Group #14574829 — subgroups

Subgroups — #14574829

Order 2432.

366 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 121 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, complemented
2	#11926950	C₂	1	2	yes	maximal, complemented
3	#11926908	C₂	1	2	yes	maximal, complemented
4	#11926865	C₂	1	4	yes	maximal, complemented
5	#11926834	C₂	1	2	yes	maximal, complemented
6	#11926824	C₂	1	2	yes	maximal, complemented
7	#11926601	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#532	C₂	1	1	yes	maximal, characteristic
9	C₂×#41×C₁₉	—	2	1	no	—
10	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₁₉×#127	C₂²	1	1	yes	characteristic
12	C₁₉×#124	—	2	1	no	—
13	C₁₉×#121	—	2	1	no	—
14	C₁₉×#121	C₂²	1	2	yes	—
15	C₄×D₄×C₁₉	—	2	1	no	—
16	C₄×D₄×C₁₉	C₂²	1	2	yes	—
17	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
18	#10597372	C₂²	1	2	yes	—
19	#10597370	—	2	1	no	—
20	#10597370	—	2	1	no	—
21	#10597316	C₂²	1	2	yes	—
22	#10597315	C₂²	1	1	yes	characteristic
23	#10597315	C₂²	1	1	yes	characteristic
24	C₄×Dic₃₈	—	2	1	no	—
25	C₄×Dic₃₈	—	2	1	no	—
26	#10597289	C₂²	1	4	yes	—
27	#10597289	C₂²	1	4	yes	—
28	C₂²⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
29	#10597265	C₂²	1	4	yes	—
30	#10597264	C₂²	1	4	yes	—
31	C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
32	#10597260	C₂²	1	2	yes	—
33	#41×C₁₉	—	4	4	no	—
34	C₂×Q₈×C₁₉	—	2	1	no	—
35	C₂×D₄×C₁₉	—	2	2	no	—
36	C₂×D₄×C₁₉	—	2	1	no	—
37	C₂×D₄×C₁₉	—	2	1	no	—
38	C₂×D₄×C₁₉	C₂³	1	2	yes	—
39	C₂²×C₄×C₁₉	—	2	2	no	—
40	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
43	C₂×Dic₃₈	—	2	1	no	—
44	C₂×Dic₃₈	—	2	1	no	—
45	C₄⋊C₄×C₁₉	—	2	1	no	—
46	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
47	C₂²⋊C₄×C₁₉	—	2	2	no	—
48	C₂²⋊C₄×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	C₄⋊Dic₁₉	—	2	1	no	—
55	C₄⋊Dic₁₉	—	2	1	no	—
56	C₄⋊Dic₁₉	C₂³	1	2	yes	—
57	C₄⋊Dic₁₉	C₂³	1	2	yes	—
58	Dic₁₉⋊C₄	—	2	2	no	—
59	Dic₁₉⋊C₄	—	2	2	no	—
60	C₄×Dic₁₉	—	2	2	no	—
61	C₂×C₁₉⋊C₈	C₂³	1	4	yes	—
62	C₂³×C₁₉	—	2	2	no	—
63	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
64	Q₈×C₁₉	—	4	2	no	—
65	D₄×C₁₉	—	2	4	no	—
66	D₄×C₁₉	—	4	2	no	—
67	D₄×C₁₉	—	4	2	no	—
68	D₄×C₁₉	—	4	4	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	—	4	1	no	—
73	C₂×C₄×C₁₉	—	4	4	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	—	4	2	no	—
83	Dic₃₈	—	4	2	no	—
84	C₁₉⋊C₈	—	2	4	no	—
85	#3235	—	19	1	no	maximal, Sylow
86	C₂²×C₁₉	—	2	1	no	—
87	C₂²×C₁₉	—	2	1	no	—
88	C₂²×C₁₉	—	2	1	no	—
89	C₂²×C₁₉	—	4	2	no	—
90	C₂²×C₁₉	—	4	2	no	—
91	C₂²×C₁₉	—	4	2	no	—
92	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
93	C₄×C₁₉	—	2	1	no	—
94	C₄×C₁₉	—	2	1	no	—
95	C₄×C₁₉	—	2	1	no	—
96	C₄×C₁₉	—	2	1	no	—
97	C₄×C₁₉	—	4	2	no	—
98	C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
99	C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
100	Dic₁₉	—	4	2	no	—
101	Dic₁₉	—	4	2	no	—
102	#533	—	19	1	no	—
103	#532	D₁₉	1	1	yes	characteristic
104	#501	—	19	2	no	—
105	#490	—	19	2	no	—
106	#482	—	19	4	no	—
107	#476	—	19	2	no	—
108	#474	—	19	2	no	—
109	#432	—	19	1	no	—
110	C₂×C₁₉	—	4	1	no	—
111	C₂×C₁₉	—	8	2	no	—
112	C₂×C₁₉	#536	1	1	yes	characteristic
113	C₂×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
114	C₂×C₁₉	#575	1	1	yes	characteristic
115	C₂×#41	—	2	1	no	—
116	C₄⋊Q₈	—	19	1	no	—
117	C₄⋊Q₈	—	19	1	no	—
118	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
119	#127	C₂×D₁₉	1	1	yes	characteristic
120	#125	—	19	2	no	—
121	#124	—	2	1	no	—
122	C₂²⋊Q₈	—	38	1	no	—
123	C₂²⋊Q₈	—	38	1	no	—
124	#121	—	2	1	no	—
125	#121	C₂×D₁₉	1	2	yes	—
126	C₄×Q₈	—	38	1	no	—
127	C₄×Q₈	—	38	1	no	—
128	C₄×D₄	—	2	1	no	—
129	C₄×D₄	C₂×D₁₉	1	2	yes	—
130	#117	—	19	2	no	—
131	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
132	#107	—	19	4	no	—
133	#106	—	19	4	no	—
134	C₄⋊C₈	—	19	2	no	—
135	#102	—	19	4	no	—
136	#102	—	19	4	no	—
137	C₂²⋊C₈	—	19	2	no	—
138	#97	—	19	2	no	—
139	C₁₉	#3235	1	1	yes	characteristic, complemented, Sylow
140	#41	—	4	4	no	—
141	C₂×Q₈	—	2	1	no	—
142	C₂×Q₈	—	38	1	no	—
143	C₂×Q₈	—	38	1	no	—
144	C₂×D₄	—	2	2	no	—
145	C₂×D₄	—	2	1	no	—
146	C₂×D₄	—	2	1	no	—
147	C₂×D₄	C₂²×D₁₉	1	2	yes	—
148	C₂²×C₄	—	2	2	no	—
149	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
150	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
151	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
152	C₂×C₈	—	19	4	no	—
153	C₄⋊C₄	—	2	1	no	—
154	C₄⋊C₄	—	19	2	no	—
155	C₄⋊C₄	—	19	2	no	—
156	C₄⋊C₄	—	38	2	no	—
157	C₄⋊C₄	—	38	2	no	—
158	C₄⋊C₄	—	38	1	no	—
159	C₄⋊C₄	—	38	1	no	—
160	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
161	C₂²⋊C₄	—	2	2	no	—
162	C₂²⋊C₄	—	2	2	no	—
163	C₂²⋊C₄	—	38	2	no	—
164	C₄²	—	38	2	no	—
165	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
166	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
167	C₄²	C₂²×D₁₉	1	1	yes	characteristic
168	C₄²	C₂²×D₁₉	1	1	yes	characteristic
169	C₂³	—	2	2	no	—
170	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
171	Q₈	—	4	2	no	—
172	Q₈	—	76	2	no	—
173	Q₈	—	76	2	no	—
174	D₄	—	2	4	no	—
175	D₄	—	4	2	no	—
176	D₄	—	4	2	no	—
177	D₄	—	4	4	no	—
178	C₂×C₄	—	2	2	no	—
179	C₂×C₄	—	2	2	no	—
180	C₂×C₄	—	2	2	no	—
181	C₂×C₄	—	4	1	no	—
182	C₂×C₄	—	4	4	no	—
183	C₂×C₄	—	38	2	no	—
184	C₂×C₄	—	38	2	no	—
185	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
186	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
187	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
188	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
189	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
190	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
191	C₈	—	38	4	no	—
192	C₂²	—	2	1	no	—
193	C₂²	—	2	1	no	—
194	C₂²	—	2	1	no	—
195	C₂²	—	4	2	no	—
196	C₂²	—	4	2	no	—
197	C₂²	—	4	2	no	—
198	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
199	C₄	—	2	1	no	—
200	C₄	—	2	1	no	—
201	C₄	—	2	1	no	—
202	C₄	—	2	1	no	—
203	C₄	—	4	2	no	—
204	C₄	—	76	2	no	—
205	C₄	—	76	2	no	—
206	C₄	#10597378	1	2	yes	—
207	C₄	#10597436	1	2	yes	—
208	C₂	—	4	1	no	—
209	C₂	—	8	2	no	—
210	C₂	#11927115	1	1	yes	characteristic
211	C₂	C₂×#10597378	1	1	yes	characteristic
212	C₂	#11927342	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927101

C₂

yes

maximal, characteristic, complemented

#11926950

C₂

yes

maximal, complemented

#11926908

C₂

yes

maximal, complemented

#11926865

C₂

yes

maximal, complemented

#11926834

C₂

yes

maximal, complemented

#11926824

C₂

yes

maximal, complemented

#11926601

C₂

yes

maximal, characteristic, complemented

C₁₉×#532

C₂

yes

maximal, characteristic

C₂×#41×C₁₉

—

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×#127

C₂²

yes

characteristic

C₁₉×#124

—

C₁₉×#121

—

C₁₉×#121

C₂²

yes

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

#10597372

C₂²

yes

—

#10597370

—

#10597370

—

#10597316

C₂²

yes

—

#10597315

C₂²

yes

characteristic

#10597315

C₂²

yes

characteristic

C₄×Dic₃₈

—

C₄×Dic₃₈

—

#10597289

C₂²

yes

—

#10597289

C₂²

yes

—

C₂²⋊(C₁₉⋊C₈)

C₂²

yes

—

#10597265

C₂²

yes

—

#10597264

C₂²

yes

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

#10597260

C₂²

yes

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂³

yes

—

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

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂³

yes

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

C₂³

yes

characteristic

C₄²×C₁₉

C₂³

yes

characteristic

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂³

yes

—

C₄⋊Dic₁₉

C₂³

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

C₂³

yes

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×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

—

#3235

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₄×C₁₉

2₋¹⁺⁴

yes

—

100

Dic₁₉

—

101

Dic₁₉

—

102

#533

—

103

#532

D₁₉

yes

characteristic

104

#501

—

105

#490

—

106

#482

—

107

#476

—

108

#474

—

109

#432

—

110

C₂×C₁₉

—

111

C₂×C₁₉

—

112

C₂×C₁₉

#536

yes

characteristic

113

C₂×C₁₉

C₂×AGL(1,ℤ/8)

yes

characteristic

114

C₂×C₁₉

#575

yes

characteristic

115

C₂×#41

—

116

C₄⋊Q₈

—

117

C₄⋊Q₈

—

118

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

119

#127

C₂×D₁₉

yes

characteristic

120

#125

—

121

#124

—

122

C₂²⋊Q₈

—

123

C₂²⋊Q₈

—

124

#121

—

125

#121

C₂×D₁₉

yes

—

126

C₄×Q₈

—

127

C₄×Q₈

—

128

C₄×D₄

—

129

C₄×D₄

C₂×D₁₉

yes

—

130

#117

—

131

C₂×C₄²

C₂×D₁₉

yes

characteristic

132

#107

—

133

#106

—

134

C₄⋊C₈

—

135

#102

—

136

#102

—

137

C₂²⋊C₈

—

138

#97

—

139

C₁₉

#3235

yes

characteristic, complemented, Sylow

140

#41

—

141

C₂×Q₈

—

142

C₂×Q₈

—

143

C₂×Q₈

—

144

C₂×D₄

—

145

C₂×D₄

—

146

C₂×D₄

—

147

C₂×D₄

C₂²×D₁₉

yes

—

148

C₂²×C₄

—

149

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

150

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

151

C₂²×C₄

C₂²×D₁₉

yes

characteristic

152

C₂×C₈

—

153

C₄⋊C₄

—

154

C₄⋊C₄

—

155

C₄⋊C₄

—

156

C₄⋊C₄

—

157

C₄⋊C₄

—

158

C₄⋊C₄

—

159

C₄⋊C₄

—

160

C₄⋊C₄

C₂²×D₁₉

yes

—

161

C₂²⋊C₄

—

162

C₂²⋊C₄

—

163

C₂²⋊C₄

—

164

C₄²

—

165

C₄²

C₂²⋊D₁₉

yes

characteristic

166

C₄²

C₂²⋊D₁₉

yes

characteristic

167

C₄²

C₂²×D₁₉

yes

characteristic

168

C₄²

C₂²×D₁₉

yes

characteristic

169

C₂³

—

170

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

171

Q₈

—

172

Q₈

—

173

Q₈

—

174

D₄

—

175

D₄

—

176

D₄

—

177

D₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

186

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

187

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

188

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

189

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

190

C₂×C₄

C₂³×D₁₉

yes

characteristic

191

C₈

—

192

C₂²

—

193

C₂²

—

194

C₂²

—

195

C₂²

—

196

C₂²

—

197

C₂²

—

198

C₂²

C₂²×C₂²⋊D₁₉

yes

characteristic

199

C₄

—

200

C₄

—

201

C₄

—

202

C₄

—

203

C₄

—

204

C₄

—

205

C₄

—

206

C₄

#10597378

yes

—

207

C₄

#10597436

yes

—

208

C₂

—

209

C₂

—

210

C₂

#11927115

yes

characteristic

211

C₂

C₂×#10597378

yes

characteristic

212

C₂

#11927342

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting, prime radical	C₁₉×#532	C₂
socle	C₂²×C₁₉	C₂²×D₄
hypercenter	#532	D₁₉
hypocenter	C₁₉	#3235
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #532

subgroup

G/H

center

C₂²

C₂²×C₂²⋊D₁₉

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting, prime radical

C₁₉×#532

C₂

socle

C₂²×C₁₉

C₂²×D₄

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #532

N	H ≅ G/N	type
1. #11927101	C₂	semidirect
2. #11926950	C₂	semidirect
3. #11926908	C₂	semidirect
4. #11926865	C₂	semidirect
5. #11926834	C₂	semidirect
6. #11926824	C₂	semidirect
7. #11926601	C₂	semidirect
139. C₁₉	#3235	semidirect

H ≅ G/N

type

1. #11927101

C₂

semidirect

2. #11926950

C₂

semidirect

3. #11926908

C₂

semidirect

4. #11926865

C₂

semidirect

5. #11926834

C₂

semidirect

6. #11926824

C₂

semidirect

7. #11926601

C₂

semidirect

139. C₁₉

#3235

semidirect

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

subgroup	index
#11927101	2
#11926950	2
#11926908	2
#11926865	2
#11926834	2
#11926824	2
#11926601	2
C₁₉×#532	2
#3235	19

subgroup

index

C₁₉×#532

Subgroups — #14574829

Conjugacy classes of subgroups

Complements

Maximal subgroups