Group #18083535 — subgroups

Subgroups — #18083535

Order 4864.

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

normal subgroups only

This group has 476 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	#14574159	C₂	1	1	yes	maximal, characteristic
2	#14573675	C₂	1	2	yes	maximal
3	#14564575	C₂	1	1	yes	maximal, characteristic
4	#14562039	C₂	1	2	yes	maximal
5	C₁₉×#1275	C₂	1	1	yes	maximal, characteristic
6	#11927101	C₂²	1	2	yes	—
7	C₂×C₄×Dic₃₈	C₂²	1	1	yes	characteristic
8	#11926953	—	2	2	no	—
9	#11926953	—	2	2	no	—
10	#11926880	—	2	2	no	—
11	#11926840	—	2	2	no	—
12	#11926755	—	2	2	no	—
13	#11926702	—	2	2	no	—
14	C₄×Dic₇₆	—	2	4	no	—
15	#11926582	—	2	2	no	—
16	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
17	#11926298	—	2	2	no	—
18	#11926276	—	2	4	no	—
19	C₁₉×#431	C₂²	1	2	yes	—
20	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
21	C₂²×Dic₃₈	D₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₉	D₄	1	2	yes	—
23	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
24	#10597372	—	2	2	no	—
25	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
26	#10597370	—	2	2	no	—
27	#10597370	—	2	2	no	—
28	C₂×Dic₁₉⋊C₄	—	2	1	no	—
29	C₂×C₄×Dic₁₉	—	2	1	no	—
30	C₂²×C₁₉⋊C₈	—	2	1	no	—
31	C₂×Dic₇₆	—	2	4	no	—
32	#10597316	—	2	2	no	—
33	#10597315	D₄	1	2	yes	—
34	#10597315	D₄	1	2	yes	—
35	C₄×Dic₃₈	—	2	2	no	—
36	C₄×Dic₃₈	—	2	2	no	—
37	C₄×Dic₃₈	—	2	2	no	—
38	C₄×Dic₃₈	—	2	2	no	—
39	C₁₉×C₄⋊C₈	—	2	2	no	—
40	C₁₉×C₂²⋊C₈	—	2	2	no	—
41	C₁₉×#97	—	2	2	no	—
42	C₄×C₈×C₁₉	D₄	1	4	yes	—
43	#10597275	—	2	2	no	—
44	#10597275	—	2	2	no	—
45	#10597275	—	2	4	no	—
46	#10597274	—	2	4	no	—
47	#10597273	—	2	4	no	—
48	#10597273	—	2	4	no	—
49	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
50	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
53	C₂²×Dic₁₉	—	2	1	no	—
54	C₂²×Dic₁₉	—	2	1	no	—
55	C₂×Dic₃₈	—	2	2	no	—
56	C₂×Dic₃₈	—	2	2	no	—
57	C₂×Dic₃₈	—	2	2	no	—
58	C₂×Dic₃₈	—	4	2	no	—
59	C₂×C₈×C₁₉	—	2	2	no	—
60	C₂×C₈×C₁₉	—	2	2	no	—
61	C₂×C₈×C₁₉	—	2	4	no	—
62	C₂×C₈×C₁₉	Q₁₆	1	4	yes	complemented
63	C₄²×C₁₉	C₂×D₄	1	2	yes	—
64	C₄²×C₁₉	C₂×D₄	1	2	yes	—
65	C₂²⋊Dic₁₉	—	4	2	no	—
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	—	2	2	no	—
71	Dic₁₉⋊C₄	—	4	2	no	—
72	Dic₁₉⋊C₄	—	4	2	no	—
73	Dic₁₉⋊C₄	—	4	2	no	—
74	C₄×Dic₁₉	—	4	1	no	—
75	C₄×Dic₁₉	—	4	1	no	—
76	C₄×Dic₁₉	—	4	2	no	—
77	C₂×C₁₉⋊C₈	—	4	1	no	—
78	C₂×C₁₉⋊C₈	—	4	2	no	—
79	Dic₇₆	—	4	8	no	—
80	#10037	—	19	1	no	maximal, Sylow
81	C₂³×C₁₉	#121	1	1	yes	characteristic
82	C₂×C₄×C₁₉	—	4	1	no	—
83	C₂×C₄×C₁₉	—	4	1	no	—
84	C₂×C₄×C₁₉	#120	1	2	yes	—
85	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
86	C₂×C₄×C₁₉	#121	1	2	yes	—
87	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
88	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
89	C₂×C₄×C₁₉	#137	1	2	yes	—
90	C₂×Dic₁₉	—	2	2	no	—
91	C₂×Dic₁₉	—	4	1	no	—
92	C₂×Dic₁₉	—	4	1	no	—
93	C₂×Dic₁₉	—	4	2	no	—
94	C₂×Dic₁₉	—	4	1	no	—
95	C₂×Dic₁₉	—	4	2	no	—
96	C₂×Dic₁₉	—	4	2	no	—
97	Dic₃₈	—	2	4	no	—
98	Dic₃₈	—	4	2	no	—
99	Dic₃₈	—	4	4	no	—
100	Dic₃₈	—	4	4	no	—
101	C₈×C₁₉	—	2	4	no	—
102	C₈×C₁₉	—	4	4	no	—
103	C₁₉⋊C₈	—	8	1	no	—
104	#3162	—	19	1	no	—
105	#3104	—	19	2	no	—
106	#1985	—	19	1	no	—
107	#1481	—	19	2	no	—
108	#1275	D₁₉	1	1	yes	characteristic
109	C₂²×C₁₉	—	2	1	no	—
110	C₂²×C₁₉	—	2	1	no	—
111	C₂²×C₁₉	#392	1	1	yes	characteristic
112	C₂²×C₁₉	#462	1	2	yes	—
113	C₄×C₁₉	—	2	2	no	—
114	C₄×C₁₉	—	2	2	no	—
115	C₄×C₁₉	#451	1	2	yes	—
116	C₄×C₁₉	#494	1	1	yes	characteristic
117	C₄×C₁₉	#497	1	1	yes	characteristic
118	Dic₁₉	—	4	2	no	—
119	Dic₁₉	—	8	2	no	—
120	Dic₁₉	—	8	2	no	—
121	Dic₁₉	—	8	1	no	—
122	#533	—	19	2	no	—
123	C₂×C₄×Q₈	—	19	1	no	—
124	#501	—	38	2	no	—
125	#501	—	38	2	no	—
126	#484	—	38	2	no	—
127	#477	—	38	2	no	—
128	#462	—	38	2	no	—
129	#451	—	38	2	no	—
130	C₄×Q₁₆	—	38	4	no	—
131	#431	C₂×D₁₉	1	2	yes	—
132	#427	—	38	2	no	—
133	C₂×C₄⋊C₈	—	19	1	no	—
134	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
135	#336	—	38	2	no	—
136	Q₈⋊C₈	—	38	4	no	—
137	C₂×C₁₉	—	2	2	no	—
138	C₂×C₁₉	#2010	1	1	yes	characteristic
139	C₂×C₁₉	#2016	1	1	yes	characteristic
140	C₂×C₁₉	#2017	1	1	yes	characteristic
141	C₂²×Q₈	—	19	1	no	—
142	C₂×Q₁₆	—	38	4	no	—
143	C₂²×C₈	—	38	1	no	—
144	C₂²×C₈	D₇₆	1	2	yes	—
145	C₄⋊Q₈	—	19	2	no	—
146	C₄⋊Q₈	—	19	2	no	—
147	#125	—	38	2	no	—
148	C₂²⋊Q₈	—	38	2	no	—
149	C₂²⋊Q₈	—	38	2	no	—
150	C₄×Q₈	—	38	2	no	—
151	C₄×Q₈	—	38	2	no	—
152	C₄×Q₈	—	38	2	no	—
153	C₄×Q₈	—	38	2	no	—
154	#117	—	38	2	no	—
155	C₂×C₄⋊C₄	—	19	1	no	—
156	C₂×C₄⋊C₄	—	38	1	no	—
157	C₂×C₄²	—	38	1	no	—
158	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
159	#107	—	38	2	no	—
160	#107	—	38	2	no	—
161	#107	—	38	4	no	—
162	#106	—	38	4	no	—
163	C₄⋊C₈	—	2	2	no	—
164	C₄⋊C₈	—	38	2	no	—
165	#103	—	38	4	no	—
166	#103	—	38	4	no	—
167	C₂²⋊C₈	—	2	2	no	—
168	#97	—	2	2	no	—
169	C₄×C₈	D₇₆	1	4	yes	—
170	C₁₉	#10037	1	1	yes	characteristic, complemented, Sylow
171	C₂×Q₈	—	38	2	no	—
172	C₂×Q₈	—	38	2	no	—
173	C₂×Q₈	—	38	2	no	—
174	C₂×Q₈	—	76	2	no	—
175	C₂²×C₄	—	38	1	no	—
176	C₂²×C₄	—	38	1	no	—
177	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
178	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
179	C₂²×C₄	#64545	1	1	yes	characteristic
180	Q₁₆	—	76	8	no	—
181	C₂×C₈	—	2	2	no	—
182	C₂×C₈	—	2	2	no	—
183	C₂×C₈	—	2	4	no	—
184	C₂×C₈	—	76	1	no	—
185	C₂×C₈	—	76	2	no	—
186	C₂×C₈	Dic₇₆	1	4	yes	complemented
187	C₄⋊C₄	—	38	2	no	—
188	C₄⋊C₄	—	38	2	no	—
189	C₄⋊C₄	—	38	2	no	—
190	C₄⋊C₄	—	38	2	no	—
191	C₄⋊C₄	—	38	2	no	—
192	C₄⋊C₄	—	76	2	no	—
193	C₄⋊C₄	—	76	2	no	—
194	C₄⋊C₄	—	76	2	no	—
195	C₂²⋊C₄	—	76	2	no	—
196	C₄²	—	76	1	no	—
197	C₄²	—	76	2	no	—
198	C₄²	—	76	1	no	—
199	C₄²	C₂×D₇₆	1	2	yes	—
200	C₄²	D₄×D₁₉	1	2	yes	—
201	C₂³	#10597341	1	1	yes	characteristic
202	Q₈	—	38	4	no	—
203	Q₈	—	76	2	no	—
204	Q₈	—	76	4	no	—
205	Q₈	—	76	4	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	—	4	1	no	—
208	C₂×C₄	—	38	2	no	—
209	C₂×C₄	—	76	1	no	—
210	C₂×C₄	—	76	1	no	—
211	C₂×C₄	—	76	2	no	—
212	C₂×C₄	—	76	1	no	—
213	C₂×C₄	—	76	2	no	—
214	C₂×C₄	—	76	2	no	—
215	C₂×C₄	#10597320	1	1	yes	characteristic
216	C₂×C₄	#10597328	1	2	yes	—
217	C₂×C₄	#10597328	1	1	yes	characteristic
218	C₂×C₄	#10597341	1	2	yes	—
219	C₂×C₄	C₂×Dic₇₆	1	2	yes	—
220	C₂×C₄	#10597355	1	2	yes	—
221	C₈	—	2	4	no	—
222	C₈	—	4	4	no	—
223	C₈	—	152	1	no	—
224	C₂²	—	2	1	no	—
225	C₂²	—	2	1	no	—
226	C₂²	#11926454	1	1	yes	characteristic
227	C₂²	#11926755	1	2	yes	—
228	C₄	—	2	2	no	—
229	C₄	—	2	2	no	—
230	C₄	—	76	2	no	—
231	C₄	—	152	2	no	—
232	C₄	—	152	1	no	—
233	C₄	—	152	2	no	—
234	C₄	#11926702	1	2	yes	—
235	C₄	#11926924	1	1	yes	characteristic
236	C₄	#11926938	1	1	yes	characteristic
237	C₂	—	2	2	no	—
238	C₂	#14564703	1	1	yes	characteristic
239	C₂	#14564737	1	1	yes	characteristic
240	C₂	#14564740	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14574159

C₂

yes

maximal, characteristic

#14573675

C₂

yes

maximal

#14564575

C₂

yes

maximal, characteristic

#14562039

C₂

yes

maximal

C₁₉×#1275

C₂

yes

maximal, characteristic

#11927101

C₂²

yes

—

C₂×C₄×Dic₃₈

C₂²

yes

—

—

—

—

—

—

C₄×Dic₇₆

—

#11926582

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

#11926298

—

#11926276

—

C₁₉×#431

C₂²

yes

—

C₂×C₁₉×#97

C₂²

yes

characteristic

C₂²×Dic₃₈

D₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

#10597372

—

C₂×C₄⋊Dic₁₉

D₄

yes

characteristic

#10597370

—

#10597370

—

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₂×Dic₇₆

—

#10597316

—

#10597315

D₄

yes

—

#10597315

D₄

yes

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₄×C₈×C₁₉

D₄

yes

—

—

—

—

—

—

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

Q₁₆

yes

complemented

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

Dic₇₆

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#120

yes

—

C₂×C₄×C₁₉

#120

yes

characteristic

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

#127

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₁₆

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

100

Dic₃₈

—

101

C₈×C₁₉

—

102

C₈×C₁₉

—

103

C₁₉⋊C₈

—

104

#3162

—

105

#3104

—

106

#1985

—

107

#1481

—

108

#1275

D₁₉

yes

characteristic

109

C₂²×C₁₉

—

110

C₂²×C₁₉

—

111

C₂²×C₁₉

#392

yes

characteristic

112

C₂²×C₁₉

#462

yes

—

113

C₄×C₁₉

—

114

C₄×C₁₉

—

115

C₄×C₁₉

#451

yes

—

116

C₄×C₁₉

#494

yes

characteristic

117

C₄×C₁₉

#497

yes

characteristic

118

Dic₁₉

—

119

Dic₁₉

—

120

Dic₁₉

—

121

Dic₁₉

—

122

#533

—

123

C₂×C₄×Q₈

—

124

#501

—

125

#501

—

126

#484

—

127

#477

—

128

#462

—

129

#451

—

130

C₄×Q₁₆

—

131

#431

C₂×D₁₉

yes

—

132

#427

—

133

C₂×C₄⋊C₈

—

134

C₂×#97

C₂×D₁₉

yes

characteristic

135

#336

—

136

Q₈⋊C₈

—

137

C₂×C₁₉

—

138

C₂×C₁₉

#2010

yes

characteristic

139

C₂×C₁₉

#2016

yes

characteristic

140

C₂×C₁₉

#2017

yes

characteristic

141

C₂²×Q₈

—

142

C₂×Q₁₆

—

143

C₂²×C₈

—

144

C₂²×C₈

D₇₆

yes

—

145

C₄⋊Q₈

—

146

C₄⋊Q₈

—

147

#125

—

148

C₂²⋊Q₈

—

149

C₂²⋊Q₈

—

150

C₄×Q₈

—

151

C₄×Q₈

—

152

C₄×Q₈

—

153

C₄×Q₈

—

154

#117

—

155

C₂×C₄⋊C₄

—

156

C₂×C₄⋊C₄

—

157

C₂×C₄²

—

158

C₂×C₄²

C₂²×D₁₉

yes

characteristic

159

#107

—

160

#107

—

161

#107

—

162

#106

—

163

C₄⋊C₈

—

164

C₄⋊C₈

—

165

#103

—

166

#103

—

167

C₂²⋊C₈

—

168

#97

—

169

C₄×C₈

D₇₆

yes

—

170

C₁₉

#10037

yes

characteristic, complemented, Sylow

171

C₂×Q₈

—

172

C₂×Q₈

—

173

C₂×Q₈

—

174

C₂×Q₈

—

175

C₂²×C₄

—

176

C₂²×C₄

—

177

C₂²×C₄

C₂×D₇₆

yes

characteristic

178

C₂²×C₄

D₄×D₁₉

yes

characteristic

179

C₂²×C₄

#64545

yes

characteristic

180

Q₁₆

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

Dic₇₆

yes

complemented

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₂²⋊C₄

—

196

C₄²

—

197

C₄²

—

198

C₄²

—

199

C₄²

C₂×D₇₆

yes

—

200

C₄²

D₄×D₁₉

yes

—

201

C₂³

#10597341

yes

characteristic

202

Q₈

—

203

Q₈

—

204

Q₈

—

205

Q₈

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

#10597320

yes

characteristic

216

C₂×C₄

#10597328

yes

—

217

C₂×C₄

#10597328

yes

characteristic

218

C₂×C₄

#10597341

yes

—

219

C₂×C₄

C₂×Dic₇₆

yes

—

220

C₂×C₄

#10597355

yes

—

221

C₈

—

222

C₈

—

223

C₈

—

152

—

224

C₂²

—

225

C₂²

—

226

C₂²

#11926454

yes

characteristic

227

C₂²

#11926755

yes

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

152

—

232

C₄

—

152

—

233

C₄

—

152

—

234

C₄

#11926702

yes

—

235

C₄

#11926924

yes

characteristic

236

C₄

#11926938

yes

characteristic

237

C₂

—

238

C₂

#14564703

yes

characteristic

239

C₂

#14564737

yes

characteristic

240

C₂

#14564740

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597320
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1275	C₂
socle	C₂²×C₁₉	#392
prime radical	C₂³×C₁₉	#121
hypercenter	#1275	D₁₉
hypocenter	C₁₉	#10037
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1275

subgroup

G/H

center

C₂×C₄

#10597320

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1275

C₂

C₂²×C₁₉

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1275

N	H ≅ G/N	type
62. C₂×C₈×C₁₉	Q₁₆	semidirect
170. C₁₉	#10037	semidirect
186. C₂×C₈	Dic₇₆	semidirect

H ≅ G/N

type

62. C₂×C₈×C₁₉

Q₁₆

semidirect

170. C₁₉

#10037

semidirect

186. C₂×C₈

Dic₇₆

semidirect

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

subgroup	index
#14574159	2
#14573675	2
#14564575	2
#14562039	2
C₁₉×#1275	2
#10037	19

subgroup

index

C₁₉×#1275

Subgroups — #18083535

Conjugacy classes of subgroups

Complements

Maximal subgroups