Subgroups — #21461746

Order 7808.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840628	C₂	1	6	yes	maximal
2	C₄²×Dic₆₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×#92420	C₂²	1	4	yes	—
4	C₂×C₄×Dic₆₁	C₄	1	3	yes	—
5	C₂×C₄×Dic₆₁	C₂²	1	3	yes	—
6	C₂×C₄²×C₆₁	C₄	1	1	yes	characteristic
7	C₂²×C₄×C₆₁	C₂×C₄	1	3	yes	—
8	C₂²×Dic₆₁	C₂×C₄	1	3	yes	—
9	C₂²×Dic₆₁	C₂³	1	1	yes	characteristic
10	C₂×#92420	—	2	12	no	—
11	C₄²×C₆₁	C₈	1	4	yes	complemented
12	C₄×Dic₆₁	—	2	6	no	—
13	C₄×Dic₆₁	—	2	6	no	—
14	C₂³×C₆₁	C₂²×C₄	1	1	yes	characteristic
15	C₂×C₄×C₆₁	—	2	3	no	—
16	C₂×C₄×C₆₁	—	2	3	no	—
17	C₂×C₄×C₆₁	C₂×C₈	1	6	yes	—
18	C₂×Dic₆₁	—	2	3	no	—
19	C₂×Dic₆₁	—	2	3	no	—
20	C₂×Dic₆₁	M₁₆	1	6	yes	—
21	C₂×Dic₆₁	#41	1	6	yes	—
22	#92420	—	4	4	no	—
23	C₂²×C₆₁	#117	1	3	yes	—
24	C₂²×C₆₁	C₂²×C₈	1	1	yes	characteristic
25	C₂²×C₆₁	C₂×M₁₆	1	3	yes	—
26	C₄×C₆₁	—	2	6	no	—
27	Dic₆₁	—	2	6	no	—
28	Dic₆₁	#126	1	4	yes	—
29	#1839	—	61	1	no	maximal, Sylow
30	C₂×C₆₁	#383	1	1	yes	characteristic
31	C₂×C₆₁	#431	1	3	yes	—
32	C₂×C₆₁	#432	1	3	yes	—
33	C₄³	—	61	1	no	—
34	#336	—	61	6	no	—
35	C₆₁	#1839	1	1	yes	characteristic, complemented, Sylow
36	C₂²×C₈	—	61	4	no	—
37	C₂×C₄²	—	61	3	no	—
38	C₂×C₄²	—	61	3	no	—
39	C₂×C₄²	#6923	1	1	yes	characteristic
40	C₂²×C₄	—	61	1	no	—
41	C₂²×C₄	—	61	3	no	—
42	C₂²×C₄	C₂×#6923	1	3	yes	—
43	C₂×C₈	—	122	12	no	—
44	C₄²	—	122	6	no	—
45	C₄²	—	122	6	no	—
46	C₄²	#92420	1	4	yes	complemented
47	C₂³	C₂²×#6923	1	1	yes	characteristic
48	C₂×C₄	—	2	3	no	—
49	C₂×C₄	—	2	3	no	—
50	C₂×C₄	—	61	6	no	—
51	C₂×C₄	—	61	6	no	—
52	C₂×C₄	—	122	3	no	—
53	C₂×C₄	—	122	3	no	—
54	C₂×C₄	C₂×#92420	1	6	yes	—
55	C₈	—	244	4	no	—
56	C₂²	#14519856	1	3	yes	—
57	C₂²	C₂²×#92420	1	1	yes	characteristic
58	C₂²	D₆₁⋊M₁₆	1	3	yes	—
59	C₄	—	2	6	no	—
60	C₄	—	61	4	no	—
61	C₄	—	122	6	no	—
62	C₂	#16840707	1	1	yes	characteristic
63	C₂	#16840778	1	3	yes	—
64	C₂	#16840785	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	#1839
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
11. C₄²×C₆₁	C₈	semidirect
35. C₆₁	#1839	semidirect
46. C₄²	#92420	semidirect