Group #20244292 — subgroups

Subgroups — #20244292

Order 6016.

296 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 83 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	C₂²×#10625336	C₂	1	1	yes	maximal, characteristic
2	C₂×#13093959	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689132	C₂	1	1	yes	maximal, characteristic, complemented
4	#15689129	C₂	1	1	yes	maximal, characteristic
5	C₂×#13093940	C₂	1	1	yes	maximal, characteristic
6	#15689081	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#101×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₁₈₈	C₂²	1	1	yes	characteristic
9	C₂×#10625336	—	2	1	no	—
10	C₂×#10625336	—	2	1	no	—
11	C₂×#10625336	—	2	2	no	—
12	C₂×#10625336	C₄	1	4	yes	complemented
13	C₂×#10625329	C₂²	1	1	yes	characteristic
14	C₂²×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
15	#13093983	C₂²	1	1	yes	characteristic
16	#13093959	—	2	2	no	—
17	#13093948	—	2	2	no	—
18	#13093946	—	2	2	no	—
19	#13093940	—	2	2	no	—
20	#13093934	—	2	1	no	—
21	C₈×Dic₄₇	—	2	1	no	—
22	C₂²×Q₈×C₄₇	C₂²	1	1	yes	characteristic
23	C₂×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
25	#101×C₄₇	—	2	2	no	—
26	C₂³×D₄₇	—	2	1	no	—
27	C₂×Q₈×C₄₇	—	2	1	no	—
28	C₂×Q₈×C₄₇	—	2	1	no	—
29	C₂×Q₈×C₄₇	—	2	1	no	—
30	C₂×Q₈×C₄₇	—	2	1	no	—
31	C₂×Q₈×C₄₇	—	2	1	no	—
32	C₂×Q₈×C₄₇	C₂×C₄	1	2	yes	—
33	C₂²×C₄×C₄₇	—	2	1	no	—
34	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
35	C₂×D₁₈₈	—	2	1	no	—
36	C₂×D₁₈₈	—	2	1	no	—
37	C₂×D₁₈₈	—	2	1	no	—
38	C₂×D₁₈₈	—	2	1	no	—
39	C₂×D₁₈₈	—	2	1	no	—
40	C₂×D₁₈₈	C₂×C₄	1	2	yes	—
41	M₁₆×C₄₇	—	2	1	no	—
42	M₁₆×C₄₇	—	2	1	no	—
43	M₁₆×C₄₇	—	2	1	no	—
44	M₁₆×C₄₇	D₄	1	2	yes	—
45	C₂×C₈×C₄₇	—	2	1	no	—
46	C₂×C₈×C₄₇	—	2	1	no	—
47	C₂²⋊Dic₄₇	—	2	1	no	—
48	#10625336	—	2	4	no	—
49	#10625336	—	2	4	no	—
50	C₄⋊Dic₄₇	D₄	1	2	yes	—
51	C₄×Dic₄₇	—	2	1	no	—
52	#10625329	—	2	1	no	—
53	#10625329	—	2	1	no	—
54	C₂×C₄₇⋊C₈	—	2	1	no	—
55	C₂×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
56	C₂×C₄₇⋊C₈	D₄	1	1	yes	characteristic
57	C₂×C₄₇⋊C₈	D₄	1	1	yes	characteristic
58	C₂×C₄₇⋊C₈	D₄	1	2	yes	—
59	C₂³×C₄₇	#41	1	1	yes	characteristic
60	C₂²×D₄₇	—	2	2	no	—
61	C₂²×D₄₇	—	4	1	no	—
62	C₂²×D₄₇	—	4	1	no	—
63	C₂²×D₄₇	—	8	2	no	—
64	Q₈×C₄₇	—	2	2	no	—
65	Q₈×C₄₇	—	2	2	no	—
66	Q₈×C₄₇	—	4	1	no	—
67	Q₈×C₄₇	—	4	1	no	—
68	C₂×C₄×C₄₇	—	2	2	no	—
69	C₂×C₄×C₄₇	—	4	1	no	—
70	C₂×C₄×C₄₇	—	4	1	no	—
71	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
72	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
73	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
74	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
75	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
76	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
77	C₂×Dic₄₇	—	2	2	no	—
78	D₁₈₈	—	2	2	no	—
79	D₁₈₈	—	2	2	no	—
80	D₁₈₈	—	4	1	no	—
81	D₁₈₈	—	4	1	no	—
82	C₈×C₄₇	—	2	2	no	—
83	C₈×C₄₇	—	4	1	no	—
84	C₄₇⋊C₈	—	4	1	no	—
85	C₄₇⋊C₈	C₂²⋊C₄	1	2	yes	—
86	C₄₇⋊C₈	C₂²⋊C₄	1	2	yes	—
87	C₂²×C₄₇	—	2	2	no	—
88	C₂²×C₄₇	C₄×D₄	1	1	yes	characteristic
89	C₂²×C₄₇	#121	1	1	yes	characteristic
90	C₂²×C₄₇	#124	1	1	yes	characteristic
91	C₂×D₄₇	—	4	2	no	—
92	C₂×D₄₇	—	8	2	no	—
93	C₂×D₄₇	—	8	2	no	—
94	C₂×D₄₇	—	8	2	no	—
95	C₄×C₄₇	—	4	2	no	—
96	C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
97	C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
98	C₄×C₄₇	#121	1	1	yes	characteristic
99	C₄×C₄₇	#127	1	1	yes	characteristic
100	Dic₄₇	—	4	2	no	—
101	#1977	—	47	1	no	maximal, Sylow
102	C₂×C₄₇	—	2	1	no	—
103	C₂×C₄₇	—	2	1	no	—
104	C₂×C₄₇	#390	1	1	yes	characteristic
105	C₂×C₄₇	#471	1	2	yes	—
106	D₄₇	—	8	2	no	—
107	C₂²×SD₁₆	—	47	1	no	—
108	C₂×#108	—	47	1	no	—
109	#419	—	47	1	no	—
110	#418	—	47	1	no	—
111	C₂×#101	D₄₇	1	1	yes	characteristic, complemented
112	C₂×#100	—	47	1	no	—
113	#405	—	47	1	no	—
114	C₄₇	#1977	1	1	yes	characteristic, complemented, Sylow
115	C₂²×Q₈	C₂×D₄₇	1	1	yes	characteristic
116	C₂²×D₄	—	47	1	no	—
117	C₂×SD₁₆	—	47	4	no	—
118	C₂×SD₁₆	—	94	1	no	—
119	C₂×SD₁₆	—	94	1	no	—
120	C₂×SD₁₆	—	94	2	no	—
121	C₂×M₁₆	—	47	1	no	—
122	C₂×M₁₆	C₂×D₄₇	1	1	yes	characteristic
123	C₂×M₁₆	C₂×D₄₇	1	1	yes	characteristic
124	C₂²×C₈	—	47	1	no	—
125	#117	—	47	1	no	—
126	#108	—	94	2	no	—
127	#103	—	94	2	no	—
128	#102	—	94	2	no	—
129	#101	—	2	2	no	—
130	#100	—	94	2	no	—
131	#97	—	94	1	no	—
132	C₄×C₈	—	94	1	no	—
133	C₂⁴	—	94	1	no	—
134	C₂×Q₈	—	2	1	no	—
135	C₂×Q₈	—	2	1	no	—
136	C₂×Q₈	—	2	1	no	—
137	C₂×Q₈	—	2	1	no	—
138	C₂×Q₈	—	2	1	no	—
139	C₂×Q₈	C₄×D₄₇	1	2	yes	—
140	C₂×D₄	—	47	2	no	—
141	C₂×D₄	—	94	1	no	—
142	C₂×D₄	—	94	1	no	—
143	C₂×D₄	—	94	1	no	—
144	C₂×D₄	—	94	1	no	—
145	C₂×D₄	—	94	1	no	—
146	C₂²×C₄	—	2	1	no	—
147	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
148	SD₁₆	—	94	4	no	—
149	SD₁₆	—	94	4	no	—
150	M₁₆	—	2	1	no	—
151	M₁₆	—	2	1	no	—
152	M₁₆	—	2	1	no	—
153	M₁₆	—	94	1	no	—
154	M₁₆	—	94	1	no	—
155	M₁₆	C₂²⋊D₄₇	1	2	yes	—
156	C₂×C₈	—	2	1	no	—
157	C₂×C₈	—	2	1	no	—
158	C₂×C₈	—	47	2	no	—
159	C₂×C₈	—	47	1	no	—
160	C₂×C₈	—	47	1	no	—
161	C₂×C₈	—	47	2	no	—
162	C₂×C₈	—	94	1	no	—
163	C₄⋊C₄	—	47	2	no	—
164	C₂²⋊C₄	—	94	1	no	—
165	C₄²	—	94	1	no	—
166	C₂³	—	94	2	no	—
167	C₂³	—	376	2	no	—
168	C₂³	—	188	1	no	—
169	C₂³	—	188	1	no	—
170	C₂³	#10625350	1	1	yes	characteristic
171	Q₈	—	2	2	no	—
172	Q₈	—	2	2	no	—
173	Q₈	—	4	1	no	—
174	Q₈	—	4	1	no	—
175	D₄	—	94	2	no	—
176	D₄	—	94	2	no	—
177	D₄	—	188	1	no	—
178	D₄	—	188	1	no	—
179	C₂×C₄	—	2	2	no	—
180	C₂×C₄	—	4	1	no	—
181	C₂×C₄	—	4	1	no	—
182	C₂×C₄	—	94	2	no	—
183	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
184	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
185	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
186	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
187	C₂×C₄	#10625352	1	1	yes	characteristic
188	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
189	C₈	—	2	2	no	—
190	C₈	—	4	1	no	—
191	C₈	—	47	2	no	—
192	C₈	—	47	2	no	—
193	C₈	—	188	1	no	—
194	C₂²	—	2	2	no	—
195	C₂²	—	376	2	no	—
196	C₂²	—	376	2	no	—
197	C₂²	—	376	2	no	—
198	C₂²	—	188	2	no	—
199	C₂²	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
200	C₂²	#13093997	1	1	yes	characteristic
201	C₂²	#13094010	1	1	yes	characteristic
202	C₄	—	4	2	no	—
203	C₄	—	188	2	no	—
204	C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
205	C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
206	C₄	#13093996	1	1	yes	characteristic
207	C₄	#13094020	1	1	yes	characteristic
208	C₂	—	2	1	no	—
209	C₂	—	2	1	no	—
210	C₂	—	376	2	no	—
211	C₂	#15689023	1	1	yes	characteristic
212	C₂	#15689389	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#10625336

C₂

yes

maximal, characteristic

C₂×#13093959

C₂

yes

maximal, characteristic, complemented

#15689132

C₂

yes

maximal, characteristic, complemented

#15689129

C₂

yes

maximal, characteristic

C₂×#13093940

C₂

yes

maximal, characteristic

#15689081

C₂

yes

maximal, characteristic, complemented

C₂×#101×C₄₇

C₂

yes

maximal, characteristic, complemented

C₂²×D₁₈₈

C₂²

yes

—

—

—

C₄

yes

complemented

C₂×#10625329

C₂²

yes

characteristic

C₂²×C₄₇⋊C₈

C₂²

yes

characteristic

#13093983

C₂²

yes

—

—

—

—

—

C₈×Dic₄₇

—

C₂²×Q₈×C₄₇

C₂²

yes

characteristic

C₂×M₁₆×C₄₇

C₂²

yes

characteristic

C₂×M₁₆×C₄₇

C₂²

yes

characteristic

#101×C₄₇

—

C₂³×D₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

C₂×C₄

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

C₂×C₄

yes

—

M₁₆×C₄₇

—

M₁₆×C₄₇

—

M₁₆×C₄₇

—

M₁₆×C₄₇

D₄

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂²⋊Dic₄₇

—

#10625336

—

#10625336

—

C₄⋊Dic₄₇

D₄

yes

—

C₄×Dic₄₇

—

#10625329

—

#10625329

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

C₂×C₄

yes

—

C₂×C₄₇⋊C₈

D₄

yes

characteristic

C₂×C₄₇⋊C₈

D₄

yes

characteristic

C₂×C₄₇⋊C₈

D₄

yes

—

C₂³×C₄₇

#41

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

#41

yes

characteristic

C₂×Dic₄₇

—

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

C₈×C₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₄₇⋊C₈

C₂²⋊C₄

yes

—

C₄₇⋊C₈

C₂²⋊C₄

yes

—

C₂²×C₄₇

—

C₂²×C₄₇

C₄×D₄

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₄₇

C₄×D₄

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

100

Dic₄₇

—

101

#1977

—

maximal, Sylow

102

C₂×C₄₇

—

103

C₂×C₄₇

—

104

C₂×C₄₇

#390

yes

characteristic

105

C₂×C₄₇

#471

yes

—

106

D₄₇

—

107

C₂²×SD₁₆

—

108

C₂×#108

—

109

#419

—

110

#418

—

111

C₂×#101

D₄₇

yes

characteristic, complemented

112

C₂×#100

—

113

#405

—

114

C₄₇

#1977

yes

characteristic, complemented, Sylow

115

C₂²×Q₈

C₂×D₄₇

yes

characteristic

116

C₂²×D₄

—

117

C₂×SD₁₆

—

118

C₂×SD₁₆

—

119

C₂×SD₁₆

—

120

C₂×SD₁₆

—

121

C₂×M₁₆

—

122

C₂×M₁₆

C₂×D₄₇

yes

characteristic

123

C₂×M₁₆

C₂×D₄₇

yes

characteristic

124

C₂²×C₈

—

125

#117

—

126

#108

—

127

#103

—

128

#102

—

129

#101

—

130

#100

—

131

#97

—

132

C₄×C₈

—

133

C₂⁴

—

134

C₂×Q₈

—

135

C₂×Q₈

—

136

C₂×Q₈

—

137

C₂×Q₈

—

138

C₂×Q₈

—

139

C₂×Q₈

C₄×D₄₇

yes

—

140

C₂×D₄

—

141

C₂×D₄

—

142

C₂×D₄

—

143

C₂×D₄

—

144

C₂×D₄

—

145

C₂×D₄

—

146

C₂²×C₄

—

147

C₂²×C₄

C₂²×D₄₇

yes

characteristic

148

SD₁₆

—

149

SD₁₆

—

150

M₁₆

—

151

M₁₆

—

152

M₁₆

—

153

M₁₆

—

154

M₁₆

—

155

M₁₆

C₂²⋊D₄₇

yes

—

156

C₂×C₈

—

157

C₂×C₈

—

158

C₂×C₈

—

159

C₂×C₈

—

160

C₂×C₈

—

161

C₂×C₈

—

162

C₂×C₈

—

163

C₄⋊C₄

—

164

C₂²⋊C₄

—

165

C₄²

—

166

C₂³

—

167

C₂³

—

376

—

168

C₂³

—

188

—

169

C₂³

—

188

—

170

C₂³

#10625350

yes

characteristic

171

Q₈

—

172

Q₈

—

173

Q₈

—

174

Q₈

—

175

D₄

—

176

D₄

—

177

D₄

—

188

—

178

D₄

—

188

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

184

C₂×C₄

D₄×D₄₇

yes

characteristic

185

C₂×C₄

D₄×D₄₇

yes

characteristic

186

C₂×C₄

D₄×D₄₇

yes

characteristic

187

C₂×C₄

#10625352

yes

characteristic

188

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

189

C₈

—

190

C₈

—

191

C₈

—

192

C₈

—

193

C₈

—

188

—

194

C₂²

—

195

C₂²

—

376

—

196

C₂²

—

376

—

197

C₂²

—

376

—

198

C₂²

—

188

—

199

C₂²

C₄×C₂²⋊D₄₇

yes

characteristic

200

C₂²

#13093997

yes

characteristic

201

C₂²

#13094010

yes

characteristic

202

C₄

—

203

C₄

—

188

—

204

C₄

C₂²⋊C₄×D₄₇

yes

characteristic

205

C₄

(C₂²⋊D₄₇)⋊C₄

yes

characteristic

206

C₄

#13093996

yes

characteristic

207

C₄

#13094020

yes

characteristic

208

C₂

—

209

C₂

—

210

C₂

—

376

—

211

C₂

#15689023

yes

characteristic

212

C₂

#15689389

yes

—

	subgroup	G/H
center	C₂²	#13093997
commutator	C₂×C₄×C₄₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₂×#101×C₄₇	C₂
socle	C₂²×C₄₇	#121
hypercenter	C₂×#101	D₄₇
hypocenter	C₄₇	#1977
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#101

subgroup

G/H

center

C₂²

#13093997

commutator

C₂×C₄×C₄₇

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₂×#101×C₄₇

C₂

C₂²×C₄₇

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#101

N	H ≅ G/N	type
2. C₂×#13093959	C₂	semidirect
3. #15689132	C₂	semidirect
6. #15689081	C₂	semidirect
7. C₂×#101×C₄₇	C₂	semidirect
12. C₂×#10625336	C₄	semidirect
111. C₂×#101	D₄₇	semidirect
114. C₄₇	#1977	semidirect

H ≅ G/N

type

2. C₂×#13093959

C₂

semidirect

3. #15689132

C₂

semidirect

6. #15689081

C₂

semidirect

7. C₂×#101×C₄₇

C₂

semidirect

12. C₂×#10625336

C₄

semidirect

111. C₂×#101

D₄₇

semidirect

114. C₄₇

#1977

semidirect

Subgroups — #20244292

Conjugacy classes of subgroups

Complements