Subgroups — #22586416

Order 9088.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17985820	C₂	1	2	yes	maximal
2	C₄×C₁₆×C₇₁	C₂	1	1	yes	maximal, characteristic
3	#14556068	—	2	2	no	—
4	C₂×C₁₆×C₇₁	C₄	1	1	yes	characteristic
5	C₂×C₁₆×C₇₁	C₄	1	1	yes	characteristic
6	C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
7	C₇₁⋊C₁₆	—	4	2	no	—
8	C₂×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
9	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
10	C₄²×C₇₁	Q₈	1	1	yes	characteristic
11	C₁₆×C₇₁	—	2	1	no	—
12	C₁₆×C₇₁	C₈	1	2	yes	—
13	C₂×C₄×C₇₁	—	2	1	no	—
14	C₂×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
15	C₈×C₇₁	C₂×C₈	1	1	yes	characteristic
16	C₈×C₇₁	M₁₆	1	1	yes	characteristic
17	C₈×C₇₁	D₈	1	1	yes	characteristic
18	C₈×C₇₁	Q₁₆	1	1	yes	characteristic
19	C₂²×C₇₁	#108	1	1	yes	characteristic
20	C₄×C₇₁	—	2	2	no	—
21	C₄×C₇₁	C₄⋊C₈	1	1	yes	characteristic
22	C₄×C₇₁	#107	1	1	yes	characteristic
23	C₂×C₇₁	—	2	1	no	—
24	C₂×C₇₁	#335	1	1	yes	characteristic
25	#1373	—	71	1	no	maximal, Sylow
26	C₇₁	#1373	1	1	yes	characteristic, complemented, Sylow
27	#364	—	71	2	no	—
28	C₄×C₁₆	D₇₁	1	1	yes	characteristic
29	M₃₂	—	142	2	no	—
30	C₂×C₁₆	Dic₇₁	1	1	yes	characteristic
31	C₂×C₁₆	Dic₇₁	1	1	yes	characteristic
32	C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
33	C₂×C₈	D₂₈₄	1	1	yes	characteristic
34	C₂×C₈	C₂×Dic₇₁	1	1	yes	characteristic
35	C₄²	Dic₁₄₂	1	1	yes	characteristic
36	C₁₆	—	2	1	no	—
37	C₁₆	—	284	2	no	—
38	C₁₆	C₇₁⋊C₈	1	2	yes	—
39	C₂×C₄	—	2	1	no	—
40	C₂×C₄	C₄⋊Dic₇₁	1	1	yes	characteristic
41	C₈	C₂×C₇₁⋊C₈	1	1	yes	characteristic
42	C₈	#11765849	1	1	yes	characteristic
43	C₈	D₅₆₈	1	1	yes	characteristic
44	C₈	Dic₂₈₄	1	1	yes	characteristic
45	C₂²	#14556064	1	1	yes	characteristic
46	C₄	—	2	2	no	—
47	C₄	C₄⋊(C₇₁⋊C₈)	1	1	yes	characteristic
48	C₄	#14556062	1	1	yes	characteristic
49	C₂	—	2	1	no	—
50	C₂	#17985752	1	1	yes	characteristic

	subgroup	G/H
center	C₈	D₅₆₈
commutator	C₈×C₇₁	C₂×C₈
Frattini	C₄×C₈	C₂×D₇₁
Fitting	C₄×C₁₆×C₇₁	C₂
socle	C₂×C₇₁	#335
hypercenter	C₄×C₁₆	D₇₁
hypocenter	C₇₁	#1373
LCS	G ▷ C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
26. C₇₁	#1373	semidirect