Subgroups — #22586517

Order 9088.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₁₃₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇₁⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#366×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₅₆₈	—	2	1	no	—
5	D₁₁₃₆	—	2	1	no	—
6	D₁₁₃₆	C₄	1	2	yes	complemented
7	C₇₁⋊C₃₂	—	2	1	no	—
8	C₂×C₁₆×C₇₁	C₂²	1	1	yes	characteristic
9	#107×C₇₁	—	2	1	no	—
10	C₂×D₂₈₄	—	4	1	no	—
11	D₅₆₈	—	2	2	no	—
12	D₅₆₈	—	4	1	no	—
13	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
14	C₄⋊C₄×C₇₁	—	4	1	no	—
15	C₁₆×C₇₁	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₇₁	D₄	1	1	yes	characteristic
17	C₂²×D₇₁	—	8	1	no	—
18	C₂×C₄×C₇₁	—	8	1	no	—
19	C₂×C₄×C₇₁	D₈	1	1	yes	characteristic
20	D₂₈₄	—	4	2	no	—
21	D₂₈₄	—	8	1	no	—
22	C₈×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
23	C₈×C₇₁	SD₁₆	1	1	yes	characteristic
24	C₂²×C₇₁	D₁₆	1	1	yes	characteristic
25	C₂×D₇₁	—	8	2	no	—
26	C₂×D₇₁	—	16	1	no	—
27	C₂×D₇₁	—	16	1	no	—
28	C₄×C₇₁	—	16	1	no	—
29	C₄×C₇₁	#102	1	1	yes	characteristic
30	C₄×C₇₁	SD₃₂	1	1	yes	characteristic
31	C₂×C₇₁	#357	1	1	yes	characteristic
32	C₂×C₇₁	D₃₂	1	1	yes	characteristic
33	C₂×C₇₁	SD₆₄	1	1	yes	characteristic
34	D₇₁	—	16	2	no	—
35	#1415	—	71	1	no	maximal, Sylow
36	C₇₁	#1415	1	1	yes	characteristic, complemented, Sylow
37	C₂×D₁₆	—	71	1	no	—
38	C₂×C₃₂	—	71	1	no	—
39	#366	D₇₁	1	1	yes	characteristic, complemented
40	C₂×D₈	—	142	1	no	—
41	D₁₆	—	71	2	no	—
42	D₁₆	—	142	1	no	—
43	C₂×C₁₆	C₂×D₇₁	1	1	yes	characteristic
44	#107	—	2	1	no	—
45	C₃₂	—	142	1	no	—
46	C₂×D₄	—	284	1	no	—
47	D₈	—	284	1	no	—
48	D₈	—	142	2	no	—
49	C₂×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
50	C₄⋊C₄	—	4	1	no	—
51	C₁₆	C₄×D₇₁	1	1	yes	characteristic
52	C₁₆	D₂₈₄	1	1	yes	characteristic
53	C₂³	—	568	1	no	—
54	D₄	—	284	2	no	—
55	D₄	—	568	1	no	—
56	C₂×C₄	—	8	1	no	—
57	C₂×C₄	#11765850	1	1	yes	characteristic
58	C₈	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
59	C₈	#11765852	1	1	yes	characteristic
60	C₂²	—	568	2	no	—
61	C₂²	—	1136	1	no	—
62	C₂²	—	1136	1	no	—
63	C₂²	#14556069	1	1	yes	characteristic
64	C₄	—	16	1	no	—
65	C₄	#14556048	1	1	yes	characteristic
66	C₄	#14556071	1	1	yes	characteristic
67	C₂	—	1136	2	no	—
68	C₂	#17985799	1	1	yes	characteristic
69	C₂	#17985834	1	1	yes	characteristic
70	C₂	#17985836	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14556069
commutator	C₁₆×C₇₁	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₇₁
Fitting	#366×C₇₁	C₂
socle	C₂²×C₇₁	D₁₆
hypercenter	#366	D₇₁
hypocenter	C₇₁	#1415
LCS	G ▷ C₁₆×C₇₁ ▷ C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #366

Complements

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

N	H ≅ G/N	type
2. C₂×C₇₁⋊C₃₂	C₂	semidirect
3. #366×C₇₁	C₂	semidirect
6. D₁₁₃₆	C₄	semidirect
36. C₇₁	#1415	semidirect
39. #366	D₇₁	semidirect