Subgroups — #21443892

Order 7808.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#11758185	C₂	1	1	yes	maximal, characteristic
2	#16839515	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#335	C₂	1	1	yes	maximal, characteristic
4	C₂×#11758185	C₄	1	1	yes	characteristic
5	C₂×#11758185	C₄	1	1	yes	characteristic
6	C₄⋊#92418	—	2	1	no	—
7	C₄⋊C₈×C₆₁	—	2	1	no	—
8	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₆₁	—	4	1	no	—
10	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
11	C₂×C₈×C₆₁	Q₈	1	1	yes	characteristic
12	C₄²×C₆₁	D₄	1	1	yes	characteristic
13	C₂×#92418	—	4	1	no	—
14	#11758185	—	2	1	no	—
15	#11758185	C₈	1	2	yes	complemented
16	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
17	C₂×C₄×C₆₁	D₈	1	1	yes	characteristic
18	C₂×C₄×C₆₁	Q₁₆	1	1	yes	characteristic
19	C₈×C₆₁	—	2	1	no	—
20	C₈×C₆₁	—	8	1	no	—
21	C₈×C₆₁	C₂×C₈	1	1	yes	characteristic
22	C₈×C₆₁	M₁₆	1	1	yes	characteristic
23	#92418	—	8	1	no	—
24	C₂²×C₆₁	#107	1	1	yes	characteristic
25	C₄×C₆₁	—	2	1	no	—
26	C₄×C₆₁	C₄⋊C₈	1	1	yes	characteristic
27	C₄×C₆₁	#108	1	1	yes	characteristic
28	C₄×C₆₁	SD₃₂	1	1	yes	characteristic
29	C₄×C₆₁	SD₃₂	1	1	yes	characteristic
30	#1372	—	61	1	no	maximal, Sylow
31	C₂×C₆₁	#335	1	1	yes	characteristic
32	C₂×C₆₁	#367	1	1	yes	characteristic
33	C₂×C₆₁	#368	1	1	yes	characteristic
34	C₄×C₁₆	—	61	1	no	—
35	#335	—	61	1	no	—
36	#335	D₆₁	1	1	yes	characteristic
37	C₆₁	#1372	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₁₆	—	61	1	no	—
39	C₂×C₁₆	—	61	1	no	—
40	C₄⋊C₈	—	2	1	no	—
41	C₄⋊C₈	—	122	1	no	—
42	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
43	C₂×C₈	—	4	1	no	—
44	C₂×C₈	—	244	1	no	—
45	C₂×C₈	Dic₁₂₂	1	1	yes	characteristic
46	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
47	C₄²	C₂²⋊D₆₁	1	1	yes	characteristic
48	C₁₆	—	61	2	no	—
49	C₁₆	—	122	1	no	—
50	C₂×C₄	#11758196	1	1	yes	characteristic
51	C₂×C₄	#11758199	1	1	yes	characteristic
52	C₂×C₄	#11758202	1	1	yes	characteristic
53	C₈	—	2	1	no	—
54	C₈	—	8	1	no	—
55	C₈	—	488	1	no	—
56	C₈	C₈×D₆₁	1	1	yes	characteristic
57	C₈	#11758189	1	1	yes	characteristic
58	C₂²	#14519710	1	1	yes	characteristic
59	C₄	—	2	1	no	—
60	C₄	#14519706	1	1	yes	characteristic
61	C₄	#14519712	1	1	yes	characteristic
62	C₄	#14519720	1	1	yes	characteristic
63	C₄	#14519721	1	1	yes	characteristic
64	C₂	#16839514	1	1	yes	characteristic
65	C₂	#16839589	1	1	yes	characteristic
66	C₂	#16839591	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#11758199
commutator	C₈×C₆₁	C₂×C₈
Frattini	C₄×C₈	C₂×D₆₁
Fitting	C₆₁×#335	C₂
socle	C₂²×C₆₁	#107
hypercenter	#335	D₆₁
hypocenter	C₆₁	#1372
LCS	G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ #335

Complements

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

N	H ≅ G/N	type
15. #11758185	C₈	semidirect
37. C₆₁	#1372	semidirect