Subgroups — #22586297

Order 9088.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17986078	C₂	1	1	yes	maximal, characteristic
2	#17985775	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊C₁₆×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11765848	—	2	1	no	—
5	C₄×D₂₈₄	C₄	1	1	yes	characteristic
6	C₂×C₇₁⋊C₁₆	—	2	1	no	—
7	C₄⋊(C₇₁⋊C₈)	C₄	1	1	yes	characteristic
8	(C₂×D₇₁)⋊C₈	—	2	1	no	—
9	C₂×C₁₆×C₇₁	—	2	1	no	—
10	C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
11	C₂×D₂₈₄	C₈	1	1	yes	characteristic
12	C₂×C₄×D₇₁	—	2	1	no	—
13	#11765848	—	4	1	no	—
14	#11765848	—	4	1	no	—
15	C₂×C₇₁⋊C₈	—	2	1	no	—
16	C₄⋊Dic₇₁	C₈	1	1	yes	characteristic
17	(C₂×D₇₁)⋊C₄	—	2	1	no	—
18	C₇₁⋊C₁₆	—	2	2	no	—
19	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
20	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
21	C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
22	C₁₆×C₇₁	—	4	1	no	—
23	C₂²×D₇₁	—	2	1	no	—
24	C₂×C₄×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
26	C₂×C₄×C₇₁	M₁₆	1	1	yes	characteristic
27	C₂×Dic₇₁	—	2	1	no	—
28	D₂₈₄	—	4	1	no	—
29	C₄×D₇₁	—	4	1	no	—
30	C₄×D₇₁	—	4	1	no	—
31	C₈×C₇₁	—	2	1	no	—
32	C₈×C₇₁	D₈	1	1	yes	characteristic
33	C₈×C₇₁	SD₁₆	1	1	yes	characteristic
34	C₇₁⋊C₈	—	4	1	no	—
35	C₂²×C₇₁	C₂²⋊C₈	1	1	yes	characteristic
36	C₂×D₇₁	—	4	1	no	—
37	C₂×D₇₁	—	4	1	no	—
38	C₂×D₇₁	—	4	1	no	—
39	C₄×C₇₁	—	2	1	no	—
40	C₄×C₇₁	—	2	1	no	—
41	C₄×C₇₁	#102	1	1	yes	characteristic
42	C₄×C₇₁	#104	1	1	yes	characteristic
43	Dic₇₁	—	4	1	no	—
44	C₂×C₇₁	D₄⋊C₈	1	1	yes	characteristic
45	C₂×C₇₁	#349	1	1	yes	characteristic
46	C₂×C₇₁	#350	1	1	yes	characteristic
47	D₇₁	—	8	1	no	—
48	#1330	—	71	1	no	maximal, Sylow
49	C₇₁	#1330	1	1	yes	characteristic, complemented, Sylow
50	#436	—	71	1	no	—
51	C₄⋊C₁₆	D₇₁	1	1	yes	characteristic, complemented
52	#346	—	71	1	no	—
53	C₂×M₁₆	—	142	1	no	—
54	C₄×D₄	—	71	1	no	—
55	C₂×C₁₆	—	2	1	no	—
56	C₂×C₁₆	—	142	1	no	—
57	C₄⋊C₈	—	71	1	no	—
58	C₂²⋊C₈	—	142	1	no	—
59	C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
60	C₂×D₄	—	71	1	no	—
61	C₂²×C₄	—	142	1	no	—
62	M₁₆	—	284	1	no	—
63	M₁₆	—	284	1	no	—
64	C₂×C₈	—	142	1	no	—
65	C₂×C₈	D₂₈₄	1	1	yes	characteristic
66	C₂×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
67	C₄⋊C₄	—	71	1	no	—
68	C₂²⋊C₄	—	142	1	no	—
69	C₄²	C₄×D₇₁	1	1	yes	characteristic
70	C₁₆	—	4	1	no	—
71	C₁₆	—	142	2	no	—
72	C₂³	—	142	1	no	—
73	D₄	—	284	1	no	—
74	C₂×C₄	—	284	1	no	—
75	C₂×C₄	—	284	1	no	—
76	C₂×C₄	—	142	1	no	—
77	C₂×C₄	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
78	C₂×C₄	C₈×D₇₁	1	1	yes	characteristic
79	C₂×C₄	#11765848	1	1	yes	characteristic
80	C₈	—	2	1	no	—
81	C₈	—	284	1	no	—
82	C₈	#11765850	1	1	yes	characteristic
83	C₈	#11765852	1	1	yes	characteristic
84	C₂²	—	284	1	no	—
85	C₂²	—	284	1	no	—
86	C₂²	—	284	1	no	—
87	C₂²	(C₂×D₇₁)⋊C₈	1	1	yes	characteristic
88	C₄	—	2	1	no	—
89	C₄	—	2	1	no	—
90	C₄	—	284	1	no	—
91	C₄	#14556048	1	1	yes	characteristic
92	C₄	#14556054	1	1	yes	characteristic
93	C₂	—	568	1	no	—
94	C₂	#17985726	1	1	yes	characteristic
95	C₂	#17985780	1	1	yes	characteristic
96	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	#1330
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
2. #17985775	C₂	semidirect
3. C₄⋊C₁₆×C₇₁	C₂	semidirect
49. C₇₁	#1330	semidirect
51. C₄⋊C₁₆	D₇₁	semidirect