Group #14565011 — subgroups

Subgroups — #14565011

Order 2432.

248 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 87 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×Dic₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597273	C₂	1	1	yes	maximal, characteristic
3	C₂×#10597267	C₂	1	1	yes	maximal, characteristic
4	#11926449	C₂	1	1	yes	maximal, characteristic
5	#11926443	C₂	1	1	yes	maximal, characteristic
6	#11926306	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#106	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
9	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Dic₁₉	—	2	1	no	—
13	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
15	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
16	C₁₉×#106	—	2	2	no	—
17	C₁₉⋊#95	—	2	1	no	—
18	C₁₉⋊#95	—	2	1	no	—
19	C₁₉⋊#95	—	2	1	no	—
20	#10597273	—	2	2	no	—
21	Dic₁₉⋊C₈	—	2	2	no	—
22	#10597267	—	2	2	no	—
23	C₂²×C₄×C₁₉	—	2	1	no	—
24	C₂²×C₄×C₁₉	—	2	1	no	—
25	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
26	C₂²×Dic₁₉	—	2	1	no	—
27	C₂²×Dic₁₉	—	2	1	no	—
28	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
29	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
30	C₂×Dic₃₈	—	2	1	no	—
31	C₂×Dic₃₈	—	2	1	no	—
32	C₂×Dic₃₈	—	2	1	no	—
33	C₂×Dic₃₈	—	2	1	no	—
34	C₂×Dic₃₈	—	2	1	no	—
35	C₂×Dic₃₈	Q₈	1	2	yes	—
36	C₂×C₈×C₁₉	—	2	1	no	—
37	C₂×C₈×C₁₉	—	2	1	no	—
38	C₂×C₈×C₁₉	D₄	1	2	yes	—
39	C₄⋊C₄×C₁₉	—	2	1	no	—
40	C₄⋊C₄×C₁₉	—	2	1	no	—
41	C₄⋊C₄×C₁₉	—	2	1	no	—
42	C₄⋊C₄×C₁₉	D₄	1	2	yes	—
43	C₄⋊Dic₁₉	—	2	1	no	—
44	C₄⋊Dic₁₉	—	2	1	no	—
45	C₄⋊Dic₁₉	—	4	2	no	—
46	C₄×Dic₁₉	—	2	1	no	—
47	C₄×Dic₁₉	—	2	1	no	—
48	C₂×C₁₉⋊C₈	—	2	1	no	—
49	C₂×C₁₉⋊C₈	—	2	1	no	—
50	C₂×C₁₉⋊C₈	—	2	1	no	—
51	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
52	C₂×C₄×C₁₉	—	2	2	no	—
53	C₂×C₄×C₁₉	—	4	1	no	—
54	C₂×C₄×C₁₉	—	4	1	no	—
55	C₂×C₄×C₁₉	—	4	1	no	—
56	C₂×C₄×C₁₉	—	4	1	no	—
57	C₂×C₄×C₁₉	—	4	1	no	—
58	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
59	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
60	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
61	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
62	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
63	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
64	C₂×Dic₁₉	—	2	1	no	—
65	C₂×Dic₁₉	—	2	1	no	—
66	C₂×Dic₁₉	—	2	1	no	—
67	C₂×Dic₁₉	—	2	2	no	—
68	C₂×Dic₁₉	—	2	1	no	—
69	C₂×Dic₁₉	—	2	1	no	—
70	C₂×Dic₁₉	—	4	1	no	—
71	C₂×Dic₁₉	—	4	1	no	—
72	C₂×Dic₁₉	—	4	1	no	—
73	C₂×Dic₁₉	—	4	1	no	—
74	C₂×Dic₁₉	—	4	1	no	—
75	C₂×Dic₁₉	SD₁₆	1	2	yes	—
76	Dic₃₈	—	2	2	no	—
77	Dic₃₈	—	2	2	no	—
78	Dic₃₈	—	4	1	no	—
79	Dic₃₈	—	4	1	no	—
80	C₈×C₁₉	—	2	2	no	—
81	C₁₉⋊C₈	—	4	1	no	—
82	#2066	—	19	1	no	maximal, Sylow
83	C₂²×C₁₉	#121	1	1	yes	characteristic
84	C₂²×C₁₉	#121	1	1	yes	characteristic
85	C₂²×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
86	C₂²×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
87	C₂²×C₁₉	#135	1	1	yes	characteristic
88	C₂²×C₁₉	#137	1	1	yes	characteristic
89	C₂²×C₁₉	#137	1	1	yes	characteristic
90	C₄×C₁₉	—	4	2	no	—
91	C₄×C₁₉	—	8	1	no	—
92	C₄×C₁₉	#121	1	1	yes	characteristic
93	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
94	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
95	C₄×C₁₉	#126	1	1	yes	characteristic
96	Dic₁₉	—	2	2	no	—
97	Dic₁₉	—	4	2	no	—
98	Dic₁₉	—	4	1	no	—
99	Dic₁₉	—	8	1	no	—
100	C₂×#106	D₁₉	1	1	yes	characteristic
101	C₂×C₄⋊C₈	—	19	1	no	—
102	C₂×#103	—	19	1	no	—
103	C₂×#103	—	19	1	no	—
104	#391	—	19	1	no	—
105	#389	—	19	1	no	—
106	#340	—	19	1	no	—
107	C₂×C₁₉	#396	1	1	yes	characteristic
108	C₂×C₁₉	#461	1	1	yes	characteristic
109	C₂×C₁₉	#464	1	1	yes	characteristic
110	C₂×C₁₉	#465	1	1	yes	characteristic
111	C₂×C₁₉	#470	1	1	yes	characteristic
112	C₂×C₁₉	#475	1	1	yes	characteristic
113	C₂×C₁₉	#479	1	1	yes	characteristic
114	C₂²×Q₈	—	19	1	no	—
115	C₂²×C₈	—	19	1	no	—
116	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
117	C₂×C₄⋊C₄	—	19	1	no	—
118	C₂×C₄⋊C₄	—	38	1	no	—
119	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
120	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
121	C₂×C₄²	—	19	1	no	—
122	#106	—	2	2	no	—
123	C₄⋊C₈	—	38	2	no	—
124	#103	—	38	2	no	—
125	#103	—	38	2	no	—
126	#95	—	38	1	no	—
127	#95	—	38	1	no	—
128	#95	—	38	1	no	—
129	C₁₉	#2066	1	1	yes	characteristic, complemented, Sylow
130	C₂×Q₈	—	19	2	no	—
131	C₂×Q₈	—	38	1	no	—
132	C₂×Q₈	—	38	1	no	—
133	C₂×Q₈	—	38	1	no	—
134	C₂×Q₈	—	38	1	no	—
135	C₂×Q₈	—	38	1	no	—
136	C₂²×C₄	—	2	1	no	—
137	C₂²×C₄	—	2	1	no	—
138	C₂²×C₄	—	19	1	no	—
139	C₂²×C₄	—	19	1	no	—
140	C₂²×C₄	—	38	1	no	—
141	C₂²×C₄	—	38	1	no	—
142	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
143	C₂×C₈	—	2	1	no	—
144	C₂×C₈	—	2	1	no	—
145	C₂×C₈	—	38	1	no	—
146	C₂×C₈	—	38	1	no	—
147	C₂×C₈	—	38	1	no	—
148	C₂×C₈	D₇₆	1	2	yes	—
149	C₄⋊C₄	—	2	1	no	—
150	C₄⋊C₄	—	2	1	no	—
151	C₄⋊C₄	—	2	1	no	—
152	C₄⋊C₄	—	38	1	no	—
153	C₄⋊C₄	—	38	1	no	—
154	C₄⋊C₄	—	76	2	no	—
155	C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
156	C₄²	—	38	1	no	—
157	C₄²	—	38	1	no	—
158	C₂³	D₄×D₁₉	1	1	yes	characteristic
159	Q₈	—	38	2	no	—
160	Q₈	—	38	2	no	—
161	Q₈	—	76	1	no	—
162	Q₈	—	76	1	no	—
163	C₂×C₄	—	2	2	no	—
164	C₂×C₄	—	4	1	no	—
165	C₂×C₄	—	4	1	no	—
166	C₂×C₄	—	4	1	no	—
167	C₂×C₄	—	4	1	no	—
168	C₂×C₄	—	4	1	no	—
169	C₂×C₄	—	19	2	no	—
170	C₂×C₄	—	38	1	no	—
171	C₂×C₄	—	38	1	no	—
172	C₂×C₄	—	38	1	no	—
173	C₂×C₄	—	38	2	no	—
174	C₂×C₄	—	38	1	no	—
175	C₂×C₄	—	38	1	no	—
176	C₂×C₄	—	76	1	no	—
177	C₂×C₄	—	76	1	no	—
178	C₂×C₄	—	76	1	no	—
179	C₂×C₄	—	76	1	no	—
180	C₂×C₄	—	76	1	no	—
181	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
182	C₂×C₄	#64541	1	1	yes	characteristic
183	C₂×C₄	#64543	1	1	yes	characteristic
184	C₂×C₄	Q₈×D₁₉	1	1	yes	characteristic
185	C₂×C₄	#64545	1	1	yes	characteristic
186	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
187	C₈	—	2	2	no	—
188	C₈	—	76	1	no	—
189	C₂²	#10597341	1	1	yes	characteristic
190	C₂²	#10597342	1	1	yes	characteristic
191	C₂²	SD₁₆×D₁₉	1	1	yes	characteristic
192	C₂²	#10597361	1	1	yes	characteristic
193	C₂²	#10597361	1	1	yes	characteristic
194	C₂²	#10597362	1	1	yes	characteristic
195	C₂²	#10597385	1	1	yes	characteristic
196	C₄	—	4	2	no	—
197	C₄	—	8	1	no	—
198	C₄	—	38	2	no	—
199	C₄	—	76	1	no	—
200	C₄	—	76	2	no	—
201	C₄	—	152	1	no	—
202	C₄	#10597343	1	1	yes	characteristic
203	C₄	#10597344	1	1	yes	characteristic
204	C₄	#10597376	1	1	yes	characteristic
205	C₄	#10597392	1	1	yes	characteristic
206	C₂	#11926466	1	1	yes	characteristic
207	C₂	#11926747	1	1	yes	characteristic
208	C₂	#11926764	1	1	yes	characteristic
209	C₂	#11926774	1	1	yes	characteristic
210	C₂	#11926803	1	1	yes	characteristic
211	C₂	#11926828	1	1	yes	characteristic
212	C₂	#11926854	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Dic₁₉⋊C₈

C₂

yes

maximal, characteristic

C₂×#10597273

C₂

yes

maximal, characteristic

C₂×#10597267

C₂

yes

maximal, characteristic

#11926449

C₂

yes

maximal, characteristic

#11926443

C₂

yes

maximal, characteristic

#11926306

C₂

yes

maximal, characteristic

C₂×C₁₉×#106

C₂

yes

maximal, characteristic

C₂²×Dic₃₈

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₁₉×#106

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₁₉⋊#95

—

#10597273

—

Dic₁₉⋊C₈

—

#10597267

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

D₄

yes

characteristic

C₂²×Dic₁₉

D₄

yes

characteristic

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

Q₈

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

D₄

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

C₂×C₄×C₁₉

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

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

SD₁₆

yes

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂²×C₁₉

C₂×SD₁₆

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#121

yes

characteristic

C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₄×C₁₉

#126

yes

characteristic

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

100

C₂×#106

D₁₉

yes

characteristic

101

C₂×C₄⋊C₈

—

102

C₂×#103

—

103

C₂×#103

—

104

#391

—

105

#389

—

106

#340

—

107

C₂×C₁₉

#396

yes

characteristic

108

C₂×C₁₉

#461

yes

characteristic

109

C₂×C₁₉

#464

yes

characteristic

110

C₂×C₁₉

#465

yes

characteristic

111

C₂×C₁₉

#470

yes

characteristic

112

C₂×C₁₉

#475

yes

characteristic

113

C₂×C₁₉

#479

yes

characteristic

114

C₂²×Q₈

—

115

C₂²×C₈

—

116

C₂²×C₈

C₂×D₁₉

yes

characteristic

117

C₂×C₄⋊C₄

—

118

C₂×C₄⋊C₄

—

119

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

120

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

121

C₂×C₄²

—

122

#106

—

123

C₄⋊C₈

—

124

#103

—

125

#103

—

126

#95

—

127

#95

—

128

#95

—

129

C₁₉

#2066

yes

characteristic, complemented, Sylow

130

C₂×Q₈

—

131

C₂×Q₈

—

132

C₂×Q₈

—

133

C₂×Q₈

—

134

C₂×Q₈

—

135

C₂×Q₈

—

136

C₂²×C₄

—

137

C₂²×C₄

—

138

C₂²×C₄

—

139

C₂²×C₄

—

140

C₂²×C₄

—

141

C₂²×C₄

—

142

C₂²×C₄

C₂²×D₁₉

yes

characteristic

143

C₂×C₈

—

144

C₂×C₈

—

145

C₂×C₈

—

146

C₂×C₈

—

147

C₂×C₈

—

148

C₂×C₈

D₇₆

yes

—

149

C₄⋊C₄

—

150

C₄⋊C₄

—

151

C₄⋊C₄

—

152

C₄⋊C₄

—

153

C₄⋊C₄

—

154

C₄⋊C₄

—

155

C₄⋊C₄

C₂²⋊D₁₉

yes

—

156

C₄²

—

157

C₄²

—

158

C₂³

D₄×D₁₉

yes

characteristic

159

Q₈

—

160

Q₈

—

161

Q₈

—

162

Q₈

—

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

C₂×D₇₆

yes

characteristic

182

C₂×C₄

#64541

yes

characteristic

183

C₂×C₄

#64543

yes

characteristic

184

C₂×C₄

Q₈×D₁₉

yes

characteristic

185

C₂×C₄

#64545

yes

characteristic

186

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

187

C₈

—

188

C₈

—

189

C₂²

#10597341

yes

characteristic

190

C₂²

#10597342

yes

characteristic

191

C₂²

SD₁₆×D₁₉

yes

characteristic

192

C₂²

#10597361

yes

characteristic

193

C₂²

#10597361

yes

characteristic

194

C₂²

#10597362

yes

characteristic

195

C₂²

#10597385

yes

characteristic

196

C₄

—

197

C₄

—

198

C₄

—

199

C₄

—

200

C₄

—

201

C₄

—

152

—

202

C₄

#10597343

yes

characteristic

203

C₄

#10597344

yes

characteristic

204

C₄

#10597376

yes

characteristic

205

C₄

#10597392

yes

characteristic

206

C₂

#11926466

yes

characteristic

207

C₂

#11926747

yes

characteristic

208

C₂

#11926764

yes

characteristic

209

C₂

#11926774

yes

characteristic

210

C₂

#11926803

yes

characteristic

211

C₂

#11926828

yes

characteristic

212

C₂

#11926854

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₁₉
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#106	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
hypercenter	C₂×#106	D₁₉
hypocenter	C₁₉	#2066
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#106

subgroup

G/H

center

C₂³

D₄×D₁₉

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#106

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#106

N	H ≅ G/N	type
129. C₁₉	#2066	semidirect

H ≅ G/N

type

129. C₁₉

#2066

semidirect

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

subgroup	index
C₂×Dic₁₉⋊C₈	2
C₂×#10597273	2
C₂×#10597267	2
#11926449	2
#11926443	2
#11926306	2
C₂×C₁₉×#106	2
#2066	19

subgroup

index

C₂×Dic₁₉⋊C₈

C₂×C₁₉×#106

Subgroups — #14565011

Conjugacy classes of subgroups

Complements

Maximal subgroups