Group #26033123 — subgroups

Subgroups — #26033123

Order 11392.

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

normal subgroups only

This group has 338 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	#19152308	C₂	1	1	yes	maximal, characteristic
2	#19151997	C₂	1	2	yes	maximal, complemented
3	#19151994	C₂	1	1	yes	maximal, characteristic, complemented
4	#19151905	C₂	1	2	yes	maximal, complemented
5	#19151895	C₂	1	2	yes	maximal
6	#19151893	C₂	1	1	yes	maximal, characteristic, complemented
7	#19151875	C₂	1	1	yes	maximal, characteristic
8	Q₈×#10623494	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#13083561	C₂	1	1	yes	maximal, characteristic
10	C₄×#13083561	C₂	1	2	yes	maximal
11	#557×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13083561	C₂²	1	1	yes	characteristic
13	#15668012	C₂²	1	1	yes	characteristic
14	#15668004	C₂²	1	2	yes	—
15	#15667990	—	2	2	no	—
16	#15667988	—	2	1	no	—
17	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
18	C₄×D₃₅₆	C₂²	1	2	yes	—
19	C₄⋊C₄×D₈₉	—	2	1	no	—
20	#15667945	C₂²	1	2	yes	—
21	#15667945	C₂²	1	2	yes	—
22	#15667943	C₂²	1	2	yes	—
23	#15667943	C₂²	1	2	yes	—
24	#15667943	C₂²	1	1	yes	characteristic
25	C₄⋊#10623494	C₂²	1	1	yes	characteristic
26	C₄⋊#10623494	C₂²	1	2	yes	—
27	#15667936	C₂²	1	2	yes	—
28	#15667936	C₂²	1	1	yes	characteristic
29	#15667932	C₂²	1	2	yes	—
30	#15667932	C₂²	1	1	yes	characteristic
31	C₄×#10623494	C₂²	1	1	yes	characteristic
32	C₄×#10623494	C₂²	1	2	yes	—
33	C₄⋊Q₈×C₈₉	—	2	1	no	—
34	C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
35	#125×C₈₉	—	2	2	no	—
36	#125×C₈₉	C₂²	1	2	yes	—
37	C₄×Q₈×C₈₉	—	2	1	no	—
38	C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
39	C₄×Q₈×C₈₉	C₂²	1	2	yes	—
40	C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×Dic₁₇₈	—	2	1	no	—
42	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
43	C₂×C₄×D₈₉	—	2	1	no	—
44	C₂×C₄×D₈₉	—	2	2	no	—
45	#13083561	Q₈	1	4	yes	complemented
46	C₂×#10623494	C₂³	1	1	yes	characteristic
47	C₂×#10623494	C₂³	1	2	yes	—
48	C₂×#10623494	C₂³	1	1	yes	characteristic
49	C₄⋊Dic₈₉	—	2	1	no	—
50	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
51	C₄⋊Dic₈₉	C₂³	1	2	yes	—
52	#13083553	—	2	2	no	—
53	#13083553	—	2	2	no	—
54	#13083551	—	2	2	no	—
55	#13083551	—	2	1	no	—
56	C₂×Q₈×C₈₉	—	2	1	no	—
57	C₂×Q₈×C₈₉	D₄	1	1	yes	characteristic
58	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
59	C₄⋊C₄×C₈₉	—	2	2	no	—
60	C₄⋊C₄×C₈₉	—	2	1	no	—
61	C₄⋊C₄×C₈₉	—	2	2	no	—
62	C₄⋊C₄×C₈₉	—	2	1	no	—
63	C₄⋊C₄×C₈₉	—	2	2	no	—
64	C₄⋊C₄×C₈₉	D₄	1	2	yes	—
65	C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
66	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
67	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
68	C₄²×C₈₉	—	2	2	no	—
69	C₄²×C₈₉	—	2	1	no	—
70	C₄²×C₈₉	C₂³	1	2	yes	—
71	C₄²×C₈₉	C₂³	1	1	yes	characteristic
72	C₂²×D₈₉	—	2	1	no	—
73	Q₈×C₈₉	—	2	2	no	—
74	Q₈×C₈₉	—	2	1	no	—
75	Q₈×C₈₉	—	4	2	no	—
76	Q₈×C₈₉	C₂×Q₈	1	2	yes	—
77	C₂×C₄×C₈₉	—	2	1	no	—
78	C₂×C₄×C₈₉	—	2	1	no	—
79	C₂×C₄×C₈₉	—	2	2	no	—
80	C₂×C₄×C₈₉	C₂×D₄	1	2	yes	—
81	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
82	C₂×C₄×C₈₉	C₂×D₄	1	2	yes	—
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	D₃₅₆	—	2	1	no	—
88	D₃₅₆	C₂×Q₈	1	2	yes	—
89	C₄×D₈₉	—	4	2	no	—
90	C₄×D₈₉	—	8	2	no	—
91	Dic₁₇₈	—	8	1	no	—
92	#10623494	—	2	1	no	—
93	#10623494	—	2	2	no	—
94	#10623494	C₂×Q₈	1	2	yes	—
95	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
96	C₂×D₈₉	—	2	2	no	—
97	C₂×D₈₉	—	4	1	no	—
98	C₂×D₈₉	—	4	1	no	—
99	C₄×C₈₉	—	2	2	no	—
100	C₄×C₈₉	—	2	2	no	—
101	C₄×C₈₉	—	2	1	no	—
102	C₄×C₈₉	—	2	2	no	—
103	C₄×C₈₉	—	4	2	no	—
104	C₄×C₈₉	—	4	1	no	—
105	C₄×C₈₉	#135	1	2	yes	—
106	C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
107	C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
108	Dic₈₉	—	4	1	no	—
109	Dic₈₉	—	4	2	no	—
110	C₂×C₈₉	D₄×Q₈	1	1	yes	characteristic
111	C₂×C₈₉	C₂×#135	1	1	yes	characteristic
112	C₂×C₈₉	#577	1	1	yes	characteristic
113	D₈₉	—	4	2	no	—
114	#3381	—	89	1	no	maximal, Sylow
115	C₈₉	#3381	1	1	yes	characteristic, complemented, Sylow
116	#557	D₈₉	1	1	yes	characteristic, complemented
117	#554	—	89	1	no	—
118	#499	—	89	2	no	—
119	#498	—	89	1	no	—
120	#479	—	89	2	no	—
121	#478	—	89	2	no	—
122	#477	—	89	1	no	—
123	#474	—	89	1	no	—
124	C₈×Q₈	—	89	1	no	—
125	C₄×SD₁₆	—	89	1	no	—
126	C₄×SD₁₆	—	89	2	no	—
127	C₂×SD₁₆	—	89	1	no	—
128	C₄⋊Q₈	—	2	1	no	—
129	C₄⋊Q₈	—	89	1	no	—
130	C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
131	#125	—	2	2	no	—
132	#125	—	89	2	no	—
133	#125	C₂×D₈₉	1	2	yes	—
134	C₂²⋊Q₈	—	178	1	no	—
135	C₂²⋊Q₈	—	178	2	no	—
136	C₄×Q₈	—	2	1	no	—
137	C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
138	C₄×Q₈	C₂×D₈₉	1	2	yes	—
139	C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
140	C₄×D₄	—	89	1	no	—
141	C₄×D₄	—	89	2	no	—
142	C₂×C₄⋊C₄	—	178	1	no	—
143	#107	—	89	2	no	—
144	#107	—	89	2	no	—
145	#106	—	89	2	no	—
146	#106	—	89	1	no	—
147	#106	—	89	2	no	—
148	C₄⋊C₈	—	89	1	no	—
149	C₄⋊C₈	—	89	2	no	—
150	#103	—	89	2	no	—
151	#103	—	89	1	no	—
152	#102	—	89	2	no	—
153	#102	—	89	1	no	—
154	C₄×C₈	—	89	1	no	—
155	C₄×C₈	—	89	2	no	—
156	C₂×Q₈	—	2	1	no	—
157	C₂×Q₈	—	178	1	no	—
158	C₂×Q₈	C₂²⋊D₈₉	1	1	yes	characteristic
159	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
160	C₂×D₄	—	89	1	no	—
161	C₂²×C₄	—	178	1	no	—
162	C₂²×C₄	—	178	2	no	—
163	SD₁₆	—	89	4	no	—
164	C₂×C₈	—	89	1	no	—
165	C₂×C₈	—	89	1	no	—
166	C₂×C₈	—	89	2	no	—
167	C₄⋊C₄	—	2	2	no	—
168	C₄⋊C₄	—	2	1	no	—
169	C₄⋊C₄	—	2	2	no	—
170	C₄⋊C₄	—	2	1	no	—
171	C₄⋊C₄	—	2	2	no	—
172	C₄⋊C₄	—	89	2	no	—
173	C₄⋊C₄	—	89	1	no	—
174	C₄⋊C₄	—	178	2	no	—
175	C₄⋊C₄	—	178	1	no	—
176	C₄⋊C₄	—	178	2	no	—
177	C₄⋊C₄	C₂²⋊D₈₉	1	1	yes	characteristic
178	C₄⋊C₄	C₂²⋊D₈₉	1	2	yes	—
179	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
180	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
181	C₂²⋊C₄	—	178	1	no	—
182	C₂²⋊C₄	—	178	2	no	—
183	C₄²	—	2	2	no	—
184	C₄²	—	2	1	no	—
185	C₄²	C₂²×D₈₉	1	2	yes	—
186	C₄²	C₂²×D₈₉	1	1	yes	characteristic
187	C₂³	—	178	1	no	—
188	Q₈	—	2	2	no	—
189	Q₈	—	2	1	no	—
190	Q₈	—	4	2	no	—
191	Q₈	—	712	1	no	—
192	Q₈	Q₈×D₈₉	1	2	yes	—
193	D₄	—	89	2	no	—
194	D₄	—	178	1	no	—
195	C₂×C₄	—	2	1	no	—
196	C₂×C₄	—	2	1	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	356	2	no	—
199	C₂×C₄	—	178	1	no	—
200	C₂×C₄	—	178	2	no	—
201	C₂×C₄	—	712	2	no	—
202	C₂×C₄	C₂×C₂²⋊D₈₉	1	2	yes	—
203	C₂×C₄	C₂×C₂²⋊D₈₉	1	2	yes	—
204	C₂×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
205	C₂×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
206	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
207	C₈	—	89	2	no	—
208	C₈	—	178	1	no	—
209	C₈	—	178	2	no	—
210	C₂²	—	356	1	no	—
211	C₂²	—	356	1	no	—
212	C₂²	—	178	2	no	—
213	C₂²	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
214	C₄	—	2	2	no	—
215	C₄	—	2	1	no	—
216	C₄	—	2	2	no	—
217	C₄	—	2	2	no	—
218	C₄	—	4	1	no	—
219	C₄	—	4	2	no	—
220	C₄	—	356	2	no	—
221	C₄	—	356	1	no	—
222	C₄	#15668032	1	2	yes	—
223	C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
224	C₄	#15668060	1	1	yes	characteristic
225	C₂	—	356	2	no	—
226	C₂	Q₈×C₂²⋊D₈₉	1	1	yes	characteristic
227	C₂	C₂×#15668032	1	1	yes	characteristic
228	C₂	#19152406	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19152308

C₂

yes

maximal, characteristic

#19151997

C₂

yes

maximal, complemented

#19151994

C₂

yes

maximal, characteristic, complemented

#19151905

C₂

yes

maximal, complemented

#19151895

C₂

yes

maximal

#19151893

C₂

yes

maximal, characteristic, complemented

#19151875

C₂

yes

maximal, characteristic

Q₈×#10623494

C₂

yes

maximal, characteristic, complemented

C₄×#13083561

C₂

yes

maximal, characteristic

C₄×#13083561

C₂

yes

maximal

#557×C₈₉

C₂

yes

maximal, characteristic, complemented

C₂×#13083561

C₂²

yes

characteristic

#15668012

C₂²

yes

characteristic

#15668004

C₂²

yes

—

#15667990

—

#15667988

—

C₄×D₃₅₆

C₂²

yes

characteristic

C₄×D₃₅₆

C₂²

yes

—

C₄⋊C₄×D₈₉

—

#15667945

C₂²

yes

—

#15667945

C₂²

yes

—

#15667943

C₂²

yes

—

#15667943

C₂²

yes

—

#15667943

C₂²

yes

characteristic

C₄⋊#10623494

C₂²

yes

characteristic

C₄⋊#10623494

C₂²

yes

—

#15667936

C₂²

yes

—

#15667936

C₂²

yes

characteristic

#15667932

C₂²

yes

—

#15667932

C₂²

yes

characteristic

C₄×#10623494

C₂²

yes

characteristic

C₄×#10623494

C₂²

yes

—

C₄⋊Q₈×C₈₉

—

C₄⋊Q₈×C₈₉

C₂²

yes

characteristic

#125×C₈₉

—

#125×C₈₉

C₂²

yes

—

C₄×Q₈×C₈₉

—

C₄×Q₈×C₈₉

C₂²

yes

characteristic

C₄×Q₈×C₈₉

C₂²

yes

—

C₄×Q₈×C₈₉

C₂²

yes

characteristic

C₂×Dic₁₇₈

—

C₂×D₃₅₆

C₂³

yes

characteristic

C₂×C₄×D₈₉

—

C₂×C₄×D₈₉

—

#13083561

Q₈

yes

complemented

C₂×#10623494

C₂³

yes

characteristic

C₂×#10623494

C₂³

yes

—

C₂×#10623494

C₂³

yes

characteristic

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

C₂³

yes

characteristic

C₄⋊Dic₈₉

C₂³

yes

—

—

—

—

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

D₄

yes

characteristic

C₂×Q₈×C₈₉

C₂³

yes

characteristic

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

D₄

yes

—

C₄⋊C₄×C₈₉

D₄

yes

characteristic

C₄⋊C₄×C₈₉

C₂³

yes

characteristic

C₄⋊C₄×C₈₉

C₂³

yes

—

C₄²×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

C₂³

yes

—

C₄²×C₈₉

C₂³

yes

characteristic

C₂²×D₈₉

—

Q₈×C₈₉

—

Q₈×C₈₉

—

Q₈×C₈₉

—

Q₈×C₈₉

C₂×Q₈

yes

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂×D₄

yes

—

C₂×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂×C₄×C₈₉

C₂×D₄

yes

—

C₂×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂×C₄×C₈₉

C₂⁴

yes

characteristic

C₂×Dic₈₉

—

C₂×Dic₈₉

—

D₃₅₆

—

D₃₅₆

C₂×Q₈

yes

—

C₄×D₈₉

—

C₄×D₈₉

—

Dic₁₇₈

—

#10623494

—

#10623494

—

#10623494

C₂×Q₈

yes

—

C₂²×C₈₉

C₂²×D₄

yes

characteristic

C₂×D₈₉

—

C₂×D₈₉

—

C₂×D₈₉

—

C₄×C₈₉

—

100

C₄×C₈₉

—

101

C₄×C₈₉

—

102

C₄×C₈₉

—

103

C₄×C₈₉

—

104

C₄×C₈₉

—

105

C₄×C₈₉

#135

yes

—

106

C₄×C₈₉

C₂²×Q₈

yes

characteristic

107

C₄×C₈₉

2₋¹⁺⁴

yes

characteristic

108

Dic₈₉

—

109

Dic₈₉

—

110

C₂×C₈₉

D₄×Q₈

yes

characteristic

111

C₂×C₈₉

C₂×#135

yes

characteristic

112

C₂×C₈₉

#577

yes

characteristic

113

D₈₉

—

114

#3381

—

maximal, Sylow

115

C₈₉

#3381

yes

characteristic, complemented, Sylow

116

#557

D₈₉

yes

characteristic, complemented

117

#554

—

118

#499

—

119

#498

—

120

#479

—

121

#478

—

122

#477

—

123

#474

—

124

C₈×Q₈

—

125

C₄×SD₁₆

—

126

C₄×SD₁₆

—

127

C₂×SD₁₆

—

128

C₄⋊Q₈

—

129

C₄⋊Q₈

—

130

C₄⋊Q₈

C₂×D₈₉

yes

characteristic

131

#125

—

132

#125

—

133

#125

C₂×D₈₉

yes

—

134

C₂²⋊Q₈

—

178

—

135

C₂²⋊Q₈

—

178

—

136

C₄×Q₈

—

137

C₄×Q₈

C₂×D₈₉

yes

characteristic

138

C₄×Q₈

C₂×D₈₉

yes

—

139

C₄×Q₈

C₂×D₈₉

yes

characteristic

140

C₄×D₄

—

141

C₄×D₄

—

142

C₂×C₄⋊C₄

—

178

—

143

#107

—

144

#107

—

145

#106

—

146

#106

—

147

#106

—

148

C₄⋊C₈

—

149

C₄⋊C₈

—

150

#103

—

151

#103

—

152

#102

—

153

#102

—

154

C₄×C₈

—

155

C₄×C₈

—

156

C₂×Q₈

—

157

C₂×Q₈

—

178

—

158

C₂×Q₈

C₂²⋊D₈₉

yes

characteristic

159

C₂×Q₈

C₂²×D₈₉

yes

characteristic

160

C₂×D₄

—

161

C₂²×C₄

—

178

—

162

C₂²×C₄

—

178

—

163

SD₁₆

—

164

C₂×C₈

—

165

C₂×C₈

—

166

C₂×C₈

—

167

C₄⋊C₄

—

168

C₄⋊C₄

—

169

C₄⋊C₄

—

170

C₄⋊C₄

—

171

C₄⋊C₄

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₄⋊C₄

—

178

—

175

C₄⋊C₄

—

178

—

176

C₄⋊C₄

—

178

—

177

C₄⋊C₄

C₂²⋊D₈₉

yes

characteristic

178

C₄⋊C₄

C₂²⋊D₈₉

yes

—

179

C₄⋊C₄

C₂²×D₈₉

yes

—

180

C₄⋊C₄

C₂²×D₈₉

yes

characteristic

181

C₂²⋊C₄

—

178

—

182

C₂²⋊C₄

—

178

—

183

C₄²

—

184

C₄²

—

185

C₄²

C₂²×D₈₉

yes

—

186

C₄²

C₂²×D₈₉

yes

characteristic

187

C₂³

—

178

—

188

Q₈

—

189

Q₈

—

190

Q₈

—

191

Q₈

—

712

—

192

Q₈

Q₈×D₈₉

yes

—

193

D₄

—

194

D₄

—

178

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

356

—

199

C₂×C₄

—

178

—

200

C₂×C₄

—

178

—

201

C₂×C₄

—

712

—

202

C₂×C₄

C₂×C₂²⋊D₈₉

yes

—

203

C₂×C₄

C₂×C₂²⋊D₈₉

yes

—

204

C₂×C₄

C₂×C₂²⋊D₈₉

yes

characteristic

205

C₂×C₄

C₂×C₂²⋊D₈₉

yes

characteristic

206

C₂×C₄

C₂³×D₈₉

yes

characteristic

207

C₈

—

208

C₈

—

178

—

209

C₈

—

178

—

210

C₂²

—

356

—

211

C₂²

—

356

—

212

C₂²

—

178

—

213

C₂²

C₂²×C₂²⋊D₈₉

yes

characteristic

214

C₄

—

215

C₄

—

216

C₄

—

217

C₄

—

218

C₄

—

219

C₄

—

220

C₄

—

356

—

221

C₄

—

356

—

222

C₄

#15668032

yes

—

223

C₄

C₂×Q₈×D₈₉

yes

characteristic

224

C₄

#15668060

yes

characteristic

225

C₂

—

356

—

226

C₂

Q₈×C₂²⋊D₈₉

yes

characteristic

227

C₂

C₂×#15668032

yes

characteristic

228

C₂

#19152406

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊D₈₉
commutator, cosocle	C₂×C₄×C₈₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₉
Fitting	#557×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₄
prime radical	C₂×D₃₅₆	C₂³
hypercenter	#557	D₈₉
hypocenter	C₈₉	#3381
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #557

subgroup

G/H

center

C₂²

C₂²×C₂²⋊D₈₉

commutator, cosocle

C₂×C₄×C₈₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₈₉

Fitting

#557×C₈₉

C₂

socle

C₂²×C₈₉

C₂²×D₄

prime radical

C₂×D₃₅₆

C₂³

D₈₉

C₈₉

G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #557

N	H ≅ G/N	type
2. #19151997	C₂	semidirect
3. #19151994	C₂	semidirect
4. #19151905	C₂	semidirect
6. #19151893	C₂	semidirect
8. Q₈×#10623494	C₂	semidirect
11. #557×C₈₉	C₂	semidirect
45. #13083561	Q₈	semidirect
115. C₈₉	#3381	semidirect
116. #557	D₈₉	semidirect

H ≅ G/N

type

2. #19151997

C₂

semidirect

3. #19151994

C₂

semidirect

4. #19151905

C₂

semidirect

6. #19151893

C₂

semidirect

8. Q₈×#10623494

C₂

semidirect

11. #557×C₈₉

C₂

semidirect

45. #13083561

Q₈

semidirect

115. C₈₉

#3381

semidirect

116. #557

D₈₉

semidirect

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

subgroup	index
#19152308	2
#19151997	2
#19151994	2
#19151905	2
#19151895	2
#19151893	2
#19151875	2
Q₈×#10623494	2
C₄×#13083561	2
#557×C₈₉	2
#3381	89

subgroup

index

#557×C₈₉

Subgroups — #26033123

Conjugacy classes of subgroups

Complements

Maximal subgroups