Subgroups — #21460839

Order 7808.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840685	C₂	1	1	yes	maximal, characteristic
2	#16840685	C₂	1	1	yes	maximal, characteristic
3	#16840161	C₂	1	1	yes	maximal, characteristic
4	#14519851	—	2	1	no	—
5	#14519851	—	2	1	no	—
6	#14519769	C₄	1	1	yes	characteristic
7	#14519710	—	2	1	no	—
8	#14519708	—	2	1	no	—
9	C₄×#92418	C₂²	1	1	yes	characteristic
10	#125×C₆₁	C₄	1	1	yes	characteristic
11	C₄⋊C₄×C₆₁	—	2	1	no	—
12	C₄⋊C₄×C₆₁	—	4	1	no	—
13	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
14	C₄⋊Dic₆₁	—	2	1	no	—
15	#11758196	—	4	1	no	—
16	C₂×#92418	D₄	1	1	yes	characteristic
17	C₂×#92418	D₄	1	1	yes	characteristic
18	#11758187	—	4	1	no	—
19	#11758187	—	4	1	no	—
20	C₂×C₄×C₆₁	—	2	1	no	—
21	C₂×C₄×C₆₁	—	4	1	no	—
22	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×Dic₆₁	—	4	1	no	—
24	#92418	SD₁₆	1	1	yes	characteristic
25	#92418	SD₁₆	1	1	yes	characteristic
26	#92418	Q₁₆	1	1	yes	characteristic
27	#92418	Q₁₆	1	1	yes	characteristic
28	C₂²×C₆₁	#100	1	1	yes	characteristic
29	C₄×C₆₁	—	4	1	no	—
30	C₄×C₆₁	—	8	1	no	—
31	C₄×C₆₁	#103	1	1	yes	characteristic
32	C₄×C₆₁	#103	1	1	yes	characteristic
33	Dic₆₁	—	8	1	no	—
34	#1366	—	61	1	no	maximal, Sylow
35	C₂×C₆₁	—	2	1	no	—
36	C₂×C₆₁	#333	1	1	yes	characteristic
37	#499	—	61	1	no	—
38	#364	—	61	1	no	—
39	#364	—	61	1	no	—
40	C₆₁	#1366	1	1	yes	characteristic, complemented, Sylow
41	#125	—	61	1	no	—
42	#125	#6923	1	1	yes	characteristic
43	M₃₂	—	122	1	no	—
44	M₃₂	—	122	1	no	—
45	#107	—	122	1	no	—
46	#106	—	122	1	no	—
47	C₄×C₈	—	61	1	no	—
48	C₂×C₈	—	61	1	no	—
49	C₂×C₈	—	61	1	no	—
50	C₄⋊C₄	—	2	1	no	—
51	C₄⋊C₄	—	4	1	no	—
52	C₄⋊C₄	—	122	1	no	—
53	C₄⋊C₄	—	244	1	no	—
54	C₄²	C₂×#6923	1	1	yes	characteristic
55	C₁₆	—	244	1	no	—
56	C₁₆	—	244	1	no	—
57	C₂×C₄	—	2	1	no	—
58	C₂×C₄	—	4	1	no	—
59	C₂×C₄	—	244	1	no	—
60	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
61	C₈	—	61	1	no	—
62	C₈	—	61	1	no	—
63	C₈	—	61	1	no	—
64	C₈	—	61	1	no	—
65	C₂²	#14519837	1	1	yes	characteristic
66	C₄	—	4	1	no	—
67	C₄	—	8	1	no	—
68	C₄	—	488	1	no	—
69	C₄	#14519840	1	1	yes	characteristic
70	C₄	#14519840	1	1	yes	characteristic
71	C₂	—	2	1	no	—
72	C₂	#16840622	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16840622
commutator	C₄²×C₆₁	C₂×C₄
Frattini	C₄²	C₂×#6923
Fitting	#125×C₆₁	C₄
socle	C₂×C₆₁	#333
hypercenter	#125	#6923
hypocenter	C₆₁	#1366
LCS	G ▷ C₄²×C₆₁ ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄² ◁ #125

Complements

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

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