Subgroups — #22586540

Order 9088.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17985825	C₂	1	2	yes	maximal
2	C₂×C₃₂×C₇₁	C₂	1	1	yes	maximal, characteristic
3	#14556062	—	2	2	no	—
4	C₂×C₁₆×C₇₁	C₂²	1	1	yes	characteristic
5	C₃₂×C₇₁	C₄	1	2	yes	complemented
6	C₄⋊Dic₇₁	—	4	2	no	—
7	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
8	C₁₆×C₇₁	C₂×C₄	1	1	yes	characteristic
9	C₁₆×C₇₁	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₇₁	D₈	1	1	yes	characteristic
11	C₂×Dic₇₁	—	8	2	no	—
12	C₈×C₇₁	C₄⋊C₄	1	1	yes	characteristic
13	C₈×C₇₁	Q₁₆	1	1	yes	characteristic
14	C₂²×C₇₁	D₁₆	1	1	yes	characteristic
15	C₄×C₇₁	#107	1	1	yes	characteristic
16	C₄×C₇₁	Q₃₂	1	1	yes	characteristic
17	Dic₇₁	—	16	2	no	—
18	C₂×C₇₁	#366	1	1	yes	characteristic
19	C₂×C₇₁	D₃₂	1	1	yes	characteristic
20	C₂×C₇₁	Q₆₄	1	1	yes	characteristic
21	#1423	—	71	1	no	maximal, Sylow
22	C₇₁	#1423	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₃₂	D₇₁	1	1	yes	characteristic
24	#366	—	71	2	no	—
25	C₂×C₁₆	C₂×D₇₁	1	1	yes	characteristic
26	#107	—	142	2	no	—
27	C₃₂	Dic₇₁	1	2	yes	complemented
28	C₂×C₈	D₂₈₄	1	1	yes	characteristic
29	C₄⋊C₄	—	284	2	no	—
30	C₁₆	Dic₁₄₂	1	1	yes	characteristic
31	C₁₆	C₂×Dic₇₁	1	1	yes	characteristic
32	C₂×C₄	—	568	2	no	—
33	C₂×C₄	D₅₆₈	1	1	yes	characteristic
34	C₈	C₄⋊Dic₇₁	1	1	yes	characteristic
35	C₈	Dic₂₈₄	1	1	yes	characteristic
36	C₂²	D₁₁₃₆	1	1	yes	characteristic
37	C₄	—	1136	2	no	—
38	C₄	#14556062	1	1	yes	characteristic
39	C₄	Dic₅₆₈	1	1	yes	characteristic
40	C₂	#17985825	1	1	yes	characteristic
41	C₂	D₂₂₇₂	1	1	yes	characteristic
42	C₂	Dic₁₁₃₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₁₁₃₆
commutator	C₁₆×C₇₁	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₇₁
Fitting	C₂×C₃₂×C₇₁	C₂
socle	C₂²×C₇₁	D₁₆
hypercenter	C₂×C₃₂	D₇₁
hypocenter	C₇₁	#1423
LCS	G ▷ C₁₆×C₇₁ ▷ C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
5. C₃₂×C₇₁	C₄	semidirect
22. C₇₁	#1423	semidirect
27. C₃₂	Dic₇₁	semidirect