Group #14565165 — subgroups

Subgroups — #14565165

Order 2432.

290 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 87 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×#10597265	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10597278	C₂	1	1	yes	maximal, characteristic
3	C₂×#10597266	C₂	1	1	yes	maximal, characteristic
4	#11926445	C₂	1	1	yes	maximal, characteristic
5	#11926413	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926298	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#106	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₇₆	C₂²	1	1	yes	characteristic
9	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
13	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
14	C₂×Dic₁₉⋊C₄	—	2	2	no	—
15	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
16	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
17	C₁₉×#106	—	2	2	no	—
18	#10597278	—	2	2	no	—
19	#10597266	—	2	2	no	—
20	#10597265	—	2	2	no	—
21	C₂³×D₁₉	—	2	1	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	D₄	1	2	yes	—
27	C₂×D₇₆	—	2	1	no	—
28	C₂×D₇₆	—	2	1	no	—
29	C₂×D₇₆	—	2	1	no	—
30	C₂×D₇₆	—	2	1	no	—
31	C₂×D₇₆	—	2	1	no	—
32	C₂×D₇₆	Q₈	1	2	yes	—
33	C₂×C₈×C₁₉	—	2	1	no	—
34	C₂×C₈×C₁₉	—	2	1	no	—
35	C₂×C₈×C₁₉	D₄	1	2	yes	—
36	C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₄⋊C₄×C₁₉	—	2	1	no	—
39	C₄⋊C₄×C₁₉	—	2	1	no	—
40	(C₂×D₁₉)⋊C₄	—	4	4	no	—
41	C₄⋊Dic₁₉	—	2	1	no	—
42	C₄⋊Dic₁₉	—	2	1	no	—
43	Dic₁₉⋊C₄	—	4	4	no	—
44	C₄×Dic₁₉	—	2	1	no	—
45	C₄×Dic₁₉	—	2	1	no	—
46	C₂×C₁₉⋊C₈	—	2	1	no	—
47	C₂×C₁₉⋊C₈	—	2	1	no	—
48	C₂×C₁₉⋊C₈	D₄	1	2	yes	—
49	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
50	C₂²×D₁₉	—	2	2	no	—
51	C₂²×D₁₉	—	4	1	no	—
52	C₂²×D₁₉	—	4	1	no	—
53	C₂²×D₁₉	—	4	2	no	—
54	C₂²×D₁₉	—	4	2	no	—
55	C₂×C₄×C₁₉	—	4	1	no	—
56	C₂×C₄×C₁₉	—	4	1	no	—
57	C₂×C₄×C₁₉	—	4	2	no	—
58	C₂×C₄×C₁₉	—	4	2	no	—
59	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
60	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
61	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
62	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
63	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
64	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
65	C₂×Dic₁₉	—	2	2	no	—
66	C₂×Dic₁₉	—	2	2	no	—
67	C₂×Dic₁₉	—	4	1	no	—
68	C₂×Dic₁₉	—	4	2	no	—
69	C₂×Dic₁₉	SD₁₆	1	4	yes	—
70	D₇₆	—	2	2	no	—
71	D₇₆	—	2	2	no	—
72	D₇₆	—	4	1	no	—
73	D₇₆	—	4	1	no	—
74	C₈×C₁₉	—	2	2	no	—
75	C₁₉⋊C₈	—	2	2	no	—
76	#2094	—	19	1	no	maximal, Sylow
77	C₂²×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
78	C₂²×C₁₉	#123	1	1	yes	characteristic
79	C₂²×C₁₉	#127	1	1	yes	characteristic
80	C₂²×C₁₉	C₂×SD₁₆	1	2	yes	—
81	C₂²×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
82	C₂×D₁₉	—	4	2	no	—
83	C₂×D₁₉	—	4	4	no	—
84	C₂×D₁₉	—	8	2	no	—
85	C₂×D₁₉	—	8	1	no	—
86	C₂×D₁₉	—	8	1	no	—
87	C₄×C₁₉	—	8	1	no	—
88	C₄×C₁₉	—	8	1	no	—
89	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
90	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
91	C₄×C₁₉	#123	1	1	yes	characteristic
92	C₄×C₁₉	#123	1	1	yes	characteristic
93	Dic₁₉	—	2	4	no	—
94	Dic₁₉	—	8	1	no	—
95	C₂×#106	—	19	1	no	—
96	C₂×#106	D₁₉	1	1	yes	characteristic, complemented
97	C₂×#102	—	19	1	no	—
98	C₂×#102	—	19	1	no	—
99	#390	—	19	1	no	—
100	#384	—	19	1	no	—
101	#336	—	19	1	no	—
102	C₂×C₁₉	#399	1	1	yes	characteristic
103	C₂×C₁₉	#476	1	2	yes	—
104	C₂×C₁₉	#481	1	2	yes	—
105	C₂×C₁₉	#492	1	1	yes	characteristic
106	C₂×C₁₉	#496	1	1	yes	characteristic
107	D₁₉	—	8	2	no	—
108	C₂²×D₄	—	19	1	no	—
109	C₂²×C₈	—	19	1	no	—
110	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
111	C₂×C₄⋊C₄	—	19	1	no	—
112	C₂×C₄⋊C₄	—	38	2	no	—
113	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
114	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
115	C₂×C₂²⋊C₄	—	38	2	no	—
116	C₂×C₄²	—	19	1	no	—
117	#106	—	2	2	no	—
118	#106	—	38	2	no	—
119	#102	—	38	2	no	—
120	#102	—	38	2	no	—
121	C₁₉	#2094	1	1	yes	characteristic, complemented, Sylow
122	C₂⁴	—	38	1	no	—
123	C₂×D₄	—	19	2	no	—
124	C₂×D₄	—	38	1	no	—
125	C₂×D₄	—	38	1	no	—
126	C₂×D₄	—	38	1	no	—
127	C₂×D₄	—	38	1	no	—
128	C₂×D₄	—	38	1	no	—
129	C₂²×C₄	—	2	1	no	—
130	C₂²×C₄	—	2	1	no	—
131	C₂²×C₄	—	19	2	no	—
132	C₂²×C₄	—	38	1	no	—
133	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
134	C₂×C₈	—	2	1	no	—
135	C₂×C₈	—	2	1	no	—
136	C₂×C₈	—	19	2	no	—
137	C₂×C₈	—	38	1	no	—
138	C₂×C₈	—	38	1	no	—
139	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
140	C₄⋊C₄	—	2	1	no	—
141	C₄⋊C₄	—	2	1	no	—
142	C₄⋊C₄	—	2	1	no	—
143	C₄⋊C₄	—	2	1	no	—
144	C₄⋊C₄	—	38	1	no	—
145	C₄⋊C₄	—	38	1	no	—
146	C₄⋊C₄	—	76	4	no	—
147	C₂²⋊C₄	—	76	4	no	—
148	C₄²	—	38	1	no	—
149	C₄²	—	38	1	no	—
150	C₂³	—	38	2	no	—
151	C₂³	—	76	1	no	—
152	C₂³	—	76	1	no	—
153	C₂³	—	76	2	no	—
154	C₂³	—	76	2	no	—
155	C₂³	D₄×D₁₉	1	1	yes	characteristic
156	D₄	—	38	2	no	—
157	D₄	—	38	2	no	—
158	D₄	—	76	1	no	—
159	D₄	—	76	1	no	—
160	C₂×C₄	—	4	1	no	—
161	C₂×C₄	—	4	1	no	—
162	C₂×C₄	—	4	2	no	—
163	C₂×C₄	—	4	2	no	—
164	C₂×C₄	—	19	4	no	—
165	C₂×C₄	—	38	2	no	—
166	C₂×C₄	—	38	2	no	—
167	C₂×C₄	—	76	1	no	—
168	C₂×C₄	—	76	2	no	—
169	C₂×C₄	#64541	1	1	yes	characteristic
170	C₂×C₄	#64541	1	1	yes	characteristic
171	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
172	C₂×C₄	Q₈×D₁₉	1	1	yes	characteristic
173	C₂×C₄	#64545	1	1	yes	characteristic
174	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
175	C₈	—	2	2	no	—
176	C₈	—	38	2	no	—
177	C₂²	—	76	4	no	—
178	C₂²	—	76	2	no	—
179	C₂²	—	152	2	no	—
180	C₂²	—	152	1	no	—
181	C₂²	—	152	1	no	—
182	C₂²	#10597340	1	1	yes	characteristic
183	C₂²	#10597342	1	1	yes	characteristic
184	C₂²	SD₁₆×D₁₉	1	2	yes	—
185	C₂²	#10597360	1	2	yes	—
186	C₂²	#10597386	1	1	yes	characteristic
187	C₄	—	8	1	no	—
188	C₄	—	8	1	no	—
189	C₄	—	38	4	no	—
190	C₄	—	152	1	no	—
191	C₄	#10597340	1	1	yes	characteristic
192	C₄	#10597342	1	1	yes	characteristic
193	C₄	#10597375	1	1	yes	characteristic
194	C₄	#10597392	1	1	yes	characteristic
195	C₂	—	152	2	no	—
196	C₂	#11926479	1	1	yes	characteristic
197	C₂	#11926833	1	2	yes	—
198	C₂	#11926864	1	2	yes	—
199	C₂	#11926915	1	1	yes	characteristic
200	C₂	#11926930	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597265

C₂

yes

maximal, characteristic, complemented

C₂×#10597278

C₂

yes

maximal, characteristic

C₂×#10597266

C₂

yes

maximal, characteristic

#11926445

C₂

yes

maximal, characteristic

#11926413

C₂

yes

maximal, characteristic, complemented

#11926298

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×#106

C₂

yes

maximal, characteristic, complemented

C₂²×D₇₆

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×(C₂×D₁₉)⋊C₄

—

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₁₉×#106

—

#10597278

—

#10597266

—

#10597265

—

C₂³×D₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

D₄

yes

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

Q₈

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

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

—

C₂×Dic₁₉

SD₁₆

yes

—

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#2094

—

maximal, Sylow

C₂²×C₁₉

C₂²⋊Q₈

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

C₂×SD₁₆

yes

—

C₂²×C₁₉

AGL(1,ℤ/8)

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₄×C₁₉

C₂²⋊Q₈

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

C₂×#106

—

C₂×#106

D₁₉

yes

characteristic, complemented

C₂×#102

—

C₂×#102

—

#390

—

100

#384

—

101

#336

—

102

C₂×C₁₉

#399

yes

characteristic

103

C₂×C₁₉

#476

yes

—

104

C₂×C₁₉

#481

yes

—

105

C₂×C₁₉

#492

yes

characteristic

106

C₂×C₁₉

#496

yes

characteristic

107

D₁₉

—

108

C₂²×D₄

—

109

C₂²×C₈

—

110

C₂²×C₈

C₂×D₁₉

yes

characteristic

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×C₂²⋊C₄

—

116

C₂×C₄²

—

117

#106

—

118

#106

—

119

#102

—

120

#102

—

121

C₁₉

#2094

yes

characteristic, complemented, Sylow

122

C₂⁴

—

123

C₂×D₄

—

124

C₂×D₄

—

125

C₂×D₄

—

126

C₂×D₄

—

127

C₂×D₄

—

128

C₂×D₄

—

129

C₂²×C₄

—

130

C₂²×C₄

—

131

C₂²×C₄

—

132

C₂²×C₄

—

133

C₂²×C₄

C₂²×D₁₉

yes

characteristic

134

C₂×C₈

—

135

C₂×C₈

—

136

C₂×C₈

—

137

C₂×C₈

—

138

C₂×C₈

—

139

C₂×C₈

C₂²⋊D₁₉

yes

—

140

C₄⋊C₄

—

141

C₄⋊C₄

—

142

C₄⋊C₄

—

143

C₄⋊C₄

—

144

C₄⋊C₄

—

145

C₄⋊C₄

—

146

C₄⋊C₄

—

147

C₂²⋊C₄

—

148

C₄²

—

149

C₄²

—

150

C₂³

—

151

C₂³

—

152

C₂³

—

153

C₂³

—

154

C₂³

—

155

C₂³

D₄×D₁₉

yes

characteristic

156

D₄

—

157

D₄

—

158

D₄

—

159

D₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

#64541

yes

characteristic

170

C₂×C₄

#64541

yes

characteristic

171

C₂×C₄

D₄×D₁₉

yes

characteristic

172

C₂×C₄

Q₈×D₁₉

yes

characteristic

173

C₂×C₄

#64545

yes

characteristic

174

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

175

C₈

—

176

C₈

—

177

C₂²

—

178

C₂²

—

179

C₂²

—

152

—

180

C₂²

—

152

—

181

C₂²

—

152

—

182

C₂²

#10597340

yes

characteristic

183

C₂²

#10597342

yes

characteristic

184

C₂²

SD₁₆×D₁₉

yes

—

185

C₂²

#10597360

yes

—

186

C₂²

#10597386

yes

characteristic

187

C₄

—

188

C₄

—

189

C₄

—

190

C₄

—

152

—

191

C₄

#10597340

yes

characteristic

192

C₄

#10597342

yes

characteristic

193

C₄

#10597375

yes

characteristic

194

C₄

#10597392

yes

characteristic

195

C₂

—

152

—

196

C₂

#11926479

yes

characteristic

197

C₂

#11926833

yes

—

198

C₂

#11926864

yes

—

199

C₂

#11926915

yes

characteristic

200

C₂

#11926930

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₁₉
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#106	C₂
socle	C₂³×C₁₉	C₂×D₄
prime radical	C₂²×D₇₆	C₂²
hypercenter	C₂×#106	D₁₉
hypocenter	C₁₉	#2094
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#106

subgroup

G/H

center

C₂³

D₄×D₁₉

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#106

C₂

socle

C₂³×C₁₉

C₂×D₄

prime radical

C₂²×D₇₆

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#106

N	H ≅ G/N	type
1. C₂×#10597265	C₂	semidirect
5. #11926413	C₂	semidirect
6. #11926298	C₂	semidirect
7. C₂×C₁₉×#106	C₂	semidirect
96. C₂×#106	D₁₉	semidirect
121. C₁₉	#2094	semidirect

H ≅ G/N

type

1. C₂×#10597265

C₂

semidirect

5. #11926413

C₂

semidirect

6. #11926298

C₂

semidirect

7. C₂×C₁₉×#106

C₂

semidirect

96. C₂×#106

D₁₉

semidirect

121. C₁₉

#2094

semidirect

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

subgroup	index
C₂×#10597265	2
C₂×#10597278	2
C₂×#10597266	2
#11926445	2
#11926413	2
#11926298	2
C₂×C₁₉×#106	2
#2094	19

subgroup

index

C₂×C₁₉×#106

Subgroups — #14565165

Conjugacy classes of subgroups

Complements

Maximal subgroups