Group #14564537 — subgroups

Subgroups — #14564537

Order 2432.

296 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 83 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×#64527	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597279	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926548	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597293	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#10597280	C₂	1	1	yes	maximal, characteristic
6	#11926500	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#419	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×D₇₆	C₂²	1	1	yes	characteristic
10	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×#117	C₂²	1	1	yes	characteristic
12	C₂×#64527	—	2	1	no	—
13	C₂×#64527	—	2	1	no	—
14	C₂×#64527	—	2	2	no	—
15	C₂×#64527	C₄	1	4	yes	complemented
16	C₂×#64520	C₂²	1	1	yes	characteristic
17	C₂×#64520	C₂²	1	1	yes	characteristic
18	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
19	C₁₉×#103	—	2	2	no	—
20	#10597293	—	2	2	no	—
21	#10597280	—	2	2	no	—
22	#10597279	—	2	2	no	—
23	#10597266	—	2	2	no	—
24	#10597260	—	2	1	no	—
25	C₄×C₁₉⋊C₈	—	2	1	no	—
26	C₂³×D₁₉	—	2	1	no	—
27	C₂×Q₈×C₁₉	—	2	1	no	—
28	C₂×Q₈×C₁₉	—	2	1	no	—
29	C₂×Q₈×C₁₉	—	2	1	no	—
30	C₂×Q₈×C₁₉	—	2	1	no	—
31	C₂×Q₈×C₁₉	—	2	1	no	—
32	C₂×Q₈×C₁₉	C₂×C₄	1	2	yes	—
33	C₂²×C₄×C₁₉	—	2	1	no	—
34	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
35	C₂×D₇₆	—	2	1	no	—
36	C₂×D₇₆	—	2	1	no	—
37	C₂×D₇₆	—	2	1	no	—
38	C₂×D₇₆	—	2	1	no	—
39	C₂×D₇₆	—	2	1	no	—
40	C₂×D₇₆	C₂×C₄	1	2	yes	—
41	M₁₆×C₁₉	—	2	1	no	—
42	M₁₆×C₁₉	—	2	1	no	—
43	C₂×C₈×C₁₉	—	2	1	no	—
44	C₄⋊C₄×C₁₉	D₄	1	2	yes	—
45	C₂²⋊C₄×C₁₉	—	2	1	no	—
46	C₄²×C₁₉	—	2	1	no	—
47	#64527	—	2	4	no	—
48	#64527	—	2	4	no	—
49	#64520	—	2	1	no	—
50	#64520	—	2	1	no	—
51	#64520	—	2	1	no	—
52	#64520	D₄	1	2	yes	—
53	C₂×C₁₉⋊C₈	—	2	1	no	—
54	C₂×C₁₉⋊C₈	—	2	1	no	—
55	C₂×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
56	C₂×C₁₉⋊C₈	D₄	1	1	yes	characteristic
57	C₂×C₁₉⋊C₈	D₄	1	1	yes	characteristic
58	C₂×C₁₉⋊C₈	D₄	1	2	yes	—
59	C₂³×C₁₉	#41	1	1	yes	characteristic
60	C₂²×D₁₉	—	2	2	no	—
61	C₂²×D₁₉	—	4	1	no	—
62	C₂²×D₁₉	—	4	1	no	—
63	C₂²×D₁₉	—	8	2	no	—
64	Q₈×C₁₉	—	2	2	no	—
65	Q₈×C₁₉	—	2	2	no	—
66	Q₈×C₁₉	—	4	1	no	—
67	Q₈×C₁₉	—	4	1	no	—
68	C₂×C₄×C₁₉	—	2	2	no	—
69	C₂×C₄×C₁₉	—	2	2	no	—
70	C₂×C₄×C₁₉	—	4	1	no	—
71	C₂×C₄×C₁₉	—	4	1	no	—
72	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
73	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	#41	1	1	yes	characteristic
78	D₇₆	—	2	2	no	—
79	D₇₆	—	2	2	no	—
80	D₇₆	—	4	1	no	—
81	D₇₆	—	4	1	no	—
82	C₈×C₁₉	—	4	1	no	—
83	C₁₉⋊C₈	—	2	2	no	—
84	C₁₉⋊C₈	—	4	1	no	—
85	C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
86	C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
87	#1977	—	19	1	no	maximal, Sylow
88	C₂²×C₁₉	—	2	2	no	—
89	C₂²×C₁₉	C₄×D₄	1	1	yes	characteristic
90	C₂²×C₁₉	#121	1	1	yes	characteristic
91	C₂²×C₁₉	#124	1	1	yes	characteristic
92	C₂×D₁₉	—	4	2	no	—
93	C₂×D₁₉	—	8	2	no	—
94	C₂×D₁₉	—	8	2	no	—
95	C₂×D₁₉	—	8	2	no	—
96	C₄×C₁₉	—	4	2	no	—
97	C₄×C₁₉	—	4	2	no	—
98	C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
99	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
100	C₄×C₁₉	#121	1	1	yes	characteristic
101	C₄×C₁₉	#127	1	1	yes	characteristic
102	C₂²×SD₁₆	—	19	1	no	—
103	C₂×#108	—	19	1	no	—
104	#419	D₁₉	1	1	yes	characteristic, complemented
105	#418	—	19	1	no	—
106	C₂×#101	—	19	1	no	—
107	C₂×#100	—	19	1	no	—
108	#405	—	19	1	no	—
109	C₂×C₁₉	—	2	1	no	—
110	C₂×C₁₉	—	2	1	no	—
111	C₂×C₁₉	#390	1	1	yes	characteristic
112	C₂×C₁₉	#471	1	2	yes	—
113	D₁₉	—	8	2	no	—
114	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
115	C₂²×D₄	—	19	1	no	—
116	C₂×SD₁₆	—	19	4	no	—
117	C₂×SD₁₆	—	38	1	no	—
118	C₂×SD₁₆	—	38	1	no	—
119	C₂×SD₁₆	—	38	2	no	—
120	C₂×M₁₆	—	19	1	no	—
121	C₂×M₁₆	—	19	1	no	—
122	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
123	C₂²×C₈	—	19	1	no	—
124	#117	C₂×D₁₉	1	1	yes	characteristic
125	#108	—	38	2	no	—
126	#103	—	2	2	no	—
127	#102	—	38	2	no	—
128	#101	—	38	2	no	—
129	#100	—	38	2	no	—
130	#97	—	38	1	no	—
131	C₄×C₈	—	38	1	no	—
132	C₁₉	#1977	1	1	yes	characteristic, complemented, Sylow
133	C₂⁴	—	38	1	no	—
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	C₄×D₁₉	1	2	yes	—
140	C₂×D₄	—	19	2	no	—
141	C₂×D₄	—	38	1	no	—
142	C₂×D₄	—	38	1	no	—
143	C₂×D₄	—	38	1	no	—
144	C₂×D₄	—	38	1	no	—
145	C₂×D₄	—	38	1	no	—
146	C₂²×C₄	—	2	1	no	—
147	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
148	SD₁₆	—	38	4	no	—
149	SD₁₆	—	38	4	no	—
150	M₁₆	—	2	1	no	—
151	M₁₆	—	2	1	no	—
152	M₁₆	—	19	2	no	—
153	M₁₆	—	38	1	no	—
154	M₁₆	—	38	1	no	—
155	M₁₆	—	38	1	no	—
156	C₂×C₈	—	2	1	no	—
157	C₂×C₈	—	19	2	no	—
158	C₂×C₈	—	19	1	no	—
159	C₂×C₈	—	19	1	no	—
160	C₂×C₈	—	19	2	no	—
161	C₂×C₈	—	38	1	no	—
162	C₂×C₈	—	38	1	no	—
163	C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
164	C₂²⋊C₄	—	2	1	no	—
165	C₄²	—	2	1	no	—
166	C₂³	—	38	2	no	—
167	C₂³	—	76	1	no	—
168	C₂³	—	76	1	no	—
169	C₂³	—	152	2	no	—
170	C₂³	#64543	1	1	yes	characteristic
171	Q₈	—	2	2	no	—
172	Q₈	—	2	2	no	—
173	Q₈	—	4	1	no	—
174	Q₈	—	4	1	no	—
175	D₄	—	38	2	no	—
176	D₄	—	38	2	no	—
177	D₄	—	76	1	no	—
178	D₄	—	76	1	no	—
179	C₂×C₄	—	2	2	no	—
180	C₂×C₄	—	2	2	no	—
181	C₂×C₄	—	4	1	no	—
182	C₂×C₄	—	4	1	no	—
183	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
184	C₂×C₄	#64541	1	1	yes	characteristic
185	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
186	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
187	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
188	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
189	C₈	—	4	1	no	—
190	C₈	—	19	2	no	—
191	C₈	—	19	2	no	—
192	C₈	—	38	2	no	—
193	C₈	—	76	1	no	—
194	C₂²	—	2	2	no	—
195	C₂²	—	76	2	no	—
196	C₂²	—	152	2	no	—
197	C₂²	—	152	2	no	—
198	C₂²	—	152	2	no	—
199	C₂²	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
200	C₂²	#10597331	1	1	yes	characteristic
201	C₂²	#10597385	1	1	yes	characteristic
202	C₄	—	4	2	no	—
203	C₄	—	4	2	no	—
204	C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
205	C₄	#10597330	1	1	yes	characteristic
206	C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
207	C₄	#10597386	1	1	yes	characteristic
208	C₂	—	2	1	no	—
209	C₂	—	2	1	no	—
210	C₂	—	152	2	no	—
211	C₂	#11926444	1	1	yes	characteristic
212	C₂	#11926809	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#64527

C₂

yes

maximal, characteristic

C₂×#10597279

C₂

yes

maximal, characteristic, complemented

#11926548

C₂

yes

maximal, characteristic

C₂×#10597293

C₂

yes

maximal, characteristic, complemented

C₂×#10597280

C₂

yes

maximal, characteristic

#11926500

C₂

yes

maximal, characteristic, complemented

C₁₉×#419

C₂

yes

maximal, characteristic, complemented

C₂²×Q₈×C₁₉

C₂²

yes

characteristic

C₂²×D₇₆

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#117

C₂²

yes

—

—

—

C₄

yes

complemented

C₂×#64520

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₁₉×#103

—

—

—

—

—

—

C₄×C₁₉⋊C₈

—

C₂³×D₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

C₂×C₄

yes

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

D₄

yes

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

—

—

—

—

—

D₄

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

C₂×C₁₉⋊C₈

D₄

yes

characteristic

C₂×C₁₉⋊C₈

D₄

yes

characteristic

C₂×C₁₉⋊C₈

D₄

yes

—

C₂³×C₁₉

#41

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²×C₄

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

#41

yes

characteristic

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

C₂²⋊C₄

yes

—

C₁₉⋊C₈

C₂²⋊C₄

yes

—

#1977

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

C₄×D₄

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₁₉

C₄×D₄

yes

characteristic

100

C₄×C₁₉

#121

yes

characteristic

101

C₄×C₁₉

#127

yes

characteristic

102

C₂²×SD₁₆

—

103

C₂×#108

—

104

#419

D₁₉

yes

characteristic, complemented

105

#418

—

106

C₂×#101

—

107

C₂×#100

—

108

#405

—

109

C₂×C₁₉

—

110

C₂×C₁₉

—

111

C₂×C₁₉

#390

yes

characteristic

112

C₂×C₁₉

#471

yes

—

113

D₁₉

—

114

C₂²×Q₈

C₂×D₁₉

yes

characteristic

115

C₂²×D₄

—

116

C₂×SD₁₆

—

117

C₂×SD₁₆

—

118

C₂×SD₁₆

—

119

C₂×SD₁₆

—

120

C₂×M₁₆

—

121

C₂×M₁₆

—

122

C₂×M₁₆

C₂×D₁₉

yes

characteristic

123

C₂²×C₈

—

124

#117

C₂×D₁₉

yes

characteristic

125

#108

—

126

#103

—

127

#102

—

128

#101

—

129

#100

—

130

#97

—

131

C₄×C₈

—

132

C₁₉

#1977

yes

characteristic, complemented, Sylow

133

C₂⁴

—

134

C₂×Q₈

—

135

C₂×Q₈

—

136

C₂×Q₈

—

137

C₂×Q₈

—

138

C₂×Q₈

—

139

C₂×Q₈

C₄×D₁₉

yes

—

140

C₂×D₄

—

141

C₂×D₄

—

142

C₂×D₄

—

143

C₂×D₄

—

144

C₂×D₄

—

145

C₂×D₄

—

146

C₂²×C₄

—

147

C₂²×C₄

C₂²×D₁₉

yes

characteristic

148

SD₁₆

—

149

SD₁₆

—

150

M₁₆

—

151

M₁₆

—

152

M₁₆

—

153

M₁₆

—

154

M₁₆

—

155

M₁₆

—

156

C₂×C₈

—

157

C₂×C₈

—

158

C₂×C₈

—

159

C₂×C₈

—

160

C₂×C₈

—

161

C₂×C₈

—

162

C₂×C₈

—

163

C₄⋊C₄

C₂²⋊D₁₉

yes

—

164

C₂²⋊C₄

—

165

C₄²

—

166

C₂³

—

167

C₂³

—

168

C₂³

—

169

C₂³

—

152

—

170

C₂³

#64543

yes

characteristic

171

Q₈

—

172

Q₈

—

173

Q₈

—

174

Q₈

—

175

D₄

—

176

D₄

—

177

D₄

—

178

D₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

184

C₂×C₄

#64541

yes

characteristic

185

C₂×C₄

D₄×D₁₉

yes

characteristic

186

C₂×C₄

D₄×D₁₉

yes

characteristic

187

C₂×C₄

D₄×D₁₉

yes

characteristic

188

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

189

C₈

—

190

C₈

—

191

C₈

—

192

C₈

—

193

C₈

—

194

C₂²

—

195

C₂²

—

196

C₂²

—

152

—

197

C₂²

—

152

—

198

C₂²

—

152

—

199

C₂²

(C₂²⋊D₁₉)⋊C₄

yes

characteristic

200

C₂²

#10597331

yes

characteristic

201

C₂²

#10597385

yes

characteristic

202

C₄

—

203

C₄

—

204

C₄

C₂²⋊C₄×D₁₉

yes

characteristic

205

C₄

#10597330

yes

characteristic

206

C₄

C₄×C₂²⋊D₁₉

yes

characteristic

207

C₄

#10597386

yes

characteristic

208

C₂

—

209

C₂

—

210

C₂

—

152

—

211

C₂

#11926444

yes

characteristic

212

C₂

#11926809

yes

—

	subgroup	G/H
center	C₂²	#10597385
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#419	C₂
socle	C₂²×C₁₉	#121
prime radical	C₂²×D₇₆	C₂²
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#419	D₁₉
hypocenter	C₁₉	#1977
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #419

subgroup

G/H

center

C₂²

#10597385

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#419

C₂

socle

C₂²×C₁₉

#121

prime radical

C₂²×D₇₆

C₂²

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #419

N	H ≅ G/N	type
2. C₂×#10597279	C₂	semidirect
4. C₂×#10597293	C₂	semidirect
6. #11926500	C₂	semidirect
7. C₁₉×#419	C₂	semidirect
15. C₂×#64527	C₄	semidirect
104. #419	D₁₉	semidirect
132. C₁₉	#1977	semidirect

H ≅ G/N

type

2. C₂×#10597279

C₂

semidirect

4. C₂×#10597293

C₂

semidirect

6. #11926500

C₂

semidirect

7. C₁₉×#419

C₂

semidirect

15. C₂×#64527

C₄

semidirect

104. #419

D₁₉

semidirect

132. C₁₉

#1977

semidirect

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

subgroup	index
C₂²×#64527	2
C₂×#10597279	2
#11926548	2
C₂×#10597293	2
C₂×#10597280	2
#11926500	2
C₁₉×#419	2
#1977	19

subgroup

index

C₂²×#64527

C₁₉×#419

Subgroups — #14564537

Conjugacy classes of subgroups

Complements

Maximal subgroups