Subgroups — #21460966

Order 7808.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840671	C₂	1	1	yes	maximal, characteristic
2	#16840669	C₂	1	1	yes	maximal, characteristic
3	#16840117	C₂	1	1	yes	maximal, characteristic
4	#14519838	—	2	1	no	—
5	#14519836	—	2	1	no	—
6	#14519769	C₄	1	1	yes	characteristic, complemented
7	#14519765	C₂²	1	1	yes	characteristic
8	#14519702	—	2	1	no	—
9	#14519699	—	2	1	no	—
10	C₄×C₈×C₆₁	C₄	1	1	yes	characteristic, complemented
11	C₂×D₂₄₄	D₄	1	1	yes	characteristic
12	C₂×Dic₁₂₂	D₄	1	1	yes	characteristic
13	C₂²⋊#6923	—	4	1	no	—
14	#11758217	—	4	1	no	—
15	C₂×C₈×C₆₁	—	2	1	no	—
16	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
17	#11758198	—	4	1	no	—
18	C₄⋊Dic₆₁	—	2	1	no	—
19	#11758196	—	4	1	no	—
20	C₂²×D₆₁	—	2	1	no	—
21	C₂×#6923	—	8	1	no	—
22	C₂×C₄×C₆₁	—	2	1	no	—
23	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
24	C₂×Dic₆₁	—	2	1	no	—
25	C₂×Dic₆₁	—	4	1	no	—
26	D₂₄₄	—	4	1	no	—
27	Dic₁₂₂	—	4	1	no	—
28	#92420	—	8	1	no	—
29	C₈×C₆₁	—	4	1	no	—
30	C₂²×C₆₁	#99	1	1	yes	characteristic
31	C₂×D₆₁	—	4	1	no	—
32	C₂×D₆₁	—	8	1	no	—
33	#6923	—	16	1	no	—
34	C₄×C₆₁	—	2	1	no	—
35	C₄×C₆₁	—	4	1	no	—
36	Dic₆₁	—	4	1	no	—
37	Dic₆₁	—	8	1	no	—
38	#1414	—	61	1	no	maximal, Sylow
39	C₂×C₆₁	—	2	1	no	—
40	C₂×C₆₁	#354	1	1	yes	characteristic
41	D₆₁	—	8	1	no	—
42	#488	—	61	1	no	—
43	#355	—	61	1	no	—
44	#354	—	61	1	no	—
45	C₆₁	#1414	1	1	yes	characteristic, complemented, Sylow
46	#125	—	61	1	no	—
47	#124	—	61	1	no	—
48	#103	—	122	1	no	—
49	#102	—	122	1	no	—
50	#101	—	122	1	no	—
51	#99	—	122	1	no	—
52	C₄×C₈	#6923	1	1	yes	characteristic, complemented
53	C₂×Q₈	—	61	1	no	—
54	C₂×D₄	—	61	1	no	—
55	M₁₆	—	244	1	no	—
56	C₂×C₈	—	2	1	no	—
57	C₄⋊C₄	—	122	1	no	—
58	C₄⋊C₄	—	244	1	no	—
59	C₂²⋊C₄	—	244	1	no	—
60	C₂²⋊C₄	—	244	1	no	—
61	C₄²	C₂×#6923	1	1	yes	characteristic
62	C₂³	—	122	1	no	—
63	Q₈	—	244	1	no	—
64	D₄	—	244	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	122	1	no	—
67	C₂×C₄	—	488	1	no	—
68	C₂×C₄	—	244	1	no	—
69	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
70	C₈	—	4	1	no	—
71	C₈	—	488	1	no	—
72	C₂²	—	488	1	no	—
73	C₂²	—	244	1	no	—
74	C₂²	#14519836	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	—	4	1	no	—
77	C₄	—	976	1	no	—
78	C₄	—	488	1	no	—
79	C₄	—	244	1	no	—
80	C₂	—	2	1	no	—
81	C₂	—	488	1	no	—
82	C₂	#16840669	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16840669
commutator	C₄²×C₆₁	C₂×C₄
Frattini	C₄²	C₂×#6923
Fitting	C₄×C₈×C₆₁	C₄
socle	C₂×C₆₁	#354
hypercenter	C₄×C₈	#6923
hypocenter	C₆₁	#1414
LCS	G ▷ C₄²×C₆₁ ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
6. #14519769	C₄	semidirect
10. C₄×C₈×C₆₁	C₄	semidirect
45. C₆₁	#1414	semidirect
52. C₄×C₈	#6923	semidirect