Group #36457558 — subgroups

Subgroups — #36457558

Order 22784.

416 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 101 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	#26021233	C₂	1	1	yes	maximal, characteristic
2	#26018750	C₂	1	2	yes	maximal
3	#26018155	C₂	1	2	yes	maximal
4	#26018081	C₂	1	1	yes	maximal, characteristic
5	C₈₉×#2399	C₂	1	1	yes	maximal, characteristic
6	#19152155	C₂²	1	1	yes	characteristic
7	#19151651	C₂²	1	2	yes	—
8	#19151622	C₂²	1	1	yes	characteristic
9	#19151358	—	2	1	no	—
10	#19151358	—	2	1	no	—
11	#19151334	—	2	2	no	—
12	#19151334	—	2	2	no	—
13	C₂×C₄×Q₈×C₈₉	—	2	1	no	—
14	#398×C₈₉	—	2	2	no	—
15	#395×C₈₉	—	2	2	no	—
16	C₄×C₄⋊C₄×C₈₉	—	2	1	no	—
17	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
18	#376×C₈₉	C₂²	1	1	yes	characteristic
19	C₂×#13083558	—	2	1	no	—
20	#15668012	Q₈	1	2	yes	complemented
21	#15668004	—	2	1	no	—
22	#15667991	—	2	2	no	—
23	C₄×Dic₁₇₈	—	2	2	no	—
24	#15667971	—	2	1	no	—
25	C₄⋊#10623494	—	2	2	no	—
26	C₄⋊#10623494	—	2	2	no	—
27	C₂²⋊#10623494	—	2	2	no	—
28	C₄×#10623494	—	2	2	no	—
29	C₂²×Q₈×C₈₉	—	2	1	no	—
30	C₄×Q₈×C₈₉	—	4	2	no	—
31	C₄×Q₈×C₈₉	—	4	2	no	—
32	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
33	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
34	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
35	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
36	C₂×C₄²×C₈₉	—	2	2	no	—
37	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
38	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
40	#95×C₈₉	—	2	1	no	—
41	#95×C₈₉	—	2	1	no	—
42	#95×C₈₉	—	2	2	no	—
43	#95×C₈₉	D₄	1	2	yes	—
44	#95×C₈₉	D₄	1	2	yes	—
45	C₂×Dic₁₇₈	—	2	2	no	—
46	#13083558	—	4	1	no	—
47	#13083558	—	4	1	no	—
48	C₂×#10623494	—	4	1	no	—
49	C₂×#10623494	—	4	2	no	—
50	C₄⋊Dic₈₉	—	2	2	no	—
51	C₄⋊Dic₈₉	—	2	2	no	—
52	#13083553	—	4	2	no	—
53	C₂²⋊Dic₈₉	—	4	1	no	—
54	C₄×Dic₈₉	—	4	1	no	—
55	C₂×Q₈×C₈₉	—	4	2	no	—
56	C₂×Q₈×C₈₉	—	4	4	no	—
57	C₂²×C₄×C₈₉	—	2	1	no	—
58	C₂²×C₄×C₈₉	—	2	1	no	—
59	C₂²×C₄×C₈₉	—	2	2	no	—
60	C₂²×C₄×C₈₉	—	2	2	no	—
61	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
62	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
63	C₄⋊C₄×C₈₉	—	4	4	no	—
64	C₄⋊C₄×C₈₉	—	4	4	no	—
65	C₄⋊C₄×C₈₉	—	4	4	no	—
66	C₄⋊C₄×C₈₉	—	4	2	no	—
67	C₄²×C₈₉	—	2	1	no	—
68	C₄²×C₈₉	—	2	1	no	—
69	C₄²×C₈₉	—	4	2	no	—
70	C₄²×C₈₉	—	4	2	no	—
71	C₄²×C₈₉	SD₁₆	1	2	yes	—
72	C₄²×C₈₉	Q₁₆	1	2	yes	—
73	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
74	C₄²×C₈₉	#41	1	2	yes	—
75	C₄²×C₈₉	#41	1	1	yes	characteristic
76	C₂³×C₈₉	#120	1	1	yes	characteristic
77	Q₈×C₈₉	—	4	8	no	—
78	C₂×C₄×C₈₉	—	2	4	no	—
79	C₂×C₄×C₈₉	—	2	2	no	—
80	C₂×C₄×C₈₉	—	2	2	no	—
81	C₂×C₄×C₈₉	—	4	2	no	—
82	C₂×C₄×C₈₉	—	4	2	no	—
83	C₂×C₄×C₈₉	—	4	2	no	—
84	C₂×C₄×C₈₉	—	4	2	no	—
85	C₂×C₄×C₈₉	—	4	2	no	—
86	C₂×C₄×C₈₉	—	4	2	no	—
87	C₂×C₄×C₈₉	—	4	2	no	—
88	C₂×C₄×C₈₉	—	4	2	no	—
89	C₂×C₄×C₈₉	C₂²⋊Q₈	1	2	yes	—
90	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
91	C₂×C₄×C₈₉	#124	1	2	yes	—
92	C₂×C₄×C₈₉	#124	1	1	yes	characteristic
93	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
94	C₂×C₄×C₈₉	C₂×Q₁₆	1	1	yes	characteristic
95	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
96	C₂×C₄×C₈₉	#137	1	1	yes	characteristic
97	C₂×Dic₈₉	—	4	2	no	—
98	Dic₁₇₈	—	8	2	no	—
99	#10623494	—	8	2	no	—
100	#10623494	—	8	1	no	—
101	C₂²×C₈₉	—	2	2	no	—
102	C₂²×C₈₉	#393	1	1	yes	characteristic
103	C₂²×C₈₉	#450	1	1	yes	characteristic
104	C₂²×C₈₉	#451	1	1	yes	characteristic
105	C₄×C₈₉	—	2	2	no	—
106	C₄×C₈₉	—	2	2	no	—
107	C₄×C₈₉	—	4	2	no	—
108	C₄×C₈₉	—	4	4	no	—
109	C₄×C₈₉	—	4	2	no	—
110	C₄×C₈₉	—	8	2	no	—
111	C₄×C₈₉	#475	1	1	yes	characteristic
112	C₄×C₈₉	#477	1	1	yes	characteristic
113	C₄×C₈₉	#487	1	1	yes	characteristic
114	C₄×C₈₉	#489	1	1	yes	characteristic
115	Dic₈₉	—	8	2	no	—
116	#10371	—	89	1	no	maximal, Sylow
117	C₂×C₈₉	—	2	1	no	—
118	C₂×C₈₉	—	2	1	no	—
119	C₂×C₈₉	#2024	1	1	yes	characteristic
120	C₂×C₈₉	#2031	1	2	yes	—
121	#2399	D₈₉	1	1	yes	characteristic
122	#1995	—	89	1	no	—
123	#1503	—	89	2	no	—
124	#1303	—	89	2	no	—
125	#1274	—	89	1	no	—
126	C₈₉	#10371	1	1	yes	characteristic, complemented, Sylow
127	#533	—	89	1	no	—
128	C₂×C₄×Q₈	—	2	1	no	—
129	#431	—	89	2	no	—
130	#423	—	89	1	no	—
131	#398	—	2	2	no	—
132	#395	—	2	2	no	—
133	C₄×C₄⋊C₄	—	2	1	no	—
134	C₄×C₄⋊C₄	C₂×D₈₉	1	2	yes	—
135	#376	C₂×D₈₉	1	1	yes	characteristic
136	#339	—	178	1	no	—
137	#339	—	178	1	no	—
138	#328	—	178	2	no	—
139	#328	—	178	2	no	—
140	C₂²×Q₈	—	2	1	no	—
141	C₂×M₁₆	—	178	1	no	—
142	C₄⋊Q₈	—	89	2	no	—
143	#125	—	178	1	no	—
144	C₂²⋊Q₈	—	178	2	no	—
145	C₄×Q₈	—	4	2	no	—
146	C₄×Q₈	—	4	2	no	—
147	C₄×Q₈	—	178	2	no	—
148	#117	—	178	1	no	—
149	C₂×C₄⋊C₄	—	2	2	no	—
150	C₂×C₄⋊C₄	—	2	1	no	—
151	C₂×C₄⋊C₄	—	2	2	no	—
152	C₂×C₄⋊C₄	—	2	2	no	—
153	C₂×C₄²	—	2	2	no	—
154	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
155	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
156	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
157	C₄⋊C₈	—	178	2	no	—
158	C₄⋊C₈	—	178	2	no	—
159	C₂²⋊C₈	—	178	2	no	—
160	C₄×C₈	—	178	2	no	—
161	#95	—	2	1	no	—
162	#95	—	2	1	no	—
163	#95	—	2	2	no	—
164	#95	C₂²⋊D₈₉	1	2	yes	—
165	#95	C₂²⋊D₈₉	1	2	yes	—
166	C₂×Q₈	—	4	2	no	—
167	C₂×Q₈	—	4	4	no	—
168	C₂×Q₈	—	178	2	no	—
169	C₂²×C₄	—	2	1	no	—
170	C₂²×C₄	—	2	1	no	—
171	C₂²×C₄	—	2	2	no	—
172	C₂²×C₄	—	2	2	no	—
173	C₂²×C₄	C₂×C₂²⋊D₈₉	1	2	yes	—
174	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
175	M₁₆	—	356	1	no	—
176	M₁₆	—	356	1	no	—
177	C₂×C₈	—	356	2	no	—
178	C₂×C₈	—	356	1	no	—
179	C₄⋊C₄	—	4	4	no	—
180	C₄⋊C₄	—	4	2	no	—
181	C₄⋊C₄	—	4	4	no	—
182	C₄⋊C₄	—	4	4	no	—
183	C₄⋊C₄	—	356	2	no	—
184	C₄⋊C₄	—	178	2	no	—
185	C₄⋊C₄	—	178	2	no	—
186	C₂²⋊C₄	—	356	1	no	—
187	C₄²	—	2	1	no	—
188	C₄²	—	2	1	no	—
189	C₄²	—	4	2	no	—
190	C₄²	—	4	2	no	—
191	C₄²	—	356	1	no	—
192	C₄²	#13083562	1	2	yes	—
193	C₄²	#13083564	1	2	yes	—
194	C₄²	Q₈×D₈₉	1	1	yes	characteristic
195	C₄²	#13083575	1	1	yes	characteristic
196	C₄²	#13083575	1	2	yes	—
197	C₂³	#15667981	1	1	yes	characteristic
198	Q₈	—	4	8	no	—
199	Q₈	—	712	2	no	—
200	C₂×C₄	—	2	4	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	4	2	no	—
204	C₂×C₄	—	4	2	no	—
205	C₂×C₄	—	4	2	no	—
206	C₂×C₄	—	4	2	no	—
207	C₂×C₄	—	4	2	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	—	4	2	no	—
210	C₂×C₄	—	4	2	no	—
211	C₂×C₄	—	356	2	no	—
212	C₂×C₄	#15667988	1	2	yes	—
213	C₂×C₄	#15667988	1	1	yes	characteristic
214	C₂×C₄	#15668001	1	2	yes	—
215	C₂×C₄	#15668001	1	1	yes	characteristic
216	C₂×C₄	C₂×#13083562	1	1	yes	characteristic
217	C₂×C₄	C₂×#13083564	1	1	yes	characteristic
218	C₂×C₄	#15668038	1	1	yes	characteristic
219	C₂×C₄	#15668043	1	1	yes	characteristic
220	C₈	—	712	2	no	—
221	C₈	—	712	1	no	—
222	C₂²	—	2	2	no	—
223	C₂²	#19151509	1	1	yes	characteristic
224	C₂²	#19151749	1	1	yes	characteristic
225	C₂²	#19151754	1	1	yes	characteristic
226	C₄	—	2	2	no	—
227	C₄	—	2	2	no	—
228	C₄	—	4	4	no	—
229	C₄	—	4	2	no	—
230	C₄	—	4	2	no	—
231	C₄	—	8	2	no	—
232	C₄	—	712	2	no	—
233	C₄	#19151880	1	1	yes	characteristic
234	C₄	#19151890	1	1	yes	characteristic
235	C₄	#19151950	1	1	yes	characteristic
236	C₄	#19151960	1	1	yes	characteristic
237	C₂	—	2	1	no	—
238	C₂	—	2	1	no	—
239	C₂	#26021390	1	1	yes	characteristic
240	C₂	#26021421	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#26021233

C₂

yes

maximal, characteristic

#26018750

C₂

yes

maximal

#26018155

C₂

yes

maximal

#26018081

C₂

yes

maximal, characteristic

C₈₉×#2399

C₂

yes

maximal, characteristic

#19152155

C₂²

yes

characteristic

#19151651

C₂²

yes

—

#19151622

C₂²

yes

—

—

—

—

C₂×C₄×Q₈×C₈₉

—

#398×C₈₉

—

#395×C₈₉

—

C₄×C₄⋊C₄×C₈₉

—

C₄×C₄⋊C₄×C₈₉

C₂²

yes

—

#376×C₈₉

C₂²

yes

characteristic

C₂×#13083558

—

#15668012

Q₈

yes

complemented

#15668004

—

#15667991

—

C₄×Dic₁₇₈

—

—

—

—

—

—

C₂²×Q₈×C₈₉

—

C₄×Q₈×C₈₉

—

C₄×Q₈×C₈₉

—

C₂×C₄⋊C₄×C₈₉

—

C₂×C₄⋊C₄×C₈₉

—

C₂×C₄⋊C₄×C₈₉

—

C₂×C₄⋊C₄×C₈₉

—

C₂×C₄²×C₈₉

—

C₂×C₄²×C₈₉

D₄

yes

characteristic

C₂×C₄²×C₈₉

D₄

yes

characteristic

C₂×C₄²×C₈₉

C₂³

yes

characteristic

#95×C₈₉

—

#95×C₈₉

—

#95×C₈₉

—

#95×C₈₉

D₄

yes

—

#95×C₈₉

D₄

yes

—

C₂×Dic₁₇₈

—

—

—

—

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

#13083553

—

C₂²⋊Dic₈₉

—

C₄×Dic₈₉

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

C₂×D₄

yes

—

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

SD₁₆

yes

—

C₄²×C₈₉

Q₁₆

yes

—

C₄²×C₈₉

C₂×Q₈

yes

characteristic

C₄²×C₈₉

#41

yes

—

C₄²×C₈₉

yes

C₂³×C₈₉

yes

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

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₈₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₈₉

#124

yes

—

C₂×C₄×C₈₉

#124

yes

characteristic

C₂×C₄×C₈₉

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₈₉

C₂×Q₁₆

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

yes

C₂×Dic₈₉

—

Dic₁₇₈

—

#10623494

—

100

#10623494

—

101

C₂²×C₈₉

—

102

C₂²×C₈₉

#393

yes

characteristic

103

C₂²×C₈₉

#450

yes

characteristic

104

C₂²×C₈₉

#451

yes

characteristic

105

C₄×C₈₉

—

106

C₄×C₈₉

—

107

C₄×C₈₉

—

108

C₄×C₈₉

—

109

C₄×C₈₉

—

110

C₄×C₈₉

—

111

C₄×C₈₉

#475

yes

characteristic

112

C₄×C₈₉

#477

yes

characteristic

113

C₄×C₈₉

#487

yes

characteristic

114

C₄×C₈₉

#489

yes

characteristic

115

Dic₈₉

—

116

#10371

—

maximal, Sylow

117

C₂×C₈₉

—

118

C₂×C₈₉

—

119

C₂×C₈₉

#2024

yes

characteristic

120

C₂×C₈₉

#2031

yes

—

121

#2399

D₈₉

yes

characteristic

122

#1995

—

123

#1503

—

124

#1303

—

125

#1274

—

126

C₈₉

#10371

yes

characteristic, complemented, Sylow

127

#533

—

128

C₂×C₄×Q₈

—

129

#431

—

130

#423

—

131

#398

—

132

#395

—

133

C₄×C₄⋊C₄

—

134

C₄×C₄⋊C₄

C₂×D₈₉

yes

—

135

#376

C₂×D₈₉

yes

characteristic

136

#339

—

178

—

137

#339

—

178

—

138

#328

—

178

—

139

#328

—

178

—

140

C₂²×Q₈

—

141

C₂×M₁₆

—

178

—

142

C₄⋊Q₈

—

143

#125

—

178

—

144

C₂²⋊Q₈

—

178

—

145

C₄×Q₈

—

146

C₄×Q₈

—

147

C₄×Q₈

—

178

—

148

#117

—

178

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

—

152

C₂×C₄⋊C₄

—

153

C₂×C₄²

—

154

C₂×C₄²

C₂²⋊D₈₉

yes

characteristic

155

C₂×C₄²

C₂²⋊D₈₉

yes

characteristic

156

C₂×C₄²

C₂²×D₈₉

yes

characteristic

157

C₄⋊C₈

—

178

—

158

C₄⋊C₈

—

178

—

159

C₂²⋊C₈

—

178

—

160

C₄×C₈

—

178

—

161

#95

—

162

#95

—

163

#95

—

164

#95

C₂²⋊D₈₉

yes

—

165

#95

C₂²⋊D₈₉

yes

—

166

C₂×Q₈

—

167

C₂×Q₈

—

168

C₂×Q₈

—

178

—

169

C₂²×C₄

—

170

C₂²×C₄

—

171

C₂²×C₄

—

172

C₂²×C₄

—

173

C₂²×C₄

C₂×C₂²⋊D₈₉

yes

—

174

C₂²×C₄

C₂×C₂²⋊D₈₉

yes

characteristic

175

M₁₆

—

356

—

176

M₁₆

—

356

—

177

C₂×C₈

—

356

—

178

C₂×C₈

—

356

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

356

—

184

C₄⋊C₄

—

178

—

185

C₄⋊C₄

—

178

—

186

C₂²⋊C₄

—

356

—

187

C₄²

—

188

C₄²

—

189

C₄²

—

190

C₄²

—

191

C₄²

—

356

—

192

C₄²

#13083562

yes

—

193

C₄²

#13083564

yes

—

194

C₄²

Q₈×D₈₉

yes

characteristic

195

C₄²

#13083575

yes

characteristic

196

C₄²

#13083575

yes

—

197

C₂³

#15667981

yes

characteristic

198

Q₈

—

199

Q₈

—

712

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

356

—

212

C₂×C₄

#15667988

yes

—

213

C₂×C₄

#15667988

yes

characteristic

214

C₂×C₄

#15668001

yes

—

215

C₂×C₄

#15668001

yes

characteristic

216

C₂×C₄

C₂×#13083562

yes

characteristic

217

C₂×C₄

C₂×#13083564

yes

characteristic

218

C₂×C₄

#15668038

yes

characteristic

219

C₂×C₄

#15668043

yes

characteristic

220

C₈

—

712

—

221

C₈

—

712

—

222

C₂²

—

223

C₂²

#19151509

yes

characteristic

224

C₂²

#19151749

yes

characteristic

225

C₂²

#19151754

yes

characteristic

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

712

—

233

C₄

#19151880

yes

characteristic

234

C₄

#19151890

yes

characteristic

235

C₄

#19151950

yes

characteristic

236

C₄

#19151960

yes

characteristic

237

C₂

—

238

C₂

—

239

C₂

#26021390

yes

characteristic

240

C₂

#26021421

yes

—

	subgroup	G/H
center	C₂×C₄	#15668001
commutator, cosocle	C₂×C₄²×C₈₉	C₂³
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₈₉×#2399	C₂
socle	C₂²×C₈₉	#393
prime radical	C₂³×C₈₉	#120
hypercenter	#2399	D₈₉
hypocenter	C₈₉	#10371
LCS	G ▷ C₂×C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2399

subgroup

G/H

center

C₂×C₄

#15668001

commutator, cosocle

C₂×C₄²×C₈₉

C₂³

Frattini

C₂×C₄²

C₂²×D₈₉

Fitting

C₈₉×#2399

C₂

C₂²×C₈₉

C₂³×C₈₉

D₈₉

C₈₉

G ▷ C₂×C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2399

N	H ≅ G/N	type
20. #15668012	Q₈	semidirect
126. C₈₉	#10371	semidirect

H ≅ G/N

type

20. #15668012

Q₈

semidirect

126. C₈₉

#10371

semidirect

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

subgroup	index
#26021233	2
#26018750	2
#26018155	2
#26018081	2
C₈₉×#2399	2
#10371	89

subgroup

index

C₈₉×#2399

Subgroups — #36457558

Conjugacy classes of subgroups

Complements

Maximal subgroups