Group #18080098 — subgroups

Subgroups — #18080098

Order 4864.

508 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 99 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	#14574092	C₂	1	1	yes	maximal, characteristic
2	#14562361	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562181	C₂	1	2	yes	maximal
4	#14561499	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2381	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10597388	—	2	2	no	—
7	#11927094	C₂²	1	1	yes	characteristic
8	#11926936	—	2	2	no	—
9	#11926923	C₄	1	2	yes	complemented
10	#11926918	C₄	1	2	yes	complemented
11	#11926601	C₂²	1	2	yes	—
12	C₄×#64520	C₂²	1	1	yes	characteristic
13	#11926293	—	2	2	no	—
14	#11926277	—	2	4	no	—
15	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₁₉×#391	—	2	2	no	—
17	C₁₉×#387	—	2	4	no	—
18	C₁₉×#383	C₂²	1	2	yes	—
19	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
20	C₂×#64541	—	2	1	no	—
21	C₁₉×C₄⋊Q₈	—	2	2	no	—
22	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
23	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
24	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
25	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
26	C₂×C₄²×C₁₉	—	2	2	no	—
27	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
28	C₂×#64528	—	2	4	no	—
29	#10597388	—	4	4	no	—
30	#10597388	—	4	4	no	—
31	C₂×#64527	—	2	4	no	—
32	#10597376	—	2	2	no	—
33	C₂×#64520	—	2	1	no	—
34	#10597321	—	2	1	no	—
35	#10597320	C₂×C₄	1	1	yes	characteristic
36	C₄×D₇₆	—	2	2	no	—
37	#10597315	C₂×C₄	1	1	yes	characteristic
38	C₁₉×#95	—	2	4	no	—
39	C₁₉×#95	—	2	2	no	—
40	C₁₉×#95	—	2	2	no	—
41	C₁₉×#95	D₄	1	4	yes	—
42	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
43	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
44	#10597260	—	2	1	no	—
45	#10597260	—	2	2	no	—
46	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
47	C₂×Q₈×C₁₉	—	2	2	no	—
48	C₂×Q₈×C₁₉	—	4	2	no	—
49	C₂×Q₈×C₁₉	—	4	2	no	—
50	C₂×Q₈×C₁₉	C₂²⋊C₄	1	4	yes	—
51	C₂²×C₄×C₁₉	—	2	2	no	—
52	C₂²×C₄×C₁₉	—	2	4	no	—
53	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
55	C₂×C₂²⋊D₁₉	—	4	1	no	—
56	#64541	—	4	2	no	—
57	#64541	—	4	2	no	—
58	C₂×D₇₆	—	2	1	no	—
59	C₂×D₇₆	—	2	2	no	—
60	C₂×C₄×D₁₉	—	4	1	no	—
61	C₂×Dic₃₈	—	2	1	no	—
62	C₄⋊C₄×C₁₉	—	2	4	no	—
63	C₄⋊C₄×C₁₉	—	2	4	no	—
64	C₄⋊C₄×C₁₉	—	8	2	no	—
65	C₄²×C₁₉	—	8	2	no	—
66	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
67	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
68	C₄²×C₁₉	#41	1	2	yes	—
69	#64528	—	4	8	no	—
70	#64527	—	4	8	no	—
71	(C₂×D₁₉)⋊C₄	—	4	2	no	—
72	C₄⋊Dic₁₉	—	2	2	no	—
73	#64520	—	2	4	no	—
74	C₂×C₁₉⋊C₈	—	2	2	no	—
75	C₂×C₁₉⋊C₈	—	4	2	no	—
76	#9429	—	19	1	no	maximal, Sylow
77	C₂³×C₁₉	#120	1	1	yes	characteristic
78	C₂²×D₁₉	—	4	1	no	—
79	Q₈×C₁₉	—	4	4	no	—
80	Q₈×C₁₉	—	8	2	no	—
81	C₂×C₄×C₁₉	—	2	2	no	—
82	C₂×C₄×C₁₉	—	2	4	no	—
83	C₂×C₄×C₁₉	—	4	2	no	—
84	C₂×C₄×C₁₉	—	4	2	no	—
85	C₂×C₄×C₁₉	—	4	2	no	—
86	C₂×C₄×C₁₉	—	4	8	no	—
87	C₂×C₄×C₁₉	—	4	4	no	—
88	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
90	C₂×C₄×C₁₉	#121	1	2	yes	—
91	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
92	C₂²⋊D₁₉	—	8	2	no	—
93	C₂×Dic₁₉	—	4	1	no	—
94	D₇₆	—	4	2	no	—
95	D₇₆	—	8	2	no	—
96	C₄×D₁₉	—	8	1	no	—
97	C₄×D₁₉	—	8	1	no	—
98	Dic₃₈	—	4	2	no	—
99	C₁₉⋊C₈	—	2	4	no	—
100	C₁₉⋊C₈	—	8	2	no	—
101	#3152	—	19	1	no	—
102	#2381	D₁₉	1	1	yes	characteristic, complemented
103	#1558	—	19	1	no	—
104	#1514	—	19	2	no	—
105	#1288	—	19	2	no	—
106	C₂²×C₁₉	—	2	2	no	—
107	C₂²×C₁₉	#386	1	1	yes	characteristic
108	C₂²×C₁₉	#453	1	2	yes	—
109	C₂×D₁₉	—	8	1	no	—
110	C₂×D₁₉	—	8	2	no	—
111	C₄×C₁₉	—	2	1	no	—
112	C₄×C₁₉	—	2	1	no	—
113	C₄×C₁₉	—	2	2	no	—
114	C₄×C₁₉	—	2	2	no	—
115	C₄×C₁₉	—	4	4	no	—
116	C₄×C₁₉	—	8	4	no	—
117	Dic₁₉	—	8	1	no	—
118	C₂×#137	—	38	2	no	—
119	#532	—	19	1	no	—
120	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
121	#497	—	38	2	no	—
122	#494	—	19	2	no	—
123	#492	—	19	2	no	—
124	#432	—	19	2	no	—
125	C₄×M₁₆	—	19	1	no	—
126	#391	—	2	2	no	—
127	#387	—	2	4	no	—
128	#383	C₂×D₁₉	1	2	yes	—
129	#333	—	38	2	no	—
130	#327	—	38	4	no	—
131	C₂×C₁₉	—	2	2	no	—
132	C₂×C₁₉	#1887	1	1	yes	characteristic
133	C₂×C₁₉	#1905	1	2	yes	—
134	D₁₉	—	16	1	no	—
135	C₂×#41	—	38	1	no	—
136	C₂²×Q₈	C₂²⋊D₁₉	1	2	yes	—
137	#137	—	76	4	no	—
138	#137	—	76	4	no	—
139	C₂×Q₁₆	—	38	4	no	—
140	C₂×SD₁₆	—	38	4	no	—
141	C₂×M₁₆	—	38	1	no	—
142	C₄⋊Q₈	—	2	2	no	—
143	C₄⋊Q₈	—	19	1	no	—
144	C₄⋊Q₈	C₄×D₁₉	1	2	yes	—
145	C₄⋊Q₈	D₇₆	1	2	yes	—
146	#127	—	19	1	no	—
147	#124	—	38	1	no	—
148	#121	—	38	2	no	—
149	C₄×D₄	—	38	2	no	—
150	C₂×C₄⋊C₄	—	2	2	no	—
151	C₂×C₄⋊C₄	—	2	2	no	—
152	C₂×C₄²	—	2	2	no	—
153	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
154	C₄⋊C₈	—	38	2	no	—
155	C₂²⋊C₈	—	38	2	no	—
156	#97	—	38	1	no	—
157	#97	—	38	2	no	—
158	C₄×C₈	—	19	2	no	—
159	#95	—	2	4	no	—
160	#95	—	2	2	no	—
161	#95	—	2	2	no	—
162	#95	C₂²⋊D₁₉	1	4	yes	—
163	C₁₉	#9429	1	1	yes	characteristic, complemented, Sylow
164	#41	—	76	2	no	—
165	#41	—	76	2	no	—
166	C₂×Q₈	—	2	2	no	—
167	C₂×Q₈	—	4	2	no	—
168	C₂×Q₈	—	4	2	no	—
169	C₂×Q₈	—	38	1	no	—
170	C₂×Q₈	(C₂×D₁₉)⋊C₄	1	4	yes	—
171	C₂×D₄	—	38	1	no	—
172	C₂×D₄	—	38	2	no	—
173	C₂×D₄	—	76	1	no	—
174	C₂²×C₄	—	2	2	no	—
175	C₂²×C₄	—	2	4	no	—
176	C₂²×C₄	—	76	1	no	—
177	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
178	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
179	Q₁₆	—	76	8	no	—
180	SD₁₆	—	76	8	no	—
181	M₁₆	—	38	4	no	—
182	C₂×C₈	—	38	2	no	—
183	C₂×C₈	—	76	2	no	—
184	C₄⋊C₄	—	2	4	no	—
185	C₄⋊C₄	—	2	4	no	—
186	C₄⋊C₄	—	8	2	no	—
187	C₄⋊C₄	—	38	2	no	—
188	C₂²⋊C₄	—	76	2	no	—
189	C₄²	—	8	2	no	—
190	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
191	C₄²	C₂×D₇₆	1	1	yes	characteristic
192	C₄²	#64541	1	2	yes	—
193	C₂³	—	76	1	no	—
194	C₂³	#10597399	1	1	yes	characteristic
195	Q₈	—	4	4	no	—
196	Q₈	—	8	2	no	—
197	Q₈	—	76	2	no	—
198	D₄	—	76	2	no	—
199	D₄	—	152	2	no	—
200	D₄	—	152	2	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	4	no	—
203	C₂×C₄	—	4	2	no	—
204	C₂×C₄	—	4	2	no	—
205	C₂×C₄	—	4	2	no	—
206	C₂×C₄	—	4	8	no	—
207	C₂×C₄	—	4	4	no	—
208	C₂×C₄	—	76	1	no	—
209	C₂×C₄	—	152	1	no	—
210	C₂×C₄	—	152	1	no	—
211	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
212	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
213	C₂×C₄	#10597375	1	1	yes	characteristic
214	C₂×C₄	#10597376	1	2	yes	—
215	C₈	—	38	4	no	—
216	C₈	—	152	2	no	—
217	C₂²	—	2	2	no	—
218	C₂²	—	152	2	no	—
219	C₂²	—	152	1	no	—
220	C₂²	#11926423	1	1	yes	characteristic
221	C₂²	#11926712	1	2	yes	—
222	C₄	—	2	2	no	—
223	C₄	—	2	2	no	—
224	C₄	—	2	1	no	—
225	C₄	—	2	1	no	—
226	C₄	—	4	4	no	—
227	C₄	—	8	4	no	—
228	C₄	—	152	1	no	—
229	C₂	—	2	2	no	—
230	C₂	—	304	1	no	—
231	C₂	#14564033	1	1	yes	characteristic
232	C₂	#14564129	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14574092

C₂

yes

maximal, characteristic

#14562361

C₂

yes

maximal, characteristic, complemented

#14562181

C₂

yes

maximal

#14561499

C₂

yes

maximal, complemented

C₁₉×#2381

C₂

yes

maximal, characteristic, complemented

C₂×#10597388

—

#11927094

C₂²

yes

characteristic

#11926936

—

#11926923

C₄

yes

complemented

#11926918

C₄

yes

complemented

#11926601

C₂²

yes

—

C₄×#64520

C₂²

yes

characteristic

#11926293

—

#11926277

—

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×#391

—

C₁₉×#387

—

C₁₉×#383

C₂²

yes

—

C₂²×Q₈×C₁₉

D₄

yes

—

C₂×#64541

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

—

—

—

—

—

—

—

C₂×C₄

yes

characteristic

C₄×D₇₆

—

#10597315

C₂×C₄

yes

characteristic

C₁₉×#95

—

C₁₉×#95

—

C₁₉×#95

—

C₁₉×#95

D₄

yes

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

#10597260

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₂²⋊D₁₉

—

#64541

—

#64541

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

#41

yes

—

#64528

—

#64527

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

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×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

#123

yes

characteristic

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

C₄×D₁₉

—

C₄×D₁₉

—

Dic₃₈

—

C₁₉⋊C₈

—

100

C₁₉⋊C₈

—

101

#3152

—

102

#2381

D₁₉

yes

characteristic, complemented

103

#1558

—

104

#1514

—

105

#1288

—

106

C₂²×C₁₉

—

107

C₂²×C₁₉

#386

yes

characteristic

108

C₂²×C₁₉

#453

yes

—

109

C₂×D₁₉

—

110

C₂×D₁₉

—

111

C₄×C₁₉

—

112

C₄×C₁₉

—

113

C₄×C₁₉

—

114

C₄×C₁₉

—

115

C₄×C₁₉

—

116

C₄×C₁₉

—

117

Dic₁₉

—

118

C₂×#137

—

119

#532

—

120

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

121

#497

—

122

#494

—

123

#492

—

124

#432

—

125

C₄×M₁₆

—

126

#391

—

127

#387

—

128

#383

C₂×D₁₉

yes

—

129

#333

—

130

#327

—

131

C₂×C₁₉

—

132

C₂×C₁₉

#1887

yes

characteristic

133

C₂×C₁₉

#1905

yes

—

134

D₁₉

—

135

C₂×#41

—

136

C₂²×Q₈

C₂²⋊D₁₉

yes

—

137

#137

—

138

#137

—

139

C₂×Q₁₆

—

140

C₂×SD₁₆

—

141

C₂×M₁₆

—

142

C₄⋊Q₈

—

143

C₄⋊Q₈

—

144

C₄⋊Q₈

C₄×D₁₉

yes

—

145

C₄⋊Q₈

D₇₆

yes

—

146

#127

—

147

#124

—

148

#121

—

149

C₄×D₄

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

—

152

C₂×C₄²

—

153

C₂×C₄²

C₂²×D₁₉

yes

characteristic

154

C₄⋊C₈

—

155

C₂²⋊C₈

—

156

#97

—

157

#97

—

158

C₄×C₈

—

159

#95

—

160

#95

—

161

#95

—

162

#95

C₂²⋊D₁₉

yes

—

163

C₁₉

#9429

yes

characteristic, complemented, Sylow

164

#41

—

165

#41

—

166

C₂×Q₈

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂×Q₈

(C₂×D₁₉)⋊C₄

yes

—

171

C₂×D₄

—

172

C₂×D₄

—

173

C₂×D₄

—

174

C₂²×C₄

—

175

C₂²×C₄

—

176

C₂²×C₄

—

177

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

178

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

179

Q₁₆

—

180

SD₁₆

—

181

M₁₆

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₂²⋊C₄

—

189

C₄²

—

190

C₄²

C₂×C₄×D₁₉

yes

characteristic

191

C₄²

C₂×D₇₆

yes

characteristic

192

C₄²

#64541

yes

—

193

C₂³

—

194

C₂³

#10597399

yes

characteristic

195

Q₈

—

196

Q₈

—

197

Q₈

—

198

D₄

—

199

D₄

—

152

—

200

D₄

—

152

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

152

—

210

C₂×C₄

—

152

—

211

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

212

C₂×C₄

C₄×C₂²⋊D₁₉

yes

—

213

C₂×C₄

#10597375

yes

characteristic

214

C₂×C₄

#10597376

yes

—

215

C₈

—

216

C₈

—

152

—

217

C₂²

—

218

C₂²

—

152

—

219

C₂²

—

152

—

220

C₂²

#11926423

yes

characteristic

221

C₂²

#11926712

yes

—

222

C₄

—

223

C₄

—

224

C₄

—

225

C₄

—

226

C₄

—

227

C₄

—

228

C₄

—

152

—

229

C₂

—

230

C₂

—

304

—

231

C₂

#14564033

yes

characteristic

232

C₂

#14564129

yes

—

	subgroup	G/H
center	C₂²	#11926423
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2381	C₂
socle	C₂²×C₁₉	#386
prime radical	#11927094	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2381	D₁₉
hypocenter	C₁₉	#9429
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2381

subgroup

G/H

center

C₂²

#11926423

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2381

C₂

C₂²×C₁₉

C₂²

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2381

N	H ≅ G/N	type
2. #14562361	C₂	semidirect
4. #14561499	C₂	semidirect
5. C₁₉×#2381	C₂	semidirect
9. #11926923	C₄	semidirect
10. #11926918	C₄	semidirect
102. #2381	D₁₉	semidirect
163. C₁₉	#9429	semidirect

H ≅ G/N

type

2. #14562361

C₂

semidirect

4. #14561499

C₂

semidirect

5. C₁₉×#2381

C₂

semidirect

9. #11926923

C₄

semidirect

10. #11926918

C₄

semidirect

102. #2381

D₁₉

semidirect

163. C₁₉

#9429

semidirect

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

subgroup	index
#14574092	2
#14562361	2
#14562181	2
#14561499	2
C₁₉×#2381	2
#9429	19

subgroup

index

C₁₉×#2381

Subgroups — #18080098

Conjugacy classes of subgroups

Complements

Maximal subgroups