Group #18083874 — subgroups

Subgroups — #18083874

Order 4864.

500 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 95 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	C₂×#11926950	C₂	1	2	yes	maximal
2	#14571703	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926285	C₂	1	2	yes	maximal
4	#14561516	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1960	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597316	C₂²	1	2	yes	—
7	#11926950	—	2	4	no	—
8	#11926950	—	2	4	no	—
9	C₂×#10597264	—	2	2	no	—
10	C₂×#10597265	—	2	2	no	—
11	C₂×#10597260	C₂²	1	2	yes	—
12	#11926484	—	2	2	no	—
13	#11926476	—	2	2	no	—
14	#11926474	—	2	2	no	—
15	#11926285	—	2	4	no	—
16	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#103	—	2	2	no	—
18	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
19	C₁₉×#382	C₂²	1	1	yes	characteristic
20	C₂²×Q₈×C₁₉	—	2	1	no	—
21	C₂²×C₈×C₁₉	—	2	1	no	—
22	C₁₉×C₄⋊Q₈	—	2	2	no	—
23	C₁₉×C₄⋊Q₈	—	2	1	no	—
24	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
25	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
26	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
27	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
28	C₂×C₄⋊Dic₁₉	—	2	2	no	—
29	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
30	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
31	C₂×Dic₁₉⋊C₄	—	2	2	no	—
32	C₂×Dic₁₉⋊C₄	—	2	2	no	—
33	C₂²×C₁₉⋊C₈	—	2	2	no	—
34	#10597316	—	2	2	no	—
35	#10597316	—	2	2	no	—
36	#10597316	—	2	2	no	—
37	#10597316	—	2	2	no	—
38	C₁₉×#103	—	4	4	no	—
39	C₁₉×#97	—	2	2	no	—
40	C₁₉×#95	—	2	2	no	—
41	C₁₉⋊#95	—	2	4	no	—
42	C₁₉⋊#95	—	2	2	no	—
43	#10597265	—	2	8	no	—
44	#10597264	—	2	8	no	—
45	#10597260	—	2	2	no	—
46	#10597260	D₄	1	4	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	—	4	1	no	—
51	C₂²×C₄×C₁₉	—	2	2	no	—
52	C₂²×C₄×C₁₉	—	4	1	no	—
53	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
54	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
55	C₂²×Dic₁₉	—	2	2	no	—
56	C₂²×Dic₁₉	—	2	2	no	—
57	C₂×C₈×C₁₉	—	2	2	no	—
58	C₂×C₈×C₁₉	—	4	1	no	—
59	C₂×C₈×C₁₉	—	4	1	no	—
60	C₄⋊C₄×C₁₉	—	2	4	no	—
61	C₄⋊C₄×C₁₉	—	4	2	no	—
62	C₄⋊C₄×C₁₉	—	4	2	no	—
63	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
64	C₄²×C₁₉	C₂×D₄	1	2	yes	—
65	C₄²×C₁₉	#41	1	1	yes	characteristic
66	C₄⋊Dic₁₉	—	2	2	no	—
67	C₄⋊Dic₁₉	—	2	2	no	—
68	C₄⋊Dic₁₉	—	2	2	no	—
69	C₄⋊Dic₁₉	—	2	2	no	—
70	C₄⋊Dic₁₉	—	8	2	no	—
71	Dic₁₉⋊C₄	—	4	2	no	—
72	Dic₁₉⋊C₄	—	4	2	no	—
73	Dic₁₉⋊C₄	—	4	2	no	—
74	Dic₁₉⋊C₄	—	4	2	no	—
75	C₂×C₁₉⋊C₈	—	2	8	no	—
76	C₂×C₁₉⋊C₈	—	2	4	no	—
77	#10087	—	19	1	no	maximal, Sylow
78	C₂³×C₁₉	#120	1	1	yes	characteristic
79	Q₈×C₁₉	—	4	4	no	—
80	Q₈×C₁₉	—	8	2	no	—
81	C₂×C₄×C₁₉	—	2	1	no	—
82	C₂×C₄×C₁₉	—	2	1	no	—
83	C₂×C₄×C₁₉	—	2	4	no	—
84	C₂×C₄×C₁₉	—	4	2	no	—
85	C₂×C₄×C₁₉	—	4	2	no	—
86	C₂×C₄×C₁₉	—	4	4	no	—
87	C₂×C₄×C₁₉	—	8	1	no	—
88	C₂×C₄×C₁₉	—	8	1	no	—
89	C₂×C₄×C₁₉	#120	1	2	yes	—
90	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
91	C₂×C₄×C₁₉	#121	1	2	yes	—
92	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
93	C₂×Dic₁₉	—	4	2	no	—
94	C₂×Dic₁₉	—	4	2	no	—
95	C₂×Dic₁₉	—	4	2	no	—
96	C₂×Dic₁₉	—	4	2	no	—
97	C₂×Dic₁₉	—	4	4	no	—
98	C₈×C₁₉	—	4	2	no	—
99	C₁₉⋊C₈	—	2	8	no	—
100	C₂×#501	—	19	2	no	—
101	#2822	—	19	1	no	—
102	#1960	D₁₉	1	1	yes	characteristic
103	C₂×#330	—	19	2	no	—
104	#1295	—	19	1	no	—
105	C₂²×C₁₉	#392	1	1	yes	characteristic
106	C₂²×C₁₉	#453	1	1	yes	characteristic
107	C₂²×C₁₉	#454	1	1	yes	characteristic
108	C₂²×C₁₉	#456	1	4	yes	—
109	C₄×C₁₉	—	2	2	no	—
110	C₄×C₁₉	—	2	2	no	—
111	C₄×C₁₉	—	2	1	no	—
112	C₄×C₁₉	—	2	1	no	—
113	C₄×C₁₉	—	8	2	no	—
114	C₄×C₁₉	—	8	2	no	—
115	Dic₁₉	—	8	2	no	—
116	Dic₁₉	—	8	2	no	—
117	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
118	C₂×#125	—	19	2	no	—
119	#501	—	38	4	no	—
120	#501	—	38	4	no	—
121	C₂×#107	—	38	2	no	—
122	C₂×#106	—	38	2	no	—
123	C₂×#103	—	2	2	no	—
124	C₂×#97	—	19	2	no	—
125	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
126	#400	—	38	2	no	—
127	#398	—	38	2	no	—
128	#398	—	38	2	no	—
129	#382	C₂×D₁₉	1	1	yes	characteristic
130	#330	—	38	4	no	—
131	C₂×C₁₉	#1660	1	2	yes	—
132	C₂×C₁₉	#1663	1	2	yes	—
133	C₂×C₁₉	#2005	1	2	yes	—
134	C₂×C₁₉	#2006	1	1	yes	characteristic
135	C₂²×Q₈	—	2	1	no	—
136	C₂²×C₈	—	2	1	no	—
137	C₂²×C₈	—	38	2	no	—
138	C₄⋊Q₈	—	2	1	no	—
139	C₄⋊Q₈	—	2	2	no	—
140	C₄⋊Q₈	D₇₆	1	2	yes	—
141	#125	—	38	2	no	—
142	#125	—	38	2	no	—
143	#125	—	38	2	no	—
144	#125	—	38	2	no	—
145	C₂×C₄⋊C₄	—	2	2	no	—
146	C₂×C₄⋊C₄	—	19	2	no	—
147	C₂×C₄⋊C₄	—	19	2	no	—
148	C₂×C₄⋊C₄	—	38	2	no	—
149	C₂×C₄⋊C₄	—	38	2	no	—
150	C₂×C₄⋊C₄	—	38	2	no	—
151	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
152	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
153	#107	—	38	8	no	—
154	#106	—	38	8	no	—
155	#103	—	4	4	no	—
156	#97	—	2	2	no	—
157	#97	—	19	4	no	—
158	#97	—	38	2	no	—
159	#95	—	2	2	no	—
160	#95	—	38	4	no	—
161	#95	—	38	2	no	—
162	C₁₉	#10087	1	1	yes	characteristic, complemented, Sylow
163	C₂×Q₈	—	2	2	no	—
164	C₂×Q₈	—	4	2	no	—
165	C₂×Q₈	—	4	2	no	—
166	C₂×Q₈	—	4	1	no	—
167	C₂²×C₄	—	2	2	no	—
168	C₂²×C₄	—	4	1	no	—
169	C₂²×C₄	—	38	2	no	—
170	C₂²×C₄	—	38	2	no	—
171	C₂²×C₄	D₄×D₁₉	1	2	yes	—
172	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
173	C₂×C₈	—	2	2	no	—
174	C₂×C₈	—	4	1	no	—
175	C₂×C₈	—	4	1	no	—
176	C₂×C₈	—	38	8	no	—
177	C₂×C₈	—	38	4	no	—
178	C₄⋊C₄	—	2	4	no	—
179	C₄⋊C₄	—	4	2	no	—
180	C₄⋊C₄	—	4	2	no	—
181	C₄⋊C₄	—	38	2	no	—
182	C₄⋊C₄	—	38	2	no	—
183	C₄⋊C₄	—	38	2	no	—
184	C₄⋊C₄	—	38	2	no	—
185	C₄⋊C₄	—	76	2	no	—
186	C₄⋊C₄	—	76	2	no	—
187	C₄⋊C₄	—	76	2	no	—
188	C₄⋊C₄	—	76	2	no	—
189	C₄⋊C₄	—	152	2	no	—
190	C₄²	C₂×D₇₆	1	1	yes	characteristic
191	C₄²	#64541	1	1	yes	characteristic
192	C₄²	D₄×D₁₉	1	2	yes	—
193	C₂³	#10597383	1	1	yes	characteristic
194	Q₈	—	4	4	no	—
195	Q₈	—	8	2	no	—
196	C₂×C₄	—	2	1	no	—
197	C₂×C₄	—	2	1	no	—
198	C₂×C₄	—	2	4	no	—
199	C₂×C₄	—	4	2	no	—
200	C₂×C₄	—	4	2	no	—
201	C₂×C₄	—	4	4	no	—
202	C₂×C₄	—	8	1	no	—
203	C₂×C₄	—	8	1	no	—
204	C₂×C₄	—	76	2	no	—
205	C₂×C₄	—	76	2	no	—
206	C₂×C₄	—	76	2	no	—
207	C₂×C₄	—	76	2	no	—
208	C₂×C₄	—	76	4	no	—
209	C₂×C₄	#10597328	1	2	yes	—
210	C₂×C₄	#10597330	1	2	yes	—
211	C₂×C₄	#10597376	1	1	yes	characteristic
212	C₂×C₄	#10597386	1	1	yes	characteristic
213	C₈	—	4	2	no	—
214	C₈	—	38	8	no	—
215	C₂²	#11926453	1	1	yes	characteristic
216	C₂²	#11926711	1	1	yes	characteristic
217	C₂²	#11926716	1	1	yes	characteristic
218	C₂²	#11926725	1	4	yes	—
219	C₄	—	2	2	no	—
220	C₄	—	2	2	no	—
221	C₄	—	2	1	no	—
222	C₄	—	2	1	no	—
223	C₄	—	8	2	no	—
224	C₄	—	8	2	no	—
225	C₄	—	152	2	no	—
226	C₄	—	152	2	no	—
227	C₂	#14562944	1	2	yes	—
228	C₂	#14562961	1	2	yes	—
229	C₂	#14564672	1	2	yes	—
230	C₂	#14564676	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926950

C₂

yes

maximal

#14571703

C₂

yes

maximal, characteristic

C₂×#11926285

C₂

yes

maximal

#14561516

C₂

yes

maximal, characteristic

C₁₉×#1960

C₂

yes

maximal, characteristic

C₂×#10597316

C₂²

yes

—

—

—

—

—

C₂²

yes

—

—

—

—

—

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₁₉×#103

—

C₂×C₁₉×#97

C₂²

yes

characteristic

C₁₉×#382

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

—

C₂²×C₈×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

D₄

yes

—

C₂×C₄⋊Dic₁₉

D₄

yes

—

C₂×Dic₁₉⋊C₄

—

C₂×Dic₁₉⋊C₄

—

C₂²×C₁₉⋊C₈

—

—

—

—

—

C₁₉×#103

—

C₁₉×#97

—

C₁₉×#95

—

C₁₉⋊#95

—

C₁₉⋊#95

—

—

—

—

D₄

yes

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

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×C₄×C₁₉

#120

yes

—

C₂×C₄×C₁₉

#121

yes

characteristic

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

#127

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

100

C₂×#501

—

101

#2822

—

102

#1960

D₁₉

yes

characteristic

103

C₂×#330

—

104

#1295

—

105

C₂²×C₁₉

#392

yes

characteristic

106

C₂²×C₁₉

#453

yes

characteristic

107

C₂²×C₁₉

#454

yes

characteristic

108

C₂²×C₁₉

#456

yes

—

109

C₄×C₁₉

—

110

C₄×C₁₉

—

111

C₄×C₁₉

—

112

C₄×C₁₉

—

113

C₄×C₁₉

—

114

C₄×C₁₉

—

115

Dic₁₉

—

116

Dic₁₉

—

117

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

118

C₂×#125

—

119

#501

—

120

#501

—

121

C₂×#107

—

122

C₂×#106

—

123

C₂×#103

—

124

C₂×#97

—

125

C₂×#97

C₂×D₁₉

yes

characteristic

126

#400

—

127

#398

—

128

#398

—

129

#382

C₂×D₁₉

yes

characteristic

130

#330

—

131

C₂×C₁₉

#1660

yes

—

132

C₂×C₁₉

#1663

yes

—

133

C₂×C₁₉

#2005

yes

—

134

C₂×C₁₉

#2006

yes

characteristic

135

C₂²×Q₈

—

136

C₂²×C₈

—

137

C₂²×C₈

—

138

C₄⋊Q₈

—

139

C₄⋊Q₈

—

140

C₄⋊Q₈

D₇₆

yes

—

141

#125

—

142

#125

—

143

#125

—

144

#125

—

145

C₂×C₄⋊C₄

—

146

C₂×C₄⋊C₄

—

147

C₂×C₄⋊C₄

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

152

C₂×C₄²

C₂²×D₁₉

yes

characteristic

153

#107

—

154

#106

—

155

#103

—

156

#97

—

157

#97

—

158

#97

—

159

#95

—

160

#95

—

161

#95

—

162

C₁₉

#10087

yes

characteristic, complemented, Sylow

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂×Q₈

—

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

—

170

C₂²×C₄

—

171

C₂²×C₄

D₄×D₁₉

yes

—

172

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

152

—

190

C₄²

C₂×D₇₆

yes

characteristic

191

C₄²

#64541

yes

characteristic

192

C₄²

D₄×D₁₉

yes

—

193

C₂³

#10597383

yes

characteristic

194

Q₈

—

195

Q₈

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

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

#10597328

yes

—

210

C₂×C₄

#10597330

yes

—

211

C₂×C₄

#10597376

yes

characteristic

212

C₂×C₄

#10597386

yes

characteristic

213

C₈

—

214

C₈

—

215

C₂²

#11926453

yes

characteristic

216

C₂²

#11926711

yes

characteristic

217

C₂²

#11926716

yes

characteristic

218

C₂²

#11926725

yes

—

219

C₄

—

220

C₄

—

221

C₄

—

222

C₄

—

223

C₄

—

224

C₄

—

225

C₄

—

152

—

226

C₄

—

152

—

227

C₂

#14562944

yes

—

228

C₂

#14562961

yes

—

229

C₂

#14564672

yes

—

230

C₂

#14564676

yes

characteristic

	subgroup	G/H
center	C₂³	#10597383
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1960	C₂
socle, prime radical	C₂³×C₁₉	#120
hypercenter	#1960	D₁₉
hypocenter	C₁₉	#10087
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1960

subgroup

G/H

center

C₂³

#10597383

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1960

C₂

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1960

N	H ≅ G/N	type
162. C₁₉	#10087	semidirect

H ≅ G/N

type

162. C₁₉

#10087

semidirect

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

subgroup	index
C₂×#11926950	2
#14571703	2
C₂×#11926285	2
#14561516	2
C₁₉×#1960	2
#10087	19

subgroup

index

C₁₉×#1960

Subgroups — #18083874

Conjugacy classes of subgroups

Complements

Maximal subgroups