Subgroups — #22549813

Order 8128.

186 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊Dic₁₂₇	C₂	1	3	yes	maximal, complemented
2	C₂×(C₂×D₁₂₇)⋊C₄	C₂	1	3	yes	maximal
3	#95×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×D₁₂₇	C₂²	1	1	yes	characteristic
5	C₂²×Dic₁₂₇	C₂²	1	3	yes	—
6	C₄⋊Dic₁₂₇	—	2	6	no	—
7	(C₂×D₁₂₇)⋊C₄	—	2	6	no	—
8	C₂²×C₄×C₁₂₇	C₂²	1	3	yes	—
9	C₂²×D₁₂₇	—	2	3	no	—
10	C₂²×D₁₂₇	—	2	3	no	—
11	C₂²×D₁₂₇	Q₈	1	2	yes	—
12	C₂×Dic₁₂₇	—	2	3	no	—
13	C₂×Dic₁₂₇	—	2	6	no	—
14	C₂³×C₁₂₇	C₂³	1	1	yes	characteristic
15	C₂×C₄×C₁₂₇	—	2	6	no	—
16	C₂×C₄×C₁₂₇	D₄	1	6	yes	—
17	C₂²×C₁₂₇	C₂×D₄	1	3	yes	—
18	C₂²×C₁₂₇	C₂×Q₈	1	1	yes	characteristic
19	C₂²×C₁₂₇	#41	1	3	yes	—
20	C₂×D₁₂₇	—	2	6	no	—
21	C₂×D₁₂₇	—	4	3	no	—
22	C₂×D₁₂₇	—	4	1	no	—
23	C₄×C₁₂₇	—	2	6	no	—
24	Dic₁₂₇	—	4	3	no	—
25	C₂×C₁₂₇	C₂²⋊Q₈	1	3	yes	—
26	C₂×C₁₂₇	#123	1	3	yes	—
27	C₂×C₁₂₇	#127	1	1	yes	characteristic
28	D₁₂₇	—	4	2	no	—
29	C₁₂₇	#399	1	1	yes	characteristic, complemented, Sylow
30	#399	—	127	1	no	maximal, Sylow
31	C₂×C₄⋊C₄	—	127	3	no	—
32	C₂×C₂²⋊C₄	—	127	3	no	—
33	#95	D₁₂₇	1	1	yes	characteristic, complemented
34	C₂⁴	—	127	1	no	—
35	C₂²×C₄	—	127	3	no	—
36	C₂²×C₄	C₂×D₁₂₇	1	3	yes	—
37	C₄⋊C₄	—	254	6	no	—
38	C₂²⋊C₄	—	254	6	no	—
39	C₂³	—	127	2	no	—
40	C₂³	—	254	3	no	—
41	C₂³	—	254	3	no	—
42	C₂³	C₂²×D₁₂₇	1	1	yes	characteristic
43	C₂×C₄	—	2	6	no	—
44	C₂×C₄	—	254	3	no	—
45	C₂×C₄	—	254	6	no	—
46	C₂×C₄	D₅₀₈	1	6	yes	—
47	C₂²	—	508	3	no	—
48	C₂²	—	508	1	no	—
49	C₂²	—	254	6	no	—
50	C₂²	C₂×D₅₀₈	1	3	yes	—
51	C₂²	Q₈×D₁₂₇	1	1	yes	characteristic
52	C₂²	#14523247	1	3	yes	—
53	C₄	—	2	6	no	—
54	C₄	—	508	3	no	—
55	C₂	—	508	2	no	—
56	C₂	#16861189	1	3	yes	—
57	C₂	#16861193	1	3	yes	—
58	C₂	#16861206	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₁₂₇
commutator, socle	C₂³×C₁₂₇	C₂³
Fitting	#95×C₁₂₇	C₂
hypercenter	#95	D₁₂₇
hypocenter	C₁₂₇	#399
LCS	G ▷ C₂³×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
1. C₂×C₄⋊Dic₁₂₇	C₂	semidirect
3. #95×C₁₂₇	C₂	semidirect
29. C₁₂₇	#399	semidirect
33. #95	D₁₂₇	semidirect