Subgroups — #22586538

Order 9088.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17985833	C₂	1	2	yes	maximal
2	C₄×C₁₆×C₇₁	C₂	1	1	yes	maximal, characteristic
3	C₇₁⋊C₃₂	—	2	2	no	—
4	C₂×C₁₆×C₇₁	C₄	1	1	yes	characteristic
5	C₂×C₁₆×C₇₁	C₂²	1	1	yes	characteristic
6	C₄×C₈×C₇₁	C₄	1	1	yes	characteristic
7	C₂×C₈×C₇₁	C₈	1	1	yes	characteristic
8	C₂×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
9	C₄²×C₇₁	C₈	1	1	yes	characteristic
10	C₁₆×C₇₁	—	2	1	no	—
11	C₁₆×C₇₁	D₄	1	1	yes	characteristic
12	C₁₆×C₇₁	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₇₁	—	2	1	no	—
14	C₂×C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
15	C₈×C₇₁	C₁₆	1	2	yes	—
16	C₈×C₇₁	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₇₁	M₁₆	1	1	yes	characteristic
18	C₂²×C₇₁	M₃₂	1	1	yes	characteristic
19	C₄×C₇₁	—	2	2	no	—
20	C₄×C₇₁	C₄⋊C₈	1	1	yes	characteristic
21	C₄×C₇₁	C₂×C₁₆	1	1	yes	characteristic
22	C₂×C₇₁	—	2	1	no	—
23	C₂×C₇₁	C₄⋊C₁₆	1	1	yes	characteristic
24	#1422	—	71	1	no	maximal, Sylow
25	C₇₁	#1422	1	1	yes	characteristic, complemented, Sylow
26	M₆₄	—	71	2	no	—
27	C₄×C₁₆	D₇₁	1	1	yes	characteristic
28	C₂×C₁₆	Dic₇₁	1	1	yes	characteristic
29	C₂×C₁₆	C₂×D₇₁	1	1	yes	characteristic
30	C₄×C₈	Dic₇₁	1	1	yes	characteristic
31	C₃₂	—	142	2	no	—
32	C₂×C₈	C₇₁⋊C₈	1	1	yes	characteristic
33	C₂×C₈	C₂×Dic₇₁	1	1	yes	characteristic
34	C₄²	C₇₁⋊C₈	1	1	yes	characteristic
35	C₁₆	—	2	1	no	—
36	C₁₆	Dic₁₄₂	1	1	yes	characteristic
37	C₁₆	D₂₈₄	1	1	yes	characteristic
38	C₂×C₄	—	2	1	no	—
39	C₂×C₄	C₂×C₇₁⋊C₈	1	1	yes	characteristic
40	C₈	C₇₁⋊C₁₆	1	2	yes	—
41	C₈	C₄⋊Dic₇₁	1	1	yes	characteristic
42	C₈	#11765849	1	1	yes	characteristic
43	C₂²	#14556068	1	1	yes	characteristic
44	C₄	—	2	2	no	—
45	C₄	C₄⋊(C₇₁⋊C₈)	1	1	yes	characteristic
46	C₄	C₂×C₇₁⋊C₁₆	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	C₄⋊(C₇₁⋊C₁₆)	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	D₂₈₄
commutator	C₄×C₇₁	C₂×C₁₆
Frattini	C₂×C₁₆	C₂×D₇₁
Fitting	C₄×C₁₆×C₇₁	C₂
socle	C₂×C₇₁	C₄⋊C₁₆
hypercenter	C₄×C₁₆	D₇₁
hypocenter	C₇₁	#1422
LCS	G ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
25. C₇₁	#1422	semidirect