Group #14574646 — subgroups

Subgroups — #14574646

Order 2432.

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

normal subgroups only

This group has 390 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	#11926939	C₂	1	2	yes	maximal, complemented
3	#11926903	C₂	1	2	yes	maximal, complemented
4	#11926751	C₂	1	2	yes	maximal, complemented
5	#11926741	C₂	1	2	yes	maximal, complemented
6	#11926706	C₂	1	4	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	C₂²	1	2	yes	—
10	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₁₉×#127	C₂²	1	1	yes	characteristic
12	C₁₉×#124	C₂²	1	2	yes	—
13	C₁₉×#121	—	2	1	no	—
14	C₁₉×#121	—	2	1	no	—
15	C₄×D₄×C₁₉	—	2	1	no	—
16	C₄×D₄×C₁₉	—	2	1	no	—
17	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×#64528	C₂²	1	4	yes	—
19	C₂×#64526	C₂²	1	4	yes	—
20	#10597372	—	2	1	no	—
21	#10597370	—	2	1	no	—
22	#10597370	C₂²	1	2	yes	—
23	#10597316	—	2	1	no	—
24	#10597315	C₂²	1	1	yes	characteristic
25	#10597315	C₂²	1	1	yes	characteristic
26	C₄×Dic₃₈	—	2	1	no	—
27	C₄×Dic₃₈	C₂²	1	2	yes	—
28	#10597292	C₂²	1	4	yes	—
29	#10597289	C₂²	1	4	yes	—
30	C₂²⋊(C₁₉⋊C₈)	C₂²	1	2	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	C₂³	1	2	yes	—
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	C₂³	1	2	yes	—
45	C₄⋊C₄×C₁₉	—	2	1	no	—
46	C₄⋊C₄×C₁₉	—	2	1	no	—
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	#64528	—	4	4	no	—
55	#64526	—	4	4	no	—
56	C₄⋊Dic₁₉	—	2	1	no	—
57	C₄⋊Dic₁₉	—	2	1	no	—
58	C₄⋊Dic₁₉	—	2	1	no	—
59	C₄⋊Dic₁₉	C₂³	1	2	yes	—
60	Dic₁₉⋊C₄	—	2	2	no	—
61	Dic₁₉⋊C₄	—	2	2	no	—
62	C₄×Dic₁₉	—	2	2	no	—
63	C₂×C₁₉⋊C₈	C₂³	1	4	yes	—
64	C₂³×C₁₉	—	2	2	no	—
65	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
66	Q₈×C₁₉	—	2	4	no	—
67	D₄×C₁₉	—	2	4	no	—
68	D₄×C₁₉	—	4	2	no	—
69	D₄×C₁₉	—	4	4	no	—
70	D₄×C₁₉	—	4	2	no	—
71	C₂×C₄×C₁₉	—	2	2	no	—
72	C₂×C₄×C₁₉	—	2	2	no	—
73	C₂×C₄×C₁₉	—	2	2	no	—
74	C₂×C₄×C₁₉	—	4	1	no	—
75	C₂×C₄×C₁₉	—	4	4	no	—
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	C₂×D₄	1	1	yes	characteristic
80	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
82	C₂×Dic₁₉	—	2	2	no	—
83	C₂×Dic₁₉	—	2	2	no	—
84	Dic₃₈	—	2	2	no	—
85	Dic₃₈	—	2	2	no	—
86	Dic₃₈	—	4	2	no	—
87	C₁₉⋊C₈	—	2	4	no	—
88	#3216	—	19	1	no	maximal, Sylow
89	C₂²×C₁₉	—	2	1	no	—
90	C₂²×C₁₉	—	2	1	no	—
91	C₂²×C₁₉	—	2	1	no	—
92	C₂²×C₁₉	—	4	2	no	—
93	C₂²×C₁₉	—	4	2	no	—
94	C₂²×C₁₉	—	4	2	no	—
95	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
96	C₄×C₁₉	—	2	1	no	—
97	C₄×C₁₉	—	2	1	no	—
98	C₄×C₁₉	—	2	1	no	—
99	C₄×C₁₉	—	2	1	no	—
100	C₄×C₁₉	—	4	2	no	—
101	C₄×C₁₉	#137	1	2	yes	—
102	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
103	Dic₁₉	—	4	2	no	—
104	Dic₁₉	—	4	2	no	—
105	#533	—	19	1	no	—
106	#532	D₁₉	1	1	yes	characteristic
107	#497	—	19	2	no	—
108	#489	—	19	2	no	—
109	#462	—	19	2	no	—
110	#460	—	19	2	no	—
111	#452	—	19	4	no	—
112	#432	—	19	1	no	—
113	C₂×C₁₉	—	4	1	no	—
114	C₂×C₁₉	—	8	2	no	—
115	C₂×C₁₉	#535	1	1	yes	characteristic
116	C₂×C₁₉	C₂×#137	1	1	yes	characteristic
117	C₂×C₁₉	#575	1	1	yes	characteristic
118	C₂×#41	C₂×D₁₉	1	2	yes	—
119	C₂×Q₁₆	—	19	4	no	—
120	C₂×SD₁₆	—	19	4	no	—
121	C₄⋊Q₈	—	19	1	no	—
122	C₄⋊Q₈	—	19	1	no	—
123	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
124	#127	C₂×D₁₉	1	1	yes	characteristic
125	#125	—	38	1	no	—
126	#124	C₂×D₁₉	1	2	yes	—
127	C₂²⋊Q₈	—	19	2	no	—
128	C₂²⋊Q₈	—	38	1	no	—
129	#121	—	2	1	no	—
130	#121	—	2	1	no	—
131	C₄×Q₈	—	19	2	no	—
132	C₄×Q₈	—	38	1	no	—
133	C₄×D₄	—	2	1	no	—
134	C₄×D₄	—	2	1	no	—
135	#117	—	38	1	no	—
136	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
137	C₄⋊C₈	—	19	2	no	—
138	#103	—	19	4	no	—
139	#102	—	19	4	no	—
140	C₂²⋊C₈	—	19	2	no	—
141	#97	—	19	2	no	—
142	C₁₉	#3216	1	1	yes	characteristic, complemented, Sylow
143	#41	—	4	4	no	—
144	C₂×Q₈	—	19	2	no	—
145	C₂×Q₈	—	38	1	no	—
146	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
147	C₂×D₄	—	2	2	no	—
148	C₂×D₄	—	2	1	no	—
149	C₂×D₄	—	2	1	no	—
150	C₂×D₄	C₂²×D₁₉	1	2	yes	—
151	C₂²×C₄	—	2	2	no	—
152	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
153	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
154	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
155	Q₁₆	—	76	4	no	—
156	SD₁₆	—	76	4	no	—
157	C₂×C₈	—	19	4	no	—
158	C₄⋊C₄	—	2	1	no	—
159	C₄⋊C₄	—	2	1	no	—
160	C₄⋊C₄	—	19	2	no	—
161	C₄⋊C₄	—	38	2	no	—
162	C₄⋊C₄	—	38	2	no	—
163	C₄⋊C₄	—	38	1	no	—
164	C₄⋊C₄	—	38	1	no	—
165	C₄⋊C₄	—	38	1	no	—
166	C₂²⋊C₄	—	2	2	no	—
167	C₂²⋊C₄	—	2	2	no	—
168	C₂²⋊C₄	—	38	2	no	—
169	C₄²	—	38	2	no	—
170	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
171	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
172	C₄²	C₂²×D₁₉	1	1	yes	characteristic
173	C₄²	C₂²×D₁₉	1	1	yes	characteristic
174	C₂³	—	2	2	no	—
175	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
176	Q₈	—	2	4	no	—
177	Q₈	—	38	2	no	—
178	Q₈	—	38	2	no	—
179	Q₈	—	76	2	no	—
180	D₄	—	2	4	no	—
181	D₄	—	4	2	no	—
182	D₄	—	4	4	no	—
183	D₄	—	4	2	no	—
184	C₂×C₄	—	2	2	no	—
185	C₂×C₄	—	2	2	no	—
186	C₂×C₄	—	2	2	no	—
187	C₂×C₄	—	4	1	no	—
188	C₂×C₄	—	4	4	no	—
189	C₂×C₄	—	38	2	no	—
190	C₂×C₄	—	38	2	no	—
191	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
192	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
193	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
194	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
195	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
196	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
197	C₈	—	38	4	no	—
198	C₂²	—	2	1	no	—
199	C₂²	—	2	1	no	—
200	C₂²	—	2	1	no	—
201	C₂²	—	4	2	no	—
202	C₂²	—	4	2	no	—
203	C₂²	—	4	2	no	—
204	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
205	C₄	—	2	1	no	—
206	C₄	—	2	1	no	—
207	C₄	—	2	1	no	—
208	C₄	—	2	1	no	—
209	C₄	—	4	2	no	—
210	C₄	—	76	2	no	—
211	C₄	—	76	2	no	—
212	C₄	#10597397	1	2	yes	—
213	C₄	#10597430	1	2	yes	—
214	C₂	—	4	1	no	—
215	C₂	—	8	2	no	—
216	C₂	#11927111	1	1	yes	characteristic
217	C₂	C₂×#10597397	1	1	yes	characteristic
218	C₂	#11927342	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927101

C₂

yes

maximal, characteristic, complemented

#11926939

C₂

yes

maximal, complemented

#11926903

C₂

yes

maximal, complemented

#11926751

C₂

yes

maximal, complemented

#11926741

C₂

yes

maximal, complemented

#11926706

C₂

yes

maximal, complemented

#11926601

C₂

yes

maximal, characteristic, complemented

C₁₉×#532

C₂

yes

maximal, characteristic

C₂×#41×C₁₉

C₂²

yes

—

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×#127

C₂²

yes

characteristic

C₁₉×#124

C₂²

yes

—

C₁₉×#121

—

C₁₉×#121

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×#64528

C₂²

yes

—

C₂×#64526

C₂²

yes

—

#10597372

—

#10597370

—

#10597370

C₂²

yes

—

#10597316

—

#10597315

C₂²

yes

characteristic

#10597315

C₂²

yes

characteristic

C₄×Dic₃₈

—

C₄×Dic₃₈

C₂²

yes

—

#10597292

C₂²

yes

—

#10597289

C₂²

yes

—

C₂²⋊(C₁₉⋊C₈)

C₂²

yes

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

#10597260

C₂²

yes

—

#41×C₁₉

—

C₂×Q₈×C₁₉

C₂³

yes

—

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

C₂³

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

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

—

#64528

—

#64526

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

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

—

Dic₃₈

—

C₁₉⋊C₈

—

#3216

—

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

—

100

C₄×C₁₉

—

101

C₄×C₁₉

#137

yes

—

102

C₄×C₁₉

H(5,𝔽₂)

yes

—

103

Dic₁₉

—

104

Dic₁₉

—

105

#533

—

106

#532

D₁₉

yes

characteristic

107

#497

—

108

#489

—

109

#462

—

110

#460

—

111

#452

—

112

#432

—

113

C₂×C₁₉

—

114

C₂×C₁₉

—

115

C₂×C₁₉

#535

yes

characteristic

116

C₂×C₁₉

C₂×#137

yes

characteristic

117

C₂×C₁₉

#575

yes

characteristic

118

C₂×#41

C₂×D₁₉

yes

—

119

C₂×Q₁₆

—

120

C₂×SD₁₆

—

121

C₄⋊Q₈

—

122

C₄⋊Q₈

—

123

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

124

#127

C₂×D₁₉

yes

characteristic

125

#125

—

126

#124

C₂×D₁₉

yes

—

127

C₂²⋊Q₈

—

128

C₂²⋊Q₈

—

129

#121

—

130

#121

—

131

C₄×Q₈

—

132

C₄×Q₈

—

133

C₄×D₄

—

134

C₄×D₄

—

135

#117

—

136

C₂×C₄²

C₂×D₁₉

yes

characteristic

137

C₄⋊C₈

—

138

#103

—

139

#102

—

140

C₂²⋊C₈

—

141

#97

—

142

C₁₉

#3216

yes

characteristic, complemented, Sylow

143

#41

—

144

C₂×Q₈

—

145

C₂×Q₈

—

146

C₂×Q₈

C₂²×D₁₉

yes

—

147

C₂×D₄

—

148

C₂×D₄

—

149

C₂×D₄

—

150

C₂×D₄

C₂²×D₁₉

yes

—

151

C₂²×C₄

—

152

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

153

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

154

C₂²×C₄

C₂²×D₁₉

yes

characteristic

155

Q₁₆

—

156

SD₁₆

—

157

C₂×C₈

—

158

C₄⋊C₄

—

159

C₄⋊C₄

—

160

C₄⋊C₄

—

161

C₄⋊C₄

—

162

C₄⋊C₄

—

163

C₄⋊C₄

—

164

C₄⋊C₄

—

165

C₄⋊C₄

—

166

C₂²⋊C₄

—

167

C₂²⋊C₄

—

168

C₂²⋊C₄

—

169

C₄²

—

170

C₄²

C₂²⋊D₁₉

yes

characteristic

171

C₄²

C₂²⋊D₁₉

yes

characteristic

172

C₄²

C₂²×D₁₉

yes

characteristic

173

C₄²

C₂²×D₁₉

yes

characteristic

174

C₂³

—

175

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

176

Q₈

—

177

Q₈

—

178

Q₈

—

179

Q₈

—

180

D₄

—

181

D₄

—

182

D₄

—

183

D₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

192

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

193

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

194

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

195

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

196

C₂×C₄

C₂³×D₁₉

yes

characteristic

197

C₈

—

198

C₂²

—

199

C₂²

—

200

C₂²

—

201

C₂²

—

202

C₂²

—

203

C₂²

—

204

C₂²

C₂²×C₂²⋊D₁₉

yes

characteristic

205

C₄

—

206

C₄

—

207

C₄

—

208

C₄

—

209

C₄

—

210

C₄

—

211

C₄

—

212

C₄

#10597397

yes

—

213

C₄

#10597430

yes

—

214

C₂

—

215

C₂

—

216

C₂

#11927111

yes

characteristic

217

C₂

C₂×#10597397

yes

characteristic

218

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	#3216
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. #11926939	C₂	semidirect
3. #11926903	C₂	semidirect
4. #11926751	C₂	semidirect
5. #11926741	C₂	semidirect
6. #11926706	C₂	semidirect
7. #11926601	C₂	semidirect
142. C₁₉	#3216	semidirect

H ≅ G/N

type

1. #11927101

C₂

semidirect

2. #11926939

C₂

semidirect

3. #11926903

C₂

semidirect

4. #11926751

C₂

semidirect

5. #11926741

C₂

semidirect

6. #11926706

C₂

semidirect

7. #11926601

C₂

semidirect

142. C₁₉

#3216

semidirect

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

subgroup	index
#11927101	2
#11926939	2
#11926903	2
#11926751	2
#11926741	2
#11926706	2
#11926601	2
C₁₉×#532	2
#3216	19

subgroup

index

C₁₉×#532

Subgroups — #14574646

Conjugacy classes of subgroups

Complements

Maximal subgroups