Subgroups — #21443879

Order 7808.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840164	C₂	1	1	yes	maximal, characteristic
2	#16839583	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#364	C₂	1	1	yes	maximal, characteristic
4	#14519769	C₄	1	2	yes	—
5	#14519717	—	2	1	no	—
6	#14519711	—	2	1	no	—
7	#14519709	—	2	1	no	—
8	M₃₂×C₆₁	—	2	1	no	—
9	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
11	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
12	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
13	C₄⋊Dic₆₁	—	2	2	no	—
14	#11758196	—	4	2	no	—
15	C₁₆×C₆₁	—	4	1	no	—
16	#11758185	—	4	1	no	—
17	C₂×C₄×C₆₁	—	2	1	no	—
18	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×Dic₆₁	—	4	2	no	—
20	C₈×C₆₁	SD₁₆	1	1	yes	characteristic
21	C₈×C₆₁	SD₁₆	1	1	yes	characteristic
22	C₈×C₆₁	Q₁₆	1	1	yes	characteristic
23	C₈×C₆₁	Q₁₆	1	1	yes	characteristic
24	C₂²×C₆₁	#100	1	1	yes	characteristic
25	C₄×C₆₁	—	4	1	no	—
26	C₄×C₆₁	#103	1	1	yes	characteristic
27	C₄×C₆₁	#103	1	1	yes	characteristic
28	Dic₆₁	—	8	2	no	—
29	#1366	—	61	1	no	maximal, Sylow
30	C₂×C₆₁	—	2	1	no	—
31	C₂×C₆₁	#333	1	1	yes	characteristic
32	#499	—	61	1	no	—
33	#364	—	61	1	no	—
34	#364	D₆₁	1	1	yes	characteristic
35	C₆₁	#1366	1	1	yes	characteristic, complemented, Sylow
36	#125	—	61	2	no	—
37	M₃₂	—	2	1	no	—
38	M₃₂	—	122	1	no	—
39	#107	—	122	1	no	—
40	#106	—	122	1	no	—
41	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
42	C₂×C₈	D₂₄₄	1	1	yes	characteristic
43	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
44	C₄⋊C₄	—	122	2	no	—
45	C₄⋊C₄	—	244	2	no	—
46	C₄²	C₄×D₆₁	1	1	yes	characteristic
47	C₁₆	—	4	1	no	—
48	C₁₆	—	244	1	no	—
49	C₂×C₄	—	2	1	no	—
50	C₂×C₄	—	244	2	no	—
51	C₂×C₄	#11758198	1	1	yes	characteristic
52	C₈	#11758190	1	1	yes	characteristic
53	C₈	Dic₂₄₄	1	1	yes	characteristic
54	C₈	#11758200	1	1	yes	characteristic
55	C₈	#11758202	1	1	yes	characteristic
56	C₂²	#14519693	1	1	yes	characteristic
57	C₄	—	4	1	no	—
58	C₄	—	488	2	no	—
59	C₄	#14519700	1	1	yes	characteristic
60	C₄	#14519702	1	1	yes	characteristic
61	C₂	—	2	1	no	—
62	C₂	#16839510	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16839510
commutator	C₄²×C₆₁	C₂×C₄
Frattini	C₄×C₈	C₂×D₆₁
Fitting	C₆₁×#364	C₂
socle	C₂×C₆₁	#333
hypercenter	#364	D₆₁
hypocenter	C₆₁	#1366
LCS	G ▷ C₄²×C₆₁ ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
35. C₆₁	#1366	semidirect