Group #14564322 — subgroups

Subgroups — #14564322

Order 2432.

248 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 91 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×#10597292	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597272	C₂	1	1	yes	maximal, characteristic
3	#11926451	C₂	1	1	yes	maximal, characteristic
4	#11926440	C₂	1	1	yes	maximal, characteristic
5	#11926307	C₂	1	1	yes	maximal, characteristic
6	#11926306	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#103	C₂	1	1	yes	maximal, characteristic
8	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
13	C₂×Dic₁₉⋊C₄	—	2	1	no	—
14	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
15	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
16	C₁₉×#103	—	2	2	no	—
17	#10597292	C₄	1	4	yes	complemented
18	C₁₉⋊#95	—	2	1	no	—
19	C₁₉⋊#95	—	2	1	no	—
20	C₁₉⋊#95	—	2	1	no	—
21	#10597272	—	2	2	no	—
22	C₂×Q₈×C₁₉	—	2	1	no	—
23	C₂×Q₈×C₁₉	—	2	1	no	—
24	C₂×Q₈×C₁₉	—	2	1	no	—
25	C₂×Q₈×C₁₉	—	2	1	no	—
26	C₂×Q₈×C₁₉	—	2	1	no	—
27	C₂×Q₈×C₁₉	C₂×C₄	1	2	yes	—
28	C₂²×C₄×C₁₉	—	2	1	no	—
29	C₂²×C₄×C₁₉	—	2	1	no	—
30	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
31	C₂²×Dic₁₉	—	2	1	no	—
32	C₂²×Dic₁₉	—	2	1	no	—
33	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
34	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
35	C₂×C₈×C₁₉	—	2	1	no	—
36	C₂×C₈×C₁₉	—	2	1	no	—
37	C₂×C₈×C₁₉	D₄	1	2	yes	—
38	C₄⋊C₄×C₁₉	—	2	1	no	—
39	C₄⋊C₄×C₁₉	—	2	1	no	—
40	C₄⋊Dic₁₉	—	2	1	no	—
41	C₄⋊Dic₁₉	—	2	1	no	—
42	C₄⋊Dic₁₉	—	2	1	no	—
43	C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
44	Dic₁₉⋊C₄	—	4	2	no	—
45	C₄×Dic₁₉	—	2	1	no	—
46	C₄×Dic₁₉	—	2	1	no	—
47	C₂×C₁₉⋊C₈	—	2	1	no	—
48	C₂×C₁₉⋊C₈	—	2	1	no	—
49	C₂×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
50	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
51	Q₈×C₁₉	—	2	2	no	—
52	Q₈×C₁₉	—	2	2	no	—
53	Q₈×C₁₉	—	4	1	no	—
54	Q₈×C₁₉	—	4	1	no	—
55	C₂×C₄×C₁₉	—	2	2	no	—
56	C₂×C₄×C₁₉	—	4	1	no	—
57	C₂×C₄×C₁₉	—	4	1	no	—
58	C₂×C₄×C₁₉	—	4	1	no	—
59	C₂×C₄×C₁₉	—	4	1	no	—
60	C₂×C₄×C₁₉	—	4	1	no	—
61	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
62	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
63	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
64	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
65	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
66	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
67	C₂×Dic₁₉	—	2	2	no	—
68	C₂×Dic₁₉	—	2	1	no	—
69	C₂×Dic₁₉	—	2	1	no	—
70	C₂×Dic₁₉	—	2	1	no	—
71	C₂×Dic₁₉	—	2	1	no	—
72	C₂×Dic₁₉	—	2	1	no	—
73	C₂×Dic₁₉	—	2	1	no	—
74	C₂×Dic₁₉	—	4	1	no	—
75	C₂×Dic₁₉	—	4	1	no	—
76	C₂×Dic₁₉	—	4	1	no	—
77	C₂×Dic₁₉	—	4	1	no	—
78	C₂×Dic₁₉	—	4	1	no	—
79	C₈×C₁₉	—	2	2	no	—
80	C₁₉⋊C₈	—	2	2	no	—
81	#1935	—	19	1	no	maximal, Sylow
82	C₂²×C₁₉	C₄×D₄	1	1	yes	characteristic
83	C₂²×C₁₉	#121	1	1	yes	characteristic
84	C₂²×C₁₉	#124	1	1	yes	characteristic
85	C₂²×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
86	C₂²×C₁₉	#137	1	1	yes	characteristic
87	C₂²×C₁₉	#137	1	1	yes	characteristic
88	C₂²×C₁₉	#137	1	1	yes	characteristic
89	C₄×C₁₉	—	4	2	no	—
90	C₄×C₁₉	—	8	1	no	—
91	C₄×C₁₉	#117	1	1	yes	characteristic
92	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
93	C₄×C₁₉	#123	1	1	yes	characteristic
94	C₄×C₁₉	#126	1	1	yes	characteristic
95	Dic₁₉	—	4	2	no	—
96	Dic₁₉	—	4	1	no	—
97	Dic₁₉	—	4	1	no	—
98	Dic₁₉	—	8	1	no	—
99	C₂×#103	—	19	1	no	—
100	C₂×#103	D₁₉	1	1	yes	characteristic
101	C₂×#97	—	19	1	no	—
102	#391	—	19	1	no	—
103	#389	—	19	1	no	—
104	#340	—	19	1	no	—
105	#340	—	19	1	no	—
106	C₂×C₁₉	#388	1	1	yes	characteristic
107	C₂×C₁₉	#440	1	1	yes	characteristic
108	C₂×C₁₉	#441	1	1	yes	characteristic
109	C₂×C₁₉	#468	1	1	yes	characteristic
110	C₂×C₁₉	#470	1	1	yes	characteristic
111	C₂×C₁₉	#489	1	1	yes	characteristic
112	C₂×C₁₉	#491	1	1	yes	characteristic
113	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
114	C₂²×C₈	—	19	1	no	—
115	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
116	C₂×C₄⋊C₄	—	19	1	no	—
117	C₂×C₄⋊C₄	—	19	1	no	—
118	C₂×C₄⋊C₄	—	38	1	no	—
119	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
120	C₂×C₄²	—	19	1	no	—
121	#103	—	2	2	no	—
122	#103	—	19	4	no	—
123	#97	—	38	2	no	—
124	#95	—	38	1	no	—
125	#95	—	38	1	no	—
126	#95	—	38	1	no	—
127	C₁₉	#1935	1	1	yes	characteristic, complemented, Sylow
128	C₂×Q₈	—	2	1	no	—
129	C₂×Q₈	—	2	1	no	—
130	C₂×Q₈	—	2	1	no	—
131	C₂×Q₈	—	2	1	no	—
132	C₂×Q₈	—	2	1	no	—
133	C₂×Q₈	C₄×D₁₉	1	2	yes	—
134	C₂²×C₄	—	2	1	no	—
135	C₂²×C₄	—	2	1	no	—
136	C₂²×C₄	—	19	1	no	—
137	C₂²×C₄	—	19	1	no	—
138	C₂²×C₄	—	38	1	no	—
139	C₂²×C₄	—	38	1	no	—
140	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
141	C₂×C₈	—	2	1	no	—
142	C₂×C₈	—	2	1	no	—
143	C₂×C₈	—	19	2	no	—
144	C₂×C₈	—	38	1	no	—
145	C₂×C₈	—	38	1	no	—
146	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
147	C₄⋊C₄	—	2	1	no	—
148	C₄⋊C₄	—	2	1	no	—
149	C₄⋊C₄	—	19	2	no	—
150	C₄⋊C₄	—	38	1	no	—
151	C₄⋊C₄	—	38	1	no	—
152	C₄⋊C₄	—	38	1	no	—
153	C₄⋊C₄	—	76	2	no	—
154	C₄²	—	38	1	no	—
155	C₄²	—	38	1	no	—
156	C₂³	D₄×D₁₉	1	1	yes	characteristic
157	Q₈	—	2	2	no	—
158	Q₈	—	2	2	no	—
159	Q₈	—	4	1	no	—
160	Q₈	—	4	1	no	—
161	C₂×C₄	—	2	2	no	—
162	C₂×C₄	—	4	1	no	—
163	C₂×C₄	—	4	1	no	—
164	C₂×C₄	—	4	1	no	—
165	C₂×C₄	—	4	1	no	—
166	C₂×C₄	—	4	1	no	—
167	C₂×C₄	—	38	1	no	—
168	C₂×C₄	—	38	1	no	—
169	C₂×C₄	—	38	2	no	—
170	C₂×C₄	—	38	1	no	—
171	C₂×C₄	—	38	1	no	—
172	C₂×C₄	—	38	1	no	—
173	C₂×C₄	—	38	1	no	—
174	C₂×C₄	—	76	1	no	—
175	C₂×C₄	—	76	1	no	—
176	C₂×C₄	—	76	1	no	—
177	C₂×C₄	—	76	1	no	—
178	C₂×C₄	—	76	1	no	—
179	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
180	C₂×C₄	#64541	1	1	yes	characteristic
181	C₂×C₄	#64543	1	1	yes	characteristic
182	C₂×C₄	#64543	1	1	yes	characteristic
183	C₂×C₄	#64543	1	1	yes	characteristic
184	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
185	C₈	—	2	2	no	—
186	C₈	—	38	2	no	—
187	C₂²	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
188	C₂²	#10597331	1	1	yes	characteristic
189	C₂²	#10597360	1	1	yes	characteristic
190	C₂²	#10597361	1	1	yes	characteristic
191	C₂²	#10597364	1	1	yes	characteristic
192	C₂²	#10597364	1	1	yes	characteristic
193	C₂²	#10597384	1	1	yes	characteristic
194	C₄	—	4	2	no	—
195	C₄	—	8	1	no	—
196	C₄	—	76	1	no	—
197	C₄	—	76	1	no	—
198	C₄	—	76	2	no	—
199	C₄	—	152	1	no	—
200	C₄	#10597323	1	1	yes	characteristic
201	C₄	#10597325	1	1	yes	characteristic
202	C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
203	C₄	#10597381	1	1	yes	characteristic
204	C₂	#11926432	1	1	yes	characteristic
205	C₂	#11926647	1	1	yes	characteristic
206	C₂	#11926648	1	1	yes	characteristic
207	C₂	#11926787	1	1	yes	characteristic
208	C₂	#11926799	1	1	yes	characteristic
209	C₂	#11926905	1	1	yes	characteristic
210	C₂	#11926911	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597292

C₂

yes

maximal, characteristic

C₂×#10597272

C₂

yes

maximal, characteristic

#11926451

C₂

yes

maximal, characteristic

#11926440

C₂

yes

maximal, characteristic

#11926307

C₂

yes

maximal, characteristic

#11926306

C₂

yes

maximal, characteristic

C₂×C₁₉×#103

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₁₉×#103

—

#10597292

C₄

yes

complemented

C₁₉⋊#95

—

C₁₉⋊#95

—

C₁₉⋊#95

—

#10597272

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

D₄

yes

characteristic

C₂²×Dic₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂×C₄

yes

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1935

—

maximal, Sylow

C₂²×C₁₉

C₄×D₄

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#117

yes

characteristic

C₄×C₁₉

C₄×D₄

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂×#103

—

100

C₂×#103

D₁₉

yes

characteristic

101

C₂×#97

—

102

#391

—

103

#389

—

104

#340

—

105

#340

—

106

C₂×C₁₉

#388

yes

characteristic

107

C₂×C₁₉

#440

yes

characteristic

108

C₂×C₁₉

#441

yes

characteristic

109

C₂×C₁₉

#468

yes

characteristic

110

C₂×C₁₉

#470

yes

characteristic

111

C₂×C₁₉

#489

yes

characteristic

112

C₂×C₁₉

#491

yes

characteristic

113

C₂²×Q₈

C₂×D₁₉

yes

characteristic

114

C₂²×C₈

—

115

C₂²×C₈

C₂×D₁₉

yes

characteristic

116

C₂×C₄⋊C₄

—

117

C₂×C₄⋊C₄

—

118

C₂×C₄⋊C₄

—

119

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

120

C₂×C₄²

—

121

#103

—

122

#103

—

123

#97

—

124

#95

—

125

#95

—

126

#95

—

127

C₁₉

#1935

yes

characteristic, complemented, Sylow

128

C₂×Q₈

—

129

C₂×Q₈

—

130

C₂×Q₈

—

131

C₂×Q₈

—

132

C₂×Q₈

—

133

C₂×Q₈

C₄×D₁₉

yes

—

134

C₂²×C₄

—

135

C₂²×C₄

—

136

C₂²×C₄

—

137

C₂²×C₄

—

138

C₂²×C₄

—

139

C₂²×C₄

—

140

C₂²×C₄

C₂²×D₁₉

yes

characteristic

141

C₂×C₈

—

142

C₂×C₈

—

143

C₂×C₈

—

144

C₂×C₈

—

145

C₂×C₈

—

146

C₂×C₈

C₂²⋊D₁₉

yes

—

147

C₄⋊C₄

—

148

C₄⋊C₄

—

149

C₄⋊C₄

—

150

C₄⋊C₄

—

151

C₄⋊C₄

—

152

C₄⋊C₄

—

153

C₄⋊C₄

—

154

C₄²

—

155

C₄²

—

156

C₂³

D₄×D₁₉

yes

characteristic

157

Q₈

—

158

Q₈

—

159

Q₈

—

160

Q₈

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

180

C₂×C₄

#64541

yes

characteristic

181

C₂×C₄

#64543

yes

characteristic

182

C₂×C₄

#64543

yes

characteristic

183

C₂×C₄

#64543

yes

characteristic

184

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

185

C₈

—

186

C₈

—

187

C₂²

(C₂²⋊D₁₉)⋊C₄

yes

characteristic

188

C₂²

#10597331

yes

characteristic

189

C₂²

#10597360

yes

characteristic

190

C₂²

#10597361

yes

characteristic

191

C₂²

#10597364

yes

characteristic

192

C₂²

#10597364

yes

characteristic

193

C₂²

#10597384

yes

characteristic

194

C₄

—

195

C₄

—

196

C₄

—

197

C₄

—

198

C₄

—

199

C₄

—

152

—

200

C₄

#10597323

yes

characteristic

201

C₄

#10597325

yes

characteristic

202

C₄

C₄×C₂²⋊D₁₉

yes

characteristic

203

C₄

#10597381

yes

characteristic

204

C₂

#11926432

yes

characteristic

205

C₂

#11926647

yes

characteristic

206

C₂

#11926648

yes

characteristic

207

C₂

#11926787

yes

characteristic

208

C₂

#11926799

yes

characteristic

209

C₂

#11926905

yes

characteristic

210

C₂

#11926911

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#103	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂×#103	D₁₉
hypocenter	C₁₉	#1935
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#103

subgroup

G/H

center

C₂³

D₄×D₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#103

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#103

N	H ≅ G/N	type
17. #10597292	C₄	semidirect
127. C₁₉	#1935	semidirect

H ≅ G/N

type

17. #10597292

C₄

semidirect

127. C₁₉

#1935

semidirect

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

subgroup	index
C₂×#10597292	2
C₂×#10597272	2
#11926451	2
#11926440	2
#11926307	2
#11926306	2
C₂×C₁₉×#103	2
#1935	19

subgroup

index

C₂×C₁₉×#103

Subgroups — #14564322

Conjugacy classes of subgroups

Complements

Maximal subgroups