Subgroups — #22549658

Order 8128.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16861149	C₂	1	2	yes	maximal, complemented
2	C₂×M₁₆×C₁₂₇	C₂	1	1	yes	maximal, characteristic
3	C₁₂₇⋊C₁₆	—	2	2	no	—
4	C₂²×C₄×C₁₂₇	C₄	1	1	yes	characteristic
5	M₁₆×C₁₂₇	—	2	2	no	—
6	C₂×C₈×C₁₂₇	C₄	1	1	yes	characteristic
7	C₂×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
8	C₂³×C₁₂₇	C₈	1	1	yes	characteristic
9	C₂×C₄×C₁₂₇	—	2	1	no	—
10	C₂×C₄×C₁₂₇	—	2	1	no	—
11	C₂×C₄×C₁₂₇	C₈	1	1	yes	characteristic
12	C₂×C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
13	C₈×C₁₂₇	—	2	1	no	—
14	C₈×C₁₂₇	D₄	1	2	yes	—
15	C₂²×C₁₂₇	—	2	1	no	—
16	C₂²×C₁₂₇	—	4	1	no	—
17	C₂²×C₁₂₇	C₂×C₈	1	1	yes	characteristic
18	C₄×C₁₂₇	—	2	1	no	—
19	C₄×C₁₂₇	C₂²⋊C₄	1	1	yes	characteristic
20	C₄×C₁₂₇	M₁₆	1	1	yes	characteristic
21	C₂×C₁₂₇	—	2	1	no	—
22	C₂×C₁₂₇	—	4	1	no	—
23	C₂×C₁₂₇	C₂²⋊C₈	1	1	yes	characteristic
24	C₁₂₇	#349	1	1	yes	characteristic, complemented, Sylow
25	#349	—	127	1	no	maximal, Sylow
26	C₂×M₁₆	D₁₂₇	1	1	yes	characteristic
27	M₃₂	—	127	2	no	—
28	C₂²×C₄	Dic₁₂₇	1	1	yes	characteristic
29	M₁₆	—	2	2	no	—
30	C₂×C₈	Dic₁₂₇	1	1	yes	characteristic
31	C₂×C₈	C₂×D₁₂₇	1	1	yes	characteristic
32	C₁₆	—	254	2	no	—
33	C₂³	C₁₂₇⋊C₈	1	1	yes	characteristic
34	C₂×C₄	—	2	1	no	—
35	C₂×C₄	—	2	1	no	—
36	C₂×C₄	C₁₂₇⋊C₈	1	1	yes	characteristic
37	C₂×C₄	C₂×Dic₁₂₇	1	1	yes	characteristic
38	C₈	—	2	1	no	—
39	C₈	C₂²⋊D₁₂₇	1	2	yes	—
40	C₂²	—	2	1	no	—
41	C₂²	—	4	1	no	—
42	C₂²	C₂×C₁₂₇⋊C₈	1	1	yes	characteristic
43	C₄	—	2	1	no	—
44	C₄	C₂²⋊Dic₁₂₇	1	1	yes	characteristic
45	C₄	#14523232	1	1	yes	characteristic
46	C₂	—	2	1	no	—
47	C₂	—	4	1	no	—
48	C₂	C₂²⋊(C₁₂₇⋊C₈)	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊Dic₁₂₇
commutator	C₂²×C₁₂₇	C₂×C₈
Frattini	C₂×C₈	C₂×D₁₂₇
Fitting	C₂×M₁₆×C₁₂₇	C₂
socle	C₂×C₁₂₇	C₂²⋊C₈
hypercenter	C₂×M₁₆	D₁₂₇
hypocenter	C₁₂₇	#349
LCS	G ▷ C₂²×C₁₂₇ ▷ C₂×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
1. #16861149	C₂	semidirect
24. C₁₂₇	#349	semidirect