Subgroups — Q₈×C₁₂₇⋊C₈ #22550002

Order 8128.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊(C₁₂₇⋊C₈)	C₂	1	3	yes	maximal
2	C₄×C₁₂₇⋊C₈	C₂	1	3	yes	maximal
3	C₄×Q₈×C₁₂₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₂₇⋊C₈	C₂²	1	3	yes	—
5	C₂×C₁₂₇⋊C₈	C₂²	1	1	yes	characteristic
6	C₂×Q₈×C₁₂₇	C₄	1	1	yes	characteristic
7	C₄⋊C₄×C₁₂₇	C₄	1	3	yes	—
8	C₄²×C₁₂₇	C₂²	1	3	yes	—
9	C₁₂₇⋊C₈	—	2	3	no	—
10	C₁₂₇⋊C₈	Q₈	1	2	yes	direct product factor
11	Q₈×C₁₂₇	C₈	1	4	yes	complemented
12	C₂×C₄×C₁₂₇	C₂×C₄	1	3	yes	—
13	C₂×C₄×C₁₂₇	C₂×C₄	1	3	yes	—
14	C₂×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
15	C₂²×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
16	C₄×C₁₂₇	—	2	3	no	—
17	C₄×C₁₂₇	C₂×C₈	1	6	yes	—
18	C₄×C₁₂₇	C₂×Q₈	1	1	yes	characteristic
19	C₄×C₁₂₇	#41	1	1	yes	characteristic
20	C₂×C₁₂₇	C₄×Q₈	1	1	yes	characteristic
21	C₂×C₁₂₇	C₂²×C₈	1	1	yes	characteristic
22	C₂×C₁₂₇	#131	1	1	yes	characteristic
23	C₁₂₇	C₈×Q₈	1	1	yes	characteristic, complemented, Sylow
24	C₈×Q₈	—	127	1	no	maximal, Sylow
25	C₄×Q₈	D₁₂₇	1	1	yes	characteristic
26	C₄⋊C₈	—	127	3	no	—
27	C₄×C₈	—	127	3	no	—
28	C₂×Q₈	Dic₁₂₇	1	1	yes	characteristic
29	C₂×C₈	—	127	1	no	—
30	C₂×C₈	—	127	3	no	—
31	C₄⋊C₄	Dic₁₂₇	1	3	yes	—
32	C₄²	C₂×D₁₂₇	1	3	yes	—
33	Q₈	C₁₂₇⋊C₈	1	4	yes	direct product factor
34	C₂×C₄	C₂×Dic₁₂₇	1	3	yes	—
35	C₂×C₄	C₂×Dic₁₂₇	1	3	yes	—
36	C₂×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
37	C₈	—	127	2	no	—
38	C₈	—	254	3	no	—
39	C₂²	C₂²×Dic₁₂₇	1	1	yes	characteristic
40	C₄	—	2	3	no	—
41	C₄	C₂×C₁₂₇⋊C₈	1	6	yes	—
42	C₄	Q₈×D₁₂₇	1	1	yes	characteristic
43	C₄	#14523249	1	1	yes	characteristic
44	C₂	Q₈×Dic₁₂₇	1	1	yes	characteristic
45	C₂	C₂²×C₁₂₇⋊C₈	1	1	yes	characteristic
46	C₂	#16861216	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₁₂₇
commutator	C₂×C₁₂₇	C₂²×C₈
Fitting	C₄×Q₈×C₁₂₇	C₂
socle	C₂²×C₁₂₇	C₂²×C₄
hypercenter	C₄×Q₈	D₁₂₇
hypocenter	C₁₂₇	C₈×Q₈
LCS	G ▷ C₂×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
10. C₁₂₇⋊C₈	Q₈	direct (N × H)
11. Q₈×C₁₂₇	C₈	semidirect
23. C₁₂₇	C₈×Q₈	semidirect
33. Q₈	C₁₂₇⋊C₈	direct (N × H)

Subgroups — Q8×C127⋊C8 #22550002

Conjugacy classes of subgroups

Complements

Subgroups — Q₈×C₁₂₇⋊C₈ #22550002