Subgroups — #22586380

Order 9088.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17986372	C₂	1	1	yes	maximal, characteristic
2	#17985820	C₂	1	1	yes	maximal, characteristic, complemented
3	#364×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11765854	—	2	1	no	—
5	C₂×#11765854	—	2	1	no	—
6	#14556128	C₄	1	1	yes	characteristic
7	#14556125	C₄	1	1	yes	characteristic
8	#14556068	—	2	1	no	—
9	M₃₂×C₇₁	—	2	1	no	—
10	C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
11	C₂×Dic₁₄₂	—	2	1	no	—
12	C₂×D₂₈₄	—	2	1	no	—
13	C₂×D₂₈₄	—	4	1	no	—
14	#11765854	—	4	1	no	—
15	#11765854	—	4	1	no	—
16	#11765854	—	4	1	no	—
17	#11765854	—	4	1	no	—
18	C₄⋊Dic₇₁	—	4	1	no	—
19	C₇₁⋊C₁₆	—	4	1	no	—
20	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
21	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
22	C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
23	C₁₆×C₇₁	—	4	1	no	—
24	C₂²×D₇₁	—	4	1	no	—
25	C₂×C₄×C₇₁	—	2	1	no	—
26	C₂×C₄×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×Dic₇₁	—	4	1	no	—
28	D₂₈₄	—	4	1	no	—
29	D₂₈₄	—	4	1	no	—
30	D₂₈₄	—	8	2	no	—
31	Dic₁₄₂	—	4	1	no	—
32	Dic₁₄₂	—	4	1	no	—
33	C₈×C₇₁	D₈	1	1	yes	characteristic
34	C₈×C₇₁	D₈	1	1	yes	characteristic
35	C₈×C₇₁	SD₁₆	1	1	yes	characteristic
36	C₈×C₇₁	SD₁₆	1	1	yes	characteristic
37	C₂²×C₇₁	#100	1	1	yes	characteristic
38	C₂×D₇₁	—	8	2	no	—
39	C₂×D₇₁	—	8	1	no	—
40	C₄×C₇₁	—	2	2	no	—
41	C₄×C₇₁	#102	1	1	yes	characteristic
42	C₄×C₇₁	#102	1	1	yes	characteristic
43	Dic₇₁	—	8	1	no	—
44	C₂×C₇₁	—	2	1	no	—
45	C₂×C₇₁	#331	1	1	yes	characteristic
46	D₇₁	—	16	1	no	—
47	#1359	—	71	1	no	maximal, Sylow
48	C₇₁	#1359	1	1	yes	characteristic, complemented, Sylow
49	#492	—	71	1	no	—
50	#364	—	71	1	no	—
51	#364	D₇₁	1	1	yes	characteristic, complemented
52	C₂×SD₁₆	—	142	1	no	—
53	C₂×SD₁₆	—	142	1	no	—
54	C₄⋊Q₈	—	71	1	no	—
55	#127	—	71	1	no	—
56	M₃₂	—	2	1	no	—
57	M₃₂	—	142	1	no	—
58	C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
59	C₂×Q₈	—	142	1	no	—
60	C₂×D₄	—	284	1	no	—
61	C₂×D₄	—	142	1	no	—
62	SD₁₆	—	284	1	no	—
63	SD₁₆	—	284	1	no	—
64	SD₁₆	—	284	1	no	—
65	SD₁₆	—	284	1	no	—
66	C₂×C₈	D₂₈₄	1	1	yes	characteristic
67	C₂×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
68	C₄⋊C₄	—	284	1	no	—
69	C₄²	C₄×D₇₁	1	1	yes	characteristic
70	C₁₆	—	4	1	no	—
71	C₁₆	—	284	1	no	—
72	C₂³	—	284	1	no	—
73	Q₈	—	284	1	no	—
74	Q₈	—	284	1	no	—
75	D₄	—	284	1	no	—
76	D₄	—	284	1	no	—
77	D₄	—	568	2	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	284	1	no	—
80	C₂×C₄	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
81	C₈	#11765850	1	1	yes	characteristic
82	C₈	D₅₆₈	1	1	yes	characteristic
83	C₈	#11765852	1	1	yes	characteristic
84	C₈	#11765854	1	1	yes	characteristic
85	C₂²	—	568	2	no	—
86	C₂²	—	568	1	no	—
87	C₂²	#14556044	1	1	yes	characteristic
88	C₄	—	2	2	no	—
89	C₄	—	568	1	no	—
90	C₄	#14556048	1	1	yes	characteristic
91	C₄	#14556050	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	1136	1	no	—
94	C₂	#17985742	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#17985742
commutator	C₄²×C₇₁	C₂×C₄
Frattini	C₄×C₈	C₂×D₇₁
Fitting	#364×C₇₁	C₂
socle	C₂×C₇₁	#331
hypercenter	#364	D₇₁
hypocenter	C₇₁	#1359
LCS	G ▷ C₄²×C₇₁ ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
2. #17985820	C₂	semidirect
3. #364×C₇₁	C₂	semidirect
48. C₇₁	#1359	semidirect
51. #364	D₇₁	semidirect