Group #36448802 — subgroups

Subgroups — #36448802

Order 22784.

428 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 115 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	#26021222	C₂	1	1	yes	maximal, characteristic
2	#26020421	C₂	1	2	yes	maximal
3	C₂×#19151340	C₂	1	1	yes	maximal, characteristic
4	#26018133	C₂	1	2	yes	maximal
5	C₈₉×#2382	C₂	1	1	yes	maximal, characteristic
6	C₂×#15667945	—	2	2	no	—
7	C₂×#15667943	—	2	2	no	—
8	C₂×#15667923	C₂²	1	1	yes	characteristic
9	C₂×#15667923	C₂²	1	2	yes	—
10	#19151468	C₂²	1	1	yes	characteristic
11	#19151360	—	2	2	no	—
12	#19151340	C₄	1	4	yes	complemented
13	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
14	#389×C₈₉	—	2	2	no	—
15	#387×C₈₉	—	2	2	no	—
16	#387×C₈₉	—	2	2	no	—
17	#382×C₈₉	C₂²	1	2	yes	—
18	C₂²×#10623494	—	2	2	no	—
19	C₂²×#10623494	—	2	1	no	—
20	C₂×C₄⋊Dic₈₉	—	2	1	no	—
21	C₂×C₄⋊Dic₈₉	—	2	2	no	—
22	#15667945	—	4	4	no	—
23	#15667943	—	4	4	no	—
24	#15667923	—	2	2	no	—
25	#15667923	—	2	2	no	—
26	#15667923	C₂×C₄	1	4	yes	—
27	#125×C₈₉	—	2	2	no	—
28	#125×C₈₉	C₂×C₄	1	2	yes	—
29	#125×C₈₉	Q₈	1	2	yes	—
30	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
31	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
32	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
33	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
34	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
35	C₂×C₄²×C₈₉	—	2	2	no	—
36	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
37	#95×C₈₉	—	2	2	no	—
38	#95×C₈₉	—	2	2	no	—
39	#95×C₈₉	—	2	2	no	—
40	#95×C₈₉	—	2	2	no	—
41	C₂²×Dic₈₉	—	4	1	no	—
42	C₂×#10623494	—	2	4	no	—
43	C₂×#10623494	—	2	4	no	—
44	C₂×#10623494	—	2	4	no	—
45	C₂×#10623494	—	2	2	no	—
46	C₂×#10623494	—	4	1	no	—
47	C₂×#10623494	—	4	1	no	—
48	C₄⋊Dic₈₉	—	4	2	no	—
49	C₄⋊Dic₈₉	—	4	2	no	—
50	C₄⋊Dic₈₉	—	4	2	no	—
51	C₂²×C₄×C₈₉	—	2	2	no	—
52	C₂²×C₄×C₈₉	—	2	2	no	—
53	C₂²×C₄×C₈₉	—	2	2	no	—
54	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
56	C₄⋊C₄×C₈₉	—	2	4	no	—
57	C₄⋊C₄×C₈₉	—	2	4	no	—
58	C₄⋊C₄×C₈₉	—	2	2	no	—
59	C₄⋊C₄×C₈₉	—	4	2	no	—
60	C₄⋊C₄×C₈₉	—	4	2	no	—
61	C₄⋊C₄×C₈₉	—	8	2	no	—
62	C₄⋊C₄×C₈₉	C₄⋊C₄	1	4	yes	—
63	C₄²×C₈₉	—	8	2	no	—
64	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
65	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
66	C₄²×C₈₉	#41	1	2	yes	—
67	C₂³×C₈₉	#120	1	1	yes	characteristic
68	C₂×C₄×C₈₉	—	2	2	no	—
69	C₂×C₄×C₈₉	—	2	1	no	—
70	C₂×C₄×C₈₉	—	2	1	no	—
71	C₂×C₄×C₈₉	—	2	2	no	—
72	C₂×C₄×C₈₉	—	2	4	no	—
73	C₂×C₄×C₈₉	—	4	2	no	—
74	C₂×C₄×C₈₉	—	4	2	no	—
75	C₂×C₄×C₈₉	—	4	2	no	—
76	C₂×C₄×C₈₉	—	4	2	no	—
77	C₂×C₄×C₈₉	—	4	2	no	—
78	C₂×C₄×C₈₉	—	4	2	no	—
79	C₂×C₄×C₈₉	—	4	2	no	—
80	C₂×C₄×C₈₉	—	4	2	no	—
81	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
82	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
83	C₂×C₄×C₈₉	C₂²⋊Q₈	1	2	yes	—
84	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
85	C₂×Dic₈₉	—	8	2	no	—
86	C₂×Dic₈₉	—	8	1	no	—
87	#10623494	—	2	8	no	—
88	#10623494	—	4	2	no	—
89	C₂²×C₈₉	#385	1	1	yes	characteristic
90	C₂²×C₈₉	#453	1	2	yes	—
91	C₂²×C₈₉	#454	1	1	yes	characteristic
92	C₂²×C₈₉	#456	1	1	yes	characteristic
93	C₂²×C₈₉	#456	1	2	yes	—
94	C₄×C₈₉	—	2	1	no	—
95	C₄×C₈₉	—	2	1	no	—
96	C₄×C₈₉	—	2	2	no	—
97	C₄×C₈₉	—	2	2	no	—
98	C₄×C₈₉	—	4	4	no	—
99	C₄×C₈₉	—	8	2	no	—
100	C₄×C₈₉	—	8	2	no	—
101	Dic₈₉	—	16	1	no	—
102	#8913	—	89	1	no	maximal, Sylow
103	C₂×C₈₉	#1656	1	1	yes	characteristic
104	C₂×C₈₉	#1660	1	2	yes	—
105	C₂×C₈₉	#1663	1	1	yes	characteristic
106	C₂×C₈₉	#1857	1	1	yes	characteristic
107	C₂×C₈₉	#1859	1	2	yes	—
108	#2382	D₈₉	1	1	yes	characteristic
109	#1992	—	89	1	no	—
110	#1847	—	89	2	no	—
111	C₂×#330	—	89	1	no	—
112	#1295	—	89	2	no	—
113	C₈₉	#8913	1	1	yes	characteristic, complemented, Sylow
114	C₂×#125	C₂×D₈₉	1	1	yes	characteristic
115	C₂×#107	—	178	2	no	—
116	C₂×#106	—	178	2	no	—
117	C₂×#97	—	89	2	no	—
118	C₂×#97	—	89	1	no	—
119	#389	—	2	2	no	—
120	#387	—	2	2	no	—
121	#387	—	2	2	no	—
122	#384	—	89	1	no	—
123	#382	C₂×D₈₉	1	2	yes	—
124	#340	—	178	2	no	—
125	#330	—	89	4	no	—
126	C₂²×C₈	—	178	1	no	—
127	C₂²×C₈	—	178	2	no	—
128	#125	—	2	2	no	—
129	#125	Dic₁₇₈	1	2	yes	—
130	#125	C₄×D₈₉	1	2	yes	—
131	C₂×C₄⋊C₄	—	2	2	no	—
132	C₂×C₄⋊C₄	—	2	2	no	—
133	C₂×C₄⋊C₄	—	178	1	no	—
134	C₂×C₄⋊C₄	—	178	2	no	—
135	C₂×C₄⋊C₄	C₂²⋊D₈₉	1	2	yes	—
136	C₂×C₄⋊C₄	C₂²⋊D₈₉	1	2	yes	—
137	C₂×C₄⋊C₄	C₂²⋊D₈₉	1	2	yes	—
138	C₂×C₄²	—	2	2	no	—
139	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
140	#107	—	356	4	no	—
141	#106	—	356	4	no	—
142	#97	—	89	4	no	—
143	#97	—	178	2	no	—
144	#97	—	178	2	no	—
145	#95	—	2	2	no	—
146	#95	—	2	2	no	—
147	#95	—	2	2	no	—
148	#95	—	2	2	no	—
149	C₂²×C₄	—	2	2	no	—
150	C₂²×C₄	—	2	2	no	—
151	C₂²×C₄	—	2	2	no	—
152	C₂²×C₄	—	356	1	no	—
153	C₂²×C₄	C₂×C₂²⋊D₈₉	1	2	yes	—
154	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
155	C₂×C₈	—	356	1	no	—
156	C₂×C₈	—	356	1	no	—
157	C₂×C₈	—	178	2	no	—
158	C₂×C₈	—	178	4	no	—
159	C₂×C₈	—	178	4	no	—
160	C₂×C₈	—	178	4	no	—
161	C₄⋊C₄	—	2	4	no	—
162	C₄⋊C₄	—	2	4	no	—
163	C₄⋊C₄	—	2	2	no	—
164	C₄⋊C₄	—	4	2	no	—
165	C₄⋊C₄	—	4	2	no	—
166	C₄⋊C₄	—	8	2	no	—
167	C₄⋊C₄	—	356	2	no	—
168	C₄⋊C₄	—	356	2	no	—
169	C₄⋊C₄	—	356	2	no	—
170	C₄⋊C₄	#13083553	1	4	yes	—
171	C₄²	—	8	2	no	—
172	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
173	C₄²	C₂×Dic₁₇₈	1	1	yes	characteristic
174	C₄²	#13083574	1	2	yes	—
175	C₂³	#15667981	1	1	yes	characteristic
176	C₂×C₄	—	2	2	no	—
177	C₂×C₄	—	2	1	no	—
178	C₂×C₄	—	2	1	no	—
179	C₂×C₄	—	2	2	no	—
180	C₂×C₄	—	2	4	no	—
181	C₂×C₄	—	4	2	no	—
182	C₂×C₄	—	4	2	no	—
183	C₂×C₄	—	4	2	no	—
184	C₂×C₄	—	4	2	no	—
185	C₂×C₄	—	4	2	no	—
186	C₂×C₄	—	4	2	no	—
187	C₂×C₄	—	4	2	no	—
188	C₂×C₄	—	4	2	no	—
189	C₂×C₄	—	712	2	no	—
190	C₂×C₄	—	712	1	no	—
191	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
192	C₂×C₄	C₄×C₂²⋊D₈₉	1	2	yes	—
193	C₂×C₄	#15667991	1	2	yes	—
194	C₂×C₄	#15667995	1	1	yes	characteristic
195	C₈	—	356	2	no	—
196	C₈	—	178	8	no	—
197	C₂²	#19151471	1	1	yes	characteristic
198	C₂²	#19151766	1	2	yes	—
199	C₂²	#19151771	1	1	yes	characteristic
200	C₂²	#19151781	1	1	yes	characteristic
201	C₂²	#19151781	1	2	yes	—
202	C₄	—	2	1	no	—
203	C₄	—	2	1	no	—
204	C₄	—	2	2	no	—
205	C₄	—	2	2	no	—
206	C₄	—	4	4	no	—
207	C₄	—	8	2	no	—
208	C₄	—	8	2	no	—
209	C₄	—	1424	1	no	—
210	C₂	#26019545	1	1	yes	characteristic
211	C₂	#26019563	1	2	yes	—
212	C₂	#26019580	1	1	yes	characteristic
213	C₂	#26020467	1	1	yes	characteristic
214	C₂	#26020478	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#26021222

C₂

yes

maximal, characteristic

#26020421

C₂

yes

maximal

C₂×#19151340

C₂

yes

maximal, characteristic

#26018133

C₂

yes

maximal

C₈₉×#2382

C₂

yes

maximal, characteristic

C₂×#15667945

—

C₂×#15667943

—

C₂×#15667923

C₂²

yes

characteristic

C₂×#15667923

C₂²

yes

—

#19151468

C₂²

yes

characteristic

#19151360

—

#19151340

C₄

yes

complemented

C₂×#125×C₈₉

C₂²

yes

characteristic

#389×C₈₉

—

#387×C₈₉

—

#387×C₈₉

—

#382×C₈₉

C₂²

yes

—

C₂²×#10623494

—

C₂²×#10623494

—

C₂×C₄⋊Dic₈₉

—

C₂×C₄⋊Dic₈₉

—

—

—

—

—

C₂×C₄

yes

—

#125×C₈₉

—

#125×C₈₉

C₂×C₄

yes

—

#125×C₈₉

Q₈

yes

—

C₂×C₄⋊C₄×C₈₉

—

C₂×C₄⋊C₄×C₈₉

—

C₂×C₄⋊C₄×C₈₉

D₄

yes

—

C₂×C₄⋊C₄×C₈₉

D₄

yes

—

C₂×C₄⋊C₄×C₈₉

D₄

yes

—

C₂×C₄²×C₈₉

—

C₂×C₄²×C₈₉

C₂³

yes

characteristic

#95×C₈₉

—

#95×C₈₉

—

#95×C₈₉

—

#95×C₈₉

—

C₂²×Dic₈₉

—

—

—

—

—

—

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₈₉

C₂×D₄

yes

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

C₄⋊C₄

yes

—

C₄²×C₈₉

—

C₄²×C₈₉

C₂²×C₄

yes

characteristic

C₄²×C₈₉

C₂×Q₈

yes

characteristic

C₄²×C₈₉

#41

yes

—

C₂³×C₈₉

#120

yes

characteristic

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₈₉

C₄×D₄

yes

—

C₂×C₄×C₈₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₈₉

#123

yes

characteristic

C₂×Dic₈₉

—

C₂×Dic₈₉

—

#10623494

—

#10623494

—

C₂²×C₈₉

#385

yes

characteristic

C₂²×C₈₉

#453

yes

—

C₂²×C₈₉

yes

C₂²×C₈₉

yes

C₂²×C₈₉

yes

—

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

—

100

C₄×C₈₉

—

101

Dic₈₉

—

102

#8913

—

maximal, Sylow

103

C₂×C₈₉

#1656

yes

characteristic

104

C₂×C₈₉

#1660

yes

—

105

C₂×C₈₉

#1663

yes

characteristic

106

C₂×C₈₉

#1857

yes

characteristic

107

C₂×C₈₉

#1859

yes

—

108

#2382

D₈₉

yes

characteristic

109

#1992

—

110

#1847

—

111

C₂×#330

—

112

#1295

—

113

C₈₉

#8913

yes

characteristic, complemented, Sylow

114

C₂×#125

C₂×D₈₉

yes

characteristic

115

C₂×#107

—

178

—

116

C₂×#106

—

178

—

117

C₂×#97

—

118

C₂×#97

—

119

#389

—

120

#387

—

121

#387

—

122

#384

—

123

#382

C₂×D₈₉

yes

—

124

#340

—

178

—

125

#330

—

126

C₂²×C₈

—

178

—

127

C₂²×C₈

—

178

—

128

#125

—

129

#125

Dic₁₇₈

yes

—

130

#125

C₄×D₈₉

yes

—

131

C₂×C₄⋊C₄

—

132

C₂×C₄⋊C₄

—

133

C₂×C₄⋊C₄

—

178

—

134

C₂×C₄⋊C₄

—

178

—

135

C₂×C₄⋊C₄

C₂²⋊D₈₉

yes

—

136

C₂×C₄⋊C₄

C₂²⋊D₈₉

yes

—

137

C₂×C₄⋊C₄

C₂²⋊D₈₉

yes

—

138

C₂×C₄²

—

139

C₂×C₄²

C₂²×D₈₉

yes

characteristic

140

#107

—

356

—

141

#106

—

356

—

142

#97

—

143

#97

—

178

—

144

#97

—

178

—

145

#95

—

146

#95

—

147

#95

—

148

#95

—

149

C₂²×C₄

—

150

C₂²×C₄

—

151

C₂²×C₄

—

152

C₂²×C₄

—

356

—

153

C₂²×C₄

C₂×C₂²⋊D₈₉

yes

—

154

C₂²×C₄

C₂×C₂²⋊D₈₉

yes

characteristic

155

C₂×C₈

—

356

—

156

C₂×C₈

—

356

—

157

C₂×C₈

—

178

—

158

C₂×C₈

—

178

—

159

C₂×C₈

—

178

—

160

C₂×C₈

—

178

—

161

C₄⋊C₄

—

162

C₄⋊C₄

—

163

C₄⋊C₄

—

164

C₄⋊C₄

—

165

C₄⋊C₄

—

166

C₄⋊C₄

—

167

C₄⋊C₄

—

356

—

168

C₄⋊C₄

—

356

—

169

C₄⋊C₄

—

356

—

170

C₄⋊C₄

#13083553

yes

—

171

C₄²

—

172

C₄²

C₂×C₄×D₈₉

yes

characteristic

173

C₄²

C₂×Dic₁₇₈

yes

characteristic

174

C₄²

#13083574

yes

—

175

C₂³

#15667981

yes

characteristic

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

—

712

—

190

C₂×C₄

—

712

—

191

C₂×C₄

C₂×#13083553

yes

characteristic

192

C₂×C₄

C₄×C₂²⋊D₈₉

yes

—

193

C₂×C₄

#15667991

yes

—

194

C₂×C₄

#15667995

yes

characteristic

195

C₈

—

356

—

196

C₈

—

178

—

197

C₂²

#19151471

yes

characteristic

198

C₂²

#19151766

yes

—

199

C₂²

#19151771

yes

characteristic

200

C₂²

#19151781

yes

characteristic

201

C₂²

#19151781

yes

—

202

C₄

—

203

C₄

—

204

C₄

—

205

C₄

—

206

C₄

—

207

C₄

—

208

C₄

—

209

C₄

—

1424

—

210

C₂

#26019545

yes

characteristic

211

C₂

#26019563

yes

—

212

C₂

#26019580

yes

characteristic

213

C₂

#26020467

yes

characteristic

214

C₂

#26020478

yes

—

	subgroup	G/H
center	C₂³	#15667981
commutator	C₄²×C₈₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₈₉×#2382	C₂
socle, prime radical	C₂³×C₈₉	#120
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	#2382	D₈₉
hypocenter	C₈₉	#8913
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2382

subgroup

G/H

center

C₂³

#15667981

commutator

C₄²×C₈₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₈₉

Fitting

C₈₉×#2382

C₂

socle, prime radical

C₂³×C₈₉

#120

cosocle

C₂×C₄²×C₈₉

C₂³

D₈₉

C₈₉

G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2382

N	H ≅ G/N	type
12. #19151340	C₄	semidirect
113. C₈₉	#8913	semidirect

H ≅ G/N

type

12. #19151340

C₄

semidirect

113. C₈₉

#8913

semidirect

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

subgroup	index
#26021222	2
#26020421	2
C₂×#19151340	2
#26018133	2
C₈₉×#2382	2
#8913	89

subgroup

index

C₈₉×#2382

Subgroups — #36448802

Conjugacy classes of subgroups

Complements

Maximal subgroups