Subgroups — #22586413

Order 9088.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₇₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	#17985752	C₂	1	1	yes	maximal, characteristic
3	#335×C₇₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₇₁⋊C₁₆	C₄	1	1	yes	characteristic
5	C₂×C₇₁⋊C₁₆	C₄	1	1	yes	characteristic
6	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
7	C₄⋊C₈×C₇₁	—	2	1	no	—
8	C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
9	C₂×C₇₁⋊C₈	—	4	1	no	—
10	C₇₁⋊C₁₆	—	2	1	no	—
11	C₇₁⋊C₁₆	C₈	1	2	yes	complemented
12	C₂×C₈×C₇₁	—	4	1	no	—
13	C₂×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₇₁	Q₈	1	1	yes	characteristic
15	C₄²×C₇₁	D₄	1	1	yes	characteristic
16	C₂×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
17	C₂×C₄×C₇₁	D₈	1	1	yes	characteristic
18	C₂×C₄×C₇₁	Q₁₆	1	1	yes	characteristic
19	C₈×C₇₁	—	2	1	no	—
20	C₈×C₇₁	—	8	1	no	—
21	C₈×C₇₁	C₂×C₈	1	1	yes	characteristic
22	C₈×C₇₁	M₁₆	1	1	yes	characteristic
23	C₇₁⋊C₈	—	8	1	no	—
24	C₂²×C₇₁	#107	1	1	yes	characteristic
25	C₄×C₇₁	—	2	1	no	—
26	C₄×C₇₁	C₄⋊C₈	1	1	yes	characteristic
27	C₄×C₇₁	#108	1	1	yes	characteristic
28	C₄×C₇₁	SD₃₂	1	1	yes	characteristic
29	C₄×C₇₁	SD₃₂	1	1	yes	characteristic
30	C₂×C₇₁	#335	1	1	yes	characteristic
31	C₂×C₇₁	#367	1	1	yes	characteristic
32	C₂×C₇₁	#368	1	1	yes	characteristic
33	#1372	—	71	1	no	maximal, Sylow
34	C₇₁	#1372	1	1	yes	characteristic, complemented, Sylow
35	C₄×C₁₆	—	71	1	no	—
36	#335	—	71	1	no	—
37	#335	D₇₁	1	1	yes	characteristic
38	C₂×C₁₆	—	71	1	no	—
39	C₂×C₁₆	—	71	1	no	—
40	C₄⋊C₈	—	2	1	no	—
41	C₄⋊C₈	—	142	1	no	—
42	C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
43	C₂×C₈	—	4	1	no	—
44	C₂×C₈	—	284	1	no	—
45	C₂×C₈	Dic₁₄₂	1	1	yes	characteristic
46	C₂×C₈	C₄×D₇₁	1	1	yes	characteristic
47	C₄²	C₂²⋊D₇₁	1	1	yes	characteristic
48	C₁₆	—	71	2	no	—
49	C₁₆	—	142	1	no	—
50	C₂×C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
51	C₂×C₄	#11765850	1	1	yes	characteristic
52	C₂×C₄	#11765855	1	1	yes	characteristic
53	C₈	—	2	1	no	—
54	C₈	—	8	1	no	—
55	C₈	—	568	1	no	—
56	C₈	C₈×D₇₁	1	1	yes	characteristic
57	C₈	#11765848	1	1	yes	characteristic
58	C₂²	#14556061	1	1	yes	characteristic
59	C₄	—	2	1	no	—
60	C₄	Dic₇₁⋊C₈	1	1	yes	characteristic
61	C₄	#14556063	1	1	yes	characteristic
62	C₄	#14556071	1	1	yes	characteristic
63	C₄	#14556072	1	1	yes	characteristic
64	C₂	#17985751	1	1	yes	characteristic
65	C₂	#17985826	1	1	yes	characteristic
66	C₂	#17985828	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#11765850
commutator	C₈×C₇₁	C₂×C₈
Frattini	C₄×C₈	C₂×D₇₁
Fitting	#335×C₇₁	C₂
socle	C₂²×C₇₁	#107
hypercenter	#335	D₇₁
hypocenter	C₇₁	#1372
LCS	G ▷ C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ #335

Complements

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

N	H ≅ G/N	type
11. C₇₁⋊C₁₆	C₈	semidirect
34. C₇₁	#1372	semidirect