Subgroups — #21460973

Order 7808.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840695	C₂	1	1	yes	maximal, characteristic, complemented
2	#16840689	C₂	1	1	yes	maximal, characteristic, complemented
3	#16840195	C₂	1	1	yes	maximal, characteristic
4	#14519846	—	2	1	no	—
5	#14519827	—	2	1	no	—
6	#14519800	—	2	1	no	—
7	#14519720	—	2	1	no	—
8	D₉₇₆	C₄	1	1	yes	characteristic, complemented
9	C₁₆×D₆₁	C₂²	1	1	yes	characteristic
10	Q₃₂×C₆₁	C₄	1	1	yes	characteristic, complemented
11	#11758226	—	4	1	no	—
12	C₄⋊#6923	—	4	1	no	—
13	Q₁₆×C₆₁	—	2	1	no	—
14	#11758201	—	4	1	no	—
15	D₄₈₈	—	2	1	no	—
16	C₈×D₆₁	D₄	1	1	yes	characteristic
17	C₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
18	#11758185	D₄	1	1	yes	characteristic
19	C₂×#6923	—	8	1	no	—
20	Q₈×C₆₁	—	4	1	no	—
21	D₂₄₄	—	4	1	no	—
22	D₂₄₄	—	8	1	no	—
23	C₄×D₆₁	—	8	1	no	—
24	C₄×D₆₁	D₈	1	1	yes	characteristic
25	C₈×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
26	#92418	SD₁₆	1	1	yes	characteristic
27	C₂×D₆₁	—	8	1	no	—
28	C₂×D₆₁	D₁₆	1	1	yes	characteristic
29	#6923	—	16	1	no	—
30	C₄×C₆₁	—	8	1	no	—
31	C₄×C₆₁	#102	1	1	yes	characteristic
32	Dic₆₁	SD₃₂	1	1	yes	characteristic
33	#1418	—	61	1	no	maximal, Sylow
34	C₂×C₆₁	#357	1	1	yes	characteristic
35	D₆₁	—	2	1	no	—
36	D₆₁	—	16	1	no	—
37	#508	—	61	1	no	—
38	M₆₄	—	61	1	no	—
39	#367	—	61	1	no	—
40	C₆₁	#1418	1	1	yes	characteristic, complemented, Sylow
41	#135	—	122	1	no	—
42	Q₃₂	#6923	1	1	yes	characteristic, complemented
43	SD₃₂	—	122	1	no	—
44	D₁₆	—	61	1	no	—
45	C₂×C₁₆	—	61	1	no	—
46	#107	—	122	1	no	—
47	C₃₂	—	122	1	no	—
48	#41	—	244	1	no	—
49	Q₁₆	—	2	1	no	—
50	SD₁₆	—	244	1	no	—
51	D₈	—	122	1	no	—
52	C₂×C₈	—	61	1	no	—
53	C₄⋊C₄	—	244	1	no	—
54	C₁₆	—	61	1	no	—
55	C₁₆	C₂×#6923	1	1	yes	characteristic
56	Q₈	—	4	1	no	—
57	D₄	—	488	1	no	—
58	D₄	—	244	1	no	—
59	C₂×C₄	—	61	1	no	—
60	C₂×C₄	—	488	1	no	—
61	C₂×C₄	—	488	1	no	—
62	C₈	—	61	1	no	—
63	C₈	C₂²⋊#6923	1	1	yes	characteristic
64	C₂²	—	61	1	no	—
65	C₂²	—	488	1	no	—
66	C₄	—	8	1	no	—
67	C₄	—	61	1	no	—
68	C₄	—	976	1	no	—
69	C₄	#14519839	1	1	yes	characteristic
70	C₂	—	122	1	no	—
71	C₂	—	976	1	no	—
72	C₂	#16840674	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16840674
commutator	C₁₆×C₆₁	C₂×C₄
Frattini	C₁₆	C₂×#6923
Fitting	Q₃₂×C₆₁	C₄
socle	C₂×C₆₁	#357
hypercenter	Q₃₂	#6923
hypocenter	C₆₁	#1418
LCS	G ▷ C₁₆×C₆₁ ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
1. #16840695	C₂	semidirect
2. #16840689	C₂	semidirect
8. D₉₇₆	C₄	semidirect
10. Q₃₂×C₆₁	C₄	semidirect
40. C₆₁	#1418	semidirect
42. Q₃₂	#6923	semidirect