Group #22610838 — subgroups

Subgroups — #22610838

Order 9344.

316 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 83 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	C₂²×#11924013	C₂	1	1	yes	maximal, characteristic
2	C₂×#14556526	C₂	1	1	yes	maximal, characteristic, complemented
3	#17988593	C₂	1	1	yes	maximal, characteristic, complemented
4	#17988592	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#14556507	C₂	1	1	yes	maximal, characteristic, complemented
6	#17988545	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#100×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₂₉₂	C₂²	1	1	yes	characteristic
9	C₂×#11924013	—	2	1	no	—
10	C₂×#11924013	—	2	1	no	—
11	C₂×#11924013	—	2	2	no	—
12	C₂×#11924013	C₄	1	4	yes	complemented
13	C₂×#11924012	C₂²	1	1	yes	characteristic
14	C₂²×#10596831	C₂²	1	1	yes	characteristic
15	#14556550	C₂²	1	1	yes	characteristic
16	#14556526	—	2	2	no	—
17	#14556513	—	2	2	no	—
18	#14556512	—	2	2	no	—
19	#14556507	—	2	2	no	—
20	#14556501	—	2	1	no	—
21	C₈×Dic₇₃	—	2	1	no	—
22	C₂²×D₄×C₇₃	C₂²	1	1	yes	characteristic
23	C₂×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
24	C₂×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
25	#100×C₇₃	—	2	2	no	—
26	C₂³×D₇₃	—	2	1	no	—
27	C₂×D₂₉₂	—	2	1	no	—
28	C₂×D₂₉₂	—	2	1	no	—
29	C₂×D₂₉₂	—	2	1	no	—
30	C₂×D₂₉₂	—	2	1	no	—
31	C₂×D₂₉₂	—	2	1	no	—
32	C₂×D₂₉₂	C₂×C₄	1	2	yes	—
33	#11924013	—	2	4	no	—
34	#11924013	—	2	4	no	—
35	#11924012	—	2	1	no	—
36	#11924012	—	2	1	no	—
37	C₂×#10596831	—	2	1	no	—
38	C₂×#10596831	C₂×C₄	1	2	yes	—
39	C₂×#10596831	D₄	1	1	yes	characteristic
40	C₂×#10596831	D₄	1	1	yes	characteristic
41	C₂×#10596831	D₄	1	2	yes	—
42	C₄⋊Dic₇₃	D₄	1	2	yes	—
43	C₂²⋊Dic₇₃	—	2	1	no	—
44	C₄×Dic₇₃	—	2	1	no	—
45	C₂⁴×C₇₃	—	2	1	no	—
46	C₂×D₄×C₇₃	—	2	1	no	—
47	C₂×D₄×C₇₃	—	2	1	no	—
48	C₂×D₄×C₇₃	—	2	1	no	—
49	C₂×D₄×C₇₃	—	2	1	no	—
50	C₂×D₄×C₇₃	—	2	1	no	—
51	C₂×D₄×C₇₃	C₂×C₄	1	2	yes	—
52	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
53	M₁₆×C₇₃	—	2	1	no	—
54	M₁₆×C₇₃	—	2	1	no	—
55	M₁₆×C₇₃	—	2	1	no	—
56	M₁₆×C₇₃	D₄	1	2	yes	—
57	C₂×C₈×C₇₃	—	2	1	no	—
58	C₂×C₈×C₇₃	—	2	1	no	—
59	C₂³×C₇₃	—	2	2	no	—
60	C₂³×C₇₃	—	4	1	no	—
61	C₂³×C₇₃	—	4	1	no	—
62	C₂³×C₇₃	—	8	2	no	—
63	C₂³×C₇₃	#41	1	1	yes	characteristic
64	C₂²×D₇₃	—	2	2	no	—
65	C₂²×D₇₃	—	4	1	no	—
66	C₂²×D₇₃	—	4	1	no	—
67	C₂²×D₇₃	—	8	2	no	—
68	D₄×C₇₃	—	2	2	no	—
69	D₄×C₇₃	—	2	2	no	—
70	D₄×C₇₃	—	4	1	no	—
71	D₄×C₇₃	—	4	1	no	—
72	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
73	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
74	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
75	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
76	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
77	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
78	C₂×Dic₇₃	—	2	2	no	—
79	D₂₉₂	—	2	2	no	—
80	D₂₉₂	—	2	2	no	—
81	D₂₉₂	—	4	1	no	—
82	D₂₉₂	—	4	1	no	—
83	C₈×C₇₃	—	2	2	no	—
84	C₈×C₇₃	—	4	1	no	—
85	#10596831	—	4	1	no	—
86	#10596831	C₂²⋊C₄	1	2	yes	—
87	#10596831	C₂²⋊C₄	1	2	yes	—
88	C₂²×C₇₃	—	2	2	no	—
89	C₂²×C₇₃	—	4	2	no	—
90	C₂²×C₇₃	—	8	2	no	—
91	C₂²×C₇₃	—	8	2	no	—
92	C₂²×C₇₃	—	8	2	no	—
93	C₂²×C₇₃	C₄×D₄	1	1	yes	characteristic
94	C₂²×C₇₃	#121	1	1	yes	characteristic
95	C₂²×C₇₃	#124	1	1	yes	characteristic
96	C₂×D₇₃	—	4	2	no	—
97	C₂×D₇₃	—	8	2	no	—
98	C₂×D₇₃	—	8	2	no	—
99	C₂×D₇₃	—	8	2	no	—
100	C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
101	C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
102	C₄×C₇₃	#121	1	1	yes	characteristic
103	C₄×C₇₃	#127	1	1	yes	characteristic
104	Dic₇₃	—	4	2	no	—
105	C₂×C₇₃	—	2	1	no	—
106	C₂×C₇₃	—	2	1	no	—
107	C₂×C₇₃	—	8	2	no	—
108	C₂×C₇₃	#390	1	1	yes	characteristic
109	C₂×C₇₃	#472	1	2	yes	—
110	D₇₃	—	8	2	no	—
111	#1978	—	73	1	no	maximal, Sylow
112	C₇₃	#1978	1	1	yes	characteristic, complemented, Sylow
113	C₂²×D₈	—	73	1	no	—
114	C₂×#108	—	73	1	no	—
115	#418	—	73	1	no	—
116	#418	—	73	1	no	—
117	C₂×#100	—	73	1	no	—
118	C₂×#100	D₇₃	1	1	yes	characteristic, complemented
119	#405	—	73	1	no	—
120	C₂²×D₄	—	73	1	no	—
121	C₂²×D₄	C₂×D₇₃	1	1	yes	characteristic
122	C₂×D₈	—	73	4	no	—
123	C₂×D₈	—	146	1	no	—
124	C₂×D₈	—	146	1	no	—
125	C₂×D₈	—	146	2	no	—
126	C₂×M₁₆	—	73	1	no	—
127	C₂×M₁₆	C₂×D₇₃	1	1	yes	characteristic
128	C₂×M₁₆	C₂×D₇₃	1	1	yes	characteristic
129	C₂²×C₈	—	73	1	no	—
130	#117	—	73	1	no	—
131	#108	—	146	2	no	—
132	#102	—	146	2	no	—
133	#102	—	146	2	no	—
134	#100	—	2	2	no	—
135	#100	—	146	2	no	—
136	#97	—	146	1	no	—
137	C₄×C₈	—	146	1	no	—
138	C₂⁴	—	2	1	no	—
139	C₂⁴	—	146	1	no	—
140	C₂×D₄	—	2	1	no	—
141	C₂×D₄	—	2	1	no	—
142	C₂×D₄	—	2	1	no	—
143	C₂×D₄	—	2	1	no	—
144	C₂×D₄	—	2	1	no	—
145	C₂×D₄	—	73	2	no	—
146	C₂×D₄	—	146	1	no	—
147	C₂×D₄	—	146	1	no	—
148	C₂×D₄	—	146	1	no	—
149	C₂×D₄	—	146	1	no	—
150	C₂×D₄	—	146	1	no	—
151	C₂×D₄	C₄×D₇₃	1	2	yes	—
152	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
153	D₈	—	146	4	no	—
154	D₈	—	146	4	no	—
155	M₁₆	—	2	1	no	—
156	M₁₆	—	2	1	no	—
157	M₁₆	—	2	1	no	—
158	M₁₆	—	146	1	no	—
159	M₁₆	—	146	1	no	—
160	M₁₆	C₂²⋊D₇₃	1	2	yes	—
161	C₂×C₈	—	2	1	no	—
162	C₂×C₈	—	2	1	no	—
163	C₂×C₈	—	73	2	no	—
164	C₂×C₈	—	73	1	no	—
165	C₂×C₈	—	73	1	no	—
166	C₂×C₈	—	73	2	no	—
167	C₂×C₈	—	146	1	no	—
168	C₄⋊C₄	—	73	2	no	—
169	C₂²⋊C₄	—	146	1	no	—
170	C₄²	—	146	1	no	—
171	C₂³	—	2	2	no	—
172	C₂³	—	4	1	no	—
173	C₂³	—	4	1	no	—
174	C₂³	—	8	2	no	—
175	C₂³	—	292	1	no	—
176	C₂³	—	292	1	no	—
177	C₂³	—	584	2	no	—
178	C₂³	—	146	2	no	—
179	C₂³	#11924028	1	1	yes	characteristic
180	D₄	—	2	2	no	—
181	D₄	—	2	2	no	—
182	D₄	—	4	1	no	—
183	D₄	—	4	1	no	—
184	D₄	—	292	1	no	—
185	D₄	—	292	1	no	—
186	D₄	—	146	2	no	—
187	D₄	—	146	2	no	—
188	C₂×C₄	—	146	2	no	—
189	C₂×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
190	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
191	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
192	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
193	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
194	C₂×C₄	#11924027	1	1	yes	characteristic
195	C₈	—	2	2	no	—
196	C₈	—	4	1	no	—
197	C₈	—	292	1	no	—
198	C₈	—	73	2	no	—
199	C₈	—	73	2	no	—
200	C₂²	—	2	2	no	—
201	C₂²	—	4	2	no	—
202	C₂²	—	8	2	no	—
203	C₂²	—	8	2	no	—
204	C₂²	—	8	2	no	—
205	C₂²	—	292	2	no	—
206	C₂²	—	584	2	no	—
207	C₂²	—	584	2	no	—
208	C₂²	—	584	2	no	—
209	C₂²	C₄×C₂²⋊D₇₃	1	1	yes	characteristic
210	C₂²	#14556564	1	1	yes	characteristic
211	C₂²	#14556577	1	1	yes	characteristic
212	C₄	—	292	2	no	—
213	C₄	C₂²⋊C₄×D₇₃	1	1	yes	characteristic
214	C₄	#14556551	1	1	yes	characteristic
215	C₄	#14556563	1	1	yes	characteristic
216	C₄	#14556587	1	1	yes	characteristic
217	C₂	—	2	1	no	—
218	C₂	—	2	1	no	—
219	C₂	—	8	2	no	—
220	C₂	—	584	2	no	—
221	C₂	#17988487	1	1	yes	characteristic
222	C₂	#17988856	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#11924013

C₂

yes

maximal, characteristic

C₂×#14556526

C₂

yes

maximal, characteristic, complemented

#17988593

C₂

yes

maximal, characteristic, complemented

#17988592

C₂

yes

maximal, characteristic, complemented

C₂×#14556507

C₂

yes

maximal, characteristic, complemented

#17988545

C₂

yes

maximal, characteristic, complemented

C₂×#100×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂²×D₂₉₂

C₂²

yes

—

—

—

C₄

yes

complemented

C₂×#11924012

C₂²

yes

characteristic

C₂²×#10596831

C₂²

yes

characteristic

#14556550

C₂²

yes

—

—

—

—

—

C₈×Dic₇₃

—

C₂²×D₄×C₇₃

C₂²

yes

characteristic

C₂×M₁₆×C₇₃

C₂²

yes

characteristic

C₂×M₁₆×C₇₃

C₂²

yes

characteristic

#100×C₇₃

—

C₂³×D₇₃

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

C₂×C₄

yes

—

—

—

—

—

—

C₂×C₄

yes

—

C₂×#10596831

D₄

yes

characteristic

C₂×#10596831

D₄

yes

characteristic

C₂×#10596831

D₄

yes

—

C₄⋊Dic₇₃

D₄

yes

—

C₂²⋊Dic₇₃

—

C₄×Dic₇₃

—

C₂⁴×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

C₂×C₄

yes

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

M₁₆×C₇₃

—

M₁₆×C₇₃

—

M₁₆×C₇₃

—

M₁₆×C₇₃

D₄

yes

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

#41

yes

characteristic

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

#41

yes

characteristic

C₂×Dic₇₃

—

D₂₉₂

—

D₂₉₂

—

D₂₉₂

—

D₂₉₂

—

C₈×C₇₃

—

C₈×C₇₃

—

#10596831

—

#10596831

C₂²⋊C₄

yes

—

#10596831

C₂²⋊C₄

yes

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

C₄×D₄

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

100

C₄×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

101

C₄×C₇₃

C₄×D₄

yes

characteristic

102

C₄×C₇₃

#121

yes

characteristic

103

C₄×C₇₃

#127

yes

characteristic

104

Dic₇₃

—

105

C₂×C₇₃

—

106

C₂×C₇₃

—

107

C₂×C₇₃

—

108

C₂×C₇₃

#390

yes

characteristic

109

C₂×C₇₃

#472

yes

—

110

D₇₃

—

111

#1978

—

maximal, Sylow

112

C₇₃

#1978

yes

characteristic, complemented, Sylow

113

C₂²×D₈

—

114

C₂×#108

—

115

#418

—

116

#418

—

117

C₂×#100

—

118

C₂×#100

D₇₃

yes

characteristic, complemented

119

#405

—

120

C₂²×D₄

—

121

C₂²×D₄

C₂×D₇₃

yes

characteristic

122

C₂×D₈

—

123

C₂×D₈

—

146

—

124

C₂×D₈

—

146

—

125

C₂×D₈

—

146

—

126

C₂×M₁₆

—

127

C₂×M₁₆

C₂×D₇₃

yes

characteristic

128

C₂×M₁₆

C₂×D₇₃

yes

characteristic

129

C₂²×C₈

—

130

#117

—

131

#108

—

146

—

132

#102

—

146

—

133

#102

—

146

—

134

#100

—

135

#100

—

146

—

136

#97

—

146

—

137

C₄×C₈

—

146

—

138

C₂⁴

—

139

C₂⁴

—

146

—

140

C₂×D₄

—

141

C₂×D₄

—

142

C₂×D₄

—

143

C₂×D₄

—

144

C₂×D₄

—

145

C₂×D₄

—

146

C₂×D₄

—

146

—

147

C₂×D₄

—

146

—

148

C₂×D₄

—

146

—

149

C₂×D₄

—

146

—

150

C₂×D₄

—

146

—

151

C₂×D₄

C₄×D₇₃

yes

—

152

C₂²×C₄

C₂²×D₇₃

yes

characteristic

153

D₈

—

146

—

154

D₈

—

146

—

155

M₁₆

—

156

M₁₆

—

157

M₁₆

—

158

M₁₆

—

146

—

159

M₁₆

—

146

—

160

M₁₆

C₂²⋊D₇₃

yes

—

161

C₂×C₈

—

162

C₂×C₈

—

163

C₂×C₈

—

164

C₂×C₈

—

165

C₂×C₈

—

166

C₂×C₈

—

167

C₂×C₈

—

146

—

168

C₄⋊C₄

—

169

C₂²⋊C₄

—

146

—

170

C₄²

—

146

—

171

C₂³

—

172

C₂³

—

173

C₂³

—

174

C₂³

—

175

C₂³

—

292

—

176

C₂³

—

292

—

177

C₂³

—

584

—

178

C₂³

—

146

—

179

C₂³

#11924028

yes

characteristic

180

D₄

—

181

D₄

—

182

D₄

—

183

D₄

—

184

D₄

—

292

—

185

D₄

—

292

—

186

D₄

—

146

—

187

D₄

—

146

—

188

C₂×C₄

—

146

—

189

C₂×C₄

C₂×C₄×D₇₃

yes

characteristic

190

C₂×C₄

D₄×D₇₃

yes

characteristic

191

C₂×C₄

D₄×D₇₃

yes

characteristic

192

C₂×C₄

D₄×D₇₃

yes

characteristic

193

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

194

C₂×C₄

#11924027

yes

characteristic

195

C₈

—

196

C₈

—

197

C₈

—

292

—

198

C₈

—

199

C₈

—

200

C₂²

—

201

C₂²

—

202

C₂²

—

203

C₂²

—

204

C₂²

—

205

C₂²

—

292

—

206

C₂²

—

584

—

207

C₂²

—

584

—

208

C₂²

—

584

—

209

C₂²

C₄×C₂²⋊D₇₃

yes

characteristic

210

C₂²

#14556564

yes

characteristic

211

C₂²

#14556577

yes

characteristic

212

C₄

—

292

—

213

C₄

C₂²⋊C₄×D₇₃

yes

characteristic

214

C₄

#14556551

yes

characteristic

215

C₄

#14556563

yes

characteristic

216

C₄

#14556587

yes

characteristic

217

C₂

—

218

C₂

—

219

C₂

—

220

C₂

—

584

—

221

C₂

#17988487

yes

characteristic

222

C₂

#17988856

yes

—

	subgroup	G/H
center	C₂²	#14556564
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	C₂×#100×C₇₃	C₂
socle	C₂²×C₇₃	#121
hypercenter	C₂×#100	D₇₃
hypocenter	C₇₃	#1978
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#100

subgroup

G/H

center

C₂²

#14556564

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

C₂×#100×C₇₃

C₂

C₂²×C₇₃

D₇₃

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#100

N	H ≅ G/N	type
2. C₂×#14556526	C₂	semidirect
3. #17988593	C₂	semidirect
4. #17988592	C₂	semidirect
5. C₂×#14556507	C₂	semidirect
6. #17988545	C₂	semidirect
7. C₂×#100×C₇₃	C₂	semidirect
12. C₂×#11924013	C₄	semidirect
112. C₇₃	#1978	semidirect
118. C₂×#100	D₇₃	semidirect

H ≅ G/N

type

2. C₂×#14556526

C₂

semidirect

3. #17988593

C₂

semidirect

4. #17988592

C₂

semidirect

5. C₂×#14556507

C₂

semidirect

6. #17988545

C₂

semidirect

7. C₂×#100×C₇₃

C₂

semidirect

12. C₂×#11924013

C₄

semidirect

112. C₇₃

#1978

semidirect

118. C₂×#100

D₇₃

semidirect

Subgroups — #22610838

Conjugacy classes of subgroups

Complements