Subgroups — #21445435

Order 7808.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840165	C₂	1	4	yes	maximal
2	#16840142	C₂	1	1	yes	maximal, characteristic
3	C₈×#92418	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#494	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₂₄₄	—	2	2	no	—
6	#14519777	C₂²	1	2	yes	—
7	#14519710	—	2	8	no	—
8	C₄×#92418	C₂²	1	2	yes	—
9	C₂×Q₁₆×C₆₁	—	2	2	no	—
10	C₄⋊Q₈×C₆₁	C₂²	1	2	yes	—
11	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
12	C₂×Q₈×C₆₁	—	2	2	no	—
13	C₂×Dic₁₂₂	—	2	2	no	—
14	Q₁₆×C₆₁	—	4	4	no	—
15	C₂×C₈×C₆₁	D₄	1	2	yes	—
16	C₄⋊C₄×C₆₁	—	2	4	no	—
17	C₄²×C₆₁	C₂³	1	1	yes	characteristic
18	C₄⋊Dic₆₁	—	2	4	no	—
19	C₂×#92418	D₄	1	4	yes	—
20	Dic₂₄₄	—	4	4	no	—
21	Q₈×C₆₁	—	4	4	no	—
22	C₂×C₄×C₆₁	—	4	2	no	—
23	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
24	C₂×C₄×C₆₁	C₂×D₄	1	2	yes	—
25	C₂×Dic₆₁	—	4	2	no	—
26	Dic₁₂₂	—	4	4	no	—
27	C₈×C₆₁	D₈	1	4	yes	—
28	#92418	Q₁₆	1	8	yes	complemented
29	C₂²×C₆₁	#127	1	1	yes	characteristic
30	C₄×C₆₁	—	8	2	no	—
31	C₄×C₆₁	C₂×D₈	1	2	yes	—
32	C₄×C₆₁	C₂×Q₁₆	1	4	yes	—
33	Dic₆₁	—	8	2	no	—
34	#1713	—	61	1	no	maximal, Sylow
35	C₂×C₆₁	#493	1	1	yes	characteristic
36	C₂×C₆₁	#494	1	2	yes	—
37	#500	—	61	4	no	—
38	#494	—	61	1	no	—
39	#494	D₆₁	1	1	yes	characteristic
40	C₈²	—	61	1	no	—
41	C₆₁	#1713	1	1	yes	characteristic, complemented, Sylow
42	C₂×Q₁₆	—	2	2	no	—
43	C₂×Q₁₆	—	122	2	no	—
44	C₄⋊Q₈	—	61	2	no	—
45	C₄⋊Q₈	C₂×D₆₁	1	2	yes	—
46	#107	—	122	8	no	—
47	C₄×C₈	—	61	2	no	—
48	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
49	C₂×Q₈	—	2	2	no	—
50	C₂×Q₈	—	122	2	no	—
51	Q₁₆	—	4	4	no	—
52	Q₁₆	—	244	4	no	—
53	C₂×C₈	—	61	4	no	—
54	C₂×C₈	C₂²⋊D₆₁	1	2	yes	—
55	C₄⋊C₄	—	2	4	no	—
56	C₄⋊C₄	—	122	4	no	—
57	C₄²	C₂²×D₆₁	1	1	yes	characteristic
58	Q₈	—	4	4	no	—
59	Q₈	—	244	4	no	—
60	C₂×C₄	—	4	2	no	—
61	C₂×C₄	—	244	2	no	—
62	C₂×C₄	D₄×D₆₁	1	2	yes	—
63	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
64	C₈	—	61	8	no	—
65	C₈	#11758199	1	4	yes	—
66	C₂²	#14519773	1	1	yes	characteristic
67	C₄	—	8	2	no	—
68	C₄	—	488	2	no	—
69	C₄	C₂×#11758199	1	2	yes	—
70	C₄	Q₁₆×D₆₁	1	4	yes	—
71	C₂	#16840138	1	1	yes	characteristic
72	C₂	#16840140	1	2	yes	—

	subgroup	G/H
center	C₂²	#14519773
commutator	C₄²×C₆₁	C₂³
Frattini	C₄²	C₂²×D₆₁
Fitting	C₆₁×#494	C₂
socle	C₂²×C₆₁	#127
hypercenter	#494	D₆₁
hypocenter	C₆₁	#1713
LCS	G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #494

Complements

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

N	H ≅ G/N	type
28. #92418	Q₁₆	semidirect
41. C₆₁	#1713	semidirect