Group #36447350 — subgroups

Subgroups — #36447350

Order 22784.

398 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 137 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	C₂×Q₈×#10623494	C₂	1	1	yes	maximal, characteristic
2	#26020248	C₂	1	1	yes	maximal, characteristic
3	#26019007	C₂	1	2	yes	maximal
4	#26018126	C₂	1	2	yes	maximal
5	C₈₉×#1801	C₂	1	1	yes	maximal, characteristic
6	Q₈×#10623494	—	2	2	no	—
7	Q₈×#10623494	—	2	2	no	—
8	#19151622	C₂²	1	2	yes	—
9	C₂×C₄⋊#10623494	C₄	1	2	yes	—
10	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
11	C₂×#15667931	—	2	1	no	—
12	C₂×C₄×#10623494	C₄	1	2	yes	—
13	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
14	#19151367	—	2	1	no	—
15	#19151348	—	2	2	no	—
16	#19151348	—	2	2	no	—
17	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
18	#423×C₈₉	C₂²	1	2	yes	—
19	C₂×#101×C₈₉	—	2	1	no	—
20	#343×C₈₉	—	2	1	no	—
21	C₂×#13083558	—	2	2	no	—
22	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
23	C₂²×#10623494	C₂×C₄	1	2	yes	—
24	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
25	C₄⋊#10623494	—	2	4	no	—
26	C₄⋊#10623494	—	2	2	no	—
27	C₄⋊#10623494	—	2	2	no	—
28	C₄⋊#10623494	—	2	2	no	—
29	#15667931	—	4	2	no	—
30	C₄×#10623494	—	2	2	no	—
31	C₄×#10623494	—	2	2	no	—
32	C₄×#10623494	D₄	1	2	yes	—
33	C₄×#10623494	D₄	1	2	yes	—
34	C₂²×Q₈×C₈₉	D₄	1	1	yes	characteristic
35	C₂×M₁₆×C₈₉	—	2	2	no	—
36	C₄×Q₈×C₈₉	—	2	2	no	—
37	C₄×Q₈×C₈₉	—	2	2	no	—
38	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
39	C₂×C₄⋊C₄×C₈₉	Q₈	1	2	yes	—
40	C₂×C₄²×C₈₉	C₂×C₄	1	2	yes	—
41	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
42	C₄⋊C₈×C₈₉	—	2	2	no	—
43	C₄⋊C₈×C₈₉	—	2	2	no	—
44	#101×C₈₉	—	4	2	no	—
45	#13083558	—	4	2	no	—
46	#13083558	—	4	2	no	—
47	C₂×#10623494	—	2	2	no	—
48	C₂×#10623494	—	2	2	no	—
49	C₂×#10623494	—	4	1	no	—
50	C₂×#10623494	—	4	2	no	—
51	C₂×#10623494	—	4	2	no	—
52	C₂×#10623494	C₂²⋊C₄	1	1	yes	characteristic
53	C₂×#10623494	C₂²⋊C₄	1	2	yes	—
54	C₂×#10623494	C₂²⋊C₄	1	1	yes	characteristic
55	C₂×Q₈×C₈₉	—	2	2	no	—
56	C₂×Q₈×C₈₉	—	2	2	no	—
57	C₂×Q₈×C₈₉	SD₁₆	1	2	yes	—
58	C₂×Q₈×C₈₉	SD₁₆	1	2	yes	—
59	C₂²×C₄×C₈₉	C₄⋊C₄	1	2	yes	—
60	C₂²×C₄×C₈₉	C₄⋊C₄	1	2	yes	—
61	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
64	M₁₆×C₈₉	—	4	2	no	—
65	M₁₆×C₈₉	—	4	2	no	—
66	C₂×C₈×C₈₉	—	4	2	no	—
67	C₄⋊C₄×C₈₉	—	2	2	no	—
68	C₄⋊C₄×C₈₉	—	2	4	no	—
69	C₄²×C₈₉	—	2	2	no	—
70	C₄²×C₈₉	—	2	2	no	—
71	C₄²×C₈₉	C₂×D₄	1	2	yes	—
72	C₄²×C₈₉	#41	1	2	yes	—
73	C₂³×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
74	Q₈×C₈₉	—	2	4	no	—
75	Q₈×C₈₉	—	2	4	no	—
76	C₂×C₄×C₈₉	—	2	2	no	—
77	C₂×C₄×C₈₉	—	2	2	no	—
78	C₂×C₄×C₈₉	—	2	1	no	—
79	C₂×C₄×C₈₉	—	2	1	no	—
80	C₂×C₄×C₈₉	—	2	2	no	—
81	C₂×C₄×C₈₉	—	4	1	no	—
82	C₂×C₄×C₈₉	—	4	2	no	—
83	C₂×C₄×C₈₉	#106	1	4	yes	—
84	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
85	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
86	C₂×C₄×C₈₉	#121	1	2	yes	—
87	C₂×C₄×C₈₉	C₂²⋊Q₈	1	2	yes	—
88	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
89	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
90	C₂×C₄×C₈₉	#135	1	2	yes	—
91	C₈×C₈₉	—	8	2	no	—
92	#10623494	—	2	1	no	—
93	#10623494	—	2	2	no	—
94	#10623494	—	4	2	no	—
95	#10623494	—	8	2	no	—
96	#10623494	#101	1	2	yes	complemented
97	C₂²×C₈₉	—	2	1	no	—
98	C₂²×C₈₉	—	2	1	no	—
99	C₂²×C₈₉	#380	1	1	yes	characteristic
100	C₂²×C₈₉	C₂×#106	1	1	yes	characteristic
101	C₂²×C₈₉	#427	1	1	yes	characteristic
102	C₄×C₈₉	—	2	1	no	—
103	C₄×C₈₉	—	2	4	no	—
104	C₄×C₈₉	—	2	2	no	—
105	C₄×C₈₉	—	4	2	no	—
106	C₄×C₈₉	C₂×#101	1	1	yes	characteristic
107	C₄×C₈₉	#413	1	1	yes	characteristic
108	C₄×C₈₉	#465	1	2	yes	—
109	C₄×C₈₉	#465	1	2	yes	—
110	#8615	—	89	1	no	maximal, Sylow
111	C₂×C₈₉	—	2	1	no	—
112	C₂×C₈₉	—	2	1	no	—
113	C₂×C₈₉	#1801	1	1	yes	characteristic
114	C₂×C₈₉	#1807	1	1	yes	characteristic
115	C₂×C₈₉	#1813	1	1	yes	characteristic
116	C₂×C₈×Q₈	—	89	1	no	—
117	#1801	—	89	1	no	—
118	#1801	D₈₉	1	1	yes	characteristic
119	#1566	—	89	2	no	—
120	#1292	—	89	2	no	—
121	C₈₉	#8615	1	1	yes	characteristic, complemented, Sylow
122	C₂×C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
123	C₈×Q₈	—	178	2	no	—
124	C₈×Q₈	—	178	2	no	—
125	#423	—	89	2	no	—
126	#423	C₂×D₈₉	1	2	yes	—
127	C₂×C₄⋊C₈	—	89	2	no	—
128	C₂×C₄⋊C₈	—	89	1	no	—
129	C₂×#101	—	2	1	no	—
130	C₂×#101	—	178	1	no	—
131	C₂×C₄×C₈	—	89	1	no	—
132	C₂×C₄×C₈	—	89	2	no	—
133	#343	—	2	1	no	—
134	#343	—	178	1	no	—
135	#334	—	178	2	no	—
136	#334	—	178	2	no	—
137	C₂²×Q₈	C₂²⋊D₈₉	1	1	yes	characteristic
138	C₂×M₁₆	—	2	2	no	—
139	C₂×M₁₆	—	178	2	no	—
140	C₂²×C₈	—	89	1	no	—
141	C₂²×C₈	—	89	1	no	—
142	C₂²×C₈	—	89	2	no	—
143	C₄×Q₈	—	2	2	no	—
144	C₄×Q₈	—	2	2	no	—
145	C₂×C₄⋊C₄	Dic₁₇₈	1	2	yes	—
146	C₂×C₄⋊C₄	C₂²⋊D₈₉	1	1	yes	characteristic
147	C₂×C₄²	C₄×D₈₉	1	2	yes	—
148	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
149	C₄⋊C₈	—	2	2	no	—
150	C₄⋊C₈	—	2	2	no	—
151	C₄⋊C₈	—	178	4	no	—
152	C₄⋊C₈	—	178	2	no	—
153	C₄⋊C₈	—	178	2	no	—
154	C₄⋊C₈	—	178	2	no	—
155	#101	—	4	2	no	—
156	#101	—	356	2	no	—
157	C₄×C₈	—	89	2	no	—
158	C₄×C₈	—	89	2	no	—
159	C₄×C₈	—	178	2	no	—
160	C₄×C₈	—	178	2	no	—
161	C₂×Q₈	—	2	2	no	—
162	C₂×Q₈	—	2	2	no	—
163	C₂×Q₈	#13083561	1	2	yes	—
164	C₂×Q₈	#13083562	1	2	yes	—
165	C₂²×C₄	#13083553	1	2	yes	—
166	C₂²×C₄	#13083553	1	2	yes	—
167	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
168	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
169	C₂²×C₄	C₂×Dic₁₇₈	1	1	yes	characteristic
170	M₁₆	—	4	2	no	—
171	M₁₆	—	4	2	no	—
172	M₁₆	—	356	2	no	—
173	M₁₆	—	356	2	no	—
174	C₂×C₈	—	4	2	no	—
175	C₂×C₈	—	89	1	no	—
176	C₂×C₈	—	89	1	no	—
177	C₂×C₈	—	89	2	no	—
178	C₂×C₈	—	356	2	no	—
179	C₂×C₈	—	356	1	no	—
180	C₂×C₈	—	356	2	no	—
181	C₂×C₈	—	178	2	no	—
182	C₂×C₈	—	178	2	no	—
183	C₄⋊C₄	—	2	2	no	—
184	C₄⋊C₄	—	2	4	no	—
185	C₄²	—	2	2	no	—
186	C₄²	—	2	2	no	—
187	C₄²	D₄×D₈₉	1	2	yes	—
188	C₄²	#13083573	1	2	yes	—
189	C₂³	C₂×#13083553	1	1	yes	characteristic
190	Q₈	—	2	4	no	—
191	Q₈	—	2	4	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	2	1	no	—
195	C₂×C₄	—	2	1	no	—
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	—	4	1	no	—
198	C₂×C₄	—	4	2	no	—
199	C₂×C₄	#15667943	1	4	yes	—
200	C₂×C₄	C₂²⋊C₄×D₈₉	1	1	yes	characteristic
201	C₂×C₄	#15667968	1	1	yes	characteristic
202	C₂×C₄	#15667984	1	2	yes	—
203	C₂×C₄	#15667989	1	2	yes	—
204	C₂×C₄	C₂×#13083561	1	1	yes	characteristic
205	C₂×C₄	C₂×#13083562	1	1	yes	characteristic
206	C₂×C₄	#15668032	1	2	yes	—
207	C₈	—	8	2	no	—
208	C₈	—	89	2	no	—
209	C₈	—	356	2	no	—
210	C₈	—	178	1	no	—
211	C₈	—	178	2	no	—
212	C₈	—	712	2	no	—
213	C₂²	—	2	1	no	—
214	C₂²	—	2	1	no	—
215	C₂²	#19151456	1	1	yes	characteristic
216	C₂²	C₂×#15667943	1	1	yes	characteristic
217	C₂²	#19151634	1	1	yes	characteristic
218	C₄	—	2	1	no	—
219	C₄	—	2	4	no	—
220	C₄	—	2	2	no	—
221	C₄	—	4	2	no	—
222	C₄	#101×D₈₉	1	1	yes	characteristic
223	C₄	#19151581	1	1	yes	characteristic
224	C₄	#19151825	1	2	yes	—
225	C₄	#19151829	1	2	yes	—
226	C₂	—	2	1	no	—
227	C₂	—	2	1	no	—
228	C₂	#26020246	1	1	yes	characteristic
229	C₂	#26020275	1	1	yes	characteristic
230	C₂	#26020300	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Q₈×#10623494

C₂

yes

maximal, characteristic

#26020248

C₂

yes

maximal, characteristic

#26019007

C₂

yes

maximal

#26018126

C₂

yes

maximal

C₈₉×#1801

C₂

yes

maximal, characteristic

Q₈×#10623494

—

Q₈×#10623494

—

#19151622

C₂²

yes

—

C₂×C₄⋊#10623494

C₄

yes

—

C₂×C₄⋊#10623494

C₂²

yes

characteristic

C₂×#15667931

—

C₂×C₄×#10623494

C₄

yes

—

C₂×C₄×#10623494

C₂²

yes

—

—

—

C₂×C₄×Q₈×C₈₉

C₂²

yes

characteristic

#423×C₈₉

C₂²

yes

—

C₂×#101×C₈₉

—

#343×C₈₉

—

C₂×#13083558

—

C₂²×#10623494

C₂×C₄

yes

characteristic

C₂²×#10623494

C₂×C₄

yes

—

C₂²×#10623494

C₂×C₄

yes

—

—

—

—

—

—

—

D₄

yes

—

C₄×#10623494

D₄

yes

—

C₂²×Q₈×C₈₉

D₄

yes

characteristic

C₂×M₁₆×C₈₉

—

C₄×Q₈×C₈₉

—

C₄×Q₈×C₈₉

—

C₂×C₄⋊C₄×C₈₉

D₄

yes

characteristic

C₂×C₄⋊C₄×C₈₉

Q₈

yes

—

C₂×C₄²×C₈₉

C₂×C₄

yes

—

C₂×C₄²×C₈₉

C₂³

yes

characteristic

C₄⋊C₈×C₈₉

—

C₄⋊C₈×C₈₉

—

#101×C₈₉

—

—

—

—

—

—

—

—

C₂²⋊C₄

yes

characteristic

C₂×#10623494

C₂²⋊C₄

yes

—

C₂×#10623494

C₂²⋊C₄

yes

characteristic

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

SD₁₆

yes

—

C₂×Q₈×C₈₉

SD₁₆

yes

—

C₂²×C₄×C₈₉

C₄⋊C₄

yes

—

C₂²×C₄×C₈₉

C₄⋊C₄

yes

—

C₂²×C₄×C₈₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₈₉

C₂×Q₈

yes

characteristic

M₁₆×C₈₉

—

M₁₆×C₈₉

—

C₂×C₈×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

C₂×D₄

yes

—

C₄²×C₈₉

#41

yes

—

C₂³×C₈₉

C₂×C₄⋊C₄

yes

characteristic

Q₈×C₈₉

—

Q₈×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

#106

yes

—

C₂×C₄×C₈₉

C₂×C₂²⋊C₄

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

yes

—

C₂×C₄×C₈₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₈₉

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₈₉

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₈₉

#135

yes

—

C₈×C₈₉

—

—

—

—

—

yes

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

#380

yes

characteristic

100

C₂²×C₈₉

C₂×#106

yes

characteristic

101

C₂²×C₈₉

#427

yes

characteristic

102

C₄×C₈₉

—

103

C₄×C₈₉

—

104

C₄×C₈₉

—

105

C₄×C₈₉

—

106

C₄×C₈₉

C₂×#101

yes

characteristic

107

C₄×C₈₉

#413

yes

characteristic

108

C₄×C₈₉

#465

yes

—

109

C₄×C₈₉

#465

yes

—

110

#8615

—

maximal, Sylow

111

C₂×C₈₉

—

112

C₂×C₈₉

—

113

C₂×C₈₉

#1801

yes

characteristic

114

C₂×C₈₉

#1807

yes

characteristic

115

C₂×C₈₉

#1813

yes

characteristic

116

C₂×C₈×Q₈

—

117

#1801

—

118

#1801

D₈₉

yes

characteristic

119

#1566

—

120

#1292

—

121

C₈₉

#8615

yes

characteristic, complemented, Sylow

122

C₂×C₄×Q₈

C₂×D₈₉

yes

characteristic

123

C₈×Q₈

—

178

—

124

C₈×Q₈

—

178

—

125

#423

—

126

#423

C₂×D₈₉

yes

—

127

C₂×C₄⋊C₈

—

128

C₂×C₄⋊C₈

—

129

C₂×#101

—

130

C₂×#101

—

178

—

131

C₂×C₄×C₈

—

132

C₂×C₄×C₈

—

133

#343

—

134

#343

—

178

—

135

#334

—

178

—

136

#334

—

178

—

137

C₂²×Q₈

C₂²⋊D₈₉

yes

characteristic

138

C₂×M₁₆

—

139

C₂×M₁₆

—

178

—

140

C₂²×C₈

—

141

C₂²×C₈

—

142

C₂²×C₈

—

143

C₄×Q₈

—

144

C₄×Q₈

—

145

C₂×C₄⋊C₄

Dic₁₇₈

yes

—

146

C₂×C₄⋊C₄

C₂²⋊D₈₉

yes

characteristic

147

C₂×C₄²

C₄×D₈₉

yes

—

148

C₂×C₄²

C₂²×D₈₉

yes

characteristic

149

C₄⋊C₈

—

150

C₄⋊C₈

—

151

C₄⋊C₈

—

178

—

152

C₄⋊C₈

—

178

—

153

C₄⋊C₈

—

178

—

154

C₄⋊C₈

—

178

—

155

#101

—

156

#101

—

356

—

157

C₄×C₈

—

158

C₄×C₈

—

159

C₄×C₈

—

178

—

160

C₄×C₈

—

178

—

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

#13083561

yes

—

164

C₂×Q₈

#13083562

yes

—

165

C₂²×C₄

#13083553

yes

—

166

C₂²×C₄

#13083553

yes

—

167

C₂²×C₄

C₂×C₄×D₈₉

yes

characteristic

168

C₂²×C₄

C₂×C₂²⋊D₈₉

yes

characteristic

169

C₂²×C₄

C₂×Dic₁₇₈

yes

characteristic

170

M₁₆

—

171

M₁₆

—

172

M₁₆

—

356

—

173

M₁₆

—

356

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₂×C₈

—

356

—

179

C₂×C₈

—

356

—

180

C₂×C₈

—

356

—

181

C₂×C₈

—

178

—

182

C₂×C₈

—

178

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄²

—

186

C₄²

—

187

C₄²

D₄×D₈₉

yes

—

188

C₄²

#13083573

yes

—

189

C₂³

C₂×#13083553

yes

characteristic

190

Q₈

—

191

Q₈

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

#15667943

yes

—

200

C₂×C₄

C₂²⋊C₄×D₈₉

yes

characteristic

201

C₂×C₄

#15667968

yes

characteristic

202

C₂×C₄

#15667984

yes

—

203

C₂×C₄

#15667989

yes

—

204

C₂×C₄

C₂×#13083561

yes

characteristic

205

C₂×C₄

C₂×#13083562

yes

characteristic

206

C₂×C₄

#15668032

yes

—

207

C₈

—

208

C₈

—

209

C₈

—

356

—

210

C₈

—

178

—

211

C₈

—

178

—

212

C₈

—

712

—

213

C₂²

—

214

C₂²

—

215

C₂²

#19151456

yes

characteristic

216

C₂²

C₂×#15667943

yes

characteristic

217

C₂²

#19151634

yes

characteristic

218

C₄

—

219

C₄

—

220

C₄

—

221

C₄

—

222

C₄

#101×D₈₉

yes

characteristic

223

C₄

#19151581

yes

characteristic

224

C₄

#19151825

yes

—

225

C₄

#19151829

yes

—

226

C₂

—

227

C₂

—

228

C₂

#26020246

yes

characteristic

229

C₂

#26020275

yes

characteristic

230

C₂

#26020300

yes

characteristic

	subgroup	G/H
center	C₂²	#19151456
commutator	C₂²×C₄×C₈₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₈₉×#1801	C₂
socle	C₂²×C₈₉	#380
prime radical	C₂³×C₈₉	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	#1801	D₈₉
hypocenter	C₈₉	#8615
LCS	G ▷ C₂²×C₄×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1801

subgroup

G/H

center

C₂²

#19151456

commutator

C₂²×C₄×C₈₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₈₉

Fitting

C₈₉×#1801

C₂

socle

C₂²×C₈₉

#380

prime radical

C₂³×C₈₉

C₂×C₄⋊C₄

cosocle

C₂×C₄²×C₈₉

C₂³

D₈₉

C₈₉

G ▷ C₂²×C₄×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1801

N	H ≅ G/N	type
96. #10623494	#101	semidirect
121. C₈₉	#8615	semidirect

H ≅ G/N

type

96. #10623494

#101

semidirect

121. C₈₉

#8615

semidirect

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

subgroup	index
C₂×Q₈×#10623494	2
#26020248	2
#26019007	2
#26018126	2
C₈₉×#1801	2
#8615	89

subgroup

index

C₈₉×#1801

Subgroups — #36447350

Conjugacy classes of subgroups

Complements

Maximal subgroups