

 

LATT -1

SYMM +X +1/2, -Y +1/2, +Z

Pa

7

Glide Plane

 

AT

LATT -1

SYMM -X , -Y , +Z
SYMM +X +1/2, -Y +1/2, +Z +1/2
SYMM -X +1/2, +Y +1/2, +Z +1/2

Pnn2

34

2-fold rotation axis
Glide Plane
Glide Plane

1

P112 (3)

2

Unknown Pn11 (7)

3

Pn (7)

AU

LATT -1

SYMM -X , -Y , +Z +1/2
SYMM -X +1/2, +Y +1/2, +Z +1/2
SYMM +X +1/2, -Y +1/2, +Z

Pna21

33

2-fold screw axis
Glide Plane
Glide Plane

1

P1121 (4)

2

Pa (7)

3

Unknown Pn11 (7)

AV

LATT -1

SYMM -X , -Y , +Z +1/2
SYMM -X +1/2, +Y +1/2, +Z +1/2
SYMM +X +1/2, -Y +1/2, +Z

Pna21

33

2-fold screw axis
Glide Plane
Glide Plane

1

P1121 (4)

2

Pa (7)

3

Unknown Pn11 (7)

AW

LATT -1

SYMM -X , -Y , +Z
SYMM -X +1/2, +Y +1/2, +Z
SYMM +X +1/2, -Y +1/2, +Z

Pba2

32

2-fold rotation axis
Glide Plane
Glide Plane

1

P112 (3)

2

Pa (7)

3

Unknown Pn11 (7)

 

LATT -1

SYMM -X +1/2, +Y +1/2, +Z

Unknown Pn11 (7)

7

Glide Plane

 

AX

LATT -1

SYMM -X , -Y , +Z
SYMM +X , -Y +1/2, +Z +1/2
SYMM -X , +Y +1/2, +Z +1/2

Pnc2

30

2-fold rotation axis
Glide Plane
Glide Plane

1

P112 (3)

2

Pn11 (7)

3

Pc (7)

 

LATT -1

SYMM -X , +Y +1/2, +Z +1/2

Pn11

7

Glide Plane

 

AY

LATT -1

SYMM -X , -Y , +Z +1/2
SYMM -X +1/2, +Y , +Z +1/2
SYMM +X +1/2, -Y , +Z

Pca21

29

2-fold screw axis
Glide Plane
Glide Plane

1

P1121 (4)

2

Pa (7)

3

Unknown Pc11 (7)

 

LATT -1

SYMM -X +1/2, +Y , +Z +1/2

Unknown Pc11 (7)

7

Glide Plane

 

AZ

LATT -1

SYMM +X +1/2, -Y +1/2, -Z
SYMM -X , +Y +1/2, -Z +1/2
SYMM -X +1/2, -Y , +Z +1/2

P212121

19

2-fold screw axis
2-fold screw axis
2-fold screw axis

1

P2111 (4)

2

P1121 (4)

3

P21 (4)

BA

LATT -1

SYMM +X +1/2, -Y +1/2, -Z
SYMM -X , +Y +1/2, -Z
SYMM -X +1/2, -Y , +Z

P21212

18

2-fold rotation axis
2-fold screw axis
2-fold screw axis

1

P2111 (4)

2

Unknown P112 (3)

3

P21 (4)

BB

LATT -1

SYMM +X +1/2, -Y , -Z
SYMM -X , -Y +1/2, +Z
SYMM -X +1/2, +Y +1/2, -Z

Unknown P21212

18

2-fold rotation axis
2-fold screw axis
2-fold screw axis

1

P2111 (4)

2

P21 (4)

3

Unknown P112 (3)

 

LATT -1

SYMM -X , -Y +1/2, +Z

Unknown P112 (3)

3

2-fold rotation axis

 

BC

LATT -1

SYMM -X , -Y , +Z +1/2
SYMM -X , +Y , -Z
SYMM +X , -Y , -Z +1/2

P2221

17

2-fold rotation axis
2-fold rotation axis
2-fold screw axis

1

P1121 (4)

2

Unknown P211 (3)

3

P2 (3)

 

LATT -1

SYMM -X , -Y , +Z +1/2

P1121

4

2-fold screw axis

 

 

LATT -1

SYMM +X , -Y , -Z +1/2

Unknown P211 (3)

3

2-fold rotation axis

 

BD

LATT -1

SYMM -X , -Y , +Z +1/2
SYMM -X +1/2, +Y +1/2, +Z +1/2
SYMM +X +1/2, -Y +1/2, +Z

Pna21

33

2-fold screw axis
Glide Plane
Glide Plane

1

P1121 (4)

2

Pa (7)

3

Unknown Pn11 (7)

BE

LATT -1

SYMM -X , -Y , +Z
SYMM -X +1/2, +Y +1/2, +Z +1/2
SYMM +X +1/2, -Y +1/2, +Z +1/2

Pnn2

34

2-fold rotation axis
Glide Plane
Glide Plane

1

P112 (3)

2

Pn (7)

3

Unknown Pn11 (7)

BF

LATT -1

SYMM -X , -Y , +Z +1/2
SYMM +X +1/2, -Y +1/2, +Z
SYMM -X +1/2, +Y +1/2, +Z +1/2

Pna21

33

2-fold screw axis
Glide Plane
Glide Plane

1

P1121 (4)

2

Unknown Pn11 (7)

3

Pa (7)

BG

LATT -1

SYMM -X , -Y , +Z
SYMM -X +1/2, +Y +1/2, +Z
SYMM +X +1/2, -Y +1/2, +Z

Pba2

32

2-fold rotation axis
Glide Plane
Glide Plane

1

P112 (3)

2

Pa (7)

3

Unknown Pn11 (7)

BH

LATT -1

SYMM -X , -Y , +Z +1/2
SYMM -X +1/2, +Y , +Z +1/2
SYMM +X +1/2, -Y , +Z

Pca21

29

2-fold screw axis
Glide Plane
Glide Plane

1

P1121 (4)

2

Pa (7)

3

Unknown Pc11 (7)

BI

LATT -1

SYMM -X , -Y , +Z
SYMM +X , -Y +1/2, +Z +1/2
SYMM -X , +Y +1/2, +Z +1/2

Pnc2

30

2-fold rotation axis
Glide Plane
Glide Plane

1

P112 (3)

2

Pn11 (7)

3

Pc (7)

BJ

LATT -1

SYMM -X , -Y , +Z +1/2
SYMM -X +1/2, +Y , +Z
SYMM +X +1/2, -Y , +Z +1/2

Unknown Pmn21

31

2-fold screw axis
Mirror Plane
Glide Plane

1

P1121 (4)

2

Pn (7)

3

Unknown Pm11 (6)

BK

LATT -1

SYMM -X , -Y , +Z
SYMM -X +1/2, +Y , +Z
SYMM +X +1/2, -Y , +Z

Pma2

31

2-fold rotation axis
Mirror Plane
Glide Plane

1

P1121 (4)

2

Pa (7)

3

Unknown Pm11 (6)

 

LATT -1

SYMM -X +1/2, +Y , +Z

Unknown Pm11 (6)

6

Mirror Plane

 

CA

LATT 1

 

P-1

2

Inversion

1

CB

LATT 1

SYMM +X +1/2, -Y +1/2, -Z
SYMM -X , +Y +1/2, -Z +1/2
SYMM -X +1/2, -Y , +Z +1/2

Pbca

61

Inversion
2-fold screw axis
2-fold screw axis
2-fold screw axis
Glide Plane
Glide Plane
Glide Plane

1

P212121 (19)

2

P21ca (29)

3

Unknown  Pb21a (29)

4

P1121/a (14)

5

Unknown Pbc21 (29)

6

P21/c (14)

7

P21/b11 (14)

 

LATT -1

SYMM -X +1/2, -Y , +Z +1/2
SYMM -X +1/2, +Y +1/2, +Z
SYMM +X , -Y +1/2, +Z +1/2

Unknown Pbc21 (29)

29

2-fold screw axis
Glide Plane
Glide Plane

 

 

LATT -1

SYMM -X , +Y +1/2, -Z +1/2
SYMM -X +1/2, +Y +1/2, +Z
SYMM +X +1/2, +Y , -Z +1/2

Unknown Pb21a (29)

29

2-fold screw axis
Glide Plane
Glide Plane

 

 

LATT -1

SYMM +X +1/2, -Y +1/2, -Z
SYMM +X , -Y +1/2, +Z +1/2
SYMM +X +1/2, +Y , -Z +1/2

P21ca

29

2-fold screw axis
Glide Plane
Glide Plane

 

CC

LATT 1

SYMM +X +1/2, -Y +1/2, -Z
SYMM -X , +Y +1/2, -Z +1/2
SYMM -X +1/2, -Y , +Z +1/2

Pbca

61

Inversion
2-fold screw axis
2-fold screw axis
2-fold screw axis
Glide Plane
Glide Plane
Glide Plane

1

P212121 (19)

2

P21ca (29)

3

Unknown  Pb21a (29)

4

P1121/a (14)

5

Unknown Pbc21 (29)

6

P21/c (14)

7

P21/b11 (14)

CD

LATT 1

SYMM +X +1/2, -Y +1/2, -Z
SYMM -X , +Y , -Z +1/2
SYMM -X +1/2, -Y +1/2, +Z +1/2

Pbcn

60

Inversion
2-fold rotation axis
2-fold screw axis
2-fold screw axis
Glide Plane
Glide Plane
Glide Plane

1

Unknown P21221 (18)

2

Unknown P21cn (33)

3

Unknown Pb2n (30)

4

P1121/n (14)

5

Unknown Pbc21 (29)

6

P2/c (13)

7

P21/b11 (14)

 

LATT -1

SYMM +X +1/2, -Y +1/2, -Z
SYMM -X , +Y , -Z +1/2
SYMM -X +1/2, -Y +1/2, +Z +1/2

Unknown P21221 (18)

18

2-fold rotation axis
2-fold screw axis
2-fold screw axis

 

 

LATT -1

SYMM +X +1/2, -Y +1/2, -Z
SYMM +X , -Y , +Z +1/2
SYMM +X +1/2, +Y +1/2, -Z +1/2

Unknown P21cn (33)

33

2-fold screw axis
Glide Plane
Glide Plane

 

 

LATT -1

SYMM -X , +Y , -Z +1/2
SYMM -X +1/2, +Y +1/2, +Z
SYMM +X +1/2, +Y +1/2, -Z +1/2

Unknown Pb2n (30)

30

2-fold rotation axis
Glide Plane
Glide Plane

 

 

LATT -1

SYMM -X +1/2, -Y +1/2, +Z +1/2
SYMM -X +1/2, +Y +1/2, +Z
SYMM +X , -Y , +Z +1/2

Unknown Pbc21 (29)

29

2-fold screw axis
Glide Plane
Glide Plane

 

CE

LATT 1

SYMM +X +1/2, -Y +1/2, -Z
SYMM -X , +Y , -Z +1/2
SYMM -X +1/2, -Y +1/2, +Z +1/2

Pbcn

60

Inversion
2-fold rotation axis
2-fold screw axis
2-fold screw axis
Glide Plane
Glide Plane
Glide Plane

1

Unknown P21221 (18)

2

Unknown P21cn (33)

3

Unknown Pb2n (30)

4

P1121/n (14)

5

Unknown Pbc21 (29)

6

P2/c (13)

7

P21/b11 (14)

DA

LATT -7

SYMM +X , -Y , +Z +1/2

Cc

9

Glide Plane

1

C1 (P1,1)

 

LATT -7

 

C1

1

 

 

DB

LATT -7

SYMM -X , +Y , -Z

C2

5

2-fold rotation axis
2-fold screw axis

1

C1 (P1,1)

DC

LATT 7

SYMM -X , +Y , -Z +1/2

C2/c

15

Inversion
2-fold rotation axis
2-fold screw axis
Glide Plane

1

C2 (5)

2

Cc (9)

3

C-1 (P-1,2)

DD

LATT 7

SYMM -X , +Y , -Z +1/2

C2/c

15

Inversion
2-fold rotation axis
2-fold screw axis
Glide Plane

1

C2 (5)

2

Cc (9)

3

C-1 (P-1,2)

DE

LATT 7

SYMM -X , +Y , -Z +1/2

C2/c

15

Inversion
2-fold rotation axis
2-fold screw axis
Glide Plane

1

C2 (5)

2

Cc (9)

3

C-1 (P-1,2)

 

LATT 7

 

C-1

2

Inversion

 

FA

LATT 1

SYMM -X , +Y +1/2, -Z +1/2

P21/c

14

Inversion
2-fold screw axis
Glide Plane

1

P21 (4)

2

Pc (7)

3

P-1 (2)

FB

LATT 1

SYMM -X , +Y +1/2, -Z

P21/m

11

Inversion
2-fold rotation axis
Mirror Plane

1

P21 (4)

2

Pm (6)

3

P-1 (2)

FC

LATT 1

SYMM -X , +Y +1/2, -Z +1/2

P21/c

14

Inversion
2-fold screw axis
Glide Plane

1

P21 (4)

2

Pc (7)

3

P-1 (2)

FD

LATT 1

SYMM -X , +Y , -Z +1/2

P2/c

13

Inversion
2-fold rotation axis
Glide Plane

1

Unknown P2 (3)

2

Pc (7)

3

P-1 (2)

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