Subgroups — #22586378

Order 9088.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17986379	C₂	1	1	yes	maximal, characteristic
2	#17985820	C₂	1	1	yes	maximal, characteristic
3	#364×C₇₁	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₈₄	—	2	1	no	—
5	C₂×Dic₂₈₄	—	2	1	no	—
6	#14556128	C₄	1	2	yes	—
7	#14556068	—	2	1	no	—
8	M₃₂×C₇₁	—	2	1	no	—
9	C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
10	C₂×Dic₁₄₂	—	2	2	no	—
11	Dic₂₈₄	—	4	1	no	—
12	Dic₂₈₄	—	4	1	no	—
13	Dic₂₈₄	—	4	1	no	—
14	Dic₂₈₄	—	4	1	no	—
15	C₄⋊Dic₇₁	—	4	2	no	—
16	C₇₁⋊C₁₆	—	4	1	no	—
17	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
18	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
19	C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
20	C₁₆×C₇₁	—	4	1	no	—
21	C₂×C₄×C₇₁	—	2	1	no	—
22	C₂×C₄×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×Dic₇₁	—	4	2	no	—
24	Dic₁₄₂	—	4	2	no	—
25	Dic₁₄₂	—	4	2	no	—
26	C₈×C₇₁	D₈	1	1	yes	characteristic
27	C₈×C₇₁	D₈	1	1	yes	characteristic
28	C₈×C₇₁	SD₁₆	1	1	yes	characteristic
29	C₈×C₇₁	SD₁₆	1	1	yes	characteristic
30	C₂²×C₇₁	#100	1	1	yes	characteristic
31	C₄×C₇₁	—	2	2	no	—
32	C₄×C₇₁	#102	1	1	yes	characteristic
33	C₄×C₇₁	#102	1	1	yes	characteristic
34	Dic₇₁	—	8	2	no	—
35	C₂×C₇₁	—	2	1	no	—
36	C₂×C₇₁	#331	1	1	yes	characteristic
37	#1358	—	71	1	no	maximal, Sylow
38	C₇₁	#1358	1	1	yes	characteristic, complemented, Sylow
39	#494	—	71	1	no	—
40	#364	—	71	1	no	—
41	#364	D₇₁	1	1	yes	characteristic
42	C₂×Q₁₆	—	142	1	no	—
43	C₂×Q₁₆	—	142	1	no	—
44	C₄⋊Q₈	—	71	2	no	—
45	M₃₂	—	2	1	no	—
46	M₃₂	—	142	1	no	—
47	C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
48	C₂×Q₈	—	142	2	no	—
49	Q₁₆	—	284	1	no	—
50	Q₁₆	—	284	1	no	—
51	Q₁₆	—	284	1	no	—
52	Q₁₆	—	284	1	no	—
53	C₂×C₈	D₂₈₄	1	1	yes	characteristic
54	C₂×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
55	C₄⋊C₄	—	284	2	no	—
56	C₄²	C₄×D₇₁	1	1	yes	characteristic
57	C₁₆	—	4	1	no	—
58	C₁₆	—	284	1	no	—
59	Q₈	—	284	2	no	—
60	Q₈	—	284	2	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	284	2	no	—
63	C₂×C₄	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
64	C₈	#11765850	1	1	yes	characteristic
65	C₈	D₅₆₈	1	1	yes	characteristic
66	C₈	#11765852	1	1	yes	characteristic
67	C₈	#11765854	1	1	yes	characteristic
68	C₂²	#14556044	1	1	yes	characteristic
69	C₄	—	2	2	no	—
70	C₄	—	568	2	no	—
71	C₄	#14556048	1	1	yes	characteristic
72	C₄	#14556050	1	1	yes	characteristic
73	C₂	—	2	1	no	—
74	C₂	#17985742	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#17985742
commutator	C₄²×C₇₁	C₂×C₄
Frattini	C₄×C₈	C₂×D₇₁
Fitting	#364×C₇₁	C₂
socle	C₂×C₇₁	#331
hypercenter	#364	D₇₁
hypocenter	C₇₁	#1358
LCS	G ▷ C₄²×C₇₁ ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
38. C₇₁	#1358	semidirect