Subgroups — #16840665

Order 3904.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14519837	C₂	1	1	yes	maximal, characteristic
2	#14519835	C₂	1	1	yes	maximal, characteristic
3	#14519761	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂²⋊D₆₁	C₂²	1	1	yes	characteristic
5	C₂²×Dic₆₁	C₄	1	1	yes	characteristic, complemented
6	C₂²⋊#6923	—	2	1	no	—
7	#11758217	—	2	1	no	—
8	C₂²⋊C₄×C₆₁	C₄	1	1	yes	characteristic, complemented
9	#11758198	—	2	1	no	—
10	C₄⋊Dic₆₁	—	2	1	no	—
11	C₂³×C₆₁	C₂×C₄	1	1	yes	characteristic
12	C₂²×D₆₁	D₄	1	1	yes	characteristic
13	C₂×#6923	—	4	1	no	—
14	C₂×C₄×C₆₁	—	2	1	no	—
15	C₂²⋊D₆₁	—	4	1	no	—
16	C₂×Dic₆₁	—	2	1	no	—
17	C₂×Dic₆₁	—	4	1	no	—
18	C₂×Dic₆₁	D₄	1	1	yes	characteristic
19	#92420	—	4	1	no	—
20	C₂²×C₆₁	—	2	1	no	—
21	C₂²×C₆₁	—	4	1	no	—
22	C₂²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×D₆₁	—	2	1	no	—
24	C₂×D₆₁	—	4	1	no	—
25	#6923	—	8	1	no	—
26	C₄×C₆₁	—	4	1	no	—
27	Dic₆₁	—	2	1	no	—
28	Dic₆₁	—	4	1	no	—
29	C₂×C₆₁	—	2	1	no	—
30	C₂×C₆₁	—	4	1	no	—
31	C₂×C₆₁	#99	1	1	yes	characteristic
32	D₆₁	—	4	1	no	—
33	#352	—	61	1	no	maximal, Sylow
34	C₆₁	#352	1	1	yes	characteristic, complemented, Sylow
35	#123	—	61	1	no	—
36	#100	—	61	1	no	—
37	#99	—	61	1	no	—
38	C₂×D₄	—	61	1	no	—
39	C₂²×C₄	—	61	1	no	—
40	M₁₆	—	122	1	no	—
41	C₄⋊C₄	—	122	1	no	—
42	C₂²⋊C₄	—	122	1	no	—
43	C₂²⋊C₄	—	122	1	no	—
44	C₂²⋊C₄	#6923	1	1	yes	characteristic, complemented
45	C₂³	—	61	1	no	—
46	C₂³	C₂×#6923	1	1	yes	characteristic
47	D₄	—	244	1	no	—
48	C₂×C₄	—	2	1	no	—
49	C₂×C₄	—	61	1	no	—
50	C₂×C₄	—	122	1	no	—
51	C₂×C₄	—	244	1	no	—
52	C₂×C₄	—	244	1	no	—
53	C₈	—	244	1	no	—
54	C₂²	—	2	1	no	—
55	C₂²	—	4	1	no	—
56	C₂²	—	122	1	no	—
57	C₂²	—	244	1	no	—
58	C₂²	C₂²⋊#6923	1	1	yes	characteristic
59	C₄	—	4	1	no	—
60	C₄	—	122	1	no	—
61	C₄	—	488	1	no	—
62	C₄	—	244	1	no	—
63	C₂	—	2	1	no	—
64	C₂	—	4	1	no	—
65	C₂	—	244	1	no	—
66	C₂	#14519836	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14519836
commutator	C₂³×C₆₁	C₂×C₄
Frattini	C₂³	C₂×#6923
Fitting	C₂²⋊C₄×C₆₁	C₄
socle	C₂×C₆₁	#99
prime radical, cosocle	C₂×C₂²⋊D₆₁	C₂²
hypercenter	C₂²⋊C₄	#6923
hypocenter	C₆₁	#352
LCS	G ▷ C₂³×C₆₁ ▷ C₂²×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂³ ◁ C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
5. C₂²×Dic₆₁	C₄	semidirect
8. C₂²⋊C₄×C₆₁	C₄	semidirect
34. C₆₁	#352	semidirect
44. C₂²⋊C₄	#6923	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#14519837	2
#14519835	2
#14519761	2
#352	61