Group #26031173 — subgroups

Subgroups — #26031173

Order 11392.

428 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 125 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	#19152146	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Q₈×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#19151970	C₂	1	1	yes	maximal, characteristic, complemented
4	#19151949	C₂	1	1	yes	maximal, characteristic, complemented
5	#19151948	C₂	1	1	yes	maximal, characteristic, complemented
6	#19151801	C₂	1	4	yes	maximal, complemented
7	#19151735	C₂	1	4	yes	maximal, complemented
8	#19151649	C₂	1	1	yes	maximal, characteristic, complemented
9	#492×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#13083573	—	2	1	no	—
11	C₂×Q₈×D₈₉	C₂²	1	2	yes	—
12	C₂×#13083562	C₂²	1	4	yes	—
13	#15668012	C₂²	1	1	yes	characteristic
14	#15668012	C₂²	1	1	yes	characteristic
15	#15668011	—	2	1	no	—
16	#15668011	—	2	1	no	—
17	#15668010	C₂²	1	2	yes	—
18	#15667999	—	2	1	no	—
19	#15667983	—	2	1	no	—
20	#15667983	C₂²	1	2	yes	—
21	D₄×Dic₈₉	—	2	1	no	—
22	D₄×Dic₈₉	C₂²	1	2	yes	—
23	C₄⋊C₄×D₈₉	—	2	1	no	—
24	C₄⋊C₄×D₈₉	—	2	1	no	—
25	C₄²×D₈₉	C₂²	1	1	yes	characteristic
26	#15667941	C₂²	1	2	yes	—
27	#15667937	C₂²	1	4	yes	—
28	#15667936	C₂²	1	4	yes	—
29	#15667924	C₂²	1	2	yes	—
30	C₄×#10623494	C₂²	1	1	yes	characteristic
31	C₂×SD₁₆×C₈₉	C₂²	1	4	yes	—
32	C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
33	#127×C₈₉	C₂²	1	1	yes	characteristic
34	C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
35	#13083573	—	4	4	no	—
36	C₂×Dic₁₇₈	—	2	1	no	—
37	C₂×Dic₁₇₈	—	2	2	no	—
38	C₂×Dic₁₇₈	C₂³	1	2	yes	—
39	Q₈×D₈₉	—	4	4	no	—
40	C₂×C₂²⋊D₈₉	—	2	2	no	—
41	C₂²×Dic₈₉	—	2	2	no	—
42	C₂×C₄×D₈₉	—	2	2	no	—
43	C₂×C₄×D₈₉	D₄	1	1	yes	characteristic
44	C₂×C₄×D₈₉	D₄	1	1	yes	characteristic
45	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
46	#13083562	—	4	4	no	—
47	C₂×#10623494	C₂³	1	2	yes	—
48	C₄⋊Dic₈₉	—	2	1	no	—
49	C₄⋊Dic₈₉	—	2	1	no	—
50	C₄⋊Dic₈₉	—	2	1	no	—
51	C₄⋊Dic₈₉	C₂³	1	2	yes	—
52	#13083553	—	2	2	no	—
53	#13083553	—	2	2	no	—
54	C₂²⋊Dic₈₉	—	2	2	no	—
55	C₂²⋊Dic₈₉	—	2	2	no	—
56	C₄×Dic₈₉	D₄	1	1	yes	characteristic
57	C₄×Dic₈₉	D₄	1	1	yes	characteristic
58	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
59	C₂×Q₈×C₈₉	C₂³	1	2	yes	—
60	C₂×D₄×C₈₉	—	2	1	no	—
61	C₂×D₄×C₈₉	—	2	1	no	—
62	C₂×D₄×C₈₉	C₂³	1	2	yes	—
63	SD₁₆×C₈₉	—	4	4	no	—
64	C₂×C₈×C₈₉	C₂³	1	2	yes	—
65	C₄⋊C₄×C₈₉	—	2	1	no	—
66	C₄⋊C₄×C₈₉	—	2	1	no	—
67	C₄²×C₈₉	C₂³	1	1	yes	characteristic
68	C₂³×C₈₉	—	2	2	no	—
69	C₂²×D₈₉	C₂×D₄	1	1	yes	characteristic
70	Q₈×C₈₉	—	2	4	no	—
71	D₄×C₈₉	—	2	4	no	—
72	D₄×C₈₉	—	4	2	no	—
73	D₄×C₈₉	—	4	2	no	—
74	C₂×C₄×C₈₉	—	2	2	no	—
75	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
76	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
77	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
78	C₂²⋊D₈₉	—	4	4	no	—
79	C₂×Dic₈₉	—	2	2	no	—
80	C₂×Dic₈₉	—	2	2	no	—
81	C₂×Dic₈₉	—	4	4	no	—
82	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
83	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
84	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
85	C₄×D₈₉	—	2	2	no	—
86	C₄×D₈₉	—	2	2	no	—
87	C₄×D₈₉	—	4	4	no	—
88	C₄×D₈₉	SD₁₆	1	4	yes	complemented
89	Dic₁₇₈	—	2	4	no	—
90	Dic₁₇₈	—	4	4	no	—
91	Dic₁₇₈	—	4	2	no	—
92	C₈×C₈₉	—	2	2	no	—
93	#10623494	—	2	2	no	—
94	C₂²×C₈₉	—	4	2	no	—
95	C₂²×C₈₉	—	4	2	no	—
96	C₂²×C₈₉	—	4	2	no	—
97	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
98	C₂×D₈₉	—	2	1	no	—
99	C₂×D₈₉	—	2	1	no	—
100	C₂×D₈₉	C₂×SD₁₆	1	2	yes	—
101	C₄×C₈₉	—	4	2	no	—
102	C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
103	C₄×C₈₉	#137	1	2	yes	—
104	C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
105	Dic₈₉	—	2	1	no	—
106	Dic₈₉	—	2	1	no	—
107	Dic₈₉	—	4	2	no	—
108	Dic₈₉	—	4	2	no	—
109	Dic₈₉	C₂×SD₁₆	1	2	yes	—
110	C₂×C₈₉	—	8	2	no	—
111	C₂×C₈₉	#535	1	1	yes	characteristic
112	C₂×C₈₉	C₂²×SD₁₆	1	1	yes	characteristic
113	C₂×C₈₉	C₂×#137	1	1	yes	characteristic
114	D₈₉	—	2	2	no	—
115	#3206	—	89	1	no	maximal, Sylow
116	C₈₉	#3206	1	1	yes	characteristic, complemented, Sylow
117	#532	—	89	1	no	—
118	C₂×C₄⋊Q₈	—	89	1	no	—
119	#492	—	89	1	no	—
120	#492	D₈₉	1	1	yes	characteristic, complemented
121	#487	—	89	1	no	—
122	#487	—	89	1	no	—
123	#461	—	89	4	no	—
124	#448	—	89	4	no	—
125	#431	—	89	1	no	—
126	C₂×#41	—	178	1	no	—
127	C₂²×Q₈	—	89	2	no	—
128	C₂×SD₁₆	—	89	4	no	—
129	C₂×SD₁₆	C₂×D₈₉	1	4	yes	—
130	C₄⋊Q₈	—	89	2	no	—
131	C₄⋊Q₈	—	89	1	no	—
132	C₄⋊Q₈	—	89	1	no	—
133	C₄⋊Q₈	—	178	1	no	—
134	C₄⋊Q₈	—	178	1	no	—
135	C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
136	#127	C₂×D₈₉	1	1	yes	characteristic
137	#124	—	178	1	no	—
138	#121	—	89	2	no	—
139	#121	—	178	1	no	—
140	C₄×D₄	—	89	2	no	—
141	C₄×D₄	—	178	1	no	—
142	C₂×C₄⋊C₄	—	178	1	no	—
143	C₂×C₄⋊C₄	—	178	1	no	—
144	C₂×C₄²	—	89	1	no	—
145	C₄⋊C₈	—	89	2	no	—
146	#103	—	89	4	no	—
147	#103	—	89	4	no	—
148	C₂²⋊C₈	—	89	2	no	—
149	C₄×C₈	—	89	1	no	—
150	C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
151	#41	—	356	4	no	—
152	C₂×Q₈	—	89	2	no	—
153	C₂×Q₈	—	356	4	no	—
154	C₂×Q₈	—	178	2	no	—
155	C₂×Q₈	—	178	1	no	—
156	C₂×Q₈	C₂²×D₈₉	1	2	yes	—
157	C₂×D₄	—	2	1	no	—
158	C₂×D₄	—	2	1	no	—
159	C₂×D₄	—	178	2	no	—
160	C₂×D₄	C₂²×D₈₉	1	2	yes	—
161	C₂²×C₄	—	89	1	no	—
162	C₂²×C₄	—	89	1	no	—
163	C₂²×C₄	—	89	1	no	—
164	C₂²×C₄	—	178	2	no	—
165	C₂²×C₄	—	178	2	no	—
166	SD₁₆	—	4	4	no	—
167	SD₁₆	—	356	4	no	—
168	C₂×C₈	—	89	2	no	—
169	C₂×C₈	C₂²×D₈₉	1	2	yes	—
170	C₄⋊C₄	—	2	1	no	—
171	C₄⋊C₄	—	2	1	no	—
172	C₄⋊C₄	—	89	2	no	—
173	C₄⋊C₄	—	178	2	no	—
174	C₄⋊C₄	—	178	2	no	—
175	C₄⋊C₄	—	178	1	no	—
176	C₄⋊C₄	—	178	1	no	—
177	C₄⋊C₄	—	178	1	no	—
178	C₂²⋊C₄	—	178	2	no	—
179	C₂²⋊C₄	—	178	2	no	—
180	C₄²	—	89	1	no	—
181	C₄²	—	89	1	no	—
182	C₄²	—	89	1	no	—
183	C₄²	C₂²×D₈₉	1	1	yes	characteristic
184	C₂³	—	2	2	no	—
185	C₂³	—	89	1	no	—
186	Q₈	—	2	4	no	—
187	Q₈	—	356	4	no	—
188	Q₈	—	356	2	no	—
189	Q₈	—	178	4	no	—
190	D₄	—	2	4	no	—
191	D₄	—	4	2	no	—
192	D₄	—	4	2	no	—
193	D₄	—	356	4	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	89	1	no	—
196	C₂×C₄	—	89	4	no	—
197	C₂×C₄	—	89	1	no	—
198	C₂×C₄	—	89	1	no	—
199	C₂×C₄	—	356	4	no	—
200	C₂×C₄	—	356	4	no	—
201	C₂×C₄	—	178	2	no	—
202	C₂×C₄	—	178	2	no	—
203	C₂×C₄	—	178	2	no	—
204	C₂×C₄	—	178	2	no	—
205	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
206	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
207	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
208	C₈	—	2	2	no	—
209	C₈	—	178	2	no	—
210	C₂²	—	4	2	no	—
211	C₂²	—	4	2	no	—
212	C₂²	—	4	2	no	—
213	C₂²	—	89	2	no	—
214	C₂²	—	178	1	no	—
215	C₂²	—	178	1	no	—
216	C₂²	C₂×D₄×D₈₉	1	1	yes	characteristic
217	C₄	—	4	2	no	—
218	C₄	—	89	2	no	—
219	C₄	—	356	2	no	—
220	C₄	—	356	2	no	—
221	C₄	—	178	1	no	—
222	C₄	—	178	1	no	—
223	C₄	SD₁₆×D₈₉	1	2	yes	—
224	C₄	#15668041	1	2	yes	—
225	C₄	#15668057	1	2	yes	—
226	C₂	—	8	2	no	—
227	C₂	—	178	2	no	—
228	C₂	#19152161	1	1	yes	characteristic
229	C₂	C₂×SD₁₆×D₈₉	1	1	yes	characteristic
230	C₂	C₂×#15668041	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19152146

C₂

yes

maximal, characteristic

C₄⋊Q₈×D₈₉

C₂

yes

maximal, characteristic, complemented

#19151970

C₂

yes

maximal, characteristic, complemented

#19151949

C₂

yes

maximal, characteristic, complemented

#19151948

C₂

yes

maximal, characteristic, complemented

#19151801

C₂

yes

maximal, complemented

#19151735

C₂

yes

maximal, complemented

#19151649

C₂

yes

maximal, characteristic, complemented

#492×C₈₉

C₂

yes

maximal, characteristic, complemented

C₂×#13083573

—

C₂×Q₈×D₈₉

C₂²

yes

—

C₂×#13083562

C₂²

yes

—

#15668012

C₂²

yes

characteristic

#15668012

C₂²

yes

—

—

C₂²

yes

—

#15667999

—

#15667983

—

#15667983

C₂²

yes

—

D₄×Dic₈₉

—

D₄×Dic₈₉

C₂²

yes

—

C₄⋊C₄×D₈₉

—

C₄⋊C₄×D₈₉

—

C₄²×D₈₉

C₂²

yes

characteristic

#15667941

C₂²

yes

—

#15667937

C₂²

yes

—

#15667936

C₂²

yes

—

#15667924

C₂²

yes

—

C₄×#10623494

C₂²

yes

characteristic

C₂×SD₁₆×C₈₉

C₂²

yes

—

C₄⋊Q₈×C₈₉

C₂²

yes

characteristic

#127×C₈₉

C₂²

yes

characteristic

C₄×C₈×C₈₉

C₂²

yes

characteristic

#13083573

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

C₂³

yes

—

Q₈×D₈₉

—

C₂×C₂²⋊D₈₉

—

C₂²×Dic₈₉

—

C₂×C₄×D₈₉

—

C₂×C₄×D₈₉

D₄

yes

characteristic

C₂×C₄×D₈₉

D₄

yes

characteristic

C₂×C₄×D₈₉

C₂³

yes

characteristic

#13083562

—

C₂×#10623494

C₂³

yes

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

C₂³

yes

—

#13083553

—

#13083553

—

C₂²⋊Dic₈₉

—

C₂²⋊Dic₈₉

—

C₄×Dic₈₉

D₄

yes

characteristic

C₄×Dic₈₉

D₄

yes

characteristic

C₄×Dic₈₉

C₂³

yes

characteristic

C₂×Q₈×C₈₉

C₂³

yes

—

C₂×D₄×C₈₉

—

C₂×D₄×C₈₉

—

C₂×D₄×C₈₉

C₂³

yes

—

SD₁₆×C₈₉

—

C₂×C₈×C₈₉

C₂³

yes

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄²×C₈₉

C₂³

yes

characteristic

C₂³×C₈₉

—

C₂²×D₈₉

C₂×D₄

yes

characteristic

Q₈×C₈₉

—

D₄×C₈₉

—

D₄×C₈₉

—

D₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂×C₄×C₈₉

C₂⁴

yes

characteristic

C₂²⋊D₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

C₂×D₄

yes

characteristic

C₂×Dic₈₉

C₂×D₄

yes

characteristic

C₂×Dic₈₉

C₂×D₄

yes

characteristic

C₄×D₈₉

—

C₄×D₈₉

—

C₄×D₈₉

—

C₄×D₈₉

SD₁₆

yes

complemented

Dic₁₇₈

—

Dic₁₇₈

—

Dic₁₇₈

—

C₈×C₈₉

—

#10623494

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

C₂²×D₄

yes

characteristic

C₂×D₈₉

—

C₂×D₈₉

—

100

C₂×D₈₉

C₂×SD₁₆

yes

—

101

C₄×C₈₉

—

102

C₄×C₈₉

C₂×SD₁₆

yes

—

103

C₄×C₈₉

#137

yes

—

104

C₄×C₈₉

H(5,𝔽₂)

yes

—

105

Dic₈₉

—

106

Dic₈₉

—

107

Dic₈₉

—

108

Dic₈₉

—

109

Dic₈₉

C₂×SD₁₆

yes

—

110

C₂×C₈₉

—

111

C₂×C₈₉

#535

yes

characteristic

112

C₂×C₈₉

C₂²×SD₁₆

yes

characteristic

113

C₂×C₈₉

C₂×#137

yes

characteristic

114

D₈₉

—

115

#3206

—

maximal, Sylow

116

C₈₉

#3206

yes

characteristic, complemented, Sylow

117

#532

—

118

C₂×C₄⋊Q₈

—

119

#492

—

120

#492

D₈₉

yes

characteristic, complemented

121

#487

—

122

#487

—

123

#461

—

124

#448

—

125

#431

—

126

C₂×#41

—

178

—

127

C₂²×Q₈

—

128

C₂×SD₁₆

—

129

C₂×SD₁₆

C₂×D₈₉

yes

—

130

C₄⋊Q₈

—

131

C₄⋊Q₈

—

132

C₄⋊Q₈

—

133

C₄⋊Q₈

—

178

—

134

C₄⋊Q₈

—

178

—

135

C₄⋊Q₈

C₂×D₈₉

yes

characteristic

136

#127

C₂×D₈₉

yes

characteristic

137

#124

—

178

—

138

#121

—

139

#121

—

178

—

140

C₄×D₄

—

141

C₄×D₄

—

178

—

142

C₂×C₄⋊C₄

—

178

—

143

C₂×C₄⋊C₄

—

178

—

144

C₂×C₄²

—

145

C₄⋊C₈

—

146

#103

—

147

#103

—

148

C₂²⋊C₈

—

149

C₄×C₈

—

150

C₄×C₈

C₂×D₈₉

yes

characteristic

151

#41

—

356

—

152

C₂×Q₈

—

153

C₂×Q₈

—

356

—

154

C₂×Q₈

—

178

—

155

C₂×Q₈

—

178

—

156

C₂×Q₈

C₂²×D₈₉

yes

—

157

C₂×D₄

—

158

C₂×D₄

—

159

C₂×D₄

—

178

—

160

C₂×D₄

C₂²×D₈₉

yes

—

161

C₂²×C₄

—

162

C₂²×C₄

—

163

C₂²×C₄

—

164

C₂²×C₄

—

178

—

165

C₂²×C₄

—

178

—

166

SD₁₆

—

167

SD₁₆

—

356

—

168

C₂×C₈

—

169

C₂×C₈

C₂²×D₈₉

yes

—

170

C₄⋊C₄

—

171

C₄⋊C₄

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

178

—

174

C₄⋊C₄

—

178

—

175

C₄⋊C₄

—

178

—

176

C₄⋊C₄

—

178

—

177

C₄⋊C₄

—

178

—

178

C₂²⋊C₄

—

178

—

179

C₂²⋊C₄

—

178

—

180

C₄²

—

181

C₄²

—

182

C₄²

—

183

C₄²

C₂²×D₈₉

yes

characteristic

184

C₂³

—

185

C₂³

—

186

Q₈

—

187

Q₈

—

356

—

188

Q₈

—

356

—

189

Q₈

—

178

—

190

D₄

—

191

D₄

—

192

D₄

—

193

D₄

—

356

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

356

—

200

C₂×C₄

—

356

—

201

C₂×C₄

—

178

—

202

C₂×C₄

—

178

—

203

C₂×C₄

—

178

—

204

C₂×C₄

—

178

—

205

C₂×C₄

D₄×D₈₉

yes

characteristic

206

C₂×C₄

D₄×D₈₉

yes

characteristic

207

C₂×C₄

C₂³×D₈₉

yes

characteristic

208

C₈

—

209

C₈

—

178

—

210

C₂²

—

211

C₂²

—

212

C₂²

—

213

C₂²

—

214

C₂²

—

178

—

215

C₂²

—

178

—

216

C₂²

C₂×D₄×D₈₉

yes

characteristic

217

C₄

—

218

C₄

—

219

C₄

—

356

—

220

C₄

—

356

—

221

C₄

—

178

—

222

C₄

—

178

—

223

C₄

SD₁₆×D₈₉

yes

—

224

C₄

#15668041

yes

—

225

C₄

#15668057

yes

—

226

C₂

—

227

C₂

—

178

—

228

C₂

#19152161

yes

characteristic

229

C₂

C₂×SD₁₆×D₈₉

yes

characteristic

230

C₂

C₂×#15668041

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₈₉
commutator, cosocle	C₂×C₄×C₈₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₉
Fitting	#492×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₄
prime radical	#19152146	C₂
hypercenter	#492	D₈₉
hypocenter	C₈₉	#3206
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #492

subgroup

G/H

center

C₂²

C₂×D₄×D₈₉

commutator, cosocle

C₂×C₄×C₈₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₈₉

Fitting

#492×C₈₉

C₂

socle

C₂²×C₈₉

C₂²×D₄

C₂

D₈₉

C₈₉

G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #492

N	H ≅ G/N	type
2. C₄⋊Q₈×D₈₉	C₂	semidirect
3. #19151970	C₂	semidirect
4. #19151949	C₂	semidirect
5. #19151948	C₂	semidirect
6. #19151801	C₂	semidirect
7. #19151735	C₂	semidirect
8. #19151649	C₂	semidirect
9. #492×C₈₉	C₂	semidirect
88. C₄×D₈₉	SD₁₆	semidirect
116. C₈₉	#3206	semidirect
120. #492	D₈₉	semidirect

H ≅ G/N

type

2. C₄⋊Q₈×D₈₉

C₂

semidirect

3. #19151970

C₂

semidirect

4. #19151949

C₂

semidirect

5. #19151948

C₂

semidirect

6. #19151801

C₂

semidirect

7. #19151735

C₂

semidirect

8. #19151649

C₂

semidirect

9. #492×C₈₉

C₂

semidirect

88. C₄×D₈₉

SD₁₆

semidirect

116. C₈₉

#3206

semidirect

120. #492

D₈₉

semidirect

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

subgroup	index
#19152146	2
C₄⋊Q₈×D₈₉	2
#19151970	2
#19151949	2
#19151948	2
#19151801	2
#19151735	2
#19151649	2
#492×C₈₉	2
#3206	89

subgroup

index

C₄⋊Q₈×D₈₉

#492×C₈₉

Subgroups — #26031173

Conjugacy classes of subgroups

Complements

Maximal subgroups