Subgroups — #22586541

Order 9088.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇₁⋊C₃₂	C₂	1	1	yes	maximal, characteristic
2	#17985825	C₂	1	1	yes	maximal, characteristic
3	#366×C₇₁	C₂	1	1	yes	maximal, characteristic
4	#14556062	—	2	1	no	—
5	C₇₁⋊C₃₂	C₄	1	2	yes	complemented
6	C₂×C₁₆×C₇₁	C₂²	1	1	yes	characteristic
7	#107×C₇₁	—	2	1	no	—
8	C₄⋊Dic₇₁	—	4	1	no	—
9	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
10	C₄⋊C₄×C₇₁	—	4	1	no	—
11	C₁₆×C₇₁	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₇₁	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₇₁	—	8	1	no	—
14	C₂×C₄×C₇₁	D₈	1	1	yes	characteristic
15	C₂×Dic₇₁	—	8	1	no	—
16	C₈×C₇₁	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₇₁	Q₁₆	1	1	yes	characteristic
18	C₂²×C₇₁	D₁₆	1	1	yes	characteristic
19	C₄×C₇₁	—	16	1	no	—
20	C₄×C₇₁	#107	1	1	yes	characteristic
21	C₄×C₇₁	Q₃₂	1	1	yes	characteristic
22	Dic₇₁	—	16	1	no	—
23	C₂×C₇₁	#366	1	1	yes	characteristic
24	C₂×C₇₁	SD₆₄	1	1	yes	characteristic
25	C₂×C₇₁	SD₆₄	1	1	yes	characteristic
26	#1424	—	71	1	no	maximal, Sylow
27	C₇₁	#1424	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃₂	—	71	1	no	—
29	#366	—	71	1	no	—
30	#366	D₇₁	1	1	yes	characteristic
31	C₂×C₁₆	C₂×D₇₁	1	1	yes	characteristic
32	#107	—	2	1	no	—
33	#107	—	142	1	no	—
34	C₃₂	—	71	2	no	—
35	C₂×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
36	C₄⋊C₄	—	4	1	no	—
37	C₄⋊C₄	—	284	1	no	—
38	C₁₆	Dic₁₄₂	1	1	yes	characteristic
39	C₁₆	C₄×D₇₁	1	1	yes	characteristic
40	C₂×C₄	—	8	1	no	—
41	C₂×C₄	—	568	1	no	—
42	C₂×C₄	#11765850	1	1	yes	characteristic
43	C₈	Dic₇₁⋊C₄	1	1	yes	characteristic
44	C₈	#11765855	1	1	yes	characteristic
45	C₂²	#14556069	1	1	yes	characteristic
46	C₄	—	16	1	no	—
47	C₄	—	1136	1	no	—
48	C₄	#14556061	1	1	yes	characteristic
49	C₄	#14556074	1	1	yes	characteristic
50	C₂	#17985824	1	1	yes	characteristic
51	C₂	#17985836	1	1	yes	characteristic
52	C₂	#17985837	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14556069
commutator	C₁₆×C₇₁	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₇₁
Fitting	#366×C₇₁	C₂
socle	C₂²×C₇₁	D₁₆
hypercenter	#366	D₇₁
hypocenter	C₇₁	#1424
LCS	G ▷ C₁₆×C₇₁ ▷ C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #366

Complements

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

N	H ≅ G/N	type
5. C₇₁⋊C₃₂	C₄	semidirect
27. C₇₁	#1424	semidirect