Group #14571663 — subgroups

Subgroups — #14571663

Order 2432.

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

normal subgroups only

This group has 528 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	C₂×#10597370	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926480	C₂	1	2	yes	maximal, complemented
3	#11926475	C₂	1	2	yes	maximal, complemented
4	#11926458	C₂	1	4	yes	maximal, complemented
5	#11926458	C₂	1	2	yes	maximal, complemented
6	#11926456	C₂	1	2	yes	maximal, complemented
7	#11926407	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×#121	C₂	1	1	yes	maximal, characteristic
9	C₂²×D₄×C₁₉	C₂²	1	2	yes	—
10	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
13	C₁₉×#121	—	2	4	no	—
14	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
16	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	—
17	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	—
18	C₂×C₂²⋊Dic₁₉	C₂²	1	4	yes	—
19	C₂×C₂²⋊Dic₁₉	C₂²	1	4	yes	—
20	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
21	#10597370	—	2	4	no	—
22	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
23	C₂×Dic₁₉⋊C₄	C₂²	1	4	yes	—
24	C₁₉⋊#95	C₂²	1	2	yes	—
25	C₁₉⋊#95	C₂²	1	2	yes	—
26	C₁₉⋊#95	C₂²	1	4	yes	—
27	C₂⁴×C₁₉	C₂³	1	2	yes	—
28	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
29	C₂×D₄×C₁₉	—	2	4	no	—
30	C₂×D₄×C₁₉	—	2	2	no	—
31	C₂×D₄×C₁₉	—	4	2	no	—
32	C₂×D₄×C₁₉	—	4	4	no	—
33	C₂²×C₄×C₁₉	—	4	2	no	—
34	C₂²×C₄×C₁₉	D₄	1	4	yes	—
35	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
36	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
37	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
38	C₂²×Dic₁₉	C₂³	1	2	yes	—
39	C₂²×Dic₁₉	C₂³	1	4	yes	—
40	C₂²×Dic₁₉	C₂³	1	2	yes	—
41	C₂×Dic₃₈	—	2	2	no	—
42	C₂×Dic₃₈	—	4	2	no	—
43	C₄⋊C₄×C₁₉	—	2	2	no	—
44	C₂²⋊C₄×C₁₉	—	2	4	no	—
45	C₂²⋊Dic₁₉	—	2	4	no	—
46	C₂²⋊Dic₁₉	—	4	4	no	—
47	C₂²⋊Dic₁₉	—	4	2	no	—
48	C₂²⋊Dic₁₉	—	4	4	no	—
49	C₄⋊Dic₁₉	—	2	2	no	—
50	Dic₁₉⋊C₄	—	2	4	no	—
51	Dic₁₉⋊C₄	—	4	4	no	—
52	C₂³×C₁₉	—	2	2	no	—
53	C₂³×C₁₉	—	2	2	no	—
54	C₂³×C₁₉	—	2	2	no	—
55	C₂³×C₁₉	—	2	2	no	—
56	C₂³×C₁₉	—	2	4	no	—
57	C₂³×C₁₉	—	2	4	no	—
58	C₂³×C₁₉	—	2	4	no	—
59	C₂³×C₁₉	C₂×D₄	1	2	yes	—
60	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
61	D₄×C₁₉	—	4	4	no	—
62	D₄×C₁₉	—	4	8	no	—
63	C₂×C₄×C₁₉	—	2	2	no	—
64	C₂×C₄×C₁₉	—	2	2	no	—
65	C₂×C₄×C₁₉	—	2	2	no	—
66	C₂×C₄×C₁₉	—	2	4	no	—
67	C₂×C₄×C₁₉	—	4	4	no	—
68	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
69	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
70	C₂×Dic₁₉	—	2	2	no	—
71	C₂×Dic₁₉	—	2	2	no	—
72	C₂×Dic₁₉	—	2	2	no	—
73	C₂×Dic₁₉	—	2	4	no	—
74	C₂×Dic₁₉	—	2	2	no	—
75	C₂×Dic₁₉	—	2	4	no	—
76	C₂×Dic₁₉	—	2	4	no	—
77	C₂×Dic₁₉	—	2	4	no	—
78	Dic₃₈	—	4	4	no	—
79	#2816	—	19	1	no	maximal, Sylow
80	C₂²×C₁₉	—	2	2	no	—
81	C₂²×C₁₉	—	2	2	no	—
82	C₂²×C₁₉	—	2	2	no	—
83	C₂²×C₁₉	—	4	4	no	—
84	C₂²×C₁₉	—	4	2	no	—
85	C₂²×C₁₉	—	4	2	no	—
86	C₂²×C₁₉	—	4	2	no	—
87	C₂²×C₁₉	—	4	8	no	—
88	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
89	C₂²×C₁₉	H(5,𝔽₂)	1	2	yes	—
90	C₂²×C₁₉	H(5,𝔽₂)	1	2	yes	—
91	C₂²×C₁₉	2₋¹⁺⁴	1	2	yes	—
92	C₄×C₁₉	—	2	2	no	—
93	C₄×C₁₉	—	2	2	no	—
94	C₄×C₁₉	—	4	2	no	—
95	Dic₁₉	—	4	2	no	—
96	Dic₁₉	—	4	2	no	—
97	Dic₁₉	—	4	4	no	—
98	C₂×C₂²⋊Q₈	—	19	1	no	—
99	C₂×#121	D₁₉	1	1	yes	characteristic
100	#399	—	19	2	no	—
101	#398	—	19	2	no	—
102	#394	—	19	2	no	—
103	#394	—	19	4	no	—
104	#393	—	19	2	no	—
105	#381	—	19	1	no	—
106	C₂×C₁₉	—	4	2	no	—
107	C₂×C₁₉	—	8	2	no	—
108	C₂×C₁₉	#534	1	1	yes	characteristic
109	C₂×C₁₉	#535	1	1	yes	characteristic
110	C₂×C₁₉	#536	1	1	yes	characteristic
111	C₂×C₁₉	#562	1	4	yes	—
112	C₂²×Q₈	—	19	1	no	—
113	C₂²×D₄	C₂×D₁₉	1	2	yes	—
114	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
115	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
116	C₂²⋊Q₈	—	38	4	no	—
117	#121	—	2	4	no	—
118	C₂×C₄⋊C₄	—	19	2	no	—
119	C₂×C₄⋊C₄	—	19	1	no	—
120	C₂×C₄⋊C₄	—	19	4	no	—
121	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
122	C₂×C₂²⋊C₄	—	19	2	no	—
123	C₂×C₂²⋊C₄	—	19	2	no	—
124	C₂×C₂²⋊C₄	—	19	4	no	—
125	C₂×C₂²⋊C₄	—	19	4	no	—
126	C₂×C₂²⋊C₄	C₂×D₁₉	1	2	yes	—
127	#95	—	19	2	no	—
128	#95	—	19	2	no	—
129	#95	—	19	4	no	—
130	C₁₉	#2816	1	1	yes	characteristic, complemented, Sylow
131	C₂⁴	C₂²×D₁₉	1	2	yes	—
132	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
133	C₂×Q₈	—	38	2	no	—
134	C₂×Q₈	—	76	2	no	—
135	C₂×D₄	—	2	4	no	—
136	C₂×D₄	—	2	2	no	—
137	C₂×D₄	—	4	2	no	—
138	C₂×D₄	—	4	4	no	—
139	C₂²×C₄	—	4	2	no	—
140	C₂²×C₄	—	19	4	no	—
141	C₂²×C₄	—	19	2	no	—
142	C₂²×C₄	—	19	2	no	—
143	C₂²×C₄	C₂²⋊D₁₉	1	4	yes	—
144	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
145	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
146	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
147	C₄⋊C₄	—	2	2	no	—
148	C₄⋊C₄	—	38	4	no	—
149	C₄⋊C₄	—	38	2	no	—
150	C₄⋊C₄	—	76	4	no	—
151	C₂²⋊C₄	—	2	4	no	—
152	C₂²⋊C₄	—	38	4	no	—
153	C₂²⋊C₄	—	76	2	no	—
154	C₂²⋊C₄	—	76	4	no	—
155	C₂²⋊C₄	—	76	4	no	—
156	C₂³	—	2	2	no	—
157	C₂³	—	2	2	no	—
158	C₂³	—	2	2	no	—
159	C₂³	—	2	4	no	—
160	C₂³	—	2	4	no	—
161	C₂³	—	2	4	no	—
162	C₂³	—	2	2	no	—
163	C₂³	C₂×C₂²⋊D₁₉	1	2	yes	—
164	C₂³	C₂³×D₁₉	1	1	yes	characteristic
165	Q₈	—	76	4	no	—
166	D₄	—	4	4	no	—
167	D₄	—	4	8	no	—
168	C₂×C₄	—	2	2	no	—
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	—	2	4	no	—
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	—	4	4	no	—
173	C₂×C₄	—	38	2	no	—
174	C₂×C₄	—	38	4	no	—
175	C₂×C₄	—	38	4	no	—
176	C₂×C₄	—	38	4	no	—
177	C₂×C₄	—	38	2	no	—
178	C₂×C₄	—	38	4	no	—
179	C₂×C₄	—	38	2	no	—
180	C₂×C₄	—	38	2	no	—
181	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
182	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
183	C₂²	—	2	2	no	—
184	C₂²	—	2	2	no	—
185	C₂²	—	2	2	no	—
186	C₂²	—	4	4	no	—
187	C₂²	—	4	2	no	—
188	C₂²	—	4	2	no	—
189	C₂²	—	4	2	no	—
190	C₂²	—	4	8	no	—
191	C₂²	#10597430	1	2	yes	—
192	C₂²	#10597430	1	2	yes	—
193	C₂²	#10597436	1	2	yes	—
194	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
195	C₄	—	2	2	no	—
196	C₄	—	2	2	no	—
197	C₄	—	4	2	no	—
198	C₄	—	76	2	no	—
199	C₄	—	76	2	no	—
200	C₄	—	76	4	no	—
201	C₂	—	4	2	no	—
202	C₂	—	8	2	no	—
203	C₂	#11927103	1	1	yes	characteristic
204	C₂	#11927111	1	1	yes	characteristic
205	C₂	#11927115	1	1	yes	characteristic
206	C₂	#11927289	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597370

C₂

yes

maximal, characteristic, complemented

#11926480

C₂

yes

maximal, complemented

#11926475

C₂

yes

maximal, complemented

#11926458

C₂

yes

maximal, complemented

#11926458

C₂

yes

maximal, complemented

#11926456

C₂

yes

maximal, complemented

#11926407

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×#121

C₂

yes

maximal, characteristic

C₂²×D₄×C₁₉

C₂²

yes

—

C₂²×D₄×C₁₉

C₂²

yes

characteristic

C₂³×C₄×C₁₉

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

characteristic

C₁₉×#121

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

#10597370

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂⁴×C₁₉

C₂³

yes

—

C₂⁴×C₁₉

C₂³

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

—

C₂³×C₁₉

C₂⁴

yes

characteristic

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

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

#2816

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

H(5,𝔽₂)

yes

—

C₂²×C₁₉

H(5,𝔽₂)

yes

—

C₂²×C₁₉

2₋¹⁺⁴

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂×C₂²⋊Q₈

—

C₂×#121

D₁₉

yes

characteristic

100

#399

—

101

#398

—

102

#394

—

103

#394

—

104

#393

—

105

#381

—

106

C₂×C₁₉

—

107

C₂×C₁₉

—

108

C₂×C₁₉

#534

yes

characteristic

109

C₂×C₁₉

#535

yes

characteristic

110

C₂×C₁₉

#536

yes

characteristic

111

C₂×C₁₉

#562

yes

—

112

C₂²×Q₈

—

113

C₂²×D₄

C₂×D₁₉

yes

—

114

C₂²×D₄

C₂×D₁₉

yes

characteristic

115

C₂³×C₄

C₂×D₁₉

yes

characteristic

116

C₂²⋊Q₈

—

117

#121

—

118

C₂×C₄⋊C₄

—

119

C₂×C₄⋊C₄

—

120

C₂×C₄⋊C₄

—

121

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

122

C₂×C₂²⋊C₄

—

123

C₂×C₂²⋊C₄

—

124

C₂×C₂²⋊C₄

—

125

C₂×C₂²⋊C₄

—

126

C₂×C₂²⋊C₄

C₂×D₁₉

yes

—

127

#95

—

128

#95

—

129

#95

—

130

C₁₉

#2816

yes

characteristic, complemented, Sylow

131

C₂⁴

C₂²×D₁₉

yes

—

132

C₂⁴

C₂²×D₁₉

yes

characteristic

133

C₂×Q₈

—

134

C₂×Q₈

—

135

C₂×D₄

—

136

C₂×D₄

—

137

C₂×D₄

—

138

C₂×D₄

—

139

C₂²×C₄

—

140

C₂²×C₄

—

141

C₂²×C₄

—

142

C₂²×C₄

—

143

C₂²×C₄

C₂²⋊D₁₉

yes

—

144

C₂²×C₄

C₂²×D₁₉

yes

—

145

C₂²×C₄

C₂²×D₁₉

yes

characteristic

146

C₂²×C₄

C₂²×D₁₉

yes

characteristic

147

C₄⋊C₄

—

148

C₄⋊C₄

—

149

C₄⋊C₄

—

150

C₄⋊C₄

—

151

C₂²⋊C₄

—

152

C₂²⋊C₄

—

153

C₂²⋊C₄

—

154

C₂²⋊C₄

—

155

C₂²⋊C₄

—

156

C₂³

—

157

C₂³

—

158

C₂³

—

159

C₂³

—

160

C₂³

—

161

C₂³

—

162

C₂³

—

163

C₂³

C₂×C₂²⋊D₁₉

yes

—

164

C₂³

C₂³×D₁₉

yes

characteristic

165

Q₈

—

166

D₄

—

167

D₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

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

C₂×C₂²⋊D₁₉

yes

—

182

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

183

C₂²

—

184

C₂²

—

185

C₂²

—

186

C₂²

—

187

C₂²

—

188

C₂²

—

189

C₂²

—

190

C₂²

—

191

C₂²

#10597430

yes

—

192

C₂²

#10597430

yes

—

193

C₂²

#10597436

yes

—

194

C₂²

C₂²×C₂²⋊D₁₉

yes

characteristic

195

C₄

—

196

C₄

—

197

C₄

—

198

C₄

—

199

C₄

—

200

C₄

—

201

C₂

—

202

C₂

—

203

C₂

#11927103

yes

characteristic

204

C₂

#11927111

yes

characteristic

205

C₂

#11927115

yes

characteristic

206

C₂

#11927289

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting, prime radical	C₂×C₁₉×#121	C₂
hypercenter	C₂×#121	D₁₉
hypocenter	C₁₉	#2816
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×#121

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting, prime radical

C₂×C₁₉×#121

C₂

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ C₂×#121

N	H ≅ G/N	type
1. C₂×#10597370	C₂	semidirect
2. #11926480	C₂	semidirect
3. #11926475	C₂	semidirect
4. #11926458	C₂	semidirect
5. #11926458	C₂	semidirect
6. #11926456	C₂	semidirect
7. #11926407	C₂	semidirect
130. C₁₉	#2816	semidirect

H ≅ G/N

type

1. C₂×#10597370

C₂

semidirect

2. #11926480

C₂

semidirect

3. #11926475

C₂

semidirect

4. #11926458

C₂

semidirect

5. #11926458

C₂

semidirect

6. #11926456

C₂

semidirect

7. #11926407

C₂

semidirect

130. C₁₉

#2816

semidirect

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

subgroup	index
C₂×#10597370	2
#11926480	2
#11926475	2
#11926458	2
#11926456	2
#11926407	2
C₂×C₁₉×#121	2
#2816	19

subgroup

index

C₂×C₁₉×#121

Subgroups — #14571663

Conjugacy classes of subgroups

Complements

Maximal subgroups