Subgroups — #22586432

Order 9088.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14556062	C₂	1	2	yes	maximal
2	C₂²×C₁₆×C₇₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊Dic₇₁	—	2	2	no	—
4	#14556062	—	2	2	no	—
5	#14556062	C₄	1	4	yes	complemented
6	C₂²×C₈×C₇₁	C₂²	1	1	yes	characteristic
7	C₂×C₁₆×C₇₁	—	2	2	no	—
8	C₂×C₁₆×C₇₁	C₄	1	2	yes	complemented
9	C₂²×Dic₇₁	—	4	2	no	—
10	C₄⋊Dic₇₁	—	2	4	no	—
11	C₄⋊Dic₇₁	—	4	2	no	—
12	C₂²×C₄×C₇₁	D₄	1	1	yes	characteristic
13	C₂×C₈×C₇₁	C₂×C₄	1	2	yes	—
14	C₂×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₇₁	D₄	1	2	yes	—
16	C₂×C₈×C₇₁	Q₈	1	1	yes	characteristic
17	C₁₆×C₇₁	—	2	2	no	—
18	C₂³×C₇₁	D₈	1	1	yes	characteristic
19	C₂×C₄×C₇₁	C₂²⋊C₄	1	2	yes	—
20	C₂×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₄×C₇₁	SD₁₆	1	2	yes	—
22	C₂×C₄×C₇₁	Q₁₆	1	1	yes	characteristic
23	C₂×Dic₇₁	—	4	4	no	—
24	C₂×Dic₇₁	—	8	2	no	—
25	C₂×Dic₇₁	—	8	2	no	—
26	C₈×C₇₁	C₄²	1	1	yes	characteristic
27	C₈×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
28	C₈×C₇₁	C₄⋊C₄	1	2	yes	—
29	C₂²×C₇₁	#102	1	2	yes	—
30	C₂²×C₇₁	#107	1	1	yes	characteristic
31	C₂²×C₇₁	D₁₆	1	1	yes	characteristic
32	C₂²×C₇₁	SD₃₂	1	2	yes	—
33	C₂²×C₇₁	Q₃₂	1	1	yes	characteristic
34	C₄×C₇₁	#95	1	1	yes	characteristic
35	C₄×C₇₁	#103	1	2	yes	—
36	C₄×C₇₁	#106	1	1	yes	characteristic
37	Dic₇₁	—	8	4	no	—
38	C₂×C₇₁	#340	1	1	yes	characteristic
39	C₂×C₇₁	#357	1	2	yes	—
40	C₂×C₇₁	#358	1	2	yes	—
41	C₂×C₇₁	#366	1	1	yes	characteristic
42	C₂×C₇₁	#367	1	1	yes	characteristic
43	#1380	—	71	1	no	maximal, Sylow
44	C₇₁	#1380	1	1	yes	characteristic, complemented, Sylow
45	C₂²×C₁₆	D₇₁	1	1	yes	characteristic
46	C₂×#107	—	71	2	no	—
47	C₂²×C₈	C₂×D₇₁	1	1	yes	characteristic
48	C₂×C₄⋊C₄	—	142	2	no	—
49	C₂×C₁₆	—	2	2	no	—
50	C₂×C₁₆	Dic₇₁	1	2	yes	complemented
51	#107	—	71	4	no	—
52	#107	—	142	2	no	—
53	C₂²×C₄	—	284	2	no	—
54	C₂²×C₄	D₂₈₄	1	1	yes	characteristic
55	C₂×C₈	Dic₁₄₂	1	1	yes	characteristic
56	C₂×C₈	C₄×D₇₁	1	2	yes	—
57	C₂×C₈	C₂×Dic₇₁	1	1	yes	characteristic
58	C₂×C₈	C₂²⋊D₇₁	1	2	yes	—
59	C₄⋊C₄	—	284	2	no	—
60	C₄⋊C₄	—	142	4	no	—
61	C₁₆	—	2	2	no	—
62	C₂³	D₅₆₈	1	1	yes	characteristic
63	C₂×C₄	—	284	4	no	—
64	C₂×C₄	—	568	2	no	—
65	C₂×C₄	—	568	2	no	—
66	C₂×C₄	(C₂×D₇₁)⋊C₄	1	2	yes	—
67	C₂×C₄	C₄⋊Dic₇₁	1	1	yes	characteristic
68	C₂×C₄	#11765854	1	2	yes	—
69	C₂×C₄	Dic₂₈₄	1	1	yes	characteristic
70	C₈	C₄×Dic₇₁	1	1	yes	characteristic
71	C₈	C₂²⋊Dic₇₁	1	1	yes	characteristic
72	C₈	Dic₇₁⋊C₄	1	2	yes	—
73	C₂²	#14556050	1	2	yes	—
74	C₂²	#14556062	1	1	yes	characteristic
75	C₂²	D₁₁₃₆	1	1	yes	characteristic
76	C₂²	#14556073	1	2	yes	—
77	C₂²	Dic₅₆₈	1	1	yes	characteristic
78	C₄	—	568	4	no	—
79	C₄	C₇₁⋊#95	1	1	yes	characteristic
80	C₄	#14556053	1	2	yes	—
81	C₄	#14556060	1	1	yes	characteristic
82	C₂	#17985762	1	1	yes	characteristic
83	C₂	#17985801	1	2	yes	—
84	C₂	#17985804	1	2	yes	—
85	C₂	#17985825	1	1	yes	characteristic
86	C₂	#17985827	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₅₆₈
commutator	C₈×C₇₁	C₄²
Frattini	C₂²×C₈	C₂×D₇₁
Fitting	C₂²×C₁₆×C₇₁	C₂
socle	C₂³×C₇₁	D₈
hypercenter	C₂²×C₁₆	D₇₁
hypocenter	C₇₁	#1380
LCS	G ▷ C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
5. #14556062	C₄	semidirect
8. C₂×C₁₆×C₇₁	C₄	semidirect
44. C₇₁	#1380	semidirect
50. C₂×C₁₆	Dic₇₁	semidirect