Group #14564103 — subgroups

Subgroups — #14564103

Order 2432.

338 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 97 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
2	C₂×#10597281	C₂	1	2	yes	maximal, complemented
3	#11926508	C₂	1	1	yes	maximal, characteristic
4	#11926312	C₂	1	2	yes	maximal, complemented
5	C₂²×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
8	C₂×M₁₆×C₁₉	—	2	1	no	—
9	C₂×M₁₆×C₁₉	—	2	4	no	—
10	C₂×M₁₆×C₁₉	C₂²	1	2	yes	—
11	C₂²×C₈×C₁₉	—	2	1	no	—
12	C₂×C₂²⋊Dic₁₉	C₄	1	2	yes	—
13	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
14	#10597370	—	2	1	no	—
15	#10597370	—	2	1	no	—
16	#10597370	—	2	1	no	—
17	#10597370	—	2	1	no	—
18	C₂×Dic₁₉⋊C₄	C₄	1	2	yes	—
19	C₂×#64520	C₂²	1	2	yes	—
20	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
21	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
22	#10597281	—	2	4	no	—
23	C₂⁴×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₄×C₁₉	—	2	2	no	—
25	C₂²×C₄×C₁₉	—	2	2	no	—
26	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
28	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
29	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
30	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
31	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
32	C₂²×Dic₁₉	C₂×C₄	1	2	yes	—
33	C₂²×Dic₁₉	C₂×C₄	1	2	yes	—
34	C₂×Dic₃₈	—	2	2	no	—
35	C₂×Dic₃₈	—	2	1	no	—
36	C₂×Dic₃₈	—	2	1	no	—
37	C₂×Dic₃₈	—	2	2	no	—
38	M₁₆×C₁₉	—	2	4	no	—
39	M₁₆×C₁₉	—	2	2	no	—
40	M₁₆×C₁₉	D₄	1	4	yes	—
41	C₂×C₈×C₁₉	—	2	4	no	—
42	C₂×C₈×C₁₉	—	2	2	no	—
43	C₂²⋊Dic₁₉	—	2	2	no	—
44	C₂²⋊Dic₁₉	—	2	2	no	—
45	C₄⋊Dic₁₉	—	2	1	no	—
46	C₄⋊Dic₁₉	—	2	1	no	—
47	Dic₁₉⋊C₄	—	2	2	no	—
48	Dic₁₉⋊C₄	—	2	2	no	—
49	#64520	—	2	2	no	—
50	#64520	—	2	2	no	—
51	C₂×C₁₉⋊C₈	—	2	2	no	—
52	C₂³×C₁₉	—	2	2	no	—
53	C₂³×C₁₉	—	2	2	no	—
54	C₂³×C₁₉	—	4	1	no	—
55	C₂³×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
56	C₂³×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
57	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
58	C₂×C₄×C₁₉	—	2	2	no	—
59	C₂×C₄×C₁₉	—	2	1	no	—
60	C₂×C₄×C₁₉	—	2	1	no	—
61	C₂×C₄×C₁₉	—	2	2	no	—
62	C₂×C₄×C₁₉	—	2	2	no	—
63	C₂×C₄×C₁₉	—	2	1	no	—
64	C₂×C₄×C₁₉	—	2	1	no	—
65	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
66	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
68	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
69	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
70	C₂×C₄×C₁₉	#41	1	2	yes	—
71	C₂×Dic₁₉	—	2	2	no	—
72	C₂×Dic₁₉	—	2	2	no	—
73	C₂×Dic₁₉	—	2	4	no	—
74	C₂×Dic₁₉	—	4	2	no	—
75	Dic₃₈	—	4	1	no	—
76	Dic₃₈	—	4	2	no	—
77	Dic₃₈	—	4	1	no	—
78	C₈×C₁₉	—	2	4	no	—
79	C₁₉⋊C₈	—	4	2	no	—
80	#1901	—	19	1	no	maximal, Sylow
81	C₂²×C₁₉	—	2	1	no	—
82	C₂²×C₁₉	—	2	1	no	—
83	C₂²×C₁₉	—	2	1	no	—
84	C₂²×C₁₉	—	2	1	no	—
85	C₂²×C₁₉	—	2	1	no	—
86	C₂²×C₁₉	—	2	1	no	—
87	C₂²×C₁₉	—	2	1	no	—
88	C₂²×C₁₉	—	4	4	no	—
89	C₂²×C₁₉	#101	1	2	yes	complemented
90	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
91	C₂²×C₁₉	C₄×D₄	1	2	yes	—
92	C₄×C₁₉	—	2	1	no	—
93	C₄×C₁₉	—	2	1	no	—
94	C₄×C₁₉	#120	1	1	yes	characteristic
95	C₄×C₁₉	#121	1	2	yes	—
96	C₄×C₁₉	#123	1	1	yes	characteristic
97	Dic₁₉	—	4	2	no	—
98	Dic₁₉	—	4	2	no	—
99	C₂²×M₁₆	D₁₉	1	1	yes	characteristic
100	C₂×C₂²⋊Q₈	—	19	1	no	—
101	C₂×#101	—	19	2	no	—
102	#407	—	19	1	no	—
103	#343	—	19	2	no	—
104	C₂×C₁₉	—	2	2	no	—
105	C₂×C₁₉	—	2	2	no	—
106	C₂×C₁₉	—	4	1	no	—
107	C₂×C₁₉	#386	1	1	yes	characteristic
108	C₂×C₁₉	C₂×#101	1	1	yes	characteristic
109	C₂×C₁₉	#413	1	1	yes	characteristic
110	C₂²×Q₈	—	19	1	no	—
111	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
112	C₂×M₁₆	—	2	1	no	—
113	C₂×M₁₆	—	2	4	no	—
114	C₂×M₁₆	—	19	2	no	—
115	C₂×M₁₆	C₂×D₁₉	1	2	yes	—
116	C₂²×C₈	—	2	1	no	—
117	C₂²⋊Q₈	—	38	1	no	—
118	C₂²⋊Q₈	—	38	1	no	—
119	C₂²⋊Q₈	—	38	1	no	—
120	C₂²⋊Q₈	—	38	1	no	—
121	C₂×C₄⋊C₄	—	19	2	no	—
122	C₂×C₄⋊C₄	—	19	1	no	—
123	C₂×C₂²⋊C₄	—	19	2	no	—
124	#101	—	38	4	no	—
125	C₂²⋊C₈	—	38	1	no	—
126	C₂²⋊C₈	—	38	1	no	—
127	C₁₉	#1901	1	1	yes	characteristic, complemented, Sylow
128	C₂⁴	C₄×D₁₉	1	1	yes	characteristic
129	C₂×Q₈	—	38	1	no	—
130	C₂×Q₈	—	38	2	no	—
131	C₂×Q₈	—	38	2	no	—
132	C₂×Q₈	—	38	1	no	—
133	C₂²×C₄	—	2	2	no	—
134	C₂²×C₄	—	2	2	no	—
135	C₂²×C₄	—	19	2	no	—
136	C₂²×C₄	—	19	2	no	—
137	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
138	C₂²×C₄	D₇₆	1	1	yes	characteristic
139	C₂²×C₄	D₇₆	1	1	yes	characteristic
140	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
141	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
142	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
143	M₁₆	—	2	4	no	—
144	M₁₆	—	2	2	no	—
145	M₁₆	—	38	2	no	—
146	M₁₆	—	38	2	no	—
147	M₁₆	C₂²⋊D₁₉	1	4	yes	—
148	C₂×C₈	—	2	4	no	—
149	C₂×C₈	—	2	2	no	—
150	C₂×C₈	—	38	2	no	—
151	C₄⋊C₄	—	38	2	no	—
152	C₄⋊C₄	—	38	2	no	—
153	C₄⋊C₄	—	38	1	no	—
154	C₄⋊C₄	—	38	1	no	—
155	C₂²⋊C₄	—	38	2	no	—
156	C₂²⋊C₄	—	38	2	no	—
157	C₂³	—	2	2	no	—
158	C₂³	—	2	2	no	—
159	C₂³	—	4	1	no	—
160	C₂³	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
161	C₂³	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
162	C₂³	C₂×C₄×D₁₉	1	1	yes	characteristic
163	Q₈	—	76	2	no	—
164	Q₈	—	76	1	no	—
165	Q₈	—	76	1	no	—
166	C₂×C₄	—	2	2	no	—
167	C₂×C₄	—	2	2	no	—
168	C₂×C₄	—	2	2	no	—
169	C₂×C₄	—	2	1	no	—
170	C₂×C₄	—	2	1	no	—
171	C₂×C₄	—	2	1	no	—
172	C₂×C₄	—	2	1	no	—
173	C₂×C₄	—	38	2	no	—
174	C₂×C₄	—	38	2	no	—
175	C₂×C₄	—	38	4	no	—
176	C₂×C₄	—	76	2	no	—
177	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
178	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
179	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
180	C₂×C₄	#64541	1	2	yes	—
181	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
182	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
183	C₈	—	2	4	no	—
184	C₈	—	76	2	no	—
185	C₂²	—	2	1	no	—
186	C₂²	—	2	1	no	—
187	C₂²	—	2	1	no	—
188	C₂²	—	2	1	no	—
189	C₂²	—	2	1	no	—
190	C₂²	—	2	1	no	—
191	C₂²	—	2	1	no	—
192	C₂²	—	4	4	no	—
193	C₂²	#10597281	1	2	yes	complemented
194	C₂²	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
195	C₂²	C₄×C₂²⋊D₁₉	1	2	yes	—
196	C₄	—	2	1	no	—
197	C₄	—	2	1	no	—
198	C₄	—	76	2	no	—
199	C₄	—	76	2	no	—
200	C₄	#10597375	1	1	yes	characteristic
201	C₄	#10597376	1	2	yes	—
202	C₄	#10597399	1	1	yes	characteristic
203	C₂	—	2	2	no	—
204	C₂	—	2	2	no	—
205	C₂	—	4	1	no	—
206	C₂	#11926423	1	1	yes	characteristic
207	C₂	C₂×#10597281	1	1	yes	characteristic
208	C₂	#11926526	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597370

C₂

yes

maximal, characteristic

C₂×#10597281

C₂

yes

maximal, complemented

#11926508

C₂

yes

maximal, characteristic

#11926312

C₂

yes

maximal, complemented

C₂²×M₁₆×C₁₉

C₂

yes

maximal, characteristic

C₂³×C₄×C₁₉

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

C₂²

yes

—

C₂²×C₈×C₁₉

—

C₂×C₂²⋊Dic₁₉

C₄

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

—

—

—

C₂×Dic₁₉⋊C₄

C₄

yes

—

C₂×#64520

C₂²

yes

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

#10597281

—

C₂⁴×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂×C₄

yes

—

C₂²×Dic₁₉

C₂×C₄

yes

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

D₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂²⋊C₄

yes

characteristic

C₂³×C₁₉

C₂²⋊C₄

yes

characteristic

C₂³×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

—

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

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1901

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#101

yes

complemented

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉

C₄×D₄

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#120

yes

characteristic

C₄×C₁₉

#121

yes

—

C₄×C₁₉

#123

yes

characteristic

Dic₁₉

—

Dic₁₉

—

C₂²×M₁₆

D₁₉

yes

characteristic

100

C₂×C₂²⋊Q₈

—

101

C₂×#101

—

102

#407

—

103

#343

—

104

C₂×C₁₉

—

105

C₂×C₁₉

—

106

C₂×C₁₉

—

107

C₂×C₁₉

#386

yes

characteristic

108

C₂×C₁₉

C₂×#101

yes

characteristic

109

C₂×C₁₉

#413

yes

characteristic

110

C₂²×Q₈

—

111

C₂³×C₄

C₂×D₁₉

yes

characteristic

112

C₂×M₁₆

—

113

C₂×M₁₆

—

114

C₂×M₁₆

—

115

C₂×M₁₆

C₂×D₁₉

yes

—

116

C₂²×C₈

—

117

C₂²⋊Q₈

—

118

C₂²⋊Q₈

—

119

C₂²⋊Q₈

—

120

C₂²⋊Q₈

—

121

C₂×C₄⋊C₄

—

122

C₂×C₄⋊C₄

—

123

C₂×C₂²⋊C₄

—

124

#101

—

125

C₂²⋊C₈

—

126

C₂²⋊C₈

—

127

C₁₉

#1901

yes

characteristic, complemented, Sylow

128

C₂⁴

C₄×D₁₉

yes

characteristic

129

C₂×Q₈

—

130

C₂×Q₈

—

131

C₂×Q₈

—

132

C₂×Q₈

—

133

C₂²×C₄

—

134

C₂²×C₄

—

135

C₂²×C₄

—

136

C₂²×C₄

—

137

C₂²×C₄

C₄×D₁₉

yes

characteristic

138

C₂²×C₄

D₇₆

yes

characteristic

139

C₂²×C₄

D₇₆

yes

characteristic

140

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

141

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

142

C₂²×C₄

C₂²×D₁₉

yes

characteristic

143

M₁₆

—

144

M₁₆

—

145

M₁₆

—

146

M₁₆

—

147

M₁₆

C₂²⋊D₁₉

yes

—

148

C₂×C₈

—

149

C₂×C₈

—

150

C₂×C₈

—

151

C₄⋊C₄

—

152

C₄⋊C₄

—

153

C₄⋊C₄

—

154

C₄⋊C₄

—

155

C₂²⋊C₄

—

156

C₂²⋊C₄

—

157

C₂³

—

158

C₂³

—

159

C₂³

—

160

C₂³

(C₂×D₁₉)⋊C₄

yes

characteristic

161

C₂³

(C₂×D₁₉)⋊C₄

yes

characteristic

162

C₂³

C₂×C₄×D₁₉

yes

characteristic

163

Q₈

—

164

Q₈

—

165

Q₈

—

166

C₂×C₄

—

167

C₂×C₄

—

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

(C₂×D₁₉)⋊C₄

yes

characteristic

178

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

179

C₂×C₄

C₂×D₇₆

yes

characteristic

180

C₂×C₄

#64541

yes

—

181

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

182

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

183

C₈

—

184

C₈

—

185

C₂²

—

186

C₂²

—

187

C₂²

—

188

C₂²

—

189

C₂²

—

190

C₂²

—

191

C₂²

—

192

C₂²

—

193

C₂²

#10597281

yes

complemented

194

C₂²

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

195

C₂²

C₄×C₂²⋊D₁₉

yes

—

196

C₄

—

197

C₄

—

198

C₄

—

199

C₄

—

200

C₄

#10597375

yes

characteristic

201

C₄

#10597376

yes

—

202

C₄

#10597399

yes

characteristic

203

C₂

—

204

C₂

—

205

C₂

—

206

C₂

#11926423

yes

characteristic

207

C₂

C₂×#10597281

yes

characteristic

208

C₂

#11926526

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×(C₂×D₁₉)⋊C₄
commutator	C₂³×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂²×M₁₆×C₁₉	C₂
socle	C₂²×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₉	C₂×C₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂²×M₁₆	D₁₉
hypocenter	C₁₉	#1901
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂²×M₁₆

subgroup

G/H

center

C₂²

C₂×(C₂×D₁₉)⋊C₄

commutator

C₂³×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂²×M₁₆×C₁₉

C₂

socle

C₂²×C₁₉

C₂×C₂²⋊C₄

prime radical

C₂⁴×C₁₉

C₂×C₄

cosocle

C₂²×C₄×C₁₉

C₂³

hypercenter

C₂²×M₁₆

D₁₉

hypocenter

C₁₉

#1901

LCS

G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂²×M₁₆

N	H ≅ G/N	type
2. C₂×#10597281	C₂	semidirect
4. #11926312	C₂	semidirect
89. C₂²×C₁₉	#101	semidirect
127. C₁₉	#1901	semidirect
193. C₂²	#10597281	semidirect

H ≅ G/N

type

2. C₂×#10597281

C₂

semidirect

4. #11926312

C₂

semidirect

89. C₂²×C₁₉

#101

semidirect

127. C₁₉

#1901

semidirect

193. C₂²

#10597281

semidirect

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

subgroup	index
C₂×#10597370	2
C₂×#10597281	2
#11926508	2
#11926312	2
C₂²×M₁₆×C₁₉	2
#1901	19

subgroup

index

C₂²×M₁₆×C₁₉

Subgroups — #14564103

Conjugacy classes of subgroups

Complements

Maximal subgroups