Group #14575096 — subgroups

Subgroups — #14575096

Order 2432.

346 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 117 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	#11927165	C₂	1	2	yes	maximal, complemented
2	#11926840	C₂	1	2	yes	maximal, complemented
3	#11926825	C₂	1	2	yes	maximal, complemented
4	#11926790	C₂	1	2	yes	maximal, complemented
5	#11926785	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926780	C₂	1	1	yes	maximal, characteristic
7	#11926767	C₂	1	2	yes	maximal, complemented
8	#11926760	C₂	1	2	yes	maximal, complemented
9	C₁₉×#424	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#117	C₂²	1	1	yes	characteristic
13	#10597376	C₂²	1	2	yes	—
14	#10597370	C₂²	1	2	yes	—
15	C₂×Dic₇₆	C₂²	1	1	yes	characteristic
16	C₂×D₁₅₂	C₂²	1	1	yes	characteristic
17	C₂×#64516	C₂²	1	2	yes	—
18	#10597344	—	2	2	no	—
19	#10597342	—	2	2	no	—
20	#10597331	—	2	2	no	—
21	#10597329	—	2	2	no	—
22	#10597321	C₂²	1	2	yes	—
23	C₄×D₇₆	C₂²	1	2	yes	—
24	#10597315	C₂²	1	2	yes	—
25	C₄×Dic₃₈	C₂²	1	2	yes	—
26	C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
27	C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
28	#10597278	C₂²	1	2	yes	—
29	#10597278	C₂²	1	2	yes	—
30	#10597275	C₂²	1	1	yes	characteristic
31	#10597275	C₂²	1	2	yes	—
32	#10597275	C₂²	1	1	yes	characteristic
33	#10597273	C₂²	1	2	yes	—
34	#10597273	C₂²	1	2	yes	—
35	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
36	C₂×C₂²⋊D₁₉	—	2	2	no	—
37	C₂×D₇₆	C₂³	1	2	yes	—
38	C₂×C₄×D₁₉	—	2	2	no	—
39	C₂×Dic₃₈	—	2	2	no	—
40	C₂×Dic₃₈	C₂³	1	2	yes	—
41	M₁₆×C₁₉	—	4	1	no	—
42	C₂×C₈×C₁₉	—	4	1	no	—
43	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
44	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
45	C₂×C₈×C₁₉	C₂³	1	2	yes	—
46	C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
47	C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
48	C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
49	C₄²×C₁₉	C₂³	1	2	yes	—
50	C₂²⋊Dic₁₉	—	2	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	C₂³	1	2	yes	—
57	C₄⋊Dic₁₉	C₂³	1	2	yes	—
58	Dic₁₉⋊C₄	—	2	2	no	—
59	Dic₁₉⋊C₄	—	2	2	no	—
60	C₄×Dic₁₉	—	2	2	no	—
61	Dic₇₆	—	4	1	no	—
62	D₁₅₂	—	4	1	no	—
63	#64516	—	4	2	no	—
64	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
65	C₂²×D₁₉	—	2	2	no	—
66	C₂×C₄×C₁₉	—	2	1	no	—
67	C₂×C₄×C₁₉	—	2	1	no	—
68	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
69	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
70	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
71	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
72	C₂²⋊D₁₉	—	8	2	no	—
73	C₂×Dic₁₉	—	2	2	no	—
74	C₂×Dic₁₉	—	2	2	no	—
75	C₂×Dic₁₉	—	2	2	no	—
76	D₇₆	—	2	2	no	—
77	D₇₆	—	2	2	no	—
78	C₄×D₁₉	—	8	2	no	—
79	Dic₃₈	—	2	2	no	—
80	Dic₃₈	—	2	2	no	—
81	Dic₃₈	—	8	2	no	—
82	C₈×C₁₉	—	2	2	no	—
83	C₈×C₁₉	—	2	1	no	—
84	C₈×C₁₉	—	2	1	no	—
85	#3262	—	19	1	no	maximal, Sylow
86	C₂²×C₁₉	—	2	1	no	—
87	C₂²×C₁₉	—	2	1	no	—
88	C₂²×C₁₉	—	2	1	no	—
89	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
90	C₂×D₁₉	—	4	2	no	—
91	C₂×D₁₉	—	4	2	no	—
92	C₂×D₁₉	—	4	2	no	—
93	C₄×C₁₉	—	2	1	no	—
94	C₄×C₁₉	—	2	2	no	—
95	C₄×C₁₉	—	2	2	no	—
96	C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
97	C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
98	Dic₁₉	—	4	2	no	—
99	Dic₁₉	—	4	2	no	—
100	Dic₁₉	—	4	2	no	—
101	#542	—	19	2	no	—
102	#477	—	19	2	no	—
103	#474	—	19	2	no	—
104	#468	—	19	2	no	—
105	#467	—	19	1	no	—
106	#466	—	19	1	no	—
107	#464	—	19	2	no	—
108	#463	—	19	2	no	—
109	#424	D₁₉	1	1	yes	characteristic, complemented
110	C₂×C₁₉	—	4	1	no	—
111	C₂×C₁₉	#537	1	1	yes	characteristic
112	C₂×C₁₉	#576	1	1	yes	characteristic
113	C₂×C₁₉	#578	1	1	yes	characteristic
114	D₁₉	—	8	2	no	—
115	C₂×Q₁₆	—	19	1	no	—
116	C₂×SD₁₆	—	19	2	no	—
117	C₂×D₈	—	19	1	no	—
118	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
119	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
120	C₄⋊Q₈	—	19	2	no	—
121	#126	—	38	2	no	—
122	#124	—	19	2	no	—
123	#124	—	38	2	no	—
124	#123	—	38	2	no	—
125	C₂²⋊Q₈	—	19	2	no	—
126	C₂²⋊Q₈	—	38	2	no	—
127	#121	—	19	2	no	—
128	C₄×Q₈	—	19	2	no	—
129	C₄×D₄	—	19	2	no	—
130	#117	C₂×D₁₉	1	1	yes	characteristic
131	#107	—	19	1	no	—
132	#107	—	19	1	no	—
133	#107	—	19	2	no	—
134	C₄⋊C₈	C₂×D₁₉	1	2	yes	—
135	C₄⋊C₈	C₂×D₁₉	1	2	yes	—
136	#103	—	19	2	no	—
137	#103	—	19	2	no	—
138	#102	—	19	2	no	—
139	#102	—	19	2	no	—
140	C₁₉	#3262	1	1	yes	characteristic, complemented, Sylow
141	C₂×Q₈	—	19	2	no	—
142	C₂×Q₈	—	38	2	no	—
143	C₂×D₄	—	19	2	no	—
144	C₂×D₄	—	38	2	no	—
145	C₂²×C₄	—	38	2	no	—
146	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
147	Q₁₆	—	76	1	no	—
148	SD₁₆	—	76	2	no	—
149	D₈	—	76	1	no	—
150	M₁₆	—	4	1	no	—
151	C₂×C₈	—	4	1	no	—
152	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
153	C₂×C₈	C₂²×D₁₉	1	2	yes	—
154	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
155	C₄⋊C₄	—	19	2	no	—
156	C₄⋊C₄	—	19	2	no	—
157	C₄⋊C₄	—	38	2	no	—
158	C₄⋊C₄	—	38	2	no	—
159	C₄⋊C₄	—	38	2	no	—
160	C₄⋊C₄	D₇₆	1	1	yes	characteristic
161	C₄⋊C₄	D₇₆	1	1	yes	characteristic
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	C₂²⋊C₄	—	38	2	no	—
167	C₂²⋊C₄	D₇₆	1	2	yes	—
168	C₄²	—	38	2	no	—
169	C₄²	C₂²×D₁₉	1	2	yes	—
170	C₂³	—	38	2	no	—
171	C₂³	C₂×D₇₆	1	1	yes	characteristic
172	Q₈	—	38	2	no	—
173	Q₈	—	38	2	no	—
174	Q₈	—	152	2	no	—
175	D₄	—	38	2	no	—
176	D₄	—	38	2	no	—
177	D₄	—	152	2	no	—
178	C₂×C₄	—	2	1	no	—
179	C₂×C₄	—	2	1	no	—
180	C₂×C₄	—	38	2	no	—
181	C₂×C₄	—	38	2	no	—
182	C₂×C₄	—	38	2	no	—
183	C₂×C₄	—	152	2	no	—
184	C₂×C₄	C₂×D₇₆	1	2	yes	—
185	C₂×C₄	C₂×D₇₆	1	2	yes	—
186	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
187	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
188	C₈	—	2	1	no	—
189	C₈	—	2	1	no	—
190	C₈	—	2	2	no	—
191	C₂²	—	2	1	no	—
192	C₂²	—	2	1	no	—
193	C₂²	—	2	1	no	—
194	C₂²	—	76	2	no	—
195	C₂²	—	76	2	no	—
196	C₂²	—	76	2	no	—
197	C₂²	C₂²×D₇₆	1	1	yes	characteristic
198	C₄	—	2	2	no	—
199	C₄	—	2	2	no	—
200	C₄	—	2	1	no	—
201	C₄	—	76	2	no	—
202	C₄	—	76	2	no	—
203	C₄	—	76	2	no	—
204	C₄	#10597430	1	1	yes	characteristic
205	C₄	#10597433	1	1	yes	characteristic
206	C₂	—	4	1	no	—
207	C₂	—	152	2	no	—
208	C₂	#11927125	1	1	yes	characteristic
209	C₂	#11927349	1	1	yes	characteristic
210	C₂	#11927361	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927165

C₂

yes

maximal, complemented

#11926840

C₂

yes

maximal, complemented

#11926825

C₂

yes

maximal, complemented

#11926790

C₂

yes

maximal, complemented

#11926785

C₂

yes

maximal, characteristic, complemented

#11926780

C₂

yes

maximal, characteristic

#11926767

C₂

yes

maximal, complemented

#11926760

C₂

yes

maximal, complemented

C₁₉×#424

C₂

yes

maximal, characteristic, complemented

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#117

C₂²

yes

characteristic

#10597376

C₂²

yes

—

#10597370

C₂²

yes

—

C₂×Dic₇₆

C₂²

yes

characteristic

C₂×D₁₅₂

C₂²

yes

characteristic

C₂×#64516

C₂²

yes

—

—

—

—

—

C₂²

yes

—

C₄×D₇₆

C₂²

yes

—

#10597315

C₂²

yes

—

C₄×Dic₃₈

C₂²

yes

—

C₁₉×C₄⋊C₈

C₂²

yes

—

C₁₉×C₄⋊C₈

C₂²

yes

—

#10597278

C₂²

yes

—

#10597278

C₂²

yes

—

#10597275

C₂²

yes

characteristic

#10597275

C₂²

yes

—

#10597275

C₂²

yes

characteristic

#10597273

C₂²

yes

—

#10597273

C₂²

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊D₁₉

—

C₂×D₇₆

C₂³

yes

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

C₂³

yes

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂²⋊C₄×C₁₉

D₄

yes

—

C₄²×C₁₉

C₂³

yes

—

C₂²⋊Dic₁₉

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂³

yes

—

C₄⋊Dic₁₉

C₂³

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

Dic₇₆

—

D₁₅₂

—

#64516

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

C₄×D₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

#3262

—

maximal, Sylow

C₂²×C₁₉

—

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

—

100

Dic₁₉

—

101

#542

—

102

#477

—

103

#474

—

104

#468

—

105

#467

—

106

#466

—

107

#464

—

108

#463

—

109

#424

D₁₉

yes

characteristic, complemented

110

C₂×C₁₉

—

111

C₂×C₁₉

#537

yes

characteristic

112

C₂×C₁₉

#576

yes

characteristic

113

C₂×C₁₉

#578

yes

characteristic

114

D₁₉

—

115

C₂×Q₁₆

—

116

C₂×SD₁₆

—

117

C₂×D₈

—

118

C₂×M₁₆

C₂×D₁₉

yes

characteristic

119

C₂²×C₈

C₂×D₁₉

yes

characteristic

120

C₄⋊Q₈

—

121

#126

—

122

#124

—

123

#124

—

124

#123

—

125

C₂²⋊Q₈

—

126

C₂²⋊Q₈

—

127

#121

—

128

C₄×Q₈

—

129

C₄×D₄

—

130

#117

C₂×D₁₉

yes

characteristic

131

#107

—

132

#107

—

133

#107

—

134

C₄⋊C₈

C₂×D₁₉

yes

—

135

C₄⋊C₈

C₂×D₁₉

yes

—

136

#103

—

137

#103

—

138

#102

—

139

#102

—

140

C₁₉

#3262

yes

characteristic, complemented, Sylow

141

C₂×Q₈

—

142

C₂×Q₈

—

143

C₂×D₄

—

144

C₂×D₄

—

145

C₂²×C₄

—

146

C₂²×C₄

C₂²×D₁₉

yes

characteristic

147

Q₁₆

—

148

SD₁₆

—

149

D₈

—

150

M₁₆

—

151

C₂×C₈

—

152

C₂×C₈

C₂²×D₁₉

yes

characteristic

153

C₂×C₈

C₂²×D₁₉

yes

—

154

C₂×C₈

C₂²×D₁₉

yes

characteristic

155

C₄⋊C₄

—

156

C₄⋊C₄

—

157

C₄⋊C₄

—

158

C₄⋊C₄

—

159

C₄⋊C₄

—

160

C₄⋊C₄

D₇₆

yes

characteristic

161

C₄⋊C₄

D₇₆

yes

characteristic

162

C₂²⋊C₄

—

163

C₂²⋊C₄

—

164

C₂²⋊C₄

—

165

C₂²⋊C₄

—

166

C₂²⋊C₄

—

167

C₂²⋊C₄

D₇₆

yes

—

168

C₄²

—

169

C₄²

C₂²×D₁₉

yes

—

170

C₂³

—

171

C₂³

C₂×D₇₆

yes

characteristic

172

Q₈

—

173

Q₈

—

174

Q₈

—

152

—

175

D₄

—

176

D₄

—

177

D₄

—

152

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

152

—

184

C₂×C₄

C₂×D₇₆

yes

—

185

C₂×C₄

C₂×D₇₆

yes

—

186

C₂×C₄

C₂×D₇₆

yes

characteristic

187

C₂×C₄

C₂³×D₁₉

yes

characteristic

188

C₈

—

189

C₈

—

190

C₈

—

191

C₂²

—

192

C₂²

—

193

C₂²

—

194

C₂²

—

195

C₂²

—

196

C₂²

—

197

C₂²

C₂²×D₇₆

yes

characteristic

198

C₄

—

199

C₄

—

200

C₄

—

201

C₄

—

202

C₄

—

203

C₄

—

204

C₄

#10597430

yes

characteristic

205

C₄

#10597433

yes

characteristic

206

C₂

—

207

C₂

—

152

—

208

C₂

#11927125

yes

characteristic

209

C₂

#11927349

yes

characteristic

210

C₂

#11927361

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²×D₇₆
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#424	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	#11926780	C₂
hypercenter	#424	D₁₉
hypocenter	C₁₉	#3262
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #117 ◁ #424

subgroup

G/H

center

C₂²

C₂²×D₇₆

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₁₉×#424

C₂

socle

C₂²×C₁₉

C₂²×D₄

C₂

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ #117 ◁ #424

N	H ≅ G/N	type
1. #11927165	C₂	semidirect
2. #11926840	C₂	semidirect
3. #11926825	C₂	semidirect
4. #11926790	C₂	semidirect
5. #11926785	C₂	semidirect
7. #11926767	C₂	semidirect
8. #11926760	C₂	semidirect
9. C₁₉×#424	C₂	semidirect
109. #424	D₁₉	semidirect
140. C₁₉	#3262	semidirect

H ≅ G/N

type

1. #11927165

C₂

semidirect

2. #11926840

C₂

semidirect

3. #11926825

C₂

semidirect

4. #11926790

C₂

semidirect

5. #11926785

C₂

semidirect

7. #11926767

C₂

semidirect

8. #11926760

C₂

semidirect

9. C₁₉×#424

C₂

semidirect

109. #424

D₁₉

semidirect

140. C₁₉

#3262

semidirect

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

subgroup	index
#11927165	2
#11926840	2
#11926825	2
#11926790	2
#11926785	2
#11926780	2
#11926767	2
#11926760	2
C₁₉×#424	2
#3262	19

subgroup

index

C₁₉×#424

Subgroups — #14575096

Conjugacy classes of subgroups

Complements

Maximal subgroups