Group #18075556 — subgroups

Subgroups — #18075556

Order 4864.

404 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 101 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	#14572346	C₂	1	1	yes	maximal, characteristic
2	#14562390	C₂	1	2	yes	maximal, complemented
3	#14562368	C₂	1	2	yes	maximal
4	C₁₉⋊#1309	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1309	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10597353	C₄	1	2	yes	—
7	#11927094	C₂²	1	1	yes	characteristic
8	#11926621	—	2	2	no	—
9	#11926609	—	2	2	no	—
10	#11926568	C₂²	1	2	yes	—
11	#11926512	C₄	1	2	yes	—
12	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
13	#11926294	—	2	2	no	—
14	#11926294	—	2	2	no	—
15	#11926292	—	2	2	no	—
16	#11926287	—	2	2	no	—
17	C₁₉×#423	C₂²	1	2	yes	—
18	C₁₉×#423	C₂²	1	1	yes	characteristic
19	C₂×#64541	C₂×C₄	1	2	yes	—
20	C₂×M₁₆×C₁₉	—	2	2	no	—
21	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
22	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
23	#10597376	—	2	2	no	—
24	C₂×#64520	—	2	2	no	—
25	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
27	#10597353	—	4	4	no	—
28	C₂×#64515	—	2	2	no	—
29	C₂×C₈×D₁₉	—	2	2	no	—
30	#10597321	Q₈	1	2	yes	—
31	#10597320	D₄	1	1	yes	characteristic
32	C₄×D₇₆	—	2	2	no	—
33	#10597315	D₄	1	1	yes	characteristic
34	C₁₉×C₄⋊C₈	—	2	2	no	—
35	C₁₉×C₄⋊C₈	—	2	2	no	—
36	C₁₉×C₄⋊C₈	—	2	2	no	—
37	(C₂×D₁₉)⋊C₈	—	2	4	no	—
38	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
39	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
40	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
41	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
42	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₉	#41	1	2	yes	—
44	C₂×C₂²⋊D₁₉	—	2	2	no	—
45	#64541	—	4	2	no	—
46	#64541	—	4	2	no	—
47	C₂×D₇₆	—	2	2	no	—
48	C₂×D₇₆	C₄⋊C₄	1	2	yes	—
49	C₂×C₄×D₁₉	—	2	2	no	—
50	C₂×Dic₃₈	C₄⋊C₄	1	2	yes	—
51	M₁₆×C₁₉	—	4	2	no	—
52	M₁₆×C₁₉	—	8	2	no	—
53	C₂×C₈×C₁₉	—	2	2	no	—
54	C₂×C₈×C₁₉	—	4	2	no	—
55	C₄²×C₁₉	C₂×D₄	1	2	yes	—
56	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
57	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
58	(C₂×D₁₉)⋊C₄	—	2	4	no	—
59	C₄⋊Dic₁₉	—	2	2	no	—
60	#64520	—	8	2	no	—
61	C₂×C₁₉⋊C₈	—	2	2	no	—
62	C₂×C₁₉⋊C₈	—	4	1	no	—
63	C₂×C₁₉⋊C₈	—	4	2	no	—
64	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
65	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
66	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
67	#64515	—	4	4	no	—
68	C₈×D₁₉	—	4	4	no	—
69	#8636	—	19	1	no	maximal, Sylow
70	C₂³×C₁₉	#117	1	1	yes	characteristic
71	C₂²×D₁₉	—	2	2	no	—
72	C₂×C₄×C₁₉	—	2	1	no	—
73	C₂×C₄×C₁₉	—	2	1	no	—
74	C₂×C₄×C₁₉	—	2	2	no	—
75	C₂×C₄×C₁₉	—	2	2	no	—
76	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
77	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
78	C₂×C₄×C₁₉	#121	1	2	yes	—
79	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
80	C₂²⋊D₁₉	—	4	4	no	—
81	C₂×Dic₁₉	—	2	2	no	—
82	D₇₆	—	4	2	no	—
83	D₇₆	—	4	2	no	—
84	D₇₆	—	4	2	no	—
85	C₄×D₁₉	—	4	2	no	—
86	C₄×D₁₉	—	4	2	no	—
87	Dic₃₈	—	4	2	no	—
88	C₈×C₁₉	—	4	2	no	—
89	C₈×C₁₉	—	8	2	no	—
90	C₁₉⋊C₈	—	2	1	no	—
91	C₁₉⋊C₈	—	2	2	no	—
92	C₁₉⋊C₈	—	8	2	no	—
93	C₁₉⋊C₈	#100	1	2	yes	—
94	#2931	—	19	1	no	—
95	#1566	—	19	2	no	—
96	#1560	—	19	2	no	—
97	#1309	—	19	1	no	—
98	#1309	D₁₉	1	1	yes	characteristic, complemented
99	C₂²×C₁₉	—	2	1	no	—
100	C₂²×C₁₉	—	2	2	no	—
101	C₂²×C₁₉	#380	1	1	yes	characteristic
102	C₂×D₁₉	—	4	2	no	—
103	C₂×D₁₉	—	4	4	no	—
104	C₄×C₁₉	—	2	1	no	—
105	C₄×C₁₉	—	2	2	no	—
106	C₄×C₁₉	C₂×#100	1	1	yes	characteristic
107	C₄×C₁₉	#413	1	1	yes	characteristic
108	C₄×C₁₉	#471	1	2	yes	—
109	C₄×C₁₉	#471	1	2	yes	—
110	Dic₁₉	—	4	2	no	—
111	C₂×#131	—	19	2	no	—
112	#532	—	19	1	no	—
113	#436	—	38	2	no	—
114	C₈×D₄	—	38	2	no	—
115	#423	—	19	2	no	—
116	#423	C₂×D₁₉	1	2	yes	—
117	#423	C₂×D₁₉	1	1	yes	characteristic
118	#408	—	19	2	no	—
119	C₂×C₄×C₈	—	19	1	no	—
120	#334	—	38	2	no	—
121	#334	—	38	2	no	—
122	#333	—	38	2	no	—
123	#331	—	38	2	no	—
124	C₂×C₁₉	—	4	1	no	—
125	C₂×C₁₉	#1800	1	1	yes	characteristic
126	C₂×C₁₉	#1815	1	2	yes	—
127	D₁₉	—	8	2	no	—
128	C₂×#41	—	19	2	no	—
129	#131	—	76	4	no	—
130	C₂×M₁₆	—	2	2	no	—
131	C₂×M₁₆	—	38	2	no	—
132	C₂×M₁₆	—	38	2	no	—
133	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
134	C₂²×C₈	—	19	1	no	—
135	C₂²×C₈	—	19	1	no	—
136	C₂²×C₈	—	38	2	no	—
137	C₄⋊Q₈	—	19	1	no	—
138	#127	—	19	1	no	—
139	#124	—	19	2	no	—
140	#121	—	38	2	no	—
141	C₄×D₄	—	38	2	no	—
142	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
143	C₄⋊C₈	—	2	2	no	—
144	C₄⋊C₈	—	2	2	no	—
145	C₄⋊C₈	—	2	2	no	—
146	C₄⋊C₈	—	38	2	no	—
147	C₄⋊C₈	—	38	2	no	—
148	C₂²⋊C₈	—	38	4	no	—
149	C₄×C₈	—	19	2	no	—
150	C₄×C₈	—	19	2	no	—
151	C₁₉	#8636	1	1	yes	characteristic, complemented, Sylow
152	#41	—	76	2	no	—
153	#41	—	76	2	no	—
154	C₂×Q₈	—	19	2	no	—
155	C₂×D₄	—	19	2	no	—
156	C₂×D₄	—	38	2	no	—
157	C₂×D₄	—	38	2	no	—
158	C₂²×C₄	—	38	2	no	—
159	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
160	C₂²×C₄	#64541	1	2	yes	—
161	M₁₆	—	4	2	no	—
162	M₁₆	—	8	2	no	—
163	M₁₆	—	76	4	no	—
164	M₁₆	—	152	2	no	—
165	C₂×C₈	—	2	2	no	—
166	C₂×C₈	—	4	2	no	—
167	C₂×C₈	—	19	1	no	—
168	C₂×C₈	—	19	2	no	—
169	C₂×C₈	—	19	1	no	—
170	C₂×C₈	—	38	2	no	—
171	C₂×C₈	—	76	4	no	—
172	C₂×C₈	—	76	1	no	—
173	C₂×C₈	—	76	2	no	—
174	C₄⋊C₄	—	38	2	no	—
175	C₂²⋊C₄	—	38	4	no	—
176	C₄²	D₄×D₁₉	1	2	yes	—
177	C₄²	D₄×D₁₉	1	1	yes	characteristic
178	C₄²	Q₈×D₁₉	1	1	yes	characteristic
179	C₂³	—	38	2	no	—
180	C₂³	#10597318	1	1	yes	characteristic
181	Q₈	—	76	2	no	—
182	D₄	—	76	2	no	—
183	D₄	—	76	4	no	—
184	D₄	—	76	2	no	—
185	D₄	—	76	2	no	—
186	C₂×C₄	—	2	2	no	—
187	C₂×C₄	—	2	2	no	—
188	C₂×C₄	—	2	1	no	—
189	C₂×C₄	—	2	1	no	—
190	C₂×C₄	—	38	2	no	—
191	C₂×C₄	—	76	2	no	—
192	C₂×C₄	—	76	2	no	—
193	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
194	C₂×C₄	#10597330	1	2	yes	—
195	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
196	C₂×C₄	#10597342	1	2	yes	—
197	C₈	—	4	2	no	—
198	C₈	—	8	2	no	—
199	C₈	—	19	2	no	—
200	C₈	—	38	1	no	—
201	C₈	—	38	2	no	—
202	C₈	—	152	2	no	—
203	C₂²	—	2	1	no	—
204	C₂²	—	2	2	no	—
205	C₂²	—	76	2	no	—
206	C₂²	—	76	4	no	—
207	C₂²	#11926403	1	1	yes	characteristic
208	C₄	—	2	1	no	—
209	C₄	—	2	2	no	—
210	C₄	—	76	2	no	—
211	C₄	#100×D₁₉	1	1	yes	characteristic
212	C₄	#11926527	1	1	yes	characteristic
213	C₄	#11926806	1	2	yes	—
214	C₄	#11926810	1	2	yes	—
215	C₂	—	4	1	no	—
216	C₂	—	152	2	no	—
217	C₂	#14563626	1	1	yes	characteristic
218	C₂	#14563693	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14572346

C₂

yes

maximal, characteristic

#14562390

C₂

yes

maximal, complemented

#14562368

C₂

yes

maximal

C₁₉⋊#1309

C₂

yes

maximal, characteristic, complemented

C₁₉×#1309

C₂

yes

maximal, characteristic, complemented

C₂×#10597353

C₄

yes

—

#11927094

C₂²

yes

—

—

C₂²

yes

—

#11926512

C₄

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

—

—

—

C₁₉×#423

C₂²

yes

—

C₁₉×#423

C₂²

yes

characteristic

C₂×#64541

C₂×C₄

yes

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

#10597376

—

C₂×#64520

—

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

#10597353

—

C₂×#64515

—

C₂×C₈×D₁₉

—

#10597321

Q₈

yes

—

#10597320

D₄

yes

characteristic

C₄×D₇₆

—

#10597315

D₄

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

(C₂×D₁₉)⋊C₈

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂×C₂²⋊D₁₉

—

#64541

—

#64541

—

C₂×D₇₆

—

C₂×D₇₆

C₄⋊C₄

yes

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

C₄⋊C₄

yes

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

—

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

characteristic

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

characteristic

#64515

—

C₈×D₁₉

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

D₇₆

—

C₄×D₁₉

—

C₄×D₁₉

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

#100

yes

—

—

—

—

—

D₁₉

yes

characteristic, complemented

C₂²×C₁₉

—

100

C₂²×C₁₉

—

101

C₂²×C₁₉

#380

yes

characteristic

102

C₂×D₁₉

—

103

C₂×D₁₉

—

104

C₄×C₁₉

—

105

C₄×C₁₉

—

106

C₄×C₁₉

C₂×#100

yes

characteristic

107

C₄×C₁₉

#413

yes

characteristic

108

C₄×C₁₉

#471

yes

—

109

C₄×C₁₉

#471

yes

—

110

Dic₁₉

—

111

C₂×#131

—

112

#532

—

113

#436

—

114

C₈×D₄

—

115

#423

—

116

#423

C₂×D₁₉

yes

—

117

#423

C₂×D₁₉

yes

characteristic

118

#408

—

119

C₂×C₄×C₈

—

120

#334

—

121

#334

—

122

#333

—

123

#331

—

124

C₂×C₁₉

—

125

C₂×C₁₉

#1800

yes

characteristic

126

C₂×C₁₉

#1815

yes

—

127

D₁₉

—

128

C₂×#41

—

129

#131

—

130

C₂×M₁₆

—

131

C₂×M₁₆

—

132

C₂×M₁₆

—

133

C₂×M₁₆

C₄×D₁₉

yes

—

134

C₂²×C₈

—

135

C₂²×C₈

—

136

C₂²×C₈

—

137

C₄⋊Q₈

—

138

#127

—

139

#124

—

140

#121

—

141

C₄×D₄

—

142

C₂×C₄²

C₂²×D₁₉

yes

characteristic

143

C₄⋊C₈

—

144

C₄⋊C₈

—

145

C₄⋊C₈

—

146

C₄⋊C₈

—

147

C₄⋊C₈

—

148

C₂²⋊C₈

—

149

C₄×C₈

—

150

C₄×C₈

—

151

C₁₉

#8636

yes

characteristic, complemented, Sylow

152

#41

—

153

#41

—

154

C₂×Q₈

—

155

C₂×D₄

—

156

C₂×D₄

—

157

C₂×D₄

—

158

C₂²×C₄

—

159

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

160

C₂²×C₄

#64541

yes

—

161

M₁₆

—

162

M₁₆

—

163

M₁₆

—

164

M₁₆

—

152

—

165

C₂×C₈

—

166

C₂×C₈

—

167

C₂×C₈

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₄⋊C₄

—

175

C₂²⋊C₄

—

176

C₄²

D₄×D₁₉

yes

—

177

C₄²

D₄×D₁₉

yes

characteristic

178

C₄²

Q₈×D₁₉

yes

characteristic

179

C₂³

—

180

C₂³

#10597318

yes

characteristic

181

Q₈

—

182

D₄

—

183

D₄

—

184

D₄

—

185

D₄

—

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

C₂²⋊C₄×D₁₉

yes

characteristic

194

C₂×C₄

#10597330

yes

—

195

C₂×C₄

C₄⋊C₄×D₁₉

yes

characteristic

196

C₂×C₄

#10597342

yes

—

197

C₈

—

198

C₈

—

199

C₈

—

200

C₈

—

201

C₈

—

202

C₈

—

152

—

203

C₂²

—

204

C₂²

—

205

C₂²

—

206

C₂²

—

207

C₂²

#11926403

yes

characteristic

208

C₄

—

209

C₄

—

210

C₄

—

211

C₄

#100×D₁₉

yes

characteristic

212

C₄

#11926527

yes

characteristic

213

C₄

#11926806

yes

—

214

C₄

#11926810

yes

—

215

C₂

—

216

C₂

—

152

—

217

C₂

#14563626

yes

characteristic

218

C₂

#14563693

yes

—

	subgroup	G/H
center	C₂²	#11926403
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1309	C₂
socle	C₂²×C₁₉	#380
prime radical	#11927094	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1309	D₁₉
hypocenter	C₁₉	#8636
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1309

subgroup

G/H

center

C₂²

#11926403

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1309

C₂

C₂²×C₁₉

C₂²

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1309

N	H ≅ G/N	type
2. #14562390	C₂	semidirect
4. C₁₉⋊#1309	C₂	semidirect
5. C₁₉×#1309	C₂	semidirect
98. #1309	D₁₉	semidirect
151. C₁₉	#8636	semidirect

H ≅ G/N

type

2. #14562390

C₂

semidirect

4. C₁₉⋊#1309

C₂

semidirect

5. C₁₉×#1309

C₂

semidirect

98. #1309

D₁₉

semidirect

151. C₁₉

#8636

semidirect

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

subgroup	index
#14572346	2
#14562390	2
#14562368	2
C₁₉⋊#1309	2
C₁₉×#1309	2
#8636	19

subgroup

index

#14572346

#14562390

#14562368

C₁₉⋊#1309

C₁₉×#1309

#8636

Subgroups — #18075556

Conjugacy classes of subgroups

Complements

Maximal subgroups