Group #21462047 — subgroups

Subgroups — #21462047

Order 7808.

260 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 82 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	C₂×#14519852	C₂	1	2	yes	maximal, complemented
2	#16840657	C₂	1	2	yes	maximal, complemented
3	C₂²⋊#11758187	C₂	1	2	yes	maximal, complemented
4	C₂²×C₈×D₆₁	C₂	1	1	yes	maximal, characteristic
5	#14519852	—	2	4	no	—
6	C₂×#11758187	C₂²	1	4	yes	complemented
7	C₂²×C₄×D₆₁	C₄	1	1	yes	characteristic
8	C₂²×#92418	C₂²	1	1	yes	characteristic
9	C₂×C₈×D₆₁	—	2	4	no	—
10	C₂×C₈×D₆₁	C₄	1	1	yes	characteristic
11	C₂×C₈×D₆₁	C₄	1	1	yes	characteristic
12	C₂×C₈×D₆₁	C₂²	1	1	yes	characteristic
13	C₂×C₈×D₆₁	C₂²	1	1	yes	characteristic
14	C₂²×C₈×C₆₁	C₄	1	1	yes	characteristic
15	C₂³×D₆₁	C₈	1	1	yes	characteristic
16	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
17	C₂²×Dic₆₁	C₈	1	1	yes	characteristic
18	C₂×C₄×D₆₁	—	2	2	no	—
19	C₂×C₄×D₆₁	—	2	2	no	—
20	C₂×C₄×D₆₁	C₈	1	1	yes	characteristic
21	C₂×C₄×D₆₁	C₈	1	1	yes	characteristic
22	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₆₁	—	2	2	no	—
25	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
26	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
27	C₂×#92418	—	2	2	no	—
28	C₂×#92418	C₂×C₄	1	1	yes	characteristic
29	C₂×#92418	C₂³	1	1	yes	characteristic
30	C₈×D₆₁	—	2	2	no	—
31	C₈×D₆₁	—	2	2	no	—
32	C₈×D₆₁	—	2	2	no	—
33	C₈×D₆₁	D₄	1	4	yes	—
34	#11758187	—	2	4	no	—
35	C₂³×C₆₁	C₂×C₈	1	1	yes	characteristic
36	C₂²×D₆₁	—	2	2	no	—
37	C₂²×D₆₁	—	2	2	no	—
38	C₂²×D₆₁	—	2	2	no	—
39	C₂²×D₆₁	C₂×C₈	1	1	yes	characteristic
40	C₂²×D₆₁	C₂×C₈	1	1	yes	characteristic
41	C₂×C₄×C₆₁	—	2	1	no	—
42	C₂×C₄×C₆₁	—	2	1	no	—
43	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
44	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
45	C₂×Dic₆₁	—	2	2	no	—
46	C₂×Dic₆₁	C₂×C₈	1	1	yes	characteristic
47	C₂×Dic₆₁	C₂×C₈	1	1	yes	characteristic
48	C₄×D₆₁	—	2	2	no	—
49	C₄×D₆₁	—	2	1	no	—
50	C₄×D₆₁	—	2	1	no	—
51	C₄×D₆₁	—	2	2	no	—
52	C₄×D₆₁	C₂²⋊C₄	1	2	yes	—
53	C₄×D₆₁	M₁₆	1	2	yes	—
54	C₈×C₆₁	—	2	1	no	—
55	C₈×C₆₁	C₂²⋊C₄	1	2	yes	—
56	#92418	—	2	1	no	—
57	#92418	C₂×D₄	1	2	yes	—
58	C₂²×C₆₁	—	2	1	no	—
59	C₂²×C₆₁	—	2	1	no	—
60	C₂²×C₆₁	M₃₂	1	2	yes	complemented
61	C₂²×C₆₁	C₂²×C₈	1	1	yes	characteristic
62	C₂×D₆₁	—	2	8	no	—
63	C₂×D₆₁	—	2	1	no	—
64	C₂×D₆₁	—	2	1	no	—
65	C₂×D₆₁	—	2	1	no	—
66	C₂×D₆₁	—	2	1	no	—
67	C₂×D₆₁	C₂²⋊C₈	1	2	yes	—
68	C₂×D₆₁	M₃₂	1	2	yes	complemented
69	C₄×C₆₁	—	2	1	no	—
70	C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
71	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
72	Dic₆₁	—	2	1	no	—
73	Dic₆₁	C₂²⋊C₈	1	2	yes	—
74	#2112	—	61	1	no	maximal, Sylow
75	C₂×C₆₁	—	2	2	no	—
76	C₂×C₆₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
77	C₂×C₆₁	C₂×M₃₂	1	1	yes	characteristic
78	C₂×C₆₁	C₂×M₃₂	1	1	yes	characteristic
79	D₆₁	—	2	2	no	—
80	D₆₁	—	2	2	no	—
81	C₂³×C₈	—	61	1	no	—
82	C₂×M₃₂	—	61	2	no	—
83	C₂²⋊C₁₆	—	61	2	no	—
84	C₂²⋊C₁₆	—	61	2	no	—
85	C₆₁	#2112	1	1	yes	characteristic, complemented, Sylow
86	C₂³×C₄	—	61	1	no	—
87	C₂²×C₈	—	61	1	no	—
88	C₂²×C₈	—	61	1	no	—
89	C₂²×C₈	—	61	1	no	—
90	C₂²×C₈	—	61	1	no	—
91	C₂²×C₈	—	61	1	no	—
92	C₂²×C₈	—	122	4	no	—
93	C₂²×C₈	#6923	1	1	yes	characteristic
94	M₃₂	—	122	4	no	—
95	C₂×C₁₆	—	61	4	no	—
96	C₂⁴	—	61	1	no	—
97	C₂²×C₄	—	61	1	no	—
98	C₂²×C₄	—	61	1	no	—
99	C₂²×C₄	—	61	1	no	—
100	C₂²×C₄	—	61	1	no	—
101	C₂²×C₄	—	61	1	no	—
102	C₂²×C₄	—	122	2	no	—
103	C₂²×C₄	—	122	2	no	—
104	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
105	C₂×C₈	—	2	2	no	—
106	C₂×C₈	—	61	1	no	—
107	C₂×C₈	—	61	4	no	—
108	C₂×C₈	—	61	1	no	—
109	C₂×C₈	—	122	2	no	—
110	C₂×C₈	—	122	2	no	—
111	C₂×C₈	—	122	2	no	—
112	C₂×C₈	—	122	2	no	—
113	C₂×C₈	C₂×#6923	1	1	yes	characteristic
114	C₂×C₈	C₂×#6923	1	1	yes	characteristic
115	C₁₆	—	122	4	no	—
116	C₂³	—	61	1	no	—
117	C₂³	—	61	1	no	—
118	C₂³	—	122	2	no	—
119	C₂³	—	122	2	no	—
120	C₂³	—	122	2	no	—
121	C₂³	D₆₁⋊C₈	1	1	yes	characteristic
122	C₂×C₄	—	2	1	no	—
123	C₂×C₄	—	2	1	no	—
124	C₂×C₄	—	61	1	no	—
125	C₂×C₄	—	61	2	no	—
126	C₂×C₄	—	61	2	no	—
127	C₂×C₄	—	61	1	no	—
128	C₂×C₄	—	122	2	no	—
129	C₂×C₄	—	122	2	no	—
130	C₂×C₄	—	122	2	no	—
131	C₂×C₄	—	122	1	no	—
132	C₂×C₄	—	122	1	no	—
133	C₂×C₄	D₆₁⋊C₈	1	1	yes	characteristic
134	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
135	C₈	—	2	1	no	—
136	C₈	—	61	2	no	—
137	C₈	—	122	1	no	—
138	C₈	C₂²⋊#6923	1	2	yes	—
139	C₂²	—	2	1	no	—
140	C₂²	—	2	1	no	—
141	C₂²	—	61	2	no	—
142	C₂²	—	61	2	no	—
143	C₂²	—	122	8	no	—
144	C₂²	—	122	1	no	—
145	C₂²	—	122	1	no	—
146	C₂²	—	122	1	no	—
147	C₂²	—	122	1	no	—
148	C₂²	#14519852	1	2	yes	complemented
149	C₂²	C₂×D₆₁⋊C₈	1	1	yes	characteristic
150	C₄	—	2	1	no	—
151	C₄	—	61	2	no	—
152	C₄	—	122	1	no	—
153	C₄	C₂×C₂²⋊#6923	1	1	yes	characteristic
154	C₄	D₆₁⋊M₁₆	1	1	yes	characteristic
155	C₂	—	2	2	no	—
156	C₂	—	122	2	no	—
157	C₂	—	122	2	no	—
158	C₂	D₆₁⋊(C₂²⋊C₈)	1	1	yes	characteristic
159	C₂	D₆₁⋊M₃₂	1	1	yes	characteristic
160	C₂	C₂×#14519852	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519852

C₂

yes

maximal, complemented

#16840657

C₂

yes

maximal, complemented

C₂²⋊#11758187

C₂

yes

maximal, complemented

C₂²×C₈×D₆₁

C₂

yes

maximal, characteristic

#14519852

—

C₂×#11758187

C₂²

yes

complemented

C₂²×C₄×D₆₁

C₄

yes

characteristic

C₂²×#92418

C₂²

yes

characteristic

C₂×C₈×D₆₁

—

C₂×C₈×D₆₁

C₄

yes

characteristic

C₂×C₈×D₆₁

C₄

yes

characteristic

C₂×C₈×D₆₁

C₂²

yes

characteristic

C₂×C₈×D₆₁

C₂²

yes

characteristic

C₂²×C₈×C₆₁

C₄

yes

characteristic

C₂³×D₆₁

C₈

yes

characteristic

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂²×Dic₆₁

C₈

yes

characteristic

C₂×C₄×D₆₁

—

C₂×C₄×D₆₁

—

C₂×C₄×D₆₁

C₈

yes

characteristic

C₂×C₄×D₆₁

C₈

yes

characteristic

C₂×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×#92418

—

C₂×#92418

C₂×C₄

yes

characteristic

C₂×#92418

C₂³

yes

characteristic

C₈×D₆₁

—

C₈×D₆₁

—

C₈×D₆₁

—

C₈×D₆₁

D₄

yes

—

#11758187

—

C₂³×C₆₁

C₂×C₈

yes

characteristic

C₂²×D₆₁

—

C₂²×D₆₁

—

C₂²×D₆₁

—

C₂²×D₆₁

C₂×C₈

yes

characteristic

C₂²×D₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

C₂×C₈

yes

characteristic

C₂×Dic₆₁

C₂×C₈

yes

characteristic

C₄×D₆₁

—

C₄×D₆₁

—

C₄×D₆₁

—

C₄×D₆₁

—

C₄×D₆₁

C₂²⋊C₄

yes

—

C₄×D₆₁

M₁₆

yes

—

C₈×C₆₁

—

C₈×C₆₁

C₂²⋊C₄

yes

—

#92418

—

#92418

C₂×D₄

yes

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

M₃₂

yes

complemented

C₂²×C₆₁

C₂²×C₈

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

C₂²⋊C₈

yes

—

C₂×D₆₁

M₃₂

yes

complemented

C₄×C₆₁

—

C₄×C₆₁

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₆₁

C₂×M₁₆

yes

characteristic

Dic₆₁

—

Dic₆₁

C₂²⋊C₈

yes

—

#2112

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

C₂×C₂²⋊C₈

yes

characteristic

C₂×C₆₁

C₂×M₃₂

yes

characteristic

C₂×C₆₁

C₂×M₃₂

yes

characteristic

D₆₁

—

D₆₁

—

C₂³×C₈

—

C₂×M₃₂

—

C₂²⋊C₁₆

—

C₂²⋊C₁₆

—

C₆₁

#2112

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

122

—

C₂²×C₈

#6923

yes

characteristic

M₃₂

—

122

—

C₂×C₁₆

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

—

122

—

103

C₂²×C₄

—

122

—

104

C₂²×C₄

C₂×#6923

yes

characteristic

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

122

—

110

C₂×C₈

—

122

—

111

C₂×C₈

—

122

—

112

C₂×C₈

—

122

—

113

C₂×C₈

C₂×#6923

yes

characteristic

114

C₂×C₈

C₂×#6923

yes

characteristic

115

C₁₆

—

122

—

116

C₂³

—

117

C₂³

—

118

C₂³

—

122

—

119

C₂³

—

122

—

120

C₂³

—

122

—

121

C₂³

D₆₁⋊C₈

yes

characteristic

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

122

—

129

C₂×C₄

—

122

—

130

C₂×C₄

—

122

—

131

C₂×C₄

—

122

—

132

C₂×C₄

—

122

—

133

C₂×C₄

D₆₁⋊C₈

yes

characteristic

134

C₂×C₄

C₂²×#6923

yes

characteristic

135

C₈

—

136

C₈

—

137

C₈

—

122

—

138

C₈

C₂²⋊#6923

yes

—

139

C₂²

—

140

C₂²

—

141

C₂²

—

142

C₂²

—

143

C₂²

—

122

—

144

C₂²

—

122

—

145

C₂²

—

122

—

146

C₂²

—

122

—

147

C₂²

—

122

—

148

C₂²

#14519852

yes

complemented

149

C₂²

C₂×D₆₁⋊C₈

yes

characteristic

150

C₄

—

151

C₄

—

152

C₄

—

122

—

153

C₄

C₂×C₂²⋊#6923

yes

characteristic

154

C₄

D₆₁⋊M₁₆

yes

characteristic

155

C₂

—

156

C₂

—

122

—

157

C₂

—

122

—

158

C₂

D₆₁⋊(C₂²⋊C₈)

yes

characteristic

159

C₂

D₆₁⋊M₃₂

yes

characteristic

160

C₂

C₂×#14519852

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#6923
commutator, socle	C₂²×C₆₁	C₂²×C₈
Fitting	C₂²×C₈×C₆₁	C₄
hypercenter	C₂²×C₈	#6923
hypocenter	C₆₁	#2112
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#6923

commutator, socle

C₂²×C₆₁

C₂²×C₈

Fitting

C₂²×C₈×C₆₁

C₄

C₂²×C₈

C₆₁

G ▷ C₂²×C₆₁ ▷ C₆₁

C₁ ◁ C₂×C₄ ◁ C₂²×C₈

N	H ≅ G/N	type
1. C₂×#14519852	C₂	semidirect
2. #16840657	C₂	semidirect
3. C₂²⋊#11758187	C₂	semidirect
6. C₂×#11758187	C₂²	semidirect
60. C₂²×C₆₁	M₃₂	semidirect
68. C₂×D₆₁	M₃₂	semidirect
85. C₆₁	#2112	semidirect
148. C₂²	#14519852	semidirect

H ≅ G/N

type

1. C₂×#14519852

C₂

semidirect

2. #16840657

C₂

semidirect

3. C₂²⋊#11758187

C₂

semidirect

6. C₂×#11758187

C₂²

semidirect

60. C₂²×C₆₁

M₃₂

semidirect

68. C₂×D₆₁

M₃₂

semidirect

85. C₆₁

#2112

semidirect

148. C₂²

#14519852

semidirect

Subgroups — #21462047

Conjugacy classes of subgroups

Complements