Group #24999345 — subgroups

Subgroups — #24999345

Order 11008.

576 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 113 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	#19145739	C₂	1	2	yes	maximal
2	#19135572	C₂	1	1	yes	maximal, characteristic
3	#19133267	C₂	1	2	yes	maximal
4	#19132428	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#2868	C₂	1	1	yes	maximal, characteristic
6	#14583456	C₂²	1	1	yes	characteristic
7	#14583295	—	2	2	no	—
8	#14583251	—	2	2	no	—
9	#14583229	—	2	4	no	—
10	#14583181	—	2	4	no	—
11	#14582952	C₂²	1	2	yes	—
12	#14582923	C₂²	1	1	yes	characteristic
13	#14582659	—	2	2	no	—
14	#14582645	—	2	4	no	—
15	C₂×C₄⋊Q₈×C₄₃	—	2	2	no	—
16	C₂×C₄⋊Q₈×C₄₃	C₂²	1	2	yes	—
17	C₄₃×#384	—	2	4	no	—
18	C₄³×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×#10621877	—	2	1	no	—
20	#13063325	D₄	1	2	yes	—
21	#13063317	—	2	1	no	—
22	#13063304	—	2	2	no	—
23	C₄×Dic₈₆	—	2	2	no	—
24	#13063284	—	2	1	no	—
25	#13063256	—	2	8	no	—
26	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
27	C₄⋊(C₄₃⋊C₈)	D₄	1	4	yes	—
28	#13063248	—	2	8	no	—
29	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
30	C₄×C₄₃⋊C₈	—	2	2	no	—
31	C₂²×Q₈×C₄₃	—	2	2	no	—
32	C₄⋊Q₈×C₄₃	—	2	2	no	—
33	C₄⋊Q₈×C₄₃	—	2	2	no	—
34	C₄⋊Q₈×C₄₃	—	2	2	no	—
35	C₄⋊Q₈×C₄₃	—	2	2	no	—
36	C₄⋊Q₈×C₄₃	—	4	4	no	—
37	C₄⋊Q₈×C₄₃	—	4	4	no	—
38	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
39	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
40	C₂×C₄⋊C₄×C₄₃	D₄	1	4	yes	—
41	C₂×C₄²×C₄₃	—	2	2	no	—
42	C₂×C₄²×C₄₃	D₄	1	2	yes	—
43	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
44	C₂×Q₈×C₄₃	—	4	2	no	—
45	C₂×Q₈×C₄₃	—	4	2	no	—
46	C₂×Q₈×C₄₃	—	4	4	no	—
47	C₂×Q₈×C₄₃	—	4	4	no	—
48	C₂²×C₄×C₄₃	—	2	2	no	—
49	C₂²×C₄×C₄₃	—	2	4	no	—
50	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
51	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
52	C₂×Dic₈₆	—	2	2	no	—
53	C₄⋊C₄×C₄₃	—	2	4	no	—
54	C₄⋊C₄×C₄₃	—	2	4	no	—
55	C₄⋊C₄×C₄₃	—	4	16	no	—
56	C₄⋊C₄×C₄₃	—	4	2	no	—
57	C₄⋊C₄×C₄₃	—	4	2	no	—
58	C₄²×C₄₃	—	2	8	no	—
59	C₄²×C₄₃	—	2	2	no	—
60	C₄²×C₄₃	SD₁₆	1	4	yes	—
61	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
62	C₄²×C₄₃	C₂×D₄	1	2	yes	—
63	C₄²×C₄₃	#41	1	1	yes	characteristic
64	C₂²⋊Dic₄₃	—	4	1	no	—
65	C₄⋊Dic₄₃	—	2	2	no	—
66	C₄⋊Dic₄₃	—	2	2	no	—
67	Dic₄₃⋊C₄	—	4	2	no	—
68	C₄×Dic₄₃	—	4	1	no	—
69	#10621877	—	4	2	no	—
70	C₂×C₄₃⋊C₈	—	2	4	no	—
71	C₂×C₄₃⋊C₈	—	4	1	no	—
72	C₂³×C₄₃	#120	1	1	yes	characteristic
73	Q₈×C₄₃	—	8	4	no	—
74	Q₈×C₄₃	—	8	2	no	—
75	Q₈×C₄₃	—	8	2	no	—
76	C₂×C₄×C₄₃	—	2	8	no	—
77	C₂×C₄×C₄₃	—	2	4	no	—
78	C₂×C₄×C₄₃	—	2	4	no	—
79	C₂×C₄×C₄₃	—	4	4	no	—
80	C₂×C₄×C₄₃	—	4	8	no	—
81	C₂×C₄×C₄₃	#120	1	2	yes	—
82	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
83	C₂×C₄×C₄₃	#121	1	2	yes	—
84	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
85	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
86	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
87	C₂×Dic₄₃	—	4	2	no	—
88	Dic₈₆	—	4	4	no	—
89	C₄₃⋊C₈	—	4	4	no	—
90	C₄₃⋊C₈	—	8	1	no	—
91	#10299	—	43	1	no	maximal, Sylow
92	C₂²×C₄₃	—	2	2	no	—
93	C₂²×C₄₃	#392	1	1	yes	characteristic
94	C₂²×C₄₃	#450	1	2	yes	—
95	C₄×C₄₃	—	2	8	no	—
96	C₄×C₄₃	—	2	2	no	—
97	C₄×C₄₃	—	8	4	no	—
98	C₄×C₄₃	#456	1	4	yes	—
99	C₄×C₄₃	#460	1	2	yes	—
100	C₄×C₄₃	#492	1	1	yes	characteristic
101	C₄×C₄₃	#496	1	1	yes	characteristic
102	Dic₄₃	—	8	2	no	—
103	#3229	—	43	2	no	—
104	#2868	D₄₃	1	1	yes	characteristic
105	#1994	—	43	1	no	—
106	#1546	—	43	2	no	—
107	#1276	—	43	1	no	—
108	C₂×C₄₃	—	2	2	no	—
109	C₂×C₄₃	#2005	1	2	yes	—
110	C₂×C₄₃	#2014	1	1	yes	characteristic
111	#533	—	43	1	no	—
112	C₂×C₄⋊Q₈	—	2	2	no	—
113	C₂×C₄⋊Q₈	C₂×D₄₃	1	2	yes	—
114	#498	—	86	2	no	—
115	#487	—	86	2	no	—
116	#483	—	86	4	no	—
117	#475	—	86	4	no	—
118	#431	—	43	2	no	—
119	#423	—	43	1	no	—
120	#384	—	2	4	no	—
121	C₄³	C₂×D₄₃	1	1	yes	characteristic
122	#339	—	86	2	no	—
123	#332	—	86	4	no	—
124	C₄₃	#10299	1	1	yes	characteristic, complemented, Sylow
125	C₂²×Q₈	—	2	2	no	—
126	C₂×M₁₆	—	86	1	no	—
127	C₄⋊Q₈	—	2	2	no	—
128	C₄⋊Q₈	—	2	2	no	—
129	C₄⋊Q₈	—	2	2	no	—
130	C₄⋊Q₈	—	2	2	no	—
131	C₄⋊Q₈	—	4	4	no	—
132	C₄⋊Q₈	—	4	4	no	—
133	C₄⋊Q₈	—	43	2	no	—
134	#125	—	86	1	no	—
135	C₂²⋊Q₈	—	86	2	no	—
136	C₄×Q₈	—	86	2	no	—
137	#117	—	86	1	no	—
138	C₂×C₄⋊C₄	—	2	8	no	—
139	C₂×C₄⋊C₄	—	2	2	no	—
140	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	4	yes	—
141	C₂×C₄²	—	2	2	no	—
142	C₂×C₄²	C₂²⋊D₄₃	1	2	yes	—
143	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
144	#106	—	86	8	no	—
145	C₄⋊C₈	—	43	4	no	—
146	C₄⋊C₈	—	86	2	no	—
147	#103	—	86	8	no	—
148	C₂²⋊C₈	—	86	2	no	—
149	C₄×C₈	—	86	2	no	—
150	C₂×Q₈	—	4	2	no	—
151	C₂×Q₈	—	4	2	no	—
152	C₂×Q₈	—	4	4	no	—
153	C₂×Q₈	—	4	4	no	—
154	C₂×Q₈	—	86	2	no	—
155	C₂²×C₄	—	2	2	no	—
156	C₂²×C₄	—	2	4	no	—
157	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
158	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
159	M₁₆	—	172	2	no	—
160	C₂×C₈	—	86	4	no	—
161	C₂×C₈	—	172	1	no	—
162	C₄⋊C₄	—	2	4	no	—
163	C₄⋊C₄	—	2	4	no	—
164	C₄⋊C₄	—	4	16	no	—
165	C₄⋊C₄	—	4	2	no	—
166	C₄⋊C₄	—	4	2	no	—
167	C₄⋊C₄	—	86	2	no	—
168	C₄⋊C₄	—	86	2	no	—
169	C₄⋊C₄	—	172	2	no	—
170	C₂²⋊C₄	—	172	1	no	—
171	C₄²	—	2	8	no	—
172	C₄²	—	2	2	no	—
173	C₄²	—	172	1	no	—
174	C₄²	#10621883	1	4	yes	—
175	C₄²	D₄×D₄₃	1	1	yes	characteristic
176	C₄²	D₄×D₄₃	1	2	yes	—
177	C₄²	#10621900	1	1	yes	characteristic
178	C₂³	#13063294	1	1	yes	characteristic
179	Q₈	—	8	4	no	—
180	Q₈	—	8	2	no	—
181	Q₈	—	8	2	no	—
182	Q₈	—	172	4	no	—
183	C₂×C₄	—	2	8	no	—
184	C₂×C₄	—	2	4	no	—
185	C₂×C₄	—	2	4	no	—
186	C₂×C₄	—	4	8	no	—
187	C₂×C₄	—	4	4	no	—
188	C₂×C₄	—	172	2	no	—
189	C₂×C₄	#13063293	1	2	yes	—
190	C₂×C₄	#13063296	1	1	yes	characteristic
191	C₂×C₄	#13063297	1	2	yes	—
192	C₂×C₄	#13063321	1	1	yes	characteristic
193	C₂×C₄	C₂×#10621883	1	2	yes	—
194	C₂×C₄	#13063351	1	2	yes	—
195	C₈	—	344	1	no	—
196	C₈	—	172	4	no	—
197	C₂²	—	2	2	no	—
198	C₂²	#14582807	1	1	yes	characteristic
199	C₂²	#14583050	1	2	yes	—
200	C₄	—	2	8	no	—
201	C₄	—	2	2	no	—
202	C₄	—	8	4	no	—
203	C₄	—	344	2	no	—
204	C₄	#14583081	1	4	yes	—
205	C₄	#14583096	1	2	yes	—
206	C₄	#14583271	1	1	yes	characteristic
207	C₄	#14583286	1	1	yes	characteristic
208	C₂	—	2	2	no	—
209	C₂	#19135631	1	2	yes	—
210	C₂	#19135683	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19145739

C₂

yes

maximal

#19135572

C₂

yes

maximal, characteristic

#19133267

C₂

yes

maximal

#19132428

C₂

yes

maximal, characteristic

C₄₃×#2868

C₂

yes

maximal, characteristic

#14583456

C₂²

yes

—

—

—

—

C₂²

yes

—

#14582923

C₂²

yes

characteristic

#14582659

—

#14582645

—

C₂×C₄⋊Q₈×C₄₃

—

C₂×C₄⋊Q₈×C₄₃

C₂²

yes

—

C₄₃×#384

—

C₄³×C₄₃

C₂²

yes

characteristic

C₂×#10621877

—

#13063325

D₄

yes

—

#13063317

—

#13063304

—

C₄×Dic₈₆

—

#13063284

—

#13063256

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

D₄

yes

—

#13063248

—

C₂²⋊(C₄₃⋊C₈)

—

C₄×C₄₃⋊C₈

—

C₂²×Q₈×C₄₃

—

C₄⋊Q₈×C₄₃

—

C₄⋊Q₈×C₄₃

—

C₄⋊Q₈×C₄₃

—

C₄⋊Q₈×C₄₃

—

C₄⋊Q₈×C₄₃

—

C₄⋊Q₈×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

—

C₂×C₄²×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₈₆

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

SD₁₆

yes

—

C₄²×C₄₃

C₂×D₄

yes

characteristic

C₄²×C₄₃

C₂×D₄

yes

—

C₄²×C₄₃

#41

yes

characteristic

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

#120

yes

characteristic

Q₈×C₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#120

yes

—

C₂×C₄×C₄₃

#121

yes

characteristic

C₂×C₄×C₄₃

#121

yes

—

C₂×C₄×C₄₃

#127

yes

characteristic

C₂×C₄×C₄₃

C₂×SD₁₆

yes

—

C₂×C₄×C₄₃

AGL(1,ℤ/8)

yes

—

C₂×Dic₄₃

—

Dic₈₆

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

#10299

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

#392

yes

characteristic

C₂²×C₄₃

#450

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#456

yes

—

C₄×C₄₃

#460

yes

—

100

C₄×C₄₃

#492

yes

characteristic

101

C₄×C₄₃

#496

yes

characteristic

102

Dic₄₃

—

103

#3229

—

104

#2868

D₄₃

yes

characteristic

105

#1994

—

106

#1546

—

107

#1276

—

108

C₂×C₄₃

—

109

C₂×C₄₃

#2005

yes

—

110

C₂×C₄₃

#2014

yes

characteristic

111

#533

—

112

C₂×C₄⋊Q₈

—

113

C₂×C₄⋊Q₈

C₂×D₄₃

yes

—

114

#498

—

115

#487

—

116

#483

—

117

#475

—

118

#431

—

119

#423

—

120

#384

—

121

C₄³

C₂×D₄₃

yes

characteristic

122

#339

—

123

#332

—

124

C₄₃

#10299

yes

characteristic, complemented, Sylow

125

C₂²×Q₈

—

126

C₂×M₁₆

—

127

C₄⋊Q₈

—

128

C₄⋊Q₈

—

129

C₄⋊Q₈

—

130

C₄⋊Q₈

—

131

C₄⋊Q₈

—

132

C₄⋊Q₈

—

133

C₄⋊Q₈

—

134

#125

—

135

C₂²⋊Q₈

—

136

C₄×Q₈

—

137

#117

—

138

C₂×C₄⋊C₄

—

139

C₂×C₄⋊C₄

—

140

C₂×C₄⋊C₄

C₂²⋊D₄₃

yes

—

141

C₂×C₄²

—

142

C₂×C₄²

C₂²⋊D₄₃

yes

—

143

C₂×C₄²

C₂²×D₄₃

yes

characteristic

144

#106

—

145

C₄⋊C₈

—

146

C₄⋊C₈

—

147

#103

—

148

C₂²⋊C₈

—

149

C₄×C₈

—

150

C₂×Q₈

—

151

C₂×Q₈

—

152

C₂×Q₈

—

153

C₂×Q₈

—

154

C₂×Q₈

—

155

C₂²×C₄

—

156

C₂²×C₄

—

157

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

—

158

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

159

M₁₆

—

172

—

160

C₂×C₈

—

161

C₂×C₈

—

172

—

162

C₄⋊C₄

—

163

C₄⋊C₄

—

164

C₄⋊C₄

—

165

C₄⋊C₄

—

166

C₄⋊C₄

—

167

C₄⋊C₄

—

168

C₄⋊C₄

—

169

C₄⋊C₄

—

172

—

170

C₂²⋊C₄

—

172

—

171

C₄²

—

172

C₄²

—

173

C₄²

—

172

—

174

C₄²

#10621883

yes

—

175

C₄²

D₄×D₄₃

yes

characteristic

176

C₄²

D₄×D₄₃

yes

—

177

C₄²

#10621900

yes

characteristic

178

C₂³

#13063294

yes

characteristic

179

Q₈

—

180

Q₈

—

181

Q₈

—

182

Q₈

—

172

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

—

172

—

189

C₂×C₄

#13063293

yes

—

190

C₂×C₄

#13063296

yes

characteristic

191

C₂×C₄

#13063297

yes

—

192

C₂×C₄

#13063321

yes

characteristic

193

C₂×C₄

C₂×#10621883

yes

—

194

C₂×C₄

#13063351

yes

—

195

C₈

—

344

—

196

C₈

—

172

—

197

C₂²

—

198

C₂²

#14582807

yes

characteristic

199

C₂²

#14583050

yes

—

200

C₄

—

201

C₄

—

202

C₄

—

203

C₄

—

344

—

204

C₄

#14583081

yes

—

205

C₄

#14583096

yes

—

206

C₄

#14583271

yes

characteristic

207

C₄

#14583286

yes

characteristic

208

C₂

—

209

C₂

#19135631

yes

—

210

C₂

#19135683

yes

characteristic

	subgroup	G/H
center	C₂²	#14582807
commutator, cosocle	C₂×C₄²×C₄₃	C₂³
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#2868	C₂
socle	C₂²×C₄₃	#392
prime radical	C₂³×C₄₃	#120
hypercenter	#2868	D₄₃
hypocenter	C₄₃	#10299
LCS	G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2868

subgroup

G/H

center

C₂²

#14582807

commutator, cosocle

C₂×C₄²×C₄₃

C₂³

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#2868

C₂

C₂²×C₄₃

C₂³×C₄₃

D₄₃

C₄₃

G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2868

N	H ≅ G/N	type
124. C₄₃	#10299	semidirect

H ≅ G/N

type

124. C₄₃

#10299

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#19145739	2
#19135572	2
#19133267	2
#19132428	2
C₄₃×#2868	2
#10299	43

subgroup

index

C₄₃×#2868

Subgroups — #24999345

Conjugacy classes of subgroups

Complements

Maximal subgroups