Group #26033288 — subgroups

Subgroups — #26033288

Order 11392.

350 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 117 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	#19152323	C₂	1	1	yes	maximal, characteristic, complemented
2	#19152322	C₂	1	1	yes	maximal, characteristic
3	#19151991	C₂	1	2	yes	maximal
4	#19151822	C₂	1	2	yes	maximal
5	#19151806	C₂	1	2	yes	maximal, complemented
6	#19151805	C₂	1	1	yes	maximal, characteristic, complemented
7	#19151800	C₂	1	1	yes	maximal, characteristic
8	#19151728	C₂	1	1	yes	maximal, characteristic, complemented
9	#19151705	C₂	1	2	yes	maximal, complemented
10	C₄×#13083563	C₂	1	1	yes	maximal, characteristic
11	#494×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13083564	C₂²	1	2	yes	—
13	C₂×#13083563	C₂²	1	1	yes	characteristic
14	C₂×#13083561	C₂²	1	2	yes	—
15	#15668010	C₂²	1	2	yes	—
16	#15668007	—	2	2	no	—
17	#15668003	—	2	1	no	—
18	#15668002	—	2	2	no	—
19	#15668001	C₂²	1	2	yes	—
20	#15667992	—	2	1	no	—
21	Q₈×Dic₈₉	C₂²	1	2	yes	—
22	Q₈×Dic₈₉	C₂²	1	2	yes	—
23	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
24	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
25	#15667977	—	2	1	no	—
26	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
27	#15667970	—	2	1	no	—
28	#15667944	C₂²	1	1	yes	characteristic
29	C₄⋊#10623494	C₂²	1	1	yes	characteristic
30	#15667941	C₂²	1	2	yes	—
31	#15667937	C₂²	1	1	yes	characteristic
32	#15667936	C₂²	1	2	yes	—
33	#15667936	C₂²	1	2	yes	—
34	#15667934	C₂²	1	1	yes	characteristic
35	#15667922	C₂²	1	2	yes	—
36	C₂×Q₁₆×C₈₉	C₂²	1	2	yes	—
37	C₂×Q₁₆×C₈₉	C₂²	1	2	yes	—
38	C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
39	C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
40	C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×Dic₁₇₈	D₄	1	1	yes	characteristic
42	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
43	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
44	C₂×C₄×D₈₉	—	2	1	no	—
45	#13083564	—	4	2	no	—
46	#13083563	—	2	2	no	—
47	#13083561	—	4	2	no	—
48	C₂×#10623494	C₂³	1	2	yes	—
49	C₄⋊Dic₈₉	—	2	2	no	—
50	C₄⋊Dic₈₉	—	2	2	no	—
51	C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
52	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
53	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
54	#13083553	—	2	1	no	—
55	#13083553	—	2	2	no	—
56	#13083553	—	2	2	no	—
57	#13083553	D₄	1	2	yes	—
58	#13083551	—	2	1	no	—
59	#13083551	—	2	2	no	—
60	#13083551	—	2	2	no	—
61	C₄×Dic₈₉	—	2	1	no	—
62	C₄×Dic₈₉	—	2	2	no	—
63	C₄×Dic₈₉	—	2	2	no	—
64	C₄×Dic₈₉	C₂³	1	2	yes	—
65	C₂×Q₈×C₈₉	C₂³	1	2	yes	—
66	C₂×Q₈×C₈₉	C₂³	1	2	yes	—
67	Q₁₆×C₈₉	—	2	4	no	—
68	Q₁₆×C₈₉	—	4	2	no	—
69	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
70	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
71	C₄⋊C₄×C₈₉	—	2	1	no	—
72	C₄⋊C₄×C₈₉	—	2	1	no	—
73	C₄⋊C₄×C₈₉	—	2	1	no	—
74	C₄⋊C₄×C₈₉	—	2	1	no	—
75	C₄²×C₈₉	C₂³	1	1	yes	characteristic
76	C₂²×D₈₉	—	2	1	no	—
77	Q₈×C₈₉	—	2	2	no	—
78	Q₈×C₈₉	—	2	2	no	—
79	Q₈×C₈₉	—	2	2	no	—
80	Q₈×C₈₉	—	2	2	no	—
81	C₂×C₄×C₈₉	—	2	2	no	—
82	C₂×C₄×C₈₉	—	2	2	no	—
83	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
84	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
85	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
86	C₂×Dic₈₉	—	2	1	no	—
87	C₂×Dic₈₉	—	2	1	no	—
88	C₂×Dic₈₉	—	2	1	no	—
89	C₂×Dic₈₉	C₂×D₄	1	2	yes	—
90	C₂×Dic₈₉	C₂×D₄	1	2	yes	—
91	D₃₅₆	—	2	1	no	—
92	D₃₅₆	—	2	1	no	—
93	C₄×D₈₉	—	4	2	no	—
94	Dic₁₇₈	—	2	2	no	—
95	Dic₁₇₈	—	2	1	no	—
96	Dic₁₇₈	—	2	1	no	—
97	C₈×C₈₉	—	2	1	no	—
98	C₈×C₈₉	#41	1	2	yes	—
99	#10623494	—	2	2	no	—
100	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
101	C₂×D₈₉	—	4	1	no	—
102	C₂×D₈₉	—	4	1	no	—
103	C₂×D₈₉	—	4	1	no	—
104	C₄×C₈₉	—	2	1	no	—
105	C₄×C₈₉	—	4	2	no	—
106	C₄×C₈₉	—	4	2	no	—
107	C₄×C₈₉	#137	1	2	yes	—
108	C₄×C₈₉	C₂×#41	1	1	yes	characteristic
109	C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
110	Dic₈₉	—	2	2	no	—
111	Dic₈₉	—	2	2	no	—
112	Dic₈₉	—	4	1	no	—
113	Dic₈₉	—	4	1	no	—
114	Dic₈₉	—	4	1	no	—
115	C₂×C₈₉	#550	1	1	yes	characteristic
116	C₂×C₈₉	C₂×#137	1	1	yes	characteristic
117	C₂×C₈₉	#578	1	1	yes	characteristic
118	D₈₉	—	8	1	no	—
119	#3398	—	89	1	no	maximal, Sylow
120	C₈₉	#3398	1	1	yes	characteristic, complemented, Sylow
121	#557	—	89	1	no	—
122	#556	—	89	1	no	—
123	#497	—	89	2	no	—
124	#494	D₈₉	1	1	yes	characteristic, complemented
125	#464	—	89	2	no	—
126	#462	—	89	2	no	—
127	#462	—	89	1	no	—
128	#461	—	89	1	no	—
129	#446	—	89	1	no	—
130	#441	—	89	2	no	—
131	C₄×SD₁₆	—	89	1	no	—
132	C₂×Q₁₆	—	89	2	no	—
133	C₂×Q₁₆	C₂×D₈₉	1	2	yes	—
134	C₂×Q₁₆	C₂×D₈₉	1	2	yes	—
135	C₂×SD₁₆	—	89	2	no	—
136	C₂×SD₁₆	—	89	1	no	—
137	C₄⋊Q₈	—	89	2	no	—
138	C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
139	C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
140	#126	—	178	2	no	—
141	#125	—	178	2	no	—
142	#125	—	178	1	no	—
143	#124	—	89	2	no	—
144	C₂²⋊Q₈	—	178	1	no	—
145	C₄×Q₈	—	89	1	no	—
146	C₄×Q₈	—	89	2	no	—
147	C₄×Q₈	—	89	2	no	—
148	C₄×Q₈	—	89	1	no	—
149	C₄×Q₈	—	178	1	no	—
150	C₄×D₄	—	89	1	no	—
151	#117	—	178	1	no	—
152	#106	—	89	1	no	—
153	C₄⋊C₈	—	89	2	no	—
154	C₄⋊C₈	—	89	1	no	—
155	#103	—	89	2	no	—
156	#103	—	89	2	no	—
157	#103	—	89	1	no	—
158	#102	—	89	1	no	—
159	#97	—	89	2	no	—
160	C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
161	C₂×Q₈	—	89	1	no	—
162	C₂×Q₈	—	89	1	no	—
163	C₂×Q₈	C₂²×D₈₉	1	2	yes	—
164	C₂×Q₈	C₂²×D₈₉	1	2	yes	—
165	C₂×D₄	—	89	1	no	—
166	C₂²×C₄	—	178	1	no	—
167	Q₁₆	—	2	4	no	—
168	Q₁₆	—	4	2	no	—
169	Q₁₆	—	356	2	no	—
170	SD₁₆	—	356	2	no	—
171	SD₁₆	—	178	2	no	—
172	C₂×C₈	—	89	2	no	—
173	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
174	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
175	C₄⋊C₄	—	2	1	no	—
176	C₄⋊C₄	—	2	1	no	—
177	C₄⋊C₄	—	2	1	no	—
178	C₄⋊C₄	—	2	1	no	—
179	C₄⋊C₄	—	89	1	no	—
180	C₄⋊C₄	—	89	2	no	—
181	C₄⋊C₄	—	89	1	no	—
182	C₄⋊C₄	—	89	1	no	—
183	C₄⋊C₄	—	178	2	no	—
184	C₄⋊C₄	—	178	2	no	—
185	C₄⋊C₄	—	178	2	no	—
186	C₄⋊C₄	—	178	2	no	—
187	C₄⋊C₄	—	178	1	no	—
188	C₂²⋊C₄	—	178	2	no	—
189	C₂²⋊C₄	—	178	2	no	—
190	C₂²⋊C₄	—	178	1	no	—
191	C₄²	—	89	2	no	—
192	C₄²	—	178	2	no	—
193	C₄²	—	178	2	no	—
194	C₄²	—	178	1	no	—
195	C₄²	C₂²×D₈₉	1	1	yes	characteristic
196	C₂³	—	178	1	no	—
197	Q₈	—	2	2	no	—
198	Q₈	—	2	2	no	—
199	Q₈	—	2	2	no	—
200	Q₈	—	2	2	no	—
201	Q₈	—	178	1	no	—
202	Q₈	—	178	1	no	—
203	Q₈	—	178	2	no	—
204	D₄	—	178	1	no	—
205	D₄	—	178	1	no	—
206	C₂×C₄	—	2	2	no	—
207	C₂×C₄	—	2	2	no	—
208	C₂×C₄	—	89	2	no	—
209	C₂×C₄	—	89	2	no	—
210	C₂×C₄	—	356	2	no	—
211	C₂×C₄	—	178	1	no	—
212	C₂×C₄	—	178	1	no	—
213	C₂×C₄	—	178	1	no	—
214	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
215	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
216	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
217	C₈	—	2	1	no	—
218	C₈	—	178	2	no	—
219	C₈	#13083573	1	2	yes	—
220	C₂²	—	356	1	no	—
221	C₂²	—	356	1	no	—
222	C₂²	—	356	1	no	—
223	C₂²	C₂×D₄×D₈₉	1	1	yes	characteristic
224	C₄	—	2	1	no	—
225	C₄	—	4	2	no	—
226	C₄	—	4	2	no	—
227	C₄	—	356	1	no	—
228	C₄	—	356	1	no	—
229	C₄	—	356	1	no	—
230	C₄	—	178	2	no	—
231	C₄	—	178	2	no	—
232	C₄	#15668044	1	2	yes	—
233	C₄	C₂×#13083573	1	1	yes	characteristic
234	C₄	#15668057	1	1	yes	characteristic
235	C₂	—	712	1	no	—
236	C₂	#19152268	1	1	yes	characteristic
237	C₂	C₂×#15668044	1	1	yes	characteristic
238	C₂	#19152411	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19152323

C₂

yes

maximal, characteristic, complemented

#19152322

C₂

yes

maximal, characteristic

#19151991

C₂

yes

maximal

#19151822

C₂

yes

maximal

#19151806

C₂

yes

maximal, complemented

#19151805

C₂

yes

maximal, characteristic, complemented

#19151800

C₂

yes

maximal, characteristic

#19151728

C₂

yes

maximal, characteristic, complemented

#19151705

C₂

yes

maximal, complemented

C₄×#13083563

C₂

yes

maximal, characteristic

#494×C₈₉

C₂

yes

maximal, characteristic, complemented

C₂×#13083564

C₂²

yes

—

C₂×#13083563

C₂²

yes

characteristic

C₂×#13083561

C₂²

yes

—

#15668010

C₂²

yes

—

—

—

—

C₂²

yes

—

#15667992

—

Q₈×Dic₈₉

C₂²

yes

—

Q₈×Dic₈₉

C₂²

yes

—

C₄×Dic₁₇₈

C₂²

yes

characteristic

C₄×Dic₁₇₈

C₂²

yes

characteristic

#15667977

—

C₄×D₃₅₆

C₂²

yes

characteristic

#15667970

—

#15667944

C₂²

yes

characteristic

C₄⋊#10623494

C₂²

yes

characteristic

#15667941

C₂²

yes

—

#15667937

C₂²

yes

characteristic

#15667936

C₂²

yes

—

#15667936

C₂²

yes

—

#15667934

C₂²

yes

characteristic

#15667922

C₂²

yes

—

C₂×Q₁₆×C₈₉

C₂²

yes

—

C₂×Q₁₆×C₈₉

C₂²

yes

—

C₄⋊Q₈×C₈₉

C₂²

yes

characteristic

C₄⋊Q₈×C₈₉

C₂²

yes

characteristic

C₄×C₈×C₈₉

C₂²

yes

characteristic

C₂×Dic₁₇₈

D₄

yes

characteristic

C₂×Dic₁₇₈

C₂³

yes

characteristic

C₂×D₃₅₆

C₂³

yes

characteristic

C₂×C₄×D₈₉

—

—

—

—

C₂³

yes

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

D₄

yes

characteristic

C₄⋊Dic₈₉

C₂³

yes

characteristic

C₄⋊Dic₈₉

C₂³

yes

—

—

—

D₄

yes

—

#13083551

—

#13083551

—

#13083551

—

C₄×Dic₈₉

—

C₄×Dic₈₉

—

C₄×Dic₈₉

—

C₄×Dic₈₉

C₂³

yes

—

C₂×Q₈×C₈₉

C₂³

yes

—

C₂×Q₈×C₈₉

C₂³

yes

—

Q₁₆×C₈₉

—

Q₁₆×C₈₉

—

C₂×C₈×C₈₉

C₂³

yes

characteristic

C₂×C₈×C₈₉

C₂³

yes

characteristic

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄²×C₈₉

C₂³

yes

characteristic

C₂²×D₈₉

—

Q₈×C₈₉

—

Q₈×C₈₉

—

Q₈×C₈₉

—

Q₈×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂×C₄×C₈₉

C₂⁴

yes

characteristic

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

C₂×D₄

yes

—

C₂×Dic₈₉

C₂×D₄

yes

—

D₃₅₆

—

D₃₅₆

—

C₄×D₈₉

—

Dic₁₇₈

—

Dic₁₇₈

—

Dic₁₇₈

—

C₈×C₈₉

—

C₈×C₈₉

#41

yes

—

#10623494

—

100

C₂²×C₈₉

C₂²×D₄

yes

characteristic

101

C₂×D₈₉

—

102

C₂×D₈₉

—

103

C₂×D₈₉

—

104

C₄×C₈₉

—

105

C₄×C₈₉

—

106

C₄×C₈₉

—

107

C₄×C₈₉

#137

yes

—

108

C₄×C₈₉

C₂×#41

yes

characteristic

109

C₄×C₈₉

H(5,𝔽₂)

yes

characteristic

110

Dic₈₉

—

111

Dic₈₉

—

112

Dic₈₉

—

113

Dic₈₉

—

114

Dic₈₉

—

115

C₂×C₈₉

#550

yes

characteristic

116

C₂×C₈₉

C₂×#137

yes

characteristic

117

C₂×C₈₉

#578

yes

characteristic

118

D₈₉

—

119

#3398

—

maximal, Sylow

120

C₈₉

#3398

yes

characteristic, complemented, Sylow

121

#557

—

122

#556

—

123

#497

—

124

#494

D₈₉

yes

characteristic, complemented

125

#464

—

126

#462

—

127

#462

—

128

#461

—

129

#446

—

130

#441

—

131

C₄×SD₁₆

—

132

C₂×Q₁₆

—

133

C₂×Q₁₆

C₂×D₈₉

yes

—

134

C₂×Q₁₆

C₂×D₈₉

yes

—

135

C₂×SD₁₆

—

136

C₂×SD₁₆

—

137

C₄⋊Q₈

—

138

C₄⋊Q₈

C₂×D₈₉

yes

characteristic

139

C₄⋊Q₈

C₂×D₈₉

yes

characteristic

140

#126

—

178

—

141

#125

—

178

—

142

#125

—

178

—

143

#124

—

144

C₂²⋊Q₈

—

178

—

145

C₄×Q₈

—

146

C₄×Q₈

—

147

C₄×Q₈

—

148

C₄×Q₈

—

149

C₄×Q₈

—

178

—

150

C₄×D₄

—

151

#117

—

178

—

152

#106

—

153

C₄⋊C₈

—

154

C₄⋊C₈

—

155

#103

—

156

#103

—

157

#103

—

158

#102

—

159

#97

—

160

C₄×C₈

C₂×D₈₉

yes

characteristic

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

C₂²×D₈₉

yes

—

164

C₂×Q₈

C₂²×D₈₉

yes

—

165

C₂×D₄

—

166

C₂²×C₄

—

178

—

167

Q₁₆

—

168

Q₁₆

—

169

Q₁₆

—

356

—

170

SD₁₆

—

356

—

171

SD₁₆

—

178

—

172

C₂×C₈

—

173

C₂×C₈

C₂²×D₈₉

yes

characteristic

174

C₂×C₈

C₂²×D₈₉

yes

characteristic

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

178

—

184

C₄⋊C₄

—

178

—

185

C₄⋊C₄

—

178

—

186

C₄⋊C₄

—

178

—

187

C₄⋊C₄

—

178

—

188

C₂²⋊C₄

—

178

—

189

C₂²⋊C₄

—

178

—

190

C₂²⋊C₄

—

178

—

191

C₄²

—

192

C₄²

—

178

—

193

C₄²

—

178

—

194

C₄²

—

178

—

195

C₄²

C₂²×D₈₉

yes

characteristic

196

C₂³

—

178

—

197

Q₈

—

198

Q₈

—

199

Q₈

—

200

Q₈

—

201

Q₈

—

178

—

202

Q₈

—

178

—

203

Q₈

—

178

—

204

D₄

—

178

—

205

D₄

—

178

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

356

—

211

C₂×C₄

—

178

—

212

C₂×C₄

—

178

—

213

C₂×C₄

—

178

—

214

C₂×C₄

D₄×D₈₉

yes

characteristic

215

C₂×C₄

D₄×D₈₉

yes

characteristic

216

C₂×C₄

C₂³×D₈₉

yes

characteristic

217

C₈

—

218

C₈

—

178

—

219

C₈

#13083573

yes

—

220

C₂²

—

356

—

221

C₂²

—

356

—

222

C₂²

—

356

—

223

C₂²

C₂×D₄×D₈₉

yes

characteristic

224

C₄

—

225

C₄

—

226

C₄

—

227

C₄

—

356

—

228

C₄

—

356

—

229

C₄

—

356

—

230

C₄

—

178

—

231

C₄

—

178

—

232

C₄

#15668044

yes

—

233

C₄

C₂×#13083573

yes

characteristic

234

C₄

#15668057

yes

characteristic

235

C₂

—

712

—

236

C₂

#19152268

yes

characteristic

237

C₂

C₂×#15668044

yes

characteristic

238

C₂

#19152411

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₈₉
commutator, cosocle	C₂×C₄×C₈₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₉
Fitting	#494×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₄
prime radical	C₂×D₃₅₆	C₂³
hypercenter	#494	D₈₉
hypocenter	C₈₉	#3398
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #494

subgroup

G/H

center

C₂²

C₂×D₄×D₈₉

commutator, cosocle

C₂×C₄×C₈₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₈₉

Fitting

#494×C₈₉

C₂

socle

C₂²×C₈₉

C₂²×D₄

prime radical

C₂×D₃₅₆

C₂³

D₈₉

C₈₉

G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #494

N	H ≅ G/N	type
1. #19152323	C₂	semidirect
5. #19151806	C₂	semidirect
6. #19151805	C₂	semidirect
8. #19151728	C₂	semidirect
9. #19151705	C₂	semidirect
11. #494×C₈₉	C₂	semidirect
120. C₈₉	#3398	semidirect
124. #494	D₈₉	semidirect

H ≅ G/N

type

1. #19152323

C₂

semidirect

5. #19151806

C₂

semidirect

6. #19151805

C₂

semidirect

8. #19151728

C₂

semidirect

9. #19151705

C₂

semidirect

11. #494×C₈₉

C₂

semidirect

120. C₈₉

#3398

semidirect

124. #494

D₈₉

semidirect

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

subgroup	index
#19152323	2
#19152322	2
#19151991	2
#19151822	2
#19151806	2
#19151805	2
#19151800	2
#19151728	2
#19151705	2
C₄×#13083563	2
#494×C₈₉	2
#3398	89

subgroup

index

#494×C₈₉

Subgroups — #26033288

Conjugacy classes of subgroups

Complements

Maximal subgroups