Subgroups — #22590650

Order 9088.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17986432	C₂	1	2	yes	maximal, complemented
2	#17985836	C₂	1	2	yes	maximal, complemented
3	D₂₂₇₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₂×D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
5	Q₆₄×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#14556151	—	2	2	no	—
7	#14556071	—	2	2	no	—
8	D₁₁₃₆	C₂²	1	2	yes	—
9	C₁₆×D₇₁	C₂²	1	1	yes	characteristic
10	C₇₁⋊C₃₂	C₂²	1	1	yes	characteristic
11	Q₃₂×C₇₁	C₂²	1	2	yes	—
12	C₃₂×C₇₁	C₂²	1	1	yes	characteristic
13	#11765866	—	4	2	no	—
14	#11765852	—	4	2	no	—
15	D₅₆₈	—	2	2	no	—
16	C₈×D₇₁	D₄	1	1	yes	characteristic
17	C₇₁⋊C₁₆	D₄	1	1	yes	characteristic
18	Q₁₆×C₇₁	—	2	2	no	—
19	C₁₆×C₇₁	C₂³	1	1	yes	characteristic
20	Q₈×C₇₁	—	4	2	no	—
21	D₂₈₄	—	4	2	no	—
22	D₂₈₄	—	8	2	no	—
23	C₄×D₇₁	—	8	2	no	—
24	C₄×D₇₁	D₈	1	1	yes	characteristic
25	C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
26	C₇₁⋊C₈	D₈	1	1	yes	characteristic
27	C₂×D₇₁	—	8	2	no	—
28	C₂×D₇₁	D₁₆	1	1	yes	characteristic
29	C₄×C₇₁	—	8	2	no	—
30	C₄×C₇₁	C₂×D₈	1	1	yes	characteristic
31	Dic₇₁	D₁₆	1	1	yes	characteristic
32	C₂×C₇₁	C₂×D₁₆	1	1	yes	characteristic
33	D₇₁	—	2	1	no	—
34	D₇₁	—	16	2	no	—
35	#2262	—	71	1	no	maximal, Sylow
36	C₇₁	#2262	1	1	yes	characteristic, complemented, Sylow
37	#508	—	71	2	no	—
38	Q₆₄	D₇₁	1	1	yes	characteristic, complemented
39	SD₆₄	—	71	2	no	—
40	D₃₂	—	71	1	no	—
41	C₂×C₃₂	—	71	1	no	—
42	#135	—	142	2	no	—
43	Q₃₂	C₂×D₇₁	1	2	yes	—
44	SD₃₂	—	142	2	no	—
45	D₁₆	—	71	2	no	—
46	C₂×C₁₆	—	71	1	no	—
47	C₃₂	—	71	1	no	—
48	C₃₂	C₂×D₇₁	1	1	yes	characteristic
49	#41	—	284	2	no	—
50	Q₁₆	—	2	2	no	—
51	SD₁₆	—	284	2	no	—
52	D₈	—	142	2	no	—
53	C₂×C₈	—	71	1	no	—
54	C₁₆	—	71	1	no	—
55	C₁₆	C₂²×D₇₁	1	1	yes	characteristic
56	Q₈	—	4	2	no	—
57	D₄	—	284	2	no	—
58	D₄	—	568	2	no	—
59	C₂×C₄	—	568	2	no	—
60	C₂×C₄	—	71	1	no	—
61	C₈	—	71	1	no	—
62	C₈	D₄×D₇₁	1	1	yes	characteristic
63	C₂²	—	568	2	no	—
64	C₂²	—	71	1	no	—
65	C₄	—	8	2	no	—
66	C₄	—	71	1	no	—
67	C₄	D₈×D₇₁	1	1	yes	characteristic
68	C₂	—	1136	2	no	—
69	C₂	—	142	1	no	—
70	C₂	D₁₆×D₇₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₆×D₇₁
commutator	C₁₆×C₇₁	C₂³
Frattini	C₁₆	C₂²×D₇₁
Fitting	Q₆₄×C₇₁	C₂
socle	C₂×C₇₁	C₂×D₁₆
hypercenter	Q₆₄	D₇₁
hypocenter	C₇₁	#2262
LCS	G ▷ C₁₆×C₇₁ ▷ C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ Q₆₄

Complements

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

N	H ≅ G/N	type
1. #17986432	C₂	semidirect
2. #17985836	C₂	semidirect
3. D₂₂₇₂	C₂	semidirect
4. C₃₂×D₇₁	C₂	semidirect
5. Q₆₄×C₇₁	C₂	semidirect
36. C₇₁	#2262	semidirect
38. Q₆₄	D₇₁	semidirect