Group #14574592 — subgroups

Subgroups — #14574592

Order 2432.

394 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 117 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	#11927099	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927092	C₂	1	1	yes	maximal, characteristic
3	#11926924	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926916	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926896	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926765	C₂	1	4	yes	maximal, complemented
7	#11926707	C₂	1	4	yes	maximal, complemented
8	#11926595	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#486	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#64543	C₂²	1	2	yes	—
11	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₁₉×#127	C₂²	1	1	yes	characteristic
13	#10597392	—	2	1	no	—
14	Q₈×Dic₁₉	—	2	1	no	—
15	#10597384	—	2	1	no	—
16	#10597384	—	2	1	no	—
17	#10597382	C₂²	1	2	yes	—
18	D₄×Dic₁₉	—	2	1	no	—
19	D₄×Dic₁₉	—	2	1	no	—
20	C₂×#64526	C₂²	1	4	yes	—
21	C₂×Dic₇₆	C₂²	1	4	yes	—
22	#10597343	C₂²	1	2	yes	—
23	#10597338	—	2	1	no	—
24	#10597336	—	2	1	no	—
25	#10597333	C₂²	1	2	yes	—
26	C₄²×D₁₉	C₂²	1	1	yes	characteristic
27	#10597315	C₂²	1	1	yes	characteristic
28	#10597315	C₂²	1	1	yes	characteristic
29	C₁₉×#102	C₂²	1	4	yes	—
30	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
31	(C₂×D₁₉)⋊C₈	C₂²	1	2	yes	—
32	Dic₁₉⋊C₈	C₂²	1	2	yes	—
33	#10597267	C₂²	1	4	yes	—
34	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×Q₈×C₁₉	—	2	1	no	—
36	C₂×D₄×C₁₉	—	2	1	no	—
37	C₂×D₄×C₁₉	—	2	1	no	—
38	C₂×D₄×C₁₉	C₂³	1	2	yes	—
39	C₂×C₂²⋊D₁₉	—	2	2	no	—
40	C₂²×Dic₁₉	—	2	2	no	—
41	#64543	—	4	4	no	—
42	C₂×C₄×D₁₉	D₄	1	1	yes	characteristic
43	C₂×C₄×D₁₉	D₄	1	1	yes	characteristic
44	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
45	C₂×Dic₃₈	C₂³	1	2	yes	—
46	C₂×Dic₃₈	C₂³	1	2	yes	—
47	C₂×C₈×C₁₉	C₂³	1	2	yes	—
48	C₄⋊C₄×C₁₉	—	2	1	no	—
49	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
50	C₄²×C₁₉	C₂³	1	1	yes	characteristic
51	C₂²⋊Dic₁₉	—	2	2	no	—
52	C₂²⋊Dic₁₉	—	2	2	no	—
53	#64526	—	4	4	no	—
54	(C₂×D₁₉)⋊C₄	—	2	2	no	—
55	C₄⋊Dic₁₉	—	2	1	no	—
56	C₄⋊Dic₁₉	—	2	1	no	—
57	C₄⋊Dic₁₉	—	2	1	no	—
58	C₄⋊Dic₁₉	—	2	1	no	—
59	C₄⋊Dic₁₉	—	2	2	no	—
60	Dic₁₉⋊C₄	—	2	2	no	—
61	C₄×Dic₁₉	—	2	2	no	—
62	C₄×Dic₁₉	D₄	1	1	yes	characteristic
63	C₄×Dic₁₉	D₄	1	1	yes	characteristic
64	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
65	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
66	Dic₇₆	—	4	4	no	—
67	C₂³×C₁₉	—	2	2	no	—
68	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
69	Q₈×C₁₉	—	4	2	no	—
70	D₄×C₁₉	—	2	4	no	—
71	D₄×C₁₉	—	4	2	no	—
72	D₄×C₁₉	—	4	2	no	—
73	C₂×C₄×C₁₉	—	2	2	no	—
74	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
75	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
76	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
77	C₂²⋊D₁₉	—	4	4	no	—
78	C₂×Dic₁₉	—	2	2	no	—
79	C₂×Dic₁₉	—	2	2	no	—
80	C₂×Dic₁₉	—	4	4	no	—
81	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
82	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
83	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
84	C₄×D₁₉	—	2	2	no	—
85	C₄×D₁₉	—	2	2	no	—
86	C₄×D₁₉	—	2	2	no	—
87	Dic₃₈	—	2	4	no	—
88	Dic₃₈	—	2	4	no	—
89	C₈×C₁₉	—	2	2	no	—
90	C₁₉⋊C₈	—	2	2	no	—
91	#3210	—	19	1	no	maximal, Sylow
92	C₂²×C₁₉	—	4	2	no	—
93	C₂²×C₁₉	—	4	2	no	—
94	C₂²×C₁₉	—	4	2	no	—
95	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
96	C₂×D₁₉	—	2	1	no	—
97	C₂×D₁₉	—	2	1	no	—
98	C₂×D₁₉	—	2	1	no	—
99	C₄×C₁₉	—	4	2	no	—
100	C₄×C₁₉	#135	1	2	yes	—
101	C₄×C₁₉	#137	1	2	yes	—
102	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
103	Dic₁₉	—	2	1	no	—
104	Dic₁₉	—	2	1	no	—
105	Dic₁₉	—	2	1	no	—
106	Dic₁₉	—	4	2	no	—
107	Dic₁₉	—	4	2	no	—
108	#533	—	19	1	no	—
109	#532	—	19	1	no	—
110	#494	—	19	1	no	—
111	#492	—	19	1	no	—
112	#487	—	19	1	no	—
113	#486	D₁₉	1	1	yes	characteristic, complemented
114	#464	—	19	4	no	—
115	#452	—	19	4	no	—
116	#431	—	19	1	no	—
117	C₂×C₁₉	—	8	2	no	—
118	C₂×C₁₉	#535	1	1	yes	characteristic
119	C₂×C₁₉	C₂×#135	1	1	yes	characteristic
120	C₂×C₁₉	C₂×#137	1	1	yes	characteristic
121	D₁₉	—	4	1	no	—
122	C₂×#41	—	19	2	no	—
123	C₂×Q₁₆	—	19	4	no	—
124	C₂×SD₁₆	—	19	4	no	—
125	C₄⋊Q₈	—	19	1	no	—
126	C₄⋊Q₈	—	19	1	no	—
127	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
128	#127	C₂×D₁₉	1	1	yes	characteristic
129	#125	—	38	1	no	—
130	#124	—	19	2	no	—
131	C₂²⋊Q₈	—	19	2	no	—
132	C₂²⋊Q₈	—	38	1	no	—
133	#121	—	38	1	no	—
134	#121	—	38	1	no	—
135	C₄×Q₈	—	19	2	no	—
136	C₄×Q₈	—	38	1	no	—
137	C₄×D₄	—	38	1	no	—
138	C₄×D₄	—	38	1	no	—
139	#117	—	38	1	no	—
140	C₂×C₄²	—	19	1	no	—
141	C₄⋊C₈	—	19	2	no	—
142	#103	—	19	4	no	—
143	#102	C₂×D₁₉	1	4	yes	—
144	C₂²⋊C₈	—	19	2	no	—
145	C₄×C₈	—	19	1	no	—
146	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
147	C₁₉	#3210	1	1	yes	characteristic, complemented, Sylow
148	#41	—	76	4	no	—
149	C₂×Q₈	—	2	1	no	—
150	C₂×Q₈	—	19	2	no	—
151	C₂×Q₈	—	19	2	no	—
152	C₂×D₄	—	2	1	no	—
153	C₂×D₄	—	2	1	no	—
154	C₂×D₄	—	38	2	no	—
155	C₂×D₄	C₂²×D₁₉	1	2	yes	—
156	C₂²×C₄	—	19	1	no	—
157	C₂²×C₄	—	19	1	no	—
158	C₂²×C₄	—	19	1	no	—
159	C₂²×C₄	—	38	2	no	—
160	Q₁₆	—	76	4	no	—
161	SD₁₆	—	76	4	no	—
162	C₂×C₈	—	19	2	no	—
163	C₂×C₈	C₂²×D₁₉	1	2	yes	—
164	C₄⋊C₄	—	2	1	no	—
165	C₄⋊C₄	—	38	2	no	—
166	C₄⋊C₄	—	38	2	no	—
167	C₄⋊C₄	—	38	1	no	—
168	C₄⋊C₄	—	38	1	no	—
169	C₄⋊C₄	—	38	1	no	—
170	C₄⋊C₄	—	38	1	no	—
171	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
172	C₂²⋊C₄	—	38	2	no	—
173	C₂²⋊C₄	—	38	2	no	—
174	C₂²⋊C₄	—	38	2	no	—
175	C₄²	—	19	1	no	—
176	C₄²	—	19	1	no	—
177	C₄²	—	19	1	no	—
178	C₄²	—	38	2	no	—
179	C₄²	C₂²×D₁₉	1	1	yes	characteristic
180	C₂³	—	2	2	no	—
181	C₂³	—	19	1	no	—
182	Q₈	—	4	2	no	—
183	Q₈	—	38	4	no	—
184	Q₈	—	38	4	no	—
185	D₄	—	2	4	no	—
186	D₄	—	4	2	no	—
187	D₄	—	4	2	no	—
188	D₄	—	76	4	no	—
189	C₂×C₄	—	2	2	no	—
190	C₂×C₄	—	19	1	no	—
191	C₂×C₄	—	19	1	no	—
192	C₂×C₄	—	19	1	no	—
193	C₂×C₄	—	38	2	no	—
194	C₂×C₄	—	38	2	no	—
195	C₂×C₄	—	38	2	no	—
196	C₂×C₄	—	38	2	no	—
197	C₂×C₄	—	38	2	no	—
198	C₂×C₄	—	76	4	no	—
199	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
200	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
201	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
202	C₈	—	2	2	no	—
203	C₈	—	38	2	no	—
204	C₂²	—	4	2	no	—
205	C₂²	—	4	2	no	—
206	C₂²	—	4	2	no	—
207	C₂²	—	38	1	no	—
208	C₂²	—	38	1	no	—
209	C₂²	—	38	1	no	—
210	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
211	C₄	—	4	2	no	—
212	C₄	—	38	1	no	—
213	C₄	—	38	1	no	—
214	C₄	—	38	1	no	—
215	C₄	—	76	2	no	—
216	C₄	—	76	2	no	—
217	C₄	#10597358	1	2	yes	—
218	C₄	#10597361	1	2	yes	—
219	C₄	#10597435	1	2	yes	—
220	C₂	—	8	2	no	—
221	C₂	—	76	1	no	—
222	C₂	#11927112	1	1	yes	characteristic
223	C₂	C₂×#10597358	1	1	yes	characteristic
224	C₂	C₂×#10597361	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927099

C₂

yes

maximal, characteristic, complemented

#11927092

C₂

yes

maximal, characteristic

#11926924

C₂

yes

maximal, characteristic, complemented

#11926916

C₂

yes

maximal, characteristic, complemented

#11926896

C₂

yes

maximal, characteristic, complemented

#11926765

C₂

yes

maximal, complemented

#11926707

C₂

yes

maximal, complemented

#11926595

C₂

yes

maximal, characteristic, complemented

C₁₉×#486

C₂

yes

maximal, characteristic, complemented

C₂×#64543

C₂²

yes

—

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×#127

C₂²

yes

characteristic

#10597392

—

Q₈×Dic₁₉

—

#10597384

—

#10597384

—

#10597382

C₂²

yes

—

D₄×Dic₁₉

—

D₄×Dic₁₉

—

C₂×#64526

C₂²

yes

—

C₂×Dic₇₆

C₂²

yes

—

#10597343

C₂²

yes

—

#10597338

—

#10597336

—

#10597333

C₂²

yes

—

C₄²×D₁₉

C₂²

yes

characteristic

#10597315

C₂²

yes

characteristic

#10597315

C₂²

yes

characteristic

C₁₉×#102

C₂²

yes

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

(C₂×D₁₉)⋊C₈

C₂²

yes

—

Dic₁₉⋊C₈

C₂²

yes

—

#10597267

C₂²

yes

—

C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂³

yes

—

C₂×C₂²⋊D₁₉

—

C₂²×Dic₁₉

—

#64543

—

C₂×C₄×D₁₉

D₄

yes

characteristic

C₂×C₄×D₁₉

D₄

yes

characteristic

C₂×C₄×D₁₉

C₂³

yes

characteristic

C₂×Dic₃₈

C₂³

yes

—

C₂×Dic₃₈

C₂³

yes

—

C₂×C₈×C₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂³

yes

—

C₄²×C₁₉

C₂³

yes

characteristic

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

#64526

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

D₄

yes

characteristic

C₄×Dic₁₉

D₄

yes

characteristic

C₄×Dic₁₉

C₂³

yes

characteristic

C₂×C₁₉⋊C₈

C₂³

yes

—

Dic₇₆

—

C₂³×C₁₉

—

C₂²×D₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

C₂×D₄

yes

characteristic

C₄×D₁₉

—

C₄×D₁₉

—

C₄×D₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#3210

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

100

C₄×C₁₉

#135

yes

—

101

C₄×C₁₉

#137

yes

—

102

C₄×C₁₉

H(5,𝔽₂)

yes

—

103

Dic₁₉

—

104

Dic₁₉

—

105

Dic₁₉

—

106

Dic₁₉

—

107

Dic₁₉

—

108

#533

—

109

#532

—

110

#494

—

111

#492

—

112

#487

—

113

#486

D₁₉

yes

characteristic, complemented

114

#464

—

115

#452

—

116

#431

—

117

C₂×C₁₉

—

118

C₂×C₁₉

#535

yes

characteristic

119

C₂×C₁₉

C₂×#135

yes

characteristic

120

C₂×C₁₉

C₂×#137

yes

characteristic

121

D₁₉

—

122

C₂×#41

—

123

C₂×Q₁₆

—

124

C₂×SD₁₆

—

125

C₄⋊Q₈

—

126

C₄⋊Q₈

—

127

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

128

#127

C₂×D₁₉

yes

characteristic

129

#125

—

130

#124

—

131

C₂²⋊Q₈

—

132

C₂²⋊Q₈

—

133

#121

—

134

#121

—

135

C₄×Q₈

—

136

C₄×Q₈

—

137

C₄×D₄

—

138

C₄×D₄

—

139

#117

—

140

C₂×C₄²

—

141

C₄⋊C₈

—

142

#103

—

143

#102

C₂×D₁₉

yes

—

144

C₂²⋊C₈

—

145

C₄×C₈

—

146

C₄×C₈

C₂×D₁₉

yes

characteristic

147

C₁₉

#3210

yes

characteristic, complemented, Sylow

148

#41

—

149

C₂×Q₈

—

150

C₂×Q₈

—

151

C₂×Q₈

—

152

C₂×D₄

—

153

C₂×D₄

—

154

C₂×D₄

—

155

C₂×D₄

C₂²×D₁₉

yes

—

156

C₂²×C₄

—

157

C₂²×C₄

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

Q₁₆

—

161

SD₁₆

—

162

C₂×C₈

—

163

C₂×C₈

C₂²×D₁₉

yes

—

164

C₄⋊C₄

—

165

C₄⋊C₄

—

166

C₄⋊C₄

—

167

C₄⋊C₄

—

168

C₄⋊C₄

—

169

C₄⋊C₄

—

170

C₄⋊C₄

—

171

C₄⋊C₄

C₂²×D₁₉

yes

—

172

C₂²⋊C₄

—

173

C₂²⋊C₄

—

174

C₂²⋊C₄

—

175

C₄²

—

176

C₄²

—

177

C₄²

—

178

C₄²

—

179

C₄²

C₂²×D₁₉

yes

characteristic

180

C₂³

—

181

C₂³

—

182

Q₈

—

183

Q₈

—

184

Q₈

—

185

D₄

—

186

D₄

—

187

D₄

—

188

D₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

D₄×D₁₉

yes

characteristic

200

C₂×C₄

D₄×D₁₉

yes

characteristic

201

C₂×C₄

C₂³×D₁₉

yes

characteristic

202

C₈

—

203

C₈

—

204

C₂²

—

205

C₂²

—

206

C₂²

—

207

C₂²

—

208

C₂²

—

209

C₂²

—

210

C₂²

C₂×D₄×D₁₉

yes

characteristic

211

C₄

—

212

C₄

—

213

C₄

—

214

C₄

—

215

C₄

—

216

C₄

—

217

C₄

#10597358

yes

—

218

C₄

#10597361

yes

—

219

C₄

#10597435

yes

—

220

C₂

—

221

C₂

—

222

C₂

#11927112

yes

characteristic

223

C₂

C₂×#10597358

yes

characteristic

224

C₂

C₂×#10597361

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#486	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	#11927092	C₂
hypercenter	#486	D₁₉
hypocenter	C₁₉	#3210
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #486

subgroup

G/H

center

C₂²

C₂×D₄×D₁₉

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₁₉×#486

C₂

socle

C₂²×C₁₉

C₂²×D₄

C₂

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #486

N	H ≅ G/N	type
1. #11927099	C₂	semidirect
3. #11926924	C₂	semidirect
4. #11926916	C₂	semidirect
5. #11926896	C₂	semidirect
6. #11926765	C₂	semidirect
7. #11926707	C₂	semidirect
8. #11926595	C₂	semidirect
9. C₁₉×#486	C₂	semidirect
113. #486	D₁₉	semidirect
147. C₁₉	#3210	semidirect

H ≅ G/N

type

1. #11927099

C₂

semidirect

3. #11926924

C₂

semidirect

4. #11926916

C₂

semidirect

5. #11926896

C₂

semidirect

6. #11926765

C₂

semidirect

7. #11926707

C₂

semidirect

8. #11926595

C₂

semidirect

9. C₁₉×#486

C₂

semidirect

113. #486

D₁₉

semidirect

147. C₁₉

#3210

semidirect

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

subgroup	index
#11927099	2
#11927092	2
#11926924	2
#11926916	2
#11926896	2
#11926765	2
#11926707	2
#11926595	2
C₁₉×#486	2
#3210	19

subgroup

index

C₁₉×#486

Subgroups — #14574592

Conjugacy classes of subgroups

Complements

Maximal subgroups