Group #14564397 — subgroups

Subgroups — #14564397

Order 2432.

256 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 107 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×#10597274	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597265	C₂	1	1	yes	maximal, characteristic
3	C₂×Dic₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#11926413	C₂	1	1	yes	maximal, characteristic
5	C₄⋊C₄×Dic₁₉	C₂	1	1	yes	maximal, characteristic
6	#11926306	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#340	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
13	C₂×Dic₁₉⋊C₄	—	2	1	no	—
14	C₂×Dic₁₉⋊C₄	—	2	1	no	—
15	C₂×C₄×Dic₁₉	—	2	1	no	—
16	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
17	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
18	C₁₉⋊#95	—	2	1	no	—
19	#10597274	—	2	2	no	—
20	Dic₁₉⋊C₈	C₄	1	4	yes	complemented
21	#10597265	—	2	2	no	—
22	C₂²×C₄×C₁₉	—	2	1	no	—
23	C₂²×C₄×C₁₉	—	2	1	no	—
24	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
25	C₂²×Dic₁₉	—	2	1	no	—
26	C₂²×Dic₁₉	—	2	1	no	—
27	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
28	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
29	C₂×C₈×C₁₉	—	2	1	no	—
30	C₂×C₈×C₁₉	—	2	1	no	—
31	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
32	C₄⋊C₄×C₁₉	—	2	1	no	—
33	C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₄⋊C₄×C₁₉	—	2	1	no	—
35	C₄⋊C₄×C₁₉	Q₈	1	2	yes	—
36	C₄⋊Dic₁₉	—	2	1	no	—
37	C₄⋊Dic₁₉	—	2	1	no	—
38	C₄⋊Dic₁₉	—	2	1	no	—
39	C₄⋊Dic₁₉	D₄	1	2	yes	—
40	Dic₁₉⋊C₄	—	4	2	no	—
41	Dic₁₉⋊C₄	—	4	2	no	—
42	C₄×Dic₁₉	—	4	2	no	—
43	C₄×Dic₁₉	C₂×C₄	1	2	yes	—
44	C₄×Dic₁₉	Q₈	1	2	yes	—
45	C₂×C₁₉⋊C₈	—	2	1	no	—
46	C₂×C₁₉⋊C₈	—	2	1	no	—
47	C₂×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
48	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₁₉	—	2	2	no	—
50	C₂×C₄×C₁₉	—	4	1	no	—
51	C₂×C₄×C₁₉	—	4	1	no	—
52	C₂×C₄×C₁₉	—	4	1	no	—
53	C₂×C₄×C₁₉	—	4	1	no	—
54	C₂×C₄×C₁₉	—	4	1	no	—
55	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
56	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
57	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
58	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
59	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
60	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
61	C₂×Dic₁₉	—	2	1	no	—
62	C₂×Dic₁₉	—	2	1	no	—
63	C₂×Dic₁₉	—	2	2	no	—
64	C₂×Dic₁₉	—	4	1	no	—
65	C₂×Dic₁₉	—	4	1	no	—
66	C₂×Dic₁₉	—	4	1	no	—
67	C₂×Dic₁₉	—	4	1	no	—
68	C₂×Dic₁₉	—	4	1	no	—
69	C₂×Dic₁₉	C₄⋊C₄	1	2	yes	—
70	C₂×Dic₁₉	C₄⋊C₄	1	2	yes	—
71	C₂×Dic₁₉	SD₁₆	1	2	yes	—
72	C₂×Dic₁₉	SD₁₆	1	2	yes	—
73	C₈×C₁₉	—	2	2	no	—
74	C₁₉⋊C₈	—	2	2	no	—
75	#1948	—	19	1	no	maximal, Sylow
76	C₂²×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
77	C₂²×C₁₉	#121	1	1	yes	characteristic
78	C₂²×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
79	C₂²×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
80	C₂²×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
81	C₂²×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
82	C₂²×C₁₉	#137	1	1	yes	characteristic
83	C₄×C₁₉	—	4	2	no	—
84	C₄×C₁₉	—	8	1	no	—
85	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
86	C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
87	C₄×C₁₉	#125	1	1	yes	characteristic
88	C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
89	Dic₁₉	—	2	2	no	—
90	Dic₁₉	—	4	2	no	—
91	Dic₁₉	—	8	1	no	—
92	Dic₁₉	#106	1	4	yes	complemented
93	C₂×#106	—	19	1	no	—
94	C₂×#106	—	19	1	no	—
95	C₂×C₄⋊C₈	—	19	1	no	—
96	#384	—	19	1	no	—
97	C₄×C₄⋊C₄	—	19	1	no	—
98	#340	—	19	1	no	—
99	#340	D₁₉	1	1	yes	characteristic
100	C₂×C₁₉	#389	1	1	yes	characteristic
101	C₂×C₁₉	C₂×#106	1	1	yes	characteristic
102	C₂×C₁₉	#428	1	1	yes	characteristic
103	C₂×C₁₉	#460	1	1	yes	characteristic
104	C₂×C₁₉	#461	1	1	yes	characteristic
105	C₂×C₁₉	#475	1	1	yes	characteristic
106	C₂×C₁₉	#476	1	1	yes	characteristic
107	C₂²×C₈	—	19	1	no	—
108	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
109	C₂×C₄⋊C₄	—	19	1	no	—
110	C₂×C₄⋊C₄	—	19	1	no	—
111	C₂×C₄⋊C₄	—	38	1	no	—
112	C₂×C₄⋊C₄	—	38	1	no	—
113	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
114	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
115	C₂×C₄²	—	19	1	no	—
116	C₂×C₄²	—	38	1	no	—
117	#106	—	38	2	no	—
118	#106	—	38	2	no	—
119	C₄⋊C₈	—	19	4	no	—
120	#95	—	38	1	no	—
121	C₁₉	#1948	1	1	yes	characteristic, complemented, Sylow
122	C₂²×C₄	—	2	1	no	—
123	C₂²×C₄	—	2	1	no	—
124	C₂²×C₄	—	19	1	no	—
125	C₂²×C₄	—	19	1	no	—
126	C₂²×C₄	—	38	1	no	—
127	C₂²×C₄	—	38	1	no	—
128	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
129	C₂×C₈	—	2	1	no	—
130	C₂×C₈	—	2	1	no	—
131	C₂×C₈	—	19	2	no	—
132	C₂×C₈	—	38	1	no	—
133	C₂×C₈	—	38	1	no	—
134	C₂×C₈	C₄×D₁₉	1	2	yes	—
135	C₄⋊C₄	—	2	1	no	—
136	C₄⋊C₄	—	2	1	no	—
137	C₄⋊C₄	—	2	1	no	—
138	C₄⋊C₄	—	19	2	no	—
139	C₄⋊C₄	—	38	1	no	—
140	C₄⋊C₄	—	38	1	no	—
141	C₄⋊C₄	—	38	1	no	—
142	C₄⋊C₄	—	76	2	no	—
143	C₄⋊C₄	—	76	2	no	—
144	C₄⋊C₄	Dic₃₈	1	2	yes	—
145	C₄²	—	19	2	no	—
146	C₄²	—	19	2	no	—
147	C₄²	—	76	2	no	—
148	C₂³	D₄×D₁₉	1	1	yes	characteristic
149	C₂×C₄	—	2	2	no	—
150	C₂×C₄	—	4	1	no	—
151	C₂×C₄	—	4	1	no	—
152	C₂×C₄	—	4	1	no	—
153	C₂×C₄	—	4	1	no	—
154	C₂×C₄	—	4	1	no	—
155	C₂×C₄	—	19	2	no	—
156	C₂×C₄	—	19	2	no	—
157	C₂×C₄	—	19	2	no	—
158	C₂×C₄	—	19	2	no	—
159	C₂×C₄	—	38	1	no	—
160	C₂×C₄	—	38	1	no	—
161	C₂×C₄	—	38	2	no	—
162	C₂×C₄	—	76	1	no	—
163	C₂×C₄	—	76	1	no	—
164	C₂×C₄	—	76	1	no	—
165	C₂×C₄	—	76	1	no	—
166	C₂×C₄	—	76	1	no	—
167	C₂×C₄	C₂×Dic₃₈	1	1	yes	characteristic
168	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
169	C₂×C₄	#64541	1	1	yes	characteristic
170	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
171	C₂×C₄	#64543	1	1	yes	characteristic
172	C₂×C₄	Q₈×D₁₉	1	1	yes	characteristic
173	C₈	—	2	2	no	—
174	C₈	—	38	2	no	—
175	C₂²	#10597324	1	1	yes	characteristic
176	C₂²	#10597330	1	1	yes	characteristic
177	C₂²	C₄⋊C₄×D₁₉	1	1	yes	characteristic
178	C₂²	#10597357	1	1	yes	characteristic
179	C₂²	SD₁₆×D₁₉	1	1	yes	characteristic
180	C₂²	SD₁₆×D₁₉	1	1	yes	characteristic
181	C₂²	#10597364	1	1	yes	characteristic
182	C₄	—	4	2	no	—
183	C₄	—	8	1	no	—
184	C₄	—	19	4	no	—
185	C₄	—	38	2	no	—
186	C₄	—	76	2	no	—
187	C₄	—	152	1	no	—
188	C₄	C₄×Dic₃₈	1	1	yes	characteristic
189	C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
190	C₄	#10597334	1	1	yes	characteristic
191	C₄	#10597335	1	1	yes	characteristic
192	C₂	#11926441	1	1	yes	characteristic
193	C₂	#106×D₁₉	1	1	yes	characteristic
194	C₂	#11926585	1	1	yes	characteristic
195	C₂	#11926743	1	1	yes	characteristic
196	C₂	#11926748	1	1	yes	characteristic
197	C₂	#11926827	1	1	yes	characteristic
198	C₂	#11926832	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597274

C₂

yes

maximal, characteristic

C₂×#10597265

C₂

yes

maximal, characteristic

C₂×Dic₁₉⋊C₈

C₂

yes

maximal, characteristic

#11926413

C₂

yes

maximal, characteristic

C₄⋊C₄×Dic₁₉

C₂

yes

maximal, characteristic

#11926306

C₂

yes

maximal, characteristic

C₁₉×#340

C₂

yes

maximal, characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×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×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₁₉⋊#95

—

#10597274

—

Dic₁₉⋊C₈

C₄

yes

complemented

#10597265

—

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×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

Q₈

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

D₄

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

C₂×C₄

yes

—

C₄×Dic₁₉

Q₈

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×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×Q₈

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

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

C₄⋊C₄

yes

—

C₂×Dic₁₉

C₄⋊C₄

yes

—

C₂×Dic₁₉

SD₁₆

yes

—

C₂×Dic₁₉

SD₁₆

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1948

—

maximal, Sylow

C₂²×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₉

#121

yes

characteristic

C₂²×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂²×C₁₉

C₂×SD₁₆

yes

characteristic

C₂²×C₁₉

C₂×SD₁₆

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₄×D₄

yes

characteristic

C₄×C₁₉

C₄×Q₈

yes

characteristic

C₄×C₁₉

#125

yes

characteristic

C₄×C₁₉

C₄⋊Q₈

yes

characteristic

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

yes

—

—

C₂×C₄⋊C₈

—

#384

—

C₄×C₄⋊C₄

—

#340

—

#340

D₁₉

yes

characteristic

100

C₂×C₁₉

#389

yes

characteristic

101

C₂×C₁₉

C₂×#106

yes

characteristic

102

C₂×C₁₉

#428

yes

characteristic

103

C₂×C₁₉

#460

yes

characteristic

104

C₂×C₁₉

#461

yes

characteristic

105

C₂×C₁₉

#475

yes

characteristic

106

C₂×C₁₉

#476

yes

characteristic

107

C₂²×C₈

—

108

C₂²×C₈

C₂×D₁₉

yes

characteristic

109

C₂×C₄⋊C₄

—

110

C₂×C₄⋊C₄

—

111

C₂×C₄⋊C₄

—

112

C₂×C₄⋊C₄

—

113

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

114

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

115

C₂×C₄²

—

116

C₂×C₄²

—

117

#106

—

118

#106

—

119

C₄⋊C₈

—

120

#95

—

121

C₁₉

#1948

yes

characteristic, complemented, Sylow

122

C₂²×C₄

—

123

C₂²×C₄

—

124

C₂²×C₄

—

125

C₂²×C₄

—

126

C₂²×C₄

—

127

C₂²×C₄

—

128

C₂²×C₄

C₂²×D₁₉

yes

characteristic

129

C₂×C₈

—

130

C₂×C₈

—

131

C₂×C₈

—

132

C₂×C₈

—

133

C₂×C₈

—

134

C₂×C₈

C₄×D₁₉

yes

—

135

C₄⋊C₄

—

136

C₄⋊C₄

—

137

C₄⋊C₄

—

138

C₄⋊C₄

—

139

C₄⋊C₄

—

140

C₄⋊C₄

—

141

C₄⋊C₄

—

142

C₄⋊C₄

—

143

C₄⋊C₄

—

144

C₄⋊C₄

Dic₃₈

yes

—

145

C₄²

—

146

C₄²

—

147

C₄²

—

148

C₂³

D₄×D₁₉

yes

characteristic

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

C₂×Dic₃₈

yes

characteristic

168

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

169

C₂×C₄

#64541

yes

characteristic

170

C₂×C₄

D₄×D₁₉

yes

characteristic

171

C₂×C₄

#64543

yes

characteristic

172

C₂×C₄

Q₈×D₁₉

yes

characteristic

173

C₈

—

174

C₈

—

175

C₂²

#10597324

yes

characteristic

176

C₂²

#10597330

yes

characteristic

177

C₂²

C₄⋊C₄×D₁₉

yes

characteristic

178

C₂²

#10597357

yes

characteristic

179

C₂²

SD₁₆×D₁₉

yes

characteristic

180

C₂²

SD₁₆×D₁₉

yes

characteristic

181

C₂²

#10597364

yes

characteristic

182

C₄

—

183

C₄

—

184

C₄

—

185

C₄

—

186

C₄

—

187

C₄

—

152

—

188

C₄

C₄×Dic₃₈

yes

characteristic

189

C₄

(C₂²⋊D₁₉)⋊C₄

yes

characteristic

190

C₄

#10597334

yes

characteristic

191

C₄

#10597335

yes

characteristic

192

C₂

#11926441

yes

characteristic

193

C₂

#106×D₁₉

yes

characteristic

194

C₂

#11926585

yes

characteristic

195

C₂

#11926743

yes

characteristic

196

C₂

#11926748

yes

characteristic

197

C₂

#11926827

yes

characteristic

198

C₂

#11926832

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#340	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#340	D₁₉
hypocenter	C₁₉	#1948
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

subgroup

G/H

center

C₂³

D₄×D₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#340

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

N	H ≅ G/N	type
20. Dic₁₉⋊C₈	C₄	semidirect
92. Dic₁₉	#106	semidirect
121. C₁₉	#1948	semidirect

H ≅ G/N

type

20. Dic₁₉⋊C₈

C₄

semidirect

92. Dic₁₉

#106

semidirect

121. C₁₉

#1948

semidirect

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

subgroup	index
C₂×#10597274	2
C₂×#10597265	2
C₂×Dic₁₉⋊C₈	2
#11926413	2
C₄⋊C₄×Dic₁₉	2
#11926306	2
C₁₉×#340	2
#1948	19

subgroup

index

C₂×Dic₁₉⋊C₈

C₄⋊C₄×Dic₁₉

C₁₉×#340

Subgroups — #14564397

Conjugacy classes of subgroups

Complements

Maximal subgroups