Subgroups — C₄³×Dic₆₁ #29601079

Order 15616.

3966 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×Dic₆₁	C₂	1	14	yes	maximal
2	C₂×C₄³×C₆₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×Dic₆₁	C₂²	1	28	yes	—
4	C₄²×Dic₆₁	C₄	1	112	yes	direct product factor
5	C₂²×C₄²×C₆₁	C₂²	1	7	yes	—
6	C₄³×C₆₁	C₄	1	8	yes	complemented
7	C₂³×Dic₆₁	C₂³	1	8	yes	—
8	C₂×C₄×Dic₆₁	C₂×C₄	1	336	yes	—
9	C₂³×C₄×C₆₁	C₂³	1	7	yes	—
10	C₂×C₄²×C₆₁	C₂×C₄	1	56	yes	—
11	C₂×C₄²×C₆₁	C₂×C₄	1	28	yes	—
12	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
13	C₂²×C₄×C₆₁	C₂²×C₄	1	84	yes	—
14	C₂²×C₄×C₆₁	C₂²×C₄	1	14	yes	—
15	C₂²×Dic₆₁	C₂²×C₄	1	112	yes	—
16	C₄²×C₆₁	C₄²	1	112	yes	complemented
17	C₄×Dic₆₁	C₄²	1	448	yes	direct product factor
18	C₂³×C₆₁	C₂³×C₄	1	14	yes	—
19	C₂³×C₆₁	C₂³×C₄	1	1	yes	characteristic
20	C₂×C₄×C₆₁	C₂×C₄²	1	112	yes	—
21	C₂×C₄×C₆₁	C₂×C₄²	1	84	yes	—
22	C₂×Dic₆₁	C₂×C₄²	1	224	yes	—
23	C₄⁴	—	61	1	no	maximal, Sylow
24	C₂²×C₆₁	C₂²×C₄²	1	28	yes	—
25	C₂²×C₆₁	C₂²×C₄²	1	7	yes	—
26	C₄×C₆₁	C₄³	1	56	yes	complemented
27	Dic₆₁	C₄³	1	64	yes	direct product factor
28	C₂×C₄³	—	61	14	no	—
29	C₂×C₄³	D₆₁	1	1	yes	characteristic
30	C₂×C₆₁	C₂×C₄³	1	8	yes	—
31	C₂×C₆₁	C₂×C₄³	1	7	yes	—
32	C₂²×C₄²	—	61	28	no	—
33	C₂²×C₄²	C₂×D₆₁	1	7	yes	—
34	C₄³	—	61	112	no	—
35	C₄³	Dic₆₁	1	8	yes	direct product factor
36	C₆₁	C₄⁴	1	1	yes	characteristic, complemented, Sylow
37	C₂³×C₄	—	61	8	no	—
38	C₂³×C₄	C₂²×D₆₁	1	7	yes	—
39	C₂×C₄²	—	61	336	no	—
40	C₂×C₄²	C₄×D₆₁	1	56	yes	—
41	C₂×C₄²	C₂×Dic₆₁	1	28	yes	—
42	C₂⁴	C₂³×D₆₁	1	1	yes	characteristic
43	C₂²×C₄	—	61	112	no	—
44	C₂²×C₄	C₂×C₄×D₆₁	1	84	yes	—
45	C₂²×C₄	C₂²×Dic₆₁	1	14	yes	—
46	C₄²	—	61	448	no	—
47	C₄²	C₄×Dic₆₁	1	112	yes	direct product factor
48	C₂³	C₂²×C₄×D₆₁	1	14	yes	—
49	C₂³	C₂³×Dic₆₁	1	1	yes	characteristic
50	C₂×C₄	—	61	224	no	—
51	C₂×C₄	C₄²×D₆₁	1	112	yes	—
52	C₂×C₄	C₂×C₄×Dic₆₁	1	84	yes	—
53	C₂²	C₂×C₄²×D₆₁	1	28	yes	—
54	C₂²	C₂²×C₄×Dic₆₁	1	7	yes	—
55	C₄	—	61	64	no	—
56	C₄	C₄²×Dic₆₁	1	56	yes	direct product factor
57	C₂	C₄³×D₆₁	1	8	yes	—
58	C₂	C₂×C₄²×Dic₆₁	1	7	yes	—

	subgroup	G/H
center, hypercenter	C₂×C₄³	D₆₁
commutator, hypocenter	C₆₁	C₄⁴
Frattini	C₂⁴	C₂³×D₆₁
Fitting	C₂×C₄³×C₆₁	C₂
socle, prime radical, cosocle	C₂⁴×C₆₁	C₂⁴
LCS	G ▷ C₆₁
UCS	C₁ ◁ C₂×C₄³

Complements

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

N	H ≅ G/N	type
4. C₄²×Dic₆₁	C₄	direct (N × H)
6. C₄³×C₆₁	C₄	semidirect
16. C₄²×C₆₁	C₄²	semidirect
17. C₄×Dic₆₁	C₄²	direct (N × H)
26. C₄×C₆₁	C₄³	semidirect
27. Dic₆₁	C₄³	direct (N × H)
35. C₄³	Dic₆₁	direct (N × H)
36. C₆₁	C₄⁴	semidirect
47. C₄²	C₄×Dic₆₁	direct (N × H)
56. C₄	C₄²×Dic₆₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄²×Dic₆₁	2
C₂×C₄³×C₆₁	2
C₄⁴	61

Subgroups — C43×Dic61 #29601079

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄³×Dic₆₁ #29601079