Group #20247047 — subgroups

Subgroups — #20247047

Order 6016.

852 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 852 conjugacy classes of subgroups — too many to draw. Only its 181 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	C₂³×Dic₉₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13094011	C₂	1	2	yes	maximal, complemented
3	#15689035	C₂	1	4	yes	maximal, complemented
4	#15689028	C₂	1	2	yes	maximal, complemented
5	#15689003	C₂	1	4	yes	maximal, complemented
6	C₄×C₂²⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#121×C₄₇	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₉₄	—	2	4	no	—
9	C₂²×Dic₉₄	—	2	8	no	—
10	C₂²×Dic₉₄	C₂²	1	2	yes	—
11	C₂²×Dic₉₄	C₂²	1	2	yes	—
12	C₂³×Dic₄₇	C₂²	1	2	yes	—
13	#13094011	—	2	8	no	—
14	C₂×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
15	C₂×C₂²⋊Dic₄₇	C₂²	1	8	yes	—
16	C₂×C₄×Dic₄₇	C₂²	1	2	yes	—
17	C₄₇⋊#95	C₂²	1	2	yes	—
18	C₄₇⋊#95	C₂²	1	8	yes	—
19	C₂²×D₄×C₄₇	C₂²	1	2	yes	—
20	C₂²×D₄×C₄₇	C₂²	1	1	yes	characteristic
21	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
22	#121×C₄₇	—	2	4	no	—
23	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
25	C₂⁴×C₄₇	C₂³	1	2	yes	—
26	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
27	C₂×D₄×C₄₇	—	2	4	no	—
28	C₂×D₄×C₄₇	—	2	8	no	—
29	C₂×D₄×C₄₇	—	2	2	no	—
30	C₂×D₄×C₄₇	—	2	4	no	—
31	C₂²×C₄×C₄₇	—	2	4	no	—
32	C₂²×C₄×C₄₇	D₄	1	4	yes	—
33	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
34	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
35	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
36	C₂²×Dic₄₇	—	2	4	no	—
37	C₂²×Dic₄₇	—	2	8	no	—
38	C₂²×Dic₄₇	C₂³	1	4	yes	—
39	C₂²×Dic₄₇	C₂³	1	4	yes	—
40	C₂×Dic₉₄	—	2	32	no	—
41	C₂×Dic₉₄	—	2	4	no	—
42	C₂×Dic₉₄	—	2	4	no	—
43	C₂×Dic₉₄	—	2	4	no	—
44	C₂×Dic₉₄	—	2	8	no	—
45	C₂×Dic₉₄	D₄	1	8	yes	complemented
46	C₄⋊C₄×C₄₇	—	2	2	no	—
47	C₂²⋊C₄×C₄₇	—	2	4	no	—
48	C₂²⋊Dic₄₇	—	2	4	no	—
49	C₂²⋊Dic₄₇	—	2	16	no	—
50	C₄×Dic₄₇	—	2	4	no	—
51	C₂³×C₄₇	—	2	2	no	—
52	C₂³×C₄₇	—	2	2	no	—
53	C₂³×C₄₇	—	2	4	no	—
54	C₂³×C₄₇	—	2	2	no	—
55	C₂³×C₄₇	—	2	4	no	—
56	C₂³×C₄₇	—	2	4	no	—
57	C₂³×C₄₇	C₂×D₄	1	2	yes	—
58	C₂³×C₄₇	#41	1	4	yes	—
59	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
60	D₄×C₄₇	—	4	8	no	—
61	D₄×C₄₇	—	4	4	no	—
62	C₂×C₄×C₄₇	—	2	2	no	—
63	C₂×C₄×C₄₇	—	2	8	no	—
64	C₂×C₄×C₄₇	—	2	2	no	—
65	C₂×C₄×C₄₇	—	2	4	no	—
66	C₂×C₄×C₄₇	C₂×D₄	1	4	yes	—
67	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
68	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
69	C₂×Dic₄₇	—	2	16	no	—
70	C₂×Dic₄₇	—	2	4	no	—
71	C₂×Dic₄₇	—	2	4	no	—
72	C₂×Dic₄₇	—	2	4	no	—
73	C₂×Dic₄₇	—	2	4	no	—
74	C₂×Dic₄₇	—	2	4	no	—
75	C₂×Dic₄₇	C₂×D₄	1	8	yes	—
76	Dic₉₄	—	2	16	no	—
77	Dic₉₄	—	2	16	no	—
78	C₂²×C₄₇	—	2	2	no	—
79	C₂²×C₄₇	—	2	2	no	—
80	C₂²×C₄₇	—	2	8	no	—
81	C₂²×C₄₇	—	4	2	no	—
82	C₂²×C₄₇	—	4	2	no	—
83	C₂²×C₄₇	—	4	2	no	—
84	C₂²×C₄₇	—	4	8	no	—
85	C₂²×C₄₇	#124	1	4	yes	complemented
86	C₂²×C₄₇	C₂²×D₄	1	2	yes	—
87	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
88	C₂²×C₄₇	C₂×#41	1	2	yes	—
89	C₂²×C₄₇	2₋¹⁺⁴	1	2	yes	—
90	C₄×C₄₇	—	2	2	no	—
91	C₄×C₄₇	—	4	2	no	—
92	C₄×C₄₇	#120	1	4	yes	—
93	Dic₄₇	—	2	8	no	—
94	Dic₄₇	—	4	4	no	—
95	#2436	—	47	1	no	maximal, Sylow
96	C₂×C₄₇	—	2	4	no	—
97	C₂×C₄₇	—	8	2	no	—
98	C₂×C₄₇	C₂×#120	1	1	yes	characteristic
99	C₂×C₄₇	C₂×#124	1	1	yes	characteristic
100	C₂×C₄₇	#536	1	1	yes	characteristic
101	C₂×C₄₇	#548	1	4	yes	—
102	C₂³×Q₈	—	47	1	no	—
103	C₂×#124	—	47	2	no	—
104	C₂×#121	D₄₇	1	1	yes	characteristic
105	#393	—	47	4	no	—
106	#391	—	47	2	no	—
107	#386	—	47	4	no	—
108	C₄×C₂²⋊C₄	—	47	1	no	—
109	C₄₇	#2436	1	1	yes	characteristic, complemented, Sylow
110	C₂²×Q₈	—	47	2	no	—
111	C₂²×Q₈	—	47	2	no	—
112	C₂²×Q₈	—	94	8	no	—
113	C₂²×Q₈	—	94	4	no	—
114	C₂²×D₄	C₂×D₄₇	1	1	yes	characteristic
115	C₂²×D₄	C₂×D₄₇	1	2	yes	—
116	C₂³×C₄	—	47	2	no	—
117	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
118	#124	—	94	8	no	—
119	#121	—	2	4	no	—
120	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
121	C₂×C₂²⋊C₄	—	47	8	no	—
122	C₂×C₂²⋊C₄	—	47	2	no	—
123	C₂×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
124	C₂×C₄²	—	47	2	no	—
125	#95	—	47	2	no	—
126	#95	—	47	8	no	—
127	C₂⁴	C₂²×D₄₇	1	2	yes	—
128	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
129	C₂×Q₈	—	47	8	no	—
130	C₂×Q₈	—	94	8	no	—
131	C₂×Q₈	—	94	32	no	—
132	C₂×Q₈	—	94	4	no	—
133	C₂×Q₈	—	94	4	no	—
134	C₂×Q₈	—	94	4	no	—
135	C₂×D₄	—	2	8	no	—
136	C₂×D₄	—	2	4	no	—
137	C₂×D₄	—	2	4	no	—
138	C₂×D₄	—	2	2	no	—
139	C₂²×C₄	—	2	4	no	—
140	C₂²×C₄	—	47	4	no	—
141	C₂²×C₄	—	47	4	no	—
142	C₂²×C₄	—	94	8	no	—
143	C₂²×C₄	—	94	4	no	—
144	C₂²×C₄	C₂²⋊D₄₇	1	4	yes	—
145	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
146	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
147	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
148	C₄⋊C₄	—	2	2	no	—
149	C₂²⋊C₄	—	2	4	no	—
150	C₂²⋊C₄	—	94	16	no	—
151	C₂²⋊C₄	—	94	4	no	—
152	C₄²	—	94	4	no	—
153	C₂³	—	2	2	no	—
154	C₂³	—	2	2	no	—
155	C₂³	—	2	4	no	—
156	C₂³	—	2	2	no	—
157	C₂³	—	2	4	no	—
158	C₂³	—	2	4	no	—
159	C₂³	#10625352	1	4	yes	—
160	C₂³	C₂×C₂²⋊D₄₇	1	2	yes	—
161	C₂³	C₂³×D₄₇	1	1	yes	characteristic
162	Q₈	—	94	16	no	—
163	Q₈	—	94	16	no	—
164	D₄	—	4	8	no	—
165	D₄	—	4	4	no	—
166	C₂×C₄	—	2	2	no	—
167	C₂×C₄	—	2	8	no	—
168	C₂×C₄	—	2	2	no	—
169	C₂×C₄	—	2	4	no	—
170	C₂×C₄	—	47	8	no	—
171	C₂×C₄	—	94	16	no	—
172	C₂×C₄	—	94	4	no	—
173	C₂×C₄	—	94	4	no	—
174	C₂×C₄	—	94	4	no	—
175	C₂×C₄	—	94	4	no	—
176	C₂×C₄	—	94	4	no	—
177	C₂×C₄	D₄×D₄₇	1	4	yes	—
178	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
179	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
180	C₂²	—	2	8	no	—
181	C₂²	—	2	2	no	—
182	C₂²	—	2	2	no	—
183	C₂²	—	4	8	no	—
184	C₂²	—	4	2	no	—
185	C₂²	—	4	2	no	—
186	C₂²	—	4	2	no	—
187	C₂²	#13094011	1	4	yes	complemented
188	C₂²	C₂×D₄×D₄₇	1	2	yes	—
189	C₂²	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
190	C₂²	C₂×#10625352	1	2	yes	—
191	C₂²	#13094071	1	2	yes	—
192	C₄	—	2	2	no	—
193	C₄	—	4	2	no	—
194	C₄	—	94	8	no	—
195	C₄	—	188	4	no	—
196	C₄	#13093992	1	4	yes	—
197	C₂	—	2	4	no	—
198	C₂	—	8	2	no	—
199	C₂	C₂×#13093992	1	1	yes	characteristic
200	C₂	C₂×#13094011	1	1	yes	characteristic
201	C₂	#15689694	1	1	yes	characteristic
202	C₂	#15689779	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂³×Dic₉₄

C₂

yes

maximal, characteristic, complemented

C₂×#13094011

C₂

yes

maximal, complemented

#15689035

C₂

yes

maximal, complemented

#15689028

C₂

yes

maximal, complemented

#15689003

C₂

yes

maximal, complemented

C₄×C₂²⋊Dic₄₇

C₂

yes

maximal, characteristic, complemented

C₂×#121×C₄₇

C₂

yes

maximal, characteristic

C₂²×Dic₉₄

—

C₂²×Dic₉₄

—

C₂²×Dic₉₄

C₂²

yes

—

C₂²×Dic₉₄

C₂²

yes

—

C₂³×Dic₄₇

C₂²

yes

—

#13094011

—

C₂×C₂²⋊Dic₄₇

C₂²

yes

—

C₂×C₂²⋊Dic₄₇

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₂²×D₄×C₄₇

C₂²

yes

—

C₂²×D₄×C₄₇

C₂²

yes

characteristic

C₂³×C₄×C₄₇

C₂²

yes

characteristic

#121×C₄₇

—

C₂×C₄⋊C₄×C₄₇

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₄₇

C₂²

yes

—

C₂⁴×C₄₇

C₂³

yes

—

C₂⁴×C₄₇

C₂³

yes

characteristic

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

D₄

yes

complemented

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₂²⋊Dic₄₇

—

C₂²⋊Dic₄₇

—

C₄×Dic₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂×D₄

yes

—

C₂³×C₄₇

#41

yes

—

C₂³×C₄₇

C₂⁴

yes

characteristic

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂×D₄

yes

—

Dic₉₄

—

Dic₉₄

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

#124

yes

complemented

C₂²×C₄₇

C₂²×D₄

yes

—

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₂²×C₄₇

C₂×#41

yes

—

C₂²×C₄₇

2₋¹⁺⁴

yes

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#120

yes

—

Dic₄₇

—

Dic₄₇

—

#2436

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

yes

C₂×C₄₇

yes

100

C₂×C₄₇

#536

yes

characteristic

101

C₂×C₄₇

#548

yes

—

102

C₂³×Q₈

—

103

C₂×#124

—

104

C₂×#121

D₄₇

yes

characteristic

105

#393

—

106

#391

—

107

#386

—

108

C₄×C₂²⋊C₄

—

109

C₄₇

#2436

yes

characteristic, complemented, Sylow

110

C₂²×Q₈

—

111

C₂²×Q₈

—

112

C₂²×Q₈

—

113

C₂²×Q₈

—

114

C₂²×D₄

C₂×D₄₇

yes

characteristic

115

C₂²×D₄

C₂×D₄₇

yes

—

116

C₂³×C₄

—

117

C₂³×C₄

C₂×D₄₇

yes

characteristic

118

#124

—

119

#121

—

120

C₂×C₄⋊C₄

C₂×D₄₇

yes

characteristic

121

C₂×C₂²⋊C₄

—

122

C₂×C₂²⋊C₄

—

123

C₂×C₂²⋊C₄

C₂×D₄₇

yes

—

124

C₂×C₄²

—

125

#95

—

126

#95

—

127

C₂⁴

C₂²×D₄₇

yes

—

128

C₂⁴

C₂²×D₄₇

yes

characteristic

129

C₂×Q₈

—

130

C₂×Q₈

—

131

C₂×Q₈

—

132

C₂×Q₈

—

133

C₂×Q₈

—

134

C₂×Q₈

—

135

C₂×D₄

—

136

C₂×D₄

—

137

C₂×D₄

—

138

C₂×D₄

—

139

C₂²×C₄

—

140

C₂²×C₄

—

141

C₂²×C₄

—

142

C₂²×C₄

—

143

C₂²×C₄

—

144

C₂²×C₄

C₂²⋊D₄₇

yes

—

145

C₂²×C₄

C₂²×D₄₇

yes

—

146

C₂²×C₄

C₂²×D₄₇

yes

characteristic

147

C₂²×C₄

C₂²×D₄₇

yes

characteristic

148

C₄⋊C₄

—

149

C₂²⋊C₄

—

150

C₂²⋊C₄

—

151

C₂²⋊C₄

—

152

C₄²

—

153

C₂³

—

154

C₂³

—

155

C₂³

—

156

C₂³

—

157

C₂³

—

158

C₂³

—

159

C₂³

#10625352

yes

—

160

C₂³

C₂×C₂²⋊D₄₇

yes

—

161

C₂³

C₂³×D₄₇

yes

characteristic

162

Q₈

—

163

Q₈

—

164

D₄

—

165

D₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

D₄×D₄₇

yes

—

178

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

179

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

180

C₂²

—

181

C₂²

—

182

C₂²

—

183

C₂²

—

184

C₂²

—

185

C₂²

—

186

C₂²

—

187

C₂²

#13094011

yes

complemented

188

C₂²

C₂×D₄×D₄₇

yes

—

189

C₂²

C₂²×C₂²⋊D₄₇

yes

characteristic

190

C₂²

C₂×#10625352

yes

—

191

C₂²

#13094071

yes

—

192

C₄

—

193

C₄

—

194

C₄

—

195

C₄

—

188

—

196

C₄

#13093992

yes

—

197

C₂

—

198

C₂

—

199

C₂

C₂×#13093992

yes

characteristic

200

C₂

C₂×#13094011

yes

characteristic

201

C₂

#15689694

yes

characteristic

202

C₂

#15689779

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂⁴
Fitting	C₂×#121×C₄₇	C₂
hypercenter	C₂×#121	D₄₇
hypocenter	C₄₇	#2436
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×#121

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₇

commutator, socle

C₂³×C₄₇

C₂⁴

Fitting

C₂×#121×C₄₇

C₂

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂³ ◁ C₂×#121

N	H ≅ G/N	type
1. C₂³×Dic₉₄	C₂	semidirect
2. C₂×#13094011	C₂	semidirect
3. #15689035	C₂	semidirect
4. #15689028	C₂	semidirect
5. #15689003	C₂	semidirect
6. C₄×C₂²⋊Dic₄₇	C₂	semidirect
45. C₂×Dic₉₄	D₄	semidirect
85. C₂²×C₄₇	#124	semidirect
109. C₄₇	#2436	semidirect
187. C₂²	#13094011	semidirect

H ≅ G/N

type

1. C₂³×Dic₉₄

C₂

semidirect

2. C₂×#13094011

C₂

semidirect

3. #15689035

C₂

semidirect

4. #15689028

C₂

semidirect

5. #15689003

C₂

semidirect

6. C₄×C₂²⋊Dic₄₇

C₂

semidirect

45. C₂×Dic₉₄

D₄

semidirect

85. C₂²×C₄₇

#124

semidirect

109. C₄₇

#2436

semidirect

187. C₂²

#13094011

semidirect

Subgroups — #20247047

Conjugacy classes of subgroups

Complements