Subgroups — #22586303

Order 9088.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Dic₂₈₄	C₂	1	1	yes	maximal, characteristic
2	C₄×C₇₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	#335×C₇₁	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₈₄	C₄	1	1	yes	characteristic
5	C₄×Dic₁₄₂	—	2	1	no	—
6	C₂×C₇₁⋊C₁₆	—	2	1	no	—
7	#14556062	C₄	1	1	yes	characteristic
8	#14556053	—	2	1	no	—
9	C₄⋊C₈×C₇₁	—	2	1	no	—
10	C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
11	C₂×Dic₁₄₂	—	2	1	no	—
12	Dic₂₈₄	—	2	1	no	—
13	Dic₂₈₄	C₈	1	2	yes	complemented
14	C₄⋊Dic₇₁	—	2	1	no	—
15	Dic₇₁⋊C₄	—	4	1	no	—
16	C₄×Dic₇₁	—	4	1	no	—
17	C₇₁⋊C₁₆	—	2	2	no	—
18	C₂×C₈×C₇₁	—	4	1	no	—
19	C₂×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
21	C₄²×C₇₁	D₄	1	1	yes	characteristic
22	C₂×C₄×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₄×C₇₁	D₈	1	1	yes	characteristic
24	C₂×C₄×C₇₁	SD₁₆	1	1	yes	characteristic
25	C₂×Dic₇₁	—	4	1	no	—
26	C₂×Dic₇₁	—	4	1	no	—
27	Dic₁₄₂	—	2	2	no	—
28	Dic₁₄₂	—	4	1	no	—
29	C₈×C₇₁	—	2	1	no	—
30	C₈×C₇₁	—	8	1	no	—
31	C₈×C₇₁	C₂×C₈	1	1	yes	characteristic
32	C₈×C₇₁	M₁₆	1	1	yes	characteristic
33	C₂²×C₇₁	#102	1	1	yes	characteristic
34	C₄×C₇₁	—	2	1	no	—
35	C₄×C₇₁	C₂²⋊C₈	1	1	yes	characteristic
36	C₄×C₇₁	#104	1	1	yes	characteristic
37	C₄×C₇₁	SD₃₂	1	1	yes	characteristic
38	C₄×C₇₁	Q₃₂	1	1	yes	characteristic
39	Dic₇₁	—	4	2	no	—
40	Dic₇₁	—	8	1	no	—
41	C₂×C₇₁	D₄⋊C₈	1	1	yes	characteristic
42	C₂×C₇₁	#358	1	1	yes	characteristic
43	C₂×C₇₁	#359	1	1	yes	characteristic
44	#1332	—	71	1	no	maximal, Sylow
45	C₇₁	#1332	1	1	yes	characteristic, complemented, Sylow
46	C₄×Q₁₆	—	71	1	no	—
47	C₄×C₁₆	—	71	1	no	—
48	#335	D₇₁	1	1	yes	characteristic
49	C₂×Q₁₆	—	71	1	no	—
50	C₄×Q₈	—	142	1	no	—
51	C₂×C₁₆	—	142	1	no	—
52	#107	—	71	1	no	—
53	C₄⋊C₈	—	2	1	no	—
54	#103	—	142	1	no	—
55	C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
56	C₂×Q₈	—	142	1	no	—
57	Q₁₆	—	71	2	no	—
58	Q₁₆	—	142	1	no	—
59	C₂×C₈	—	4	1	no	—
60	C₂×C₈	C₄×D₇₁	1	1	yes	characteristic
61	C₂×C₈	D₂₈₄	1	1	yes	characteristic
62	C₄⋊C₄	—	284	1	no	—
63	C₄⋊C₄	—	142	1	no	—
64	C₄²	—	284	1	no	—
65	C₄²	C₂²⋊D₇₁	1	1	yes	characteristic
66	C₁₆	—	142	2	no	—
67	Q₈	—	284	1	no	—
68	Q₈	—	142	2	no	—
69	C₂×C₄	—	284	1	no	—
70	C₂×C₄	—	284	1	no	—
71	C₂×C₄	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
72	C₂×C₄	#11765850	1	1	yes	characteristic
73	C₂×C₄	#11765852	1	1	yes	characteristic
74	C₈	—	2	1	no	—
75	C₈	—	8	1	no	—
76	C₈	C₈×D₇₁	1	1	yes	characteristic
77	C₈	#11765848	1	1	yes	characteristic
78	C₂²	#14556048	1	1	yes	characteristic
79	C₄	—	2	1	no	—
80	C₄	—	284	2	no	—
81	C₄	—	568	1	no	—
82	C₄	(C₂×D₇₁)⋊C₈	1	1	yes	characteristic
83	C₄	#14556054	1	1	yes	characteristic
84	C₄	#14556072	1	1	yes	characteristic
85	C₄	#14556074	1	1	yes	characteristic
86	C₂	#17985726	1	1	yes	characteristic
87	C₂	#17985802	1	1	yes	characteristic
88	C₂	#17985805	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#11765850
commutator	C₈×C₇₁	C₂×C₈
Frattini	C₄×C₈	C₂×D₇₁
Fitting	#335×C₇₁	C₂
socle	C₂²×C₇₁	#102
hypercenter	#335	D₇₁
hypocenter	C₇₁	#1332
LCS	G ▷ C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ #335

Complements

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

N	H ≅ G/N	type
13. Dic₂₈₄	C₈	semidirect
45. C₇₁	#1332	semidirect