Subgroups — #22586415

Order 9088.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17985820	C₂	1	1	yes	maximal, characteristic
2	C₄×C₇₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	#364×C₇₁	C₂	1	1	yes	maximal, characteristic
4	#14556068	—	2	1	no	—
5	C₂×C₇₁⋊C₁₆	C₄	1	1	yes	characteristic
6	C₂×C₇₁⋊C₁₆	C₄	1	1	yes	characteristic
7	M₃₂×C₇₁	—	2	1	no	—
8	C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
9	C₇₁⋊C₁₆	—	2	1	no	—
10	C₇₁⋊C₁₆	—	4	1	no	—
11	C₇₁⋊C₁₆	C₈	1	2	yes	—
12	C₂×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
14	C₄²×C₇₁	Q₈	1	1	yes	characteristic
15	C₁₆×C₇₁	—	4	1	no	—
16	C₂×C₄×C₇₁	—	2	1	no	—
17	C₂×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
18	C₈×C₇₁	C₂×C₈	1	1	yes	characteristic
19	C₈×C₇₁	M₁₆	1	1	yes	characteristic
20	C₈×C₇₁	D₈	1	1	yes	characteristic
21	C₈×C₇₁	Q₁₆	1	1	yes	characteristic
22	C₂²×C₇₁	#108	1	1	yes	characteristic
23	C₄×C₇₁	—	2	2	no	—
24	C₄×C₇₁	C₄⋊C₈	1	1	yes	characteristic
25	C₄×C₇₁	#107	1	1	yes	characteristic
26	C₂×C₇₁	—	2	1	no	—
27	C₂×C₇₁	#335	1	1	yes	characteristic
28	#1373	—	71	1	no	maximal, Sylow
29	C₇₁	#1373	1	1	yes	characteristic, complemented, Sylow
30	#364	—	71	1	no	—
31	#364	D₇₁	1	1	yes	characteristic
32	C₄×C₁₆	—	71	1	no	—
33	M₃₂	—	2	1	no	—
34	M₃₂	—	142	1	no	—
35	C₂×C₁₆	—	71	1	no	—
36	C₂×C₁₆	—	71	1	no	—
37	C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
38	C₂×C₈	C₄×D₇₁	1	1	yes	characteristic
39	C₂×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
40	C₄²	Dic₁₄₂	1	1	yes	characteristic
41	C₁₆	—	4	1	no	—
42	C₁₆	—	284	1	no	—
43	C₁₆	—	71	2	no	—
44	C₁₆	—	142	1	no	—
45	C₂×C₄	—	2	1	no	—
46	C₂×C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
47	C₈	C₈×D₇₁	1	1	yes	characteristic
48	C₈	#11765848	1	1	yes	characteristic
49	C₈	#11765850	1	1	yes	characteristic
50	C₈	#11765855	1	1	yes	characteristic
51	C₂²	#14556063	1	1	yes	characteristic
52	C₄	—	2	2	no	—
53	C₄	Dic₇₁⋊C₈	1	1	yes	characteristic
54	C₄	#14556061	1	1	yes	characteristic
55	C₂	—	2	1	no	—
56	C₂	#17985751	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#11765850
commutator	C₈×C₇₁	C₂×C₈
Frattini	C₄×C₈	C₂×D₇₁
Fitting	#364×C₇₁	C₂
socle	C₂×C₇₁	#335
hypercenter	#364	D₇₁
hypocenter	C₇₁	#1373
LCS	G ▷ C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
29. C₇₁	#1373	semidirect