Group #14564774 — subgroups

Subgroups — #14564774

Order 2432.

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

normal subgroups only

This group has 290 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	C₂×#10597334	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597292	C₂	1	1	yes	maximal, characteristic
3	#11926451	C₂	1	1	yes	maximal, characteristic
4	#11926307	C₂	1	1	yes	maximal, characteristic
5	#11926306	C₂	1	1	yes	maximal, characteristic
6	#11926298	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#103	C₂	1	1	yes	maximal, characteristic
8	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×Dic₃₈	—	2	1	no	—
10	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
14	C₂×Dic₁₉⋊C₄	—	2	1	no	—
15	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
16	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
17	#10597334	—	2	2	no	—
18	#10597334	—	2	2	no	—
19	C₁₉×#103	—	2	2	no	—
20	#10597292	—	2	2	no	—
21	C₁₉⋊#95	—	2	1	no	—
22	C₁₉⋊#95	—	2	1	no	—
23	C₂×Q₈×C₁₉	—	2	1	no	—
24	C₂×Q₈×C₁₉	—	2	1	no	—
25	C₂×Q₈×C₁₉	—	2	1	no	—
26	C₂×Q₈×C₁₉	—	2	1	no	—
27	C₂×Q₈×C₁₉	—	2	1	no	—
28	C₂×Q₈×C₁₉	Q₈	1	2	yes	complemented
29	C₂²×C₄×C₁₉	—	2	1	no	—
30	C₂²×C₄×C₁₉	—	2	1	no	—
31	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
32	C₂²×Dic₁₉	—	2	1	no	—
33	C₂²×Dic₁₉	—	2	1	no	—
34	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
35	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
36	C₂×Dic₃₈	—	2	4	no	—
37	C₂×Dic₃₈	—	4	2	no	—
38	C₂×Dic₃₈	—	4	2	no	—
39	C₂×C₈×C₁₉	—	2	1	no	—
40	C₂×C₈×C₁₉	—	2	1	no	—
41	C₂×C₈×C₁₉	—	2	1	no	—
42	C₄⋊C₄×C₁₉	—	2	1	no	—
43	C₄⋊C₄×C₁₉	D₄	1	2	yes	—
44	C₄⋊Dic₁₉	—	2	1	no	—
45	C₄⋊Dic₁₉	—	2	1	no	—
46	C₄⋊Dic₁₉	—	2	1	no	—
47	C₄⋊Dic₁₉	D₄	1	2	yes	—
48	Dic₁₉⋊C₄	—	2	4	no	—
49	C₄×Dic₁₉	—	2	1	no	—
50	C₄×Dic₁₉	—	2	1	no	—
51	C₂×C₁₉⋊C₈	—	2	1	no	—
52	C₂×C₁₉⋊C₈	—	2	1	no	—
53	C₂×C₁₉⋊C₈	—	2	1	no	—
54	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
55	Q₈×C₁₉	—	2	2	no	—
56	Q₈×C₁₉	—	2	2	no	—
57	Q₈×C₁₉	—	4	1	no	—
58	Q₈×C₁₉	—	4	1	no	—
59	C₂×C₄×C₁₉	—	2	2	no	—
60	C₂×C₄×C₁₉	—	2	2	no	—
61	C₂×C₄×C₁₉	—	4	1	no	—
62	C₂×C₄×C₁₉	—	4	1	no	—
63	C₂×C₄×C₁₉	—	4	1	no	—
64	C₂×C₄×C₁₉	—	4	1	no	—
65	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
66	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
67	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
68	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
69	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
70	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
71	C₂×Dic₁₉	—	2	1	no	—
72	C₂×Dic₁₉	—	2	1	no	—
73	C₂×Dic₁₉	—	2	1	no	—
74	C₂×Dic₁₉	—	2	1	no	—
75	C₂×Dic₁₉	—	2	2	no	—
76	C₂×Dic₁₉	—	4	1	no	—
77	C₂×Dic₁₉	—	4	1	no	—
78	C₂×Dic₁₉	—	4	1	no	—
79	C₂×Dic₁₉	—	4	1	no	—
80	C₂×Dic₁₉	—	4	1	no	—
81	C₂×Dic₁₉	SD₁₆	1	2	yes	—
82	C₂×Dic₁₉	Q₁₆	1	2	yes	—
83	Dic₃₈	—	4	8	no	—
84	C₈×C₁₉	—	4	1	no	—
85	C₁₉⋊C₈	—	4	1	no	—
86	#2024	—	19	1	no	maximal, Sylow
87	C₂²×C₁₉	#120	1	1	yes	characteristic
88	C₂²×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
89	C₂²×C₁₉	#124	1	1	yes	characteristic
90	C₂²×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
91	C₂²×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
92	C₂²×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
93	C₂²×C₁₉	#137	1	1	yes	characteristic
94	C₄×C₁₉	—	4	2	no	—
95	C₄×C₁₉	—	4	2	no	—
96	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
97	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
98	C₄×C₁₉	#124	1	1	yes	characteristic
99	C₄×C₁₉	#124	1	1	yes	characteristic
100	Dic₁₉	—	2	2	no	—
101	Dic₁₉	—	2	2	no	—
102	Dic₁₉	—	4	2	no	—
103	Dic₁₉	—	8	1	no	—
104	C₂×C₄⋊Q₈	—	19	1	no	—
105	C₂×#103	—	19	1	no	—
106	C₂×#103	D₁₉	1	1	yes	characteristic
107	#391	—	19	1	no	—
108	#340	—	19	1	no	—
109	#340	—	19	1	no	—
110	#336	—	19	1	no	—
111	C₂×C₁₉	#393	1	1	yes	characteristic
112	C₂×C₁₉	#450	1	1	yes	characteristic
113	C₂×C₁₉	#451	1	1	yes	characteristic
114	C₂×C₁₉	#475	1	1	yes	characteristic
115	C₂×C₁₉	#477	1	1	yes	characteristic
116	C₂×C₁₉	#487	1	1	yes	characteristic
117	C₂×C₁₉	#489	1	1	yes	characteristic
118	C₂²×Q₈	—	38	1	no	—
119	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
120	C₂²×C₈	—	19	1	no	—
121	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
122	C₄⋊Q₈	—	38	2	no	—
123	C₄⋊Q₈	—	38	2	no	—
124	C₂×C₄⋊C₄	—	19	1	no	—
125	C₂×C₄⋊C₄	—	19	1	no	—
126	C₂×C₄⋊C₄	—	38	1	no	—
127	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
128	C₂×C₄²	—	19	1	no	—
129	#103	—	2	2	no	—
130	#103	—	38	2	no	—
131	#95	—	38	1	no	—
132	#95	—	38	1	no	—
133	C₁₉	#2024	1	1	yes	characteristic, complemented, Sylow
134	C₂×Q₈	—	2	1	no	—
135	C₂×Q₈	—	2	1	no	—
136	C₂×Q₈	—	2	1	no	—
137	C₂×Q₈	—	2	1	no	—
138	C₂×Q₈	—	2	1	no	—
139	C₂×Q₈	—	38	4	no	—
140	C₂×Q₈	—	76	2	no	—
141	C₂×Q₈	—	76	2	no	—
142	C₂×Q₈	Dic₃₈	1	2	yes	complemented
143	C₂²×C₄	—	2	1	no	—
144	C₂²×C₄	—	2	1	no	—
145	C₂²×C₄	—	19	1	no	—
146	C₂²×C₄	—	19	1	no	—
147	C₂²×C₄	—	38	1	no	—
148	C₂²×C₄	—	38	1	no	—
149	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
150	C₂×C₈	—	2	1	no	—
151	C₂×C₈	—	2	1	no	—
152	C₂×C₈	—	2	1	no	—
153	C₂×C₈	—	38	1	no	—
154	C₂×C₈	—	38	1	no	—
155	C₂×C₈	—	38	1	no	—
156	C₄⋊C₄	—	2	1	no	—
157	C₄⋊C₄	—	19	2	no	—
158	C₄⋊C₄	—	38	4	no	—
159	C₄⋊C₄	—	38	1	no	—
160	C₄⋊C₄	—	38	1	no	—
161	C₄⋊C₄	—	38	1	no	—
162	C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
163	C₄²	—	38	1	no	—
164	C₄²	—	38	1	no	—
165	C₂³	D₄×D₁₉	1	1	yes	characteristic
166	Q₈	—	2	2	no	—
167	Q₈	—	2	2	no	—
168	Q₈	—	4	1	no	—
169	Q₈	—	4	1	no	—
170	Q₈	—	76	8	no	—
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	—	2	2	no	—
173	C₂×C₄	—	4	1	no	—
174	C₂×C₄	—	4	1	no	—
175	C₂×C₄	—	4	1	no	—
176	C₂×C₄	—	4	1	no	—
177	C₂×C₄	—	19	2	no	—
178	C₂×C₄	—	19	2	no	—
179	C₂×C₄	—	38	1	no	—
180	C₂×C₄	—	38	1	no	—
181	C₂×C₄	—	38	1	no	—
182	C₂×C₄	—	38	1	no	—
183	C₂×C₄	—	38	2	no	—
184	C₂×C₄	—	76	1	no	—
185	C₂×C₄	—	76	1	no	—
186	C₂×C₄	—	76	1	no	—
187	C₂×C₄	—	76	1	no	—
188	C₂×C₄	—	76	1	no	—
189	C₂×C₄	C₂×Dic₃₈	1	1	yes	characteristic
190	C₂×C₄	#64541	1	1	yes	characteristic
191	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
192	C₂×C₄	#64543	1	1	yes	characteristic
193	C₂×C₄	#64543	1	1	yes	characteristic
194	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
195	C₈	—	4	1	no	—
196	C₈	—	76	1	no	—
197	C₂²	#10597324	1	1	yes	characteristic
198	C₂²	#10597331	1	1	yes	characteristic
199	C₂²	SD₁₆×D₁₉	1	1	yes	characteristic
200	C₂²	#10597360	1	1	yes	characteristic
201	C₂²	Q₁₆×D₁₉	1	1	yes	characteristic
202	C₂²	#10597364	1	1	yes	characteristic
203	C₂²	#10597383	1	1	yes	characteristic
204	C₄	—	4	2	no	—
205	C₄	—	4	2	no	—
206	C₄	—	38	2	no	—
207	C₄	—	38	2	no	—
208	C₄	—	76	2	no	—
209	C₄	—	152	1	no	—
210	C₄	#10597324	1	1	yes	characteristic
211	C₄	#10597331	1	1	yes	characteristic
212	C₄	#10597370	1	1	yes	characteristic
213	C₄	#10597382	1	1	yes	characteristic
214	C₂	#11926456	1	1	yes	characteristic
215	C₂	#11926693	1	1	yes	characteristic
216	C₂	#11926698	1	1	yes	characteristic
217	C₂	#11926827	1	1	yes	characteristic
218	C₂	#11926837	1	1	yes	characteristic
219	C₂	#11926893	1	1	yes	characteristic
220	C₂	#11926905	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597334

C₂

yes

maximal, characteristic

C₂×#10597292

C₂

yes

maximal, characteristic

#11926451

C₂

yes

maximal, characteristic

#11926307

C₂

yes

maximal, characteristic

#11926306

C₂

yes

maximal, characteristic

#11926298

C₂

yes

maximal, characteristic

C₂×C₁₉×#103

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

C₂²

yes

characteristic

C₂²×Dic₃₈

—

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

#10597334

—

#10597334

—

C₁₉×#103

—

#10597292

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

Q₈

yes

complemented

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×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

D₄

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

D₄

yes

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

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×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

SD₁₆

yes

—

C₂×Dic₁₉

Q₁₆

yes

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

—

C₂²×C₁₉

yes

C₂²×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂²×C₁₉

#124

yes

characteristic

C₂²×C₁₉

C₂×SD₁₆

yes

characteristic

C₂²×C₁₉

C₂×Q₁₆

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₄×C₁₉

C₂²⋊Q₈

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

100

Dic₁₉

—

101

Dic₁₉

—

102

Dic₁₉

—

103

Dic₁₉

—

104

C₂×C₄⋊Q₈

—

105

C₂×#103

—

106

C₂×#103

D₁₉

yes

characteristic

107

#391

—

108

#340

—

109

#340

—

110

#336

—

111

C₂×C₁₉

#393

yes

characteristic

112

C₂×C₁₉

#450

yes

characteristic

113

C₂×C₁₉

#451

yes

characteristic

114

C₂×C₁₉

#475

yes

characteristic

115

C₂×C₁₉

#477

yes

characteristic

116

C₂×C₁₉

#487

yes

characteristic

117

C₂×C₁₉

#489

yes

characteristic

118

C₂²×Q₈

—

119

C₂²×Q₈

C₂×D₁₉

yes

characteristic

120

C₂²×C₈

—

121

C₂²×C₈

C₂×D₁₉

yes

characteristic

122

C₄⋊Q₈

—

123

C₄⋊Q₈

—

124

C₂×C₄⋊C₄

—

125

C₂×C₄⋊C₄

—

126

C₂×C₄⋊C₄

—

127

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

128

C₂×C₄²

—

129

#103

—

130

#103

—

131

#95

—

132

#95

—

133

C₁₉

#2024

yes

characteristic, complemented, Sylow

134

C₂×Q₈

—

135

C₂×Q₈

—

136

C₂×Q₈

—

137

C₂×Q₈

—

138

C₂×Q₈

—

139

C₂×Q₈

—

140

C₂×Q₈

—

141

C₂×Q₈

—

142

C₂×Q₈

Dic₃₈

yes

complemented

143

C₂²×C₄

—

144

C₂²×C₄

—

145

C₂²×C₄

—

146

C₂²×C₄

—

147

C₂²×C₄

—

148

C₂²×C₄

—

149

C₂²×C₄

C₂²×D₁₉

yes

characteristic

150

C₂×C₈

—

151

C₂×C₈

—

152

C₂×C₈

—

153

C₂×C₈

—

154

C₂×C₈

—

155

C₂×C₈

—

156

C₄⋊C₄

—

157

C₄⋊C₄

—

158

C₄⋊C₄

—

159

C₄⋊C₄

—

160

C₄⋊C₄

—

161

C₄⋊C₄

—

162

C₄⋊C₄

C₂²⋊D₁₉

yes

—

163

C₄²

—

164

C₄²

—

165

C₂³

D₄×D₁₉

yes

characteristic

166

Q₈

—

167

Q₈

—

168

Q₈

—

169

Q₈

—

170

Q₈

—

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

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

C₂×Dic₃₈

yes

characteristic

190

C₂×C₄

#64541

yes

characteristic

191

C₂×C₄

D₄×D₁₉

yes

characteristic

192

C₂×C₄

#64543

yes

characteristic

193

C₂×C₄

#64543

yes

characteristic

194

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

195

C₈

—

196

C₈

—

197

C₂²

#10597324

yes

characteristic

198

C₂²

#10597331

yes

characteristic

199

C₂²

SD₁₆×D₁₉

yes

characteristic

200

C₂²

#10597360

yes

characteristic

201

C₂²

Q₁₆×D₁₉

yes

characteristic

202

C₂²

#10597364

yes

characteristic

203

C₂²

#10597383

yes

characteristic

204

C₄

—

205

C₄

—

206

C₄

—

207

C₄

—

208

C₄

—

209

C₄

—

152

—

210

C₄

#10597324

yes

characteristic

211

C₄

#10597331

yes

characteristic

212

C₄

#10597370

yes

characteristic

213

C₄

#10597382

yes

characteristic

214

C₂

#11926456

yes

characteristic

215

C₂

#11926693

yes

characteristic

216

C₂

#11926698

yes

characteristic

217

C₂

#11926827

yes

characteristic

218

C₂

#11926837

yes

characteristic

219

C₂

#11926893

yes

characteristic

220

C₂

#11926905

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₁₉
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#103	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
hypercenter	C₂×#103	D₁₉
hypocenter	C₁₉	#2024
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#103

subgroup

G/H

center

C₂³

D₄×D₁₉

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#103

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#103

N	H ≅ G/N	type
28. C₂×Q₈×C₁₉	Q₈	semidirect
133. C₁₉	#2024	semidirect
142. C₂×Q₈	Dic₃₈	semidirect

H ≅ G/N

type

28. C₂×Q₈×C₁₉

Q₈

semidirect

133. C₁₉

#2024

semidirect

142. C₂×Q₈

Dic₃₈

semidirect

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

subgroup	index
C₂×#10597334	2
C₂×#10597292	2
#11926451	2
#11926307	2
#11926306	2
#11926298	2
C₂×C₁₉×#103	2
#2024	19

subgroup

index

C₂×C₁₉×#103

Subgroups — #14564774

Conjugacy classes of subgroups

Complements

Maximal subgroups