Group #18084831 — subgroups

Subgroups — #18084831

Order 4864.

466 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 105 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	#14574776	C₂	1	2	yes	maximal
2	#14564455	C₂	1	1	yes	maximal, characteristic
3	#14562199	C₂	1	2	yes	maximal
4	#14561480	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#3162	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597315	C₂²	1	1	yes	characteristic
7	#11926940	—	2	2	no	—
8	#11926894	—	2	2	no	—
9	#11926872	—	2	4	no	—
10	#11926829	—	2	4	no	—
11	#11926597	C₂²	1	2	yes	—
12	C₂×#10597273	—	2	2	no	—
13	#11926410	C₂²	1	1	yes	characteristic
14	#11926281	—	2	4	no	—
15	C₁₉×#533	C₂²	1	2	yes	—
16	C₁₉×#501	—	2	2	no	—
17	C₁₉×#501	—	2	2	no	—
18	C₁₉×#427	—	2	2	no	—
19	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
20	C₂²×Dic₃₈	—	2	1	no	—
21	C₂²×C₈×C₁₉	D₄	1	2	yes	—
22	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
23	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
24	C₁₉×#125	—	2	2	no	—
25	C₁₉×C₂²⋊Q₈	—	2	2	no	—
26	C₁₉×C₂²⋊Q₈	—	2	2	no	—
27	C₄×Q₈×C₁₉	—	2	2	no	—
28	C₄×Q₈×C₁₉	—	2	2	no	—
29	C₁₉×#117	—	2	2	no	—
30	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
31	C₂×C₄⋊Dic₁₉	—	2	2	no	—
32	C₂×C₄⋊Dic₁₉	—	2	1	no	—
33	#10597315	—	2	2	no	—
34	#10597315	—	2	1	no	—
35	#10597315	D₄	1	2	yes	—
36	C₁₉×#107	—	2	4	no	—
37	C₁₉×#106	—	2	2	no	—
38	C₁₉×#106	—	2	2	no	—
39	C₁₉×#97	—	2	2	no	—
40	#10597292	—	2	8	no	—
41	C₁₉⋊#95	—	2	2	no	—
42	C₂²⋊(C₁₉⋊C₈)	D₄	1	4	yes	—
43	#10597273	—	4	4	no	—
44	#10597265	—	2	8	no	—
45	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
46	C₄×C₁₉⋊C₈	—	2	2	no	—
47	C₂×Q₈×C₁₉	—	2	2	no	—
48	C₂×Q₈×C₁₉	—	2	2	no	—
49	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
50	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂²×Dic₁₉	—	4	1	no	—
52	C₂²×Dic₁₉	—	4	1	no	—
53	C₂×Dic₃₈	—	2	2	no	—
54	C₂×Dic₃₈	—	4	2	no	—
55	C₂×Dic₃₈	—	4	2	no	—
56	C₂×Dic₃₈	—	4	1	no	—
57	C₂×C₈×C₁₉	—	2	2	no	—
58	C₂×C₈×C₁₉	—	2	2	no	—
59	C₂×C₈×C₁₉	SD₁₆	1	4	yes	—
60	C₄⋊C₄×C₁₉	—	2	2	no	—
61	C₄⋊C₄×C₁₉	—	2	2	no	—
62	C₄⋊C₄×C₁₉	—	2	2	no	—
63	C₄⋊C₄×C₁₉	—	2	2	no	—
64	C₄⋊C₄×C₁₉	—	4	2	no	—
65	C₄⋊C₄×C₁₉	—	4	2	no	—
66	C₂²⋊C₄×C₁₉	—	4	2	no	—
67	C₄²×C₁₉	—	4	2	no	—
68	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
69	C₄²×C₁₉	C₂×D₄	1	2	yes	—
70	C₄²×C₁₉	#41	1	1	yes	characteristic
71	C₄⋊Dic₁₉	—	2	4	no	—
72	C₄⋊Dic₁₉	—	4	2	no	—
73	C₄⋊Dic₁₉	—	4	2	no	—
74	C₂×C₁₉⋊C₈	—	2	4	no	—
75	#10227	—	19	1	no	maximal, Sylow
76	C₂³×C₁₉	#127	1	1	yes	characteristic
77	Q₈×C₁₉	—	4	4	no	—
78	Q₈×C₁₉	—	8	2	no	—
79	C₂×C₄×C₁₉	—	4	2	no	—
80	C₂×C₄×C₁₉	—	4	2	no	—
81	C₂×C₄×C₁₉	—	4	2	no	—
82	C₂×C₄×C₁₉	#120	1	2	yes	—
83	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
84	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
85	C₂×C₄×C₁₉	#121	1	2	yes	—
86	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
87	C₂×C₄×C₁₉	#137	1	2	yes	—
88	C₂×Dic₁₉	—	4	2	no	—
89	C₂×Dic₁₉	—	8	1	no	—
90	C₂×Dic₁₉	—	8	1	no	—
91	C₂×Dic₁₉	—	8	2	no	—
92	C₂×Dic₁₉	—	8	1	no	—
93	Dic₃₈	—	4	4	no	—
94	Dic₃₈	—	8	2	no	—
95	C₈×C₁₉	—	2	4	no	—
96	C₁₉⋊C₈	—	4	4	no	—
97	#3229	—	19	2	no	—
98	#3162	D₁₉	1	1	yes	characteristic
99	#1960	—	19	1	no	—
100	#1518	—	19	2	no	—
101	#1281	—	19	1	no	—
102	C₂²×C₁₉	—	2	2	no	—
103	C₂²×C₁₉	#392	1	1	yes	characteristic
104	C₂²×C₁₉	#492	1	1	yes	characteristic
105	C₂²×C₁₉	#497	1	1	yes	characteristic
106	C₄×C₁₉	—	2	2	no	—
107	C₄×C₁₉	—	2	2	no	—
108	C₄×C₁₉	—	8	2	no	—
109	C₄×C₁₉	—	8	2	no	—
110	C₄×C₁₉	#448	1	2	yes	—
111	C₄×C₁₉	#461	1	2	yes	—
112	Dic₁₉	—	8	2	no	—
113	Dic₁₉	—	16	1	no	—
114	#533	C₂×D₁₉	1	2	yes	—
115	C₂×C₄⋊Q₈	—	19	1	no	—
116	#501	—	2	2	no	—
117	#501	—	2	2	no	—
118	#498	—	38	2	no	—
119	#487	—	38	2	no	—
120	#483	—	38	4	no	—
121	#475	—	38	4	no	—
122	#431	—	19	2	no	—
123	#427	—	2	2	no	—
124	C₂×#103	—	38	2	no	—
125	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
126	#382	—	19	1	no	—
127	#328	—	38	4	no	—
128	C₂×C₁₉	—	2	1	no	—
129	C₂×C₁₉	—	2	1	no	—
130	C₂×C₁₉	#2009	1	2	yes	—
131	C₂×C₁₉	#2013	1	1	yes	characteristic
132	C₂²×Q₈	—	38	1	no	—
133	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
134	C₄⋊Q₈	—	19	2	no	—
135	C₄⋊Q₈	—	38	1	no	—
136	C₄⋊Q₈	—	38	2	no	—
137	C₄⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
138	C₄⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
139	#125	—	2	2	no	—
140	C₂²⋊Q₈	—	2	2	no	—
141	C₂²⋊Q₈	—	2	2	no	—
142	C₄×Q₈	—	2	2	no	—
143	C₄×Q₈	—	2	2	no	—
144	#117	—	2	2	no	—
145	C₂×C₄⋊C₄	—	38	2	no	—
146	C₂×C₄⋊C₄	—	38	1	no	—
147	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
148	#107	—	2	4	no	—
149	#106	—	2	2	no	—
150	#106	—	2	2	no	—
151	#106	—	38	8	no	—
152	C₄⋊C₈	—	38	2	no	—
153	#103	—	38	8	no	—
154	#103	—	76	4	no	—
155	C₂²⋊C₈	—	19	4	no	—
156	#97	—	2	2	no	—
157	C₄×C₈	—	38	2	no	—
158	#95	—	38	2	no	—
159	C₁₉	#10227	1	1	yes	characteristic, complemented, Sylow
160	C₂×Q₈	—	2	2	no	—
161	C₂×Q₈	—	2	2	no	—
162	C₂×Q₈	—	38	2	no	—
163	C₂×Q₈	—	76	1	no	—
164	C₂×Q₈	—	76	2	no	—
165	C₂×Q₈	—	76	2	no	—
166	C₂²×C₄	—	76	1	no	—
167	C₂²×C₄	—	76	1	no	—
168	C₂²×C₄	D₄×D₁₉	1	2	yes	—
169	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
170	C₂×C₈	—	2	2	no	—
171	C₂×C₈	—	2	2	no	—
172	C₂×C₈	—	38	4	no	—
173	C₂×C₈	#64527	1	4	yes	—
174	C₄⋊C₄	—	2	2	no	—
175	C₄⋊C₄	—	2	2	no	—
176	C₄⋊C₄	—	2	2	no	—
177	C₄⋊C₄	—	2	2	no	—
178	C₄⋊C₄	—	4	2	no	—
179	C₄⋊C₄	—	4	2	no	—
180	C₄⋊C₄	—	38	4	no	—
181	C₄⋊C₄	—	76	2	no	—
182	C₄⋊C₄	—	76	2	no	—
183	C₂²⋊C₄	—	4	2	no	—
184	C₄²	—	4	2	no	—
185	C₄²	D₄×D₁₉	1	1	yes	characteristic
186	C₄²	#64543	1	1	yes	characteristic
187	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
188	C₂³	#10597386	1	1	yes	characteristic
189	Q₈	—	4	4	no	—
190	Q₈	—	8	2	no	—
191	Q₈	—	76	4	no	—
192	Q₈	—	152	2	no	—
193	C₂×C₄	—	4	2	no	—
194	C₂×C₄	—	4	2	no	—
195	C₂×C₄	—	4	2	no	—
196	C₂×C₄	—	76	2	no	—
197	C₂×C₄	—	152	2	no	—
198	C₂×C₄	—	152	1	no	—
199	C₂×C₄	—	152	1	no	—
200	C₂×C₄	—	152	1	no	—
201	C₂×C₄	#10597383	1	2	yes	—
202	C₂×C₄	#10597384	1	1	yes	characteristic
203	C₂×C₄	#10597385	1	2	yes	—
204	C₂×C₄	C₂×#64527	1	2	yes	—
205	C₂×C₄	#10597388	1	2	yes	—
206	C₂×C₄	#10597399	1	1	yes	characteristic
207	C₈	—	2	4	no	—
208	C₈	—	76	4	no	—
209	C₂²	—	2	2	no	—
210	C₂²	#11926452	1	1	yes	characteristic
211	C₂²	#11926918	1	1	yes	characteristic
212	C₂²	#11926936	1	1	yes	characteristic
213	C₄	—	2	2	no	—
214	C₄	—	2	2	no	—
215	C₄	—	8	2	no	—
216	C₄	—	8	2	no	—
217	C₄	—	304	1	no	—
218	C₄	—	152	2	no	—
219	C₄	#11926683	1	2	yes	—
220	C₄	#11926746	1	2	yes	—
221	C₂	—	2	1	no	—
222	C₂	—	2	1	no	—
223	C₂	#14564692	1	2	yes	—
224	C₂	#14564718	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14574776

C₂

yes

maximal

#14564455

C₂

yes

maximal, characteristic

#14562199

C₂

yes

maximal

#14561480

C₂

yes

maximal, characteristic

C₁₉×#3162

C₂

yes

maximal, characteristic

C₂×#10597315

C₂²

yes

—

—

—

—

C₂²

yes

—

C₂×#10597273

—

#11926410

C₂²

yes

characteristic

#11926281

—

C₁₉×#533

C₂²

yes

—

C₁₉×#501

—

C₁₉×#501

—

C₁₉×#427

—

C₂×C₁₉×#97

C₂²

yes

characteristic

C₂²×Dic₃₈

—

C₂²×C₈×C₁₉

D₄

yes

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×#125

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₁₉×#117

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

#10597315

—

#10597315

—

#10597315

D₄

yes

—

C₁₉×#107

—

C₁₉×#106

—

C₁₉×#106

—

C₁₉×#97

—

#10597292

—

C₁₉⋊#95

—

C₂²⋊(C₁₉⋊C₈)

D₄

yes

—

#10597273

—

#10597265

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

SD₁₆

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#120

yes

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#3229

—

#3162

D₁₉

yes

characteristic

#1960

—

100

#1518

—

101

#1281

—

102

C₂²×C₁₉

—

103

C₂²×C₁₉

#392

yes

characteristic

104

C₂²×C₁₉

#492

yes

characteristic

105

C₂²×C₁₉

#497

yes

characteristic

106

C₄×C₁₉

—

107

C₄×C₁₉

—

108

C₄×C₁₉

—

109

C₄×C₁₉

—

110

C₄×C₁₉

#448

yes

—

111

C₄×C₁₉

#461

yes

—

112

Dic₁₉

—

113

Dic₁₉

—

114

#533

C₂×D₁₉

yes

—

115

C₂×C₄⋊Q₈

—

116

#501

—

117

#501

—

118

#498

—

119

#487

—

120

#483

—

121

#475

—

122

#431

—

123

#427

—

124

C₂×#103

—

125

C₂×#97

C₂×D₁₉

yes

characteristic

126

#382

—

127

#328

—

128

C₂×C₁₉

—

129

C₂×C₁₉

—

130

C₂×C₁₉

#2009

yes

—

131

C₂×C₁₉

#2013

yes

characteristic

132

C₂²×Q₈

—

133

C₂²×C₈

C₂²⋊D₁₉

yes

—

134

C₄⋊Q₈

—

135

C₄⋊Q₈

—

136

C₄⋊Q₈

—

137

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

138

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

139

#125

—

140

C₂²⋊Q₈

—

141

C₂²⋊Q₈

—

142

C₄×Q₈

—

143

C₄×Q₈

—

144

#117

—

145

C₂×C₄⋊C₄

—

146

C₂×C₄⋊C₄

—

147

C₂×C₄²

C₂²×D₁₉

yes

characteristic

148

#107

—

149

#106

—

150

#106

—

151

#106

—

152

C₄⋊C₈

—

153

#103

—

154

#103

—

155

C₂²⋊C₈

—

156

#97

—

157

C₄×C₈

—

158

#95

—

159

C₁₉

#10227

yes

characteristic, complemented, Sylow

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂²×C₄

—

167

C₂²×C₄

—

168

C₂²×C₄

D₄×D₁₉

yes

—

169

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

170

C₂×C₈

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

#64527

yes

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₂²⋊C₄

—

184

C₄²

—

185

C₄²

D₄×D₁₉

yes

characteristic

186

C₄²

#64543

yes

characteristic

187

C₄²

C₂×C₂²⋊D₁₉

yes

—

188

C₂³

#10597386

yes

characteristic

189

Q₈

—

190

Q₈

—

191

Q₈

—

192

Q₈

—

152

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

152

—

198

C₂×C₄

—

152

—

199

C₂×C₄

—

152

—

200

C₂×C₄

—

152

—

201

C₂×C₄

#10597383

yes

—

202

C₂×C₄

#10597384

yes

characteristic

203

C₂×C₄

#10597385

yes

—

204

C₂×C₄

C₂×#64527

yes

—

205

C₂×C₄

#10597388

yes

—

206

C₂×C₄

#10597399

yes

characteristic

207

C₈

—

208

C₈

—

209

C₂²

—

210

C₂²

#11926452

yes

characteristic

211

C₂²

#11926918

yes

characteristic

212

C₂²

#11926936

yes

characteristic

213

C₄

—

214

C₄

—

215

C₄

—

216

C₄

—

217

C₄

—

304

—

218

C₄

—

152

—

219

C₄

#11926683

yes

—

220

C₄

#11926746

yes

—

221

C₂

—

222

C₂

—

223

C₂

#14564692

yes

—

224

C₂

#14564718

yes

characteristic

	subgroup	G/H
center	C₂²	#11926452
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#3162	C₂
socle	C₂²×C₁₉	#392
prime radical	C₂³×C₁₉	#127
hypercenter	#3162	D₁₉
hypocenter	C₁₉	#10227
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3162

subgroup

G/H

center

C₂²

#11926452

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#3162

C₂

C₂²×C₁₉

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3162

N	H ≅ G/N	type
159. C₁₉	#10227	semidirect

H ≅ G/N

type

159. C₁₉

#10227

semidirect

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

subgroup	index
#14574776	2
#14564455	2
#14562199	2
#14561480	2
C₁₉×#3162	2
#10227	19

subgroup

index

C₁₉×#3162

Subgroups — #18084831

Conjugacy classes of subgroups

Complements

Maximal subgroups