Subgroups — #22586293

Order 9088.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17985781	C₂	1	2	yes	maximal
2	#424×C₇₁	C₂	1	1	yes	maximal, characteristic
3	#14556068	—	2	2	no	—
4	C₂×M₁₆×C₇₁	C₂²	1	1	yes	characteristic
5	C₂²×C₈×C₇₁	C₄	1	1	yes	characteristic
6	#117×C₇₁	C₄	1	1	yes	characteristic
7	C₄⋊C₈×C₇₁	—	2	2	no	—
8	C₇₁⋊C₁₆	—	4	2	no	—
9	C₂²×C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
10	M₁₆×C₇₁	—	4	1	no	—
11	C₂×C₈×C₇₁	—	2	1	no	—
12	C₂×C₈×C₇₁	—	4	1	no	—
13	C₂×C₈×C₇₁	D₄	1	2	yes	—
14	C₄⋊C₄×C₇₁	—	2	1	no	—
15	C₂²⋊C₄×C₇₁	C₈	1	2	yes	—
16	C₄²×C₇₁	—	2	1	no	—
17	C₂³×C₇₁	C₂×C₈	1	1	yes	characteristic
18	C₂×C₄×C₇₁	—	2	1	no	—
19	C₂×C₄×C₇₁	—	2	1	no	—
20	C₂×C₄×C₇₁	—	2	2	no	—
21	C₂×C₄×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₄×C₇₁	M₁₆	1	1	yes	characteristic
23	C₈×C₇₁	—	2	2	no	—
24	C₈×C₇₁	—	4	1	no	—
25	C₂²×C₇₁	—	2	1	no	—
26	C₂²×C₇₁	—	4	1	no	—
27	C₂²×C₇₁	C₂²⋊C₈	1	1	yes	characteristic
28	C₄×C₇₁	—	2	1	no	—
29	C₄×C₇₁	—	4	2	no	—
30	C₄×C₇₁	#99	1	1	yes	characteristic
31	C₄×C₇₁	#101	1	1	yes	characteristic
32	C₂×C₇₁	—	2	1	no	—
33	C₂×C₇₁	—	4	1	no	—
34	C₂×C₇₁	#324	1	1	yes	characteristic
35	#1328	—	71	1	no	maximal, Sylow
36	C₇₁	#1328	1	1	yes	characteristic, complemented, Sylow
37	#424	D₇₁	1	1	yes	characteristic
38	#349	—	71	2	no	—
39	C₂×M₁₆	C₂×D₇₁	1	1	yes	characteristic
40	C₂²×C₈	Dic₇₁	1	1	yes	characteristic
41	#117	Dic₇₁	1	1	yes	characteristic
42	M₃₂	—	142	2	no	—
43	C₄⋊C₈	—	2	2	no	—
44	C₂²×C₄	C₂×Dic₇₁	1	1	yes	characteristic
45	M₁₆	—	4	1	no	—
46	C₂×C₈	—	2	1	no	—
47	C₂×C₈	—	4	1	no	—
48	C₂×C₈	C₂²⋊D₇₁	1	2	yes	—
49	C₄⋊C₄	—	2	1	no	—
50	C₂²⋊C₄	C₇₁⋊C₈	1	2	yes	—
51	C₄²	—	2	1	no	—
52	C₁₆	—	284	2	no	—
53	C₂³	C₂×C₇₁⋊C₈	1	1	yes	characteristic
54	C₂×C₄	—	2	1	no	—
55	C₂×C₄	—	2	1	no	—
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	C₂²⋊Dic₇₁	1	1	yes	characteristic
58	C₂×C₄	#11765849	1	1	yes	characteristic
59	C₈	—	2	2	no	—
60	C₈	—	4	1	no	—
61	C₂²	—	2	1	no	—
62	C₂²	—	4	1	no	—
63	C₂²	C₂²⋊(C₇₁⋊C₈)	1	1	yes	characteristic
64	C₄	—	2	1	no	—
65	C₄	—	4	2	no	—
66	C₄	#14556043	1	1	yes	characteristic
67	C₄	#14556047	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	4	1	no	—
70	C₂	#17985725	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14556043
commutator	C₂³×C₇₁	C₂×C₈
Frattini	C₂×M₁₆	C₂×D₇₁
Fitting	#424×C₇₁	C₂
socle	C₂×C₇₁	#324
hypercenter	#424	D₇₁
hypocenter	C₇₁	#1328
LCS	G ▷ C₂³×C₇₁ ▷ C₂²×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #424

Complements

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

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