Group #14564784 — subgroups

Subgroups — #14564784

Order 2432.

258 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 85 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×#10597336	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597292	C₂	1	1	yes	maximal, characteristic
3	#11926451	C₂	1	1	yes	maximal, characteristic
4	#11926307	C₂	1	1	yes	maximal, characteristic
5	#11926306	C₂	1	1	yes	maximal, characteristic
6	#11926298	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	—	2	1	no	—
12	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
14	C₂×Dic₁₉⋊C₄	—	2	1	no	—
15	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
16	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
17	#10597336	—	2	2	no	—
18	#10597336	—	2	2	no	—
19	C₁₉×#103	—	2	2	no	—
20	#10597292	—	2	2	no	—
21	C₁₉⋊#95	—	2	1	no	—
22	C₁₉⋊#95	—	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	—	2	1	no	—
28	C₂×Q₈×C₁₉	Q₈	1	2	yes	—
29	C₂²×C₄×C₁₉	—	2	1	no	—
30	C₂²×C₄×C₁₉	—	2	1	no	—
31	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
32	C₂²×Dic₁₉	—	2	1	no	—
33	C₂²×Dic₁₉	—	2	1	no	—
34	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
35	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
36	C₂×C₈×C₁₉	—	2	1	no	—
37	C₂×C₈×C₁₉	—	2	1	no	—
38	C₂×C₈×C₁₉	—	2	1	no	—
39	C₄⋊C₄×C₁₉	—	2	1	no	—
40	C₄⋊C₄×C₁₉	D₄	1	2	yes	—
41	C₄⋊Dic₁₉	—	2	4	no	—
42	C₄⋊Dic₁₉	—	2	1	no	—
43	C₄⋊Dic₁₉	—	2	1	no	—
44	C₄⋊Dic₁₉	—	2	1	no	—
45	C₄⋊Dic₁₉	D₄	1	2	yes	—
46	Dic₁₉⋊C₄	—	2	4	no	—
47	C₄×Dic₁₉	—	2	1	no	—
48	C₄×Dic₁₉	—	2	1	no	—
49	C₂×C₁₉⋊C₈	—	2	1	no	—
50	C₂×C₁₉⋊C₈	—	2	1	no	—
51	C₂×C₁₉⋊C₈	—	2	1	no	—
52	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
53	Q₈×C₁₉	—	2	2	no	—
54	Q₈×C₁₉	—	2	2	no	—
55	Q₈×C₁₉	—	4	1	no	—
56	Q₈×C₁₉	—	4	1	no	—
57	C₂×C₄×C₁₉	—	2	2	no	—
58	C₂×C₄×C₁₉	—	2	2	no	—
59	C₂×C₄×C₁₉	—	4	1	no	—
60	C₂×C₄×C₁₉	—	4	1	no	—
61	C₂×C₄×C₁₉	—	4	1	no	—
62	C₂×C₄×C₁₉	—	4	1	no	—
63	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
64	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
65	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
66	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
67	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
68	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
69	C₂×Dic₁₉	—	2	1	no	—
70	C₂×Dic₁₉	—	2	1	no	—
71	C₂×Dic₁₉	—	2	2	no	—
72	C₂×Dic₁₉	—	2	1	no	—
73	C₂×Dic₁₉	—	2	1	no	—
74	C₂×Dic₁₉	—	2	1	no	—
75	C₂×Dic₁₉	—	2	1	no	—
76	C₂×Dic₁₉	—	4	1	no	—
77	C₂×Dic₁₉	—	4	1	no	—
78	C₂×Dic₁₉	—	4	1	no	—
79	C₂×Dic₁₉	—	4	1	no	—
80	C₂×Dic₁₉	—	4	1	no	—
81	C₈×C₁₉	—	4	1	no	—
82	C₁₉⋊C₈	—	4	1	no	—
83	#2026	—	19	1	no	maximal, Sylow
84	C₂²×C₁₉	#120	1	1	yes	characteristic
85	C₂²×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
86	C₂²×C₁₉	#124	1	1	yes	characteristic
87	C₂²×C₁₉	#135	1	1	yes	characteristic
88	C₂²×C₁₉	#135	1	1	yes	characteristic
89	C₂²×C₁₉	#137	1	1	yes	characteristic
90	C₂²×C₁₉	#137	1	1	yes	characteristic
91	C₄×C₁₉	—	4	2	no	—
92	C₄×C₁₉	—	4	2	no	—
93	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
94	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
95	C₄×C₁₉	#124	1	1	yes	characteristic
96	C₄×C₁₉	#124	1	1	yes	characteristic
97	Dic₁₉	—	4	1	no	—
98	Dic₁₉	—	4	1	no	—
99	Dic₁₉	—	4	2	no	—
100	Dic₁₉	—	8	1	no	—
101	C₂×#125	—	19	1	no	—
102	C₂×#103	—	19	1	no	—
103	C₂×#103	D₁₉	1	1	yes	characteristic
104	#391	—	19	1	no	—
105	#340	—	19	1	no	—
106	#340	—	19	1	no	—
107	#336	—	19	1	no	—
108	C₂×C₁₉	#393	1	1	yes	characteristic
109	C₂×C₁₉	#452	1	1	yes	characteristic
110	C₂×C₁₉	#452	1	1	yes	characteristic
111	C₂×C₁₉	#479	1	1	yes	characteristic
112	C₂×C₁₉	#479	1	1	yes	characteristic
113	C₂×C₁₉	#488	1	1	yes	characteristic
114	C₂×C₁₉	#491	1	1	yes	characteristic
115	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
116	C₂²×C₈	—	19	1	no	—
117	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
118	#125	—	38	2	no	—
119	#125	—	38	2	no	—
120	C₂×C₄⋊C₄	—	19	1	no	—
121	C₂×C₄⋊C₄	—	19	1	no	—
122	C₂×C₄⋊C₄	—	38	1	no	—
123	C₂×C₄⋊C₄	—	38	1	no	—
124	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
125	C₂×C₄²	—	19	1	no	—
126	#103	—	2	2	no	—
127	#103	—	38	2	no	—
128	#95	—	38	1	no	—
129	#95	—	38	1	no	—
130	C₁₉	#2026	1	1	yes	characteristic, complemented, Sylow
131	C₂×Q₈	—	2	1	no	—
132	C₂×Q₈	—	2	1	no	—
133	C₂×Q₈	—	2	1	no	—
134	C₂×Q₈	—	2	1	no	—
135	C₂×Q₈	—	2	1	no	—
136	C₂×Q₈	Dic₃₈	1	2	yes	—
137	C₂²×C₄	—	2	1	no	—
138	C₂²×C₄	—	2	1	no	—
139	C₂²×C₄	—	19	1	no	—
140	C₂²×C₄	—	19	1	no	—
141	C₂²×C₄	—	38	1	no	—
142	C₂²×C₄	—	38	1	no	—
143	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
144	C₂×C₈	—	2	1	no	—
145	C₂×C₈	—	2	1	no	—
146	C₂×C₈	—	2	1	no	—
147	C₂×C₈	—	38	1	no	—
148	C₂×C₈	—	38	1	no	—
149	C₂×C₈	—	38	1	no	—
150	C₄⋊C₄	—	2	1	no	—
151	C₄⋊C₄	—	19	2	no	—
152	C₄⋊C₄	—	38	4	no	—
153	C₄⋊C₄	—	38	4	no	—
154	C₄⋊C₄	—	38	1	no	—
155	C₄⋊C₄	—	38	1	no	—
156	C₄⋊C₄	—	38	1	no	—
157	C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
158	C₄²	—	38	1	no	—
159	C₄²	—	38	1	no	—
160	C₂³	D₄×D₁₉	1	1	yes	characteristic
161	Q₈	—	2	2	no	—
162	Q₈	—	2	2	no	—
163	Q₈	—	4	1	no	—
164	Q₈	—	4	1	no	—
165	C₂×C₄	—	2	2	no	—
166	C₂×C₄	—	2	2	no	—
167	C₂×C₄	—	4	1	no	—
168	C₂×C₄	—	4	1	no	—
169	C₂×C₄	—	4	1	no	—
170	C₂×C₄	—	4	1	no	—
171	C₂×C₄	—	38	1	no	—
172	C₂×C₄	—	38	1	no	—
173	C₂×C₄	—	38	2	no	—
174	C₂×C₄	—	38	1	no	—
175	C₂×C₄	—	38	1	no	—
176	C₂×C₄	—	38	1	no	—
177	C₂×C₄	—	38	1	no	—
178	C₂×C₄	—	76	1	no	—
179	C₂×C₄	—	76	1	no	—
180	C₂×C₄	—	76	1	no	—
181	C₂×C₄	—	76	1	no	—
182	C₂×C₄	—	76	1	no	—
183	C₂×C₄	C₂×Dic₃₈	1	1	yes	characteristic
184	C₂×C₄	#64541	1	1	yes	characteristic
185	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
186	C₂×C₄	#64543	1	1	yes	characteristic
187	C₂×C₄	#64543	1	1	yes	characteristic
188	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
189	C₈	—	4	1	no	—
190	C₈	—	76	1	no	—
191	C₂²	#10597324	1	1	yes	characteristic
192	C₂²	#10597331	1	1	yes	characteristic
193	C₂²	#10597361	1	1	yes	characteristic
194	C₂²	#10597362	1	1	yes	characteristic
195	C₂²	#10597364	1	1	yes	characteristic
196	C₂²	#10597365	1	1	yes	characteristic
197	C₂²	#10597383	1	1	yes	characteristic
198	C₄	—	4	2	no	—
199	C₄	—	4	2	no	—
200	C₄	—	76	1	no	—
201	C₄	—	76	1	no	—
202	C₄	—	76	2	no	—
203	C₄	—	152	1	no	—
204	C₄	#10597324	1	1	yes	characteristic
205	C₄	#10597331	1	1	yes	characteristic
206	C₄	#10597370	1	1	yes	characteristic
207	C₄	#10597382	1	1	yes	characteristic
208	C₂	#11926456	1	1	yes	characteristic
209	C₂	#11926703	1	1	yes	characteristic
210	C₂	#11926705	1	1	yes	characteristic
211	C₂	#11926849	1	1	yes	characteristic
212	C₂	#11926853	1	1	yes	characteristic
213	C₂	#11926900	1	1	yes	characteristic
214	C₂	#11926911	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597336

C₂

yes

maximal, characteristic

C₂×#10597292

C₂

yes

maximal, characteristic

#11926451

C₂

yes

maximal, characteristic

#11926307

C₂

yes

maximal, characteristic

#11926306

C₂

yes

maximal, characteristic

#11926298

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

—

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

#10597336

—

#10597336

—

C₁₉×#103

—

#10597292

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

Q₈

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

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

D₄

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

D₄

yes

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

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

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

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

—

—

C₂²×C₁₉

yes

C₂²×C₁₉

C₂²⋊Q₈

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₄×C₁₉

C₂²⋊Q₈

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

100

Dic₁₉

—

101

C₂×#125

—

102

C₂×#103

—

103

C₂×#103

D₁₉

yes

characteristic

104

#391

—

105

#340

—

106

#340

—

107

#336

—

108

C₂×C₁₉

#393

yes

characteristic

109

C₂×C₁₉

#452

yes

characteristic

110

C₂×C₁₉

#452

yes

characteristic

111

C₂×C₁₉

#479

yes

characteristic

112

C₂×C₁₉

#479

yes

characteristic

113

C₂×C₁₉

#488

yes

characteristic

114

C₂×C₁₉

#491

yes

characteristic

115

C₂²×Q₈

C₂×D₁₉

yes

characteristic

116

C₂²×C₈

—

117

C₂²×C₈

C₂×D₁₉

yes

characteristic

118

#125

—

119

#125

—

120

C₂×C₄⋊C₄

—

121

C₂×C₄⋊C₄

—

122

C₂×C₄⋊C₄

—

123

C₂×C₄⋊C₄

—

124

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

125

C₂×C₄²

—

126

#103

—

127

#103

—

128

#95

—

129

#95

—

130

C₁₉

#2026

yes

characteristic, complemented, Sylow

131

C₂×Q₈

—

132

C₂×Q₈

—

133

C₂×Q₈

—

134

C₂×Q₈

—

135

C₂×Q₈

—

136

C₂×Q₈

Dic₃₈

yes

—

137

C₂²×C₄

—

138

C₂²×C₄

—

139

C₂²×C₄

—

140

C₂²×C₄

—

141

C₂²×C₄

—

142

C₂²×C₄

—

143

C₂²×C₄

C₂²×D₁₉

yes

characteristic

144

C₂×C₈

—

145

C₂×C₈

—

146

C₂×C₈

—

147

C₂×C₈

—

148

C₂×C₈

—

149

C₂×C₈

—

150

C₄⋊C₄

—

151

C₄⋊C₄

—

152

C₄⋊C₄

—

153

C₄⋊C₄

—

154

C₄⋊C₄

—

155

C₄⋊C₄

—

156

C₄⋊C₄

—

157

C₄⋊C₄

C₂²⋊D₁₉

yes

—

158

C₄²

—

159

C₄²

—

160

C₂³

D₄×D₁₉

yes

characteristic

161

Q₈

—

162

Q₈

—

163

Q₈

—

164

Q₈

—

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

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

C₂×Dic₃₈

yes

characteristic

184

C₂×C₄

#64541

yes

characteristic

185

C₂×C₄

D₄×D₁₉

yes

characteristic

186

C₂×C₄

#64543

yes

characteristic

187

C₂×C₄

#64543

yes

characteristic

188

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

189

C₈

—

190

C₈

—

191

C₂²

#10597324

yes

characteristic

192

C₂²

#10597331

yes

characteristic

193

C₂²

#10597361

yes

characteristic

194

C₂²

#10597362

yes

characteristic

195

C₂²

#10597364

yes

characteristic

196

C₂²

#10597365

yes

characteristic

197

C₂²

#10597383

yes

characteristic

198

C₄

—

199

C₄

—

200

C₄

—

201

C₄

—

202

C₄

—

203

C₄

—

152

—

204

C₄

#10597324

yes

characteristic

205

C₄

#10597331

yes

characteristic

206

C₄

#10597370

yes

characteristic

207

C₄

#10597382

yes

characteristic

208

C₂

#11926456

yes

characteristic

209

C₂

#11926703

yes

characteristic

210

C₂

#11926705

yes

characteristic

211

C₂

#11926849

yes

characteristic

212

C₂

#11926853

yes

characteristic

213

C₂

#11926900

yes

characteristic

214

C₂

#11926911

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₁₉
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#103	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
hypercenter	C₂×#103	D₁₉
hypocenter	C₁₉	#2026
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#103

subgroup

G/H

center

C₂³

D₄×D₁₉

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#103

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#103

N	H ≅ G/N	type
130. C₁₉	#2026	semidirect

H ≅ G/N

type

130. C₁₉

#2026

semidirect

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

subgroup	index
C₂×#10597336	2
C₂×#10597292	2
#11926451	2
#11926307	2
#11926306	2
#11926298	2
C₂×C₁₉×#103	2
#2026	19

subgroup

index

C₂×C₁₉×#103

Subgroups — #14564784

Conjugacy classes of subgroups

Complements

Maximal subgroups