Group #36472848 — subgroups

Subgroups — #36472848

Order 22784.

402 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 123 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×#19151428	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151414	C₂	1	2	yes	maximal
3	#26021848	C₂	1	1	yes	maximal, characteristic
4	#26021168	C₂	1	2	yes	maximal
5	C₂²×Q₃₂×C₈₉	C₂	1	1	yes	maximal, characteristic
6	C₂×#15667952	C₂²	1	1	yes	characteristic
7	C₂×#15667948	C₂²	1	2	yes	—
8	#19151607	—	2	2	no	—
9	C₂×#15667931	—	2	2	no	—
10	#19151553	C₂²	1	1	yes	characteristic
11	#19151428	—	2	2	no	—
12	#19151414	—	2	4	no	—
13	#19151373	—	2	1	no	—
14	C₁₆×Dic₈₉	—	2	1	no	—
15	C₂²×Q₁₆×C₈₉	C₂²	1	2	yes	—
16	C₂×Q₃₂×C₈₉	—	2	1	no	—
17	C₂×Q₃₂×C₈₉	—	2	1	no	—
18	C₂×Q₃₂×C₈₉	—	2	2	no	—
19	C₂×Q₃₂×C₈₉	C₄	1	4	yes	complemented
20	C₂²×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#13083558	—	2	2	no	—
22	C₂×#13083558	D₄	1	1	yes	characteristic
23	#15667971	D₄	1	1	yes	characteristic
24	#15667952	—	2	1	no	—
25	#15667952	D₄	1	2	yes	—
26	C₂×#13083549	—	2	1	no	—
27	#15667948	—	2	2	no	—
28	#15667948	—	2	2	no	—
29	#15667936	—	4	4	no	—
30	#15667931	—	4	4	no	—
31	#15667922	—	2	1	no	—
32	C₈×Dic₈₉	—	2	1	no	—
33	C₂²×Q₈×C₈₉	—	2	2	no	—
34	C₂×Q₁₆×C₈₉	—	2	2	no	—
35	C₂×Q₁₆×C₈₉	—	2	2	no	—
36	C₂×Q₁₆×C₈₉	—	2	2	no	—
37	C₂×Q₁₆×C₈₉	—	2	2	no	—
38	C₂×Q₁₆×C₈₉	—	2	2	no	—
39	C₂×Q₁₆×C₈₉	C₂×C₄	1	4	yes	—
40	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
41	Q₃₂×C₈₉	—	2	4	no	—
42	Q₃₂×C₈₉	—	2	4	no	—
43	C₂×C₁₆×C₈₉	C₂×C₄	1	2	yes	—
44	C₂×C₁₆×C₈₉	D₄	1	1	yes	characteristic
45	C₂×C₁₆×C₈₉	D₄	1	1	yes	characteristic
46	C₂×C₁₆×C₈₉	D₄	1	2	yes	—
47	#13083558	—	2	1	no	—
48	#13083558	—	4	2	no	—
49	#13083558	—	4	2	no	—
50	#13083558	D₈	1	2	yes	—
51	C₂×#10623494	—	2	1	no	—
52	C₂×#10623494	—	4	2	no	—
53	C₄⋊Dic₈₉	D₈	1	2	yes	—
54	C₂²⋊Dic₈₉	—	2	1	no	—
55	C₄×Dic₈₉	—	2	1	no	—
56	#13083549	—	2	2	no	—
57	C₂×Q₈×C₈₉	—	2	4	no	—
58	C₂×Q₈×C₈₉	—	4	2	no	—
59	C₂×Q₈×C₈₉	—	4	2	no	—
60	C₂×Q₈×C₈₉	—	4	2	no	—
61	C₂×Q₈×C₈₉	—	4	2	no	—
62	C₂×Q₈×C₈₉	—	4	2	no	—
63	C₂²×C₄×C₈₉	—	4	2	no	—
64	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
65	Q₁₆×C₈₉	—	2	4	no	—
66	Q₁₆×C₈₉	—	2	4	no	—
67	Q₁₆×C₈₉	—	4	2	no	—
68	Q₁₆×C₈₉	—	4	2	no	—
69	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
70	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
71	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
72	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
73	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
74	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
75	C₁₆×C₈₉	C₂²⋊C₄	1	2	yes	—
76	C₁₆×C₈₉	C₂²⋊C₄	1	2	yes	—
77	C₂³×C₈₉	#135	1	1	yes	characteristic
78	Q₈×C₈₉	—	4	4	no	—
79	Q₈×C₈₉	—	4	4	no	—
80	Q₈×C₈₉	—	8	2	no	—
81	Q₈×C₈₉	—	8	2	no	—
82	C₂×C₄×C₈₉	—	4	4	no	—
83	C₂×C₄×C₈₉	—	8	2	no	—
84	C₂×C₄×C₈₉	—	8	2	no	—
85	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
86	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
87	C₂×C₄×C₈₉	#127	1	1	yes	characteristic
88	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
89	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
90	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
91	C₂×Dic₈₉	—	2	2	no	—
92	C₈×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
93	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
94	C₈×C₈₉	#121	1	1	yes	characteristic
95	C₈×C₈₉	#124	1	1	yes	characteristic
96	#10623494	—	2	2	no	—
97	#10623494	—	8	2	no	—
98	C₂²×C₈₉	—	2	2	no	—
99	C₂²×C₈₉	C₄×D₈	1	1	yes	characteristic
100	C₂²×C₈₉	#466	1	1	yes	characteristic
101	C₂²×C₈₉	#495	1	1	yes	characteristic
102	C₄×C₈₉	—	8	4	no	—
103	C₄×C₈₉	#390	1	1	yes	characteristic
104	C₄×C₈₉	C₄×D₈	1	1	yes	characteristic
105	C₄×C₈₉	#466	1	1	yes	characteristic
106	C₄×C₈₉	#493	1	1	yes	characteristic
107	Dic₈₉	—	4	2	no	—
108	#13244	—	89	1	no	maximal, Sylow
109	C₂×C₈₉	—	2	1	no	—
110	C₂×C₈₉	—	2	1	no	—
111	C₂×C₈₉	#1970	1	1	yes	characteristic
112	C₂×C₈₉	#2222	1	2	yes	—
113	C₂²×Q₃₂	D₈₉	1	1	yes	characteristic
114	C₂×#368	—	89	1	no	—
115	C₂×#362	—	89	2	no	—
116	#2108	—	89	1	no	—
117	#1979	—	89	2	no	—
118	C₈₉	#13244	1	1	yes	characteristic, complemented, Sylow
119	C₂²×Q₁₆	C₂×D₈₉	1	2	yes	—
120	C₂×Q₃₂	—	2	1	no	—
121	C₂×Q₃₂	—	2	1	no	—
122	C₂×Q₃₂	—	2	2	no	—
123	C₂×Q₃₂	Dic₈₉	1	4	yes	complemented
124	C₂×M₃₂	—	89	1	no	—
125	C₂²×C₁₆	C₂×D₈₉	1	1	yes	characteristic
126	C₂×#108	—	89	2	no	—
127	#419	—	178	2	no	—
128	C₂×#101	—	178	2	no	—
129	#405	—	89	1	no	—
130	#368	—	178	2	no	—
131	#362	—	178	4	no	—
132	#346	—	178	1	no	—
133	C₄×C₁₆	—	178	1	no	—
134	C₂²×Q₈	—	2	2	no	—
135	C₂×Q₁₆	—	2	2	no	—
136	C₂×Q₁₆	—	2	2	no	—
137	C₂×Q₁₆	—	2	2	no	—
138	C₂×Q₁₆	—	2	2	no	—
139	C₂×Q₁₆	—	2	2	no	—
140	C₂×Q₁₆	C₂×Dic₈₉	1	4	yes	—
141	C₂×M₁₆	—	89	1	no	—
142	C₂×M₁₆	—	178	2	no	—
143	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
144	#117	—	89	1	no	—
145	Q₃₂	—	2	4	no	—
146	Q₃₂	—	2	4	no	—
147	M₃₂	—	89	2	no	—
148	M₃₂	—	178	1	no	—
149	C₂×C₁₆	—	178	1	no	—
150	C₂×C₁₆	C₂×Dic₈₉	1	2	yes	—
151	C₂×C₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
152	C₂×C₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
153	C₂×C₁₆	C₂²⋊D₈₉	1	2	yes	—
154	#108	—	178	2	no	—
155	#108	—	178	2	no	—
156	#103	—	356	4	no	—
157	#101	—	356	4	no	—
158	#97	—	178	1	no	—
159	C₄×C₈	—	178	1	no	—
160	C₂×Q₈	—	2	4	no	—
161	C₂×Q₈	—	4	2	no	—
162	C₂×Q₈	—	4	2	no	—
163	C₂×Q₈	—	4	2	no	—
164	C₂×Q₈	—	4	2	no	—
165	C₂×Q₈	—	4	2	no	—
166	C₂²×C₄	—	4	2	no	—
167	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
168	Q₁₆	—	2	4	no	—
169	Q₁₆	—	2	4	no	—
170	Q₁₆	—	4	2	no	—
171	Q₁₆	—	4	2	no	—
172	M₁₆	—	89	2	no	—
173	M₁₆	—	356	2	no	—
174	M₁₆	—	356	2	no	—
175	M₁₆	—	178	1	no	—
176	C₂×C₈	—	356	2	no	—
177	C₂×C₈	—	178	1	no	—
178	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
179	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
180	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
181	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
182	C₂×C₈	#13083573	1	1	yes	characteristic
183	C₂×C₈	#13083573	1	1	yes	characteristic
184	C₄⋊C₄	—	89	2	no	—
185	C₂²⋊C₄	—	178	1	no	—
186	C₄²	—	178	1	no	—
187	C₁₆	—	178	2	no	—
188	C₁₆	C₂²⋊Dic₈₉	1	2	yes	—
189	C₁₆	C₂²⋊Dic₈₉	1	2	yes	—
190	C₂³	#15668031	1	1	yes	characteristic
191	Q₈	—	4	4	no	—
192	Q₈	—	4	4	no	—
193	Q₈	—	8	2	no	—
194	Q₈	—	8	2	no	—
195	C₂×C₄	—	4	4	no	—
196	C₂×C₄	—	8	2	no	—
197	C₂×C₄	—	8	2	no	—
198	C₂×C₄	—	178	2	no	—
199	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
200	C₂×C₄	#15667983	1	1	yes	characteristic
201	C₂×C₄	#15668008	1	1	yes	characteristic
202	C₂×C₄	D₈×D₈₉	1	1	yes	characteristic
203	C₂×C₄	D₈×D₈₉	1	1	yes	characteristic
204	C₂×C₄	#15668031	1	1	yes	characteristic
205	C₈	—	178	2	no	—
206	C₈	—	712	2	no	—
207	C₈	C₂×C₂²⋊Dic₈₉	1	1	yes	characteristic
208	C₈	D₄×Dic₈₉	1	1	yes	characteristic
209	C₈	#15667983	1	1	yes	characteristic
210	C₈	#15667999	1	1	yes	characteristic
211	C₂²	—	2	2	no	—
212	C₂²	D₈×Dic₈₉	1	1	yes	characteristic
213	C₂²	#19151831	1	1	yes	characteristic
214	C₂²	#19151981	1	1	yes	characteristic
215	C₄	—	8	4	no	—
216	C₄	—	356	2	no	—
217	C₄	#19151501	1	1	yes	characteristic
218	C₄	D₈×Dic₈₉	1	1	yes	characteristic
219	C₄	#19151831	1	1	yes	characteristic
220	C₄	#19151973	1	1	yes	characteristic
221	C₂	—	2	1	no	—
222	C₂	—	2	1	no	—
223	C₂	#26021119	1	1	yes	characteristic
224	C₂	#26022374	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19151428

C₂

yes

maximal, characteristic

C₂×#19151414

C₂

yes

maximal

#26021848

C₂

yes

maximal, characteristic

#26021168

C₂

yes

maximal

C₂²×Q₃₂×C₈₉

C₂

yes

maximal, characteristic

C₂×#15667952

C₂²

yes

characteristic

C₂×#15667948

C₂²

yes

—

#19151607

—

C₂×#15667931

—

#19151553

C₂²

yes

—

—

—

C₁₆×Dic₈₉

—

C₂²×Q₁₆×C₈₉

C₂²

yes

—

C₂×Q₃₂×C₈₉

—

C₂×Q₃₂×C₈₉

—

C₂×Q₃₂×C₈₉

—

C₂×Q₃₂×C₈₉

C₄

yes

complemented

C₂²×C₁₆×C₈₉

C₂²

yes

characteristic

C₂×#13083558

—

C₂×#13083558

D₄

yes

characteristic

#15667971

D₄

yes

characteristic

#15667952

—

#15667952

D₄

yes

—

—

—

—

—

—

—

C₈×Dic₈₉

—

C₂²×Q₈×C₈₉

—

C₂×Q₁₆×C₈₉

—

C₂×Q₁₆×C₈₉

—

C₂×Q₁₆×C₈₉

—

C₂×Q₁₆×C₈₉

—

C₂×Q₁₆×C₈₉

—

C₂×Q₁₆×C₈₉

C₂×C₄

yes

—

C₂²×C₈×C₈₉

C₂³

yes

characteristic

Q₃₂×C₈₉

—

Q₃₂×C₈₉

—

C₂×C₁₆×C₈₉

C₂×C₄

yes

—

C₂×C₁₆×C₈₉

D₄

yes

characteristic

C₂×C₁₆×C₈₉

D₄

yes

characteristic

C₂×C₁₆×C₈₉

D₄

yes

—

—

—

—

D₈

yes

—

C₂×#10623494

—

C₂×#10623494

—

C₄⋊Dic₈₉

D₈

yes

—

C₂²⋊Dic₈₉

—

C₄×Dic₈₉

—

#13083549

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

Q₁₆×C₈₉

—

Q₁₆×C₈₉

—

Q₁₆×C₈₉

—

Q₁₆×C₈₉

—

C₂×C₈×C₈₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₈₉

C₂×D₄

yes

characteristic

C₂×C₈×C₈₉

C₂×D₄

yes

characteristic

C₂×C₈×C₈₉

C₂×D₄

yes

C₂×C₈×C₈₉

yes

C₂×C₈×C₈₉

yes

C₁₆×C₈₉

C₂²⋊C₄

yes

—

C₁₆×C₈₉

C₂²⋊C₄

yes

—

C₂³×C₈₉

#135

yes

characteristic

Q₈×C₈₉

—

Q₈×C₈₉

—

Q₈×C₈₉

—

Q₈×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₄×D₄

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

C₂×D₈

yes

characteristic

C₂×C₄×C₈₉

C₂×D₈

yes

characteristic

C₂×C₄×C₈₉

#135

yes

characteristic

C₂×Dic₈₉

—

C₈×C₈₉

C₂×C₂²⋊C₄

yes

characteristic

C₈×C₈₉

C₄×D₄

yes

C₈×C₈₉

yes

C₈×C₈₉

yes

—

—

C₂²×C₈₉

—

C₂²×C₈₉

C₄×D₈

yes

characteristic

100

C₂²×C₈₉

#466

yes

characteristic

101

C₂²×C₈₉

#495

yes

characteristic

102

C₄×C₈₉

—

103

C₄×C₈₉

#390

yes

characteristic

104

C₄×C₈₉

C₄×D₈

yes

characteristic

105

C₄×C₈₉

#466

yes

characteristic

106

C₄×C₈₉

#493

yes

characteristic

107

Dic₈₉

—

108

#13244

—

maximal, Sylow

109

C₂×C₈₉

—

110

C₂×C₈₉

—

111

C₂×C₈₉

#1970

yes

characteristic

112

C₂×C₈₉

#2222

yes

—

113

C₂²×Q₃₂

D₈₉

yes

characteristic

114

C₂×#368

—

115

C₂×#362

—

116

#2108

—

117

#1979

—

118

C₈₉

#13244

yes

characteristic, complemented, Sylow

119

C₂²×Q₁₆

C₂×D₈₉

yes

—

120

C₂×Q₃₂

—

121

C₂×Q₃₂

—

122

C₂×Q₃₂

—

123

C₂×Q₃₂

Dic₈₉

yes

complemented

124

C₂×M₃₂

—

125

C₂²×C₁₆

C₂×D₈₉

yes

characteristic

126

C₂×#108

—

127

#419

—

178

—

128

C₂×#101

—

178

—

129

#405

—

130

#368

—

178

—

131

#362

—

178

—

132

#346

—

178

—

133

C₄×C₁₆

—

178

—

134

C₂²×Q₈

—

135

C₂×Q₁₆

—

136

C₂×Q₁₆

—

137

C₂×Q₁₆

—

138

C₂×Q₁₆

—

139

C₂×Q₁₆

—

140

C₂×Q₁₆

C₂×Dic₈₉

yes

—

141

C₂×M₁₆

—

142

C₂×M₁₆

—

178

—

143

C₂²×C₈

C₂²×D₈₉

yes

characteristic

144

#117

—

145

Q₃₂

—

146

Q₃₂

—

147

M₃₂

—

148

M₃₂

—

178

—

149

C₂×C₁₆

—

178

—

150

C₂×C₁₆

C₂×Dic₈₉

yes

—

151

C₂×C₁₆

C₂²⋊D₈₉

yes

characteristic

152

C₂×C₁₆

C₂²⋊D₈₉

yes

characteristic

153

C₂×C₁₆

C₂²⋊D₈₉

yes

—

154

#108

—

178

—

155

#108

—

178

—

156

#103

—

356

—

157

#101

—

356

—

158

#97

—

178

—

159

C₄×C₈

—

178

—

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂²×C₄

—

167

C₂²×C₄

D₄×D₈₉

yes

characteristic

168

Q₁₆

—

169

Q₁₆

—

170

Q₁₆

—

171

Q₁₆

—

172

M₁₆

—

173

M₁₆

—

356

—

174

M₁₆

—

356

—

175

M₁₆

—

178

—

176

C₂×C₈

—

356

—

177

C₂×C₈

—

178

—

178

C₂×C₈

C₂²×Dic₈₉

yes

characteristic

179

C₂×C₈

D₄×D₈₉

yes

characteristic

180

C₂×C₈

C₂×C₂²⋊D₈₉

yes

characteristic

181

C₂×C₈

C₂×C₂²⋊D₈₉

yes

characteristic

182

C₂×C₈

#13083573

yes

characteristic

183

C₂×C₈

#13083573

yes

characteristic

184

C₄⋊C₄

—

185

C₂²⋊C₄

—

178

—

186

C₄²

—

178

—

187

C₁₆

—

178

—

188

C₁₆

C₂²⋊Dic₈₉

yes

—

189

C₁₆

C₂²⋊Dic₈₉

yes

—

190

C₂³

#15668031

yes

characteristic

191

Q₈

—

192

Q₈

—

193

Q₈

—

194

Q₈

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

178

—

199

C₂×C₄

D₄×Dic₈₉

yes

characteristic

200

C₂×C₄

#15667983

yes

characteristic

201

C₂×C₄

#15668008

yes

characteristic

202

C₂×C₄

D₈×D₈₉

yes

characteristic

203

C₂×C₄

D₈×D₈₉

yes

characteristic

204

C₂×C₄

#15668031

yes

characteristic

205

C₈

—

178

—

206

C₈

—

712

—

207

C₈

C₂×C₂²⋊Dic₈₉

yes

characteristic

208

C₈

D₄×Dic₈₉

yes

characteristic

209

C₈

#15667983

yes

characteristic

210

C₈

#15667999

yes

characteristic

211

C₂²

—

212

C₂²

D₈×Dic₈₉

yes

characteristic

213

C₂²

#19151831

yes

characteristic

214

C₂²

#19151981

yes

characteristic

215

C₄

—

216

C₄

—

356

—

217

C₄

#19151501

yes

characteristic

218

C₄

D₈×Dic₈₉

yes

characteristic

219

C₄

#19151831

yes

characteristic

220

C₄

#19151973

yes

characteristic

221

C₂

—

222

C₂

—

223

C₂

#26021119

yes

characteristic

224

C₂

#26022374

yes

—

	subgroup	G/H
center	C₂²	#19151831
commutator	C₂×C₈×C₈₉	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₈₉
Fitting	C₂²×Q₃₂×C₈₉	C₂
socle	C₂²×C₈₉	#466
prime radical	C₂³×C₈₉	#135
cosocle	C₂²×C₈×C₈₉	C₂³
hypercenter	C₂²×Q₃₂	D₈₉
hypocenter	C₈₉	#13244
LCS	G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₃₂

subgroup

G/H

center

C₂²

#19151831

commutator

C₂×C₈×C₈₉

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₈₉

Fitting

C₂²×Q₃₂×C₈₉

C₂

C₂²×C₈₉

C₂³×C₈₉

C₂²×C₈×C₈₉

C₂³

hypercenter

C₂²×Q₃₂

D₈₉

hypocenter

C₈₉

#13244

LCS

G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₃₂

N	H ≅ G/N	type
19. C₂×Q₃₂×C₈₉	C₄	semidirect
118. C₈₉	#13244	semidirect
123. C₂×Q₃₂	Dic₈₉	semidirect

H ≅ G/N

type

19. C₂×Q₃₂×C₈₉

C₄

semidirect

118. C₈₉

#13244

semidirect

123. C₂×Q₃₂

Dic₈₉

semidirect

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

subgroup	index
C₂×#19151428	2
C₂×#19151414	2
#26021848	2
#26021168	2
C₂²×Q₃₂×C₈₉	2
#13244	89

subgroup

index

C₂²×Q₃₂×C₈₉

Subgroups — #36472848

Conjugacy classes of subgroups

Complements

Maximal subgroups