Subgroups — #21443882

Order 7808.

76 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	C₈×#92418	C₂	1	1	yes	maximal, characteristic
3	C₆₁×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂×#11758185	—	2	1	no	—
5	C₄×#92418	C₄	1	1	yes	characteristic
6	C₄×#92418	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₆₁	—	2	1	no	—
8	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
10	C₂×C₈×C₆₁	Q₈	1	1	yes	characteristic
11	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
12	C₂×#92418	—	2	1	no	—
13	C₂×#92418	C₈	1	1	yes	characteristic
14	C₂×#92418	C₈	1	1	yes	characteristic
15	C₁₆×C₆₁	—	4	1	no	—
16	#11758185	—	4	1	no	—
17	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
19	C₂×C₄×C₆₁	M₁₆	1	1	yes	characteristic
20	C₈×C₆₁	—	2	1	no	—
21	C₈×C₆₁	SD₁₆	1	1	yes	characteristic
22	C₈×C₆₁	SD₁₆	1	1	yes	characteristic
23	#92418	—	2	2	no	—
24	#92418	—	2	1	no	—
25	#92418	C₁₆	1	2	yes	complemented
26	C₂²×C₆₁	C₄⋊C₈	1	1	yes	characteristic
27	C₄×C₆₁	—	2	1	no	—
28	C₄×C₆₁	#106	1	1	yes	characteristic
29	C₄×C₆₁	#108	1	1	yes	characteristic
30	C₄×C₆₁	C₂×C₁₆	1	1	yes	characteristic
31	C₄×C₆₁	M₃₂	1	1	yes	characteristic
32	#1367	—	61	1	no	maximal, Sylow
33	C₂×C₆₁	#334	1	1	yes	characteristic
34	C₂×C₆₁	C₄⋊C₁₆	1	1	yes	characteristic
35	C₂×C₆₁	#364	1	1	yes	characteristic
36	C₄⋊C₁₆	—	61	1	no	—
37	C₄⋊C₁₆	D₆₁	1	1	yes	characteristic
38	C₈²	—	61	1	no	—
39	C₆₁	#1367	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₁₆	—	2	1	no	—
41	C₂×C₁₆	—	122	1	no	—
42	C₄×C₈	—	61	1	no	—
43	C₄×C₈	—	61	1	no	—
44	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
45	C₂×C₈	—	61	1	no	—
46	C₂×C₈	—	61	1	no	—
47	C₂×C₈	—	122	1	no	—
48	C₂×C₈	Dic₁₂₂	1	1	yes	characteristic
49	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
50	C₄²	C₄×D₆₁	1	1	yes	characteristic
51	C₁₆	—	4	1	no	—
52	C₁₆	—	244	1	no	—
53	C₂×C₄	C₈×D₆₁	1	1	yes	characteristic
54	C₂×C₄	#11758189	1	1	yes	characteristic
55	C₂×C₄	#11758196	1	1	yes	characteristic
56	C₈	—	2	1	no	—
57	C₈	—	61	2	no	—
58	C₈	—	122	2	no	—
59	C₈	—	122	1	no	—
60	C₈	#11758200	1	1	yes	characteristic
61	C₈	#11758201	1	1	yes	characteristic
62	C₂²	#14519706	1	1	yes	characteristic
63	C₄	—	2	1	no	—
64	C₄	#14519708	1	1	yes	characteristic
65	C₄	#14519712	1	1	yes	characteristic
66	C₄	C₁₆×D₆₁	1	1	yes	characteristic
67	C₄	#14519716	1	1	yes	characteristic
68	C₂	#16839512	1	1	yes	characteristic
69	C₂	#16839580	1	1	yes	characteristic
70	C₂	#16839582	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²⋊D₆₁
commutator	C₄×C₆₁	C₂×C₁₆
Frattini	C₄×C₈	C₂×D₆₁
Fitting	C₆₁×C₄⋊C₁₆	C₂
socle	C₂²×C₆₁	C₄⋊C₈
hypercenter	C₄⋊C₁₆	D₆₁
hypocenter	C₆₁	#1367
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
25. #92418	C₁₆	semidirect
39. C₆₁	#1367	semidirect