I4mm No. 107 I4mm C4v9

Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(1/21/21/2); (2); (3); (5)

General position

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates

(0, 0, 0)+  (1/21/21/2)+
 16 e 1
 (1) x, y, z (2) -x, -y, z (3) -y, x, z (4) y, -x, z (5) x, -y, z (6) -x, y, z (7) -y, -x, z (8) y, x, z

I Maximal translationengleiche subgroups

 [2] I411 (79, I4) (1; 2; 3; 4)+ [2] I2m1 (44, Imm2) (1; 2; 5; 6)+ [2] I21m (42, Fmm2) (1; 2; 7; 8)+ a - b, a + b, c

II Maximal klassengleiche subgroups

• Loss of centring translations
 [2] P42mc (105) 1; 2; 5; 6; (3; 4; 7; 8) + (1/2, 1/2, 1/2) 0, 1/2, 0 [2] P4nc (104) 1; 2; 3; 4; (5; 6; 7; 8) + (1/2, 1/2, 1/2) [2] P42nm (102) 1; 2; 7; 8; (3; 4; 5; 6) + (1/2, 1/2, 1/2) [2] P4mm (99) 1; 2; 3; 4; 5; 6; 7; 8
• Enlarged unit cell

[3] c' = 3c

 I4mm (107) <2; 3; 5> a, b, 3c
• Series of maximal isomorphic subgroups

[p] c' = pc

 I4mm (107) <2; 3; 5> a, b, pc p > 2 no conjugate subgroups

[p2] a' = pa, b' = pb

 I4mm (107) <2 + (2u, 2v, 0); 3 + (u + v, -u + v, 0); 5 + (0, 2v, 0)> pa, pb, c u, v, 0 p > 2; 0 ≤ u < p; 0 ≤ v < p p2 conjugate subgroups for the prime p

I Minimal translationengleiche supergroups

 [2] I4/mmm (139)

II Minimal non-isomorphic klassengleiche supergroups