Subgroups — #21460950

Order 7808.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840667	C₂	1	2	yes	maximal, complemented
2	#16840138	C₂	1	1	yes	maximal, characteristic
3	#14519836	—	2	2	no	—
4	C₂×#11758199	—	2	2	no	—
5	#14519774	C₂²	1	1	yes	characteristic
6	C₄×#92418	C₄	1	1	yes	characteristic, complemented
7	#127×C₆₁	C₄	1	1	yes	characteristic, complemented
8	C₂×D₄×C₆₁	—	2	1	no	—
9	C₂×D₄×C₆₁	—	4	1	no	—
10	C₂×D₂₄₄	—	4	1	no	—
11	C₂×D₂₄₄	D₄	1	2	yes	—
12	C₂²⋊#6923	—	4	2	no	—
13	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
14	#11758199	—	4	4	no	—
15	C₂×#92418	—	2	1	no	—
16	C₂³×C₆₁	—	4	1	no	—
17	C₂²×D₆₁	—	2	2	no	—
18	C₂×#6923	—	8	2	no	—
19	D₄×C₆₁	—	4	2	no	—
20	D₄×C₆₁	—	8	2	no	—
21	C₂×C₄×C₆₁	—	2	1	no	—
22	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
23	D₂₄₄	—	4	2	no	—
24	D₂₄₄	—	8	2	no	—
25	#92418	—	2	2	no	—
26	C₂²×C₆₁	—	8	2	no	—
27	C₂²×C₆₁	—	8	1	no	—
28	C₂²×C₆₁	#99	1	1	yes	characteristic
29	C₂×D₆₁	—	4	2	no	—
30	C₂×D₆₁	—	8	2	no	—
31	#6923	—	16	2	no	—
32	C₄×C₆₁	—	2	2	no	—
33	C₄×C₆₁	—	2	1	no	—
34	#1408	—	61	1	no	maximal, Sylow
35	C₂×C₆₁	—	2	1	no	—
36	C₂×C₆₁	—	16	1	no	—
37	C₂×C₆₁	#353	1	1	yes	characteristic
38	D₆₁	—	8	2	no	—
39	#493	—	61	1	no	—
40	#353	—	61	2	no	—
41	C₆₁	#1408	1	1	yes	characteristic, complemented, Sylow
42	C₂×D₈	—	122	2	no	—
43	#127	—	61	1	no	—
44	#127	#6923	1	1	yes	characteristic, complemented
45	#99	—	122	2	no	—
46	C₄×C₈	—	61	1	no	—
47	C₂×D₄	—	2	1	no	—
48	C₂×D₄	—	4	1	no	—
49	C₂×D₄	—	61	2	no	—
50	C₂×D₄	—	244	1	no	—
51	D₈	—	244	4	no	—
52	C₂×C₈	—	122	1	no	—
53	C₂²⋊C₄	—	244	2	no	—
54	C₄²	C₂×#6923	1	1	yes	characteristic
55	C₂³	—	4	1	no	—
56	C₂³	—	122	2	no	—
57	D₄	—	4	2	no	—
58	D₄	—	8	2	no	—
59	D₄	—	488	2	no	—
60	D₄	—	244	2	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	488	2	no	—
63	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
64	C₈	—	122	2	no	—
65	C₂²	—	8	2	no	—
66	C₂²	—	8	1	no	—
67	C₂²	—	488	2	no	—
68	C₂²	—	244	2	no	—
69	C₂²	#14519835	1	1	yes	characteristic
70	C₄	—	2	2	no	—
71	C₄	—	2	1	no	—
72	C₄	—	976	2	no	—
73	C₂	—	2	1	no	—
74	C₂	—	16	1	no	—
75	C₂	—	488	2	no	—
76	C₂	#16840666	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16840666
commutator	C₄²×C₆₁	C₂×C₄
Frattini	C₄²	C₂×#6923
Fitting	#127×C₆₁	C₄
socle	C₂×C₆₁	#353
hypercenter	#127	#6923
hypocenter	C₆₁	#1408
LCS	G ▷ C₄²×C₆₁ ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #127

Complements

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

N	H ≅ G/N	type
1. #16840667	C₂	semidirect
6. C₄×#92418	C₄	semidirect
7. #127×C₆₁	C₄	semidirect
41. C₆₁	#1408	semidirect
44. #127	#6923	semidirect