Subgroups — #21448129

Order 7808.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840195	C₂	1	2	yes	maximal, complemented
2	#16839599	C₂	1	2	yes	maximal, complemented
3	D₁₉₅₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₂×D₆₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×Q₆₄	C₂	1	1	yes	maximal, characteristic, complemented
6	#14519800	—	2	2	no	—
7	#14519720	—	2	2	no	—
8	D₉₇₆	C₂²	1	2	yes	—
9	C₁₆×D₆₁	C₂²	1	1	yes	characteristic
10	#14519683	C₂²	1	1	yes	characteristic
11	Q₃₂×C₆₁	C₂²	1	2	yes	—
12	C₃₂×C₆₁	C₂²	1	1	yes	characteristic
13	#11758226	—	4	2	no	—
14	Q₁₆×C₆₁	—	2	2	no	—
15	#11758201	—	4	2	no	—
16	D₄₈₈	—	2	2	no	—
17	C₈×D₆₁	D₄	1	1	yes	characteristic
18	C₁₆×C₆₁	C₂³	1	1	yes	characteristic
19	#11758185	D₄	1	1	yes	characteristic
20	Q₈×C₆₁	—	4	2	no	—
21	D₂₄₄	—	4	2	no	—
22	D₂₄₄	—	8	2	no	—
23	C₄×D₆₁	—	8	2	no	—
24	C₄×D₆₁	D₈	1	1	yes	characteristic
25	C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
26	#92418	D₈	1	1	yes	characteristic
27	C₂×D₆₁	—	8	2	no	—
28	C₂×D₆₁	D₁₆	1	1	yes	characteristic
29	C₄×C₆₁	—	8	2	no	—
30	C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
31	Dic₆₁	D₁₆	1	1	yes	characteristic
32	#2262	—	61	1	no	maximal, Sylow
33	C₂×C₆₁	C₂×D₁₆	1	1	yes	characteristic
34	D₆₁	—	2	1	no	—
35	D₆₁	—	16	2	no	—
36	#508	—	61	2	no	—
37	Q₆₄	D₆₁	1	1	yes	characteristic, complemented
38	SD₆₄	—	61	2	no	—
39	D₃₂	—	61	1	no	—
40	C₂×C₃₂	—	61	1	no	—
41	C₆₁	#2262	1	1	yes	characteristic, complemented, Sylow
42	#135	—	122	2	no	—
43	Q₃₂	C₂×D₆₁	1	2	yes	—
44	SD₃₂	—	122	2	no	—
45	D₁₆	—	61	2	no	—
46	C₂×C₁₆	—	61	1	no	—
47	C₃₂	—	61	1	no	—
48	C₃₂	C₂×D₆₁	1	1	yes	characteristic
49	#41	—	244	2	no	—
50	Q₁₆	—	2	2	no	—
51	SD₁₆	—	244	2	no	—
52	D₈	—	122	2	no	—
53	C₂×C₈	—	61	1	no	—
54	C₁₆	—	61	1	no	—
55	C₁₆	C₂²×D₆₁	1	1	yes	characteristic
56	Q₈	—	4	2	no	—
57	D₄	—	488	2	no	—
58	D₄	—	244	2	no	—
59	C₂×C₄	—	61	1	no	—
60	C₂×C₄	—	488	2	no	—
61	C₈	—	61	1	no	—
62	C₈	D₄×D₆₁	1	1	yes	characteristic
63	C₂²	—	61	1	no	—
64	C₂²	—	488	2	no	—
65	C₄	—	8	2	no	—
66	C₄	—	61	1	no	—
67	C₄	D₈×D₆₁	1	1	yes	characteristic
68	C₂	—	122	1	no	—
69	C₂	—	976	2	no	—
70	C₂	D₁₆×D₆₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₆×D₆₁
commutator	C₁₆×C₆₁	C₂³
Frattini	C₁₆	C₂²×D₆₁
Fitting	C₆₁×Q₆₄	C₂
socle	C₂×C₆₁	C₂×D₁₆
hypercenter	Q₆₄	D₆₁
hypocenter	C₆₁	#2262
LCS	G ▷ C₁₆×C₆₁ ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ Q₆₄

Complements

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

N	H ≅ G/N	type
1. #16840195	C₂	semidirect
2. #16839599	C₂	semidirect
3. D₁₉₅₂	C₂	semidirect
4. C₃₂×D₆₁	C₂	semidirect
5. C₆₁×Q₆₄	C₂	semidirect
37. Q₆₄	D₆₁	semidirect
41. C₆₁	#2262	semidirect