Subgroups — #22586532

Order 9088.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₅₆₈	C₂	1	1	yes	maximal, characteristic
2	#17985833	C₂	1	1	yes	maximal, characteristic
3	#368×C₇₁	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₈₄	—	2	1	no	—
5	Dic₅₆₈	—	2	1	no	—
6	Dic₅₆₈	C₄	1	2	yes	—
7	C₇₁⋊C₃₂	—	2	1	no	—
8	C₂×C₁₆×C₇₁	C₂²	1	1	yes	characteristic
9	#108×C₇₁	—	2	1	no	—
10	C₂×Dic₁₄₂	—	4	1	no	—
11	Dic₂₈₄	—	2	2	no	—
12	Dic₂₈₄	—	4	1	no	—
13	M₁₆×C₇₁	—	4	1	no	—
14	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
15	C₁₆×C₇₁	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₇₁	D₄	1	1	yes	characteristic
17	C₂×C₄×C₇₁	D₈	1	1	yes	characteristic
18	C₂×Dic₇₁	—	8	1	no	—
19	Dic₁₄₂	—	4	2	no	—
20	Dic₁₄₂	—	8	1	no	—
21	C₈×C₇₁	—	8	1	no	—
22	C₈×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
23	C₈×C₇₁	SD₁₆	1	1	yes	characteristic
24	C₂²×C₇₁	SD₃₂	1	1	yes	characteristic
25	C₄×C₇₁	#102	1	1	yes	characteristic
26	C₄×C₇₁	D₁₆	1	1	yes	characteristic
27	Dic₇₁	—	8	2	no	—
28	C₂×C₇₁	—	2	1	no	—
29	C₂×C₇₁	#357	1	1	yes	characteristic
30	#1420	—	71	1	no	maximal, Sylow
31	C₇₁	#1420	1	1	yes	characteristic, complemented, Sylow
32	C₂×Q₃₂	—	71	1	no	—
33	M₆₄	—	71	1	no	—
34	#368	D₇₁	1	1	yes	characteristic
35	C₂×Q₁₆	—	142	1	no	—
36	Q₃₂	—	71	2	no	—
37	Q₃₂	—	142	1	no	—
38	C₂×C₁₆	C₂×D₇₁	1	1	yes	characteristic
39	#108	—	2	1	no	—
40	C₃₂	—	142	1	no	—
41	C₂×Q₈	—	284	1	no	—
42	Q₁₆	—	284	1	no	—
43	Q₁₆	—	142	2	no	—
44	M₁₆	—	4	1	no	—
45	C₂×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
46	C₁₆	C₄×D₇₁	1	1	yes	characteristic
47	C₁₆	D₂₈₄	1	1	yes	characteristic
48	Q₈	—	284	2	no	—
49	Q₈	—	568	1	no	—
50	C₂×C₄	—	568	1	no	—
51	C₂×C₄	#11765850	1	1	yes	characteristic
52	C₈	—	8	1	no	—
53	C₈	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
54	C₈	#11765852	1	1	yes	characteristic
55	C₂²	#14556071	1	1	yes	characteristic
56	C₄	—	568	2	no	—
57	C₄	#14556048	1	1	yes	characteristic
58	C₄	#14556069	1	1	yes	characteristic
59	C₂	—	2	1	no	—
60	C₂	#17985799	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#17985799
commutator	C₁₆×C₇₁	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₇₁
Fitting	#368×C₇₁	C₂
socle	C₂×C₇₁	#357
hypercenter	#368	D₇₁
hypocenter	C₇₁	#1420
LCS	G ▷ C₁₆×C₇₁ ▷ C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #368

Complements

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

N	H ≅ G/N	type
31. C₇₁	#1420	semidirect