Subgroups — #22549653

Order 8128.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16861149	C₂	1	1	yes	maximal, characteristic
2	#16861119	C₂	1	1	yes	maximal, characteristic
3	M₃₂×C₁₂₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₂₇⋊C₈	C₄	1	1	yes	characteristic
5	C₄×Dic₁₂₇	C₄	1	1	yes	characteristic
6	C₁₂₇⋊C₁₆	C₄	1	2	yes	complemented
7	C₂×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
8	C₁₆×C₁₂₇	C₄	1	2	yes	complemented
9	C₂×Dic₁₂₇	—	2	1	no	—
10	C₁₂₇⋊C₈	—	2	1	no	—
11	C₂×C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
12	C₈×C₁₂₇	C₂×C₄	1	1	yes	characteristic
13	C₈×C₁₂₇	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₁₂₇	M₁₆	1	1	yes	characteristic
15	C₄×C₁₂₇	C₄²	1	1	yes	characteristic
16	C₄×C₁₂₇	M₁₆	1	1	yes	characteristic
17	Dic₁₂₇	—	4	1	no	—
18	C₂×C₁₂₇	—	2	1	no	—
19	C₂×C₁₂₇	#97	1	1	yes	characteristic
20	C₁₂₇	#347	1	1	yes	characteristic, complemented, Sylow
21	#347	—	127	1	no	maximal, Sylow
22	M₃₂	—	127	1	no	—
23	M₃₂	D₁₂₇	1	1	yes	characteristic
24	#97	—	127	1	no	—
25	C₂×C₈	—	127	1	no	—
26	C₂×C₈	C₂×D₁₂₇	1	1	yes	characteristic
27	C₄²	—	127	1	no	—
28	C₁₆	—	127	2	no	—
29	C₁₆	Dic₁₂₇	1	2	yes	complemented
30	C₂×C₄	—	254	1	no	—
31	C₂×C₄	C₄×D₁₂₇	1	1	yes	characteristic
32	C₈	—	254	1	no	—
33	C₈	C₄×D₁₂₇	1	1	yes	characteristic
34	C₈	C₂×Dic₁₂₇	1	1	yes	characteristic
35	C₂²	#14523231	1	1	yes	characteristic
36	C₄	—	508	1	no	—
37	C₄	C₄×Dic₁₂₇	1	1	yes	characteristic
38	C₄	#14523231	1	1	yes	characteristic
39	C₂	—	2	1	no	—
40	C₂	#16861119	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄×Dic₁₂₇
commutator	C₄×C₁₂₇	C₄²
Frattini	C₂×C₈	C₂×D₁₂₇
Fitting	M₃₂×C₁₂₇	C₂
socle	C₂×C₁₂₇	#97
hypercenter	M₃₂	D₁₂₇
hypocenter	C₁₂₇	#347
LCS	G ▷ C₄×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₄ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
6. C₁₂₇⋊C₁₆	C₄	semidirect
8. C₁₆×C₁₂₇	C₄	semidirect
20. C₁₂₇	#347	semidirect
29. C₁₆	Dic₁₂₇	semidirect