Group #18087285 — subgroups

Subgroups — #18087285

Order 4864.

350 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 119 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	#14564571	C₂	1	1	yes	maximal, characteristic
2	#14563763	C₂	1	1	yes	maximal, characteristic
3	#14563641	C₂	1	2	yes	maximal
4	#14561519	C₂	1	2	yes	maximal
5	C₁₉×#1277	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Dic₃₈	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
8	C₂×#10597273	—	2	2	no	—
9	#11926414	C₂²	1	2	yes	—
10	#11926307	—	2	2	no	—
11	#11926307	—	2	2	no	—
12	#11926298	—	2	2	no	—
13	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×Dic₃₈	D₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₉	—	2	2	no	—
17	C₂²×C₈×C₁₉	D₄	1	2	yes	—
18	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
19	C₂×C₄⋊Dic₁₉	—	2	2	no	—
20	C₂×C₄⋊Dic₁₉	—	2	2	no	—
21	C₂×C₄⋊Dic₁₉	—	2	2	no	—
22	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
23	C₂×Dic₁₉⋊C₄	—	2	1	no	—
24	C₂×C₄×Dic₁₉	—	2	1	no	—
25	C₂²×C₁₉⋊C₈	—	2	1	no	—
26	C₄×Dic₃₈	—	2	2	no	—
27	C₄×Dic₃₈	—	2	2	no	—
28	C₁₉×C₄⋊C₈	—	2	2	no	—
29	C₁₉×C₄⋊C₈	—	2	2	no	—
30	C₄×C₈×C₁₉	—	2	2	no	—
31	#10597273	—	4	4	no	—
32	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
33	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
34	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
35	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
36	C₂²×Dic₁₉	—	2	1	no	—
37	C₂²×Dic₁₉	—	2	1	no	—
38	C₂²×Dic₁₉	—	4	2	no	—
39	C₂×Dic₃₈	—	2	2	no	—
40	C₂×Dic₃₈	—	2	2	no	—
41	C₂×Dic₃₈	—	2	1	no	—
42	C₂×Dic₃₈	D₈	1	2	yes	—
43	C₂×C₈×C₁₉	—	2	2	no	—
44	C₂×C₈×C₁₉	—	2	2	no	—
45	C₂×C₈×C₁₉	—	2	2	no	—
46	C₂×C₈×C₁₉	—	4	2	no	—
47	C₂×C₈×C₁₉	—	4	2	no	—
48	C₂×C₈×C₁₉	—	4	2	no	—
49	C₄²×C₁₉	#41	1	2	yes	—
50	C₄²×C₁₉	#41	1	2	yes	—
51	C₄⋊Dic₁₉	—	2	2	no	—
52	C₄⋊Dic₁₉	—	4	2	no	—
53	C₄⋊Dic₁₉	—	4	2	no	—
54	C₄⋊Dic₁₉	—	4	2	no	—
55	C₄⋊Dic₁₉	—	4	2	no	—
56	C₄⋊Dic₁₉	—	8	2	no	—
57	Dic₁₉⋊C₄	—	4	2	no	—
58	C₄×Dic₁₉	—	4	1	no	—
59	C₄×Dic₁₉	—	4	1	no	—
60	C₂×C₁₉⋊C₈	—	4	1	no	—
61	C₂×C₁₉⋊C₈	—	4	2	no	—
62	#10623	—	19	1	no	maximal, Sylow
63	C₂³×C₁₉	#121	1	1	yes	characteristic
64	C₂×C₄×C₁₉	—	2	2	no	—
65	C₂×C₄×C₁₉	#123	1	2	yes	—
66	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
67	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
68	C₂×C₄×C₁₉	#126	1	2	yes	—
69	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
70	C₂×C₄×C₁₉	#135	1	2	yes	—
71	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
72	C₂×C₄×C₁₉	#137	1	2	yes	—
73	C₂×C₄×C₁₉	#137	1	2	yes	—
74	C₂×Dic₁₉	—	2	2	no	—
75	C₂×Dic₁₉	—	4	1	no	—
76	C₂×Dic₁₉	—	4	1	no	—
77	C₂×Dic₁₉	—	4	1	no	—
78	C₂×Dic₁₉	—	4	2	no	—
79	C₂×Dic₁₉	—	8	2	no	—
80	C₂×Dic₁₉	—	8	2	no	—
81	C₂×Dic₁₉	—	8	2	no	—
82	Dic₃₈	—	2	4	no	—
83	Dic₃₈	—	4	2	no	—
84	C₈×C₁₉	—	4	2	no	—
85	C₈×C₁₉	—	8	2	no	—
86	C₁₉⋊C₈	—	8	1	no	—
87	#1984	—	19	1	no	—
88	#1834	—	19	1	no	—
89	#1803	—	19	2	no	—
90	#1296	—	19	2	no	—
91	#1277	D₁₉	1	1	yes	characteristic
92	C₂²×C₁₉	#397	1	1	yes	characteristic
93	C₂²×C₁₉	#464	1	2	yes	—
94	C₂²×C₁₉	#466	1	1	yes	characteristic
95	C₂²×C₁₉	#470	1	1	yes	characteristic
96	C₂²×C₁₉	#471	1	2	yes	—
97	C₄×C₁₉	—	2	2	no	—
98	C₄×C₁₉	#480	1	2	yes	—
99	C₄×C₁₉	#485	1	2	yes	—
100	C₄×C₁₉	#485	1	2	yes	—
101	C₄×C₁₉	#488	1	1	yes	characteristic
102	C₄×C₁₉	#491	1	1	yes	characteristic
103	Dic₁₉	—	4	2	no	—
104	Dic₁₉	—	8	1	no	—
105	Dic₁₉	—	16	2	no	—
106	C₂×C₄×Q₈	—	19	1	no	—
107	C₂×C₄⋊C₈	—	19	1	no	—
108	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
109	C₂×#103	—	38	2	no	—
110	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
111	#384	—	19	2	no	—
112	#340	—	38	2	no	—
113	#340	—	38	2	no	—
114	#336	—	38	2	no	—
115	C₂×C₁₉	#1682	1	2	yes	—
116	C₂×C₁₉	#1704	1	2	yes	—
117	C₂×C₁₉	#2074	1	1	yes	characteristic
118	C₂×C₁₉	#2075	1	1	yes	characteristic
119	C₂×C₁₉	#2079	1	1	yes	characteristic
120	C₂²×Q₈	—	19	1	no	—
121	C₂²×C₈	—	2	2	no	—
122	C₂²×C₈	—	38	1	no	—
123	C₂²×C₈	D₇₆	1	2	yes	—
124	C₄×Q₈	—	38	2	no	—
125	C₄×Q₈	—	38	2	no	—
126	C₂×C₄⋊C₄	—	19	1	no	—
127	C₂×C₄⋊C₄	—	38	1	no	—
128	C₂×C₄⋊C₄	—	38	2	no	—
129	C₂×C₄⋊C₄	—	38	2	no	—
130	C₂×C₄⋊C₄	—	38	2	no	—
131	C₂×C₄²	—	38	1	no	—
132	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
133	C₄⋊C₈	—	2	2	no	—
134	C₄⋊C₈	—	2	2	no	—
135	C₄⋊C₈	—	38	2	no	—
136	#103	—	76	4	no	—
137	C₄×C₈	—	2	2	no	—
138	C₁₉	#10623	1	1	yes	characteristic, complemented, Sylow
139	C₂×Q₈	—	19	2	no	—
140	C₂×Q₈	—	38	1	no	—
141	C₂×Q₈	—	38	2	no	—
142	C₂×Q₈	—	38	2	no	—
143	C₂²×C₄	—	38	1	no	—
144	C₂²×C₄	—	38	1	no	—
145	C₂²×C₄	—	76	2	no	—
146	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
147	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
148	C₂²×C₄	#64545	1	1	yes	characteristic
149	C₂×C₈	—	2	2	no	—
150	C₂×C₈	—	2	2	no	—
151	C₂×C₈	—	2	2	no	—
152	C₂×C₈	—	4	2	no	—
153	C₂×C₈	—	4	2	no	—
154	C₂×C₈	—	4	2	no	—
155	C₂×C₈	—	76	1	no	—
156	C₂×C₈	—	76	2	no	—
157	C₄⋊C₄	—	38	2	no	—
158	C₄⋊C₄	—	76	2	no	—
159	C₄⋊C₄	—	76	2	no	—
160	C₄⋊C₄	—	76	2	no	—
161	C₄⋊C₄	—	76	2	no	—
162	C₄⋊C₄	—	76	2	no	—
163	C₄⋊C₄	—	152	2	no	—
164	C₄²	—	76	1	no	—
165	C₄²	—	76	1	no	—
166	C₄²	#64541	1	2	yes	—
167	C₄²	#64543	1	2	yes	—
168	C₂³	#10597341	1	1	yes	characteristic
169	Q₈	—	38	4	no	—
170	Q₈	—	76	2	no	—
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	—	38	2	no	—
173	C₂×C₄	—	76	1	no	—
174	C₂×C₄	—	76	1	no	—
175	C₂×C₄	—	76	2	no	—
176	C₂×C₄	—	76	1	no	—
177	C₂×C₄	—	152	2	no	—
178	C₂×C₄	—	152	2	no	—
179	C₂×C₄	—	152	2	no	—
180	C₂×C₄	#10597321	1	1	yes	characteristic
181	C₂×C₄	#10597329	1	2	yes	—
182	C₂×C₄	#10597332	1	1	yes	characteristic
183	C₂×C₄	#10597344	1	2	yes	—
184	C₂×C₄	#10597350	1	2	yes	—
185	C₂×C₄	#10597355	1	2	yes	—
186	C₂×C₄	D₈×D₁₉	1	1	yes	characteristic
187	C₂×C₄	#10597361	1	2	yes	—
188	C₂×C₄	#10597365	1	1	yes	characteristic
189	C₈	—	4	2	no	—
190	C₈	—	8	2	no	—
191	C₈	—	152	1	no	—
192	C₂²	#11926471	1	1	yes	characteristic
193	C₂²	#11926767	1	2	yes	—
194	C₂²	#11926781	1	1	yes	characteristic
195	C₂²	#11926803	1	1	yes	characteristic
196	C₂²	#11926808	1	2	yes	—
197	C₄	—	2	2	no	—
198	C₄	—	304	2	no	—
199	C₄	—	76	2	no	—
200	C₄	—	152	1	no	—
201	C₄	#11926856	1	2	yes	—
202	C₄	#11926884	1	2	yes	—
203	C₄	#11926886	1	2	yes	—
204	C₄	#11926899	1	1	yes	characteristic
205	C₄	#11926913	1	1	yes	characteristic
206	C₂	#14563080	1	2	yes	—
207	C₂	#14563218	1	2	yes	—
208	C₂	#14565055	1	1	yes	characteristic
209	C₂	#14565060	1	1	yes	characteristic
210	C₂	#14565082	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14564571

C₂

yes

maximal, characteristic

#14563763

C₂

yes

maximal, characteristic

#14563641

C₂

yes

maximal

#14561519

C₂

yes

maximal

C₁₉×#1277

C₂

yes

maximal, characteristic

C₂×C₄×Dic₃₈

C₂²

yes

characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×#10597273

—

#11926414

C₂²

yes

—

#11926307

—

#11926307

—

#11926298

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂²×Dic₃₈

D₄

yes

characteristic

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

D₄

yes

characteristic

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₄×C₈×C₁₉

—

#10597273

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

D₈

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

#41

yes

—

C₄²×C₁₉

#41

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#123

yes

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

#135

yes

characteristic

C₂×C₄×C₁₉

#137

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

—

—

—

—

D₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₄×C₁₉

—

C₄×C₁₉

#480

yes

—

C₄×C₁₉

#485

yes

—

100

C₄×C₁₉

#485

yes

—

101

C₄×C₁₉

#488

yes

characteristic

102

C₄×C₁₉

#491

yes

characteristic

103

Dic₁₉

—

104

Dic₁₉

—

105

Dic₁₉

—

106

C₂×C₄×Q₈

—

107

C₂×C₄⋊C₈

—

108

C₂×C₄⋊C₈

C₂×D₁₉

yes

—

109

C₂×#103

—

110

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

111

#384

—

112

#340

—

113

#340

—

114

#336

—

115

C₂×C₁₉

#1682

yes

—

116

C₂×C₁₉

#1704

yes

—

117

C₂×C₁₉

#2074

yes

characteristic

118

C₂×C₁₉

#2075

yes

characteristic

119

C₂×C₁₉

#2079

yes

characteristic

120

C₂²×Q₈

—

121

C₂²×C₈

—

122

C₂²×C₈

—

123

C₂²×C₈

D₇₆

yes

—

124

C₄×Q₈

—

125

C₄×Q₈

—

126

C₂×C₄⋊C₄

—

127

C₂×C₄⋊C₄

—

128

C₂×C₄⋊C₄

—

129

C₂×C₄⋊C₄

—

130

C₂×C₄⋊C₄

—

131

C₂×C₄²

—

132

C₂×C₄²

C₂²×D₁₉

yes

characteristic

133

C₄⋊C₈

—

134

C₄⋊C₈

—

135

C₄⋊C₈

—

136

#103

—

137

C₄×C₈

—

138

C₁₉

#10623

yes

characteristic, complemented, Sylow

139

C₂×Q₈

—

140

C₂×Q₈

—

141

C₂×Q₈

—

142

C₂×Q₈

—

143

C₂²×C₄

—

144

C₂²×C₄

—

145

C₂²×C₄

—

146

C₂²×C₄

C₂×D₇₆

yes

characteristic

147

C₂²×C₄

D₄×D₁₉

yes

characteristic

148

C₂²×C₄

#64545

yes

characteristic

149

C₂×C₈

—

150

C₂×C₈

—

151

C₂×C₈

—

152

C₂×C₈

—

153

C₂×C₈

—

154

C₂×C₈

—

155

C₂×C₈

—

156

C₂×C₈

—

157

C₄⋊C₄

—

158

C₄⋊C₄

—

159

C₄⋊C₄

—

160

C₄⋊C₄

—

161

C₄⋊C₄

—

162

C₄⋊C₄

—

163

C₄⋊C₄

—

152

—

164

C₄²

—

165

C₄²

—

166

C₄²

#64541

yes

—

167

C₄²

#64543

yes

—

168

C₂³

#10597341

yes

characteristic

169

Q₈

—

170

Q₈

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

152

—

178

C₂×C₄

—

152

—

179

C₂×C₄

—

152

—

180

C₂×C₄

#10597321

yes

characteristic

181

C₂×C₄

#10597329

yes

—

182

C₂×C₄

#10597332

yes

characteristic

183

C₂×C₄

#10597344

yes

—

184

C₂×C₄

#10597350

yes

—

185

C₂×C₄

#10597355

yes

—

186

C₂×C₄

D₈×D₁₉

yes

characteristic

187

C₂×C₄

#10597361

yes

—

188

C₂×C₄

#10597365

yes

characteristic

189

C₈

—

190

C₈

—

191

C₈

—

152

—

192

C₂²

#11926471

yes

characteristic

193

C₂²

#11926767

yes

—

194

C₂²

#11926781

yes

characteristic

195

C₂²

#11926803

yes

characteristic

196

C₂²

#11926808

yes

—

197

C₄

—

198

C₄

—

304

—

199

C₄

—

200

C₄

—

152

—

201

C₄

#11926856

yes

—

202

C₄

#11926884

yes

—

203

C₄

#11926886

yes

—

204

C₄

#11926899

yes

characteristic

205

C₄

#11926913

yes

characteristic

206

C₂

#14563080

yes

—

207

C₂

#14563218

yes

—

208

C₂

#14565055

yes

characteristic

209

C₂

#14565060

yes

characteristic

210

C₂

#14565082

yes

characteristic

	subgroup	G/H
center	C₂³	#10597341
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1277	C₂
socle, prime radical	C₂³×C₁₉	#121
hypercenter	#1277	D₁₉
hypocenter	C₁₉	#10623
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1277

subgroup

G/H

center

C₂³

#10597341

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1277

C₂

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1277

N	H ≅ G/N	type
138. C₁₉	#10623	semidirect

H ≅ G/N

type

138. C₁₉

#10623

semidirect

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

subgroup	index
#14564571	2
#14563763	2
#14563641	2
#14561519	2
C₁₉×#1277	2
#10623	19

subgroup

index

C₁₉×#1277

Subgroups — #18087285

Conjugacy classes of subgroups

Complements

Maximal subgroups