Group #26032905 — subgroups

Subgroups — #26032905

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	#19152322	C₂	1	1	yes	maximal, characteristic, complemented
2	#19152305	C₂	1	1	yes	maximal, characteristic, complemented
3	#19151954	C₂	1	2	yes	maximal, complemented
4	#19151948	C₂	1	1	yes	maximal, characteristic, complemented
5	#19151903	C₂	1	2	yes	maximal, complemented
6	#19151889	C₂	1	1	yes	maximal, characteristic, complemented
7	#19151815	C₂	1	2	yes	maximal
8	#19151722	C₂	1	1	yes	maximal, characteristic, complemented
9	SD₁₆×Dic₈₉	C₂	1	2	yes	maximal, complemented
10	C₄×#13083559	C₂	1	1	yes	maximal, characteristic
11	#461×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13083559	C₂²	1	1	yes	characteristic
13	#15668012	C₂²	1	1	yes	characteristic
14	#15668007	—	2	2	no	—
15	#15668003	C₂²	1	2	yes	—
16	#15668001	C₂²	1	2	yes	—
17	#15667992	—	2	1	no	—
18	#15667991	—	2	1	no	—
19	#15667989	—	2	2	no	—
20	Q₈×Dic₈₉	C₂²	1	2	yes	—
21	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
22	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
23	D₄×Dic₈₉	C₂²	1	2	yes	—
24	#15667970	—	2	1	no	—
25	C₂×C₄⋊Dic₈₉	—	2	1	no	—
26	#15667945	C₂²	1	1	yes	characteristic
27	#15667944	C₂²	1	2	yes	—
28	#15667941	C₂²	1	2	yes	—
29	#15667936	C₂²	1	2	yes	—
30	#15667936	C₂²	1	2	yes	—
31	#15667934	C₂²	1	2	yes	—
32	#15667933	C₂²	1	1	yes	characteristic
33	#15667932	C₂²	1	1	yes	characteristic
34	C₄×#10623494	C₂²	1	1	yes	characteristic
35	C₈×Dic₈₉	C₂²	1	2	yes	—
36	C₂×SD₁₆×C₈₉	C₂²	1	2	yes	—
37	C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
38	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
39	C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
40	#103×C₈₉	C₂²	1	2	yes	—
41	C₂×Dic₁₇₈	—	2	1	no	—
42	C₂×Dic₁₇₈	D₄	1	1	yes	characteristic
43	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
44	C₂²×Dic₈₉	—	2	2	no	—
45	C₂×C₄×D₈₉	—	2	1	no	—
46	#13083559	—	2	2	no	—
47	C₂×#10623494	C₂³	1	1	yes	characteristic
48	C₂×#10623494	C₂³	1	1	yes	characteristic
49	C₄⋊Dic₈₉	—	2	1	no	—
50	C₄⋊Dic₈₉	—	2	2	no	—
51	C₄⋊Dic₈₉	—	2	2	no	—
52	C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
53	C₄⋊Dic₈₉	C₂³	1	2	yes	—
54	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
55	#13083553	—	2	2	no	—
56	#13083553	D₄	1	2	yes	—
57	C₂²⋊Dic₈₉	—	2	2	no	—
58	#13083551	—	2	1	no	—
59	#13083551	—	2	2	no	—
60	#13083551	—	2	2	no	—
61	C₄×Dic₈₉	—	2	2	no	—
62	C₄×Dic₈₉	C₂³	1	2	yes	—
63	C₂×Q₈×C₈₉	C₂³	1	2	yes	—
64	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
65	C₂²×C₄×C₈₉	—	2	1	no	—
66	SD₁₆×C₈₉	—	2	4	no	—
67	C₂×C₈×C₈₉	C₂³	1	2	yes	—
68	C₄⋊C₄×C₈₉	—	2	1	no	—
69	C₄⋊C₄×C₈₉	—	2	1	no	—
70	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
71	C₂²⋊C₄×C₈₉	—	2	1	no	—
72	C₄²×C₈₉	C₂³	1	1	yes	characteristic
73	C₂³×C₈₉	—	2	1	no	—
74	C₂²×D₈₉	—	2	1	no	—
75	Q₈×C₈₉	—	2	2	no	—
76	Q₈×C₈₉	—	2	2	no	—
77	D₄×C₈₉	—	2	1	no	—
78	D₄×C₈₉	#41	1	2	yes	—
79	C₂×C₄×C₈₉	—	2	1	no	—
80	C₂×C₄×C₈₉	—	2	2	no	—
81	C₂×C₄×C₈₉	—	4	2	no	—
82	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
83	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
84	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
85	C₂×Dic₈₉	—	2	1	no	—
86	C₂×Dic₈₉	—	2	2	no	—
87	C₂×Dic₈₉	—	8	2	no	—
88	C₂×Dic₈₉	C₂×D₄	1	2	yes	—
89	C₂×Dic₈₉	C₂×D₄	1	2	yes	—
90	D₃₅₆	—	2	1	no	—
91	D₃₅₆	—	2	1	no	—
92	C₄×D₈₉	—	4	2	no	—
93	Dic₁₇₈	—	2	2	no	—
94	Dic₁₇₈	—	8	1	no	—
95	C₈×C₈₉	—	2	2	no	—
96	#10623494	—	2	1	no	—
97	#10623494	—	2	1	no	—
98	C₂²×C₈₉	—	2	2	no	—
99	C₂²×C₈₉	—	4	1	no	—
100	C₂²×C₈₉	—	4	1	no	—
101	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
102	C₂×D₈₉	—	4	1	no	—
103	C₂×D₈₉	—	4	1	no	—
104	C₂×D₈₉	—	4	1	no	—
105	C₄×C₈₉	—	2	1	no	—
106	C₄×C₈₉	—	4	2	no	—
107	C₄×C₈₉	—	4	1	no	—
108	C₄×C₈₉	#135	1	2	yes	—
109	C₄×C₈₉	C₂×#41	1	1	yes	characteristic
110	C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
111	Dic₈₉	—	2	2	no	—
112	Dic₈₉	—	2	2	no	—
113	Dic₈₉	—	4	1	no	—
114	Dic₈₉	—	4	2	no	—
115	C₂×C₈₉	—	4	2	no	—
116	C₂×C₈₉	#548	1	1	yes	characteristic
117	C₂×C₈₉	C₂×#135	1	1	yes	characteristic
118	C₂×C₈₉	#577	1	1	yes	characteristic
119	D₈₉	—	8	1	no	—
120	#3360	—	89	1	no	maximal, Sylow
121	C₈₉	#3360	1	1	yes	characteristic, complemented, Sylow
122	#556	—	89	1	no	—
123	#554	—	89	1	no	—
124	#488	—	89	2	no	—
125	#487	—	89	1	no	—
126	#479	—	89	2	no	—
127	#476	—	89	1	no	—
128	#463	—	89	2	no	—
129	#461	D₈₉	1	1	yes	characteristic, complemented
130	C₈×Q₈	—	89	1	no	—
131	C₄×SD₁₆	—	89	2	no	—
132	C₄×D₈	—	89	1	no	—
133	C₂×SD₁₆	C₂×D₈₉	1	2	yes	—
134	C₂×D₈	—	89	1	no	—
135	C₄⋊Q₈	—	89	1	no	—
136	C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
137	#126	—	178	2	no	—
138	#125	—	89	2	no	—
139	#124	—	89	2	no	—
140	C₂²⋊Q₈	—	178	2	no	—
141	C₂²⋊Q₈	—	178	1	no	—
142	C₂²⋊Q₈	—	178	1	no	—
143	C₄×Q₈	—	89	1	no	—
144	C₄×Q₈	—	89	2	no	—
145	C₄×D₄	—	89	2	no	—
146	C₄×D₄	—	89	1	no	—
147	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
148	#117	—	178	1	no	—
149	C₂×C₄⋊C₄	—	178	1	no	—
150	#107	—	89	1	no	—
151	#106	—	89	2	no	—
152	C₄⋊C₈	—	89	2	no	—
153	C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
154	#103	—	89	2	no	—
155	#103	—	89	2	no	—
156	#103	C₂×D₈₉	1	2	yes	—
157	#102	—	89	1	no	—
158	#102	—	89	2	no	—
159	#102	—	89	1	no	—
160	C₄×C₈	—	89	2	no	—
161	C₄×C₈	—	89	1	no	—
162	C₂×Q₈	—	89	1	no	—
163	C₂×Q₈	—	178	1	no	—
164	C₂×Q₈	C₂²×D₈₉	1	2	yes	—
165	C₂×D₄	—	89	1	no	—
166	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
167	C₂²×C₄	—	2	1	no	—
168	C₂²×C₄	—	178	2	no	—
169	C₂²×C₄	—	178	1	no	—
170	SD₁₆	—	2	4	no	—
171	D₈	—	178	2	no	—
172	C₂×C₈	—	89	1	no	—
173	C₂×C₈	—	89	1	no	—
174	C₂×C₈	C₂²×D₈₉	1	2	yes	—
175	C₄⋊C₄	—	2	1	no	—
176	C₄⋊C₄	—	2	1	no	—
177	C₄⋊C₄	—	89	1	no	—
178	C₄⋊C₄	—	89	2	no	—
179	C₄⋊C₄	—	89	2	no	—
180	C₄⋊C₄	—	89	1	no	—
181	C₄⋊C₄	—	178	2	no	—
182	C₄⋊C₄	—	178	2	no	—
183	C₄⋊C₄	—	178	2	no	—
184	C₄⋊C₄	—	178	1	no	—
185	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
186	C₂²⋊C₄	—	2	1	no	—
187	C₂²⋊C₄	—	178	2	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	C₂²×D₈₉	1	1	yes	characteristic
194	C₂³	—	2	1	no	—
195	C₂³	—	178	1	no	—
196	Q₈	—	2	2	no	—
197	Q₈	—	2	2	no	—
198	Q₈	—	178	2	no	—
199	Q₈	—	712	1	no	—
200	D₄	—	2	1	no	—
201	D₄	—	178	1	no	—
202	D₄	—	178	1	no	—
203	D₄	#13083573	1	2	yes	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	1	no	—
206	C₂×C₄	—	4	2	no	—
207	C₂×C₄	—	89	2	no	—
208	C₂×C₄	—	89	2	no	—
209	C₂×C₄	—	356	2	no	—
210	C₂×C₄	—	178	1	no	—
211	C₂×C₄	—	178	2	no	—
212	C₂×C₄	—	712	2	no	—
213	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
214	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
215	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
216	C₈	—	2	2	no	—
217	C₈	—	178	1	no	—
218	C₈	—	178	1	no	—
219	C₂²	—	2	2	no	—
220	C₂²	—	4	1	no	—
221	C₂²	—	4	1	no	—
222	C₂²	—	356	1	no	—
223	C₂²	—	356	1	no	—
224	C₂²	—	356	1	no	—
225	C₂²	C₂×D₄×D₈₉	1	1	yes	characteristic
226	C₄	—	2	1	no	—
227	C₄	—	4	2	no	—
228	C₄	—	4	1	no	—
229	C₄	—	356	2	no	—
230	C₄	—	356	1	no	—
231	C₄	—	178	2	no	—
232	C₄	—	178	2	no	—
233	C₄	#15668033	1	2	yes	—
234	C₄	C₂×#13083573	1	1	yes	characteristic
235	C₄	#15668059	1	1	yes	characteristic
236	C₂	—	4	2	no	—
237	C₂	—	712	1	no	—
238	C₂	#19152254	1	1	yes	characteristic
239	C₂	C₂×#15668033	1	1	yes	characteristic
240	C₂	#19152407	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19152322

C₂

yes

maximal, characteristic, complemented

#19152305

C₂

yes

maximal, characteristic, complemented

#19151954

C₂

yes

maximal, complemented

#19151948

C₂

yes

maximal, characteristic, complemented

#19151903

C₂

yes

maximal, complemented

#19151889

C₂

yes

maximal, characteristic, complemented

#19151815

C₂

yes

maximal

#19151722

C₂

yes

maximal, characteristic, complemented

SD₁₆×Dic₈₉

C₂

yes

maximal, complemented

C₄×#13083559

C₂

yes

maximal, characteristic

#461×C₈₉

C₂

yes

maximal, characteristic, complemented

C₂×#13083559

C₂²

yes

characteristic

#15668012

C₂²

yes

characteristic

#15668007

—

#15668003

C₂²

yes

—

#15668001

C₂²

yes

—

#15667992

—

#15667991

—

#15667989

—

Q₈×Dic₈₉

C₂²

yes

—

C₄×Dic₁₇₈

C₂²

yes

characteristic

C₄×D₃₅₆

C₂²

yes

characteristic

D₄×Dic₈₉

C₂²

yes

—

#15667970

—

C₂×C₄⋊Dic₈₉

—

#15667945

C₂²

yes

characteristic

#15667944

C₂²

yes

—

#15667941

C₂²

yes

—

#15667936

C₂²

yes

—

#15667936

C₂²

yes

—

#15667934

C₂²

yes

—

#15667933

C₂²

yes

characteristic

#15667932

C₂²

yes

characteristic

C₄×#10623494

C₂²

yes

characteristic

C₈×Dic₈₉

C₂²

yes

—

C₂×SD₁₆×C₈₉

C₂²

yes

—

C₄⋊Q₈×C₈₉

C₂²

yes

characteristic

C₄×D₄×C₈₉

C₂²

yes

characteristic

C₄⋊C₈×C₈₉

C₂²

yes

characteristic

#103×C₈₉

C₂²

yes

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

D₄

yes

characteristic

C₂×D₃₅₆

C₂³

yes

characteristic

C₂²×Dic₈₉

—

C₂×C₄×D₈₉

—

#13083559

—

C₂×#10623494

C₂³

yes

characteristic

C₂×#10623494

C₂³

yes

characteristic

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

D₄

yes

characteristic

C₄⋊Dic₈₉

C₂³

yes

—

C₄⋊Dic₈₉

C₂³

yes

characteristic

#13083553

—

#13083553

D₄

yes

—

C₂²⋊Dic₈₉

—

#13083551

—

#13083551

—

#13083551

—

C₄×Dic₈₉

—

C₄×Dic₈₉

C₂³

yes

—

C₂×Q₈×C₈₉

C₂³

yes

—

C₂×D₄×C₈₉

C₂³

yes

characteristic

C₂²×C₄×C₈₉

—

SD₁₆×C₈₉

—

C₂×C₈×C₈₉

C₂³

yes

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

C₂³

yes

characteristic

C₂²⋊C₄×C₈₉

—

C₄²×C₈₉

C₂³

yes

characteristic

C₂³×C₈₉

—

C₂²×D₈₉

—

Q₈×C₈₉

—

Q₈×C₈₉

—

D₄×C₈₉

—

D₄×C₈₉

#41

yes

—

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×Dic₈₉

C₂×D₄

yes

—

C₂×Dic₈₉

C₂×D₄

yes

—

D₃₅₆

—

D₃₅₆

—

C₄×D₈₉

—

Dic₁₇₈

—

Dic₁₇₈

—

C₈×C₈₉

—

#10623494

—

#10623494

—

C₂²×C₈₉

—

C₂²×C₈₉

—

100

C₂²×C₈₉

—

101

C₂²×C₈₉

C₂²×D₄

yes

characteristic

102

C₂×D₈₉

—

103

C₂×D₈₉

—

104

C₂×D₈₉

—

105

C₄×C₈₉

—

106

C₄×C₈₉

—

107

C₄×C₈₉

—

108

C₄×C₈₉

#135

yes

—

109

C₄×C₈₉

C₂×#41

yes

characteristic

110

C₄×C₈₉

2₋¹⁺⁴

yes

characteristic

111

Dic₈₉

—

112

Dic₈₉

—

113

Dic₈₉

—

114

Dic₈₉

—

115

C₂×C₈₉

—

116

C₂×C₈₉

#548

yes

characteristic

117

C₂×C₈₉

C₂×#135

yes

characteristic

118

C₂×C₈₉

#577

yes

characteristic

119

D₈₉

—

120

#3360

—

maximal, Sylow

121

C₈₉

#3360

yes

characteristic, complemented, Sylow

122

#556

—

123

#554

—

124

#488

—

125

#487

—

126

#479

—

127

#476

—

128

#463

—

129

#461

D₈₉

yes

characteristic, complemented

130

C₈×Q₈

—

131

C₄×SD₁₆

—

132

C₄×D₈

—

133

C₂×SD₁₆

C₂×D₈₉

yes

—

134

C₂×D₈

—

135

C₄⋊Q₈

—

136

C₄⋊Q₈

C₂×D₈₉

yes

characteristic

137

#126

—

178

—

138

#125

—

139

#124

—

140

C₂²⋊Q₈

—

178

—

141

C₂²⋊Q₈

—

178

—

142

C₂²⋊Q₈

—

178

—

143

C₄×Q₈

—

144

C₄×Q₈

—

145

C₄×D₄

—

146

C₄×D₄

—

147

C₄×D₄

C₂×D₈₉

yes

characteristic

148

#117

—

178

—

149

C₂×C₄⋊C₄

—

178

—

150

#107

—

151

#106

—

152

C₄⋊C₈

—

153

C₄⋊C₈

C₂×D₈₉

yes

characteristic

154

#103

—

155

#103

—

156

#103

C₂×D₈₉

yes

—

157

#102

—

158

#102

—

159

#102

—

160

C₄×C₈

—

161

C₄×C₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

178

—

164

C₂×Q₈

C₂²×D₈₉

yes

—

165

C₂×D₄

—

166

C₂×D₄

C₂²×D₈₉

yes

characteristic

167

C₂²×C₄

—

168

C₂²×C₄

—

178

—

169

C₂²×C₄

—

178

—

170

SD₁₆

—

171

D₈

—

178

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

C₂²×D₈₉

yes

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

178

—

182

C₄⋊C₄

—

178

—

183

C₄⋊C₄

—

178

—

184

C₄⋊C₄

—

178

—

185

C₄⋊C₄

C₂²×D₈₉

yes

characteristic

186

C₂²⋊C₄

—

187

C₂²⋊C₄

—

178

—

188

C₂²⋊C₄

—

178

—

189

C₂²⋊C₄

—

178

—

190

C₂²⋊C₄

—

178

—

191

C₄²

—

192

C₄²

—

178

—

193

C₄²

C₂²×D₈₉

yes

characteristic

194

C₂³

—

195

C₂³

—

178

—

196

Q₈

—

197

Q₈

—

198

Q₈

—

178

—

199

Q₈

—

712

—

200

D₄

—

201

D₄

—

178

—

202

D₄

—

178

—

203

D₄

#13083573

yes

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

356

—

210

C₂×C₄

—

178

—

211

C₂×C₄

—

178

—

212

C₂×C₄

—

712

—

213

C₂×C₄

D₄×D₈₉

yes

characteristic

214

C₂×C₄

D₄×D₈₉

yes

characteristic

215

C₂×C₄

C₂³×D₈₉

yes

characteristic

216

C₈

—

217

C₈

—

178

—

218

C₈

—

178

—

219

C₂²

—

220

C₂²

—

221

C₂²

—

222

C₂²

—

356

—

223

C₂²

—

356

—

224

C₂²

—

356

—

225

C₂²

C₂×D₄×D₈₉

yes

characteristic

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

356

—

230

C₄

—

356

—

231

C₄

—

178

—

232

C₄

—

178

—

233

C₄

#15668033

yes

—

234

C₄

C₂×#13083573

yes

characteristic

235

C₄

#15668059

yes

characteristic

236

C₂

—

237

C₂

—

712

—

238

C₂

#19152254

yes

characteristic

239

C₂

C₂×#15668033

yes

characteristic

240

C₂

#19152407

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₈₉
commutator, cosocle	C₂×C₄×C₈₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₉
Fitting	#461×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₄
prime radical	C₂×#13083559	C₂²
hypercenter	#461	D₈₉
hypocenter	C₈₉	#3360
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #461

subgroup

G/H

center

C₂²

C₂×D₄×D₈₉

commutator, cosocle

C₂×C₄×C₈₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₈₉

Fitting

#461×C₈₉

C₂

socle

C₂²×C₈₉

C₂²×D₄

C₂²

D₈₉

C₈₉

G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #461

N	H ≅ G/N	type
1. #19152322	C₂	semidirect
2. #19152305	C₂	semidirect
3. #19151954	C₂	semidirect
4. #19151948	C₂	semidirect
5. #19151903	C₂	semidirect
6. #19151889	C₂	semidirect
8. #19151722	C₂	semidirect
9. SD₁₆×Dic₈₉	C₂	semidirect
11. #461×C₈₉	C₂	semidirect
121. C₈₉	#3360	semidirect
129. #461	D₈₉	semidirect

H ≅ G/N

type

1. #19152322

C₂

semidirect

2. #19152305

C₂

semidirect

3. #19151954

C₂

semidirect

4. #19151948

C₂

semidirect

5. #19151903

C₂

semidirect

6. #19151889

C₂

semidirect

8. #19151722

C₂

semidirect

9. SD₁₆×Dic₈₉

C₂

semidirect

11. #461×C₈₉

C₂

semidirect

121. C₈₉

#3360

semidirect

129. #461

D₈₉

semidirect

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

subgroup	index
#19152322	2
#19152305	2
#19151954	2
#19151948	2
#19151903	2
#19151889	2
#19151815	2
#19151722	2
SD₁₆×Dic₈₉	2
C₄×#13083559	2
#461×C₈₉	2
#3360	89

subgroup

index

SD₁₆×Dic₈₉

#461×C₈₉

Subgroups — #26032905

Conjugacy classes of subgroups

Complements

Maximal subgroups