Group #36445444 — subgroups

Subgroups — #36445444

Order 22784.

436 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 133 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	#26028964	C₂	1	1	yes	maximal, characteristic
2	#26018844	C₂	1	1	yes	maximal, characteristic
3	#26018542	C₂	1	2	yes	maximal, complemented
4	#26018143	C₂	1	2	yes	maximal, complemented
5	C₈₉×#1543	C₂	1	1	yes	maximal, characteristic
6	C₂×#15668019	C₄	1	2	yes	—
7	#19151676	—	2	2	no	—
8	D₄×#10623494	—	2	2	no	—
9	#19151622	C₂²	1	1	yes	characteristic
10	#19151565	C₄	1	2	yes	—
11	C₄×#13083558	C₂²	1	2	yes	—
12	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
13	#19151338	C₄	1	4	yes	—
14	#19151320	—	2	2	no	—
15	#19151319	—	2	2	no	—
16	#532×C₈₉	C₂²	1	1	yes	characteristic
17	#431×C₈₉	C₂²	1	2	yes	—
18	#333×C₈₉	C₄	1	2	yes	—
19	#331×C₈₉	C₄	1	2	yes	—
20	#15668019	—	4	4	no	—
21	C₂×#13083558	—	2	2	no	—
22	C₂×#13083558	—	2	2	no	—
23	C₂×#13083558	C₂×C₄	1	2	yes	—
24	C₂²×#10623494	—	2	2	no	—
25	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
26	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
27	C₄⋊#10623494	—	2	2	no	—
28	C₂²⋊#10623494	—	2	4	no	—
29	#15667923	C₂×C₄	1	4	yes	—
30	C₄×#10623494	—	2	2	no	—
31	C₄×#10623494	D₄	1	2	yes	—
32	C₄×#10623494	D₄	1	2	yes	—
33	C₂×#41×C₈₉	C₂×C₄	1	2	yes	—
34	C₄⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
35	#127×C₈₉	C₂×C₄	1	1	yes	characteristic
36	#124×C₈₉	C₂×C₄	1	2	yes	—
37	#121×C₈₉	—	2	2	no	—
38	C₄×D₄×C₈₉	—	2	2	no	—
39	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
40	C₄⋊C₈×C₈₉	C₂×C₄	1	4	yes	—
41	C₂²⋊C₈×C₈₉	—	2	2	no	—
42	C₄×C₈×C₈₉	—	2	2	no	—
43	#13083558	—	4	4	no	—
44	#13083558	—	4	4	no	—
45	#13083558	—	4	2	no	—
46	C₂×#10623494	—	2	2	no	—
47	C₂×#10623494	—	2	2	no	—
48	C₂×#10623494	—	2	4	no	—
49	C₂×#10623494	—	4	1	no	—
50	C₂×#10623494	—	4	4	no	—
51	C₂×#10623494	C₂²⋊C₄	1	1	yes	characteristic
52	C₂×#10623494	C₂²⋊C₄	1	2	yes	—
53	C₂×#10623494	C₂²⋊C₄	1	1	yes	characteristic
54	#41×C₈₉	—	4	2	no	—
55	#41×C₈₉	—	4	2	no	—
56	C₂×Q₈×C₈₉	C₄²	1	2	yes	—
57	C₂×D₄×C₈₉	—	2	2	no	—
58	C₂×D₄×C₈₉	—	2	2	no	—
59	C₂×D₄×C₈₉	C₄²	1	2	yes	—
60	C₂²×C₄×C₈₉	—	2	2	no	—
61	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₈₉	#41	1	2	yes	—
63	C₂×C₈×C₈₉	—	2	4	no	—
64	C₄⋊C₄×C₈₉	—	2	2	no	—
65	C₂²⋊C₄×C₈₉	—	2	4	no	—
66	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
67	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
68	C₄²×C₈₉	C₂×D₄	1	2	yes	—
69	C₂³×C₈₉	—	2	2	no	—
70	C₂³×C₈₉	#117	1	1	yes	characteristic
71	Q₈×C₈₉	—	4	2	no	—
72	D₄×C₈₉	—	4	2	no	—
73	D₄×C₈₉	—	4	4	no	—
74	D₄×C₈₉	—	4	4	no	—
75	C₂×C₄×C₈₉	—	2	1	no	—
76	C₂×C₄×C₈₉	—	2	1	no	—
77	C₂×C₄×C₈₉	—	2	4	no	—
78	C₂×C₄×C₈₉	—	2	2	no	—
79	C₂×C₄×C₈₉	—	4	2	no	—
80	C₂×C₄×C₈₉	—	4	2	no	—
81	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
82	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
84	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
85	C₈×C₈₉	—	4	4	no	—
86	#10623494	—	2	1	no	—
87	#10623494	—	2	2	no	—
88	#10623494	—	4	4	no	—
89	#10623494	—	4	2	no	—
90	#10623494	#100	1	2	yes	—
91	C₂²×C₈₉	—	2	1	no	—
92	C₂²×C₈₉	—	2	2	no	—
93	C₂²×C₈₉	—	4	2	no	—
94	C₂²×C₈₉	—	4	4	no	—
95	C₂²×C₈₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
96	C₄×C₈₉	—	2	1	no	—
97	C₄×C₈₉	—	2	2	no	—
98	C₄×C₈₉	—	4	2	no	—
99	C₄×C₈₉	C₂×#100	1	1	yes	characteristic
100	C₄×C₈₉	#413	1	1	yes	characteristic
101	C₄×C₈₉	#444	1	4	yes	—
102	#8243	—	89	1	no	maximal, Sylow
103	C₂×C₈₉	—	4	1	no	—
104	C₂×C₈₉	—	8	2	no	—
105	C₂×C₈₉	C₄×#100	1	1	yes	characteristic
106	C₂×C₈₉	#1765	1	2	yes	—
107	#2931	—	89	1	no	—
108	#1543	D₈₉	1	1	yes	characteristic
109	#1525	—	89	1	no	—
110	#1451	—	89	2	no	—
111	#1299	—	89	2	no	—
112	C₈₉	#8243	1	1	yes	characteristic, complemented, Sylow
113	C₂×#131	—	89	2	no	—
114	#532	C₂×D₈₉	1	1	yes	characteristic
115	#436	—	178	2	no	—
116	C₈×D₄	—	178	2	no	—
117	#431	C₂×D₈₉	1	2	yes	—
118	#423	—	89	1	no	—
119	#408	—	89	2	no	—
120	C₄×M₁₆	—	89	2	no	—
121	C₂×C₄×C₈	—	89	1	no	—
122	#333	Dic₈₉	1	2	yes	—
123	#331	Dic₈₉	1	2	yes	—
124	#329	—	89	4	no	—
125	#322	—	178	2	no	—
126	#322	—	178	2	no	—
127	C₂×#41	C₄×D₈₉	1	2	yes	—
128	#131	—	356	4	no	—
129	C₂×M₁₆	—	89	2	no	—
130	C₂×M₁₆	—	178	2	no	—
131	C₂×M₁₆	—	178	2	no	—
132	C₂²×C₈	—	89	1	no	—
133	C₂²×C₈	—	89	1	no	—
134	C₂²×C₈	—	178	2	no	—
135	C₄⋊Q₈	C₂×Dic₈₉	1	1	yes	characteristic
136	#127	C₂×Dic₈₉	1	1	yes	characteristic
137	#124	C₄×D₈₉	1	2	yes	—
138	#121	—	2	2	no	—
139	C₄×D₄	—	2	2	no	—
140	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
141	C₄⋊C₈	—	178	2	no	—
142	C₄⋊C₈	C₂×Dic₈₉	1	4	yes	—
143	C₂²⋊C₈	—	2	2	no	—
144	C₂²⋊C₈	—	178	4	no	—
145	#97	—	89	4	no	—
146	C₄×C₈	—	2	2	no	—
147	C₄×C₈	—	89	2	no	—
148	C₄×C₈	—	89	2	no	—
149	C₄×C₈	—	178	2	no	—
150	#41	—	4	2	no	—
151	#41	—	4	2	no	—
152	C₂×Q₈	C₄×Dic₈₉	1	2	yes	—
153	C₂×D₄	—	2	2	no	—
154	C₂×D₄	—	2	2	no	—
155	C₂×D₄	C₄×Dic₈₉	1	2	yes	—
156	C₂²×C₄	—	2	2	no	—
157	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
158	C₂²×C₄	#13083573	1	2	yes	—
159	M₁₆	—	356	4	no	—
160	M₁₆	—	356	4	no	—
161	M₁₆	—	356	2	no	—
162	C₂×C₈	—	2	4	no	—
163	C₂×C₈	—	89	1	no	—
164	C₂×C₈	—	89	2	no	—
165	C₂×C₈	—	89	1	no	—
166	C₂×C₈	—	356	4	no	—
167	C₂×C₈	—	356	1	no	—
168	C₂×C₈	—	178	2	no	—
169	C₂×C₈	—	178	4	no	—
170	C₂×C₈	—	178	2	no	—
171	C₄⋊C₄	—	2	2	no	—
172	C₂²⋊C₄	—	2	4	no	—
173	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
174	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
175	C₄²	D₄×D₈₉	1	2	yes	—
176	C₂³	—	2	2	no	—
177	C₂³	#15667968	1	1	yes	characteristic
178	Q₈	—	4	2	no	—
179	D₄	—	4	2	no	—
180	D₄	—	4	4	no	—
181	D₄	—	4	4	no	—
182	C₂×C₄	—	2	4	no	—
183	C₂×C₄	—	2	1	no	—
184	C₂×C₄	—	2	1	no	—
185	C₂×C₄	—	2	2	no	—
186	C₂×C₄	—	4	2	no	—
187	C₂×C₄	—	4	2	no	—
188	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
189	C₂×C₄	C₂²⋊C₄×D₈₉	1	1	yes	characteristic
190	C₂×C₄	#15667972	1	2	yes	—
191	C₂×C₄	D₄×Dic₈₉	1	2	yes	—
192	C₈	—	4	4	no	—
193	C₈	—	89	2	no	—
194	C₈	—	356	4	no	—
195	C₈	—	356	2	no	—
196	C₈	—	178	1	no	—
197	C₈	—	178	2	no	—
198	C₂²	—	2	2	no	—
199	C₂²	—	2	1	no	—
200	C₂²	—	4	4	no	—
201	C₂²	—	4	2	no	—
202	C₂²	C₂²⋊C₄×Dic₈₉	1	1	yes	characteristic
203	C₄	—	2	2	no	—
204	C₄	—	2	1	no	—
205	C₄	—	4	2	no	—
206	C₄	#100×D₈₉	1	1	yes	characteristic
207	C₄	#19151579	1	1	yes	characteristic
208	C₄	#19151720	1	4	yes	—
209	C₂	—	4	1	no	—
210	C₂	—	8	2	no	—
211	C₂	#100×Dic₈₉	1	1	yes	characteristic
212	C₂	#26020099	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#26028964

C₂

yes

maximal, characteristic

#26018844

C₂

yes

maximal, characteristic

#26018542

C₂

yes

maximal, complemented

#26018143

C₂

yes

maximal, complemented

C₈₉×#1543

C₂

yes

maximal, characteristic

C₂×#15668019

C₄

yes

—

#19151676

—

D₄×#10623494

—

#19151622

C₂²

yes

characteristic

#19151565

C₄

yes

—

C₄×#13083558

C₂²

yes

—

C₂×C₄×#10623494

C₂²

yes

characteristic

#19151338

C₄

yes

—

#19151320

—

#19151319

—

#532×C₈₉

C₂²

yes

characteristic

#431×C₈₉

C₂²

yes

—

#333×C₈₉

C₄

yes

—

#331×C₈₉

C₄

yes

—

—

—

—

C₂×C₄

yes

—

C₂²×#10623494

—

C₂²×#10623494

C₂×C₄

yes

characteristic

C₂²×#10623494

C₂×C₄

yes

—

—

C₂×C₄

yes

—

C₄×#10623494

—

C₄×#10623494

D₄

yes

—

C₄×#10623494

D₄

yes

—

C₂×#41×C₈₉

C₂×C₄

yes

—

C₄⋊Q₈×C₈₉

C₂×C₄

yes

characteristic

#127×C₈₉

C₂×C₄

yes

characteristic

#124×C₈₉

C₂×C₄

yes

—

#121×C₈₉

—

C₄×D₄×C₈₉

—

C₂×C₄²×C₈₉

C₂³

yes

characteristic

C₄⋊C₈×C₈₉

C₂×C₄

yes

—

C₂²⋊C₈×C₈₉

—

C₄×C₈×C₈₉

—

—

—

—

—

—

—

—

—

C₂²⋊C₄

yes

characteristic

C₂×#10623494

C₂²⋊C₄

yes

—

C₂×#10623494

C₂²⋊C₄

yes

characteristic

#41×C₈₉

—

#41×C₈₉

—

C₂×Q₈×C₈₉

C₄²

yes

—

C₂×D₄×C₈₉

—

C₂×D₄×C₈₉

—

C₂×D₄×C₈₉

C₄²

yes

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₈₉

#41

yes

—

C₂×C₈×C₈₉

—

C₄⋊C₄×C₈₉

—

C₂²⋊C₄×C₈₉

—

C₄²×C₈₉

C₂²×C₄

yes

characteristic

C₄²×C₈₉

C₂²×C₄

yes

characteristic

C₄²×C₈₉

C₂×D₄

yes

—

C₂³×C₈₉

—

C₂³×C₈₉

#117

yes

characteristic

Q₈×C₈₉

—

D₄×C₈₉

—

D₄×C₈₉

—

D₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂×C₄²

yes

characteristic

C₂×C₄×C₈₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₈₉

C₄×D₄

yes

—

C₂×C₄×C₈₉

C₄×D₄

yes

—

C₈×C₈₉

—

—

—

—

—

yes

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

C₄×C₂²⋊C₄

yes

characteristic

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

C₂×#100

yes

characteristic

100

C₄×C₈₉

#413

yes

characteristic

101

C₄×C₈₉

#444

yes

—

102

#8243

—

maximal, Sylow

103

C₂×C₈₉

—

104

C₂×C₈₉

—

105

C₂×C₈₉

C₄×#100

yes

characteristic

106

C₂×C₈₉

#1765

yes

—

107

#2931

—

108

#1543

D₈₉

yes

characteristic

109

#1525

—

110

#1451

—

111

#1299

—

112

C₈₉

#8243

yes

characteristic, complemented, Sylow

113

C₂×#131

—

114

#532

C₂×D₈₉

yes

characteristic

115

#436

—

178

—

116

C₈×D₄

—

178

—

117

#431

C₂×D₈₉

yes

—

118

#423

—

119

#408

—

120

C₄×M₁₆

—

121

C₂×C₄×C₈

—

122

#333

Dic₈₉

yes

—

123

#331

Dic₈₉

yes

—

124

#329

—

125

#322

—

178

—

126

#322

—

178

—

127

C₂×#41

C₄×D₈₉

yes

—

128

#131

—

356

—

129

C₂×M₁₆

—

130

C₂×M₁₆

—

178

—

131

C₂×M₁₆

—

178

—

132

C₂²×C₈

—

133

C₂²×C₈

—

134

C₂²×C₈

—

178

—

135

C₄⋊Q₈

C₂×Dic₈₉

yes

characteristic

136

#127

C₂×Dic₈₉

yes

characteristic

137

#124

C₄×D₈₉

yes

—

138

#121

—

139

C₄×D₄

—

140

C₂×C₄²

C₂²×D₈₉

yes

characteristic

141

C₄⋊C₈

—

178

—

142

C₄⋊C₈

C₂×Dic₈₉

yes

—

143

C₂²⋊C₈

—

144

C₂²⋊C₈

—

178

—

145

#97

—

146

C₄×C₈

—

147

C₄×C₈

—

148

C₄×C₈

—

149

C₄×C₈

—

178

—

150

#41

—

151

#41

—

152

C₂×Q₈

C₄×Dic₈₉

yes

—

153

C₂×D₄

—

154

C₂×D₄

—

155

C₂×D₄

C₄×Dic₈₉

yes

—

156

C₂²×C₄

—

157

C₂²×C₄

C₂×C₄×D₈₉

yes

characteristic

158

C₂²×C₄

#13083573

yes

—

159

M₁₆

—

356

—

160

M₁₆

—

356

—

161

M₁₆

—

356

—

162

C₂×C₈

—

163

C₂×C₈

—

164

C₂×C₈

—

165

C₂×C₈

—

166

C₂×C₈

—

356

—

167

C₂×C₈

—

356

—

168

C₂×C₈

—

178

—

169

C₂×C₈

—

178

—

170

C₂×C₈

—

178

—

171

C₄⋊C₄

—

172

C₂²⋊C₄

—

173

C₄²

C₂×C₄×D₈₉

yes

characteristic

174

C₄²

C₂²×Dic₈₉

yes

characteristic

175

C₄²

D₄×D₈₉

yes

—

176

C₂³

—

177

C₂³

#15667968

yes

characteristic

178

Q₈

—

179

D₄

—

180

D₄

—

181

D₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

C₂×C₄×Dic₈₉

yes

characteristic

189

C₂×C₄

C₂²⋊C₄×D₈₉

yes

characteristic

190

C₂×C₄

#15667972

yes

—

191

C₂×C₄

D₄×Dic₈₉

yes

—

192

C₈

—

193

C₈

—

194

C₈

—

356

—

195

C₈

—

356

—

196

C₈

—

178

—

197

C₈

—

178

—

198

C₂²

—

199

C₂²

—

200

C₂²

—

201

C₂²

—

202

C₂²

C₂²⋊C₄×Dic₈₉

yes

characteristic

203

C₄

—

204

C₄

—

205

C₄

—

206

C₄

#100×D₈₉

yes

characteristic

207

C₄

#19151579

yes

characteristic

208

C₄

#19151720

yes

—

209

C₂

—

210

C₂

—

211

C₂

#100×Dic₈₉

yes

characteristic

212

C₂

#26020099

yes

—

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₈₉×#1543	C₂
socle	C₂²×C₈₉	C₄×C₂²⋊C₄
prime radical	#532×C₈₉	C₂²
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	#1543	D₈₉
hypocenter	C₈₉	#8243
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1543

subgroup

G/H

center

C₂×C₄

C₂²⋊C₄×D₈₉

commutator

C₂×C₄×C₈₉

C₂×C₄²

Frattini

C₂×C₄²

C₂²×D₈₉

Fitting

C₈₉×#1543

C₂

socle

C₂²×C₈₉

C₄×C₂²⋊C₄

prime radical

#532×C₈₉

C₂²

cosocle

C₂×C₄²×C₈₉

C₂³

D₈₉

C₈₉

G ▷ C₂×C₄×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1543

N	H ≅ G/N	type
3. #26018542	C₂	semidirect
4. #26018143	C₂	semidirect
112. C₈₉	#8243	semidirect

H ≅ G/N

type

3. #26018542

C₂

semidirect

4. #26018143

C₂

semidirect

112. C₈₉

#8243

semidirect

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

subgroup	index
#26028964	2
#26018844	2
#26018542	2
#26018143	2
C₈₉×#1543	2
#8243	89

subgroup

index

C₈₉×#1543

Subgroups — #36445444

Conjugacy classes of subgroups

Complements

Maximal subgroups