Group #18085621 — subgroups

Subgroups — #18085621

Order 4864.

392 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 89 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	#14571910	C₂	1	1	yes	maximal, characteristic
2	#14564608	C₂	1	2	yes	maximal
3	#14564454	C₂	1	1	yes	maximal, characteristic
4	#14561517	C₂	1	2	yes	maximal
5	C₁₉×#1295	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597315	C₂²	1	1	yes	characteristic
7	C₂×#10597267	—	2	2	no	—
8	C₂×#10597260	C₂²	1	1	yes	characteristic
9	#11926478	—	2	2	no	—
10	#11926477	—	2	2	no	—
11	#11926476	—	2	2	no	—
12	#11926410	C₂²	1	2	yes	—
13	#11926307	—	2	2	no	—
14	#11926307	—	2	2	no	—
15	C₂×C₁₉×#97	C₂²	1	2	yes	—
16	C₁₉×#382	C₂²	1	1	yes	characteristic
17	C₂²×Dic₃₈	—	2	1	no	—
18	C₂²×C₈×C₁₉	—	2	2	no	—
19	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
20	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
21	C₂×C₄⋊Dic₁₉	—	2	2	no	—
22	C₂×C₄⋊Dic₁₉	—	2	2	no	—
23	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
24	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
25	C₂×Dic₁₉⋊C₄	—	2	2	no	—
26	C₂×Dic₁₉⋊C₄	—	2	2	no	—
27	C₂²×C₁₉⋊C₈	—	2	1	no	—
28	#10597315	—	2	2	no	—
29	#10597315	—	2	1	no	—
30	#10597315	Q₈	1	2	yes	—
31	C₁₉×#97	—	2	2	no	—
32	C₁₉×#97	—	2	2	no	—
33	C₁₉×#95	—	2	2	no	—
34	C₁₉⋊#95	—	2	2	no	—
35	C₁₉⋊#95	—	2	2	no	—
36	C₁₉⋊#95	—	2	2	no	—
37	#10597267	—	4	4	no	—
38	#10597260	—	2	2	no	—
39	C₂²×C₄×C₁₉	—	2	2	no	—
40	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
42	C₂²×Dic₁₉	—	2	2	no	—
43	C₂²×Dic₁₉	—	2	2	no	—
44	C₂²×Dic₁₉	—	4	1	no	—
45	C₂×Dic₃₈	—	2	2	no	—
46	C₂×Dic₃₈	—	4	2	no	—
47	C₂×Dic₃₈	—	4	2	no	—
48	C₂×Dic₃₈	—	4	1	no	—
49	C₂×C₈×C₁₉	—	2	4	no	—
50	C₂×C₈×C₁₉	—	4	2	no	—
51	C₂×C₈×C₁₉	—	4	2	no	—
52	C₄⋊C₄×C₁₉	—	4	2	no	—
53	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
54	C₄²×C₁₉	#41	1	2	yes	—
55	C₄²×C₁₉	#41	1	1	yes	characteristic
56	C₄⋊Dic₁₉	—	2	4	no	—
57	C₄⋊Dic₁₉	—	4	2	no	—
58	C₄⋊Dic₁₉	—	4	2	no	—
59	C₄⋊Dic₁₉	—	4	2	no	—
60	C₄⋊Dic₁₉	—	8	2	no	—
61	Dic₁₉⋊C₄	—	8	2	no	—
62	Dic₁₉⋊C₄	—	8	2	no	—
63	C₂×C₁₉⋊C₈	—	2	2	no	—
64	C₂×C₁₉⋊C₈	—	4	1	no	—
65	C₂×C₁₉⋊C₈	—	4	1	no	—
66	#10361	—	19	1	no	maximal, Sylow
67	C₂³×C₁₉	#120	1	1	yes	characteristic
68	C₂×C₄×C₁₉	—	2	1	no	—
69	C₂×C₄×C₁₉	—	2	1	no	—
70	C₂×C₄×C₁₉	—	2	2	no	—
71	C₂×C₄×C₁₉	—	2	2	no	—
72	C₂×C₄×C₁₉	—	4	2	no	—
73	C₂×C₄×C₁₉	—	4	2	no	—
74	C₂×C₄×C₁₉	—	4	2	no	—
75	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
76	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
77	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
78	C₂×C₄×C₁₉	#124	1	2	yes	—
79	C₂×Dic₁₉	—	4	2	no	—
80	C₂×Dic₁₉	—	4	2	no	—
81	C₂×Dic₁₉	—	4	2	no	—
82	C₂×Dic₁₉	—	4	2	no	—
83	C₂×Dic₁₉	—	4	2	no	—
84	C₂×Dic₁₉	—	4	2	no	—
85	C₂×Dic₁₉	—	4	2	no	—
86	C₂×Dic₁₉	—	8	1	no	—
87	C₂×Dic₁₉	—	8	1	no	—
88	Dic₃₈	—	4	4	no	—
89	Dic₃₈	—	8	2	no	—
90	C₈×C₁₉	—	4	4	no	—
91	C₁₉⋊C₈	—	4	2	no	—
92	#2845	—	19	1	no	—
93	#1993	—	19	2	no	—
94	#1960	—	19	1	no	—
95	#1295	—	19	2	no	—
96	#1295	D₁₉	1	1	yes	characteristic
97	C₂²×C₁₉	#393	1	1	yes	characteristic
98	C₂²×C₁₉	#453	1	1	yes	characteristic
99	C₂²×C₁₉	#454	1	1	yes	characteristic
100	C₂²×C₁₉	#455	1	2	yes	—
101	C₂²×C₁₉	#456	1	2	yes	—
102	C₄×C₁₉	—	2	1	no	—
103	C₄×C₁₉	—	2	1	no	—
104	C₄×C₁₉	—	2	2	no	—
105	C₄×C₁₉	—	2	2	no	—
106	C₄×C₁₉	—	8	2	no	—
107	Dic₁₉	—	8	2	no	—
108	Dic₁₉	—	8	2	no	—
109	Dic₁₉	—	8	2	no	—
110	C₂×C₄⋊Q₈	—	19	1	no	—
111	C₂×#103	—	38	2	no	—
112	C₂×#97	—	19	1	no	—
113	C₂×#97	C₂×D₁₉	1	2	yes	—
114	#398	—	38	2	no	—
115	#398	—	38	2	no	—
116	#398	—	38	2	no	—
117	#382	—	19	2	no	—
118	#382	C₂×D₁₉	1	1	yes	characteristic
119	#340	—	38	2	no	—
120	#340	—	38	2	no	—
121	C₂×C₁₉	#1661	1	2	yes	—
122	C₂×C₁₉	#1662	1	1	yes	characteristic
123	C₂×C₁₉	#1663	1	1	yes	characteristic
124	C₂×C₁₉	#2027	1	1	yes	characteristic
125	C₂×C₁₉	#2028	1	2	yes	—
126	C₂²×Q₈	—	38	1	no	—
127	C₂²×C₈	—	2	2	no	—
128	C₂²×C₈	—	38	1	no	—
129	C₄⋊Q₈	—	19	2	no	—
130	C₄⋊Q₈	—	38	2	no	—
131	C₄⋊Q₈	—	38	1	no	—
132	C₂×C₄⋊C₄	—	19	2	no	—
133	C₂×C₄⋊C₄	—	19	2	no	—
134	C₂×C₄⋊C₄	—	38	2	no	—
135	C₂×C₄⋊C₄	—	38	2	no	—
136	C₂×C₄⋊C₄	—	38	2	no	—
137	C₂×C₄⋊C₄	—	38	2	no	—
138	C₂×C₄⋊C₄	D₇₆	1	2	yes	—
139	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
140	#103	—	76	4	no	—
141	#97	—	2	2	no	—
142	#97	—	2	2	no	—
143	#97	—	38	2	no	—
144	#95	—	2	2	no	—
145	#95	—	38	2	no	—
146	#95	—	38	2	no	—
147	#95	—	38	2	no	—
148	C₁₉	#10361	1	1	yes	characteristic, complemented, Sylow
149	C₂×Q₈	—	38	2	no	—
150	C₂×Q₈	—	76	2	no	—
151	C₂×Q₈	—	76	2	no	—
152	C₂×Q₈	—	76	1	no	—
153	C₂²×C₄	—	2	2	no	—
154	C₂²×C₄	—	38	2	no	—
155	C₂²×C₄	—	38	2	no	—
156	C₂²×C₄	—	76	1	no	—
157	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
158	C₂²×C₄	D₄×D₁₉	1	2	yes	—
159	C₂×C₈	—	2	4	no	—
160	C₂×C₈	—	4	2	no	—
161	C₂×C₈	—	4	2	no	—
162	C₂×C₈	—	38	2	no	—
163	C₂×C₈	—	76	1	no	—
164	C₂×C₈	—	76	1	no	—
165	C₄⋊C₄	—	4	2	no	—
166	C₄⋊C₄	—	38	4	no	—
167	C₄⋊C₄	—	76	2	no	—
168	C₄⋊C₄	—	76	2	no	—
169	C₄⋊C₄	—	76	2	no	—
170	C₄⋊C₄	—	152	2	no	—
171	C₄⋊C₄	—	152	2	no	—
172	C₄⋊C₄	—	152	2	no	—
173	C₄²	#64541	1	2	yes	—
174	C₄²	#64543	1	1	yes	characteristic
175	C₄²	Q₈×D₁₉	1	1	yes	characteristic
176	C₂³	#10597328	1	1	yes	characteristic
177	Q₈	—	76	4	no	—
178	Q₈	—	152	2	no	—
179	C₂×C₄	—	2	1	no	—
180	C₂×C₄	—	2	1	no	—
181	C₂×C₄	—	2	2	no	—
182	C₂×C₄	—	2	2	no	—
183	C₂×C₄	—	4	2	no	—
184	C₂×C₄	—	4	2	no	—
185	C₂×C₄	—	4	2	no	—
186	C₂×C₄	—	76	2	no	—
187	C₂×C₄	—	76	2	no	—
188	C₂×C₄	—	76	2	no	—
189	C₂×C₄	—	76	2	no	—
190	C₂×C₄	—	76	2	no	—
191	C₂×C₄	—	76	2	no	—
192	C₂×C₄	—	76	2	no	—
193	C₂×C₄	—	152	1	no	—
194	C₂×C₄	—	152	1	no	—
195	C₂×C₄	#10597321	1	1	yes	characteristic
196	C₂×C₄	#10597331	1	2	yes	—
197	C₂×C₄	#10597342	1	2	yes	—
198	C₂×C₄	#10597343	1	1	yes	characteristic
199	C₈	—	4	4	no	—
200	C₈	—	76	2	no	—
201	C₂²	#11926457	1	1	yes	characteristic
202	C₂²	#11926714	1	1	yes	characteristic
203	C₂²	#11926719	1	1	yes	characteristic
204	C₂²	#11926723	1	2	yes	—
205	C₂²	#11926728	1	2	yes	—
206	C₄	—	2	1	no	—
207	C₄	—	2	1	no	—
208	C₄	—	2	2	no	—
209	C₄	—	2	2	no	—
210	C₄	—	8	2	no	—
211	C₄	—	152	2	no	—
212	C₄	—	152	2	no	—
213	C₄	—	152	2	no	—
214	C₂	#14562953	1	2	yes	—
215	C₂	#14562959	1	1	yes	characteristic
216	C₂	#14562964	1	1	yes	characteristic
217	C₂	#14564792	1	1	yes	characteristic
218	C₂	#14564795	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14571910

C₂

yes

maximal, characteristic

#14564608

C₂

yes

maximal

#14564454

C₂

yes

maximal, characteristic

#14561517

C₂

yes

maximal

C₁₉×#1295

C₂

yes

maximal, characteristic

C₂×#10597315

C₂²

yes

characteristic

C₂×#10597267

—

C₂×#10597260

C₂²

yes

—

—

—

C₂²

yes

—

#11926307

—

#11926307

—

C₂×C₁₉×#97

C₂²

yes

—

C₁₉×#382

C₂²

yes

characteristic

C₂²×Dic₃₈

—

C₂²×C₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

D₄

yes

—

C₂×C₄⋊Dic₁₉

D₄

yes

—

C₂×Dic₁₉⋊C₄

—

C₂×Dic₁₉⋊C₄

—

C₂²×C₁₉⋊C₈

—

#10597315

—

#10597315

—

#10597315

Q₈

yes

—

C₁₉×#97

—

C₁₉×#97

—

C₁₉×#95

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₁₉⋊#95

—

#10597267

—

#10597260

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₄²×C₁₉

#41

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₉

C₂²⋊Q₈

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

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

—

—

—

—

D₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

100

C₂²×C₁₉

#455

yes

—

101

C₂²×C₁₉

#456

yes

—

102

C₄×C₁₉

—

103

C₄×C₁₉

—

104

C₄×C₁₉

—

105

C₄×C₁₉

—

106

C₄×C₁₉

—

107

Dic₁₉

—

108

Dic₁₉

—

109

Dic₁₉

—

110

C₂×C₄⋊Q₈

—

111

C₂×#103

—

112

C₂×#97

—

113

C₂×#97

C₂×D₁₉

yes

—

114

#398

—

115

#398

—

116

#398

—

117

#382

—

118

#382

C₂×D₁₉

yes

characteristic

119

#340

—

120

#340

—

121

C₂×C₁₉

#1661

yes

—

122

C₂×C₁₉

#1662

yes

characteristic

123

C₂×C₁₉

#1663

yes

characteristic

124

C₂×C₁₉

#2027

yes

characteristic

125

C₂×C₁₉

#2028

yes

—

126

C₂²×Q₈

—

127

C₂²×C₈

—

128

C₂²×C₈

—

129

C₄⋊Q₈

—

130

C₄⋊Q₈

—

131

C₄⋊Q₈

—

132

C₂×C₄⋊C₄

—

133

C₂×C₄⋊C₄

—

134

C₂×C₄⋊C₄

—

135

C₂×C₄⋊C₄

—

136

C₂×C₄⋊C₄

—

137

C₂×C₄⋊C₄

—

138

C₂×C₄⋊C₄

D₇₆

yes

—

139

C₂×C₄²

C₂²×D₁₉

yes

characteristic

140

#103

—

141

#97

—

142

#97

—

143

#97

—

144

#95

—

145

#95

—

146

#95

—

147

#95

—

148

C₁₉

#10361

yes

characteristic, complemented, Sylow

149

C₂×Q₈

—

150

C₂×Q₈

—

151

C₂×Q₈

—

152

C₂×Q₈

—

153

C₂²×C₄

—

154

C₂²×C₄

—

155

C₂²×C₄

—

156

C₂²×C₄

—

157

C₂²×C₄

C₂×D₇₆

yes

characteristic

158

C₂²×C₄

D₄×D₁₉

yes

—

159

C₂×C₈

—

160

C₂×C₈

—

161

C₂×C₈

—

162

C₂×C₈

—

163

C₂×C₈

—

164

C₂×C₈

—

165

C₄⋊C₄

—

166

C₄⋊C₄

—

167

C₄⋊C₄

—

168

C₄⋊C₄

—

169

C₄⋊C₄

—

170

C₄⋊C₄

—

152

—

171

C₄⋊C₄

—

152

—

172

C₄⋊C₄

—

152

—

173

C₄²

#64541

yes

—

174

C₄²

#64543

yes

characteristic

175

C₄²

Q₈×D₁₉

yes

characteristic

176

C₂³

#10597328

yes

characteristic

177

Q₈

—

178

Q₈

—

152

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

152

—

194

C₂×C₄

—

152

—

195

C₂×C₄

#10597321

yes

characteristic

196

C₂×C₄

#10597331

yes

—

197

C₂×C₄

#10597342

yes

—

198

C₂×C₄

#10597343

yes

characteristic

199

C₈

—

200

C₈

—

201

C₂²

#11926457

yes

characteristic

202

C₂²

#11926714

yes

characteristic

203

C₂²

#11926719

yes

characteristic

204

C₂²

#11926723

yes

—

205

C₂²

#11926728

yes

—

206

C₄

—

207

C₄

—

208

C₄

—

209

C₄

—

210

C₄

—

211

C₄

—

152

—

212

C₄

—

152

—

213

C₄

—

152

—

214

C₂

#14562953

yes

—

215

C₂

#14562959

yes

characteristic

216

C₂

#14562964

yes

characteristic

217

C₂

#14564792

yes

characteristic

218

C₂

#14564795

yes

—

	subgroup	G/H
center	C₂³	#10597328
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1295	C₂
socle, prime radical	C₂³×C₁₉	#120
hypercenter	#1295	D₁₉
hypocenter	C₁₉	#10361
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1295

subgroup

G/H

center

C₂³

#10597328

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1295

C₂

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1295

N	H ≅ G/N	type
148. C₁₉	#10361	semidirect

H ≅ G/N

type

148. C₁₉

#10361

semidirect

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

subgroup	index
#14571910	2
#14564608	2
#14564454	2
#14561517	2
C₁₉×#1295	2
#10361	19

subgroup

index

C₁₉×#1295

Subgroups — #18085621

Conjugacy classes of subgroups

Complements

Maximal subgroups