Group #18087309 — subgroups

Subgroups — #18087309

Order 4864.

330 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 93 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	#14564467	C₂	1	1	yes	maximal, characteristic
2	#14563789	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562282	C₂	1	2	yes	maximal
4	#14561531	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1274	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927094	C₂²	1	1	yes	characteristic
7	#11926568	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
9	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
11	C₂×#10597262	—	2	1	no	—
12	C₂×#10597262	—	2	1	no	—
13	#11926289	—	2	2	no	—
14	#11926287	—	2	2	no	—
15	C₁₉×#431	C₂²	1	2	yes	—
16	C₁₉×#376	C₂²	1	1	yes	characteristic
17	C₂×#64541	—	2	1	no	—
18	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
19	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
20	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
21	#10597376	—	2	2	no	—
22	C₂×#64520	—	2	1	no	—
23	C₂²×C₁₉⋊C₈	—	2	2	no	—
24	#10597321	—	2	1	no	—
25	#10597320	D₄	1	1	yes	characteristic
26	C₄×D₇₆	—	2	2	no	—
27	#10597315	D₄	1	1	yes	characteristic
28	C₁₉×C₄⋊C₈	—	2	2	no	—
29	C₁₉×C₂²⋊C₈	—	2	2	no	—
30	C₄×C₈×C₁₉	—	2	2	no	—
31	C₁₉×#95	—	2	2	no	—
32	#10597262	—	4	2	no	—
33	#10597262	—	4	2	no	—
34	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
35	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
36	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
37	C₄⋊(C₁₉⋊C₈)	—	4	2	no	—
38	C₄⋊(C₁₉⋊C₈)	—	4	2	no	—
39	C₂²×C₄×C₁₉	—	2	1	no	—
40	C₂²×C₄×C₁₉	—	2	1	no	—
41	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	#41	1	2	yes	—
43	C₂×C₂²⋊D₁₉	—	4	1	no	—
44	#64541	—	4	1	no	—
45	#64541	—	4	1	no	—
46	#64541	—	4	1	no	—
47	#64541	—	4	1	no	—
48	C₂×D₇₆	—	2	1	no	—
49	C₂×D₇₆	—	2	2	no	—
50	C₂×C₄×D₁₉	—	4	1	no	—
51	C₂×Dic₃₈	—	2	1	no	—
52	C₂×C₈×C₁₉	—	4	2	no	—
53	C₄²×C₁₉	—	2	1	no	—
54	C₄²×C₁₉	—	2	1	no	—
55	C₄²×C₁₉	D₈	1	2	yes	—
56	C₄²×C₁₉	SD₁₆	1	2	yes	—
57	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₄²×C₁₉	#41	1	2	yes	—
59	C₄²×C₁₉	#41	1	1	yes	characteristic
60	(C₂×D₁₉)⋊C₄	—	4	2	no	—
61	C₄⋊Dic₁₉	—	2	2	no	—
62	#64520	—	4	1	no	—
63	#64520	—	4	1	no	—
64	C₂×C₁₉⋊C₈	—	4	2	no	—
65	C₂×C₁₉⋊C₈	—	4	1	no	—
66	C₂×C₁₉⋊C₈	—	4	2	no	—
67	C₂×C₁₉⋊C₈	—	4	2	no	—
68	#10627	—	19	1	no	maximal, Sylow
69	C₂³×C₁₉	#123	1	1	yes	characteristic
70	C₂²×D₁₉	—	4	1	no	—
71	C₂×C₄×C₁₉	—	2	2	no	—
72	C₂×C₄×C₁₉	—	2	2	no	—
73	C₂×C₄×C₁₉	—	4	2	no	—
74	C₂×C₄×C₁₉	—	4	2	no	—
75	C₂×C₄×C₁₉	—	4	2	no	—
76	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
77	C₂×C₄×C₁₉	#123	1	2	yes	—
78	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
79	C₂×C₄×C₁₉	#126	1	2	yes	—
80	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
81	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
82	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
83	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
84	C₂²⋊D₁₉	—	8	1	no	—
85	C₂²⋊D₁₉	—	8	1	no	—
86	C₂×Dic₁₉	—	4	1	no	—
87	D₇₆	—	4	1	no	—
88	D₇₆	—	4	1	no	—
89	D₇₆	—	8	2	no	—
90	C₄×D₁₉	—	8	1	no	—
91	C₄×D₁₉	—	8	1	no	—
92	Dic₃₈	—	4	1	no	—
93	Dic₃₈	—	4	1	no	—
94	C₈×C₁₉	—	8	2	no	—
95	C₁₉⋊C₈	—	8	2	no	—
96	C₁₉⋊C₈	—	8	1	no	—
97	#1963	—	19	1	no	—
98	#1843	—	19	1	no	—
99	#1540	—	19	2	no	—
100	#1301	—	19	2	no	—
101	#1274	D₁₉	1	1	yes	characteristic, complemented
102	C₂²×C₁₉	—	2	2	no	—
103	C₂²×C₁₉	#397	1	1	yes	characteristic
104	C₂²×C₁₉	#480	1	1	yes	characteristic
105	C₂²×C₁₉	#481	1	1	yes	characteristic
106	C₂×D₁₉	—	8	1	no	—
107	C₂×D₁₉	—	8	2	no	—
108	C₄×C₁₉	—	2	2	no	—
109	C₄×C₁₉	—	2	2	no	—
110	C₄×C₁₉	—	4	2	no	—
111	C₄×C₁₉	—	4	2	no	—
112	C₄×C₁₉	#459	1	1	yes	characteristic
113	C₄×C₁₉	#461	1	1	yes	characteristic
114	C₄×C₁₉	#486	1	1	yes	characteristic
115	C₄×C₁₉	#489	1	1	yes	characteristic
116	Dic₁₉	—	8	1	no	—
117	#532	—	19	1	no	—
118	#431	C₂×D₁₉	1	2	yes	—
119	#423	—	19	1	no	—
120	C₂×C₄⋊C₈	—	19	2	no	—
121	C₂×C₄⋊C₈	—	38	1	no	—
122	C₂×C₄⋊C₈	—	38	1	no	—
123	C₂×#104	—	38	1	no	—
124	C₂×#104	—	38	1	no	—
125	#376	C₂×D₁₉	1	1	yes	characteristic
126	#332	—	38	2	no	—
127	#331	—	38	2	no	—
128	C₂×C₁₉	—	2	1	no	—
129	C₂×C₁₉	—	2	1	no	—
130	C₂×C₁₉	#2071	1	1	yes	characteristic
131	C₂×C₁₉	#2080	1	2	yes	—
132	D₁₉	—	16	1	no	—
133	C₂×#41	—	38	1	no	—
134	C₂×M₁₆	—	38	1	no	—
135	C₂²×C₈	—	38	2	no	—
136	C₄⋊Q₈	—	19	1	no	—
137	#127	—	19	1	no	—
138	#124	—	38	1	no	—
139	#121	—	38	2	no	—
140	C₄×D₄	—	38	2	no	—
141	C₂×C₄²	D₇₆	1	1	yes	characteristic
142	C₂×C₄²	D₇₆	1	1	yes	characteristic
143	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
144	C₄⋊C₈	—	2	2	no	—
145	C₄⋊C₈	—	38	2	no	—
146	C₄⋊C₈	—	38	2	no	—
147	C₄⋊C₈	—	38	2	no	—
148	C₄⋊C₈	—	76	2	no	—
149	C₄⋊C₈	—	76	2	no	—
150	#104	—	76	2	no	—
151	#104	—	76	2	no	—
152	C₂²⋊C₈	—	2	2	no	—
153	C₄×C₈	—	2	2	no	—
154	#95	—	2	2	no	—
155	C₁₉	#10627	1	1	yes	characteristic, complemented, Sylow
156	#41	—	76	1	no	—
157	#41	—	76	1	no	—
158	#41	—	76	1	no	—
159	#41	—	76	1	no	—
160	C₂×Q₈	—	38	1	no	—
161	C₂×D₄	—	38	2	no	—
162	C₂×D₄	—	38	1	no	—
163	C₂×D₄	—	76	1	no	—
164	C₂²×C₄	—	2	1	no	—
165	C₂²×C₄	—	2	1	no	—
166	C₂²×C₄	—	76	1	no	—
167	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
168	C₂²×C₄	#64543	1	2	yes	—
169	M₁₆	—	76	1	no	—
170	M₁₆	—	76	1	no	—
171	C₂×C₈	—	4	2	no	—
172	C₂×C₈	—	76	1	no	—
173	C₂×C₈	—	76	2	no	—
174	C₂×C₈	—	76	2	no	—
175	C₂×C₈	—	76	2	no	—
176	C₄⋊C₄	—	38	2	no	—
177	C₂²⋊C₄	—	76	2	no	—
178	C₄²	—	2	1	no	—
179	C₄²	—	2	1	no	—
180	C₄²	#64516	1	2	yes	—
181	C₄²	D₁₅₂	1	2	yes	—
182	C₄²	#64541	1	2	yes	—
183	C₄²	D₄×D₁₉	1	1	yes	characteristic
184	C₄²	#64545	1	1	yes	characteristic
185	C₂³	—	76	1	no	—
186	C₂³	#10597332	1	1	yes	characteristic
187	Q₈	—	76	1	no	—
188	Q₈	—	76	1	no	—
189	D₄	—	76	1	no	—
190	D₄	—	76	1	no	—
191	D₄	—	152	2	no	—
192	D₄	—	152	1	no	—
193	D₄	—	152	1	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	4	2	no	—
197	C₂×C₄	—	4	2	no	—
198	C₂×C₄	—	4	2	no	—
199	C₂×C₄	—	76	1	no	—
200	C₂×C₄	—	152	1	no	—
201	C₂×C₄	—	152	1	no	—
202	C₂×C₄	#10597321	1	1	yes	characteristic
203	C₂×C₄	#10597329	1	2	yes	—
204	C₂×C₄	#10597341	1	1	yes	characteristic
205	C₂×C₄	#10597344	1	2	yes	—
206	C₂×C₄	C₂×#64516	1	1	yes	characteristic
207	C₂×C₄	C₂×D₁₅₂	1	1	yes	characteristic
208	C₂×C₄	#10597354	1	1	yes	characteristic
209	C₂×C₄	#10597355	1	1	yes	characteristic
210	C₈	—	8	2	no	—
211	C₈	—	152	1	no	—
212	C₈	—	152	2	no	—
213	C₂²	—	2	2	no	—
214	C₂²	—	152	1	no	—
215	C₂²	—	152	2	no	—
216	C₂²	#11926471	1	1	yes	characteristic
217	C₂²	#11926858	1	1	yes	characteristic
218	C₂²	#11926863	1	1	yes	characteristic
219	C₄	—	2	2	no	—
220	C₄	—	2	2	no	—
221	C₄	—	4	2	no	—
222	C₄	—	4	2	no	—
223	C₄	—	152	1	no	—
224	C₄	#11926740	1	1	yes	characteristic
225	C₄	#11926750	1	1	yes	characteristic
226	C₄	#11926891	1	1	yes	characteristic
227	C₄	#11926904	1	1	yes	characteristic
228	C₂	—	2	1	no	—
229	C₂	—	2	1	no	—
230	C₂	—	304	1	no	—
231	C₂	#14565040	1	1	yes	characteristic
232	C₂	#14565087	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14564467

C₂

yes

maximal, characteristic

#14563789

C₂

yes

maximal, characteristic, complemented

#14562282

C₂

yes

maximal

#14561531

C₂

yes

maximal, complemented

C₁₉×#1274

C₂

yes

maximal, characteristic, complemented

#11927094

C₂²

yes

characteristic

#11926568

C₂²

yes

characteristic

C₂×C₄⋊(C₁₉⋊C₈)

—

C₂×C₄⋊(C₁₉⋊C₈)

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

—

—

—

—

C₁₉×#431

C₂²

yes

—

C₁₉×#376

C₂²

yes

characteristic

C₂×#64541

—

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

#10597376

—

C₂×#64520

—

C₂²×C₁₉⋊C₈

—

#10597321

—

#10597320

D₄

yes

characteristic

C₄×D₇₆

—

#10597315

D₄

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

C₁₉×#95

—

#10597262

—

#10597262

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂×C₂²⋊D₁₉

—

—

—

—

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

D₈

yes

—

C₄²×C₁₉

SD₁₆

yes

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₄²×C₁₉

#41

yes

characteristic

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#121

yes

characteristic

C₂×C₄×C₁₉

#123

yes

—

C₂×C₄×C₁₉

#124

yes

characteristic

C₂×C₄×C₁₉

#126

yes

—

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

C₂×C₄×C₁₉

C₂×SD₁₆

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂²⋊D₁₉

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

D₇₆

—

C₄×D₁₉

—

C₄×D₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1963

—

#1843

—

#1540

—

100

#1301

—

101

#1274

D₁₉

yes

characteristic, complemented

102

C₂²×C₁₉

—

103

C₂²×C₁₉

#397

yes

characteristic

104

C₂²×C₁₉

#480

yes

characteristic

105

C₂²×C₁₉

#481

yes

characteristic

106

C₂×D₁₉

—

107

C₂×D₁₉

—

108

C₄×C₁₉

—

109

C₄×C₁₉

—

110

C₄×C₁₉

—

111

C₄×C₁₉

—

112

C₄×C₁₉

#459

yes

characteristic

113

C₄×C₁₉

#461

yes

characteristic

114

C₄×C₁₉

#486

yes

characteristic

115

C₄×C₁₉

#489

yes

characteristic

116

Dic₁₉

—

117

#532

—

118

#431

C₂×D₁₉

yes

—

119

#423

—

120

C₂×C₄⋊C₈

—

121

C₂×C₄⋊C₈

—

122

C₂×C₄⋊C₈

—

123

C₂×#104

—

124

C₂×#104

—

125

#376

C₂×D₁₉

yes

characteristic

126

#332

—

127

#331

—

128

C₂×C₁₉

—

129

C₂×C₁₉

—

130

C₂×C₁₉

#2071

yes

characteristic

131

C₂×C₁₉

#2080

yes

—

132

D₁₉

—

133

C₂×#41

—

134

C₂×M₁₆

—

135

C₂²×C₈

—

136

C₄⋊Q₈

—

137

#127

—

138

#124

—

139

#121

—

140

C₄×D₄

—

141

C₂×C₄²

D₇₆

yes

characteristic

142

C₂×C₄²

D₇₆

yes

characteristic

143

C₂×C₄²

C₂²×D₁₉

yes

characteristic

144

C₄⋊C₈

—

145

C₄⋊C₈

—

146

C₄⋊C₈

—

147

C₄⋊C₈

—

148

C₄⋊C₈

—

149

C₄⋊C₈

—

150

#104

—

151

#104

—

152

C₂²⋊C₈

—

153

C₄×C₈

—

154

#95

—

155

C₁₉

#10627

yes

characteristic, complemented, Sylow

156

#41

—

157

#41

—

158

#41

—

159

#41

—

160

C₂×Q₈

—

161

C₂×D₄

—

162

C₂×D₄

—

163

C₂×D₄

—

164

C₂²×C₄

—

165

C₂²×C₄

—

166

C₂²×C₄

—

167

C₂²×C₄

C₂×D₇₆

yes

characteristic

168

C₂²×C₄

#64543

yes

—

169

M₁₆

—

170

M₁₆

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₄⋊C₄

—

177

C₂²⋊C₄

—

178

C₄²

—

179

C₄²

—

180

C₄²

#64516

yes

—

181

C₄²

D₁₅₂

yes

—

182

C₄²

#64541

yes

—

183

C₄²

D₄×D₁₉

yes

characteristic

184

C₄²

#64545

yes

characteristic

185

C₂³

—

186

C₂³

#10597332

yes

characteristic

187

Q₈

—

188

Q₈

—

189

D₄

—

190

D₄

—

191

D₄

—

152

—

192

D₄

—

152

—

193

D₄

—

152

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

152

—

201

C₂×C₄

—

152

—

202

C₂×C₄

#10597321

yes

characteristic

203

C₂×C₄

#10597329

yes

—

204

C₂×C₄

#10597341

yes

characteristic

205

C₂×C₄

#10597344

yes

—

206

C₂×C₄

C₂×#64516

yes

characteristic

207

C₂×C₄

C₂×D₁₅₂

yes

characteristic

208

C₂×C₄

#10597354

yes

characteristic

209

C₂×C₄

#10597355

yes

characteristic

210

C₈

—

211

C₈

—

152

—

212

C₈

—

152

—

213

C₂²

—

214

C₂²

—

152

—

215

C₂²

—

152

—

216

C₂²

#11926471

yes

characteristic

217

C₂²

#11926858

yes

characteristic

218

C₂²

#11926863

yes

characteristic

219

C₄

—

220

C₄

—

221

C₄

—

222

C₄

—

223

C₄

—

152

—

224

C₄

#11926740

yes

characteristic

225

C₄

#11926750

yes

characteristic

226

C₄

#11926891

yes

characteristic

227

C₄

#11926904

yes

characteristic

228

C₂

—

229

C₂

—

230

C₂

—

304

—

231

C₂

#14565040

yes

characteristic

232

C₂

#14565087

yes

—

	subgroup	G/H
center	C₂×C₄	#10597321
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1274	C₂
socle	C₂²×C₁₉	#397
prime radical	#11927094	C₂²
hypercenter	#1274	D₁₉
hypocenter	C₁₉	#10627
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1274

subgroup

G/H

center

C₂×C₄

#10597321

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1274

C₂

C₂²×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1274

N	H ≅ G/N	type
2. #14563789	C₂	semidirect
4. #14561531	C₂	semidirect
5. C₁₉×#1274	C₂	semidirect
101. #1274	D₁₉	semidirect
155. C₁₉	#10627	semidirect

H ≅ G/N

type

2. #14563789

C₂

semidirect

4. #14561531

C₂

semidirect

5. C₁₉×#1274

C₂

semidirect

101. #1274

D₁₉

semidirect

155. C₁₉

#10627

semidirect

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

subgroup	index
#14564467	2
#14563789	2
#14562282	2
#14561531	2
C₁₉×#1274	2
#10627	19

subgroup

index

C₁₉×#1274

Subgroups — #18087309

Conjugacy classes of subgroups

Complements

Maximal subgroups