Group #36454117 — subgroups

Subgroups — #36454117

Order 22784.

602 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 131 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×#19151975	C₂	1	1	yes	maximal, characteristic
2	#26021092	C₂	1	2	yes	maximal, complemented
3	#26019008	C₂	1	1	yes	maximal, characteristic, complemented
4	#26018919	C₂	1	2	yes	maximal, complemented
5	C₈₉×#1451	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₇₁₂	C₄	1	4	yes	—
7	C₂×#15668009	C₂²	1	2	yes	—
8	#19151975	—	2	2	no	—
9	#19151975	—	2	1	no	—
10	#19151975	—	2	1	no	—
11	#19151622	C₂²	1	2	yes	—
12	C₂×#15667928	—	2	4	no	—
13	#19151349	—	2	2	no	—
14	#19151341	—	2	4	no	—
15	#431×C₈₉	C₂²	1	1	yes	characteristic
16	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
18	#322×C₈₉	—	2	1	no	—
19	#322×C₈₉	—	2	1	no	—
20	C₂²×D₃₅₆	—	2	2	no	—
21	C₂²×D₃₅₆	—	2	2	no	—
22	C₂²×D₃₅₆	C₂×C₄	1	4	yes	—
23	C₂×D₇₁₂	—	2	4	no	—
24	C₂×D₇₁₂	—	2	4	no	—
25	C₂×D₇₁₂	—	4	8	no	—
26	C₂×#13083558	—	2	2	no	—
27	#15668009	—	2	2	no	—
28	#15668009	—	2	2	no	—
29	#15668009	—	2	2	no	—
30	#15668009	—	2	2	no	—
31	C₄⋊#10623494	—	2	2	no	—
32	C₄⋊#10623494	—	2	2	no	—
33	#15667928	—	4	8	no	—
34	C₂×M₁₆×C₈₉	D₄	1	2	yes	—
35	C₂²×C₈×C₈₉	C₂×C₄	1	2	yes	—
36	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
37	C₄⋊C₈×C₈₉	D₄	1	2	yes	—
38	C₂²⋊C₈×C₈₉	—	2	1	no	—
39	#97×C₈₉	—	2	1	no	—
40	C₄×C₈×C₈₉	—	2	1	no	—
41	C₄×C₈×C₈₉	—	2	1	no	—
42	C₄×C₈×C₈₉	D₄	1	2	yes	—
43	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
44	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
45	C₂³×D₈₉	—	2	4	no	—
46	C₂×D₃₅₆	—	2	4	no	—
47	C₂×D₃₅₆	—	2	4	no	—
48	C₂×D₃₅₆	—	4	8	no	—
49	C₂×D₃₅₆	—	4	2	no	—
50	C₂×D₃₅₆	—	4	2	no	—
51	C₂×D₃₅₆	—	4	2	no	—
52	C₂×D₃₅₆	—	4	2	no	—
53	C₂×D₃₅₆	—	4	4	no	—
54	C₂×D₃₅₆	—	4	4	no	—
55	C₂×D₃₅₆	—	8	4	no	—
56	D₇₁₂	—	4	8	no	—
57	D₇₁₂	—	4	8	no	—
58	#13083558	—	4	4	no	—
59	C₂×#10623494	—	4	2	no	—
60	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
61	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
62	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
63	M₁₆×C₈₉	—	2	4	no	—
64	C₂×C₈×C₈₉	—	2	4	no	—
65	C₂×C₈×C₈₉	—	2	2	no	—
66	C₂×C₈×C₈₉	—	2	2	no	—
67	C₂×C₈×C₈₉	C₂²⋊C₄	1	2	yes	—
68	C₂×C₈×C₈₉	C₂²⋊C₄	1	2	yes	—
69	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
70	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
71	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
72	C₄²×C₈₉	#41	1	1	yes	characteristic
73	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
74	C₂²×D₈₉	—	4	4	no	—
75	C₂²×D₈₉	—	4	8	no	—
76	C₂²×D₈₉	—	8	4	no	—
77	C₂²×D₈₉	—	8	4	no	—
78	C₂×C₄×C₈₉	—	2	2	no	—
79	C₂×C₄×C₈₉	—	2	2	no	—
80	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
81	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
82	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
83	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
84	C₂×C₄×C₈₉	#124	1	1	yes	characteristic
85	C₂×C₄×C₈₉	#127	1	1	yes	characteristic
86	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	4	yes	—
87	D₃₅₆	—	4	8	no	—
88	D₃₅₆	—	8	4	no	—
89	D₃₅₆	—	8	4	no	—
90	D₃₅₆	—	8	4	no	—
91	D₃₅₆	—	8	4	no	—
92	D₃₅₆	—	8	2	no	—
93	D₃₅₆	—	8	2	no	—
94	C₈×C₈₉	—	2	2	no	—
95	C₈×C₈₉	—	4	2	no	—
96	C₈×C₈₉	—	4	2	no	—
97	C₈×C₈₉	#100	1	4	yes	complemented
98	#10623494	—	8	2	no	—
99	C₂²×C₈₉	—	2	1	no	—
100	C₂²×C₈₉	—	2	1	no	—
101	C₂²×C₈₉	#390	1	1	yes	characteristic
102	C₂²×C₈₉	#442	1	2	yes	—
103	C₂×D₈₉	—	8	4	no	—
104	C₂×D₈₉	—	8	4	no	—
105	C₂×D₈₉	—	8	4	no	—
106	C₂×D₈₉	—	16	8	no	—
107	C₄×C₈₉	—	2	1	no	—
108	C₄×C₈₉	—	2	1	no	—
109	C₄×C₈₉	C₂×#100	1	2	yes	—
110	C₄×C₈₉	#469	1	2	yes	—
111	C₄×C₈₉	#472	1	2	yes	—
112	C₄×C₈₉	#496	1	2	yes	—
113	#9811	—	89	1	no	maximal, Sylow
114	C₂×C₈₉	—	2	2	no	—
115	C₂×C₈₉	#1965	1	1	yes	characteristic
116	C₂×C₈₉	#1972	1	1	yes	characteristic
117	C₂×C₈₉	#1978	1	1	yes	characteristic
118	D₈₉	—	16	4	no	—
119	C₂×#493	—	89	1	no	—
120	#1965	—	89	2	no	—
121	#1566	—	89	1	no	—
122	#1545	—	89	2	no	—
123	#1451	D₈₉	1	1	yes	characteristic, complemented
124	C₈₉	#9811	1	1	yes	characteristic, complemented, Sylow
125	C₂²×D₈	—	89	4	no	—
126	C₂×#127	—	89	2	no	—
127	#493	—	178	2	no	—
128	#493	—	178	1	no	—
129	#493	—	178	1	no	—
130	#431	C₂×D₈₉	1	1	yes	characteristic
131	#423	—	89	2	no	—
132	C₂×#100	—	178	4	no	—
133	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
134	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
135	#334	—	178	2	no	—
136	#331	—	178	4	no	—
137	#322	—	2	1	no	—
138	#322	—	2	1	no	—
139	C₂²×D₄	—	89	4	no	—
140	C₂²×D₄	—	178	2	no	—
141	C₂²×D₄	—	178	2	no	—
142	C₂×D₈	—	356	8	no	—
143	C₂×D₈	—	178	4	no	—
144	C₂×D₈	—	178	4	no	—
145	C₂×M₁₆	—	178	2	no	—
146	C₂×M₁₆	D₃₅₆	1	2	yes	—
147	C₂²×C₈	C₄×D₈₉	1	2	yes	—
148	#127	—	178	2	no	—
149	#127	—	178	2	no	—
150	#127	—	178	2	no	—
151	#127	—	178	2	no	—
152	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
153	C₄⋊C₈	—	178	2	no	—
154	C₄⋊C₈	—	178	2	no	—
155	C₄⋊C₈	D₃₅₆	1	2	yes	—
156	#100	—	356	8	no	—
157	C₂²⋊C₈	—	2	1	no	—
158	#97	—	2	1	no	—
159	C₄×C₈	—	2	1	no	—
160	C₄×C₈	—	2	1	no	—
161	C₄×C₈	D₃₅₆	1	2	yes	—
162	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
163	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
164	C₂⁴	—	178	4	no	—
165	C₂×D₄	—	356	8	no	—
166	C₂×D₄	—	356	2	no	—
167	C₂×D₄	—	356	2	no	—
168	C₂×D₄	—	356	2	no	—
169	C₂×D₄	—	356	2	no	—
170	C₂×D₄	—	356	4	no	—
171	C₂×D₄	—	356	4	no	—
172	C₂×D₄	—	178	4	no	—
173	C₂×D₄	—	178	4	no	—
174	C₂×D₄	—	712	4	no	—
175	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
176	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
177	C₂²×C₄	#13083574	1	1	yes	characteristic
178	D₈	—	356	8	no	—
179	D₈	—	356	8	no	—
180	M₁₆	—	2	4	no	—
181	M₁₆	—	356	4	no	—
182	C₂×C₈	—	2	4	no	—
183	C₂×C₈	—	2	2	no	—
184	C₂×C₈	—	2	2	no	—
185	C₂×C₈	—	356	2	no	—
186	C₂×C₈	#13083551	1	2	yes	—
187	C₂×C₈	#13083551	1	2	yes	—
188	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
189	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
190	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
191	C₄²	#13083574	1	1	yes	characteristic
192	C₂³	—	356	8	no	—
193	C₂³	—	356	4	no	—
194	C₂³	—	712	4	no	—
195	C₂³	—	712	4	no	—
196	C₂³	C₄×D₃₅₆	1	1	yes	characteristic
197	D₄	—	356	8	no	—
198	D₄	—	712	4	no	—
199	D₄	—	712	4	no	—
200	D₄	—	712	2	no	—
201	D₄	—	712	2	no	—
202	D₄	—	712	4	no	—
203	D₄	—	712	4	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	C₂×#13083551	1	1	yes	characteristic
207	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
208	C₂×C₄	#15667986	1	1	yes	characteristic
209	C₂×C₄	#15667986	1	1	yes	characteristic
210	C₂×C₄	#15668000	1	1	yes	characteristic
211	C₂×C₄	#15668009	1	1	yes	characteristic
212	C₂×C₄	#15668040	1	4	yes	—
213	C₈	—	2	2	no	—
214	C₈	—	4	2	no	—
215	C₈	—	4	2	no	—
216	C₈	—	712	2	no	—
217	C₈	#15667928	1	4	yes	complemented
218	C₂²	—	2	1	no	—
219	C₂²	—	2	1	no	—
220	C₂²	—	1424	8	no	—
221	C₂²	—	712	4	no	—
222	C₂²	—	712	4	no	—
223	C₂²	—	712	4	no	—
224	C₂²	#19151500	1	1	yes	characteristic
225	C₂²	#19151711	1	2	yes	—
226	C₄	—	2	1	no	—
227	C₄	—	2	1	no	—
228	C₄	C₂×#15667928	1	2	yes	—
229	C₄	#19151851	1	2	yes	—
230	C₄	#19151868	1	2	yes	—
231	C₄	#19151987	1	2	yes	—
232	C₂	—	2	2	no	—
233	C₂	—	1424	4	no	—
234	C₂	#26021092	1	1	yes	characteristic
235	C₂	#26021128	1	1	yes	characteristic
236	C₂	#26021162	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19151975

C₂

yes

maximal, characteristic

#26021092

C₂

yes

maximal, complemented

#26019008

C₂

yes

maximal, characteristic, complemented

#26018919

C₂

yes

maximal, complemented

C₈₉×#1451

C₂

yes

maximal, characteristic, complemented

C₂²×D₇₁₂

C₄

yes

—

C₂×#15668009

C₂²

yes

—

—

—

—

C₂²

yes

—

C₂×#15667928

—

#19151349

—

#19151341

—

#431×C₈₉

C₂²

yes

characteristic

C₄×M₁₆×C₈₉

C₂²

yes

characteristic

C₂×C₄×C₈×C₈₉

C₂²

yes

characteristic

#322×C₈₉

—

#322×C₈₉

—

C₂²×D₃₅₆

—

C₂²×D₃₅₆

—

C₂²×D₃₅₆

C₂×C₄

yes

—

C₂×D₇₁₂

—

C₂×D₇₁₂

—

C₂×D₇₁₂

—

—

—

—

—

—

—

—

—

C₂×M₁₆×C₈₉

D₄

yes

—

C₂²×C₈×C₈₉

C₂×C₄

yes

—

C₂×C₄²×C₈₉

C₂³

yes

characteristic

C₄⋊C₈×C₈₉

D₄

yes

—

C₂²⋊C₈×C₈₉

—

#97×C₈₉

—

C₄×C₈×C₈₉

—

C₄×C₈×C₈₉

—

C₄×C₈×C₈₉

D₄

yes

—

C₄×C₈×C₈₉

D₄

yes

characteristic

C₄×C₈×C₈₉

D₄

yes

characteristic

C₂³×D₈₉

—

C₂×D₃₅₆

—

C₂×D₃₅₆

—

C₂×D₃₅₆

—

C₂×D₃₅₆

—

C₂×D₃₅₆

—

C₂×D₃₅₆

—

C₂×D₃₅₆

—

C₂×D₃₅₆

—

C₂×D₃₅₆

—

C₂×D₃₅₆

—

D₇₁₂

—

D₇₁₂

—

#13083558

—

C₂×#10623494

—

C₂²×C₄×C₈₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₈₉

#41

yes

characteristic

M₁₆×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

C₂²⋊C₄

yes

—

C₂×C₈×C₈₉

C₂²⋊C₄

yes

—

C₄²×C₈₉

C₂×D₄

yes

characteristic

C₄²×C₈₉

C₂×D₄

yes

characteristic

C₄²×C₈₉

C₂×D₄

yes

characteristic

C₄²×C₈₉

#41

yes

characteristic

C₂³×C₈₉

C₄×D₄

yes

characteristic

C₂²×D₈₉

—

C₂²×D₈₉

—

C₂²×D₈₉

—

C₂²×D₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₈₉

C₄×D₄

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

yes

—

D₃₅₆

—

D₃₅₆

—

D₃₅₆

—

D₃₅₆

—

D₃₅₆

—

D₃₅₆

—

D₃₅₆

—

C₈×C₈₉

—

C₈×C₈₉

—

C₈×C₈₉

—

C₈×C₈₉

#100

yes

complemented

#10623494

—

C₂²×C₈₉

—

100

C₂²×C₈₉

—

101

C₂²×C₈₉

#390

yes

characteristic

102

C₂²×C₈₉

#442

yes

—

103

C₂×D₈₉

—

104

C₂×D₈₉

—

105

C₂×D₈₉

—

106

C₂×D₈₉

—

107

C₄×C₈₉

—

108

C₄×C₈₉

—

109

C₄×C₈₉

C₂×#100

yes

—

110

C₄×C₈₉

#469

yes

—

111

C₄×C₈₉

#472

yes

—

112

C₄×C₈₉

#496

yes

—

113

#9811

—

maximal, Sylow

114

C₂×C₈₉

—

115

C₂×C₈₉

#1965

yes

characteristic

116

C₂×C₈₉

#1972

yes

characteristic

117

C₂×C₈₉

#1978

yes

characteristic

118

D₈₉

—

119

C₂×#493

—

120

#1965

—

121

#1566

—

122

#1545

—

123

#1451

D₈₉

yes

characteristic, complemented

124

C₈₉

#9811

yes

characteristic, complemented, Sylow

125

C₂²×D₈

—

126

C₂×#127

—

127

#493

—

178

—

128

#493

—

178

—

129

#493

—

178

—

130

#431

C₂×D₈₉

yes

characteristic

131

#423

—

132

C₂×#100

—

178

—

133

C₄×M₁₆

C₂×D₈₉

yes

characteristic

134

C₂×C₄×C₈

C₂×D₈₉

yes

characteristic

135

#334

—

178

—

136

#331

—

178

—

137

#322

—

138

#322

—

139

C₂²×D₄

—

140

C₂²×D₄

—

178

—

141

C₂²×D₄

—

178

—

142

C₂×D₈

—

356

—

143

C₂×D₈

—

178

—

144

C₂×D₈

—

178

—

145

C₂×M₁₆

—

178

—

146

C₂×M₁₆

D₃₅₆

yes

—

147

C₂²×C₈

C₄×D₈₉

yes

—

148

#127

—

178

—

149

#127

—

178

—

150

#127

—

178

—

151

#127

—

178

—

152

C₂×C₄²

C₂²×D₈₉

yes

characteristic

153

C₄⋊C₈

—

178

—

154

C₄⋊C₈

—

178

—

155

C₄⋊C₈

D₃₅₆

yes

—

156

#100

—

356

—

157

C₂²⋊C₈

—

158

#97

—

159

C₄×C₈

—

160

C₄×C₈

—

161

C₄×C₈

D₃₅₆

yes

—

162

C₄×C₈

C₂²⋊D₈₉

yes

characteristic

163

C₄×C₈

C₂²⋊D₈₉

yes

characteristic

164

C₂⁴

—

178

—

165

C₂×D₄

—

356

—

166

C₂×D₄

—

356

—

167

C₂×D₄

—

356

—

168

C₂×D₄

—

356

—

169

C₂×D₄

—

356

—

170

C₂×D₄

—

356

—

171

C₂×D₄

—

356

—

172

C₂×D₄

—

178

—

173

C₂×D₄

—

178

—

174

C₂×D₄

—

712

—

175

C₂²×C₄

C₂×C₄×D₈₉

yes

characteristic

176

C₂²×C₄

C₂×D₃₅₆

yes

characteristic

177

C₂²×C₄

#13083574

yes

characteristic

178

D₈

—

356

—

179

D₈

—

356

—

180

M₁₆

—

181

M₁₆

—

356

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

356

—

186

C₂×C₈

#13083551

yes

—

187

C₂×C₈

#13083551

yes

—

188

C₄²

C₂×C₂²⋊D₈₉

yes

characteristic

189

C₄²

C₂×D₃₅₆

yes

characteristic

190

C₄²

C₂×D₃₅₆

yes

characteristic

191

C₄²

#13083574

yes

characteristic

192

C₂³

—

356

—

193

C₂³

—

356

—

194

C₂³

—

712

—

195

C₂³

—

712

—

196

C₂³

C₄×D₃₅₆

yes

characteristic

197

D₄

—

356

—

198

D₄

—

712

—

199

D₄

—

712

—

200

D₄

—

712

—

201

D₄

—

712

—

202

D₄

—

712

—

203

D₄

—

712

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

C₂×#13083551

yes

characteristic

207

C₂×C₄

C₄×D₃₅₆

yes

characteristic

208

C₂×C₄

#15667986

yes

characteristic

209

C₂×C₄

#15667986

yes

characteristic

210

C₂×C₄

#15668000

yes

characteristic

211

C₂×C₄

#15668009

yes

characteristic

212

C₂×C₄

#15668040

yes

—

213

C₈

—

214

C₈

—

215

C₈

—

216

C₈

—

712

—

217

C₈

#15667928

yes

complemented

218

C₂²

—

219

C₂²

—

220

C₂²

—

1424

—

221

C₂²

—

712

—

222

C₂²

—

712

—

223

C₂²

—

712

—

224

C₂²

#19151500

yes

characteristic

225

C₂²

#19151711

yes

—

226

C₄

—

227

C₄

—

228

C₄

C₂×#15667928

yes

—

229

C₄

#19151851

yes

—

230

C₄

#19151868

yes

—

231

C₄

#19151987

yes

—

232

C₂

—

233

C₂

—

1424

—

234

C₂

#26021092

yes

characteristic

235

C₂

#26021128

yes

characteristic

236

C₂

#26021162

yes

characteristic

	subgroup	G/H
center	C₂²	#19151500
commutator	C₂²×C₄×C₈₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₈₉×#1451	C₂
socle	C₂²×C₈₉	#390
prime radical	C₂×#19151975	C₂
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	#1451	D₈₉
hypocenter	C₈₉	#9811
LCS	G ▷ C₂²×C₄×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1451

subgroup

G/H

center

C₂²

#19151500

commutator

C₂²×C₄×C₈₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₈₉

Fitting

C₈₉×#1451

C₂

C₂²×C₈₉

C₂

C₂×C₄²×C₈₉

C₂³

D₈₉

C₈₉

G ▷ C₂²×C₄×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1451

N	H ≅ G/N	type
2. #26021092	C₂	semidirect
3. #26019008	C₂	semidirect
4. #26018919	C₂	semidirect
5. C₈₉×#1451	C₂	semidirect
97. C₈×C₈₉	#100	semidirect
123. #1451	D₈₉	semidirect
124. C₈₉	#9811	semidirect
217. C₈	#15667928	semidirect

H ≅ G/N

type

2. #26021092

C₂

semidirect

3. #26019008

C₂

semidirect

4. #26018919

C₂

semidirect

5. C₈₉×#1451

C₂

semidirect

97. C₈×C₈₉

#100

semidirect

123. #1451

D₈₉

semidirect

124. C₈₉

#9811

semidirect

217. C₈

#15667928

semidirect

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

subgroup	index
C₂×#19151975	2
#26021092	2
#26019008	2
#26018919	2
C₈₉×#1451	2
#9811	89

subgroup

index

C₈₉×#1451

Subgroups — #36454117

Conjugacy classes of subgroups

Complements

Maximal subgroups