Subgroups — #22586321

Order 9088.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17986129	C₂	1	1	yes	maximal, characteristic
2	#17985775	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₁₆×C₇₁	C₂	1	1	yes	maximal, characteristic
4	C₄×Dic₁₄₂	C₄	1	1	yes	characteristic
5	C₂×C₇₁⋊C₁₆	—	2	1	no	—
6	C₄⋊(C₇₁⋊C₈)	C₄	1	1	yes	characteristic
7	Dic₇₁⋊C₈	—	2	1	no	—
8	#14556038	—	2	1	no	—
9	C₂×C₁₆×C₇₁	—	2	1	no	—
10	C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
11	C₂×Dic₁₄₂	C₈	1	1	yes	characteristic
12	C₂×C₇₁⋊C₈	—	2	1	no	—
13	C₄⋊Dic₇₁	C₈	1	1	yes	characteristic
14	Dic₇₁⋊C₄	—	2	1	no	—
15	C₄×Dic₇₁	—	2	1	no	—
16	C₇₁⋊C₁₆	—	2	2	no	—
17	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
18	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
19	C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
20	C₁₆×C₇₁	—	4	1	no	—
21	C₂×C₄×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
23	C₂×C₄×C₇₁	M₁₆	1	1	yes	characteristic
24	C₂×Dic₇₁	—	2	1	no	—
25	C₂×Dic₇₁	—	2	1	no	—
26	Dic₁₄₂	—	4	1	no	—
27	C₈×C₇₁	—	2	1	no	—
28	C₈×C₇₁	SD₁₆	1	1	yes	characteristic
29	C₈×C₇₁	Q₁₆	1	1	yes	characteristic
30	C₇₁⋊C₈	—	4	1	no	—
31	C₂²×C₇₁	C₂²⋊C₈	1	1	yes	characteristic
32	C₄×C₇₁	—	2	1	no	—
33	C₄×C₇₁	—	2	1	no	—
34	C₄×C₇₁	#103	1	1	yes	characteristic
35	C₄×C₇₁	#104	1	1	yes	characteristic
36	Dic₇₁	—	4	1	no	—
37	Dic₇₁	—	4	1	no	—
38	C₂×C₇₁	Q₈⋊C₈	1	1	yes	characteristic
39	C₂×C₇₁	#349	1	1	yes	characteristic
40	C₂×C₇₁	#350	1	1	yes	characteristic
41	#1338	—	71	1	no	maximal, Sylow
42	C₇₁	#1338	1	1	yes	characteristic, complemented, Sylow
43	#446	—	71	1	no	—
44	C₄⋊C₁₆	D₇₁	1	1	yes	characteristic
45	#346	—	71	1	no	—
46	C₄×Q₈	—	71	1	no	—
47	C₂×C₁₆	—	2	1	no	—
48	C₂×C₁₆	—	142	1	no	—
49	C₄⋊C₈	—	71	1	no	—
50	C₄⋊C₈	—	142	1	no	—
51	#97	—	142	1	no	—
52	C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
53	C₂×Q₈	—	71	1	no	—
54	C₂×C₈	—	142	1	no	—
55	C₂×C₈	D₂₈₄	1	1	yes	characteristic
56	C₂×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
57	C₄⋊C₄	—	71	1	no	—
58	C₄⋊C₄	—	142	1	no	—
59	C₄²	—	142	1	no	—
60	C₄²	C₄×D₇₁	1	1	yes	characteristic
61	C₁₆	—	4	1	no	—
62	C₁₆	—	142	2	no	—
63	Q₈	—	284	1	no	—
64	C₂×C₄	—	142	1	no	—
65	C₂×C₄	—	142	1	no	—
66	C₂×C₄	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
67	C₂×C₄	C₈×D₇₁	1	1	yes	characteristic
68	C₂×C₄	#11765848	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	—	284	1	no	—
71	C₈	#11765853	1	1	yes	characteristic
72	C₈	#11765855	1	1	yes	characteristic
73	C₂²	(C₂×D₇₁)⋊C₈	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	2	1	no	—
76	C₄	—	284	1	no	—
77	C₄	—	284	1	no	—
78	C₄	#14556051	1	1	yes	characteristic
79	C₄	#14556054	1	1	yes	characteristic
80	C₂	#17985729	1	1	yes	characteristic
81	C₂	#17985780	1	1	yes	characteristic
82	C₂	#17985782	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	(C₂×D₇₁)⋊C₄
commutator	C₂×C₄×C₇₁	C₂×C₈
Frattini	C₄×C₈	C₂×D₇₁
Fitting	C₄⋊C₁₆×C₇₁	C₂
socle	C₂²×C₇₁	C₂²⋊C₈
hypercenter	C₄⋊C₁₆	D₇₁
hypocenter	C₇₁	#1338
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
42. C₇₁	#1338	semidirect