Subgroups — #22590586

Order 9088.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17986401	C₂	1	1	yes	maximal, characteristic
2	#17986379	C₂	1	1	yes	maximal, characteristic
3	#17985804	C₂	1	4	yes	maximal
4	#346×C₇₁	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₂₈₄	—	2	1	no	—
6	C₂×Dic₂₈₄	C₂²	1	2	yes	—
7	#14556128	—	2	1	no	—
8	#14556120	—	2	1	no	—
9	#14556062	C₂²	1	2	yes	—
10	#14556060	—	2	1	no	—
11	C₂×C₁₆×C₇₁	C₂²	1	2	yes	—
12	C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
13	C₂×Dic₁₄₂	—	2	2	no	—
14	Dic₂₈₄	—	2	4	no	—
15	Dic₂₈₄	—	4	2	no	—
16	C₄⋊Dic₇₁	—	2	2	no	—
17	C₄⋊Dic₇₁	—	4	2	no	—
18	Dic₇₁⋊C₄	—	4	2	no	—
19	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
20	C₂×C₈×C₇₁	C₂³	1	1	yes	characteristic
21	C₄²×C₇₁	D₄	1	1	yes	characteristic
22	C₁₆×C₇₁	—	2	2	no	—
23	C₂×C₄×C₇₁	D₈	1	2	yes	—
24	C₂×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
25	C₂×Dic₇₁	—	4	2	no	—
26	C₂×Dic₇₁	—	4	2	no	—
27	Dic₁₄₂	—	4	2	no	—
28	Dic₁₄₂	—	4	2	no	—
29	C₈×C₇₁	SD₁₆	1	2	yes	—
30	C₈×C₇₁	#41	1	2	yes	—
31	C₂²×C₇₁	C₂×D₈	1	1	yes	characteristic
32	C₄×C₇₁	—	2	2	no	—
33	C₄×C₇₁	#124	1	1	yes	characteristic
34	C₄×C₇₁	C₂×SD₁₆	1	1	yes	characteristic
35	Dic₇₁	—	8	2	no	—
36	Dic₇₁	—	8	2	no	—
37	C₂×C₇₁	#486	1	1	yes	characteristic
38	C₂×C₇₁	#510	1	2	yes	—
39	#2245	—	71	1	no	maximal, Sylow
40	C₇₁	#2245	1	1	yes	characteristic, complemented, Sylow
41	#499	—	71	1	no	—
42	#494	—	71	1	no	—
43	#358	—	71	4	no	—
44	#346	D₇₁	1	1	yes	characteristic
45	C₂×Q₁₆	—	71	2	no	—
46	C₂×Q₁₆	—	142	1	no	—
47	C₄⋊Q₈	—	142	1	no	—
48	#125	—	142	1	no	—
49	C₂×C₁₆	C₂×D₇₁	1	2	yes	—
50	#107	—	71	2	no	—
51	#106	—	142	1	no	—
52	C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
53	C₂×Q₈	—	142	2	no	—
54	Q₁₆	—	284	2	no	—
55	Q₁₆	—	142	4	no	—
56	C₂×C₈	D₂₈₄	1	1	yes	characteristic
57	C₂×C₈	C₂²×D₇₁	1	1	yes	characteristic
58	C₄⋊C₄	—	284	2	no	—
59	C₄⋊C₄	—	284	2	no	—
60	C₄⋊C₄	—	142	2	no	—
61	C₄²	D₂₈₄	1	1	yes	characteristic
62	C₁₆	—	2	2	no	—
63	Q₈	—	284	2	no	—
64	Q₈	—	284	2	no	—
65	C₂×C₄	—	284	2	no	—
66	C₂×C₄	—	284	2	no	—
67	C₂×C₄	D₅₆₈	1	2	yes	—
68	C₂×C₄	C₂×D₂₈₄	1	1	yes	characteristic
69	C₈	#11765854	1	2	yes	—
70	C₈	#11765865	1	2	yes	—
71	C₂²	C₂×D₅₆₈	1	1	yes	characteristic
72	C₄	—	2	2	no	—
73	C₄	—	568	2	no	—
74	C₄	—	568	2	no	—
75	C₄	#14556116	1	1	yes	characteristic
76	C₄	C₂×#11765854	1	1	yes	characteristic
77	C₂	#17986346	1	1	yes	characteristic
78	C₂	#17986442	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₅₆₈
commutator	C₂×C₈×C₇₁	C₂³
Frattini	C₂×C₈	C₂²×D₇₁
Fitting	#346×C₇₁	C₂
socle	C₂²×C₇₁	C₂×D₈
hypercenter	#346	D₇₁
hypocenter	C₇₁	#2245
LCS	G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
40. C₇₁	#2245	semidirect