Subgroups — #22586310

Order 9088.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17985775	C₂	1	1	yes	maximal, characteristic
2	#17985750	C₂	1	1	yes	maximal, characteristic
3	C₄×Q₁₆×C₇₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₇₁⋊C₁₆	—	2	1	no	—
5	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
6	C₂×Q₁₆×C₇₁	C₄	1	1	yes	characteristic
7	C₄×Q₈×C₇₁	—	2	1	no	—
8	#107×C₇₁	C₄	1	1	yes	characteristic
9	#103×C₇₁	—	2	1	no	—
10	C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
11	C₂×C₇₁⋊C₈	—	4	1	no	—
12	C₇₁⋊C₁₆	—	2	2	no	—
13	C₂×Q₈×C₇₁	—	2	1	no	—
14	Q₁₆×C₇₁	—	2	1	no	—
15	Q₁₆×C₇₁	C₈	1	2	yes	complemented
16	C₂×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
18	C₄⋊C₄×C₇₁	—	2	1	no	—
19	C₄⋊C₄×C₇₁	—	4	1	no	—
20	C₄²×C₇₁	—	4	1	no	—
21	C₄²×C₇₁	D₄	1	1	yes	characteristic
22	Q₈×C₇₁	—	2	2	no	—
23	Q₈×C₇₁	—	4	1	no	—
24	C₂×C₄×C₇₁	—	4	1	no	—
25	C₂×C₄×C₇₁	—	4	1	no	—
26	C₂×C₄×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₇₁	D₈	1	1	yes	characteristic
28	C₂×C₄×C₇₁	SD₁₆	1	1	yes	characteristic
29	C₈×C₇₁	—	2	1	no	—
30	C₈×C₇₁	C₂×C₈	1	1	yes	characteristic
31	C₈×C₇₁	M₁₆	1	1	yes	characteristic
32	C₇₁⋊C₈	—	8	1	no	—
33	C₂²×C₇₁	#102	1	1	yes	characteristic
34	C₄×C₇₁	—	2	1	no	—
35	C₄×C₇₁	—	2	1	no	—
36	C₄×C₇₁	—	4	2	no	—
37	C₄×C₇₁	—	8	1	no	—
38	C₄×C₇₁	C₂²⋊C₈	1	1	yes	characteristic
39	C₄×C₇₁	#104	1	1	yes	characteristic
40	C₂×C₇₁	D₄⋊C₈	1	1	yes	characteristic
41	C₂×C₇₁	#360	1	1	yes	characteristic
42	C₂×C₇₁	#362	1	1	yes	characteristic
43	#1334	—	71	1	no	maximal, Sylow
44	C₇₁	#1334	1	1	yes	characteristic, complemented, Sylow
45	C₄×Q₁₆	D₇₁	1	1	yes	characteristic
46	#346	—	71	1	no	—
47	#334	—	71	1	no	—
48	C₂×Q₁₆	Dic₇₁	1	1	yes	characteristic
49	C₄×Q₈	—	2	1	no	—
50	C₂×C₁₆	—	142	1	no	—
51	#107	Dic₇₁	1	1	yes	characteristic
52	C₄⋊C₈	—	142	1	no	—
53	#103	—	2	1	no	—
54	C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
55	C₂×Q₈	—	2	1	no	—
56	Q₁₆	—	2	1	no	—
57	Q₁₆	C₇₁⋊C₈	1	2	yes	complemented
58	C₂×C₈	—	284	1	no	—
59	C₂×C₈	C₂×Dic₇₁	1	1	yes	characteristic
60	C₂×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
61	C₄⋊C₄	—	2	1	no	—
62	C₄⋊C₄	—	4	1	no	—
63	C₄²	—	4	1	no	—
64	C₄²	C₂²⋊D₇₁	1	1	yes	characteristic
65	C₁₆	—	142	2	no	—
66	Q₈	—	2	2	no	—
67	Q₈	—	4	1	no	—
68	C₂×C₄	—	4	1	no	—
69	C₂×C₄	—	4	1	no	—
70	C₂×C₄	C₂²⋊Dic₇₁	1	1	yes	characteristic
71	C₂×C₄	#11765850	1	1	yes	characteristic
72	C₂×C₄	#11765853	1	1	yes	characteristic
73	C₈	—	2	1	no	—
74	C₈	—	568	1	no	—
75	C₈	C₂×C₇₁⋊C₈	1	1	yes	characteristic
76	C₈	#11765849	1	1	yes	characteristic
77	C₂²	#14556049	1	1	yes	characteristic
78	C₄	—	2	1	no	—
79	C₄	—	2	1	no	—
80	C₄	—	4	2	no	—
81	C₄	—	8	1	no	—
82	C₄	C₂²⋊(C₇₁⋊C₈)	1	1	yes	characteristic
83	C₄	#14556055	1	1	yes	characteristic
84	C₂	D₄⋊(C₇₁⋊C₈)	1	1	yes	characteristic
85	C₂	#17985809	1	1	yes	characteristic
86	C₂	#17985815	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14556049
commutator	C₈×C₇₁	C₂×C₈
Frattini	C₄×C₈	C₂×D₇₁
Fitting	C₄×Q₁₆×C₇₁	C₂
socle	C₂²×C₇₁	#102
hypercenter	C₄×Q₁₆	D₇₁
hypocenter	C₇₁	#1334
LCS	G ▷ C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×Q₁₆

Complements

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

N	H ≅ G/N	type
15. Q₁₆×C₇₁	C₈	semidirect
44. C₇₁	#1334	semidirect
57. Q₁₆	C₇₁⋊C₈	semidirect