Group #14565156 — subgroups

Subgroups — #14565156

Order 2432.

274 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 85 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×#10597264	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10597265	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#10597289	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597289	C₂	1	1	yes	maximal, characteristic
5	#11926410	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926299	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#390	C₂	1	1	yes	maximal, characteristic
8	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
11	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
14	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
15	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
16	#10597289	—	2	2	no	—
17	#10597289	—	2	2	no	—
18	C₁₉⋊#95	—	2	2	no	—
19	#10597265	—	2	2	no	—
20	#10597264	—	2	2	no	—
21	C₂⁴×C₁₉	—	2	1	no	—
22	C₂×D₄×C₁₉	—	2	1	no	—
23	C₂×D₄×C₁₉	—	2	1	no	—
24	C₂×D₄×C₁₉	—	2	1	no	—
25	C₂×D₄×C₁₉	—	2	1	no	—
26	C₂×D₄×C₁₉	—	2	1	no	—
27	C₂×D₄×C₁₉	Q₈	1	2	yes	—
28	C₂²×C₄×C₁₉	—	2	1	no	—
29	C₂²×C₄×C₁₉	D₄	1	2	yes	—
30	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
31	C₂²×Dic₁₉	—	2	1	no	—
32	C₂²×Dic₁₉	—	2	1	no	—
33	C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₄⋊C₄×C₁₉	—	2	1	no	—
35	C₂²⋊C₄×C₁₉	—	4	4	no	—
36	C₄²×C₁₉	—	2	1	no	—
37	C₄²×C₁₉	—	2	1	no	—
38	C₄⋊Dic₁₉	—	2	1	no	—
39	C₄⋊Dic₁₉	—	2	1	no	—
40	C₄⋊Dic₁₉	—	2	1	no	—
41	C₄⋊Dic₁₉	—	2	1	no	—
42	C₂×C₁₉⋊C₈	—	2	1	no	—
43	C₂×C₁₉⋊C₈	—	2	1	no	—
44	C₂×C₁₉⋊C₈	—	2	1	no	—
45	C₂×C₁₉⋊C₈	—	2	1	no	—
46	C₂×C₁₉⋊C₈	D₄	1	2	yes	—
47	C₂×C₁₉⋊C₈	D₄	1	2	yes	—
48	C₂³×C₁₉	—	2	2	no	—
49	C₂³×C₁₉	—	4	1	no	—
50	C₂³×C₁₉	—	4	1	no	—
51	C₂³×C₁₉	—	4	2	no	—
52	C₂³×C₁₉	—	4	2	no	—
53	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
54	D₄×C₁₉	—	2	2	no	—
55	D₄×C₁₉	—	2	2	no	—
56	D₄×C₁₉	—	4	1	no	—
57	D₄×C₁₉	—	4	1	no	—
58	C₂×C₄×C₁₉	—	2	2	no	—
59	C₂×C₄×C₁₉	—	2	2	no	—
60	C₂×C₄×C₁₉	—	2	2	no	—
61	C₂×C₄×C₁₉	—	4	1	no	—
62	C₂×C₄×C₁₉	—	4	2	no	—
63	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
64	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
65	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
66	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
67	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
68	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
69	C₂×Dic₁₉	—	4	1	no	—
70	C₂×Dic₁₉	—	4	1	no	—
71	C₂×Dic₁₉	—	4	2	no	—
72	C₂×Dic₁₉	—	4	2	no	—
73	C₁₉⋊C₈	—	2	2	no	—
74	C₁₉⋊C₈	—	2	2	no	—
75	#2092	—	19	1	no	maximal, Sylow
76	C₂²×C₁₉	—	4	2	no	—
77	C₂²×C₁₉	—	4	4	no	—
78	C₂²×C₁₉	—	8	2	no	—
79	C₂²×C₁₉	—	8	1	no	—
80	C₂²×C₁₉	—	8	1	no	—
81	C₂²×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
82	C₂²×C₁₉	#123	1	1	yes	characteristic
83	C₂²×C₁₉	#127	1	1	yes	characteristic
84	C₂²×C₁₉	#135	1	2	yes	—
85	C₂²×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
86	C₄×C₁₉	—	4	2	no	—
87	C₄×C₁₉	—	8	1	no	—
88	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
89	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
90	C₄×C₁₉	#123	1	1	yes	characteristic
91	C₄×C₁₉	#123	1	1	yes	characteristic
92	Dic₁₉	—	8	1	no	—
93	Dic₁₉	—	8	1	no	—
94	C₂×#107	—	19	1	no	—
95	C₂×#106	—	19	1	no	—
96	C₂×#102	—	19	1	no	—
97	C₂×#102	—	19	1	no	—
98	#390	D₁₉	1	1	yes	characteristic
99	#382	—	19	1	no	—
100	#336	—	19	1	no	—
101	C₂×C₁₉	—	8	2	no	—
102	C₂×C₁₉	#399	1	1	yes	characteristic
103	C₂×C₁₉	#478	1	2	yes	—
104	C₂×C₁₉	#482	1	2	yes	—
105	C₂×C₁₉	#495	1	1	yes	characteristic
106	C₂×C₁₉	#496	1	1	yes	characteristic
107	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
108	C₂²×C₈	—	19	1	no	—
109	C₂²×C₈	—	19	1	no	—
110	C₂×C₄⋊C₄	—	19	1	no	—
111	C₂×C₄⋊C₄	—	19	1	no	—
112	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
113	C₂×C₂²⋊C₄	—	2	2	no	—
114	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
115	#107	—	38	2	no	—
116	#106	—	38	2	no	—
117	#102	—	38	2	no	—
118	#102	—	38	2	no	—
119	#95	—	38	2	no	—
120	C₁₉	#2092	1	1	yes	characteristic, complemented, Sylow
121	C₂⁴	—	2	1	no	—
122	C₂×D₄	—	2	1	no	—
123	C₂×D₄	—	2	1	no	—
124	C₂×D₄	—	2	1	no	—
125	C₂×D₄	—	2	1	no	—
126	C₂×D₄	—	2	1	no	—
127	C₂×D₄	Dic₃₈	1	2	yes	—
128	C₂²×C₄	—	2	1	no	—
129	C₂²×C₄	—	38	1	no	—
130	C₂²×C₄	—	38	1	no	—
131	C₂²×C₄	C₂²⋊D₁₉	1	2	yes	—
132	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
133	C₂×C₈	—	19	2	no	—
134	C₂×C₈	—	19	2	no	—
135	C₂×C₈	—	38	1	no	—
136	C₂×C₈	—	38	1	no	—
137	C₂×C₈	—	38	1	no	—
138	C₂×C₈	—	38	1	no	—
139	C₄⋊C₄	—	2	1	no	—
140	C₄⋊C₄	—	2	1	no	—
141	C₄⋊C₄	—	38	1	no	—
142	C₄⋊C₄	—	38	1	no	—
143	C₄⋊C₄	—	38	1	no	—
144	C₄⋊C₄	—	38	1	no	—
145	C₂²⋊C₄	—	4	4	no	—
146	C₄²	—	2	1	no	—
147	C₄²	—	2	1	no	—
148	C₂³	—	2	2	no	—
149	C₂³	—	4	2	no	—
150	C₂³	—	4	1	no	—
151	C₂³	—	4	1	no	—
152	C₂³	—	4	2	no	—
153	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
154	D₄	—	2	2	no	—
155	D₄	—	2	2	no	—
156	D₄	—	4	1	no	—
157	D₄	—	4	1	no	—
158	C₂×C₄	—	2	2	no	—
159	C₂×C₄	—	2	2	no	—
160	C₂×C₄	—	2	2	no	—
161	C₂×C₄	—	4	2	no	—
162	C₂×C₄	—	4	1	no	—
163	C₂×C₄	—	76	2	no	—
164	C₂×C₄	—	76	1	no	—
165	C₂×C₄	—	76	1	no	—
166	C₂×C₄	—	76	2	no	—
167	C₂×C₄	C₂×Dic₃₈	1	1	yes	characteristic
168	C₂×C₄	#64541	1	1	yes	characteristic
169	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
170	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
171	C₂×C₄	#64543	1	1	yes	characteristic
172	C₂×C₄	#64543	1	1	yes	characteristic
173	C₈	—	38	2	no	—
174	C₈	—	38	2	no	—
175	C₂²	—	4	4	no	—
176	C₂²	—	4	2	no	—
177	C₂²	—	8	2	no	—
178	C₂²	—	8	1	no	—
179	C₂²	—	8	1	no	—
180	C₂²	#10597370	1	1	yes	characteristic
181	C₂²	#10597378	1	2	yes	—
182	C₂²	#10597381	1	1	yes	characteristic
183	C₂²	#10597386	1	1	yes	characteristic
184	C₂²	#10597396	1	2	yes	—
185	C₄	—	4	2	no	—
186	C₄	—	8	1	no	—
187	C₄	—	152	1	no	—
188	C₄	—	152	1	no	—
189	C₄	#10597324	1	1	yes	characteristic
190	C₄	#10597324	1	1	yes	characteristic
191	C₄	#10597329	1	1	yes	characteristic
192	C₄	#10597329	1	1	yes	characteristic
193	C₂	—	8	2	no	—
194	C₂	#11926480	1	1	yes	characteristic
195	C₂	#11926844	1	2	yes	—
196	C₂	#11926865	1	2	yes	—
197	C₂	#11926926	1	1	yes	characteristic
198	C₂	#11926931	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597264

C₂

yes

maximal, characteristic, complemented

C₂×#10597265

C₂

yes

maximal, characteristic, complemented

C₂×#10597289

C₂

yes

maximal, characteristic

C₂×#10597289

C₂

yes

maximal, characteristic

#11926410

C₂

yes

maximal, characteristic, complemented

#11926299

C₂

yes

maximal, characteristic, complemented

C₁₉×#390

C₂

yes

maximal, characteristic

C₂²×D₄×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

#10597289

—

#10597289

—

C₁₉⋊#95

—

#10597265

—

#10597264

—

C₂⁴×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

Q₈

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

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×Q₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2092

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²⋊Q₈

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

AGL(1,ℤ/8)

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₄×C₁₉

C₂²⋊Q₈

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

—

—

—

—

D₁₉

yes

characteristic

#382

—

100

#336

—

101

C₂×C₁₉

—

102

C₂×C₁₉

#399

yes

characteristic

103

C₂×C₁₉

#478

yes

—

104

C₂×C₁₉

#482

yes

—

105

C₂×C₁₉

#495

yes

characteristic

106

C₂×C₁₉

#496

yes

characteristic

107

C₂²×D₄

C₂×D₁₉

yes

characteristic

108

C₂²×C₈

—

109

C₂²×C₈

—

110

C₂×C₄⋊C₄

—

111

C₂×C₄⋊C₄

—

112

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

113

C₂×C₂²⋊C₄

—

114

C₂×C₄²

C₂×D₁₉

yes

characteristic

115

#107

—

116

#106

—

117

#102

—

118

#102

—

119

#95

—

120

C₁₉

#2092

yes

characteristic, complemented, Sylow

121

C₂⁴

—

122

C₂×D₄

—

123

C₂×D₄

—

124

C₂×D₄

—

125

C₂×D₄

—

126

C₂×D₄

—

127

C₂×D₄

Dic₃₈

yes

—

128

C₂²×C₄

—

129

C₂²×C₄

—

130

C₂²×C₄

—

131

C₂²×C₄

C₂²⋊D₁₉

yes

—

132

C₂²×C₄

C₂²×D₁₉

yes

characteristic

133

C₂×C₈

—

134

C₂×C₈

—

135

C₂×C₈

—

136

C₂×C₈

—

137

C₂×C₈

—

138

C₂×C₈

—

139

C₄⋊C₄

—

140

C₄⋊C₄

—

141

C₄⋊C₄

—

142

C₄⋊C₄

—

143

C₄⋊C₄

—

144

C₄⋊C₄

—

145

C₂²⋊C₄

—

146

C₄²

—

147

C₄²

—

148

C₂³

—

149

C₂³

—

150

C₂³

—

151

C₂³

—

152

C₂³

—

153

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

154

D₄

—

155

D₄

—

156

D₄

—

157

D₄

—

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

#64541

yes

characteristic

169

C₂×C₄

D₄×D₁₉

yes

characteristic

170

C₂×C₄

D₄×D₁₉

yes

characteristic

171

C₂×C₄

#64543

yes

characteristic

172

C₂×C₄

#64543

yes

characteristic

173

C₈

—

174

C₈

—

175

C₂²

—

176

C₂²

—

177

C₂²

—

178

C₂²

—

179

C₂²

—

180

C₂²

#10597370

yes

characteristic

181

C₂²

#10597378

yes

—

182

C₂²

#10597381

yes

characteristic

183

C₂²

#10597386

yes

characteristic

184

C₂²

#10597396

yes

—

185

C₄

—

186

C₄

—

187

C₄

—

152

—

188

C₄

—

152

—

189

C₄

#10597324

yes

characteristic

190

C₄

#10597324

yes

characteristic

191

C₄

#10597329

yes

characteristic

192

C₄

#10597329

yes

characteristic

193

C₂

—

194

C₂

#11926480

yes

characteristic

195

C₂

#11926844

yes

—

196

C₂

#11926865

yes

—

197

C₂

#11926926

yes

characteristic

198

C₂

#11926931

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₁₉
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#390	C₂
socle	C₂³×C₁₉	C₂×D₄
prime radical	C₂²×D₄×C₁₉	C₂²
hypercenter	#390	D₁₉
hypocenter	C₁₉	#2092
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #390

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₁₉

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#390

C₂

socle

C₂³×C₁₉

C₂×D₄

prime radical

C₂²×D₄×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #390

N	H ≅ G/N	type
1. C₂×#10597264	C₂	semidirect
2. C₂×#10597265	C₂	semidirect
5. #11926410	C₂	semidirect
6. #11926299	C₂	semidirect
120. C₁₉	#2092	semidirect

H ≅ G/N

type

1. C₂×#10597264

C₂

semidirect

2. C₂×#10597265

C₂

semidirect

5. #11926410

C₂

semidirect

6. #11926299

C₂

semidirect

120. C₁₉

#2092

semidirect

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

subgroup	index
C₂×#10597264	2
C₂×#10597265	2
C₂×#10597289	2
#11926410	2
#11926299	2
C₁₉×#390	2
#2092	19

subgroup

index

C₁₉×#390

Subgroups — #14565156

Conjugacy classes of subgroups

Complements

Maximal subgroups