Subgroups — #22586392

Order 9088.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊(C₇₁⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
2	#17985750	C₂	1	1	yes	maximal, characteristic
3	#499×C₇₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₇₁⋊C₁₆	—	2	1	no	—
5	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
6	#125×C₇₁	—	2	1	no	—
7	#107×C₇₁	C₄	1	1	yes	characteristic
8	#107×C₇₁	C₄	1	1	yes	characteristic
9	#106×C₇₁	—	2	1	no	—
10	C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
11	C₂×C₇₁⋊C₈	—	4	1	no	—
12	C₇₁⋊C₁₆	—	4	1	no	—
13	C₂×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
15	C₄⋊C₄×C₇₁	—	2	1	no	—
16	C₄⋊C₄×C₇₁	—	2	1	no	—
17	C₄⋊C₄×C₇₁	—	4	1	no	—
18	C₄⋊C₄×C₇₁	—	4	1	no	—
19	C₄²×C₇₁	D₄	1	1	yes	characteristic
20	C₂×C₄×C₇₁	—	4	1	no	—
21	C₂×C₄×C₇₁	—	4	1	no	—
22	C₂×C₄×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₄×C₇₁	D₈	1	1	yes	characteristic
24	C₂×C₄×C₇₁	SD₁₆	1	1	yes	characteristic
25	C₈×C₇₁	—	2	1	no	—
26	C₈×C₇₁	SD₁₆	1	1	yes	characteristic
27	C₈×C₇₁	Q₁₆	1	1	yes	characteristic
28	C₇₁⋊C₈	—	8	1	no	—
29	C₂²×C₇₁	#102	1	1	yes	characteristic
30	C₄×C₇₁	—	2	1	no	—
31	C₄×C₇₁	—	2	1	no	—
32	C₄×C₇₁	—	8	1	no	—
33	C₄×C₇₁	—	8	1	no	—
34	C₄×C₇₁	#101	1	1	yes	characteristic
35	C₄×C₇₁	#103	1	1	yes	characteristic
36	C₂×C₇₁	#332	1	1	yes	characteristic
37	C₂×C₇₁	#359	1	1	yes	characteristic
38	C₂×C₇₁	#360	1	1	yes	characteristic
39	#1363	—	71	1	no	maximal, Sylow
40	C₇₁	#1363	1	1	yes	characteristic, complemented, Sylow
41	#499	D₇₁	1	1	yes	characteristic
42	C₄⋊C₁₆	—	71	1	no	—
43	#334	—	71	1	no	—
44	#125	—	2	1	no	—
45	C₂×C₁₆	—	142	1	no	—
46	#107	Dic₇₁	1	1	yes	characteristic
47	#107	Dic₇₁	1	1	yes	characteristic
48	#106	—	2	1	no	—
49	C₄⋊C₈	—	142	1	no	—
50	C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
51	C₂×C₈	—	284	1	no	—
52	C₂×C₈	C₂×Dic₇₁	1	1	yes	characteristic
53	C₂×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
54	C₄⋊C₄	—	2	1	no	—
55	C₄⋊C₄	—	2	1	no	—
56	C₄⋊C₄	—	4	1	no	—
57	C₄⋊C₄	—	4	1	no	—
58	C₄²	C₂²⋊D₇₁	1	1	yes	characteristic
59	C₁₆	—	284	1	no	—
60	C₂×C₄	—	4	1	no	—
61	C₂×C₄	—	4	1	no	—
62	C₂×C₄	C₂²⋊Dic₇₁	1	1	yes	characteristic
63	C₂×C₄	#11765850	1	1	yes	characteristic
64	C₂×C₄	#11765853	1	1	yes	characteristic
65	C₈	—	2	1	no	—
66	C₈	—	568	1	no	—
67	C₈	#11765852	1	1	yes	characteristic
68	C₈	#11765855	1	1	yes	characteristic
69	C₂²	#14556049	1	1	yes	characteristic
70	C₄	—	2	1	no	—
71	C₄	—	2	1	no	—
72	C₄	—	8	1	no	—
73	C₄	—	8	1	no	—
74	C₄	#14556047	1	1	yes	characteristic
75	C₄	#14556052	1	1	yes	characteristic
76	C₂	#17985745	1	1	yes	characteristic
77	C₂	#17985806	1	1	yes	characteristic
78	C₂	#17985809	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14556049
commutator	C₂×C₈×C₇₁	C₂×C₄
Frattini	C₄×C₈	C₂×D₇₁
Fitting	#499×C₇₁	C₂
socle	C₂²×C₇₁	#102
hypercenter	#499	D₇₁
hypocenter	C₇₁	#1363
LCS	G ▷ C₂×C₈×C₇₁ ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #499

Complements

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

N	H ≅ G/N	type
40. C₇₁	#1363	semidirect