Group #18076913 — subgroups

Subgroups — #18076913

Order 4864.

428 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 115 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	#14564605	C₂	1	1	yes	maximal, characteristic
2	#14563804	C₂	1	2	yes	maximal
3	C₂×#11926286	C₂	1	1	yes	maximal, characteristic
4	#14561516	C₂	1	2	yes	maximal
5	C₁₉×#2382	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597264	—	2	2	no	—
7	C₂×#10597265	—	2	2	no	—
8	C₂×#10597260	C₂²	1	1	yes	characteristic
9	C₂×#10597260	C₂²	1	2	yes	—
10	#11926414	C₂²	1	1	yes	characteristic
11	#11926306	—	2	2	no	—
12	#11926286	C₄	1	4	yes	complemented
13	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
14	C₁₉×#389	—	2	2	no	—
15	C₁₉×#387	—	2	2	no	—
16	C₁₉×#387	—	2	2	no	—
17	C₁₉×#382	C₂²	1	2	yes	—
18	C₁₉×#125	—	2	2	no	—
19	C₁₉×#125	C₂×C₄	1	2	yes	—
20	C₁₉×#125	Q₈	1	2	yes	—
21	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
22	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
23	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
24	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
25	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
26	C₂×C₄²×C₁₉	—	2	2	no	—
27	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
28	C₂×C₄⋊Dic₁₉	—	2	1	no	—
29	C₂×C₄⋊Dic₁₉	—	2	2	no	—
30	C₂²×C₁₉⋊C₈	—	2	2	no	—
31	C₂²×C₁₉⋊C₈	—	2	1	no	—
32	C₁₉×#95	—	2	2	no	—
33	C₁₉×#95	—	2	2	no	—
34	C₁₉×#95	—	2	2	no	—
35	C₁₉×#95	—	2	2	no	—
36	#10597265	—	4	4	no	—
37	#10597264	—	4	4	no	—
38	#10597260	—	2	2	no	—
39	#10597260	—	2	2	no	—
40	#10597260	C₂×C₄	1	4	yes	—
41	C₂²×C₄×C₁₉	—	2	2	no	—
42	C₂²×C₄×C₁₉	—	2	2	no	—
43	C₂²×C₄×C₁₉	—	2	2	no	—
44	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
45	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
46	C₂²×Dic₁₉	—	4	1	no	—
47	C₄⋊C₄×C₁₉	—	2	4	no	—
48	C₄⋊C₄×C₁₉	—	2	4	no	—
49	C₄⋊C₄×C₁₉	—	2	2	no	—
50	C₄⋊C₄×C₁₉	—	4	2	no	—
51	C₄⋊C₄×C₁₉	—	4	2	no	—
52	C₄⋊C₄×C₁₉	—	8	2	no	—
53	C₄⋊C₄×C₁₉	C₄⋊C₄	1	4	yes	—
54	C₄²×C₁₉	—	8	2	no	—
55	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
56	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
57	C₄²×C₁₉	#41	1	2	yes	—
58	C₄⋊Dic₁₉	—	4	2	no	—
59	C₄⋊Dic₁₉	—	4	2	no	—
60	C₄⋊Dic₁₉	—	4	2	no	—
61	C₂×C₁₉⋊C₈	—	2	4	no	—
62	C₂×C₁₉⋊C₈	—	2	4	no	—
63	C₂×C₁₉⋊C₈	—	2	4	no	—
64	C₂×C₁₉⋊C₈	—	2	2	no	—
65	C₂×C₁₉⋊C₈	—	4	1	no	—
66	C₂×C₁₉⋊C₈	—	4	1	no	—
67	#8913	—	19	1	no	maximal, Sylow
68	C₂³×C₁₉	#120	1	1	yes	characteristic
69	C₂×C₄×C₁₉	—	2	2	no	—
70	C₂×C₄×C₁₉	—	2	1	no	—
71	C₂×C₄×C₁₉	—	2	1	no	—
72	C₂×C₄×C₁₉	—	2	2	no	—
73	C₂×C₄×C₁₉	—	2	4	no	—
74	C₂×C₄×C₁₉	—	4	2	no	—
75	C₂×C₄×C₁₉	—	4	2	no	—
76	C₂×C₄×C₁₉	—	4	2	no	—
77	C₂×C₄×C₁₉	—	4	2	no	—
78	C₂×C₄×C₁₉	—	4	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	C₂×C₄⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
84	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
85	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
86	C₂×Dic₁₉	—	8	2	no	—
87	C₂×Dic₁₉	—	8	1	no	—
88	C₁₉⋊C₈	—	2	8	no	—
89	C₁₉⋊C₈	—	4	2	no	—
90	#2382	D₁₉	1	1	yes	characteristic
91	#1992	—	19	1	no	—
92	#1847	—	19	2	no	—
93	C₂×#330	—	19	1	no	—
94	#1295	—	19	2	no	—
95	C₂²×C₁₉	#385	1	1	yes	characteristic
96	C₂²×C₁₉	#453	1	2	yes	—
97	C₂²×C₁₉	#454	1	1	yes	characteristic
98	C₂²×C₁₉	#456	1	1	yes	characteristic
99	C₂²×C₁₉	#456	1	2	yes	—
100	C₄×C₁₉	—	2	1	no	—
101	C₄×C₁₉	—	2	1	no	—
102	C₄×C₁₉	—	2	2	no	—
103	C₄×C₁₉	—	2	2	no	—
104	C₄×C₁₉	—	4	4	no	—
105	C₄×C₁₉	—	8	2	no	—
106	C₄×C₁₉	—	8	2	no	—
107	Dic₁₉	—	16	1	no	—
108	C₂×#125	C₂×D₁₉	1	1	yes	characteristic
109	C₂×#107	—	38	2	no	—
110	C₂×#106	—	38	2	no	—
111	C₂×#97	—	19	2	no	—
112	C₂×#97	—	19	1	no	—
113	#389	—	2	2	no	—
114	#387	—	2	2	no	—
115	#387	—	2	2	no	—
116	#384	—	19	1	no	—
117	#382	C₂×D₁₉	1	2	yes	—
118	#340	—	38	2	no	—
119	#330	—	19	4	no	—
120	C₂×C₁₉	#1656	1	1	yes	characteristic
121	C₂×C₁₉	#1660	1	2	yes	—
122	C₂×C₁₉	#1663	1	1	yes	characteristic
123	C₂×C₁₉	#1857	1	1	yes	characteristic
124	C₂×C₁₉	#1859	1	2	yes	—
125	C₂²×C₈	—	38	2	no	—
126	C₂²×C₈	—	38	1	no	—
127	#125	—	2	2	no	—
128	#125	Dic₃₈	1	2	yes	—
129	#125	C₄×D₁₉	1	2	yes	—
130	C₂×C₄⋊C₄	—	2	2	no	—
131	C₂×C₄⋊C₄	—	2	2	no	—
132	C₂×C₄⋊C₄	—	38	1	no	—
133	C₂×C₄⋊C₄	—	38	2	no	—
134	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
135	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
136	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
137	C₂×C₄²	—	2	2	no	—
138	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
139	#107	—	76	4	no	—
140	#106	—	76	4	no	—
141	#97	—	19	4	no	—
142	#97	—	38	2	no	—
143	#97	—	38	2	no	—
144	#95	—	2	2	no	—
145	#95	—	2	2	no	—
146	#95	—	2	2	no	—
147	#95	—	2	2	no	—
148	C₁₉	#8913	1	1	yes	characteristic, complemented, Sylow
149	C₂²×C₄	—	2	2	no	—
150	C₂²×C₄	—	2	2	no	—
151	C₂²×C₄	—	2	2	no	—
152	C₂²×C₄	—	76	1	no	—
153	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
154	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
155	C₂×C₈	—	38	4	no	—
156	C₂×C₈	—	38	4	no	—
157	C₂×C₈	—	38	4	no	—
158	C₂×C₈	—	38	2	no	—
159	C₂×C₈	—	76	1	no	—
160	C₂×C₈	—	76	1	no	—
161	C₄⋊C₄	—	2	4	no	—
162	C₄⋊C₄	—	2	4	no	—
163	C₄⋊C₄	—	2	2	no	—
164	C₄⋊C₄	—	4	2	no	—
165	C₄⋊C₄	—	4	2	no	—
166	C₄⋊C₄	—	8	2	no	—
167	C₄⋊C₄	—	76	2	no	—
168	C₄⋊C₄	—	76	2	no	—
169	C₄⋊C₄	—	76	2	no	—
170	C₄⋊C₄	Dic₁₉⋊C₄	1	4	yes	—
171	C₄²	—	8	2	no	—
172	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
173	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
174	C₄²	#64541	1	2	yes	—
175	C₂³	#10597399	1	1	yes	characteristic
176	C₂×C₄	—	2	2	no	—
177	C₂×C₄	—	2	1	no	—
178	C₂×C₄	—	2	1	no	—
179	C₂×C₄	—	2	2	no	—
180	C₂×C₄	—	2	4	no	—
181	C₂×C₄	—	4	2	no	—
182	C₂×C₄	—	4	2	no	—
183	C₂×C₄	—	4	2	no	—
184	C₂×C₄	—	4	2	no	—
185	C₂×C₄	—	4	2	no	—
186	C₂×C₄	—	4	2	no	—
187	C₂×C₄	—	4	2	no	—
188	C₂×C₄	—	4	2	no	—
189	C₂×C₄	—	152	2	no	—
190	C₂×C₄	—	152	1	no	—
191	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
192	C₂×C₄	#10597370	1	2	yes	—
193	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
194	C₂×C₄	#10597375	1	1	yes	characteristic
195	C₈	—	38	8	no	—
196	C₈	—	76	2	no	—
197	C₂²	#11926417	1	1	yes	characteristic
198	C₂²	#11926712	1	2	yes	—
199	C₂²	#11926717	1	1	yes	characteristic
200	C₂²	#11926727	1	1	yes	characteristic
201	C₂²	#11926727	1	2	yes	—
202	C₄	—	2	1	no	—
203	C₄	—	2	1	no	—
204	C₄	—	2	2	no	—
205	C₄	—	2	2	no	—
206	C₄	—	4	4	no	—
207	C₄	—	8	2	no	—
208	C₄	—	8	2	no	—
209	C₄	—	304	1	no	—
210	C₂	#14562928	1	1	yes	characteristic
211	C₂	#14562946	1	2	yes	—
212	C₂	#14562963	1	1	yes	characteristic
213	C₂	#14563850	1	1	yes	characteristic
214	C₂	#14563861	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14564605

C₂

yes

maximal, characteristic

#14563804

C₂

yes

maximal

C₂×#11926286

C₂

yes

maximal, characteristic

#14561516

C₂

yes

maximal

C₁₉×#2382

C₂

yes

maximal, characteristic

C₂×#10597264

—

C₂×#10597265

—

C₂×#10597260

C₂²

yes

characteristic

C₂×#10597260

C₂²

yes

—

#11926414

C₂²

yes

characteristic

#11926306

—

#11926286

C₄

yes

complemented

C₂×C₁₉×#125

C₂²

yes

characteristic

C₁₉×#389

—

C₁₉×#387

—

C₁₉×#387

—

C₁₉×#382

C₂²

yes

—

C₁₉×#125

—

C₁₉×#125

C₂×C₄

yes

—

C₁₉×#125

Q₈

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

C₁₉×#95

—

C₁₉×#95

—

C₁₉×#95

—

C₁₉×#95

—

—

—

—

—

C₂×C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×Dic₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₄⋊C₄

yes

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₉

#123

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2382

D₁₉

yes

—

—

—

—

C₂²×C₁₉

#385

yes

characteristic

C₂²×C₁₉

#453

yes

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

100

C₄×C₁₉

—

101

C₄×C₁₉

—

102

C₄×C₁₉

—

103

C₄×C₁₉

—

104

C₄×C₁₉

—

105

C₄×C₁₉

—

106

C₄×C₁₉

—

107

Dic₁₉

—

108

C₂×#125

C₂×D₁₉

yes

characteristic

109

C₂×#107

—

110

C₂×#106

—

111

C₂×#97

—

112

C₂×#97

—

113

#389

—

114

#387

—

115

#387

—

116

#384

—

117

#382

C₂×D₁₉

yes

—

118

#340

—

119

#330

—

120

C₂×C₁₉

#1656

yes

characteristic

121

C₂×C₁₉

#1660

yes

—

122

C₂×C₁₉

#1663

yes

characteristic

123

C₂×C₁₉

#1857

yes

characteristic

124

C₂×C₁₉

#1859

yes

—

125

C₂²×C₈

—

126

C₂²×C₈

—

127

#125

—

128

#125

Dic₃₈

yes

—

129

#125

C₄×D₁₉

yes

—

130

C₂×C₄⋊C₄

—

131

C₂×C₄⋊C₄

—

132

C₂×C₄⋊C₄

—

133

C₂×C₄⋊C₄

—

134

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

135

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

136

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

137

C₂×C₄²

—

138

C₂×C₄²

C₂²×D₁₉

yes

characteristic

139

#107

—

140

#106

—

141

#97

—

142

#97

—

143

#97

—

144

#95

—

145

#95

—

146

#95

—

147

#95

—

148

C₁₉

#8913

yes

characteristic, complemented, Sylow

149

C₂²×C₄

—

150

C₂²×C₄

—

151

C₂²×C₄

—

152

C₂²×C₄

—

153

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

154

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

155

C₂×C₈

—

156

C₂×C₈

—

157

C₂×C₈

—

158

C₂×C₈

—

159

C₂×C₈

—

160

C₂×C₈

—

161

C₄⋊C₄

—

162

C₄⋊C₄

—

163

C₄⋊C₄

—

164

C₄⋊C₄

—

165

C₄⋊C₄

—

166

C₄⋊C₄

—

167

C₄⋊C₄

—

168

C₄⋊C₄

—

169

C₄⋊C₄

—

170

C₄⋊C₄

Dic₁₉⋊C₄

yes

—

171

C₄²

—

172

C₄²

C₂×Dic₃₈

yes

characteristic

173

C₄²

C₂×C₄×D₁₉

yes

characteristic

174

C₄²

#64541

yes

—

175

C₂³

#10597399

yes

characteristic

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

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

—

152

—

190

C₂×C₄

—

152

—

191

C₂×C₄

C₂×Dic₁₉⋊C₄

yes

characteristic

192

C₂×C₄

#10597370

yes

—

193

C₂×C₄

C₄×C₂²⋊D₁₉

yes

—

194

C₂×C₄

#10597375

yes

characteristic

195

C₈

—

196

C₈

—

197

C₂²

#11926417

yes

characteristic

198

C₂²

#11926712

yes

—

199

C₂²

#11926717

yes

characteristic

200

C₂²

#11926727

yes

characteristic

201

C₂²

#11926727

yes

—

202

C₄

—

203

C₄

—

204

C₄

—

205

C₄

—

206

C₄

—

207

C₄

—

208

C₄

—

209

C₄

—

304

—

210

C₂

#14562928

yes

characteristic

211

C₂

#14562946

yes

—

212

C₂

#14562963

yes

characteristic

213

C₂

#14563850

yes

characteristic

214

C₂

#14563861

yes

—

	subgroup	G/H
center	C₂³	#10597399
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2382	C₂
socle, prime radical	C₂³×C₁₉	#120
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2382	D₁₉
hypocenter	C₁₉	#8913
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2382

subgroup

G/H

center

C₂³

#10597399

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2382

C₂

socle, prime radical

C₂³×C₁₉

#120

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2382

N	H ≅ G/N	type
12. #11926286	C₄	semidirect
148. C₁₉	#8913	semidirect

H ≅ G/N

type

12. #11926286

C₄

semidirect

148. C₁₉

#8913

semidirect

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

subgroup	index
#14564605	2
#14563804	2
C₂×#11926286	2
#14561516	2
C₁₉×#2382	2
#8913	19

subgroup

index

C₁₉×#2382

Subgroups — #18076913

Conjugacy classes of subgroups

Complements

Maximal subgroups