Subgroups — #22590615

Order 9088.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17986404	C₂	1	2	yes	maximal
2	#17985825	C₂	1	4	yes	maximal
3	C₄×C₁₆×C₇₁	C₂	1	1	yes	maximal, characteristic
4	#14556128	—	2	2	no	—
5	#14556062	—	2	2	no	—
6	#14556062	C₂²	1	4	yes	—
7	C₂×C₁₆×C₇₁	C₂²	1	2	yes	—
8	C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
9	C₂×Dic₁₄₂	—	4	2	no	—
10	C₄⋊Dic₇₁	—	2	4	no	—
11	C₄⋊Dic₇₁	—	4	2	no	—
12	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
13	C₂×C₈×C₇₁	C₂³	1	1	yes	characteristic
14	C₄²×C₇₁	D₄	1	1	yes	characteristic
15	C₁₆×C₇₁	Q₈	1	4	yes	complemented
16	C₂×C₄×C₇₁	D₈	1	1	yes	characteristic
17	C₂×C₄×C₇₁	D₈	1	1	yes	characteristic
18	C₂×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
19	C₂×Dic₇₁	—	4	4	no	—
20	Dic₁₄₂	—	8	4	no	—
21	C₈×C₇₁	Q₁₆	1	2	yes	—
22	C₈×C₇₁	C₂×Q₈	1	2	yes	—
23	C₂²×C₇₁	C₂×D₈	1	1	yes	characteristic
24	C₄×C₇₁	D₁₆	1	2	yes	—
25	C₄×C₇₁	Q₃₂	1	2	yes	—
26	C₄×C₇₁	C₄⋊Q₈	1	1	yes	characteristic
27	C₄×C₇₁	C₂×Q₁₆	1	1	yes	characteristic
28	Dic₇₁	—	8	4	no	—
29	C₂×C₇₁	#500	1	1	yes	characteristic
30	C₂×C₇₁	C₂×D₁₆	1	1	yes	characteristic
31	C₂×C₇₁	C₂×Q₃₂	1	1	yes	characteristic
32	#2252	—	71	1	no	maximal, Sylow
33	C₇₁	#2252	1	1	yes	characteristic, complemented, Sylow
34	#500	—	71	2	no	—
35	#366	—	71	4	no	—
36	C₄×C₁₆	D₇₁	1	1	yes	characteristic
37	C₄⋊Q₈	—	142	2	no	—
38	C₂×C₁₆	C₂×D₇₁	1	2	yes	—
39	#107	—	71	4	no	—
40	#107	—	142	2	no	—
41	C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
42	C₂×Q₈	—	284	2	no	—
43	C₂×C₈	D₂₈₄	1	1	yes	characteristic
44	C₂×C₈	C₂²×D₇₁	1	1	yes	characteristic
45	C₄⋊C₄	—	284	2	no	—
46	C₄⋊C₄	—	142	4	no	—
47	C₄²	D₂₈₄	1	1	yes	characteristic
48	C₁₆	Dic₁₄₂	1	4	yes	complemented
49	Q₈	—	568	4	no	—
50	C₂×C₄	—	284	4	no	—
51	C₂×C₄	D₅₆₈	1	1	yes	characteristic
52	C₂×C₄	D₅₆₈	1	1	yes	characteristic
53	C₂×C₄	C₂×D₂₈₄	1	1	yes	characteristic
54	C₈	Dic₂₈₄	1	2	yes	—
55	C₈	C₂×Dic₁₄₂	1	2	yes	—
56	C₂²	C₂×D₅₆₈	1	1	yes	characteristic
57	C₄	—	568	4	no	—
58	C₄	D₁₁₃₆	1	2	yes	—
59	C₄	Dic₅₆₈	1	2	yes	—
60	C₄	#14556128	1	1	yes	characteristic
61	C₄	C₂×Dic₂₈₄	1	1	yes	characteristic
62	C₂	#17986404	1	1	yes	characteristic
63	C₂	C₂×D₁₁₃₆	1	1	yes	characteristic
64	C₂	C₂×Dic₅₆₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₅₆₈
commutator	C₂×C₈×C₇₁	C₂³
Frattini	C₂×C₈	C₂²×D₇₁
Fitting	C₄×C₁₆×C₇₁	C₂
socle	C₂²×C₇₁	C₂×D₈
hypercenter	C₄×C₁₆	D₇₁
hypocenter	C₇₁	#2252
LCS	G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
15. C₁₆×C₇₁	Q₈	semidirect
33. C₇₁	#2252	semidirect
48. C₁₆	Dic₁₄₂	semidirect