Subgroups — #22590653

Order 9088.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17986431	C₂	1	1	yes	maximal, characteristic, complemented
2	#17985837	C₂	1	2	yes	maximal, complemented
3	#17985834	C₂	1	2	yes	maximal, complemented
4	#17985833	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₁₆×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#14556150	—	2	1	no	—
7	Dic₅₆₈	C₂²	1	1	yes	characteristic, complemented
8	#14556073	—	2	1	no	—
9	D₁₁₃₆	C₂²	1	1	yes	characteristic, complemented
10	C₇₁⋊C₃₂	C₂²	1	2	yes	complemented
11	C₂×D₈×C₇₁	—	2	1	no	—
12	D₁₆×C₇₁	—	2	1	no	—
13	D₁₆×C₇₁	C₂²	1	2	yes	—
14	C₂×C₁₆×C₇₁	C₂²	1	1	yes	characteristic
15	#11765865	—	4	1	no	—
16	Dic₂₈₄	—	2	1	no	—
17	#11765854	—	4	1	no	—
18	D₅₆₈	—	2	1	no	—
19	C₂×D₄×C₇₁	—	4	1	no	—
20	D₈×C₇₁	—	2	2	no	—
21	D₈×C₇₁	—	4	1	no	—
22	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
23	C₁₆×C₇₁	D₄	1	1	yes	characteristic
24	C₁₆×C₇₁	C₂³	1	1	yes	characteristic
25	C₂³×C₇₁	—	8	1	no	—
26	D₄×C₇₁	—	4	2	no	—
27	D₄×C₇₁	—	8	1	no	—
28	C₂×C₄×C₇₁	D₈	1	1	yes	characteristic
29	C₂²⋊D₇₁	—	8	1	no	—
30	D₂₈₄	—	4	1	no	—
31	C₄×D₇₁	—	8	1	no	—
32	Dic₁₄₂	—	4	1	no	—
33	C₈×C₇₁	D₈	1	1	yes	characteristic
34	C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
35	C₂²×C₇₁	—	8	2	no	—
36	C₂²×C₇₁	—	16	2	no	—
37	C₂²×C₇₁	D₁₆	1	1	yes	characteristic
38	C₂×D₇₁	—	8	1	no	—
39	C₄×C₇₁	D₁₆	1	1	yes	characteristic
40	C₄×C₇₁	C₂×D₈	1	1	yes	characteristic
41	Dic₇₁	—	8	1	no	—
42	C₂×C₇₁	—	2	1	no	—
43	C₂×C₇₁	—	16	2	no	—
44	C₂×C₇₁	C₂×D₁₆	1	1	yes	characteristic
45	D₇₁	—	16	1	no	—
46	#2263	—	71	1	no	maximal, Sylow
47	C₇₁	#2263	1	1	yes	characteristic, complemented, Sylow
48	#508	—	71	1	no	—
49	C₂×D₁₆	D₇₁	1	1	yes	characteristic, complemented
50	SD₆₄	—	71	2	no	—
51	D₃₂	—	71	2	no	—
52	M₆₄	—	71	1	no	—
53	#135	—	142	1	no	—
54	C₂×D₈	—	2	1	no	—
55	Q₃₂	—	71	1	no	—
56	SD₃₂	—	142	1	no	—
57	D₁₆	—	2	1	no	—
58	D₁₆	—	71	1	no	—
59	D₁₆	C₂×D₇₁	1	2	yes	—
60	C₂×C₁₆	C₂×D₇₁	1	1	yes	characteristic
61	C₃₂	—	71	2	no	—
62	#41	—	284	1	no	—
63	C₂×D₄	—	4	1	no	—
64	Q₁₆	—	142	1	no	—
65	SD₁₆	—	284	1	no	—
66	D₈	—	2	2	no	—
67	D₈	—	4	1	no	—
68	D₈	—	142	1	no	—
69	C₂×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
70	C₁₆	C₂²⋊D₇₁	1	1	yes	characteristic
71	C₁₆	C₂²×D₇₁	1	1	yes	characteristic
72	C₂³	—	8	1	no	—
73	Q₈	—	284	1	no	—
74	D₄	—	4	2	no	—
75	D₄	—	8	1	no	—
76	D₄	—	284	1	no	—
77	D₄	—	568	1	no	—
78	C₂×C₄	—	568	1	no	—
79	C₂×C₄	#11765850	1	1	yes	characteristic
80	C₈	#11765850	1	1	yes	characteristic
81	C₈	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
82	C₂²	—	8	2	no	—
83	C₂²	—	16	2	no	—
84	C₂²	—	568	1	no	—
85	C₂²	#14556069	1	1	yes	characteristic
86	C₄	—	568	1	no	—
87	C₄	#14556069	1	1	yes	characteristic
88	C₄	C₂×#11765850	1	1	yes	characteristic
89	C₂	—	2	1	no	—
90	C₂	—	16	2	no	—
91	C₂	—	1136	1	no	—
92	C₂	C₂×#14556069	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×#14556069
commutator	C₁₆×C₇₁	C₂³
Frattini	C₁₆	C₂²×D₇₁
Fitting	C₂×D₁₆×C₇₁	C₂
socle	C₂×C₇₁	C₂×D₁₆
hypercenter	C₂×D₁₆	D₇₁
hypocenter	C₇₁	#2263
LCS	G ▷ C₁₆×C₇₁ ▷ C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×D₁₆

Complements

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

N	H ≅ G/N	type
1. #17986431	C₂	semidirect
2. #17985837	C₂	semidirect
3. #17985834	C₂	semidirect
4. #17985833	C₂	semidirect
5. C₂×D₁₆×C₇₁	C₂	semidirect
7. Dic₅₆₈	C₂²	semidirect
9. D₁₁₃₆	C₂²	semidirect
10. C₇₁⋊C₃₂	C₂²	semidirect
47. C₇₁	#2263	semidirect
49. C₂×D₁₆	D₇₁	semidirect