Subgroups — #21461751

Order 7808.

300 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊#92420	C₂	1	6	yes	maximal
2	C₄²×Dic₆₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×#92420	C₂²	1	4	yes	—
4	C₄⋊#92420	—	2	12	no	—
5	C₂×C₄×Dic₆₁	C₄	1	3	yes	—
6	C₂×C₄×Dic₆₁	C₂²	1	3	yes	—
7	C₂×C₄²×C₆₁	C₄	1	1	yes	characteristic
8	C₂²×C₄×C₆₁	C₂×C₄	1	3	yes	—
9	C₂²×Dic₆₁	C₂×C₄	1	3	yes	—
10	C₂²×Dic₆₁	C₂³	1	1	yes	characteristic
11	C₂×#92420	—	2	12	no	—
12	C₄²×C₆₁	C₈	1	4	yes	complemented
13	C₄×Dic₆₁	—	2	6	no	—
14	C₄×Dic₆₁	D₄	1	6	yes	—
15	C₄×Dic₆₁	Q₈	1	6	yes	—
16	C₂³×C₆₁	C₂²×C₄	1	1	yes	characteristic
17	C₂×C₄×C₆₁	C₄⋊C₄	1	6	yes	—
18	C₂×C₄×C₆₁	C₂×C₈	1	6	yes	—
19	C₂×C₄×C₆₁	M₁₆	1	6	yes	—
20	C₂×Dic₆₁	—	2	6	no	—
21	C₂×Dic₆₁	C₄⋊C₄	1	6	yes	—
22	C₂×Dic₆₁	C₂×D₄	1	3	yes	—
23	C₂×Dic₆₁	C₂×Q₈	1	3	yes	—
24	#92420	—	4	4	no	—
25	C₂²×C₆₁	C₂×C₄⋊C₄	1	3	yes	—
26	C₂²×C₆₁	C₂²×C₈	1	1	yes	characteristic
27	C₂²×C₆₁	C₂×M₁₆	1	3	yes	—
28	C₄×C₆₁	C₄⋊C₈	1	12	yes	complemented
29	Dic₆₁	—	2	6	no	—
30	Dic₆₁	#127	1	1	yes	characteristic
31	Dic₆₁	C₄⋊Q₈	1	3	yes	—
32	#1842	—	61	1	no	maximal, Sylow
33	C₂×C₆₁	#384	1	1	yes	characteristic
34	C₂×C₆₁	C₂×C₄⋊C₈	1	3	yes	—
35	C₂×C₆₁	#423	1	3	yes	—
36	C₂×C₄⋊C₈	—	61	6	no	—
37	C₄³	—	61	1	no	—
38	C₆₁	#1842	1	1	yes	characteristic, complemented, Sylow
39	C₂²×C₈	—	61	4	no	—
40	C₂×C₄²	—	61	3	no	—
41	C₂×C₄²	—	61	3	no	—
42	C₂×C₄²	#6923	1	1	yes	characteristic
43	C₄⋊C₈	—	122	12	no	—
44	C₂²×C₄	—	61	1	no	—
45	C₂²×C₄	—	61	3	no	—
46	C₂²×C₄	C₂×#6923	1	3	yes	—
47	C₂×C₈	—	122	12	no	—
48	C₄²	—	61	6	no	—
49	C₄²	—	61	6	no	—
50	C₄²	—	122	6	no	—
51	C₄²	#92420	1	4	yes	complemented
52	C₂³	C₂²×#6923	1	1	yes	characteristic
53	C₂×C₄	—	61	3	no	—
54	C₂×C₄	—	61	3	no	—
55	C₂×C₄	—	61	6	no	—
56	C₂×C₄	—	122	6	no	—
57	C₂×C₄	#11758213	1	6	yes	—
58	C₂×C₄	C₄⋊#6923	1	6	yes	—
59	C₂×C₄	C₂×#92420	1	6	yes	—
60	C₈	—	244	4	no	—
61	C₂²	C₂×C₄⋊#6923	1	3	yes	—
62	C₂²	C₂²×#92420	1	1	yes	characteristic
63	C₂²	C₂×#11758213	1	3	yes	—
64	C₄	—	61	1	no	—
65	C₄	—	61	3	no	—
66	C₄	—	122	6	no	—
67	C₄	C₄⋊#92420	1	12	yes	complemented
68	C₂	#16840708	1	1	yes	characteristic
69	C₂	C₂×C₄⋊#92420	1	3	yes	—
70	C₂	#16840766	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×#6923
commutator	C₂²×C₆₁	C₂²×C₈
Fitting	C₂×C₄²×C₆₁	C₄
socle	C₂³×C₆₁	C₂²×C₄
hypercenter	C₂×C₄²	#6923
hypocenter	C₆₁	#1842
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
12. C₄²×C₆₁	C₈	semidirect
28. C₄×C₆₁	C₄⋊C₈	semidirect
38. C₆₁	#1842	semidirect
51. C₄²	#92420	semidirect
67. C₄	C₄⋊#92420	semidirect