Subgroups — C₂×#401×D₆₁ #29846306

Order 15616.

2942 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁⋊#401	C₂	1	7	yes	maximal, complemented
2	#401×D₆₁	C₂	1	16	yes	maximal, direct product factor
3	C₂×#95×D₆₁	C₂	1	7	yes	maximal
4	C₂×C₆₁×#401	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×C₄×D₆₁	C₂²	1	7	yes	—
6	C₆₁⋊#401	C₂²	1	56	yes	complemented
7	C₂×#14519684	C₂²	1	21	yes	—
8	#95×D₆₁	C₂²	1	56	yes	—
9	C₆₁×#401	C₂²	1	8	yes	complemented
10	C₂×#95×C₆₁	C₂²	1	7	yes	—
11	C₂⁴×D₆₁	C₂³	1	1	yes	characteristic
12	C₂³×Dic₆₁	C₂³	1	7	yes	—
13	C₂²×C₄×D₆₁	—	2	84	no	—
14	C₂²×C₄×D₆₁	C₂³	1	28	yes	—
15	#14519684	C₂³	1	84	yes	—
16	C₂³×C₄×C₆₁	C₂³	1	7	yes	—
17	#95×C₆₁	C₂³	1	28	yes	—
18	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
19	C₂³×D₆₁	#41	1	28	yes	—
20	C₂³×D₆₁	C₂⁴	1	2	yes	—
21	C₂²×C₄×C₆₁	—	2	42	no	—
22	C₂²×C₄×C₆₁	C₂⁴	1	14	yes	—
23	C₂²×Dic₆₁	—	2	42	no	—
24	C₂²×Dic₆₁	C₂⁴	1	14	yes	—
25	C₂×C₄×D₆₁	—	2	168	no	—
26	C₂×C₄×D₆₁	—	4	112	no	—
27	C₂³×C₆₁	C₂×#41	1	14	yes	—
28	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
29	C₂²×D₆₁	#126	1	112	yes	—
30	C₂²×D₆₁	C₂×#41	1	28	yes	—
31	C₂×C₄×C₆₁	—	2	42	no	—
32	C₂×C₄×C₆₁	—	4	28	no	—
33	C₂×Dic₆₁	—	2	42	no	—
34	C₂×Dic₆₁	—	4	28	no	—
35	C₄×D₆₁	—	4	112	no	—
36	C₂²×#401	—	61	1	no	maximal, Sylow
37	C₂²×C₆₁	C₂×#126	1	28	yes	—
38	C₂²×C₆₁	C₂²×#41	1	7	yes	—
39	C₂×D₆₁	#401	1	64	yes	direct product factor
40	C₂×D₆₁	C₂×#126	1	56	yes	—
41	C₄×C₆₁	—	4	14	no	—
42	Dic₆₁	—	4	14	no	—
43	C₂×#401	—	61	16	no	—
44	C₂×#401	—	61	7	no	—
45	C₂×#401	D₆₁	1	1	yes	characteristic, direct product factor
46	C₂²×#95	—	61	7	no	—
47	C₂×C₆₁	C₂×#401	1	8	yes	complemented
48	C₂×C₆₁	C₂²×#126	1	7	yes	—
49	D₆₁	C₂×#401	1	16	yes	direct product factor
50	C₂⁴×C₄	—	61	7	no	—
51	#401	—	61	56	no	—
52	#401	C₂×D₆₁	1	8	yes	direct product factor
53	C₂×#95	—	61	21	no	—
54	C₂×#95	—	61	56	no	—
55	C₂×#95	C₂×D₆₁	1	7	yes	—
56	C₆₁	C₂²×#401	1	1	yes	characteristic, complemented, Sylow
57	C₂⁵	—	61	1	no	—
58	C₂³×C₄	—	61	7	no	—
59	C₂³×C₄	—	61	28	no	—
60	C₂³×C₄	—	122	84	no	—
61	C₂³×C₄	C₂²×D₆₁	1	7	yes	—
62	#95	—	61	84	no	—
63	#95	C₂²×D₆₁	1	28	yes	—
64	C₂⁴	—	61	28	no	—
65	C₂⁴	—	61	2	no	—
66	C₂⁴	C₂³×D₆₁	1	1	yes	characteristic
67	C₂²×C₄	—	2	42	no	—
68	C₂²×C₄	—	61	14	no	—
69	C₂²×C₄	—	122	168	no	—
70	C₂²×C₄	—	122	42	no	—
71	C₂²×C₄	—	244	112	no	—
72	C₂²×C₄	C₂³×D₆₁	1	14	yes	—
73	C₂³	—	61	112	no	—
74	C₂³	—	61	28	no	—
75	C₂³	#41×D₆₁	1	14	yes	—
76	C₂³	C₂⁴×D₆₁	1	1	yes	characteristic
77	C₂×C₄	—	2	42	no	—
78	C₂×C₄	—	4	28	no	—
79	C₂×C₄	—	122	42	no	—
80	C₂×C₄	—	244	112	no	—
81	C₂×C₄	—	244	28	no	—
82	C₂²	—	61	56	no	—
83	C₂²	—	61	64	no	—
84	C₂²	#126×D₆₁	1	28	yes	—
85	C₂²	C₂×#41×D₆₁	1	7	yes	—
86	C₄	—	4	14	no	—
87	C₄	—	244	14	no	—
88	C₂	—	61	16	no	—
89	C₂	#401×D₆₁	1	8	yes	direct product factor
90	C₂	C₂×#126×D₆₁	1	7	yes	—

	subgroup	G/H
center	C₂⁴	C₂³×D₆₁
commutator, cosocle	C₂³×C₆₁	C₂⁵
Frattini	C₂³	C₂⁴×D₆₁
Fitting	C₂×C₆₁×#401	C₂
socle	C₂⁴×C₆₁	C₂⁴
prime radical	C₂⁴×D₆₁	C₂³
hypercenter	C₂×#401	D₆₁
hypocenter	C₆₁	C₂²×#401
LCS	G ▷ C₂³×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂⁴ ◁ C₂×#401

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁⋊#401	C₂	semidirect
2. #401×D₆₁	C₂	direct (N × H)
4. C₂×C₆₁×#401	C₂	semidirect
6. C₆₁⋊#401	C₂²	semidirect
9. C₆₁×#401	C₂²	semidirect
39. C₂×D₆₁	#401	direct (N × H)
45. C₂×#401	D₆₁	direct (N × H)
47. C₂×C₆₁	C₂×#401	semidirect
49. D₆₁	C₂×#401	direct (N × H)
52. #401	C₂×D₆₁	direct (N × H)
56. C₆₁	C₂²×#401	semidirect
89. C₂	#401×D₆₁	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×C₆₁⋊#401	2
#401×D₆₁	2
C₂×#95×D₆₁	2
C₂×C₆₁×#401	2
C₂²×#401	61

Subgroups — C2×#401×D61 #29846306

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#401×D₆₁ #29846306