Subgroups — #22586642

Order 9088.

214 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#11765848	C₂	1	3	yes	maximal
2	#17985720	C₂	1	3	yes	maximal, complemented
3	C₈²×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11765848	C₄	1	6	yes	—
5	C₄²×D₇₁	C₂²	1	1	yes	characteristic
6	#14556038	C₄	1	6	yes	—
7	C₄×C₇₁⋊C₈	C₂²	1	3	yes	—
8	C₄×C₈×C₇₁	C₂²	1	3	yes	—
9	C₂×C₄×D₇₁	C₂×C₄	1	3	yes	—
10	#11765848	—	2	12	no	—
11	C₂×C₇₁⋊C₈	C₂×C₄	1	6	yes	—
12	C₄×Dic₇₁	C₂×C₄	1	3	yes	—
13	C₂×C₈×C₇₁	C₂×C₄	1	6	yes	—
14	C₄²×C₇₁	C₂³	1	1	yes	characteristic
15	C₂²×D₇₁	C₄²	1	1	yes	characteristic
16	C₂×C₄×C₇₁	C₂²×C₄	1	3	yes	—
17	C₂×Dic₇₁	C₄²	1	3	yes	—
18	C₄×D₇₁	—	2	6	no	—
19	C₈×C₇₁	M₁₆	1	12	yes	complemented
20	C₇₁⋊C₈	—	2	6	no	—
21	C₂²×C₇₁	C₂×C₄²	1	1	yes	characteristic
22	C₂×D₇₁	—	2	3	no	—
23	C₄×C₇₁	C₂×M₁₆	1	6	yes	—
24	Dic₇₁	—	2	3	no	—
25	C₂×C₇₁	C₄×M₁₆	1	3	yes	—
26	D₇₁	—	4	1	no	—
27	#1455	—	71	1	no	maximal, Sylow
28	C₇₁	#1455	1	1	yes	characteristic, complemented, Sylow
29	C₄×M₁₆	—	71	3	no	—
30	#322	—	71	3	no	—
31	C₈²	D₇₁	1	1	yes	characteristic, complemented
32	C₂×M₁₆	—	71	6	no	—
33	C₂×C₄²	—	71	1	no	—
34	#97	—	71	6	no	—
35	C₄×C₈	—	71	3	no	—
36	C₄×C₈	C₂×D₇₁	1	3	yes	—
37	C₂²×C₄	—	71	3	no	—
38	M₁₆	—	142	12	no	—
39	C₂×C₈	—	71	6	no	—
40	C₂×C₈	C₄×D₇₁	1	6	yes	—
41	C₄²	—	71	3	no	—
42	C₄²	C₂²×D₇₁	1	1	yes	characteristic
43	C₂³	—	71	1	no	—
44	C₂×C₄	—	71	3	no	—
45	C₂×C₄	—	142	6	no	—
46	C₂×C₄	C₂×C₄×D₇₁	1	3	yes	—
47	C₈	—	142	6	no	—
48	C₈	#11765848	1	12	yes	complemented
49	C₂²	—	142	3	no	—
50	C₂²	C₄²×D₇₁	1	1	yes	characteristic
51	C₄	—	142	3	no	—
52	C₄	C₂×#11765848	1	6	yes	—
53	C₂	—	284	1	no	—
54	C₂	C₄×#11765848	1	3	yes	—

	subgroup	G/H
center, Frattini	C₄²	C₂²×D₇₁
commutator, socle	C₂²×C₇₁	C₂×C₄²
Fitting	C₈²×C₇₁	C₂
hypercenter	C₈²	D₇₁
hypocenter	C₇₁	#1455
LCS	G ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
2. #17985720	C₂	semidirect
3. C₈²×C₇₁	C₂	semidirect
19. C₈×C₇₁	M₁₆	semidirect
28. C₇₁	#1455	semidirect
31. C₈²	D₇₁	semidirect
48. C₈	#11765848	semidirect