Subgroups — #22586317

Order 9088.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17986117	C₂	1	1	yes	maximal, characteristic
2	#17985820	C₂	1	1	yes	maximal, characteristic, complemented
3	#322×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#14556150	C₄	1	1	yes	characteristic
5	#14556134	—	2	1	no	—
6	#14556068	—	2	1	no	—
7	#14556064	C₄	1	1	yes	characteristic
8	#14556056	—	2	1	no	—
9	C₄×C₈×C₇₁	—	2	1	no	—
10	C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
11	#11765865	—	2	1	no	—
12	Dic₂₈₄	C₈	1	1	yes	characteristic, complemented
13	#11765854	—	2	1	no	—
14	D₅₆₈	C₈	1	1	yes	characteristic, complemented
15	#11765849	—	2	1	no	—
16	#11765848	—	4	1	no	—
17	C₈×D₇₁	—	4	1	no	—
18	C₇₁⋊C₁₆	—	4	1	no	—
19	C₂×C₈×C₇₁	—	2	2	no	—
20	C₂×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
22	C₄²×C₇₁	D₄	1	1	yes	characteristic
23	C₂×C₄×C₇₁	—	2	1	no	—
24	C₂×C₄×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
25	C₂²⋊D₇₁	—	4	1	no	—
26	D₂₈₄	—	2	1	no	—
27	C₄×D₇₁	—	4	1	no	—
28	Dic₁₄₂	—	2	1	no	—
29	C₈×C₇₁	—	4	2	no	—
30	C₈×C₇₁	C₂×C₈	1	1	yes	characteristic
31	C₈×C₇₁	M₁₆	1	1	yes	characteristic
32	C₈×C₇₁	D₈	1	1	yes	characteristic
33	C₈×C₇₁	SD₁₆	1	1	yes	characteristic
34	C₇₁⋊C₈	—	4	1	no	—
35	C₂²×C₇₁	#104	1	1	yes	characteristic
36	C₂×D₇₁	—	4	1	no	—
37	C₄×C₇₁	—	2	2	no	—
38	C₄×C₇₁	C₂²⋊C₈	1	1	yes	characteristic
39	C₄×C₇₁	#102	1	1	yes	characteristic
40	Dic₇₁	—	4	1	no	—
41	C₂×C₇₁	—	2	1	no	—
42	C₂×C₇₁	D₄⋊C₈	1	1	yes	characteristic
43	D₇₁	—	8	1	no	—
44	#1336	—	71	1	no	maximal, Sylow
45	C₇₁	#1336	1	1	yes	characteristic, complemented, Sylow
46	#443	—	71	1	no	—
47	#364	—	71	1	no	—
48	#322	D₇₁	1	1	yes	characteristic, complemented
49	#135	—	71	1	no	—
50	#131	—	142	1	no	—
51	M₃₂	—	142	1	no	—
52	#108	—	71	1	no	—
53	#104	—	142	1	no	—
54	C₄×C₈	—	2	1	no	—
55	C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
56	#41	—	142	1	no	—
57	Q₁₆	—	71	1	no	—
58	SD₁₆	—	142	1	no	—
59	D₈	—	71	1	no	—
60	M₁₆	—	284	1	no	—
61	M₁₆	—	142	1	no	—
62	C₂×C₈	—	2	2	no	—
63	C₂×C₈	—	284	1	no	—
64	C₂×C₈	C₄×D₇₁	1	1	yes	characteristic
65	C₂×C₈	D₂₈₄	1	1	yes	characteristic
66	C₄²	C₂²⋊D₇₁	1	1	yes	characteristic
67	C₁₆	—	284	1	no	—
68	Q₈	—	142	1	no	—
69	D₄	—	284	1	no	—
70	D₄	—	142	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	284	1	no	—
73	C₂×C₄	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
74	C₈	—	4	2	no	—
75	C₈	—	284	1	no	—
76	C₈	C₈×D₇₁	1	1	yes	characteristic
77	C₈	#11765848	1	1	yes	characteristic
78	C₈	D₅₆₈	1	1	yes	characteristic
79	C₈	#11765854	1	1	yes	characteristic
80	C₂²	—	284	1	no	—
81	C₂²	#14556056	1	1	yes	characteristic
82	C₄	—	2	2	no	—
83	C₄	—	284	1	no	—
84	C₄	(C₂×D₇₁)⋊C₈	1	1	yes	characteristic
85	C₄	#14556050	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	568	1	no	—
88	C₂	#17985728	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14556050
commutator	C₈×C₇₁	C₂×C₈
Frattini	C₄×C₈	C₂×D₇₁
Fitting	#322×C₇₁	C₂
socle	C₂×C₇₁	D₄⋊C₈
hypercenter	#322	D₇₁
hypocenter	C₇₁	#1336
LCS	G ▷ C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #322

Complements

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

N	H ≅ G/N	type
2. #17985820	C₂	semidirect
3. #322×C₇₁	C₂	semidirect
12. Dic₂₈₄	C₈	semidirect
14. D₅₆₈	C₈	semidirect
45. C₇₁	#1336	semidirect
48. #322	D₇₁	semidirect