Group #14573167 — subgroups

Subgroups — #14573167

Order 2432.

458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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	C₂²×#64528	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927115	C₂	1	1	yes	maximal, characteristic
3	#11927022	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926764	C₂	1	4	yes	maximal, complemented
5	#11926752	C₂	1	4	yes	maximal, complemented
6	#11926572	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926554	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926540	C₂	1	1	yes	maximal, characteristic
9	C₂×C₁₉×#137	C₂	1	1	yes	maximal, characteristic
10	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
13	C₁₉×#137	—	2	4	no	—
14	C₂×Q₁₆×C₁₉	C₂²	1	2	yes	—
15	C₂×SD₁₆×C₁₉	C₂²	1	2	yes	—
16	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
17	Q₈×Dic₁₉	—	2	2	no	—
18	Q₈×Dic₁₉	C₂²	1	4	yes	—
19	#10597390	C₂²	1	2	yes	—
20	C₂×#64528	—	2	4	no	—
21	C₂×#64528	C₂²	1	4	yes	—
22	#10597382	C₂²	1	2	yes	—
23	#10597381	—	2	2	no	—
24	#10597372	—	2	2	no	—
25	#10597372	C₂²	1	1	yes	characteristic
26	#10597372	C₂²	1	1	yes	characteristic
27	#10597370	—	2	2	no	—
28	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
29	#10597292	C₂²	1	2	yes	—
30	#10597289	C₂²	1	2	yes	—
31	#10597273	C₂²	1	4	yes	—
32	Dic₁₉⋊C₈	C₂²	1	4	yes	—
33	#41×C₁₉	—	2	2	no	—
34	#41×C₁₉	—	2	2	no	—
35	C₂×Q₈×C₁₉	—	2	1	no	—
36	C₂×Q₈×C₁₉	—	2	2	no	—
37	C₂×Q₈×C₁₉	D₄	1	4	yes	—
38	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
39	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
40	C₂×D₄×C₁₉	—	2	1	no	—
41	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	—	2	1	no	—
43	C₂²×C₄×C₁₉	—	2	1	no	—
44	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
45	C₂²×Dic₁₉	—	2	1	no	—
46	C₂×Dic₃₈	—	2	2	no	—
47	C₂×Dic₃₈	—	2	2	no	—
48	C₂×Dic₃₈	—	2	1	no	—
49	C₂×Dic₃₈	C₂³	1	2	yes	—
50	Q₁₆×C₁₉	—	2	4	no	—
51	SD₁₆×C₁₉	—	2	4	no	—
52	M₁₆×C₁₉	—	2	2	no	—
53	C₂×C₈×C₁₉	C₂³	1	2	yes	—
54	C₂²⋊Dic₁₉	—	2	1	no	—
55	C₂²⋊Dic₁₉	—	2	4	no	—
56	C₂²⋊Dic₁₉	D₄	1	2	yes	—
57	#64528	—	2	8	no	—
58	C₄⋊Dic₁₉	—	2	4	no	—
59	C₄⋊Dic₁₉	D₄	1	2	yes	—
60	C₄⋊Dic₁₉	C₂³	1	2	yes	—
61	Dic₁₉⋊C₄	—	2	4	no	—
62	C₄×Dic₁₉	—	2	1	no	—
63	C₄×Dic₁₉	—	2	4	no	—
64	C₄×Dic₁₉	C₂³	1	2	yes	—
65	C₂×C₁₉⋊C₈	—	2	2	no	—
66	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
67	C₂³×C₁₉	—	2	1	no	—
68	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
69	Q₈×C₁₉	—	2	4	no	—
70	Q₈×C₁₉	—	2	2	no	—
71	Q₈×C₁₉	—	2	1	no	—
72	Q₈×C₁₉	—	2	1	no	—
73	Q₈×C₁₉	C₂×D₄	1	4	yes	—
74	D₄×C₁₉	—	2	1	no	—
75	D₄×C₁₉	—	2	1	no	—
76	D₄×C₁₉	—	4	2	no	—
77	C₂×C₄×C₁₉	—	2	4	no	—
78	C₂×C₄×C₁₉	—	2	2	no	—
79	C₂×C₄×C₁₉	—	2	1	no	—
80	C₂×C₄×C₁₉	—	4	2	no	—
81	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
82	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
83	C₂×C₄×C₁₉	#41	1	2	yes	—
84	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
85	C₂×Dic₁₉	—	2	2	no	—
86	C₂×Dic₁₉	—	2	2	no	—
87	C₂×Dic₁₉	—	4	2	no	—
88	C₂×Dic₁₉	C₂×D₄	1	4	yes	—
89	Dic₃₈	—	2	2	no	—
90	Dic₃₈	—	2	2	no	—
91	Dic₃₈	—	4	2	no	—
92	C₈×C₁₉	—	2	2	no	—
93	C₁₉⋊C₈	—	2	2	no	—
94	#3044	—	19	1	no	maximal, Sylow
95	C₂²×C₁₉	—	2	2	no	—
96	C₂²×C₁₉	—	4	1	no	—
97	C₂²×C₁₉	—	4	2	no	—
98	C₂²×C₁₉	#121	1	2	yes	—
99	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
100	C₄×C₁₉	—	2	4	no	—
101	C₄×C₁₉	—	4	1	no	—
102	C₄×C₁₉	#121	1	2	yes	—
103	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
104	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
105	Dic₁₉	—	2	4	no	—
106	Dic₁₉	—	4	2	no	—
107	Dic₁₉	—	4	2	no	—
108	C₂×#137	D₁₉	1	1	yes	characteristic
109	C₂²×Q₁₆	—	19	1	no	—
110	#536	—	19	1	no	—
111	#519	—	19	1	no	—
112	#464	—	19	4	no	—
113	#462	—	19	4	no	—
114	#424	—	19	1	no	—
115	#419	—	19	1	no	—
116	#416	—	19	1	no	—
117	C₂×C₁₉	—	2	2	no	—
118	C₂×C₁₉	—	8	1	no	—
119	C₂×C₁₉	C₂×#121	1	1	yes	characteristic
120	C₂×C₁₉	#578	1	2	yes	—
121	C₂×#41	C₂×D₁₉	1	1	yes	characteristic
122	C₂²×Q₈	—	19	1	no	—
123	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
124	#137	—	2	4	no	—
125	C₂×Q₁₆	—	19	4	no	—
126	C₂×Q₁₆	—	38	4	no	—
127	C₂×Q₁₆	C₂×D₁₉	1	2	yes	—
128	C₂×SD₁₆	C₂×D₁₉	1	2	yes	—
129	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
130	C₂²×C₈	—	19	1	no	—
131	C₄⋊Q₈	—	19	2	no	—
132	#124	—	19	2	no	—
133	#123	—	38	2	no	—
134	C₂²⋊Q₈	—	38	2	no	—
135	C₄×Q₈	—	19	4	no	—
136	C₄×Q₈	—	38	2	no	—
137	#117	—	19	1	no	—
138	#117	—	19	1	no	—
139	#117	—	38	2	no	—
140	C₄⋊C₈	—	19	4	no	—
141	#103	—	19	2	no	—
142	#103	—	19	4	no	—
143	#102	—	19	2	no	—
144	C₁₉	#3044	1	1	yes	characteristic, complemented, Sylow
145	#41	—	2	2	no	—
146	#41	—	2	2	no	—
147	C₂×Q₈	—	2	1	no	—
148	C₂×Q₈	—	2	2	no	—
149	C₂×Q₈	—	19	2	no	—
150	C₂×Q₈	—	38	1	no	—
151	C₂×Q₈	—	38	2	no	—
152	C₂×Q₈	—	38	2	no	—
153	C₂×Q₈	C₂²⋊D₁₉	1	4	yes	—
154	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
155	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
156	C₂×D₄	—	2	1	no	—
157	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
158	C₂²×C₄	—	2	1	no	—
159	C₂²×C₄	—	2	1	no	—
160	C₂²×C₄	—	38	1	no	—
161	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
162	Q₁₆	—	2	4	no	—
163	Q₁₆	—	38	8	no	—
164	SD₁₆	—	2	4	no	—
165	M₁₆	—	2	2	no	—
166	C₂×C₈	—	19	2	no	—
167	C₂×C₈	—	38	2	no	—
168	C₂×C₈	C₂²×D₁₉	1	2	yes	—
169	C₄⋊C₄	—	19	2	no	—
170	C₄⋊C₄	—	19	2	no	—
171	C₄⋊C₄	—	38	4	no	—
172	C₄⋊C₄	—	38	4	no	—
173	C₂²⋊C₄	—	19	2	no	—
174	C₂²⋊C₄	—	38	4	no	—
175	C₂²⋊C₄	—	38	1	no	—
176	C₄²	—	19	2	no	—
177	C₄²	—	38	4	no	—
178	C₄²	—	38	1	no	—
179	C₂³	—	2	1	no	—
180	C₂³	D₄×D₁₉	1	1	yes	characteristic
181	Q₈	—	2	4	no	—
182	Q₈	—	2	2	no	—
183	Q₈	—	2	1	no	—
184	Q₈	—	2	1	no	—
185	Q₈	—	38	2	no	—
186	Q₈	—	38	2	no	—
187	Q₈	—	76	2	no	—
188	Q₈	C₂×C₂²⋊D₁₉	1	4	yes	—
189	D₄	—	2	1	no	—
190	D₄	—	2	1	no	—
191	D₄	—	4	2	no	—
192	C₂×C₄	—	2	4	no	—
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	2	1	no	—
195	C₂×C₄	—	4	2	no	—
196	C₂×C₄	—	19	4	no	—
197	C₂×C₄	—	38	2	no	—
198	C₂×C₄	—	38	2	no	—
199	C₂×C₄	—	76	2	no	—
200	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
201	C₂×C₄	#64543	1	2	yes	—
202	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
203	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
204	C₈	—	2	2	no	—
205	C₈	—	38	2	no	—
206	C₂²	—	2	2	no	—
207	C₂²	—	4	2	no	—
208	C₂²	—	4	1	no	—
209	C₂²	#10597385	1	2	yes	—
210	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
211	C₄	—	2	4	no	—
212	C₄	—	4	1	no	—
213	C₄	—	38	4	no	—
214	C₄	—	76	2	no	—
215	C₄	—	76	2	no	—
216	C₄	#10597385	1	2	yes	—
217	C₄	C₂×#64543	1	1	yes	characteristic
218	C₄	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
219	C₂	—	2	2	no	—
220	C₂	—	8	1	no	—
221	C₂	C₂×#10597385	1	1	yes	characteristic
222	C₂	#11927360	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#64528

C₂

yes

maximal, characteristic, complemented

#11927115

C₂

yes

maximal, characteristic

#11927022

C₂

yes

maximal, characteristic, complemented

#11926764

C₂

yes

maximal, complemented

#11926752

C₂

yes

maximal, complemented

#11926572

C₂

yes

maximal, characteristic, complemented

#11926554

C₂

yes

maximal, characteristic, complemented

#11926540

C₂

yes

maximal, characteristic

C₂×C₁₉×#137

C₂

yes

maximal, characteristic

C₂×#41×C₁₉

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

characteristic

C₁₉×#137

—

C₂×Q₁₆×C₁₉

C₂²

yes

—

C₂×SD₁₆×C₁₉

C₂²

yes

—

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

Q₈×Dic₁₉

—

Q₈×Dic₁₉

C₂²

yes

—

#10597390

C₂²

yes

—

C₂×#64528

—

C₂×#64528

C₂²

yes

—

#10597382

C₂²

yes

—

#10597381

—

#10597372

—

#10597372

C₂²

yes

characteristic

#10597372

C₂²

yes

characteristic

#10597370

—

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

#10597292

C₂²

yes

—

#10597289

C₂²

yes

—

#10597273

C₂²

yes

—

Dic₁₉⋊C₈

C₂²

yes

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

D₄

yes

—

C₂×Q₈×C₁₉

C₂³

yes

characteristic

C₂×Q₈×C₁₉

C₂³

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

C₂³

yes

—

Q₁₆×C₁₉

—

SD₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

C₂³

yes

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

D₄

yes

—

#64528

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

D₄

yes

—

C₄⋊Dic₁₉

C₂³

yes

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

C₂³

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂³

yes

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

C₂×D₄

yes

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×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

—

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×D₄

yes

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#3044

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#121

yes

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

100

C₄×C₁₉

—

101

C₄×C₁₉

—

102

C₄×C₁₉

#121

yes

—

103

C₄×C₁₉

C₂²×D₄

yes

characteristic

104

C₄×C₁₉

C₂×#41

yes

characteristic

105

Dic₁₉

—

106

Dic₁₉

—

107

Dic₁₉

—

108

C₂×#137

D₁₉

yes

characteristic

109

C₂²×Q₁₆

—

110

#536

—

111

#519

—

112

#464

—

113

#462

—

114

#424

—

115

#419

—

116

#416

—

117

C₂×C₁₉

—

118

C₂×C₁₉

—

119

C₂×C₁₉

C₂×#121

yes

characteristic

120

C₂×C₁₉

#578

yes

—

121

C₂×#41

C₂×D₁₉

yes

characteristic

122

C₂²×Q₈

—

123

C₂²×Q₈

C₂×D₁₉

yes

characteristic

124

#137

—

125

C₂×Q₁₆

—

126

C₂×Q₁₆

—

127

C₂×Q₁₆

C₂×D₁₉

yes

—

128

C₂×SD₁₆

C₂×D₁₉

yes

—

129

C₂×M₁₆

C₂×D₁₉

yes

characteristic

130

C₂²×C₈

—

131

C₄⋊Q₈

—

132

#124

—

133

#123

—

134

C₂²⋊Q₈

—

135

C₄×Q₈

—

136

C₄×Q₈

—

137

#117

—

138

#117

—

139

#117

—

140

C₄⋊C₈

—

141

#103

—

142

#103

—

143

#102

—

144

C₁₉

#3044

yes

characteristic, complemented, Sylow

145

#41

—

146

#41

—

147

C₂×Q₈

—

148

C₂×Q₈

—

149

C₂×Q₈

—

150

C₂×Q₈

—

151

C₂×Q₈

—

152

C₂×Q₈

—

153

C₂×Q₈

C₂²⋊D₁₉

yes

—

154

C₂×Q₈

C₂²×D₁₉

yes

characteristic

155

C₂×Q₈

C₂²×D₁₉

yes

—

156

C₂×D₄

—

157

C₂×D₄

C₂²×D₁₉

yes

characteristic

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

C₂²×D₁₉

yes

characteristic

162

Q₁₆

—

163

Q₁₆

—

164

SD₁₆

—

165

M₁₆

—

166

C₂×C₈

—

167

C₂×C₈

—

168

C₂×C₈

C₂²×D₁₉

yes

—

169

C₄⋊C₄

—

170

C₄⋊C₄

—

171

C₄⋊C₄

—

172

C₄⋊C₄

—

173

C₂²⋊C₄

—

174

C₂²⋊C₄

—

175

C₂²⋊C₄

—

176

C₄²

—

177

C₄²

—

178

C₄²

—

179

C₂³

—

180

C₂³

D₄×D₁₉

yes

characteristic

181

Q₈

—

182

Q₈

—

183

Q₈

—

184

Q₈

—

185

Q₈

—

186

Q₈

—

187

Q₈

—

188

Q₈

C₂×C₂²⋊D₁₉

yes

—

189

D₄

—

190

D₄

—

191

D₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

D₄×D₁₉

yes

characteristic

201

C₂×C₄

#64543

yes

—

202

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

203

C₂×C₄

C₂³×D₁₉

yes

characteristic

204

C₈

—

205

C₈

—

206

C₂²

—

207

C₂²

—

208

C₂²

—

209

C₂²

#10597385

yes

—

210

C₂²

C₂×D₄×D₁₉

yes

characteristic

211

C₄

—

212

C₄

—

213

C₄

—

214

C₄

—

215

C₄

—

216

C₄

#10597385

yes

—

217

C₄

C₂×#64543

yes

characteristic

218

C₄

C₂²×C₂²⋊D₁₉

yes

characteristic

219

C₂

—

220

C₂

—

221

C₂

C₂×#10597385

yes

characteristic

222

C₂

#11927360

yes

—

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₂×C₁₉×#137	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	C₂×#41×C₁₉	C₂²
hypercenter	C₂×#137	D₁₉
hypocenter	C₁₉	#3044
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#137

subgroup

G/H

center

C₂²

C₂×D₄×D₁₉

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₂×C₁₉×#137

C₂

socle

C₂²×C₁₉

C₂²×D₄

prime radical

C₂×#41×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#137

N	H ≅ G/N	type
1. C₂²×#64528	C₂	semidirect
3. #11927022	C₂	semidirect
4. #11926764	C₂	semidirect
5. #11926752	C₂	semidirect
6. #11926572	C₂	semidirect
7. #11926554	C₂	semidirect
144. C₁₉	#3044	semidirect

H ≅ G/N

type

1. C₂²×#64528

C₂

semidirect

3. #11927022

C₂

semidirect

4. #11926764

C₂

semidirect

5. #11926752

C₂

semidirect

6. #11926572

C₂

semidirect

7. #11926554

C₂

semidirect

144. C₁₉

#3044

semidirect

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

subgroup	index
C₂²×#64528	2
#11927115	2
#11927022	2
#11926764	2
#11926752	2
#11926572	2
#11926554	2
#11926540	2
C₂×C₁₉×#137	2
#3044	19

subgroup

index

C₂²×#64528

C₂×C₁₉×#137

Subgroups — #14573167

Conjugacy classes of subgroups

Complements

Maximal subgroups