Group #14575101 — subgroups

Subgroups — #14575101

Order 2432.

346 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 109 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	#11927167	C₂	1	2	yes	maximal, complemented
2	#11926833	C₂	1	2	yes	maximal, complemented
3	#11926827	C₂	1	2	yes	maximal, complemented
4	#11926797	C₂	1	1	yes	maximal, characteristic
5	#11926775	C₂	1	2	yes	maximal, complemented
6	#11926768	C₂	1	2	yes	maximal, complemented
7	#11926762	C₂	1	2	yes	maximal, complemented
8	#11926572	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#470	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
13	#10597393	C₂²	1	2	yes	—
14	Q₈×Dic₁₉	C₂²	1	2	yes	—
15	C₂×#64527	C₂²	1	2	yes	—
16	#10597376	C₂²	1	2	yes	—
17	#10597372	C₂²	1	1	yes	characteristic
18	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×D₁₅₂	C₂²	1	1	yes	characteristic
20	#10597344	—	2	2	no	—
21	#10597343	—	2	2	no	—
22	#10597339	C₂²	1	2	yes	—
23	#10597334	C₂²	1	2	yes	—
24	#10597331	—	2	2	no	—
25	#10597329	—	2	2	no	—
26	C₁₉×#106	C₂²	1	1	yes	characteristic
27	C₁₉×#103	C₂²	1	2	yes	—
28	#10597292	C₂²	1	2	yes	—
29	#10597278	C₂²	1	2	yes	—
30	#10597274	C₂²	1	1	yes	characteristic
31	Dic₁₉⋊C₈	C₂²	1	2	yes	—
32	Dic₁₉⋊C₈	C₂²	1	2	yes	—
33	#10597266	C₂²	1	2	yes	—
34	#10597265	C₂²	1	2	yes	—
35	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
36	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
37	C₂×C₂²⋊D₁₉	—	2	2	no	—
38	C₂×D₇₆	C₂³	1	2	yes	—
39	C₂×C₄×D₁₉	—	2	2	no	—
40	C₂×Dic₃₈	—	2	2	no	—
41	Q₁₆×C₁₉	—	4	1	no	—
42	M₁₆×C₁₉	—	4	1	no	—
43	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
44	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
45	C₄⋊C₄×C₁₉	—	2	2	no	—
46	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
47	C₂²⋊C₄×C₁₉	—	2	2	no	—
48	C₂²⋊Dic₁₉	D₄	1	1	yes	characteristic
49	C₂²⋊Dic₁₉	D₄	1	1	yes	characteristic
50	#64527	—	4	2	no	—
51	(C₂×D₁₉)⋊C₄	—	2	2	no	—
52	(C₂×D₁₉)⋊C₄	—	2	2	no	—
53	(C₂×D₁₉)⋊C₄	—	2	2	no	—
54	(C₂×D₁₉)⋊C₄	—	2	2	no	—
55	C₄⋊Dic₁₉	—	2	2	no	—
56	C₄⋊Dic₁₉	D₄	1	2	yes	—
57	C₄⋊Dic₁₉	C₂³	1	2	yes	—
58	Dic₁₉⋊C₄	—	2	2	no	—
59	C₄×Dic₁₉	—	2	2	no	—
60	C₄×Dic₁₉	C₂³	1	2	yes	—
61	C₂×C₁₉⋊C₈	—	4	1	no	—
62	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
63	D₁₅₂	—	4	1	no	—
64	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
65	C₂²×D₁₉	—	2	2	no	—
66	Q₈×C₁₉	—	2	2	no	—
67	Q₈×C₁₉	—	2	2	no	—
68	C₂×C₄×C₁₉	—	2	1	no	—
69	C₂×C₄×C₁₉	—	2	1	no	—
70	C₂×C₄×C₁₉	—	2	2	no	—
71	C₂×C₄×C₁₉	—	2	2	no	—
72	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
73	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
74	C₂²⋊D₁₉	—	8	2	no	—
75	C₂×Dic₁₉	—	2	2	no	—
76	C₂×Dic₁₉	C₂×D₄	1	2	yes	—
77	C₂×Dic₁₉	C₂×D₄	1	2	yes	—
78	D₇₆	—	2	2	no	—
79	D₇₆	—	2	2	no	—
80	C₄×D₁₉	—	8	2	no	—
81	Dic₃₈	—	8	2	no	—
82	C₈×C₁₉	—	2	1	no	—
83	C₈×C₁₉	—	2	1	no	—
84	C₁₉⋊C₈	—	2	2	no	—
85	#3263	—	19	1	no	maximal, Sylow
86	C₂²×C₁₉	—	2	1	no	—
87	C₂²×C₁₉	—	2	2	no	—
88	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
89	C₂×D₁₉	—	4	2	no	—
90	C₂×D₁₉	—	4	2	no	—
91	C₂×D₁₉	—	4	2	no	—
92	C₄×C₁₉	—	2	1	no	—
93	C₄×C₁₉	—	4	2	no	—
94	C₄×C₁₉	—	4	2	no	—
95	C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
96	C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
97	Dic₁₉	—	2	2	no	—
98	Dic₁₉	—	2	2	no	—
99	Dic₁₉	—	4	2	no	—
100	#542	—	19	2	no	—
101	#476	—	19	2	no	—
102	#475	—	19	2	no	—
103	#470	D₁₉	1	1	yes	characteristic, complemented
104	#469	—	19	1	no	—
105	#465	—	19	2	no	—
106	#464	—	19	2	no	—
107	#463	—	19	2	no	—
108	#424	—	19	1	no	—
109	C₂×C₁₉	—	4	1	no	—
110	C₂×C₁₉	#537	1	1	yes	characteristic
111	C₂×C₁₉	#577	1	2	yes	—
112	D₁₉	—	8	2	no	—
113	C₂×Q₁₆	C₂×D₁₉	1	1	yes	characteristic
114	C₂×SD₁₆	—	19	2	no	—
115	C₂×D₈	—	19	1	no	—
116	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
117	C₂²×C₈	—	19	1	no	—
118	C₄⋊Q₈	—	19	2	no	—
119	#126	—	38	2	no	—
120	#124	—	19	2	no	—
121	#124	—	38	2	no	—
122	#123	—	38	2	no	—
123	C₂²⋊Q₈	—	38	2	no	—
124	C₂²⋊Q₈	C₂×D₁₉	1	2	yes	—
125	#121	—	19	2	no	—
126	C₄×Q₈	—	19	2	no	—
127	C₄×D₄	—	19	2	no	—
128	#117	—	19	1	no	—
129	#106	—	19	1	no	—
130	#106	—	19	2	no	—
131	#106	C₂×D₁₉	1	1	yes	characteristic
132	C₄⋊C₈	—	19	2	no	—
133	C₄⋊C₈	—	19	2	no	—
134	#103	—	19	2	no	—
135	#103	C₂×D₁₉	1	2	yes	—
136	#102	—	19	2	no	—
137	#102	—	19	2	no	—
138	C₁₉	#3263	1	1	yes	characteristic, complemented, Sylow
139	C₂×Q₈	—	38	2	no	—
140	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
141	C₂×D₄	—	19	2	no	—
142	C₂×D₄	—	38	2	no	—
143	C₂²×C₄	—	38	2	no	—
144	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
145	Q₁₆	—	4	1	no	—
146	SD₁₆	—	76	2	no	—
147	D₈	—	76	1	no	—
148	M₁₆	—	4	1	no	—
149	C₂×C₈	—	19	2	no	—
150	C₂×C₈	—	76	1	no	—
151	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
152	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
153	C₄⋊C₄	—	2	2	no	—
154	C₄⋊C₄	—	19	2	no	—
155	C₄⋊C₄	—	19	2	no	—
156	C₄⋊C₄	—	38	2	no	—
157	C₄⋊C₄	—	38	2	no	—
158	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
159	C₂²⋊C₄	—	2	2	no	—
160	C₂²⋊C₄	—	19	1	no	—
161	C₂²⋊C₄	—	19	1	no	—
162	C₂²⋊C₄	—	38	2	no	—
163	C₂²⋊C₄	—	38	2	no	—
164	C₂²⋊C₄	—	38	2	no	—
165	C₂²⋊C₄	—	38	2	no	—
166	C₄²	—	19	2	no	—
167	C₄²	—	38	2	no	—
168	C₂³	—	38	2	no	—
169	C₂³	D₄×D₁₉	1	1	yes	characteristic
170	Q₈	—	2	2	no	—
171	Q₈	—	2	2	no	—
172	Q₈	—	152	2	no	—
173	D₄	—	38	2	no	—
174	D₄	—	38	2	no	—
175	D₄	—	152	2	no	—
176	C₂×C₄	—	2	1	no	—
177	C₂×C₄	—	2	1	no	—
178	C₂×C₄	—	2	2	no	—
179	C₂×C₄	—	2	2	no	—
180	C₂×C₄	—	19	2	no	—
181	C₂×C₄	—	19	2	no	—
182	C₂×C₄	—	38	2	no	—
183	C₂×C₄	—	152	2	no	—
184	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
185	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
186	C₈	—	2	1	no	—
187	C₈	—	2	1	no	—
188	C₈	—	38	2	no	—
189	C₂²	—	2	2	no	—
190	C₂²	—	2	1	no	—
191	C₂²	—	76	2	no	—
192	C₂²	—	76	2	no	—
193	C₂²	—	76	2	no	—
194	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
195	C₄	—	2	1	no	—
196	C₄	—	4	2	no	—
197	C₄	—	4	2	no	—
198	C₄	—	38	2	no	—
199	C₄	—	38	2	no	—
200	C₄	—	76	2	no	—
201	C₄	#10597430	1	1	yes	characteristic
202	C₄	#10597436	1	1	yes	characteristic
203	C₂	—	4	1	no	—
204	C₂	—	152	2	no	—
205	C₂	#11927121	1	1	yes	characteristic
206	C₂	#11927353	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11927167

C₂

yes

maximal, complemented

#11926833

C₂

yes

maximal, complemented

#11926827

C₂

yes

maximal, complemented

#11926797

C₂

yes

maximal, characteristic

#11926775

C₂

yes

maximal, complemented

#11926768

C₂

yes

maximal, complemented

#11926762

C₂

yes

maximal, complemented

#11926572

C₂

yes

maximal, characteristic, complemented

C₁₉×#470

C₂

yes

maximal, characteristic, complemented

C₂×Q₁₆×C₁₉

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×C₂²⋊Q₈

C₂²

yes

—

#10597393

C₂²

yes

—

Q₈×Dic₁₉

C₂²

yes

—

C₂×#64527

C₂²

yes

—

#10597376

C₂²

yes

—

#10597372

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×D₁₅₂

C₂²

yes

—

—

C₂²

yes

—

#10597334

C₂²

yes

—

#10597331

—

#10597329

—

C₁₉×#106

C₂²

yes

characteristic

C₁₉×#103

C₂²

yes

—

#10597292

C₂²

yes

—

#10597278

C₂²

yes

—

#10597274

C₂²

yes

characteristic

Dic₁₉⋊C₈

C₂²

yes

—

Dic₁₉⋊C₈

C₂²

yes

—

#10597266

C₂²

yes

—

#10597265

C₂²

yes

—

C₂×Q₈×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊D₁₉

—

C₂×D₇₆

C₂³

yes

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

—

Q₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂³

yes

—

C₂²⋊C₄×C₁₉

—

C₂²⋊Dic₁₉

D₄

yes

characteristic

C₂²⋊Dic₁₉

D₄

yes

characteristic

#64527

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

D₄

yes

—

C₄⋊Dic₁₉

C₂³

yes

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

C₂³

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂³

yes

—

D₁₅₂

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂²×D₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×D₄

yes

—

C₂×Dic₁₉

C₂×D₄

yes

—

D₇₆

—

D₇₆

—

C₄×D₁₉

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#3263

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

H(5,𝔽₂)

yes

characteristic

C₄×C₁₉

2₋¹⁺⁴

yes

characteristic

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

100

#542

—

101

#476

—

102

#475

—

103

#470

D₁₉

yes

characteristic, complemented

104

#469

—

105

#465

—

106

#464

—

107

#463

—

108

#424

—

109

C₂×C₁₉

—

110

C₂×C₁₉

#537

yes

characteristic

111

C₂×C₁₉

#577

yes

—

112

D₁₉

—

113

C₂×Q₁₆

C₂×D₁₉

yes

characteristic

114

C₂×SD₁₆

—

115

C₂×D₈

—

116

C₂×M₁₆

C₂×D₁₉

yes

characteristic

117

C₂²×C₈

—

118

C₄⋊Q₈

—

119

#126

—

120

#124

—

121

#124

—

122

#123

—

123

C₂²⋊Q₈

—

124

C₂²⋊Q₈

C₂×D₁₉

yes

—

125

#121

—

126

C₄×Q₈

—

127

C₄×D₄

—

128

#117

—

129

#106

—

130

#106

—

131

#106

C₂×D₁₉

yes

characteristic

132

C₄⋊C₈

—

133

C₄⋊C₈

—

134

#103

—

135

#103

C₂×D₁₉

yes

—

136

#102

—

137

#102

—

138

C₁₉

#3263

yes

characteristic, complemented, Sylow

139

C₂×Q₈

—

140

C₂×Q₈

C₂²×D₁₉

yes

—

141

C₂×D₄

—

142

C₂×D₄

—

143

C₂²×C₄

—

144

C₂²×C₄

C₂²×D₁₉

yes

characteristic

145

Q₁₆

—

146

SD₁₆

—

147

D₈

—

148

M₁₆

—

149

C₂×C₈

—

150

C₂×C₈

—

151

C₂×C₈

C₂²×D₁₉

yes

characteristic

152

C₂×C₈

C₂²×D₁₉

yes

characteristic

153

C₄⋊C₄

—

154

C₄⋊C₄

—

155

C₄⋊C₄

—

156

C₄⋊C₄

—

157

C₄⋊C₄

—

158

C₄⋊C₄

C₂²×D₁₉

yes

—

159

C₂²⋊C₄

—

160

C₂²⋊C₄

—

161

C₂²⋊C₄

—

162

C₂²⋊C₄

—

163

C₂²⋊C₄

—

164

C₂²⋊C₄

—

165

C₂²⋊C₄

—

166

C₄²

—

167

C₄²

—

168

C₂³

—

169

C₂³

D₄×D₁₉

yes

characteristic

170

Q₈

—

171

Q₈

—

172

Q₈

—

152

—

173

D₄

—

174

D₄

—

175

D₄

—

152

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

152

—

184

C₂×C₄

D₄×D₁₉

yes

characteristic

185

C₂×C₄

C₂³×D₁₉

yes

characteristic

186

C₈

—

187

C₈

—

188

C₈

—

189

C₂²

—

190

C₂²

—

191

C₂²

—

192

C₂²

—

193

C₂²

—

194

C₂²

C₂×D₄×D₁₉

yes

characteristic

195

C₄

—

196

C₄

—

197

C₄

—

198

C₄

—

199

C₄

—

200

C₄

—

201

C₄

#10597430

yes

characteristic

202

C₄

#10597436

yes

characteristic

203

C₂

—

204

C₂

—

152

—

205

C₂

#11927121

yes

characteristic

206

C₂

#11927353

yes

—

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#470	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	#11926797	C₂
hypercenter	#470	D₁₉
hypocenter	C₁₉	#3263
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #470

subgroup

G/H

center

C₂²

C₂×D₄×D₁₉

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₁₉×#470

C₂

socle

C₂²×C₁₉

C₂²×D₄

C₂

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #470

N	H ≅ G/N	type
1. #11927167	C₂	semidirect
2. #11926833	C₂	semidirect
3. #11926827	C₂	semidirect
5. #11926775	C₂	semidirect
6. #11926768	C₂	semidirect
7. #11926762	C₂	semidirect
8. #11926572	C₂	semidirect
9. C₁₉×#470	C₂	semidirect
103. #470	D₁₉	semidirect
138. C₁₉	#3263	semidirect

H ≅ G/N

type

1. #11927167

C₂

semidirect

2. #11926833

C₂

semidirect

3. #11926827

C₂

semidirect

5. #11926775

C₂

semidirect

6. #11926768

C₂

semidirect

7. #11926762

C₂

semidirect

8. #11926572

C₂

semidirect

9. C₁₉×#470

C₂

semidirect

103. #470

D₁₉

semidirect

138. C₁₉

#3263

semidirect

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

subgroup	index
#11927167	2
#11926833	2
#11926827	2
#11926797	2
#11926775	2
#11926768	2
#11926762	2
#11926572	2
C₁₉×#470	2
#3263	19

subgroup

index

C₁₉×#470

Subgroups — #14575101

Conjugacy classes of subgroups

Complements

Maximal subgroups