Subgroups — #21443875

Order 7808.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840167	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#11758185	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#335	C₂	1	1	yes	maximal, characteristic
4	#14519777	—	2	1	no	—
5	C₂×#11758185	—	2	1	no	—
6	#14519711	—	2	1	no	—
7	#14519711	C₄	1	2	yes	—
8	C₄⋊C₈×C₆₁	—	2	1	no	—
9	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
10	C₂×Dic₁₂₂	—	4	1	no	—
11	C₂×C₈×C₆₁	—	4	1	no	—
12	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
14	C₄²×C₆₁	D₄	1	1	yes	characteristic
15	C₄⋊Dic₆₁	—	2	2	no	—
16	C₄⋊Dic₆₁	—	4	1	no	—
17	#11758185	—	4	1	no	—
18	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×C₄×C₆₁	D₈	1	1	yes	characteristic
20	C₂×C₄×C₆₁	SD₁₆	1	1	yes	characteristic
21	C₂×Dic₆₁	—	4	2	no	—
22	Dic₁₂₂	—	8	1	no	—
23	Dic₁₂₂	—	8	1	no	—
24	C₈×C₆₁	—	2	1	no	—
25	C₈×C₆₁	—	8	1	no	—
26	C₈×C₆₁	SD₁₆	1	1	yes	characteristic
27	C₈×C₆₁	Q₁₆	1	1	yes	characteristic
28	C₂²×C₆₁	#102	1	1	yes	characteristic
29	C₄×C₆₁	—	2	1	no	—
30	C₄×C₆₁	#101	1	1	yes	characteristic
31	C₄×C₆₁	#103	1	1	yes	characteristic
32	C₄×C₆₁	D₁₆	1	1	yes	characteristic
33	C₄×C₆₁	SD₃₂	1	1	yes	characteristic
34	Dic₆₁	—	8	2	no	—
35	#1364	—	61	1	no	maximal, Sylow
36	C₂×C₆₁	#332	1	1	yes	characteristic
37	C₂×C₆₁	#357	1	1	yes	characteristic
38	C₂×C₆₁	#362	1	1	yes	characteristic
39	#500	—	61	1	no	—
40	C₄⋊C₁₆	—	61	1	no	—
41	#335	D₆₁	1	1	yes	characteristic
42	C₆₁	#1364	1	1	yes	characteristic, complemented, Sylow
43	C₄⋊Q₈	—	122	1	no	—
44	C₂×C₁₆	—	122	1	no	—
45	#107	—	61	2	no	—
46	#107	—	122	1	no	—
47	C₄⋊C₈	—	2	1	no	—
48	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
49	C₂×Q₈	—	244	1	no	—
50	C₂×C₈	—	4	1	no	—
51	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
52	C₂×C₈	D₂₄₄	1	1	yes	characteristic
53	C₄⋊C₄	—	122	2	no	—
54	C₄⋊C₄	—	244	1	no	—
55	C₄²	C₂²⋊D₆₁	1	1	yes	characteristic
56	C₁₆	—	244	1	no	—
57	Q₈	—	488	1	no	—
58	Q₈	—	488	1	no	—
59	C₂×C₄	—	244	2	no	—
60	C₂×C₄	#11758198	1	1	yes	characteristic
61	C₂×C₄	#11758199	1	1	yes	characteristic
62	C₂×C₄	#11758201	1	1	yes	characteristic
63	C₈	—	2	1	no	—
64	C₈	—	8	1	no	—
65	C₈	#11758190	1	1	yes	characteristic
66	C₈	Dic₂₄₄	1	1	yes	characteristic
67	C₂²	#14519697	1	1	yes	characteristic
68	C₄	—	2	1	no	—
69	C₄	—	488	2	no	—
70	C₄	#14519695	1	1	yes	characteristic
71	C₄	#14519702	1	1	yes	characteristic
72	C₄	#14519718	1	1	yes	characteristic
73	C₄	#14519720	1	1	yes	characteristic
74	C₂	#16839509	1	1	yes	characteristic
75	C₂	#16839562	1	1	yes	characteristic
76	C₂	#16839577	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14519697
commutator	C₂×C₈×C₆₁	C₂×C₄
Frattini	C₄×C₈	C₂×D₆₁
Fitting	C₆₁×#335	C₂
socle	C₂²×C₆₁	#102
hypercenter	#335	D₆₁
hypocenter	C₆₁	#1364
LCS	G ▷ C₂×C₈×C₆₁ ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #335

Complements

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

N	H ≅ G/N	type
42. C₆₁	#1364	semidirect