Subgroups — #21460779

Order 7808.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840651	C₂	1	1	yes	maximal, characteristic
2	#16840623	C₂	1	1	yes	maximal, characteristic
3	Q₁₆×Dic₆₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#11758187	—	2	1	no	—
5	C₄⋊#92420	—	2	1	no	—
6	Q₈×Dic₆₁	—	2	1	no	—
7	#14519711	C₄	1	1	yes	characteristic
8	#14519701	—	2	1	no	—
9	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
10	C₂×Q₁₆×C₆₁	C₄	1	1	yes	characteristic
11	C₂×Q₈×C₆₁	—	2	1	no	—
12	C₂×#92420	—	4	1	no	—
13	Q₁₆×C₆₁	—	2	1	no	—
14	Q₁₆×C₆₁	C₈	1	2	yes	complemented
15	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
16	C₄⋊Dic₆₁	—	2	1	no	—
17	C₄⋊Dic₆₁	—	4	1	no	—
18	C₄×Dic₆₁	—	4	1	no	—
19	C₄×Dic₆₁	D₄	1	1	yes	characteristic
20	C₂×#92418	D₄	1	1	yes	characteristic
21	#11758187	—	2	2	no	—
22	Q₈×C₆₁	—	2	2	no	—
23	Q₈×C₆₁	—	4	1	no	—
24	C₂×C₄×C₆₁	—	4	1	no	—
25	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×Dic₆₁	—	4	1	no	—
27	C₂×Dic₆₁	D₈	1	1	yes	characteristic
28	C₂×Dic₆₁	SD₁₆	1	1	yes	characteristic
29	#92420	—	8	1	no	—
30	C₈×C₆₁	C₂×C₈	1	1	yes	characteristic
31	C₈×C₆₁	M₁₆	1	1	yes	characteristic
32	#92418	—	2	1	no	—
33	C₂²×C₆₁	#102	1	1	yes	characteristic
34	C₄×C₆₁	—	4	2	no	—
35	C₄×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
36	C₄×C₆₁	#104	1	1	yes	characteristic
37	Dic₆₁	—	2	1	no	—
38	Dic₆₁	—	2	1	no	—
39	Dic₆₁	—	8	1	no	—
40	#1334	—	61	1	no	maximal, Sylow
41	C₂×C₆₁	D₄⋊C₈	1	1	yes	characteristic
42	C₂×C₆₁	#360	1	1	yes	characteristic
43	C₂×C₆₁	#362	1	1	yes	characteristic
44	C₄×Q₁₆	—	61	1	no	—
45	#346	—	61	1	no	—
46	#334	—	61	1	no	—
47	C₆₁	#1334	1	1	yes	characteristic, complemented, Sylow
48	C₂×Q₁₆	#6923	1	1	yes	characteristic
49	C₄×Q₈	—	122	1	no	—
50	C₂×C₁₆	—	122	1	no	—
51	#107	—	61	1	no	—
52	C₄⋊C₈	—	122	1	no	—
53	#103	—	122	1	no	—
54	C₄×C₈	—	61	1	no	—
55	C₂×Q₈	—	2	1	no	—
56	Q₁₆	—	2	1	no	—
57	Q₁₆	#92420	1	2	yes	complemented
58	C₂×C₈	—	61	1	no	—
59	C₂×C₈	—	244	1	no	—
60	C₂×C₈	C₂×#6923	1	1	yes	characteristic
61	C₄⋊C₄	—	122	1	no	—
62	C₄⋊C₄	—	244	1	no	—
63	C₄²	—	61	1	no	—
64	C₄²	—	244	1	no	—
65	C₁₆	—	122	2	no	—
66	Q₈	—	2	2	no	—
67	Q₈	—	4	1	no	—
68	C₂×C₄	—	4	1	no	—
69	C₂×C₄	—	61	1	no	—
70	C₂×C₄	—	61	1	no	—
71	C₂×C₄	—	244	1	no	—
72	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
73	C₈	—	122	1	no	—
74	C₈	—	488	1	no	—
75	C₈	C₂×#92420	1	1	yes	characteristic
76	C₈	#11758217	1	1	yes	characteristic
77	C₂²	#14519839	1	1	yes	characteristic
78	C₄	—	4	2	no	—
79	C₄	—	122	1	no	—
80	C₄	—	122	1	no	—
81	C₄	—	488	1	no	—
82	C₄	C₂²⋊#92420	1	1	yes	characteristic
83	C₄	#14519841	1	1	yes	characteristic
84	C₂	D₄⋊#92420	1	1	yes	characteristic
85	C₂	#16840679	1	1	yes	characteristic
86	C₂	#16840681	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14519839
commutator	C₈×C₆₁	C₂×C₈
Frattini	C₂×C₈	C₂×#6923
Fitting	C₂×Q₁₆×C₆₁	C₄
socle	C₂²×C₆₁	#102
hypercenter	C₂×Q₁₆	#6923
hypocenter	C₆₁	#1334
LCS	G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
14. Q₁₆×C₆₁	C₈	semidirect
47. C₆₁	#1334	semidirect
57. Q₁₆	#92420	semidirect