Subgroups — #22549701

Order 8128.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₂₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	#16861143	C₂	1	1	yes	maximal, characteristic
3	#107×C₁₂₇	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Dic₁₂₇	—	2	1	no	—
5	C₁₂₇⋊C₁₆	C₄	1	2	yes	complemented
6	C₂×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
7	C₄⋊C₄×C₁₂₇	—	2	1	no	—
8	C₂×Dic₁₂₇	—	4	1	no	—
9	C₂×C₄×C₁₂₇	—	4	1	no	—
10	C₂×C₄×C₁₂₇	D₄	1	1	yes	characteristic
11	C₈×C₁₂₇	C₂×C₄	1	1	yes	characteristic
12	C₈×C₁₂₇	Q₈	1	1	yes	characteristic
13	C₂²×C₁₂₇	D₈	1	1	yes	characteristic
14	C₄×C₁₂₇	—	8	1	no	—
15	C₄×C₁₂₇	C₄⋊C₄	1	1	yes	characteristic
16	C₄×C₁₂₇	Q₁₆	1	1	yes	characteristic
17	Dic₁₂₇	—	8	1	no	—
18	C₂×C₁₂₇	#107	1	1	yes	characteristic
19	C₂×C₁₂₇	D₁₆	1	1	yes	characteristic
20	C₂×C₁₂₇	Q₃₂	1	1	yes	characteristic
21	C₁₂₇	#366	1	1	yes	characteristic, complemented, Sylow
22	#366	—	127	1	no	maximal, Sylow
23	C₂×C₁₆	—	127	1	no	—
24	#107	—	127	1	no	—
25	#107	D₁₂₇	1	1	yes	characteristic
26	C₂×C₈	C₂×D₁₂₇	1	1	yes	characteristic
27	C₄⋊C₄	—	2	1	no	—
28	C₄⋊C₄	—	254	1	no	—
29	C₁₆	—	127	2	no	—
30	C₂×C₄	—	4	1	no	—
31	C₂×C₄	—	508	1	no	—
32	C₂×C₄	C₂²⋊D₁₂₇	1	1	yes	characteristic
33	C₈	C₄×D₁₂₇	1	1	yes	characteristic
34	C₈	Dic₂₅₄	1	1	yes	characteristic
35	C₂²	#14523233	1	1	yes	characteristic
36	C₄	—	8	1	no	—
37	C₄	—	1016	1	no	—
38	C₄	Dic₁₂₇⋊C₄	1	1	yes	characteristic
39	C₄	#14523238	1	1	yes	characteristic
40	C₂	#16861142	1	1	yes	characteristic
41	C₂	#16861150	1	1	yes	characteristic
42	C₂	#16861155	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14523233
commutator	C₈×C₁₂₇	C₂×C₄
Frattini	C₂×C₈	C₂×D₁₂₇
Fitting	#107×C₁₂₇	C₂
socle	C₂²×C₁₂₇	D₈
hypercenter	#107	D₁₂₇
hypocenter	C₁₂₇	#366
LCS	G ▷ C₈×C₁₂₇ ▷ C₄×C₁₂₇ ▷ C₂×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #107

Complements

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

N	H ≅ G/N	type
5. C₁₂₇⋊C₁₆	C₄	semidirect
21. C₁₂₇	#366	semidirect