Group #34014123 — subgroups

Subgroups — #34014123

Order 18688.

332 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 90 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	#22626270	C₂	1	1	yes	maximal, characteristic
2	#22625733	C₂	1	1	yes	maximal, characteristic
3	#22625013	C₂	1	2	yes	maximal
4	#22624998	C₂	1	2	yes	maximal
5	#22620440	C₂	1	1	yes	maximal, characteristic
6	#17989643	C₂²	1	2	yes	—
7	D₇₃⋊#108	C₂²	1	1	yes	characteristic
8	#17989597	C₂²	1	1	yes	characteristic
9	#17989550	—	2	1	no	—
10	#17989510	—	2	1	no	—
11	#17989509	—	2	1	no	—
12	#17989458	—	2	1	no	—
13	#17989142	—	2	1	no	—
14	#17988990	—	2	1	no	—
15	#17988987	—	2	1	no	—
16	#17988987	C₄	1	2	yes	complemented
17	#17988985	C₄	1	1	yes	characteristic, complemented
18	#17988622	—	2	1	no	—
19	#17988622	C₂²	1	2	yes	—
20	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
21	#498×C₇₃	C₄	1	1	yes	characteristic, complemented
22	D₇₃⋊M₁₆	—	2	1	no	—
23	#14556670	—	2	1	no	—
24	#14556666	—	2	2	no	—
25	#14556665	—	2	2	no	—
26	#14556664	—	2	2	no	—
27	#14556662	Q₈	1	2	yes	complemented
28	#14556661	—	2	1	no	—
29	#14556660	—	2	1	no	—
30	#14556659	Q₈	1	2	yes	complemented
31	#14556645	—	4	1	no	—
32	C₈×#64408	—	4	1	no	—
33	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
34	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
35	#14556591	—	2	1	no	—
36	#14556582	—	2	2	no	—
37	#14556571	—	4	1	no	—
38	#14556567	—	4	1	no	—
39	Q₈×Dic₇₃	—	4	1	no	—
40	#14556556	—	4	1	no	—
41	#14556549	—	2	2	no	—
42	C₄²×D₇₃	D₄	1	1	yes	characteristic
43	#14556524	—	2	2	no	—
44	#14556524	—	2	2	no	—
45	#14556523	—	2	1	no	—
46	#14556523	C₂×C₄	1	2	yes	—
47	C₄×#10596831	D₄	1	1	yes	characteristic
48	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
49	C₈×Dic₇₃	D₄	1	1	yes	characteristic
50	C₄⋊Q₈×C₇₃	—	2	1	no	—
51	#106×C₇₃	—	2	1	no	—
52	#106×C₇₃	C₂×C₄	1	2	yes	—
53	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
54	#11924038	—	2	2	no	—
55	#11924037	—	4	1	no	—
56	#11924036	—	4	1	no	—
57	C₄⋊#64408	—	2	2	no	—
58	C₂²⋊#64408	—	4	1	no	—
59	C₄×#64408	—	4	1	no	—
60	#11924031	—	4	2	no	—
61	C₂×Dic₁₄₆	—	4	1	no	—
62	C₂×C₄×D₇₃	—	2	1	no	—
63	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
64	C₂×#10596831	C₂²⋊C₄	1	1	yes	characteristic
65	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
66	C₈×D₇₃	SD₁₆	1	1	yes	characteristic
67	C₈×D₇₃	SD₁₆	1	1	yes	characteristic
68	C₈×D₇₃	Q₁₆	1	1	yes	characteristic
69	C₈×D₇₃	Q₁₆	1	1	yes	characteristic
70	C₈×D₇₃	C₂×Q₈	1	1	yes	characteristic
71	C₈×D₇₃	C₂×Q₈	1	1	yes	characteristic
72	C₈×D₇₃	#41	1	1	yes	characteristic
73	C₈×D₇₃	#41	1	1	yes	characteristic
74	C₄⋊Dic₇₃	—	2	2	no	—
75	C₄⋊Dic₇₃	—	4	2	no	—
76	C₄⋊Dic₇₃	—	4	1	no	—
77	#11924007	—	4	2	no	—
78	#11924005	—	4	2	no	—
79	C₄×Dic₇₃	—	2	1	no	—
80	C₄×Dic₇₃	—	4	2	no	—
81	C₄×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
82	C₂×Q₈×C₇₃	—	4	1	no	—
83	C₂×C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
85	C₄⋊C₄×C₇₃	—	2	2	no	—
86	C₄⋊C₄×C₇₃	—	4	1	no	—
87	C₄²×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
88	C₂²×D₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
89	C₂×#64408	—	4	2	no	—
90	Q₈×C₇₃	—	8	2	no	—
91	C₂×C₄×C₇₃	—	2	1	no	—
92	C₂×C₄×C₇₃	—	4	2	no	—
93	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
94	C₂×Dic₇₃	—	2	1	no	—
95	C₂×Dic₇₃	—	4	2	no	—
96	C₂×Dic₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
97	C₄×D₇₃	—	4	2	no	—
98	C₄×D₇₃	C₂²⋊Q₈	1	1	yes	characteristic
99	C₄×D₇₃	C₂²⋊Q₈	1	1	yes	characteristic
100	C₄×D₇₃	C₂×SD₁₆	1	1	yes	characteristic
101	C₄×D₇₃	C₂×Q₁₆	1	1	yes	characteristic
102	Dic₁₄₆	—	8	2	no	—
103	#10596833	—	4	2	no	—
104	C₈×C₇₃	#103	1	1	yes	characteristic
105	C₈×C₇₃	#103	1	1	yes	characteristic
106	C₈×C₇₃	C₄×Q₈	1	1	yes	characteristic
107	C₈×C₇₃	C₄×Q₈	1	1	yes	characteristic
108	#10596831	#103	1	1	yes	characteristic
109	#10596831	#103	1	1	yes	characteristic
110	#10596831	#124	1	1	yes	characteristic
111	#10596831	C₄⋊Q₈	1	1	yes	characteristic
112	C₂²×C₇₃	#418	1	1	yes	characteristic
113	C₂×D₇₃	—	4	1	no	—
114	C₂×D₇₃	#476	1	1	yes	characteristic
115	C₂×D₇₃	#477	1	1	yes	characteristic
116	#64408	—	8	2	no	—
117	C₄×C₇₃	—	2	2	no	—
118	C₄×C₇₃	—	8	2	no	—
119	C₄×C₇₃	#391	1	1	yes	characteristic
120	C₄×C₇₃	C₂×#103	1	1	yes	characteristic
121	Dic₇₃	—	4	1	no	—
122	Dic₇₃	—	8	2	no	—
123	Dic₇₃	#476	1	1	yes	characteristic
124	Dic₇₃	#477	1	1	yes	characteristic
125	#13271	—	73	1	no	maximal, Sylow
126	C₂×C₇₃	—	2	1	no	—
127	C₂×C₇₃	#1987	1	1	yes	characteristic
128	D₇₃	—	2	1	no	—
129	D₇₃	—	2	1	no	—
130	#3160	—	73	1	no	—
131	C₂×#364	—	73	1	no	—
132	#1772	—	73	1	no	—
133	#1389	—	73	2	no	—
134	#1384	—	73	2	no	—
135	C₇₃	#13271	1	1	yes	characteristic, complemented, Sylow
136	#533	—	146	1	no	—
137	C₂×M₃₂	—	73	2	no	—
138	#500	—	146	1	no	—
139	#499	—	73	2	no	—
140	#499	—	146	1	no	—
141	#498	—	73	1	no	—
142	#498	#64408	1	1	yes	characteristic, complemented
143	C₂×#108	—	73	1	no	—
144	#427	—	73	1	no	—
145	#427	—	73	2	no	—
146	#427	—	146	1	no	—
147	#405	—	146	1	no	—
148	C₂×C₄×C₈	—	73	1	no	—
149	#364	—	146	1	no	—
150	#364	—	146	1	no	—
151	#339	—	146	1	no	—
152	C₂×M₁₆	—	146	1	no	—
153	C₂²×C₈	—	73	1	no	—
154	C₂²×C₈	—	73	1	no	—
155	C₄⋊Q₈	—	2	1	no	—
156	C₄⋊Q₈	—	146	1	no	—
157	#125	—	146	2	no	—
158	C₂²⋊Q₈	—	292	1	no	—
159	C₂²⋊Q₈	—	292	1	no	—
160	C₄×Q₈	—	292	1	no	—
161	C₄×Q₈	—	292	1	no	—
162	#117	—	146	2	no	—
163	#117	—	146	1	no	—
164	C₂×C₄²	—	73	1	no	—
165	M₃₂	—	146	2	no	—
166	M₃₂	—	146	2	no	—
167	C₂×C₁₆	—	146	2	no	—
168	#108	—	73	2	no	—
169	#108	—	146	1	no	—
170	#107	—	146	2	no	—
171	#107	—	146	2	no	—
172	#107	—	146	1	no	—
173	#106	—	2	1	no	—
174	#106	—	73	2	no	—
175	#106	—	73	2	no	—
176	#106	—	146	1	no	—
177	#106	C₂×#64408	1	2	yes	—
178	#97	—	292	1	no	—
179	C₄×C₈	—	292	1	no	—
180	C₄×C₈	—	73	1	no	—
181	C₄×C₈	—	73	1	no	—
182	C₄×C₈	—	73	1	no	—
183	C₄×C₈	C₂×#64408	1	1	yes	characteristic
184	C₂×Q₈	—	4	1	no	—
185	C₂×Q₈	—	292	1	no	—
186	C₂²×C₄	—	73	1	no	—
187	C₂²×C₄	—	146	1	no	—
188	M₁₆	—	292	1	no	—
189	M₁₆	—	146	2	no	—
190	C₂×C₈	—	292	1	no	—
191	C₂×C₈	—	73	1	no	—
192	C₂×C₈	—	73	1	no	—
193	C₂×C₈	—	73	1	no	—
194	C₂×C₈	—	73	1	no	—
195	C₂×C₈	—	73	1	no	—
196	C₂×C₈	—	73	1	no	—
197	C₂×C₈	—	73	1	no	—
198	C₂×C₈	—	73	1	no	—
199	C₂×C₈	—	73	1	no	—
200	C₂×C₈	—	73	1	no	—
201	C₂×C₈	C₂²⋊#64408	1	1	yes	characteristic
202	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
203	C₄⋊C₄	—	2	2	no	—
204	C₄⋊C₄	—	4	1	no	—
205	C₄⋊C₄	—	292	1	no	—
206	C₄⋊C₄	—	292	2	no	—
207	C₄⋊C₄	—	292	2	no	—
208	C₄⋊C₄	—	146	2	no	—
209	C₄⋊C₄	—	146	2	no	—
210	C₂²⋊C₄	—	292	2	no	—
211	C₂²⋊C₄	—	292	1	no	—
212	C₄²	—	292	2	no	—
213	C₄²	—	292	1	no	—
214	C₄²	—	73	1	no	—
215	C₄²	—	146	1	no	—
216	C₄²	C₂²⋊#64408	1	1	yes	characteristic
217	C₁₆	—	292	2	no	—
218	C₂³	—	73	1	no	—
219	Q₈	—	8	2	no	—
220	Q₈	—	584	2	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	4	2	no	—
223	C₂×C₄	—	292	2	no	—
224	C₂×C₄	—	292	2	no	—
225	C₂×C₄	—	292	2	no	—
226	C₂×C₄	—	73	1	no	—
227	C₂×C₄	—	73	1	no	—
228	C₂×C₄	—	73	1	no	—
229	C₂×C₄	—	73	1	no	—
230	C₂×C₄	—	73	1	no	—
231	C₂×C₄	—	146	1	no	—
232	C₂×C₄	C₂×C₂²⋊#64408	1	1	yes	characteristic
233	C₈	—	292	2	no	—
234	C₈	—	73	1	no	—
235	C₈	—	73	1	no	—
236	C₈	—	73	1	no	—
237	C₈	—	73	1	no	—
238	C₈	#14556654	1	1	yes	characteristic
239	C₈	#14556654	1	1	yes	characteristic
240	C₈	Q₈×#64408	1	1	yes	characteristic
241	C₈	Q₈×#64408	1	1	yes	characteristic
242	C₂²	—	292	1	no	—
243	C₂²	—	73	1	no	—
244	C₂²	—	73	1	no	—
245	C₂²	#17989579	1	1	yes	characteristic
246	C₄	—	2	2	no	—
247	C₄	—	8	2	no	—
248	C₄	—	292	1	no	—
249	C₄	—	584	2	no	—
250	C₄	—	584	2	no	—
251	C₄	—	73	1	no	—
252	C₄	—	73	1	no	—
253	C₄	(C₂×#64408)⋊Q₈	1	1	yes	characteristic
254	C₄	C₂×#14556654	1	1	yes	characteristic
255	C₂	—	2	1	no	—
256	C₂	—	146	1	no	—
257	C₂	—	146	1	no	—
258	C₂	#22626109	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22626270

C₂

yes

maximal, characteristic

#22625733

C₂

yes

maximal, characteristic

#22625013

C₂

yes

maximal

#22624998

C₂

yes

maximal

#22620440

C₂

yes

maximal, characteristic

#17989643

C₂²

yes

—

D₇₃⋊#108

C₂²

yes

characteristic

#17989597

C₂²

yes

—

—

—

—

—

—

—

C₄

yes

complemented

#17988985

C₄

yes

characteristic, complemented

#17988622

—

#17988622

C₂²

yes

—

C₄×C₈×D₇₃

C₂²

yes

characteristic

#498×C₇₃

C₄

yes

characteristic, complemented

D₇₃⋊M₁₆

—

—

—

—

—

Q₈

yes

—

—

Q₈

yes

complemented

#14556645

—

C₈×#64408

—

C₂×C₈×D₇₃

D₄

yes

characteristic

C₂×C₈×D₇₃

C₂³

yes

—

—

—

—

Q₈×Dic₇₃

—

#14556556

—

#14556549

—

C₄²×D₇₃

D₄

yes

—

—

—

C₂×C₄

yes

—

C₄×#10596831

D₄

yes

characteristic

C₈×Dic₇₃

C₂×C₄

yes

characteristic

C₈×Dic₇₃

D₄

yes

characteristic

C₄⋊Q₈×C₇₃

—

#106×C₇₃

—

#106×C₇₃

C₂×C₄

yes

—

C₄×C₈×C₇₃

C₂×C₄

yes

—

—

—

—

—

—

—

C₂×Dic₁₄₆

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

C₂×D₄

yes

characteristic

C₂×#10596831

C₂²⋊C₄

yes

characteristic

C₂×#10596831

C₂×D₄

yes

characteristic

C₈×D₇₃

SD₁₆

yes

characteristic

C₈×D₇₃

SD₁₆

yes

characteristic

C₈×D₇₃

Q₁₆

yes

characteristic

C₈×D₇₃

Q₁₆

yes

characteristic

C₈×D₇₃

C₂×Q₈

yes

characteristic

C₈×D₇₃

C₂×Q₈

yes

C₈×D₇₃

yes

C₈×D₇₃

yes

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

#11924007

—

#11924005

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

C₂²⋊C₄

yes

characteristic

C₂×Q₈×C₇₃

—

C₂×C₈×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₃

C₂²×C₄

yes

characteristic

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄²×C₇₃

C₂²⋊C₄

yes

C₂²×D₇₃

yes

—

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

AGL(1,ℤ/8)

yes

characteristic

C₄×D₇₃

—

C₄×D₇₃

C₂²⋊Q₈

yes

characteristic

C₄×D₇₃

C₂²⋊Q₈

yes

characteristic

100

C₄×D₇₃

C₂×SD₁₆

yes

characteristic

101

C₄×D₇₃

C₂×Q₁₆

yes

characteristic

102

Dic₁₄₆

—

103

#10596833

—

104

C₈×C₇₃

#103

yes

characteristic

105

C₈×C₇₃

#103

yes

characteristic

106

C₈×C₇₃

C₄×Q₈

yes

characteristic

107

C₈×C₇₃

C₄×Q₈

yes

108

yes

109

yes

110

yes

111

C₄⋊Q₈

yes

characteristic

112

C₂²×C₇₃

#418

yes

characteristic

113

C₂×D₇₃

—

114

C₂×D₇₃

#476

yes

characteristic

115

C₂×D₇₃

#477

yes

characteristic

116

#64408

—

117

C₄×C₇₃

—

118

C₄×C₇₃

—

119

C₄×C₇₃

#391

yes

characteristic

120

C₄×C₇₃

C₂×#103

yes

characteristic

121

Dic₇₃

—

122

Dic₇₃

—

123

Dic₇₃

#476

yes

characteristic

124

Dic₇₃

yes

125

—

126

C₂×C₇₃

—

127

C₂×C₇₃

#1987

yes

characteristic

128

D₇₃

—

129

D₇₃

—

130

#3160

—

131

C₂×#364

—

132

#1772

—

133

#1389

—

134

#1384

—

135

C₇₃

#13271

yes

characteristic, complemented, Sylow

136

#533

—

146

—

137

C₂×M₃₂

—

138

#500

—

146

—

139

#499

—

140

#499

—

146

—

141

#498

—

142

#498

#64408

yes

characteristic, complemented

143

C₂×#108

—

144

#427

—

145

#427

—

146

#427

—

146

—

147

#405

—

146

—

148

C₂×C₄×C₈

—

149

#364

—

146

—

150

#364

—

146

—

151

#339

—

146

—

152

C₂×M₁₆

—

146

—

153

C₂²×C₈

—

154

C₂²×C₈

—

155

C₄⋊Q₈

—

156

C₄⋊Q₈

—

146

—

157

#125

—

146

—

158

C₂²⋊Q₈

—

292

—

159

C₂²⋊Q₈

—

292

—

160

C₄×Q₈

—

292

—

161

C₄×Q₈

—

292

—

162

#117

—

146

—

163

#117

—

146

—

164

C₂×C₄²

—

165

M₃₂

—

146

—

166

M₃₂

—

146

—

167

C₂×C₁₆

—

146

—

168

#108

—

169

#108

—

146

—

170

#107

—

146

—

171

#107

—

146

—

172

#107

—

146

—

173

#106

—

174

#106

—

175

#106

—

176

#106

—

146

—

177

#106

C₂×#64408

yes

—

178

#97

—

292

—

179

C₄×C₈

—

292

—

180

C₄×C₈

—

181

C₄×C₈

—

182

C₄×C₈

—

183

C₄×C₈

C₂×#64408

yes

characteristic

184

C₂×Q₈

—

185

C₂×Q₈

—

292

—

186

C₂²×C₄

—

187

C₂²×C₄

—

146

—

188

M₁₆

—

292

—

189

M₁₆

—

146

—

190

C₂×C₈

—

292

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

C₂²⋊#64408

yes

characteristic

202

C₂×C₈

C₂²×#64408

yes

characteristic

203

C₄⋊C₄

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

292

—

206

C₄⋊C₄

—

292

—

207

C₄⋊C₄

—

292

—

208

C₄⋊C₄

—

146

—

209

C₄⋊C₄

—

146

—

210

C₂²⋊C₄

—

292

—

211

C₂²⋊C₄

—

292

—

212

C₄²

—

292

—

213

C₄²

—

292

—

214

C₄²

—

215

C₄²

—

146

—

216

C₄²

C₂²⋊#64408

yes

characteristic

217

C₁₆

—

292

—

218

C₂³

—

219

Q₈

—

220

Q₈

—

584

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

292

—

224

C₂×C₄

—

292

—

225

C₂×C₄

—

292

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

146

—

232

C₂×C₄

C₂×C₂²⋊#64408

yes

characteristic

233

C₈

—

292

—

234

C₈

—

235

C₈

—

236

C₈

—

237

C₈

—

238

C₈

#14556654

yes

characteristic

239

C₈

#14556654

yes

characteristic

240

C₈

Q₈×#64408

yes

characteristic

241

C₈

Q₈×#64408

yes

characteristic

242

C₂²

—

292

—

243

C₂²

—

244

C₂²

—

245

C₂²

#17989579

yes

characteristic

246

C₄

—

247

C₄

—

248

C₄

—

292

—

249

C₄

—

584

—

250

C₄

—

584

—

251

C₄

—

252

C₄

—

253

C₄

(C₂×#64408)⋊Q₈

yes

characteristic

254

C₄

C₂×#14556654

yes

characteristic

255

C₂

—

256

C₂

—

146

—

257

C₂

—

146

—

258

C₂

#22626109

yes

characteristic

	subgroup	G/H
center	C₂	#22626109
commutator	C₂×C₈×C₇₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×#64408
Fitting	#498×C₇₃	C₄
socle	C₂×C₇₃	#1987
prime radical	C₂²×D₇₃	AGL(1,ℤ/8)
cosocle	C₂×C₈×D₇₃	C₂³
hypercenter	#498	#64408
hypocenter	C₇₃	#13271
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #498

subgroup

G/H

center

C₂

#22626109

commutator

C₂×C₈×C₇₃

C₂²×C₄

Frattini

C₂×C₈

C₂²×#64408

Fitting

#498×C₇₃

C₄

C₂×C₇₃

C₂²×D₇₃

C₂×C₈×D₇₃

C₂³

C₇₃

G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #498

N	H ≅ G/N	type
16. #17988987	C₄	semidirect
17. #17988985	C₄	semidirect
21. #498×C₇₃	C₄	semidirect
27. #14556662	Q₈	semidirect
30. #14556659	Q₈	semidirect
135. C₇₃	#13271	semidirect
142. #498	#64408	semidirect

H ≅ G/N

type

16. #17988987

C₄

semidirect

17. #17988985

C₄

semidirect

21. #498×C₇₃

C₄

semidirect

27. #14556662

Q₈

semidirect

30. #14556659

Q₈

semidirect

135. C₇₃

#13271

semidirect

142. #498

#64408

semidirect

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

subgroup	index
#22626270	2
#22625733	2
#22625013	2
#22624998	2
#22620440	2
#13271	73

subgroup

index

Subgroups — #34014123

Conjugacy classes of subgroups

Complements

Maximal subgroups