Subgroups — #21443994

Order 7808.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16839559	C₂	1	1	yes	maximal, characteristic
2	#16839557	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#488	C₂	1	1	yes	maximal, characteristic
4	#14519696	—	2	1	no	—
5	#14519692	—	2	1	no	—
6	#125×C₆₁	C₄	1	1	yes	characteristic, complemented
7	#124×C₆₁	C₂²	1	1	yes	characteristic
8	#103×C₆₁	—	2	1	no	—
9	#102×C₆₁	—	2	1	no	—
10	C₄×C₈×C₆₁	C₄	1	1	yes	characteristic, complemented
11	C₂×Q₈×C₆₁	D₄	1	1	yes	characteristic
12	C₂×D₄×C₆₁	D₄	1	1	yes	characteristic
13	C₂×C₈×C₆₁	—	2	1	no	—
14	C₄⋊C₄×C₆₁	—	2	1	no	—
15	C₄⋊C₄×C₆₁	—	4	1	no	—
16	C₂²⋊C₄×C₆₁	—	4	1	no	—
17	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
18	C₂²⋊Dic₆₁	—	4	1	no	—
19	#11758194	—	4	1	no	—
20	C₂³×C₆₁	—	2	1	no	—
21	Q₈×C₆₁	—	4	1	no	—
22	D₄×C₆₁	—	4	1	no	—
23	C₂×C₄×C₆₁	—	2	1	no	—
24	C₂×C₄×C₆₁	—	2	1	no	—
25	C₂×C₄×C₆₁	—	4	1	no	—
26	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×Dic₆₁	—	8	1	no	—
28	C₈×C₆₁	—	4	1	no	—
29	#92418	—	8	1	no	—
30	C₂²×C₆₁	—	4	1	no	—
31	C₂²×C₆₁	—	8	1	no	—
32	C₂²×C₆₁	#99	1	1	yes	characteristic
33	C₄×C₆₁	—	2	1	no	—
34	C₄×C₆₁	—	4	1	no	—
35	C₄×C₆₁	—	4	1	no	—
36	C₄×C₆₁	—	8	1	no	—
37	Dic₆₁	—	16	1	no	—
38	#1414	—	61	1	no	maximal, Sylow
39	C₂×C₆₁	—	2	1	no	—
40	C₂×C₆₁	—	8	1	no	—
41	C₂×C₆₁	#354	1	1	yes	characteristic
42	#488	D₆₁	1	1	yes	characteristic
43	#355	—	61	1	no	—
44	#354	—	61	1	no	—
45	C₆₁	#1414	1	1	yes	characteristic, complemented, Sylow
46	#125	Dic₆₁	1	1	yes	characteristic, complemented
47	#124	C₂×D₆₁	1	1	yes	characteristic
48	#103	—	2	1	no	—
49	#102	—	2	1	no	—
50	#101	—	122	1	no	—
51	#99	—	122	1	no	—
52	C₄×C₈	Dic₆₁	1	1	yes	characteristic, complemented
53	C₂×Q₈	C₂²⋊D₆₁	1	1	yes	characteristic
54	C₂×D₄	C₂²⋊D₆₁	1	1	yes	characteristic
55	M₁₆	—	244	1	no	—
56	C₂×C₈	—	2	1	no	—
57	C₄⋊C₄	—	2	1	no	—
58	C₄⋊C₄	—	4	1	no	—
59	C₂²⋊C₄	—	4	1	no	—
60	C₂²⋊C₄	—	244	1	no	—
61	C₄²	C₂×Dic₆₁	1	1	yes	characteristic
62	C₂³	—	2	1	no	—
63	Q₈	—	4	1	no	—
64	D₄	—	4	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	—	4	1	no	—
68	C₂×C₄	—	488	1	no	—
69	C₂×C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
70	C₈	—	4	1	no	—
71	C₈	—	488	1	no	—
72	C₂²	—	4	1	no	—
73	C₂²	—	8	1	no	—
74	C₂²	#14519692	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	—	4	1	no	—
77	C₄	—	4	1	no	—
78	C₄	—	8	1	no	—
79	C₄	—	976	1	no	—
80	C₂	—	2	1	no	—
81	C₂	—	8	1	no	—
82	C₂	#16839557	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16839557
commutator	C₄²×C₆₁	C₂×C₄
Frattini	#124	C₂×D₆₁
Fitting	C₆₁×#488	C₂
socle	C₂×C₆₁	#354
hypercenter	#488	D₆₁
hypocenter	C₆₁	#1414
LCS	G ▷ C₄²×C₆₁ ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #124 ◁ #488

Complements

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

N	H ≅ G/N	type
6. #125×C₆₁	C₄	semidirect
10. C₄×C₈×C₆₁	C₄	semidirect
45. C₆₁	#1414	semidirect
46. #125	Dic₆₁	semidirect
52. C₄×C₈	Dic₆₁	semidirect