(International Tables) Maximal subgroups of space group 195

P23	No. 195	P23	T¹

Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3); (5)

General position

Multiplicity, Wyckoff letter,
Site symmetry

Coordinates

12

j

1

(1) x, y, z	(2) -x, -y, z	(3) -x, y, -z	(4) x, -y, -z
(5) z, x, y	(6) z, -x, -y	(7) -z, -x, y	(8) -z, x, -y
(9) y, z, x	(10) -y, z, -x	(11) y, -z, -x	(12) -y, -z, x

I Maximal translationengleiche subgroups

[3] P21 (16, P222)

1; 2; 3; 4

	[4] P13 (146, R3)	1; 5; 9	a - b, b - c, a + b + c
	[4] P13 (146, R3)	1; 6; 12	-a - b, b + c, -a + b - c
	[4] P13 (146, R3)	1; 7; 10	a + b, -b + c, a - b - c
	[4] P13 (146, R3)	1; 8; 11	-a + b, -b - c, -a - b + c

II Maximal klassengleiche subgroups

Enlarged unit cell

[2] a' = 2a, b' = 2b, c' = 2c

F23 (196)

<2; 3; 5>

2a, 2b, 2c

[4] a' = 2a, b' = 2b, c' = 2c

	I2₁3 (199)	<5; 2 + (0, 1, 0); 3 + (1, 0, 0)>	2a, 2b, 2c
	I2₁3 (199)	<2 + (2, 1, 0); 3 + (3, 0, 0); 5 + (1, -1, 0)>	2a, 2b, 2c	1, 0, 0
	I2₁3 (199)	<2 + (0, 3, 0); 3 + (1, 0, 0); 5 + (0, 1, -1)>	2a, 2b, 2c	0, 1, 0
	I2₁3 (199)	<2 + (0, 1, 0); 3 + (1, 0, 2); 5 + (-1, 0, 1)>	2a, 2b, 2c	0, 0, 1

	I2₁3 (199)	<5; 2 + (1, 0, 0); 3 + (0, 0, 1)>	2a, 2b, 2c	1/2, 1/2, 1/2
	I2₁3 (199)	<2 + (3, 0, 0); 3 + (2, 0, 1); 5 + (1, -1, 0)>	2a, 2b, 2c	3/2, 1/2, 1/2
	I2₁3 (199)	<2 + (1, 2, 0); 3 + (0, 0, 1); 5 + (0, 1, -1)>	2a, 2b, 2c	1/2, 3/2, 1/2
	I2₁3 (199)	<2 + (1, 0, 0); 3 + (0, 0, 3); 5 + (-1, 0, 1)>	2a, 2b, 2c	1/2, 1/2, 3/2

	I23 (197)	<2; 3; 5>	2a, 2b, 2c
	I23 (197)	<(2; 3) + (2, 0, 0); 5 + (1, -1, 0)>	2a, 2b, 2c	1, 0, 0
	I23 (197)	<3; 2 + (0, 2, 0); 5 + (0, 1, -1)>	2a, 2b, 2c	0, 1, 0
	I23 (197)	<2; 3 + (0, 0, 2); 5 + (-1, 0, 1)>	2a, 2b, 2c	0, 0, 1

	I23 (197)	<5; 2 + (1, 1, 0); 3 + (1, 0, 1)>	2a, 2b, 2c	1/2, 1/2, 1/2
	I23 (197)	<2 + (3, 1, 0); 3 + (3, 0, 1); 5 + (1, -1, 0)>	2a, 2b, 2c	3/2, 1/2, 1/2
	I23 (197)	<2 + (1, 3, 0); 3 + (1, 0, 1); 5 + (0, 1, -1)>	2a, 2b, 2c	1/2, 3/2, 1/2
	I23 (197)	<2 + (1, 1, 0); 3 + (1, 0, 3); 5 + (-1, 0, 1)>	2a, 2b, 2c	1/2, 1/2, 3/2

Series of maximal isomorphic subgroups

[p³] a' = pa, b' = pb, c' = pc

P23 (195)	<2 + (2u, 2v, 0); 3 + (2u, 0, 2w); 5 + (u - w, -u + v, -v + w)>	pa, pb, pc	u, v, w
	p > 2; 0 ≤ u < p; 0 ≤ v < p; 0 ≤ w < p p³ conjugate subgroups for the prime p

I Minimal translationengleiche supergroups

[2] Pm-3 (200); [2] Pn-3 (201); [2] P432 (207); [2] P4₂32 (208); [2] P-43m (215); [2] P-43n (218)

II Minimal non-isomorphic klassengleiche supergroups

Additional centring translations

[2] I23 (197); [4] F23 (196)

Decreased unit cell

none

International Tables for Crystallography (2006). Vol. A1, ch. 2.3, Maximal subgroups of space group 195.

© International Union of Crystallography 2006

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