Group #21460313 — subgroups

Subgroups — #21460313

Order 7808.

890 conjugacy classes of subgroups; only the 455 normal subgroups are shown.

normal subgroups only

This group has 890 conjugacy classes of subgroups — too many to draw. Only its 455 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁⋊#564	C₂	1	3	yes	maximal, complemented
2	#16840489	C₂	1	12	yes	maximal, complemented
3	#16840371	C₂	1	12	yes	maximal
4	#16840318	C₂	1	3	yes	maximal
5	C₆₁×#564	C₂	1	1	yes	maximal, characteristic, complemented
6	#14519776	C₂²	1	6	yes	—
7	#14519776	C₂²	1	12	yes	—
8	#14519772	C₂²	1	12	yes	—
9	#14519771	C₂²	1	4	yes	—
10	#14519769	C₂²	1	3	yes	—
11	#14519768	C₂²	1	12	yes	—
12	#14519767	C₂²	1	12	yes	—
13	#14519767	C₂²	1	12	yes	—
14	#14519767	C₂²	1	12	yes	—
15	#14519755	C₂²	1	12	yes	—
16	C₄×Dic₁₂₂	C₂²	1	12	yes	—
17	#14519742	C₂²	1	12	yes	—
18	#14519742	C₂²	1	12	yes	—
19	#14519735	C₂²	1	6	yes	—
20	C₄²×D₆₁	C₂²	1	1	yes	characteristic
21	#125×C₆₁	C₂²	1	12	yes	—
22	#125×C₆₁	C₂²	1	3	yes	—
23	C₂×C₄×D₆₁	C₂³	1	3	yes	—
24	C₂×Dic₁₂₂	C₂³	1	12	yes	—
25	C₄⋊C₄×C₆₁	C₂³	1	6	yes	—
26	C₄⋊C₄×C₆₁	C₂³	1	12	yes	—
27	C₄⋊C₄×C₆₁	C₂³	1	12	yes	—
28	C₄²×C₆₁	C₂³	1	1	yes	characteristic
29	C₄²×C₆₁	C₂³	1	4	yes	—
30	#11758198	C₂³	1	12	yes	—
31	C₄⋊Dic₆₁	C₂³	1	6	yes	—
32	C₄⋊Dic₆₁	C₂³	1	12	yes	—
33	#11758196	C₂³	1	12	yes	—
34	#11758196	C₂³	1	12	yes	—
35	#11758196	C₂³	1	12	yes	—
36	#11758196	C₂³	1	12	yes	—
37	C₄×Dic₆₁	C₂³	1	3	yes	—
38	C₄×Dic₆₁	C₂³	1	12	yes	—
39	C₄×Dic₆₁	C₂³	1	12	yes	—
40	C₂²×D₆₁	C₂⁴	1	1	yes	characteristic
41	C₂×C₄×C₆₁	C₂⁴	1	12	yes	—
42	C₂×C₄×C₆₁	C₂⁴	1	3	yes	—
43	C₂×Dic₆₁	C₂⁴	1	12	yes	—
44	C₂×Dic₆₁	C₂⁴	1	3	yes	—
45	C₄×D₆₁	—	2	6	no	—
46	Dic₁₂₂	—	2	24	no	—
47	C₂²×C₆₁	C₂⁵	1	1	yes	characteristic
48	C₂×D₆₁	—	2	3	no	—
49	C₄×C₆₁	—	2	12	no	—
50	C₄×C₆₁	—	2	3	no	—
51	Dic₆₁	—	2	12	no	—
52	Dic₆₁	2₋¹⁺⁴	1	6	yes	—
53	#3556	—	61	1	no	maximal, Sylow
54	C₂×C₆₁	C₂×2₋¹⁺⁴	1	3	yes	—
55	D₆₁	—	4	1	no	—
56	#564	—	61	3	no	—
57	#564	D₆₁	1	1	yes	characteristic, complemented
58	#557	—	61	12	no	—
59	#541	—	61	12	no	—
60	#533	—	61	3	no	—
61	C₆₁	#3556	1	1	yes	characteristic, complemented, Sylow
62	C₄⋊Q₈	—	61	6	no	—
63	C₄⋊Q₈	—	61	12	no	—
64	#126	—	61	12	no	—
65	#126	—	61	4	no	—
66	#125	—	61	12	no	—
67	#125	—	61	12	no	—
68	#125	—	61	12	no	—
69	#125	—	61	12	no	—
70	#125	—	61	3	no	—
71	#125	C₂×D₆₁	1	3	yes	—
72	#125	C₂×D₆₁	1	12	yes	—
73	C₂²⋊Q₈	—	61	12	no	—
74	C₄×Q₈	—	61	12	no	—
75	C₄×Q₈	—	61	12	no	—
76	C₄×Q₈	—	61	12	no	—
77	#117	—	61	6	no	—
78	C₂×C₄²	—	61	1	no	—
79	C₂×Q₈	—	61	12	no	—
80	C₂²×C₄	—	61	3	no	—
81	C₄⋊C₄	—	61	12	no	—
82	C₄⋊C₄	—	61	12	no	—
83	C₄⋊C₄	—	61	12	no	—
84	C₄⋊C₄	—	61	12	no	—
85	C₄⋊C₄	—	61	6	no	—
86	C₄⋊C₄	—	61	12	no	—
87	C₄⋊C₄	C₂²×D₆₁	1	6	yes	—
88	C₄⋊C₄	C₂²×D₆₁	1	12	yes	—
89	C₄⋊C₄	C₂²×D₆₁	1	12	yes	—
90	C₂²⋊C₄	—	61	12	no	—
91	C₄²	—	61	3	no	—
92	C₄²	—	61	12	no	—
93	C₄²	—	61	12	no	—
94	C₄²	C₂²×D₆₁	1	1	yes	characteristic
95	C₄²	C₂²×D₆₁	1	4	yes	—
96	C₂³	—	61	1	no	—
97	Q₈	—	122	24	no	—
98	C₂×C₄	—	61	3	no	—
99	C₂×C₄	—	61	12	no	—
100	C₂×C₄	—	122	6	no	—
101	C₂×C₄	C₂³×D₆₁	1	12	yes	—
102	C₂×C₄	C₂³×D₆₁	1	3	yes	—
103	C₂²	—	122	3	no	—
104	C₂²	C₂⁴×D₆₁	1	1	yes	characteristic
105	C₄	—	2	3	no	—
106	C₄	—	2	12	no	—
107	C₄	—	61	6	no	—
108	C₄	—	122	12	no	—
109	C₂	—	244	1	no	—
110	C₂	2₋¹⁺⁴×D₆₁	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₆₁⋊#564

C₂

yes

maximal, complemented

#16840489

C₂

yes

maximal, complemented

#16840371

C₂

yes

maximal

#16840318

C₂

yes

maximal

C₆₁×#564

C₂

yes

maximal, characteristic, complemented

#14519776

C₂²

yes

—

#14519776

C₂²

yes

—

#14519772

C₂²

yes

—

#14519771

C₂²

yes

—

#14519769

C₂²

yes

—

#14519768

C₂²

yes

—

#14519767

C₂²

yes

—

#14519767

C₂²

yes

—

#14519767

C₂²

yes

—

#14519755

C₂²

yes

—

C₄×Dic₁₂₂

C₂²

yes

—

#14519742

C₂²

yes

—

#14519742

C₂²

yes

—

#14519735

C₂²

yes

—

C₄²×D₆₁

C₂²

yes

characteristic

#125×C₆₁

C₂²

yes

—

#125×C₆₁

C₂²

yes

—

C₂×C₄×D₆₁

C₂³

yes

—

C₂×Dic₁₂₂

C₂³

yes

—

C₄⋊C₄×C₆₁

C₂³

yes

—

C₄⋊C₄×C₆₁

C₂³

yes

—

C₄⋊C₄×C₆₁

C₂³

yes

—

C₄²×C₆₁

C₂³

yes

characteristic

C₄²×C₆₁

C₂³

yes

—

#11758198

C₂³

yes

—

C₄⋊Dic₆₁

C₂³

yes

—

C₄⋊Dic₆₁

C₂³

yes

—

#11758196

C₂³

yes

—

#11758196

C₂³

yes

—

#11758196

C₂³

yes

—

#11758196

C₂³

yes

—

C₄×Dic₆₁

C₂³

yes

—

C₄×Dic₆₁

C₂³

yes

—

C₄×Dic₆₁

C₂³

yes

—

C₂²×D₆₁

C₂⁴

yes

characteristic

C₂×C₄×C₆₁

C₂⁴

yes

—

C₂×C₄×C₆₁

C₂⁴

yes

—

C₂×Dic₆₁

C₂⁴

yes

—

C₂×Dic₆₁

C₂⁴

yes

—

C₄×D₆₁

—

Dic₁₂₂

—

C₂²×C₆₁

C₂⁵

yes

characteristic

C₂×D₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

Dic₆₁

—

Dic₆₁

2₋¹⁺⁴

yes

—

#3556

—

maximal, Sylow

C₂×C₆₁

C₂×2₋¹⁺⁴

yes

—

D₆₁

—

#564

—

#564

D₆₁

yes

characteristic, complemented

#557

—

#541

—

#533

—

C₆₁

#3556

yes

characteristic, complemented, Sylow

C₄⋊Q₈

—

C₄⋊Q₈

—

—

—

—

—

—

—

—

C₂×D₆₁

yes

—

#125

C₂×D₆₁

yes

—

C₂²⋊Q₈

—

C₄×Q₈

—

C₄×Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

—

C₂×Q₈

—

C₂²×C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂²×D₆₁

yes

—

C₄⋊C₄

C₂²×D₆₁

yes

—

C₄⋊C₄

C₂²×D₆₁

yes

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂²×D₆₁

yes

characteristic

C₄²

C₂²×D₆₁

yes

—

C₂³

—

Q₈

—

122

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

122

—

101

C₂×C₄

C₂³×D₆₁

yes

—

102

C₂×C₄

C₂³×D₆₁

yes

—

103

C₂²

—

122

—

104

C₂²

C₂⁴×D₆₁

yes

characteristic

105

C₄

—

106

C₄

—

107

C₄

—

108

C₄

—

122

—

109

C₂

—

244

—

110

C₂

2₋¹⁺⁴×D₆₁

yes

—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₁
commutator, socle	C₂²×C₆₁	C₂⁵
Fitting	C₆₁×#564	C₂
hypercenter	#564	D₆₁
hypocenter	C₆₁	#3556
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ #564

subgroup

G/H

center, Frattini

C₂²

C₂⁴×D₆₁

commutator, socle

C₂²×C₆₁

C₂⁵

Fitting

C₆₁×#564

C₂

D₆₁

C₆₁

G ▷ C₂²×C₆₁ ▷ C₆₁

C₁ ◁ C₂² ◁ #564

N	H ≅ G/N	type
1. C₆₁⋊#564	C₂	semidirect
2. #16840489	C₂	semidirect
5. C₆₁×#564	C₂	semidirect
57. #564	D₆₁	semidirect
61. C₆₁	#3556	semidirect

H ≅ G/N

type

1. C₆₁⋊#564

C₂

semidirect

2. #16840489

C₂

semidirect

5. C₆₁×#564

C₂

semidirect

57. #564

D₆₁

semidirect

61. C₆₁

#3556

semidirect

Subgroups — #21460313

Conjugacy classes of subgroups

Complements