Subgroups — #22586546

Order 9088.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17985829	C₂	1	1	yes	maximal, characteristic
2	#17985827	C₂	1	1	yes	maximal, characteristic
3	M₆₄×C₇₁	C₂	1	1	yes	maximal, characteristic
4	#14556064	—	2	1	no	—
5	#14556062	—	2	1	no	—
6	C₂×C₁₆×C₇₁	C₂²	1	1	yes	characteristic
7	C₃₂×C₇₁	C₄	1	2	yes	complemented
8	#11765849	—	4	1	no	—
9	C₄⋊Dic₇₁	—	4	1	no	—
10	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
11	C₁₆×C₇₁	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₇₁	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₇₁	D₈	1	1	yes	characteristic
14	C₂×Dic₇₁	—	8	1	no	—
15	C₈×C₇₁	C₄⋊C₄	1	1	yes	characteristic
16	C₈×C₇₁	Q₁₆	1	1	yes	characteristic
17	C₇₁⋊C₈	—	8	1	no	—
18	C₂²×C₇₁	SD₃₂	1	1	yes	characteristic
19	C₄×C₇₁	#107	1	1	yes	characteristic
20	C₄×C₇₁	SD₃₂	1	1	yes	characteristic
21	Dic₇₁	—	16	1	no	—
22	C₂×C₇₁	—	2	1	no	—
23	C₂×C₇₁	#367	1	1	yes	characteristic
24	#1426	—	71	1	no	maximal, Sylow
25	C₇₁	#1426	1	1	yes	characteristic, complemented, Sylow
26	M₆₄	D₇₁	1	1	yes	characteristic
27	#368	—	71	1	no	—
28	#367	—	71	1	no	—
29	C₂×C₁₆	C₂×D₇₁	1	1	yes	characteristic
30	#108	—	142	1	no	—
31	#107	—	142	1	no	—
32	C₃₂	Dic₇₁	1	2	yes	complemented
33	M₁₆	—	284	1	no	—
34	C₂×C₈	D₂₈₄	1	1	yes	characteristic
35	C₄⋊C₄	—	284	1	no	—
36	C₁₆	Dic₁₄₂	1	1	yes	characteristic
37	C₁₆	C₂×Dic₇₁	1	1	yes	characteristic
38	C₂×C₄	—	568	1	no	—
39	C₂×C₄	D₅₆₈	1	1	yes	characteristic
40	C₈	—	568	1	no	—
41	C₈	C₄⋊Dic₇₁	1	1	yes	characteristic
42	C₈	Dic₂₈₄	1	1	yes	characteristic
43	C₂²	#14556073	1	1	yes	characteristic
44	C₄	—	1136	1	no	—
45	C₄	#14556062	1	1	yes	characteristic
46	C₄	#14556073	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	#17985827	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#17985827
commutator	C₁₆×C₇₁	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₇₁
Fitting	M₆₄×C₇₁	C₂
socle	C₂×C₇₁	#367
hypercenter	M₆₄	D₇₁
hypocenter	C₇₁	#1426
LCS	G ▷ C₁₆×C₇₁ ▷ C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
7. C₃₂×C₇₁	C₄	semidirect
25. C₇₁	#1426	semidirect
32. C₃₂	Dic₇₁	semidirect