Group #36459168 — subgroups

Subgroups — #36459168

Order 22784.

402 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 119 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	#26021046	C₂	1	1	yes	maximal, characteristic
2	#26020249	C₂	1	2	yes	maximal
3	#26018135	C₂	1	2	yes	maximal, complemented
4	#26018087	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#1834	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₃₅₆	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊#10623494	C₂²	1	2	yes	—
8	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
9	C₂×#15667932	—	2	2	no	—
10	C₂×#15667924	—	2	2	no	—
11	#19151360	—	2	2	no	—
12	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
13	#384×C₈₉	C₂²	1	2	yes	—
14	#340×C₈₉	—	2	2	no	—
15	C₂²×D₃₅₆	D₄	1	1	yes	characteristic
16	C₂²×C₄×D₈₉	—	2	1	no	—
17	C₂²×#10623494	—	2	2	no	—
18	C₂²×#10623494	—	2	1	no	—
19	C₄×D₃₅₆	—	2	2	no	—
20	C₄×D₃₅₆	—	2	2	no	—
21	C₂×C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
22	C₂×#13083551	—	2	1	no	—
23	C₄⋊#10623494	—	2	2	no	—
24	C₄⋊#10623494	—	2	2	no	—
25	C₄⋊#10623494	—	2	2	no	—
26	#15667932	—	4	4	no	—
27	#15667924	—	4	4	no	—
28	C₂²×C₈×C₈₉	D₄	1	2	yes	—
29	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
30	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
31	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
32	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
33	C₄×C₈×C₈₉	—	2	2	no	—
34	C₂³×D₈₉	—	2	1	no	—
35	C₂×D₃₅₆	—	2	2	no	—
36	C₂×D₃₅₆	—	2	2	no	—
37	C₂×D₃₅₆	—	2	1	no	—
38	C₂×D₃₅₆	Q₁₆	1	2	yes	—
39	C₂²×Dic₈₉	—	2	1	no	—
40	C₂×C₄×D₈₉	—	4	1	no	—
41	C₂×C₄×D₈₉	—	4	1	no	—
42	C₂×C₄×D₈₉	—	4	2	no	—
43	C₂×C₄×D₈₉	—	4	2	no	—
44	C₂×#10623494	—	4	2	no	—
45	C₂×#10623494	—	4	1	no	—
46	C₂×#10623494	—	4	2	no	—
47	C₂×#10623494	—	4	2	no	—
48	C₂×#10623494	—	4	2	no	—
49	C₄⋊Dic₈₉	—	2	2	no	—
50	#13083551	—	4	2	no	—
51	C₂²×C₄×C₈₉	—	4	2	no	—
52	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
55	C₂×C₈×C₈₉	—	2	2	no	—
56	C₂×C₈×C₈₉	—	2	2	no	—
57	C₂×C₈×C₈₉	—	2	2	no	—
58	C₄⋊C₄×C₈₉	—	4	2	no	—
59	C₄⋊C₄×C₈₉	—	4	2	no	—
60	C₄⋊C₄×C₈₉	—	4	2	no	—
61	C₄⋊C₄×C₈₉	—	4	2	no	—
62	C₄⋊C₄×C₈₉	—	8	2	no	—
63	C₄²×C₈₉	#41	1	2	yes	—
64	C₄²×C₈₉	#41	1	2	yes	—
65	C₂³×C₈₉	#121	1	1	yes	characteristic
66	C₂²×D₈₉	—	2	2	no	—
67	C₂²×D₈₉	—	4	1	no	—
68	C₂²×D₈₉	—	4	2	no	—
69	C₂²×D₈₉	—	4	1	no	—
70	C₂²×D₈₉	—	4	2	no	—
71	C₂×C₄×C₈₉	—	2	2	no	—
72	C₂×C₄×C₈₉	—	8	2	no	—
73	C₂×C₄×C₈₉	—	8	2	no	—
74	C₂×C₄×C₈₉	—	8	2	no	—
75	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
76	C₂×C₄×C₈₉	#123	1	2	yes	—
77	C₂×C₄×C₈₉	#124	1	1	yes	characteristic
78	C₂×C₄×C₈₉	#126	1	2	yes	—
79	C₂×C₄×C₈₉	C₂×Q₁₆	1	1	yes	characteristic
80	C₂×C₄×C₈₉	#135	1	2	yes	—
81	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
82	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
83	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
84	C₂×Dic₈₉	—	4	1	no	—
85	C₂×Dic₈₉	—	4	2	no	—
86	D₃₅₆	—	2	4	no	—
87	D₃₅₆	—	4	2	no	—
88	C₄×D₈₉	—	8	2	no	—
89	C₄×D₈₉	—	8	1	no	—
90	C₄×D₈₉	—	8	1	no	—
91	C₈×C₈₉	—	4	2	no	—
92	#10623494	—	8	2	no	—
93	#10623494	—	8	1	no	—
94	C₂²×C₈₉	#397	1	1	yes	characteristic
95	C₂²×C₈₉	#463	1	2	yes	—
96	C₂²×C₈₉	#467	1	1	yes	characteristic
97	C₂²×C₈₉	#469	1	1	yes	characteristic
98	C₂²×C₈₉	#471	1	2	yes	—
99	C₂×D₈₉	—	4	2	no	—
100	C₂×D₈₉	—	4	4	no	—
101	C₂×D₈₉	—	8	1	no	—
102	C₂×D₈₉	—	8	1	no	—
103	C₂×D₈₉	—	8	2	no	—
104	C₄×C₈₉	—	2	2	no	—
105	C₄×C₈₉	—	16	2	no	—
106	C₄×C₈₉	#482	1	2	yes	—
107	C₄×C₈₉	#482	1	2	yes	—
108	C₄×C₈₉	#484	1	2	yes	—
109	C₄×C₈₉	#488	1	1	yes	characteristic
110	C₄×C₈₉	#490	1	1	yes	characteristic
111	Dic₈₉	—	8	1	no	—
112	#10622	—	89	1	no	maximal, Sylow
113	C₂×C₈₉	#1683	1	2	yes	—
114	C₂×C₈₉	#1701	1	2	yes	—
115	C₂×C₈₉	#2073	1	1	yes	characteristic
116	C₂×C₈₉	#2076	1	1	yes	characteristic
117	C₂×C₈₉	#2079	1	1	yes	characteristic
118	D₈₉	—	8	2	no	—
119	#1954	—	89	1	no	—
120	#1834	D₈₉	1	1	yes	characteristic, complemented
121	#1802	—	89	2	no	—
122	#1296	—	89	2	no	—
123	#1277	—	89	1	no	—
124	C₈₉	#10622	1	1	yes	characteristic, complemented, Sylow
125	C₂×C₄×D₄	—	89	1	no	—
126	C₂×C₄⋊C₈	—	89	2	no	—
127	C₂×C₄⋊C₈	—	89	1	no	—
128	C₂×#102	—	178	2	no	—
129	C₂×C₂²⋊C₈	—	178	2	no	—
130	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
131	#384	C₂×D₈₉	1	2	yes	—
132	#340	—	2	2	no	—
133	#340	—	178	2	no	—
134	C₂²×D₄	—	89	1	no	—
135	C₂³×C₄	—	178	1	no	—
136	C₂²×C₈	—	178	2	no	—
137	C₂²×C₈	—	178	1	no	—
138	C₂²×C₈	C₂²⋊D₈₉	1	2	yes	—
139	C₄×D₄	—	178	2	no	—
140	C₄×D₄	—	178	2	no	—
141	C₂×C₄⋊C₄	—	2	2	no	—
142	C₂×C₄⋊C₄	—	2	2	no	—
143	C₂×C₄⋊C₄	—	2	2	no	—
144	C₂×C₄⋊C₄	—	89	1	no	—
145	C₂×C₂²⋊C₄	—	178	1	no	—
146	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
147	C₄⋊C₈	—	178	2	no	—
148	C₄⋊C₈	—	178	2	no	—
149	C₄⋊C₈	—	178	2	no	—
150	#102	—	356	4	no	—
151	C₂²⋊C₈	—	356	4	no	—
152	C₄×C₈	—	2	2	no	—
153	C₂⁴	—	178	1	no	—
154	C₂×D₄	—	89	2	no	—
155	C₂×D₄	—	178	2	no	—
156	C₂×D₄	—	178	1	no	—
157	C₂×D₄	—	178	2	no	—
158	C₂²×C₄	—	4	2	no	—
159	C₂²×C₄	—	356	1	no	—
160	C₂²×C₄	—	356	1	no	—
161	C₂²×C₄	—	356	2	no	—
162	C₂²×C₄	—	356	2	no	—
163	C₂²×C₄	—	178	1	no	—
164	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
165	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
166	C₂²×C₄	#13083573	1	1	yes	characteristic
167	C₂×C₈	—	2	2	no	—
168	C₂×C₈	—	2	2	no	—
169	C₂×C₈	—	2	2	no	—
170	C₂×C₈	—	356	2	no	—
171	C₂×C₈	—	356	1	no	—
172	C₂×C₈	—	356	2	no	—
173	C₂×C₈	—	356	2	no	—
174	C₂×C₈	—	356	2	no	—
175	C₄⋊C₄	—	4	2	no	—
176	C₄⋊C₄	—	4	2	no	—
177	C₄⋊C₄	—	4	2	no	—
178	C₄⋊C₄	—	4	2	no	—
179	C₄⋊C₄	—	8	2	no	—
180	C₄⋊C₄	—	178	2	no	—
181	C₂²⋊C₄	—	356	2	no	—
182	C₄²	#13083574	1	2	yes	—
183	C₄²	#13083575	1	2	yes	—
184	C₂³	—	356	1	no	—
185	C₂³	—	356	2	no	—
186	C₂³	—	356	1	no	—
187	C₂³	—	356	2	no	—
188	C₂³	—	178	2	no	—
189	C₂³	#15667983	1	1	yes	characteristic
190	D₄	—	356	2	no	—
191	D₄	—	178	4	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	8	2	no	—
194	C₂×C₄	—	8	2	no	—
195	C₂×C₄	—	8	2	no	—
196	C₂×C₄	—	356	1	no	—
197	C₂×C₄	—	356	2	no	—
198	C₂×C₄	—	712	2	no	—
199	C₂×C₄	—	712	1	no	—
200	C₂×C₄	—	712	1	no	—
201	C₂×C₄	#15667995	1	1	yes	characteristic
202	C₂×C₄	#15667997	1	2	yes	—
203	C₂×C₄	#15668001	1	1	yes	characteristic
204	C₂×C₄	#15668007	1	2	yes	—
205	C₂×C₄	Q₁₆×D₈₉	1	1	yes	characteristic
206	C₂×C₄	#15668032	1	2	yes	—
207	C₂×C₄	#15668035	1	1	yes	characteristic
208	C₂×C₄	#15668036	1	2	yes	—
209	C₂×C₄	#15668037	1	2	yes	—
210	C₈	—	4	2	no	—
211	C₈	—	712	2	no	—
212	C₈	—	712	1	no	—
213	C₂²	—	356	2	no	—
214	C₂²	—	356	4	no	—
215	C₂²	—	712	1	no	—
216	C₂²	—	712	1	no	—
217	C₂²	—	712	2	no	—
218	C₂²	#19151524	1	1	yes	characteristic
219	C₂²	#19151810	1	2	yes	—
220	C₂²	#19151836	1	1	yes	characteristic
221	C₂²	#19151848	1	1	yes	characteristic
222	C₂²	#19151858	1	2	yes	—
223	C₄	—	2	2	no	—
224	C₄	—	16	2	no	—
225	C₄	—	712	1	no	—
226	C₄	#19151922	1	2	yes	—
227	C₄	#19151925	1	2	yes	—
228	C₄	#19151935	1	2	yes	—
229	C₄	#19151955	1	1	yes	characteristic
230	C₄	#19151964	1	1	yes	characteristic
231	C₂	—	712	2	no	—
232	C₂	#26019700	1	2	yes	—
233	C₂	#26019810	1	2	yes	—
234	C₂	#26021666	1	1	yes	characteristic
235	C₂	#26021681	1	1	yes	characteristic
236	C₂	#26021698	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#26021046

C₂

yes

maximal, characteristic

#26020249

C₂

yes

maximal

#26018135

C₂

yes

maximal, complemented

#26018087

C₂

yes

maximal, characteristic, complemented

C₈₉×#1834

C₂

yes

maximal, characteristic, complemented

C₂×C₄×D₃₅₆

C₂²

yes

characteristic

C₂×C₄⋊#10623494

C₂²

yes

—

C₂×C₄⋊#10623494

C₂²

yes

—

—

—

C₂×C₄×C₈×C₈₉

C₂²

yes

characteristic

#384×C₈₉

C₂²

yes

—

#340×C₈₉

—

C₂²×D₃₅₆

D₄

yes

characteristic

C₂²×C₄×D₈₉

—

C₂²×#10623494

—

C₂²×#10623494

—

C₄×D₃₅₆

—

C₄×D₃₅₆

—

C₂×C₄⋊Dic₈₉

D₄

yes

—

—

—

—

—

—

C₂²×C₈×C₈₉

D₄

yes

—

C₂×C₄⋊C₄×C₈₉

—

C₂×C₄⋊C₄×C₈₉

—

C₂×C₄⋊C₄×C₈₉

—

C₂×C₄²×C₈₉

C₂³

yes

characteristic

C₄×C₈×C₈₉

—

C₂³×D₈₉

—

C₂×D₃₅₆

—

C₂×D₃₅₆

—

C₂×D₃₅₆

—

C₂×D₃₅₆

Q₁₆

yes

—

C₂²×Dic₈₉

—

C₂×C₄×D₈₉

—

C₂×C₄×D₈₉

—

C₂×C₄×D₈₉

—

C₂×C₄×D₈₉

—

—

—

—

—

—

C₄⋊Dic₈₉

—

#13083551

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₈₉

#41

yes

characteristic

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄²×C₈₉

#41

yes

—

C₄²×C₈₉

#41

yes

—

C₂³×C₈₉

#121

yes

characteristic

C₂²×D₈₉

—

C₂²×D₈₉

—

C₂²×D₈₉

—

C₂²×D₈₉

—

C₂²×D₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

#123

yes

characteristic

C₂×C₄×C₈₉

#123

yes

—

C₂×C₄×C₈₉

#124

yes

characteristic

C₂×C₄×C₈₉

#126

yes

—

C₂×C₄×C₈₉

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₈₉

#135

yes

—

C₂×C₄×C₈₉

#135

yes

characteristic

C₂×C₄×C₈₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₈₉

AGL(1,ℤ/8)

yes

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

D₃₅₆

—

D₃₅₆

—

C₄×D₈₉

—

C₄×D₈₉

—

C₄×D₈₉

—

C₈×C₈₉

—

#10623494

—

#10623494

—

C₂²×C₈₉

#397

yes

characteristic

C₂²×C₈₉

#463

yes

—

C₂²×C₈₉

yes

C₂²×C₈₉

yes

C₂²×C₈₉

yes

—

C₂×D₈₉

—

100

C₂×D₈₉

—

101

C₂×D₈₉

—

102

C₂×D₈₉

—

103

C₂×D₈₉

—

104

C₄×C₈₉

—

105

C₄×C₈₉

—

106

C₄×C₈₉

#482

yes

—

107

C₄×C₈₉

#482

yes

—

108

C₄×C₈₉

#484

yes

—

109

C₄×C₈₉

#488

yes

characteristic

110

C₄×C₈₉

#490

yes

characteristic

111

Dic₈₉

—

112

#10622

—

maximal, Sylow

113

C₂×C₈₉

#1683

yes

—

114

C₂×C₈₉

#1701

yes

—

115

C₂×C₈₉

#2073

yes

characteristic

116

C₂×C₈₉

#2076

yes

characteristic

117

C₂×C₈₉

#2079

yes

characteristic

118

D₈₉

—

119

#1954

—

120

#1834

D₈₉

yes

characteristic, complemented

121

#1802

—

122

#1296

—

123

#1277

—

124

C₈₉

#10622

yes

characteristic, complemented, Sylow

125

C₂×C₄×D₄

—

126

C₂×C₄⋊C₈

—

127

C₂×C₄⋊C₈

—

128

C₂×#102

—

178

—

129

C₂×C₂²⋊C₈

—

178

—

130

C₂×C₄×C₈

C₂×D₈₉

yes

characteristic

131

#384

C₂×D₈₉

yes

—

132

#340

—

133

#340

—

178

—

134

C₂²×D₄

—

135

C₂³×C₄

—

178

—

136

C₂²×C₈

—

178

—

137

C₂²×C₈

—

178

—

138

C₂²×C₈

C₂²⋊D₈₉

yes

—

139

C₄×D₄

—

178

—

140

C₄×D₄

—

178

—

141

C₂×C₄⋊C₄

—

142

C₂×C₄⋊C₄

—

143

C₂×C₄⋊C₄

—

144

C₂×C₄⋊C₄

—

145

C₂×C₂²⋊C₄

—

178

—

146

C₂×C₄²

C₂²×D₈₉

yes

characteristic

147

C₄⋊C₈

—

178

—

148

C₄⋊C₈

—

178

—

149

C₄⋊C₈

—

178

—

150

#102

—

356

—

151

C₂²⋊C₈

—

356

—

152

C₄×C₈

—

153

C₂⁴

—

178

—

154

C₂×D₄

—

155

C₂×D₄

—

178

—

156

C₂×D₄

—

178

—

157

C₂×D₄

—

178

—

158

C₂²×C₄

—

159

C₂²×C₄

—

356

—

160

C₂²×C₄

—

356

—

161

C₂²×C₄

—

356

—

162

C₂²×C₄

—

356

—

163

C₂²×C₄

—

178

—

164

C₂²×C₄

D₄×D₈₉

yes

characteristic

165

C₂²×C₄

C₂×C₂²⋊D₈₉

yes

characteristic

166

C₂²×C₄

#13083573

yes

characteristic

167

C₂×C₈

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₂×C₈

—

356

—

171

C₂×C₈

—

356

—

172

C₂×C₈

—

356

—

173

C₂×C₈

—

356

—

174

C₂×C₈

—

356

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

178

—

181

C₂²⋊C₄

—

356

—

182

C₄²

#13083574

yes

—

183

C₄²

#13083575

yes

—

184

C₂³

—

356

—

185

C₂³

—

356

—

186

C₂³

—

356

—

187

C₂³

—

356

—

188

C₂³

—

178

—

189

C₂³

#15667983

yes

characteristic

190

D₄

—

356

—

191

D₄

—

178

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

356

—

197

C₂×C₄

—

356

—

198

C₂×C₄

—

712

—

199

C₂×C₄

—

712

—

200

C₂×C₄

—

712

—

201

C₂×C₄

#15667995

yes

characteristic

202

C₂×C₄

#15667997

yes

—

203

C₂×C₄

#15668001

yes

characteristic

204

C₂×C₄

#15668007

yes

—

205

C₂×C₄

Q₁₆×D₈₉

yes

characteristic

206

C₂×C₄

#15668032

yes

—

207

C₂×C₄

#15668035

yes

characteristic

208

C₂×C₄

#15668036

yes

—

209

C₂×C₄

#15668037

yes

—

210

C₈

—

211

C₈

—

712

—

212

C₈

—

712

—

213

C₂²

—

356

—

214

C₂²

—

356

—

215

C₂²

—

712

—

216

C₂²

—

712

—

217

C₂²

—

712

—

218

C₂²

#19151524

yes

characteristic

219

C₂²

#19151810

yes

—

220

C₂²

#19151836

yes

characteristic

221

C₂²

#19151848

yes

characteristic

222

C₂²

#19151858

yes

—

223

C₄

—

224

C₄

—

225

C₄

—

712

—

226

C₄

#19151922

yes

—

227

C₄

#19151925

yes

—

228

C₄

#19151935

yes

—

229

C₄

#19151955

yes

characteristic

230

C₄

#19151964

yes

characteristic

231

C₂

—

712

—

232

C₂

#26019700

yes

—

233

C₂

#26019810

yes

—

234

C₂

#26021666

yes

characteristic

235

C₂

#26021681

yes

characteristic

236

C₂

#26021698

yes

characteristic

	subgroup	G/H
center	C₂³	#15667983
commutator, cosocle	C₂×C₄²×C₈₉	C₂³
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₈₉×#1834	C₂
socle	C₂³×C₈₉	#121
prime radical	C₂²×D₃₅₆	D₄
hypercenter	#1834	D₈₉
hypocenter	C₈₉	#10622
LCS	G ▷ C₂×C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1834

subgroup

G/H

center

C₂³

#15667983

commutator, cosocle

C₂×C₄²×C₈₉

C₂³

Frattini

C₂×C₄²

C₂²×D₈₉

Fitting

C₈₉×#1834

C₂

socle

C₂³×C₈₉

#121

prime radical

C₂²×D₃₅₆

D₄

D₈₉

C₈₉

G ▷ C₂×C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1834

N	H ≅ G/N	type
3. #26018135	C₂	semidirect
4. #26018087	C₂	semidirect
5. C₈₉×#1834	C₂	semidirect
120. #1834	D₈₉	semidirect
124. C₈₉	#10622	semidirect

H ≅ G/N

type

3. #26018135

C₂

semidirect

4. #26018087

C₂

semidirect

5. C₈₉×#1834

C₂

semidirect

120. #1834

D₈₉

semidirect

124. C₈₉

#10622

semidirect

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

subgroup	index
#26021046	2
#26020249	2
#26018135	2
#26018087	2
C₈₉×#1834	2
#10622	89

subgroup

index

C₈₉×#1834

Subgroups — #36459168

Conjugacy classes of subgroups

Complements

Maximal subgroups