Subgroups — #21443797

Order 7808.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×Dic₁₂₂	C₂	1	1	yes	maximal, characteristic
2	C₄×#11758185	C₂	1	1	yes	maximal, characteristic
3	C₆₁×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₄×Dic₁₂₂	C₄	1	1	yes	characteristic
5	C₂×#11758185	—	2	1	no	—
6	C₄⋊#92418	C₄	1	1	yes	characteristic
7	#14519706	—	2	1	no	—
8	C₈×Dic₆₁	—	2	1	no	—
9	C₂×C₁₆×C₆₁	—	2	1	no	—
10	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
11	C₂×Dic₁₂₂	C₈	1	1	yes	characteristic
12	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
13	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
14	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
15	C₄⋊Dic₆₁	C₈	1	1	yes	characteristic
16	#11758196	—	2	1	no	—
17	C₄×Dic₆₁	—	2	1	no	—
18	C₂×#92418	—	2	1	no	—
19	C₁₆×C₆₁	—	4	1	no	—
20	#11758185	—	2	2	no	—
21	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
23	C₂×C₄×C₆₁	M₁₆	1	1	yes	characteristic
24	C₂×Dic₆₁	—	2	1	no	—
25	C₂×Dic₆₁	—	2	1	no	—
26	Dic₁₂₂	—	2	1	no	—
27	Dic₁₂₂	C₁₆	1	2	yes	complemented
28	C₈×C₆₁	—	2	1	no	—
29	C₈×C₆₁	SD₁₆	1	1	yes	characteristic
30	C₈×C₆₁	Q₁₆	1	1	yes	characteristic
31	#92418	—	4	1	no	—
32	C₂²×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
33	C₄×C₆₁	—	2	1	no	—
34	C₄×C₆₁	#103	1	1	yes	characteristic
35	C₄×C₆₁	#104	1	1	yes	characteristic
36	C₄×C₆₁	C₂×C₁₆	1	1	yes	characteristic
37	C₄×C₆₁	M₃₂	1	1	yes	characteristic
38	Dic₆₁	—	2	2	no	—
39	Dic₆₁	—	4	1	no	—
40	Q₈⋊C₁₆	—	61	1	no	maximal, Sylow
41	C₂×C₆₁	Q₈⋊C₈	1	1	yes	characteristic
42	C₂×C₆₁	C₂²⋊C₁₆	1	1	yes	characteristic
43	C₂×C₆₁	#350	1	1	yes	characteristic
44	C₈×Q₈	—	61	1	no	—
45	C₄⋊C₁₆	D₆₁	1	1	yes	characteristic
46	C₄×C₁₆	—	61	1	no	—
47	C₆₁	Q₈⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
48	C₄×Q₈	—	61	1	no	—
49	C₂×C₁₆	—	2	1	no	—
50	C₂×C₁₆	—	122	1	no	—
51	C₄⋊C₈	—	61	1	no	—
52	C₄⋊C₈	—	122	1	no	—
53	C₄×C₈	—	122	1	no	—
54	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
55	C₂×Q₈	—	61	1	no	—
56	C₂×C₈	—	122	1	no	—
57	C₂×C₈	D₂₄₄	1	1	yes	characteristic
58	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
59	C₄⋊C₄	—	61	1	no	—
60	C₄⋊C₄	—	122	1	no	—
61	C₄²	—	122	1	no	—
62	C₄²	C₄×D₆₁	1	1	yes	characteristic
63	C₁₆	—	4	1	no	—
64	C₁₆	—	122	2	no	—
65	Q₈	—	61	2	no	—
66	Q₈	—	122	1	no	—
67	C₂×C₄	—	122	1	no	—
68	C₂×C₄	—	122	1	no	—
69	C₂×C₄	C₈×D₆₁	1	1	yes	characteristic
70	C₂×C₄	#11758189	1	1	yes	characteristic
71	C₂×C₄	#11758198	1	1	yes	characteristic
72	C₈	—	2	1	no	—
73	C₈	—	244	1	no	—
74	C₈	#11758200	1	1	yes	characteristic
75	C₈	#11758202	1	1	yes	characteristic
76	C₂²	#14519689	1	1	yes	characteristic
77	C₄	—	2	1	no	—
78	C₄	—	122	2	no	—
79	C₄	—	244	1	no	—
80	C₄	#14519700	1	1	yes	characteristic
81	C₄	#14519703	1	1	yes	characteristic
82	C₄	C₁₆×D₆₁	1	1	yes	characteristic
83	C₄	#14519716	1	1	yes	characteristic
84	C₂	#16839492	1	1	yes	characteristic
85	C₂	#16839541	1	1	yes	characteristic
86	C₂	#16839547	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²⋊D₆₁
commutator	C₄×C₆₁	C₂×C₁₆
Frattini	C₄×C₈	C₂×D₆₁
Fitting	C₆₁×C₄⋊C₁₆	C₂
socle	C₂²×C₆₁	C₂²⋊C₈
hypercenter	C₄⋊C₁₆	D₆₁
hypocenter	C₆₁	Q₈⋊C₁₆
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
27. Dic₁₂₂	C₁₆	semidirect
47. C₆₁	Q₈⋊C₁₆	semidirect