Subgroups — #21460852

Order 7808.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840625	C₂	1	2	yes	maximal
2	C₁₆×Dic₆₁	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#92420	—	2	2	no	—
4	C₂×#11758185	C₄	1	1	yes	characteristic
5	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
6	C₂×C₁₆×C₆₁	C₄	1	1	yes	characteristic
7	C₂×#92420	—	4	2	no	—
8	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
9	C₄×Dic₆₁	D₄	1	1	yes	characteristic
10	C₂×#92418	Q₈	1	1	yes	characteristic
11	C₁₆×C₆₁	C₈	1	2	yes	complemented
12	#11758185	—	2	1	no	—
13	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
14	C₂×Dic₆₁	D₈	1	1	yes	characteristic
15	C₂×Dic₆₁	Q₁₆	1	1	yes	characteristic
16	#92420	—	8	2	no	—
17	C₈×C₆₁	C₂×C₈	1	1	yes	characteristic
18	C₈×C₆₁	M₁₆	1	1	yes	characteristic
19	#92418	—	2	1	no	—
20	C₂²×C₆₁	#107	1	1	yes	characteristic
21	C₄×C₆₁	C₄⋊C₈	1	1	yes	characteristic
22	C₄×C₆₁	#108	1	1	yes	characteristic
23	Dic₆₁	—	2	1	no	—
24	Dic₆₁	SD₃₂	1	2	yes	—
25	#1372	—	61	1	no	maximal, Sylow
26	C₂×C₆₁	#335	1	1	yes	characteristic
27	C₂×C₆₁	#367	1	1	yes	characteristic
28	C₂×C₆₁	#368	1	1	yes	characteristic
29	C₄×C₁₆	—	61	1	no	—
30	#335	—	61	2	no	—
31	C₆₁	#1372	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₁₆	—	61	1	no	—
33	C₂×C₁₆	#6923	1	1	yes	characteristic
34	C₄⋊C₈	—	122	2	no	—
35	C₄×C₈	—	61	1	no	—
36	C₂×C₈	—	61	1	no	—
37	C₂×C₈	—	244	2	no	—
38	C₂×C₈	C₂×#6923	1	1	yes	characteristic
39	C₄²	—	61	1	no	—
40	C₁₆	—	122	1	no	—
41	C₁₆	#92420	1	2	yes	complemented
42	C₂×C₄	—	61	1	no	—
43	C₂×C₄	—	61	1	no	—
44	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
45	C₈	—	122	1	no	—
46	C₈	—	488	2	no	—
47	C₈	#11758213	1	1	yes	characteristic
48	C₈	C₂×#92420	1	1	yes	characteristic
49	C₂²	#14519846	1	1	yes	characteristic
50	C₄	—	61	2	no	—
51	C₄	—	122	1	no	—
52	C₄	C₄⋊#92420	1	1	yes	characteristic
53	C₄	#14519848	1	1	yes	characteristic
54	C₂	#16840625	1	1	yes	characteristic
55	C₂	#16840689	1	1	yes	characteristic
56	C₂	#16840691	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14519846
commutator	C₈×C₆₁	C₂×C₈
Frattini	C₂×C₈	C₂×#6923
Fitting	C₂×C₁₆×C₆₁	C₄
socle	C₂²×C₆₁	#107
hypercenter	C₂×C₁₆	#6923
hypocenter	C₆₁	#1372
LCS	G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
11. C₁₆×C₆₁	C₈	semidirect
31. C₆₁	#1372	semidirect
41. C₁₆	#92420	semidirect