Subgroups — #21460954

Order 7808.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840673	C₂	1	2	yes	maximal, complemented
2	#16840134	C₂	1	1	yes	maximal, characteristic
3	#14519838	—	2	2	no	—
4	C₂×#11758200	—	2	2	no	—
5	#14519777	C₂²	1	1	yes	characteristic
6	C₄×#92418	C₄	1	1	yes	characteristic
7	#127×C₆₁	C₄	1	1	yes	characteristic
8	C₂×D₄×C₆₁	—	2	1	no	—
9	C₂×D₄×C₆₁	—	4	1	no	—
10	C₂×Dic₁₂₂	D₄	1	2	yes	—
11	#11758217	—	4	2	no	—
12	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
13	#11758200	—	4	4	no	—
14	C₄⋊Dic₆₁	—	4	1	no	—
15	C₂×#92418	—	2	1	no	—
16	C₂³×C₆₁	—	4	1	no	—
17	D₄×C₆₁	—	4	2	no	—
18	D₄×C₆₁	—	8	2	no	—
19	C₂×C₄×C₆₁	—	2	1	no	—
20	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×Dic₆₁	—	2	2	no	—
22	Dic₁₂₂	—	4	2	no	—
23	#92420	—	8	2	no	—
24	#92418	—	2	2	no	—
25	C₂²×C₆₁	—	8	2	no	—
26	C₂²×C₆₁	—	8	1	no	—
27	C₂²×C₆₁	#99	1	1	yes	characteristic
28	C₄×C₆₁	—	2	2	no	—
29	C₄×C₆₁	—	2	1	no	—
30	Dic₆₁	—	4	2	no	—
31	#1410	—	61	1	no	maximal, Sylow
32	C₂×C₆₁	—	2	1	no	—
33	C₂×C₆₁	—	16	1	no	—
34	C₂×C₆₁	#353	1	1	yes	characteristic
35	#492	—	61	1	no	—
36	#356	—	61	2	no	—
37	C₆₁	#1410	1	1	yes	characteristic, complemented, Sylow
38	C₂×SD₁₆	—	122	2	no	—
39	C₄⋊Q₈	—	61	1	no	—
40	#127	#6923	1	1	yes	characteristic
41	#101	—	122	2	no	—
42	C₄×C₈	—	61	1	no	—
43	C₂×Q₈	—	61	2	no	—
44	C₂×D₄	—	2	1	no	—
45	C₂×D₄	—	4	1	no	—
46	SD₁₆	—	244	4	no	—
47	M₁₆	—	244	2	no	—
48	C₂×C₈	—	122	1	no	—
49	C₄⋊C₄	—	244	1	no	—
50	C₄²	C₂×#6923	1	1	yes	characteristic
51	C₂³	—	4	1	no	—
52	Q₈	—	244	2	no	—
53	D₄	—	4	2	no	—
54	D₄	—	8	2	no	—
55	C₂×C₄	—	2	1	no	—
56	C₂×C₄	—	122	2	no	—
57	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
58	C₈	—	122	2	no	—
59	C₈	—	488	2	no	—
60	C₂²	—	8	2	no	—
61	C₂²	—	8	1	no	—
62	C₂²	#14519835	1	1	yes	characteristic
63	C₄	—	2	2	no	—
64	C₄	—	2	1	no	—
65	C₄	—	244	2	no	—
66	C₂	—	2	1	no	—
67	C₂	—	16	1	no	—
68	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	#1410
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. #16840673	C₂	semidirect
37. C₆₁	#1410	semidirect