Group #14573765 — subgroups

Subgroups — #14573765

Order 2432.

380 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 133 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	#11927101	C₂	1	1	yes	maximal, characteristic
2	#11926874	C₂	1	2	yes	maximal
3	#11926829	C₂	1	2	yes	maximal, complemented
4	#11926754	C₂	1	2	yes	maximal, complemented
5	#11926700	C₂	1	2	yes	maximal
6	#11926649	C₂	1	4	yes	maximal, complemented
7	#11926601	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic
9	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₄×Q₈×C₁₉	—	2	1	no	—
11	C₄×Q₈×C₁₉	—	2	1	no	—
12	C₄×Q₈×C₁₉	C₂²	1	2	yes	—
13	C₄×Q₈×C₁₉	C₂²	1	2	yes	—
14	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
15	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₄²×C₁₉	—	2	1	no	—
17	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×#64528	C₂²	1	4	yes	—
19	#10597372	—	2	1	no	—
20	#10597370	—	2	1	no	—
21	#10597370	C₂²	1	2	yes	—
22	#10597316	—	2	1	no	—
23	#10597315	C₂²	1	1	yes	characteristic
24	#10597315	C₂²	1	1	yes	characteristic
25	C₄×Dic₃₈	—	2	1	no	—
26	C₄×Dic₃₈	C₂²	1	2	yes	—
27	#10597292	C₂²	1	4	yes	—
28	C₂²⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
29	#10597267	C₂²	1	4	yes	—
30	#10597265	C₂²	1	4	yes	—
31	C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
32	#10597260	C₂²	1	2	yes	—
33	C₂×Q₈×C₁₉	—	2	4	no	—
34	C₂×Q₈×C₁₉	—	2	1	no	—
35	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
36	C₂²×C₄×C₁₉	—	2	1	no	—
37	C₂²×C₄×C₁₉	—	2	1	no	—
38	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
39	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
41	C₂×Dic₃₈	—	2	1	no	—
42	C₂×Dic₃₈	C₂³	1	2	yes	—
43	C₄⋊C₄×C₁₉	—	2	2	no	—
44	C₄⋊C₄×C₁₉	—	2	2	no	—
45	C₄⋊C₄×C₁₉	—	2	1	no	—
46	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
47	C₄²×C₁₉	—	2	2	no	—
48	C₄²×C₁₉	—	2	2	no	—
49	C₄²×C₁₉	D₄	1	1	yes	characteristic
50	C₄²×C₁₉	D₄	1	1	yes	characteristic
51	C₄²×C₁₉	C₂³	1	1	yes	characteristic
52	C₄²×C₁₉	C₂³	1	1	yes	characteristic
53	C₂²⋊Dic₁₉	—	2	2	no	—
54	#64528	—	2	8	no	—
55	C₄⋊Dic₁₉	—	2	1	no	—
56	C₄⋊Dic₁₉	—	2	1	no	—
57	C₄⋊Dic₁₉	—	2	1	no	—
58	C₄⋊Dic₁₉	C₂³	1	2	yes	—
59	Dic₁₉⋊C₄	—	2	2	no	—
60	Dic₁₉⋊C₄	—	2	2	no	—
61	C₄×Dic₁₉	—	2	2	no	—
62	C₂×C₁₉⋊C₈	C₂³	1	4	yes	—
63	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
64	Q₈×C₁₉	—	2	4	no	—
65	Q₈×C₁₉	—	2	2	no	—
66	Q₈×C₁₉	#41	1	4	yes	—
67	C₂×C₄×C₁₉	—	2	4	no	—
68	C₂×C₄×C₁₉	—	2	2	no	—
69	C₂×C₄×C₁₉	—	2	2	no	—
70	C₂×C₄×C₁₉	—	2	2	no	—
71	C₂×C₄×C₁₉	—	2	2	no	—
72	C₂×C₄×C₁₉	—	2	2	no	—
73	C₂×C₄×C₁₉	—	4	2	no	—
74	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
75	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
76	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
77	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
78	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
80	C₂×Dic₁₉	—	2	2	no	—
81	C₂×Dic₁₉	—	2	2	no	—
82	Dic₃₈	—	2	4	no	—
83	Dic₃₈	—	4	2	no	—
84	C₁₉⋊C₈	—	2	4	no	—
85	#3113	—	19	1	no	maximal, Sylow
86	C₂²×C₁₉	—	2	1	no	—
87	C₂²×C₁₉	—	2	1	no	—
88	C₂²×C₁₉	#137	1	2	yes	—
89	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
90	C₄×C₁₉	—	2	4	no	—
91	C₄×C₁₉	—	2	1	no	—
92	C₄×C₁₉	—	2	1	no	—
93	C₄×C₁₉	—	2	1	no	—
94	C₄×C₁₉	—	2	1	no	—
95	C₄×C₁₉	—	4	2	no	—
96	C₄×C₁₉	#137	1	2	yes	—
97	C₄×C₁₉	C₂×#41	1	2	yes	—
98	Dic₁₉	—	4	2	no	—
99	Dic₁₉	—	4	2	no	—
100	#533	—	19	1	no	—
101	C₂×C₄×Q₈	D₁₉	1	1	yes	characteristic
102	#483	—	19	2	no	—
103	#475	—	19	2	no	—
104	#462	—	19	2	no	—
105	#451	—	19	2	no	—
106	#441	—	19	4	no	—
107	#432	—	19	1	no	—
108	C₂×C₁₉	—	2	2	no	—
109	C₂×C₁₉	#525	1	1	yes	characteristic
110	C₂×C₁₉	C₂×#137	1	1	yes	characteristic
111	C₂×C₁₉	C₂×#137	1	1	yes	characteristic
112	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
113	C₂×Q₁₆	—	19	4	no	—
114	C₄⋊Q₈	—	19	1	no	—
115	C₄⋊Q₈	—	19	1	no	—
116	#125	—	38	1	no	—
117	C₂²⋊Q₈	—	19	2	no	—
118	C₂²⋊Q₈	—	38	1	no	—
119	C₄×Q₈	—	2	1	no	—
120	C₄×Q₈	—	2	1	no	—
121	C₄×Q₈	—	19	2	no	—
122	C₄×Q₈	—	38	1	no	—
123	C₄×Q₈	C₂×D₁₉	1	2	yes	—
124	C₄×Q₈	C₂×D₁₉	1	2	yes	—
125	#117	—	38	1	no	—
126	C₂×C₄⋊C₄	—	2	1	no	—
127	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
128	C₂×C₄²	—	2	1	no	—
129	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
130	#106	—	19	4	no	—
131	C₄⋊C₈	—	19	2	no	—
132	#103	—	19	4	no	—
133	#103	—	19	4	no	—
134	C₂²⋊C₈	—	19	2	no	—
135	#97	—	19	2	no	—
136	C₁₉	#3113	1	1	yes	characteristic, complemented, Sylow
137	C₂×Q₈	—	2	4	no	—
138	C₂×Q₈	—	2	1	no	—
139	C₂×Q₈	—	19	2	no	—
140	C₂×Q₈	—	38	1	no	—
141	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
142	C₂²×C₄	—	2	1	no	—
143	C₂²×C₄	—	2	1	no	—
144	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
145	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
146	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
147	Q₁₆	—	38	8	no	—
148	C₂×C₈	—	19	4	no	—
149	C₄⋊C₄	—	2	2	no	—
150	C₄⋊C₄	—	2	2	no	—
151	C₄⋊C₄	—	2	1	no	—
152	C₄⋊C₄	—	19	2	no	—
153	C₄⋊C₄	—	38	2	no	—
154	C₄⋊C₄	—	38	2	no	—
155	C₄⋊C₄	—	38	1	no	—
156	C₄⋊C₄	—	38	1	no	—
157	C₄⋊C₄	—	38	1	no	—
158	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
159	C₂²⋊C₄	—	38	2	no	—
160	C₄²	—	2	2	no	—
161	C₄²	—	2	2	no	—
162	C₄²	—	38	2	no	—
163	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
164	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
165	C₄²	C₂²×D₁₉	1	1	yes	characteristic
166	C₄²	C₂²×D₁₉	1	1	yes	characteristic
167	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
168	Q₈	—	2	4	no	—
169	Q₈	—	2	2	no	—
170	Q₈	—	38	4	no	—
171	Q₈	—	76	2	no	—
172	Q₈	#64541	1	4	yes	—
173	C₂×C₄	—	2	4	no	—
174	C₂×C₄	—	2	2	no	—
175	C₂×C₄	—	2	2	no	—
176	C₂×C₄	—	2	2	no	—
177	C₂×C₄	—	2	2	no	—
178	C₂×C₄	—	2	2	no	—
179	C₂×C₄	—	4	2	no	—
180	C₂×C₄	—	38	2	no	—
181	C₂×C₄	—	38	2	no	—
182	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
183	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
184	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
185	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
186	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
187	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
188	C₈	—	38	4	no	—
189	C₂²	—	2	1	no	—
190	C₂²	—	2	1	no	—
191	C₂²	#10597397	1	2	yes	—
192	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
193	C₄	—	2	4	no	—
194	C₄	—	2	1	no	—
195	C₄	—	2	1	no	—
196	C₄	—	2	1	no	—
197	C₄	—	2	1	no	—
198	C₄	—	4	2	no	—
199	C₄	—	76	2	no	—
200	C₄	—	76	2	no	—
201	C₄	#10597388	1	2	yes	—
202	C₄	C₂×#64541	1	2	yes	—
203	C₂	—	2	2	no	—
204	C₂	#11927055	1	1	yes	characteristic
205	C₂	C₂×#10597397	1	1	yes	characteristic
206	C₂	C₂×#10597388	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927101

C₂

yes

maximal, characteristic

#11926874

C₂

yes

maximal

#11926829

C₂

yes

maximal, complemented

#11926754

C₂

yes

maximal, complemented

#11926700

C₂

yes

maximal

#11926649

C₂

yes

maximal, complemented

#11926601

C₂

yes

maximal, characteristic

C₂×C₄×Q₈×C₁₉

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

C₂²

yes

characteristic

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

C₂²

yes

—

C₄×Q₈×C₁₉

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×#64528

C₂²

yes

—

#10597372

—

#10597370

—

#10597370

C₂²

yes

—

#10597316

—

#10597315

C₂²

yes

characteristic

#10597315

C₂²

yes

characteristic

C₄×Dic₃₈

—

C₄×Dic₃₈

C₂²

yes

—

#10597292

C₂²

yes

—

C₂²⋊(C₁₉⋊C₈)

C₂²

yes

—

#10597267

C₂²

yes

—

#10597265

C₂²

yes

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

#10597260

C₂²

yes

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×Dic₃₈

—

C₂×Dic₃₈

C₂³

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂³

yes

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

C₂³

yes

characteristic

C₄²×C₁₉

C₂³

yes

characteristic

C₂²⋊Dic₁₉

—

#64528

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂³

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

C₂³

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

#41

yes

—

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×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₁₉⋊C₈

—

#3113

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#137

yes

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#137

yes

—

C₄×C₁₉

C₂×#41

yes

—

Dic₁₉

—

Dic₁₉

—

100

#533

—

101

C₂×C₄×Q₈

D₁₉

yes

characteristic

102

#483

—

103

#475

—

104

#462

—

105

#451

—

106

#441

—

107

#432

—

108

C₂×C₁₉

—

109

C₂×C₁₉

#525

yes

characteristic

110

C₂×C₁₉

C₂×#137

yes

characteristic

111

C₂×C₁₉

C₂×#137

yes

characteristic

112

C₂²×Q₈

C₂×D₁₉

yes

characteristic

113

C₂×Q₁₆

—

114

C₄⋊Q₈

—

115

C₄⋊Q₈

—

116

#125

—

117

C₂²⋊Q₈

—

118

C₂²⋊Q₈

—

119

C₄×Q₈

—

120

C₄×Q₈

—

121

C₄×Q₈

—

122

C₄×Q₈

—

123

C₄×Q₈

C₂×D₁₉

yes

—

124

C₄×Q₈

C₂×D₁₉

yes

—

125

#117

—

126

C₂×C₄⋊C₄

—

127

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

128

C₂×C₄²

—

129

C₂×C₄²

C₂×D₁₉

yes

characteristic

130

#106

—

131

C₄⋊C₈

—

132

#103

—

133

#103

—

134

C₂²⋊C₈

—

135

#97

—

136

C₁₉

#3113

yes

characteristic, complemented, Sylow

137

C₂×Q₈

—

138

C₂×Q₈

—

139

C₂×Q₈

—

140

C₂×Q₈

—

141

C₂×Q₈

C₂²×D₁₉

yes

—

142

C₂²×C₄

—

143

C₂²×C₄

—

144

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

145

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

146

C₂²×C₄

C₂²×D₁₉

yes

characteristic

147

Q₁₆

—

148

C₂×C₈

—

149

C₄⋊C₄

—

150

C₄⋊C₄

—

151

C₄⋊C₄

—

152

C₄⋊C₄

—

153

C₄⋊C₄

—

154

C₄⋊C₄

—

155

C₄⋊C₄

—

156

C₄⋊C₄

—

157

C₄⋊C₄

—

158

C₄⋊C₄

C₂²×D₁₉

yes

—

159

C₂²⋊C₄

—

160

C₄²

—

161

C₄²

—

162

C₄²

—

163

C₄²

C₂²⋊D₁₉

yes

characteristic

164

C₄²

C₂²⋊D₁₉

yes

characteristic

165

C₄²

C₂²×D₁₉

yes

characteristic

166

C₄²

C₂²×D₁₉

yes

characteristic

167

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

168

Q₈

—

169

Q₈

—

170

Q₈

—

171

Q₈

—

172

Q₈

#64541

yes

—

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

C₂×C₂²⋊D₁₉

yes

characteristic

183

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

184

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

185

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

186

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

187

C₂×C₄

C₂³×D₁₉

yes

characteristic

188

C₈

—

189

C₂²

—

190

C₂²

—

191

C₂²

#10597397

yes

—

192

C₂²

C₂²×C₂²⋊D₁₉

yes

characteristic

193

C₄

—

194

C₄

—

195

C₄

—

196

C₄

—

197

C₄

—

198

C₄

—

199

C₄

—

200

C₄

—

201

C₄

#10597388

yes

—

202

C₄

C₂×#64541

yes

—

203

C₂

—

204

C₂

#11927055

yes

characteristic

205

C₂

C₂×#10597397

yes

characteristic

206

C₂

C₂×#10597388

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₂×C₄×Q₈×C₁₉	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	C₂³×C₁₉	C₂×D₄
hypercenter	C₂×C₄×Q₈	D₁₉
hypocenter	C₁₉	#3113
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×Q₈

subgroup

G/H

center

C₂²

C₂²×C₂²⋊D₁₉

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₂×C₄×Q₈×C₁₉

C₂

socle

C₂²×C₁₉

C₂²×D₄

prime radical

C₂³×C₁₉

C₂×D₄

hypercenter

C₂×C₄×Q₈

D₁₉

hypocenter

C₁₉

#3113

LCS

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×Q₈

N	H ≅ G/N	type
3. #11926829	C₂	semidirect
4. #11926754	C₂	semidirect
6. #11926649	C₂	semidirect
136. C₁₉	#3113	semidirect

H ≅ G/N

type

3. #11926829

C₂

semidirect

4. #11926754

C₂

semidirect

6. #11926649

C₂

semidirect

136. C₁₉

#3113

semidirect

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

subgroup	index
#11927101	2
#11926874	2
#11926829	2
#11926754	2
#11926700	2
#11926649	2
#11926601	2
C₂×C₄×Q₈×C₁₉	2
#3113	19

subgroup

index

C₂×C₄×Q₈×C₁₉

Subgroups — #14573765

Conjugacy classes of subgroups

Complements

Maximal subgroups