Group #21447617 — subgroups

Subgroups — #21447617

Order 7808.

160 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 81 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	C₄×C₈×D₆₁	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#11758185	C₂	1	1	yes	maximal, characteristic, complemented
3	#16839541	C₂	1	2	yes	maximal
4	C₁₆×Dic₆₁	C₂	1	2	yes	maximal, complemented
5	C₆₁×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×D₆₁	C₄	1	1	yes	characteristic
7	C₂×C₈×D₆₁	C₂²	1	1	yes	characteristic
8	C₄²×D₆₁	C₄	1	1	yes	characteristic
9	C₂×#11758185	C₂²	1	2	yes	—
10	C₄×#92418	C₄	1	1	yes	characteristic
11	C₈×Dic₆₁	C₄	1	1	yes	characteristic
12	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
13	C₂×C₁₆×C₆₁	C₂²	1	2	yes	—
14	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₆₁	C₈	1	1	yes	characteristic
16	C₂×C₄×D₆₁	C₈	1	1	yes	characteristic
17	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
20	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
21	C₄×Dic₆₁	C₈	1	1	yes	characteristic
22	C₄×Dic₆₁	C₈	1	1	yes	characteristic
23	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
24	C₂×#92418	C₂×C₄	1	1	yes	characteristic
25	C₂×#92418	C₂×C₄	1	1	yes	characteristic
26	C₈×D₆₁	—	2	1	no	—
27	C₈×D₆₁	—	2	1	no	—
28	C₈×D₆₁	—	2	2	no	—
29	C₁₆×C₆₁	—	2	2	no	—
30	#11758185	—	2	2	no	—
31	C₂²×D₆₁	C₂×C₈	1	1	yes	characteristic
32	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
33	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
34	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
35	C₂×Dic₆₁	C₂×C₈	1	1	yes	characteristic
36	C₂×Dic₆₁	C₂×C₈	1	1	yes	characteristic
37	C₂×Dic₆₁	C₂×C₈	1	1	yes	characteristic
38	C₄×D₆₁	—	2	1	no	—
39	C₄×D₆₁	—	2	1	no	—
40	C₄×D₆₁	—	2	2	no	—
41	C₄×D₆₁	C₁₆	1	4	yes	complemented
42	C₈×C₆₁	—	2	1	no	—
43	C₈×C₆₁	#41	1	1	yes	characteristic
44	C₈×C₆₁	#41	1	1	yes	characteristic
45	#92418	—	2	1	no	—
46	#92418	M₁₆	1	2	yes	—
47	C₂²×C₆₁	C₂²×C₈	1	1	yes	characteristic
48	C₂×D₆₁	—	2	1	no	—
49	C₂×D₆₁	—	2	1	no	—
50	C₂×D₆₁	C₂×C₁₆	1	2	yes	—
51	C₄×C₆₁	—	2	1	no	—
52	C₄×C₆₁	C₂×C₁₆	1	2	yes	—
53	C₄×C₆₁	#117	1	1	yes	characteristic
54	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
55	Dic₆₁	—	2	1	no	—
56	Dic₆₁	C₂×C₁₆	1	2	yes	—
57	Dic₆₁	M₃₂	1	2	yes	—
58	#2162	—	61	1	no	maximal, Sylow
59	C₂×C₆₁	#431	1	1	yes	characteristic
60	C₂×C₆₁	C₂²×C₁₆	1	1	yes	characteristic
61	C₂×C₆₁	C₂×M₃₂	1	1	yes	characteristic
62	D₆₁	—	2	2	no	—
63	C₂×C₄×C₈	—	61	1	no	—
64	C₄⋊C₁₆	—	61	1	no	—
65	C₄⋊C₁₆	D₆₁	1	1	yes	characteristic, complemented
66	C₂²⋊C₁₆	—	61	2	no	—
67	C₄×C₁₆	—	61	2	no	—
68	C₆₁	#2162	1	1	yes	characteristic, complemented, Sylow
69	C₂²×C₈	—	61	1	no	—
70	C₂²×C₈	—	61	1	no	—
71	C₂×C₄²	—	61	1	no	—
72	C₂×C₁₆	—	61	2	no	—
73	C₂×C₁₆	C₂×D₆₁	1	2	yes	—
74	C₄×C₈	—	61	1	no	—
75	C₄×C₈	—	61	1	no	—
76	C₄×C₈	—	61	1	no	—
77	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
78	C₂²×C₄	—	61	1	no	—
79	C₂²×C₄	—	61	1	no	—
80	C₂²×C₄	—	61	1	no	—
81	C₂×C₈	—	61	1	no	—
82	C₂×C₈	—	61	1	no	—
83	C₂×C₈	—	122	2	no	—
84	C₂×C₈	—	122	1	no	—
85	C₂×C₈	—	122	1	no	—
86	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
87	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
88	C₄²	—	61	1	no	—
89	C₄²	—	61	1	no	—
90	C₄²	—	61	1	no	—
91	C₄²	C₄×D₆₁	1	1	yes	characteristic
92	C₁₆	—	2	2	no	—
93	C₁₆	—	122	2	no	—
94	C₂³	—	61	1	no	—
95	C₂×C₄	—	61	1	no	—
96	C₂×C₄	—	61	1	no	—
97	C₂×C₄	—	61	4	no	—
98	C₂×C₄	—	61	1	no	—
99	C₂×C₄	—	122	2	no	—
100	C₂×C₄	—	122	1	no	—
101	C₂×C₄	—	122	1	no	—
102	C₂×C₄	C₈×D₆₁	1	1	yes	characteristic
103	C₂×C₄	C₈×D₆₁	1	1	yes	characteristic
104	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
105	C₈	—	2	1	no	—
106	C₈	—	61	2	no	—
107	C₈	—	122	1	no	—
108	C₈	#11758224	1	1	yes	characteristic
109	C₈	#11758226	1	1	yes	characteristic
110	C₂²	—	61	2	no	—
111	C₂²	—	122	1	no	—
112	C₂²	—	122	1	no	—
113	C₂²	C₂×C₈×D₆₁	1	1	yes	characteristic
114	C₄	—	2	1	no	—
115	C₄	—	61	2	no	—
116	C₄	—	61	2	no	—
117	C₄	—	122	1	no	—
118	C₄	C₁₆×D₆₁	1	2	yes	—
119	C₄	#14519735	1	1	yes	characteristic
120	C₄	M₁₆×D₆₁	1	1	yes	characteristic
121	C₂	—	122	2	no	—
122	C₂	#16839814	1	1	yes	characteristic
123	C₂	C₂×C₁₆×D₆₁	1	1	yes	characteristic
124	C₂	M₃₂×D₆₁	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×C₈×D₆₁

C₂

yes

maximal, characteristic

C₄⋊#11758185

C₂

yes

maximal, characteristic, complemented

#16839541

C₂

yes

maximal

C₁₆×Dic₆₁

C₂

yes

maximal, complemented

C₆₁×C₄⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₆₁

C₄

yes

characteristic

C₂×C₈×D₆₁

C₂²

yes

characteristic

C₄²×D₆₁

C₄

yes

characteristic

C₂×#11758185

C₂²

yes

—

C₄×#92418

C₄

yes

characteristic

C₈×Dic₆₁

C₄

yes

characteristic

C₈×Dic₆₁

C₂²

yes

characteristic

C₂×C₁₆×C₆₁

C₂²

yes

—

C₄×C₈×C₆₁

C₂²

yes

characteristic

C₂×C₄×D₆₁

C₈

yes

characteristic

C₂×C₄×D₆₁

C₈

yes

characteristic

C₂×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂³

yes

characteristic

C₄²×C₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₈

yes

characteristic

C₄×Dic₆₁

C₈

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

C₈×D₆₁

—

C₈×D₆₁

—

C₈×D₆₁

—

C₁₆×C₆₁

—

#11758185

—

C₂²×D₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

C₂×C₈

yes

characteristic

C₂×Dic₆₁

C₂×C₈

yes

characteristic

C₂×Dic₆₁

C₂×C₈

yes

characteristic

C₄×D₆₁

—

C₄×D₆₁

—

C₄×D₆₁

—

C₄×D₆₁

C₁₆

yes

complemented

C₈×C₆₁

—

C₈×C₆₁

yes

C₈×C₆₁

yes

—

M₁₆

yes

—

C₂²×C₆₁

C₂²×C₈

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

C₂×C₁₆

yes

—

C₄×C₆₁

—

C₄×C₆₁

C₂×C₁₆

yes

—

C₄×C₆₁

#117

yes

characteristic

C₄×C₆₁

C₂×M₁₆

yes

characteristic

Dic₆₁

—

Dic₆₁

C₂×C₁₆

yes

—

Dic₆₁

M₃₂

yes

—

—

C₂×C₆₁

yes

C₂×C₆₁

C₂²×C₁₆

yes

characteristic

C₂×C₆₁

C₂×M₃₂

yes

characteristic

D₆₁

—

C₂×C₄×C₈

—

C₄⋊C₁₆

—

C₄⋊C₁₆

D₆₁

yes

characteristic, complemented

C₂²⋊C₁₆

—

C₄×C₁₆

—

C₆₁

#2162

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₆₁

yes

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₆₁

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

C₄×D₆₁

yes

characteristic

C₂×C₈

C₂²×D₆₁

yes

characteristic

C₄²

—

C₄²

—

C₄²

—

C₄²

C₄×D₆₁

yes

characteristic

C₁₆

—

C₁₆

—

122

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

100

C₂×C₄

—

122

—

101

C₂×C₄

—

122

—

102

C₂×C₄

C₈×D₆₁

yes

characteristic

103

C₂×C₄

C₈×D₆₁

yes

characteristic

104

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

105

C₈

—

106

C₈

—

107

C₈

—

122

—

108

C₈

#11758224

yes

characteristic

109

C₈

#11758226

yes

characteristic

110

C₂²

—

111

C₂²

—

122

—

112

C₂²

—

122

—

113

C₂²

C₂×C₈×D₆₁

yes

characteristic

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

—

122

—

118

C₄

C₁₆×D₆₁

yes

—

119

C₄

#14519735

yes

characteristic

120

C₄

M₁₆×D₆₁

yes

characteristic

121

C₂

—

122

—

122

C₂

#16839814

yes

characteristic

123

C₂

C₂×C₁₆×D₆₁

yes

characteristic

124

C₂

M₃₂×D₆₁

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₆₁
commutator	C₂×C₆₁	C₂²×C₁₆
Fitting	C₆₁×C₄⋊C₁₆	C₂
socle	C₂²×C₆₁	C₂²×C₈
hypercenter	C₄⋊C₁₆	D₆₁
hypocenter	C₆₁	#2162
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₈ ◁ C₄⋊C₁₆

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₆₁

commutator

C₂×C₆₁

C₂²×C₁₆

Fitting

C₆₁×C₄⋊C₁₆

C₂

socle

C₂²×C₆₁

C₂²×C₈

hypercenter

C₄⋊C₁₆

D₆₁

C₆₁

G ▷ C₂×C₆₁ ▷ C₆₁

C₁ ◁ C₂×C₈ ◁ C₄⋊C₁₆

N	H ≅ G/N	type
2. C₄⋊#11758185	C₂	semidirect
4. C₁₆×Dic₆₁	C₂	semidirect
5. C₆₁×C₄⋊C₁₆	C₂	semidirect
41. C₄×D₆₁	C₁₆	semidirect
65. C₄⋊C₁₆	D₆₁	semidirect
68. C₆₁	#2162	semidirect

H ≅ G/N

type

2. C₄⋊#11758185

C₂

semidirect

4. C₁₆×Dic₆₁

C₂

semidirect

5. C₆₁×C₄⋊C₁₆

C₂

semidirect

41. C₄×D₆₁

C₁₆

semidirect

65. C₄⋊C₁₆

D₆₁

semidirect

68. C₆₁

#2162

semidirect

Subgroups — #21447617

Conjugacy classes of subgroups

Complements