Group #26030857 — subgroups

Subgroups — #26030857

Order 11392.

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

normal subgroups only

This group has 364 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	#19152153	C₂	1	1	yes	maximal, characteristic, complemented
2	#19152133	C₂	1	1	yes	maximal, characteristic
3	#19152008	C₂	1	1	yes	maximal, characteristic, complemented
4	#19151990	C₂	1	1	yes	maximal, characteristic, complemented
5	#19151958	C₂	1	1	yes	maximal, characteristic, complemented
6	#19151855	C₂	1	2	yes	maximal, complemented
7	#19151847	C₂	1	2	yes	maximal
8	#19151690	C₂	1	2	yes	maximal, complemented
9	#19151683	C₂	1	2	yes	maximal, complemented
10	#19151550	C₂	1	1	yes	maximal, characteristic, complemented
11	#491×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13083564	C₂²	1	2	yes	—
13	C₂×#13083561	C₂²	1	2	yes	—
14	C₂×#13083557	C₂²	1	2	yes	—
15	#15668012	C₂²	1	1	yes	characteristic
16	#15668007	—	2	1	no	—
17	#15668003	—	2	1	no	—
18	#15668000	C₂²	1	1	yes	characteristic
19	#15667997	—	2	1	no	—
20	#15667992	—	2	1	no	—
21	#15667992	C₂²	1	1	yes	characteristic
22	#15667988	C₂²	1	2	yes	—
23	#15667987	C₂²	1	1	yes	characteristic
24	Q₈×Dic₈₉	C₂²	1	2	yes	—
25	#15667977	—	2	1	no	—
26	#15667977	C₂²	1	1	yes	characteristic
27	#15667974	—	2	1	no	—
28	#15667974	C₂²	1	1	yes	characteristic
29	#15667970	—	2	1	no	—
30	#15667970	—	2	1	no	—
31	C₄²×D₈₉	C₂²	1	1	yes	characteristic
32	#15667945	C₂²	1	2	yes	—
33	#15667943	C₂²	1	2	yes	—
34	#15667937	C₂²	1	2	yes	—
35	#15667934	C₂²	1	2	yes	—
36	#15667923	C₂²	1	1	yes	characteristic
37	C₈×Dic₈₉	C₂²	1	2	yes	—
38	C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
39	#125×C₈₉	C₂²	1	1	yes	characteristic
40	#103×C₈₉	C₂²	1	2	yes	—
41	#103×C₈₉	C₂²	1	2	yes	—
42	#97×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×Dic₁₇₈	—	2	1	no	—
44	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
45	C₂×D₃₅₆	—	2	1	no	—
46	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
47	C₂×C₄×D₈₉	—	2	1	no	—
48	C₂×C₄×D₈₉	D₄	1	1	yes	characteristic
49	C₂×C₄×D₈₉	D₄	1	1	yes	characteristic
50	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
51	#13083564	—	2	4	no	—
52	#13083561	—	2	4	no	—
53	#13083557	—	2	4	no	—
54	C₂×#10623494	C₂³	1	2	yes	—
55	C₄⋊Dic₈₉	—	2	1	no	—
56	C₄⋊Dic₈₉	—	2	1	no	—
57	C₄⋊Dic₈₉	—	2	2	no	—
58	C₄⋊Dic₈₉	C₂³	1	2	yes	—
59	#13083553	—	2	2	no	—
60	#13083553	—	2	1	no	—
61	#13083551	—	2	2	no	—
62	#13083551	—	2	1	no	—
63	#13083551	—	2	1	no	—
64	#13083551	—	2	1	no	—
65	#13083551	—	2	1	no	—
66	#13083551	—	2	1	no	—
67	C₄×Dic₈₉	—	2	1	no	—
68	C₄×Dic₈₉	—	2	2	no	—
69	C₄×Dic₈₉	D₄	1	1	yes	characteristic
70	C₄×Dic₈₉	D₄	1	1	yes	characteristic
71	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
72	C₂×Q₈×C₈₉	C₂³	1	2	yes	—
73	C₂×C₈×C₈₉	C₂³	1	2	yes	—
74	C₄⋊C₄×C₈₉	—	2	1	no	—
75	C₄⋊C₄×C₈₉	—	2	1	no	—
76	C₄⋊C₄×C₈₉	—	2	1	no	—
77	C₄⋊C₄×C₈₉	—	2	1	no	—
78	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
79	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
80	C₄²×C₈₉	C₂³	1	1	yes	characteristic
81	C₂²×D₈₉	—	2	1	no	—
82	C₂²×D₈₉	C₂×D₄	1	1	yes	characteristic
83	Q₈×C₈₉	—	2	2	no	—
84	Q₈×C₈₉	—	2	2	no	—
85	C₂×C₄×C₈₉	—	2	1	no	—
86	C₂×C₄×C₈₉	—	2	1	no	—
87	C₂×C₄×C₈₉	—	2	2	no	—
88	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
89	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
90	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
91	C₂×Dic₈₉	—	2	1	no	—
92	C₂×Dic₈₉	—	2	2	no	—
93	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
94	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
95	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
96	D₃₅₆	—	2	2	no	—
97	D₃₅₆	—	4	2	no	—
98	C₄×D₈₉	—	2	2	no	—
99	C₄×D₈₉	—	2	2	no	—
100	C₄×D₈₉	—	4	1	no	—
101	C₄×D₈₉	—	4	2	no	—
102	Dic₁₇₈	—	2	2	no	—
103	Dic₁₇₈	—	4	2	no	—
104	C₈×C₈₉	—	2	2	no	—
105	#10623494	#41	1	4	yes	—
106	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
107	C₂×D₈₉	—	2	1	no	—
108	C₂×D₈₉	—	2	1	no	—
109	C₂×D₈₉	—	2	1	no	—
110	C₂×D₈₉	—	4	1	no	—
111	C₂×D₈₉	—	4	1	no	—
112	C₂×D₈₉	—	4	1	no	—
113	C₄×C₈₉	—	2	1	no	—
114	C₄×C₈₉	—	2	1	no	—
115	C₄×C₈₉	—	4	2	no	—
116	C₄×C₈₉	—	4	1	no	—
117	C₄×C₈₉	—	4	1	no	—
118	C₄×C₈₉	C₂×#41	1	2	yes	—
119	Dic₈₉	—	2	1	no	—
120	Dic₈₉	—	2	1	no	—
121	Dic₈₉	—	4	1	no	—
122	Dic₈₉	—	4	2	no	—
123	Dic₈₉	#137	1	2	yes	—
124	C₂×C₈₉	#532	1	1	yes	characteristic
125	C₂×C₈₉	C₂×#137	1	1	yes	characteristic
126	C₂×C₈₉	#575	1	1	yes	characteristic
127	D₈₉	—	4	1	no	—
128	D₈₉	—	8	1	no	—
129	#3172	—	89	1	no	maximal, Sylow
130	C₈₉	#3172	1	1	yes	characteristic, complemented, Sylow
131	#533	—	89	1	no	—
132	#529	—	89	1	no	—
133	#501	—	89	1	no	—
134	#497	—	89	1	no	—
135	#491	D₈₉	1	1	yes	characteristic, complemented
136	#489	—	89	1	no	—
137	#470	—	89	2	no	—
138	#468	—	89	2	no	—
139	C₄×Q₁₆	—	89	2	no	—
140	C₄×SD₁₆	—	89	2	no	—
141	C₄×M₁₆	—	89	1	no	—
142	C₂×Q₁₆	—	89	2	no	—
143	C₂×SD₁₆	—	89	2	no	—
144	C₂×M₁₆	—	89	2	no	—
145	C₄⋊Q₈	—	89	1	no	—
146	C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
147	#126	—	178	1	no	—
148	#125	—	178	1	no	—
149	#125	C₂×D₈₉	1	1	yes	characteristic
150	#124	—	89	1	no	—
151	#123	—	178	1	no	—
152	C₂²⋊Q₈	—	89	2	no	—
153	C₂²⋊Q₈	—	89	1	no	—
154	C₂²⋊Q₈	—	178	1	no	—
155	#121	—	89	1	no	—
156	C₄×Q₈	—	89	2	no	—
157	C₄×Q₈	—	89	1	no	—
158	C₄×Q₈	—	178	1	no	—
159	C₄×D₄	—	89	1	no	—
160	C₄×D₄	—	178	1	no	—
161	#117	—	178	1	no	—
162	#117	—	178	1	no	—
163	C₂×C₄²	—	89	1	no	—
164	#107	—	89	2	no	—
165	#106	—	89	2	no	—
166	#103	—	89	2	no	—
167	#103	C₂×D₈₉	1	2	yes	—
168	#103	C₂×D₈₉	1	2	yes	—
169	#102	—	89	2	no	—
170	#97	—	89	1	no	—
171	#97	C₂×D₈₉	1	1	yes	characteristic
172	C₄×C₈	—	89	2	no	—
173	C₂×Q₈	—	89	1	no	—
174	C₂×Q₈	—	178	1	no	—
175	C₂×Q₈	C₂²×D₈₉	1	2	yes	—
176	C₂×D₄	—	89	1	no	—
177	C₂×D₄	—	178	1	no	—
178	C₂²×C₄	—	89	1	no	—
179	C₂²×C₄	—	89	1	no	—
180	C₂²×C₄	—	89	1	no	—
181	C₂²×C₄	—	178	1	no	—
182	Q₁₆	—	178	4	no	—
183	SD₁₆	—	178	4	no	—
184	M₁₆	—	178	4	no	—
185	C₂×C₈	—	89	2	no	—
186	C₂×C₈	C₂²×D₈₉	1	2	yes	—
187	C₄⋊C₄	—	2	1	no	—
188	C₄⋊C₄	—	2	1	no	—
189	C₄⋊C₄	—	2	1	no	—
190	C₄⋊C₄	—	2	1	no	—
191	C₄⋊C₄	—	89	2	no	—
192	C₄⋊C₄	—	178	1	no	—
193	C₄⋊C₄	—	178	2	no	—
194	C₄⋊C₄	—	178	1	no	—
195	C₄⋊C₄	—	178	2	no	—
196	C₄⋊C₄	—	178	1	no	—
197	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
198	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
199	C₂²⋊C₄	—	178	1	no	—
200	C₂²⋊C₄	—	178	1	no	—
201	C₂²⋊C₄	—	178	2	no	—
202	C₂²⋊C₄	—	178	1	no	—
203	C₂²⋊C₄	—	178	1	no	—
204	C₂²⋊C₄	—	178	1	no	—
205	C₄²	—	89	1	no	—
206	C₄²	—	89	1	no	—
207	C₄²	—	89	1	no	—
208	C₄²	—	178	1	no	—
209	C₄²	—	178	2	no	—
210	C₄²	C₂²×D₈₉	1	1	yes	characteristic
211	C₂³	—	89	1	no	—
212	C₂³	—	178	1	no	—
213	Q₈	—	2	2	no	—
214	Q₈	—	2	2	no	—
215	Q₈	—	356	2	no	—
216	Q₈	—	178	2	no	—
217	D₄	—	356	2	no	—
218	D₄	—	178	2	no	—
219	C₂×C₄	—	2	2	no	—
220	C₂×C₄	—	2	1	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	89	1	no	—
223	C₂×C₄	—	89	1	no	—
224	C₂×C₄	—	89	1	no	—
225	C₂×C₄	—	356	1	no	—
226	C₂×C₄	—	356	2	no	—
227	C₂×C₄	—	178	2	no	—
228	C₂×C₄	—	178	1	no	—
229	C₂×C₄	—	178	2	no	—
230	C₂×C₄	—	178	2	no	—
231	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
232	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
233	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
234	C₈	—	2	2	no	—
235	C₈	—	89	4	no	—
236	C₂²	—	356	1	no	—
237	C₂²	—	356	1	no	—
238	C₂²	—	356	1	no	—
239	C₂²	—	178	1	no	—
240	C₂²	—	178	1	no	—
241	C₂²	—	178	1	no	—
242	C₂²	C₂×D₄×D₈₉	1	1	yes	characteristic
243	C₄	—	2	1	no	—
244	C₄	—	2	1	no	—
245	C₄	—	4	1	no	—
246	C₄	—	4	1	no	—
247	C₄	—	4	2	no	—
248	C₄	—	89	2	no	—
249	C₄	—	356	2	no	—
250	C₄	—	356	1	no	—
251	C₄	—	178	1	no	—
252	C₄	—	178	1	no	—
253	C₄	#41×D₈₉	1	2	yes	—
254	C₂	—	356	1	no	—
255	C₂	—	712	1	no	—
256	C₂	#19152147	1	1	yes	characteristic
257	C₂	#137×D₈₉	1	1	yes	characteristic
258	C₂	#19152397	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19152153

C₂

yes

maximal, characteristic, complemented

#19152133

C₂

yes

maximal, characteristic

#19152008

C₂

yes

maximal, characteristic, complemented

#19151990

C₂

yes

maximal, characteristic, complemented

#19151958

C₂

yes

maximal, characteristic, complemented

#19151855

C₂

yes

maximal, complemented

#19151847

C₂

yes

maximal

#19151690

C₂

yes

maximal, complemented

#19151683

C₂

yes

maximal, complemented

#19151550

C₂

yes

maximal, characteristic, complemented

#491×C₈₉

C₂

yes

maximal, characteristic, complemented

C₂×#13083564

C₂²

yes

—

C₂×#13083561

C₂²

yes

—

C₂×#13083557

C₂²

yes

—

#15668012

C₂²

yes

—

—

C₂²

yes

—

—

C₂²

yes

characteristic

#15667988

C₂²

yes

—

#15667987

C₂²

yes

characteristic

Q₈×Dic₈₉

C₂²

yes

—

#15667977

—

#15667977

C₂²

yes

characteristic

#15667974

—

#15667974

C₂²

yes

characteristic

#15667970

—

#15667970

—

C₄²×D₈₉

C₂²

yes

characteristic

#15667945

C₂²

yes

—

#15667943

C₂²

yes

—

#15667937

C₂²

yes

—

#15667934

C₂²

yes

—

#15667923

C₂²

yes

characteristic

C₈×Dic₈₉

C₂²

yes

—

C₄⋊Q₈×C₈₉

C₂²

yes

characteristic

#125×C₈₉

C₂²

yes

characteristic

#103×C₈₉

C₂²

yes

—

#103×C₈₉

C₂²

yes

—

#97×C₈₉

C₂²

yes

characteristic

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

C₂³

yes

characteristic

C₂×D₃₅₆

—

C₂×D₃₅₆

C₂³

yes

characteristic

C₂×C₄×D₈₉

—

C₂×C₄×D₈₉

D₄

yes

characteristic

C₂×C₄×D₈₉

D₄

yes

characteristic

C₂×C₄×D₈₉

C₂³

yes

—

—

—

C₂³

yes

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

C₂³

yes

—

—

—

—

—

—

—

—

—

C₄×Dic₈₉

—

C₄×Dic₈₉

—

C₄×Dic₈₉

D₄

yes

characteristic

C₄×Dic₈₉

D₄

yes

characteristic

C₄×Dic₈₉

C₂³

yes

characteristic

C₂×Q₈×C₈₉

C₂³

yes

—

C₂×C₈×C₈₉

C₂³

yes

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

C₂³

yes

characteristic

C₄⋊C₄×C₈₉

C₂³

yes

characteristic

C₄²×C₈₉

C₂³

yes

characteristic

C₂²×D₈₉

—

C₂²×D₈₉

C₂×D₄

yes

characteristic

Q₈×C₈₉

—

Q₈×C₈₉

—

C₂×C₄×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×D₄

yes

characteristic

C₂×Dic₈₉

C₂×D₄

yes

characteristic

C₂×Dic₈₉

C₂×D₄

yes

characteristic

D₃₅₆

—

D₃₅₆

—

C₄×D₈₉

—

C₄×D₈₉

—

100

C₄×D₈₉

—

101

C₄×D₈₉

—

102

Dic₁₇₈

—

103

Dic₁₇₈

—

104

C₈×C₈₉

—

105

#10623494

#41

yes

—

106

C₂²×C₈₉

C₂²×D₄

yes

characteristic

107

C₂×D₈₉

—

108

C₂×D₈₉

—

109

C₂×D₈₉

—

110

C₂×D₈₉

—

111

C₂×D₈₉

—

112

C₂×D₈₉

—

113

C₄×C₈₉

—

114

C₄×C₈₉

—

115

C₄×C₈₉

—

116

C₄×C₈₉

—

117

C₄×C₈₉

—

118

C₄×C₈₉

C₂×#41

yes

—

119

Dic₈₉

—

120

Dic₈₉

—

121

Dic₈₉

—

122

Dic₈₉

—

123

Dic₈₉

#137

yes

—

124

C₂×C₈₉

#532

yes

characteristic

125

C₂×C₈₉

C₂×#137

yes

characteristic

126

C₂×C₈₉

#575

yes

characteristic

127

D₈₉

—

128

D₈₉

—

129

#3172

—

maximal, Sylow

130

C₈₉

#3172

yes

characteristic, complemented, Sylow

131

#533

—

132

#529

—

133

#501

—

134

#497

—

135

#491

D₈₉

yes

characteristic, complemented

136

#489

—

137

#470

—

138

#468

—

139

C₄×Q₁₆

—

140

C₄×SD₁₆

—

141

C₄×M₁₆

—

142

C₂×Q₁₆

—

143

C₂×SD₁₆

—

144

C₂×M₁₆

—

145

C₄⋊Q₈

—

146

C₄⋊Q₈

C₂×D₈₉

yes

characteristic

147

#126

—

178

—

148

#125

—

178

—

149

#125

C₂×D₈₉

yes

characteristic

150

#124

—

151

#123

—

178

—

152

C₂²⋊Q₈

—

153

C₂²⋊Q₈

—

154

C₂²⋊Q₈

—

178

—

155

#121

—

156

C₄×Q₈

—

157

C₄×Q₈

—

158

C₄×Q₈

—

178

—

159

C₄×D₄

—

160

C₄×D₄

—

178

—

161

#117

—

178

—

162

#117

—

178

—

163

C₂×C₄²

—

164

#107

—

165

#106

—

166

#103

—

167

#103

C₂×D₈₉

yes

—

168

#103

C₂×D₈₉

yes

—

169

#102

—

170

#97

—

171

#97

C₂×D₈₉

yes

characteristic

172

C₄×C₈

—

173

C₂×Q₈

—

174

C₂×Q₈

—

178

—

175

C₂×Q₈

C₂²×D₈₉

yes

—

176

C₂×D₄

—

177

C₂×D₄

—

178

—

178

C₂²×C₄

—

179

C₂²×C₄

—

180

C₂²×C₄

—

181

C₂²×C₄

—

178

—

182

Q₁₆

—

178

—

183

SD₁₆

—

178

—

184

M₁₆

—

178

—

185

C₂×C₈

—

186

C₂×C₈

C₂²×D₈₉

yes

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

178

—

193

C₄⋊C₄

—

178

—

194

C₄⋊C₄

—

178

—

195

C₄⋊C₄

—

178

—

196

C₄⋊C₄

—

178

—

197

C₄⋊C₄

C₂²×D₈₉

yes

characteristic

198

C₄⋊C₄

C₂²×D₈₉

yes

characteristic

199

C₂²⋊C₄

—

178

—

200

C₂²⋊C₄

—

178

—

201

C₂²⋊C₄

—

178

—

202

C₂²⋊C₄

—

178

—

203

C₂²⋊C₄

—

178

—

204

C₂²⋊C₄

—

178

—

205

C₄²

—

206

C₄²

—

207

C₄²

—

208

C₄²

—

178

—

209

C₄²

—

178

—

210

C₄²

C₂²×D₈₉

yes

characteristic

211

C₂³

—

212

C₂³

—

178

—

213

Q₈

—

214

Q₈

—

215

Q₈

—

356

—

216

Q₈

—

178

—

217

D₄

—

356

—

218

D₄

—

178

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

356

—

226

C₂×C₄

—

356

—

227

C₂×C₄

—

178

—

228

C₂×C₄

—

178

—

229

C₂×C₄

—

178

—

230

C₂×C₄

—

178

—

231

C₂×C₄

D₄×D₈₉

yes

characteristic

232

C₂×C₄

D₄×D₈₉

yes

characteristic

233

C₂×C₄

C₂³×D₈₉

yes

characteristic

234

C₈

—

235

C₈

—

236

C₂²

—

356

—

237

C₂²

—

356

—

238

C₂²

—

356

—

239

C₂²

—

178

—

240

C₂²

—

178

—

241

C₂²

—

178

—

242

C₂²

C₂×D₄×D₈₉

yes

characteristic

243

C₄

—

244

C₄

—

245

C₄

—

246

C₄

—

247

C₄

—

248

C₄

—

249

C₄

—

356

—

250

C₄

—

356

—

251

C₄

—

178

—

252

C₄

—

178

—

253

C₄

#41×D₈₉

yes

—

254

C₂

—

356

—

255

C₂

—

712

—

256

C₂

#19152147

yes

characteristic

257

C₂

#137×D₈₉

yes

characteristic

258

C₂

#19152397

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₈₉
commutator, cosocle	C₂×C₄×C₈₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₉
Fitting	#491×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₄
prime radical	#15667987	C₂²
hypercenter	#491	D₈₉
hypocenter	C₈₉	#3172
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #491

subgroup

G/H

center

C₂²

C₂×D₄×D₈₉

commutator, cosocle

C₂×C₄×C₈₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₈₉

Fitting

#491×C₈₉

C₂

socle

C₂²×C₈₉

C₂²×D₄

C₂²

D₈₉

C₈₉

G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #491

N	H ≅ G/N	type
1. #19152153	C₂	semidirect
3. #19152008	C₂	semidirect
4. #19151990	C₂	semidirect
5. #19151958	C₂	semidirect
6. #19151855	C₂	semidirect
8. #19151690	C₂	semidirect
9. #19151683	C₂	semidirect
10. #19151550	C₂	semidirect
11. #491×C₈₉	C₂	semidirect
130. C₈₉	#3172	semidirect
135. #491	D₈₉	semidirect

H ≅ G/N

type

1. #19152153

C₂

semidirect

3. #19152008

C₂

semidirect

4. #19151990

C₂

semidirect

5. #19151958

C₂

semidirect

6. #19151855

C₂

semidirect

8. #19151690

C₂

semidirect

9. #19151683

C₂

semidirect

10. #19151550

C₂

semidirect

11. #491×C₈₉

C₂

semidirect

130. C₈₉

#3172

semidirect

135. #491

D₈₉

semidirect

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

subgroup	index
#19152153	2
#19152133	2
#19152008	2
#19151990	2
#19151958	2
#19151855	2
#19151847	2
#19151690	2
#19151683	2
#19151550	2
#491×C₈₉	2
#3172	89

subgroup

index

#491×C₈₉

Subgroups — #26030857

Conjugacy classes of subgroups

Complements

Maximal subgroups