Subgroups — #21448095

Order 7808.

116 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	#16839589	C₂	1	2	yes	maximal
3	#16839587	C₂	1	2	yes	maximal
4	C₄×#11758185	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#499	C₂	1	1	yes	maximal, characteristic
6	#14519769	—	2	1	no	—
7	C₂×#11758185	C₂²	1	1	yes	characteristic
8	C₂×#11758185	C₂²	1	1	yes	characteristic
9	#14519711	C₂²	1	2	yes	—
10	#14519709	—	2	1	no	—
11	#125×C₆₁	—	2	1	no	—
12	#107×C₆₁	C₂²	1	2	yes	—
13	#106×C₆₁	—	2	1	no	—
14	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
16	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
17	C₄⋊C₄×C₆₁	—	2	2	no	—
18	C₄⋊C₄×C₆₁	—	4	2	no	—
19	C₄²×C₆₁	D₄	1	1	yes	characteristic
20	C₄⋊Dic₆₁	—	2	2	no	—
21	#11758196	—	4	2	no	—
22	#11758185	Q₈	1	2	yes	—
23	#11758185	Q₈	1	2	yes	—
24	C₂×C₄×C₆₁	—	4	2	no	—
25	C₂×C₄×C₆₁	D₈	1	2	yes	—
26	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
27	C₂×Dic₆₁	—	4	2	no	—
28	C₈×C₆₁	Q₁₆	1	2	yes	—
29	C₈×C₆₁	C₂×Q₈	1	1	yes	characteristic
30	C₈×C₆₁	C₂×Q₈	1	1	yes	characteristic
31	C₂²×C₆₁	C₂×D₈	1	1	yes	characteristic
32	C₄×C₆₁	—	2	2	no	—
33	C₄×C₆₁	—	8	2	no	—
34	C₄×C₆₁	C₄⋊Q₈	1	1	yes	characteristic
35	C₄×C₆₁	C₂×Q₁₆	1	1	yes	characteristic
36	Dic₆₁	—	8	2	no	—
37	#2253	—	61	1	no	maximal, Sylow
38	C₂×C₆₁	#500	1	1	yes	characteristic
39	C₂×C₆₁	#508	1	2	yes	—
40	#499	—	61	1	no	—
41	#499	D₆₁	1	1	yes	characteristic
42	#367	—	61	2	no	—
43	#366	—	61	2	no	—
44	C₄×C₁₆	—	61	1	no	—
45	C₆₁	#2253	1	1	yes	characteristic, complemented, Sylow
46	#125	—	2	1	no	—
47	#125	—	122	1	no	—
48	C₂×C₁₆	—	61	1	no	—
49	C₂×C₁₆	—	61	1	no	—
50	#107	—	61	2	no	—
51	#107	C₂×D₆₁	1	2	yes	—
52	#106	—	2	1	no	—
53	#106	—	122	1	no	—
54	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
55	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
56	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
57	C₄⋊C₄	—	2	2	no	—
58	C₄⋊C₄	—	4	2	no	—
59	C₄⋊C₄	—	122	2	no	—
60	C₄⋊C₄	—	244	2	no	—
61	C₄²	C₂²⋊D₆₁	1	1	yes	characteristic
62	C₁₆	—	61	2	no	—
63	C₁₆	—	61	2	no	—
64	C₂×C₄	—	4	2	no	—
65	C₂×C₄	—	244	2	no	—
66	C₂×C₄	#11758199	1	2	yes	—
67	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
68	C₈	#11758202	1	2	yes	—
69	C₈	Q₈×D₆₁	1	1	yes	characteristic
70	C₈	Q₈×D₆₁	1	1	yes	characteristic
71	C₂²	C₂×#11758199	1	1	yes	characteristic
72	C₄	—	2	2	no	—
73	C₄	—	8	2	no	—
74	C₄	—	488	2	no	—
75	C₄	#14519775	1	1	yes	characteristic
76	C₄	C₂×#11758202	1	1	yes	characteristic
77	C₂	#16840165	1	1	yes	characteristic
78	C₂	#16840192	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#11758199
commutator	C₂×C₈×C₆₁	C₂³
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₆₁×#499	C₂
socle	C₂²×C₆₁	C₂×D₈
hypercenter	#499	D₆₁
hypocenter	C₆₁	#2253
LCS	G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #499

Complements

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

N	H ≅ G/N	type
45. C₆₁	#2253	semidirect