Subgroups — #22586292

Order 9088.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17986027	C₂	1	1	yes	maximal, characteristic
2	#17985781	C₂	1	1	yes	maximal, characteristic
3	#349×C₇₁	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₇₁⋊C₈	C₄	1	1	yes	characteristic
5	#14556087	C₄	1	1	yes	characteristic
6	#14556068	—	2	1	no	—
7	Dic₇₁⋊C₈	—	2	1	no	—
8	Dic₇₁⋊C₈	—	2	1	no	—
9	C₂×M₁₆×C₇₁	C₂²	1	1	yes	characteristic
10	M₃₂×C₇₁	—	2	1	no	—
11	C₂×C₇₁⋊C₈	—	2	1	no	—
12	C₂×C₇₁⋊C₈	—	4	1	no	—
13	C₄⋊Dic₇₁	—	2	1	no	—
14	C₂²⋊Dic₇₁	C₈	1	2	yes	—
15	C₄×Dic₇₁	—	2	1	no	—
16	C₇₁⋊C₁₆	—	4	1	no	—
17	C₂²×C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
18	M₁₆×C₇₁	—	4	1	no	—
19	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
20	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
21	C₁₆×C₇₁	—	4	1	no	—
22	C₂³×C₇₁	C₂×C₈	1	1	yes	characteristic
23	C₂×C₄×C₇₁	—	2	1	no	—
24	C₂×C₄×C₇₁	—	2	1	no	—
25	C₂×C₄×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₇₁	M₁₆	1	1	yes	characteristic
27	C₂×Dic₇₁	—	2	2	no	—
28	C₈×C₇₁	—	2	1	no	—
29	C₈×C₇₁	—	2	1	no	—
30	C₇₁⋊C₈	—	4	1	no	—
31	C₂²×C₇₁	—	2	1	no	—
32	C₂²×C₇₁	—	4	1	no	—
33	C₂²×C₇₁	C₂²⋊C₈	1	1	yes	characteristic
34	C₄×C₇₁	—	2	1	no	—
35	C₄×C₇₁	#99	1	1	yes	characteristic
36	C₄×C₇₁	#101	1	1	yes	characteristic
37	Dic₇₁	—	4	2	no	—
38	C₂×C₇₁	—	2	1	no	—
39	C₂×C₇₁	—	4	1	no	—
40	C₂×C₇₁	#324	1	1	yes	characteristic
41	#1328	—	71	1	no	maximal, Sylow
42	C₇₁	#1328	1	1	yes	characteristic, complemented, Sylow
43	#424	—	71	1	no	—
44	#349	—	71	1	no	—
45	#349	D₇₁	1	1	yes	characteristic
46	C₂×M₁₆	C₂×D₇₁	1	1	yes	characteristic
47	C₂²×C₈	—	71	1	no	—
48	#117	—	71	1	no	—
49	M₃₂	—	2	1	no	—
50	M₃₂	—	142	1	no	—
51	C₄⋊C₈	—	142	1	no	—
52	C₄⋊C₈	—	142	1	no	—
53	C₂²×C₄	C₄×D₇₁	1	1	yes	characteristic
54	M₁₆	—	4	1	no	—
55	C₂×C₈	—	284	1	no	—
56	C₂×C₈	—	142	1	no	—
57	C₂×C₈	D₂₈₄	1	1	yes	characteristic
58	C₂×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
59	C₄⋊C₄	—	142	1	no	—
60	C₂²⋊C₄	—	71	2	no	—
61	C₄²	—	142	1	no	—
62	C₁₆	—	4	1	no	—
63	C₁₆	—	284	1	no	—
64	C₂³	C₈×D₇₁	1	1	yes	characteristic
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	—	142	2	no	—
68	C₂×C₄	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
69	C₂×C₄	#11765848	1	1	yes	characteristic
70	C₈	—	2	1	no	—
71	C₈	—	2	1	no	—
72	C₈	—	284	1	no	—
73	C₂²	—	2	1	no	—
74	C₂²	—	4	1	no	—
75	C₂²	(C₂×D₇₁)⋊C₈	1	1	yes	characteristic
76	C₄	—	2	1	no	—
77	C₄	—	284	2	no	—
78	C₄	#14556042	1	1	yes	characteristic
79	C₄	#14556046	1	1	yes	characteristic
80	C₂	—	2	1	no	—
81	C₂	—	4	1	no	—
82	C₂	#17985724	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14556042
commutator	C₂³×C₇₁	C₂×C₈
Frattini	C₂×M₁₆	C₂×D₇₁
Fitting	#349×C₇₁	C₂
socle	C₂×C₇₁	#324
hypercenter	#349	D₇₁
hypocenter	C₇₁	#1328
LCS	G ▷ C₂³×C₇₁ ▷ C₂²×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #349

Complements

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

N	H ≅ G/N	type
42. C₇₁	#1328	semidirect