Group #18077049 — subgroups

Subgroups — #18077049

Order 4864.

412 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 111 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	#14572702	C₂	1	1	yes	maximal, characteristic
2	#14564464	C₂	1	1	yes	maximal, characteristic
3	#14562424	C₂	1	2	yes	maximal, complemented
4	#14561467	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1543	C₂	1	1	yes	maximal, characteristic
6	#11926622	—	2	2	no	—
7	D₄×C₁₉⋊C₈	—	2	2	no	—
8	#11926597	C₂²	1	2	yes	—
9	#11926568	C₂²	1	1	yes	characteristic
10	C₂×#10597294	—	2	2	no	—
11	#11926511	—	2	2	no	—
12	C₄²×Dic₁₉	C₂²	1	1	yes	characteristic
13	#11926297	—	2	2	no	—
14	#11926295	—	2	2	no	—
15	C₁₉×#532	C₂²	1	1	yes	characteristic
16	C₁₉×#431	C₂²	1	2	yes	—
17	C₁₉×#333	C₄	1	1	yes	characteristic, complemented
18	C₁₉×#333	C₄	1	1	yes	characteristic, complemented
19	C₁₉×#331	C₄	1	2	yes	complemented
20	C₂×#41×C₁₉	D₄	1	2	yes	—
21	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
22	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
23	C₁₉×#124	Q₈	1	2	yes	—
24	C₁₉×#121	—	2	2	no	—
25	C₄×D₄×C₁₉	—	2	2	no	—
26	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
27	C₂×C₄×Dic₁₉	—	2	1	no	—
28	C₂×C₄×Dic₁₉	—	2	2	no	—
29	C₂×#64520	—	2	2	no	—
30	C₂×#64520	—	2	1	no	—
31	C₂²×C₁₉⋊C₈	—	2	2	no	—
32	C₁₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
33	C₁₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
34	C₁₉×C₂²⋊C₈	—	2	2	no	—
35	C₄×C₈×C₁₉	—	2	2	no	—
36	#10597294	—	4	4	no	—
37	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
38	C₂²⋊(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	C₄×C₁₉⋊C₈	—	2	2	no	—
43	#41×C₁₉	—	4	2	no	—
44	#41×C₁₉	—	4	2	no	—
45	C₂×Q₈×C₁₉	C₄⋊C₄	1	2	yes	—
46	C₂×D₄×C₁₉	—	2	2	no	—
47	C₂×D₄×C₁₉	—	2	2	no	—
48	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
49	C₂²×C₄×C₁₉	—	2	2	no	—
50	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	#41	1	2	yes	—
52	C₂²×Dic₁₉	—	4	1	no	—
53	C₂×C₈×C₁₉	—	2	2	no	—
54	C₂×C₈×C₁₉	—	2	2	no	—
55	C₄⋊C₄×C₁₉	—	2	2	no	—
56	C₂²⋊C₄×C₁₉	—	2	4	no	—
57	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
58	C₄²×C₁₉	C₂×D₄	1	2	yes	—
59	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
60	C₄×Dic₁₉	—	2	2	no	—
61	C₄×Dic₁₉	—	2	4	no	—
62	C₄×Dic₁₉	—	4	2	no	—
63	C₄×Dic₁₉	—	4	1	no	—
64	#64520	—	4	2	no	—
65	#64520	—	8	2	no	—
66	C₂×C₁₉⋊C₈	—	2	2	no	—
67	C₂×C₁₉⋊C₈	—	2	2	no	—
68	C₂×C₁₉⋊C₈	—	4	1	no	—
69	C₂×C₁₉⋊C₈	—	8	2	no	—
70	#8935	—	19	1	no	maximal, Sylow
71	C₂³×C₁₉	—	2	2	no	—
72	C₂³×C₁₉	#123	1	1	yes	characteristic
73	Q₈×C₁₉	—	4	2	no	—
74	D₄×C₁₉	—	4	2	no	—
75	D₄×C₁₉	—	4	2	no	—
76	D₄×C₁₉	—	4	2	no	—
77	D₄×C₁₉	—	8	2	no	—
78	C₂×C₄×C₁₉	—	2	2	no	—
79	C₂×C₄×C₁₉	—	2	2	no	—
80	C₂×C₄×C₁₉	—	2	1	no	—
81	C₂×C₄×C₁₉	—	2	1	no	—
82	C₂×C₄×C₁₉	—	2	2	no	—
83	C₂×C₄×C₁₉	—	4	2	no	—
84	C₂×C₄×C₁₉	—	4	2	no	—
85	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
86	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
87	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
88	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
89	C₂×Dic₁₉	—	4	2	no	—
90	C₂×Dic₁₉	—	4	4	no	—
91	C₈×C₁₉	—	4	2	no	—
92	C₈×C₁₉	—	4	2	no	—
93	C₁₉⋊C₈	—	4	2	no	—
94	C₁₉⋊C₈	—	4	2	no	—
95	C₁₉⋊C₈	—	8	1	no	—
96	#2979	—	19	1	no	—
97	#1962	—	19	1	no	—
98	#1574	—	19	2	no	—
99	#1543	D₁₉	1	1	yes	characteristic
100	#1276	—	19	2	no	—
101	C₂²×C₁₉	—	2	1	no	—
102	C₂²×C₁₉	—	2	2	no	—
103	C₂²×C₁₉	—	4	2	no	—
104	C₂²×C₁₉	—	4	4	no	—
105	C₂²×C₁₉	#385	1	1	yes	characteristic
106	C₄×C₁₉	—	2	1	no	—
107	C₄×C₁₉	—	2	2	no	—
108	C₄×C₁₉	—	4	2	no	—
109	C₄×C₁₉	#443	1	2	yes	—
110	C₄×C₁₉	#444	1	2	yes	—
111	C₄×C₁₉	#453	1	1	yes	characteristic
112	C₄×C₁₉	#455	1	1	yes	characteristic
113	Dic₁₉	—	4	4	no	—
114	#532	C₂×D₁₉	1	1	yes	characteristic
115	#436	—	38	2	no	—
116	C₈×D₄	—	38	2	no	—
117	#431	—	19	2	no	—
118	#431	C₂×D₁₉	1	2	yes	—
119	#423	—	19	1	no	—
120	C₂×#104	—	38	2	no	—
121	#408	—	38	2	no	—
122	C₄³	—	19	1	no	—
123	#335	—	38	2	no	—
124	#334	—	38	2	no	—
125	#333	Dic₁₉	1	1	yes	characteristic, complemented
126	#333	Dic₁₉	1	1	yes	characteristic, complemented
127	#331	Dic₁₉	1	2	yes	complemented
128	C₂×C₁₉	—	4	1	no	—
129	C₂×C₁₉	—	8	2	no	—
130	C₂×C₁₉	#1856	1	1	yes	characteristic
131	C₂×C₁₉	#1866	1	2	yes	—
132	C₂×#41	D₇₆	1	2	yes	—
133	C₂×M₁₆	—	38	2	no	—
134	C₂×M₁₆	—	38	1	no	—
135	C₂²×C₈	—	38	2	no	—
136	C₄⋊Q₈	C₂×Dic₁₉	1	1	yes	characteristic
137	#127	C₂×Dic₁₉	1	1	yes	characteristic
138	#124	Dic₃₈	1	2	yes	—
139	#121	—	2	2	no	—
140	C₄×D₄	—	2	2	no	—
141	C₂×C₄²	—	38	1	no	—
142	C₂×C₄²	—	38	2	no	—
143	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
144	C₄⋊C₈	—	19	2	no	—
145	C₄⋊C₈	—	19	2	no	—
146	C₄⋊C₈	—	38	2	no	—
147	C₄⋊C₈	C₂×Dic₁₉	1	2	yes	—
148	C₄⋊C₈	C₂×Dic₁₉	1	2	yes	—
149	#104	—	76	4	no	—
150	C₂²⋊C₈	—	2	2	no	—
151	C₂²⋊C₈	—	38	4	no	—
152	C₂²⋊C₈	—	38	2	no	—
153	C₄×C₈	—	2	2	no	—
154	C₄×C₈	—	38	2	no	—
155	C₁₉	#8935	1	1	yes	characteristic, complemented, Sylow
156	#41	—	4	2	no	—
157	#41	—	4	2	no	—
158	C₂×Q₈	C₄⋊Dic₁₉	1	2	yes	—
159	C₂×D₄	—	2	2	no	—
160	C₂×D₄	—	2	2	no	—
161	C₂×D₄	C₄⋊Dic₁₉	1	2	yes	—
162	C₂²×C₄	—	2	2	no	—
163	C₂²×C₄	—	76	1	no	—
164	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
165	C₂²×C₄	#64543	1	2	yes	—
166	M₁₆	—	76	2	no	—
167	M₁₆	—	152	2	no	—
168	C₂×C₈	—	2	2	no	—
169	C₂×C₈	—	2	2	no	—
170	C₂×C₈	—	38	2	no	—
171	C₂×C₈	—	38	2	no	—
172	C₂×C₈	—	76	1	no	—
173	C₂×C₈	—	152	2	no	—
174	C₄⋊C₄	—	2	2	no	—
175	C₂²⋊C₄	—	2	4	no	—
176	C₄²	—	38	2	no	—
177	C₄²	—	38	4	no	—
178	C₄²	—	76	2	no	—
179	C₄²	—	76	1	no	—
180	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
181	C₄²	D₄×D₁₉	1	2	yes	—
182	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
183	C₂³	—	2	2	no	—
184	C₂³	#10597332	1	1	yes	characteristic
185	Q₈	—	4	2	no	—
186	D₄	—	4	2	no	—
187	D₄	—	4	2	no	—
188	D₄	—	4	2	no	—
189	D₄	—	8	2	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	2	2	no	—
192	C₂×C₄	—	2	1	no	—
193	C₂×C₄	—	2	1	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	4	2	no	—
196	C₂×C₄	—	4	2	no	—
197	C₂×C₄	—	76	2	no	—
198	C₂×C₄	—	76	4	no	—
199	C₂×C₄	#10597324	1	2	yes	—
200	C₂×C₄	#10597328	1	1	yes	characteristic
201	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
202	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
203	C₈	—	4	2	no	—
204	C₈	—	4	2	no	—
205	C₈	—	76	2	no	—
206	C₈	—	76	2	no	—
207	C₈	—	152	1	no	—
208	C₂²	—	2	1	no	—
209	C₂²	—	2	2	no	—
210	C₂²	—	4	2	no	—
211	C₂²	—	4	4	no	—
212	C₂²	#11926419	1	1	yes	characteristic
213	C₄	—	2	1	no	—
214	C₄	—	2	2	no	—
215	C₄	—	4	2	no	—
216	C₄	—	76	4	no	—
217	C₄	#11926661	1	2	yes	—
218	C₄	#11926666	1	2	yes	—
219	C₄	#11926714	1	1	yes	characteristic
220	C₄	#11926724	1	1	yes	characteristic
221	C₂	—	4	1	no	—
222	C₂	—	8	2	no	—
223	C₂	#14563847	1	1	yes	characteristic
224	C₂	#14563912	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14572702

C₂

yes

maximal, characteristic

#14564464

C₂

yes

maximal, characteristic

#14562424

C₂

yes

maximal, complemented

#14561467

C₂

yes

maximal, complemented

C₁₉×#1543

C₂

yes

maximal, characteristic

#11926622

—

D₄×C₁₉⋊C₈

—

#11926597

C₂²

yes

—

#11926568

C₂²

yes

characteristic

C₂×#10597294

—

#11926511

—

C₄²×Dic₁₉

C₂²

yes

characteristic

#11926297

—

#11926295

—

C₁₉×#532

C₂²

yes

characteristic

C₁₉×#431

C₂²

yes

—

C₁₉×#333

C₄

yes

characteristic, complemented

C₁₉×#333

C₄

yes

characteristic, complemented

C₁₉×#331

C₄

yes

complemented

C₂×#41×C₁₉

D₄

yes

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

characteristic

C₁₉×#127

C₂×C₄

yes

characteristic

C₁₉×#124

Q₈

yes

—

C₁₉×#121

—

C₄×D₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄×Dic₁₉

—

C₂×C₄×Dic₁₉

—

C₂×#64520

—

C₂×#64520

—

C₂²×C₁₉⋊C₈

—

C₁₉×C₄⋊C₈

C₂×C₄

yes

—

C₁₉×C₄⋊C₈

C₂×C₄

yes

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

#10597294

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

C₄×C₁₉⋊C₈

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

C₄⋊C₄

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8935

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

#123

yes

characteristic

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

#120

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

—

—

—

D₁₉

yes

characteristic

100

#1276

—

101

C₂²×C₁₉

—

102

C₂²×C₁₉

—

103

C₂²×C₁₉

—

104

C₂²×C₁₉

—

105

C₂²×C₁₉

#385

yes

characteristic

106

C₄×C₁₉

—

107

C₄×C₁₉

—

108

C₄×C₁₉

—

109

C₄×C₁₉

#443

yes

—

110

C₄×C₁₉

#444

yes

—

111

C₄×C₁₉

#453

yes

characteristic

112

C₄×C₁₉

#455

yes

characteristic

113

Dic₁₉

—

114

#532

C₂×D₁₉

yes

characteristic

115

#436

—

116

C₈×D₄

—

117

#431

—

118

#431

C₂×D₁₉

yes

—

119

#423

—

120

C₂×#104

—

121

#408

—

122

C₄³

—

123

#335

—

124

#334

—

125

#333

Dic₁₉

yes

characteristic, complemented

126

#333

Dic₁₉

yes

characteristic, complemented

127

#331

Dic₁₉

yes

complemented

128

C₂×C₁₉

—

129

C₂×C₁₉

—

130

C₂×C₁₉

#1856

yes

characteristic

131

C₂×C₁₉

#1866

yes

—

132

C₂×#41

D₇₆

yes

—

133

C₂×M₁₆

—

134

C₂×M₁₆

—

135

C₂²×C₈

—

136

C₄⋊Q₈

C₂×Dic₁₉

yes

characteristic

137

#127

C₂×Dic₁₉

yes

characteristic

138

#124

Dic₃₈

yes

—

139

#121

—

140

C₄×D₄

—

141

C₂×C₄²

—

142

C₂×C₄²

—

143

C₂×C₄²

C₂²×D₁₉

yes

characteristic

144

C₄⋊C₈

—

145

C₄⋊C₈

—

146

C₄⋊C₈

—

147

C₄⋊C₈

C₂×Dic₁₉

yes

—

148

C₄⋊C₈

C₂×Dic₁₉

yes

—

149

#104

—

150

C₂²⋊C₈

—

151

C₂²⋊C₈

—

152

C₂²⋊C₈

—

153

C₄×C₈

—

154

C₄×C₈

—

155

C₁₉

#8935

yes

characteristic, complemented, Sylow

156

#41

—

157

#41

—

158

C₂×Q₈

C₄⋊Dic₁₉

yes

—

159

C₂×D₄

—

160

C₂×D₄

—

161

C₂×D₄

C₄⋊Dic₁₉

yes

—

162

C₂²×C₄

—

163

C₂²×C₄

—

164

C₂²×C₄

C₂×D₇₆

yes

characteristic

165

C₂²×C₄

#64543

yes

—

166

M₁₆

—

167

M₁₆

—

152

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

152

—

174

C₄⋊C₄

—

175

C₂²⋊C₄

—

176

C₄²

—

177

C₄²

—

178

C₄²

—

179

C₄²

—

180

C₄²

C₂×Dic₃₈

yes

characteristic

181

C₄²

D₄×D₁₉

yes

—

182

C₄²

C₂²×Dic₁₉

yes

characteristic

183

C₂³

—

184

C₂³

#10597332

yes

characteristic

185

Q₈

—

186

D₄

—

187

D₄

—

188

D₄

—

189

D₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

#10597324

yes

—

200

C₂×C₄

#10597328

yes

characteristic

201

C₂×C₄

C₂×C₄⋊Dic₁₉

yes

characteristic

202

C₂×C₄

D₄×Dic₁₉

yes

—

203

C₈

—

204

C₈

—

205

C₈

—

206

C₈

—

207

C₈

—

152

—

208

C₂²

—

209

C₂²

—

210

C₂²

—

211

C₂²

—

212

C₂²

#11926419

yes

characteristic

213

C₄

—

214

C₄

—

215

C₄

—

216

C₄

—

217

C₄

#11926661

yes

—

218

C₄

#11926666

yes

—

219

C₄

#11926714

yes

characteristic

220

C₄

#11926724

yes

characteristic

221

C₂

—

222

C₂

—

223

C₂

#14563847

yes

characteristic

224

C₂

#14563912

yes

—

	subgroup	G/H
center	C₂×C₄	#10597328
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1543	C₂
socle	C₂²×C₁₉	#385
prime radical	C₁₉×#532	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1543	D₁₉
hypocenter	C₁₉	#8935
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1543

subgroup

G/H

center

C₂×C₄

#10597328

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1543

C₂

socle

C₂²×C₁₉

#385

prime radical

C₁₉×#532

C₂²

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1543

N	H ≅ G/N	type
3. #14562424	C₂	semidirect
4. #14561467	C₂	semidirect
17. C₁₉×#333	C₄	semidirect
18. C₁₉×#333	C₄	semidirect
19. C₁₉×#331	C₄	semidirect
125. #333	Dic₁₉	semidirect
126. #333	Dic₁₉	semidirect
127. #331	Dic₁₉	semidirect
155. C₁₉	#8935	semidirect

H ≅ G/N

type

3. #14562424

C₂

semidirect

4. #14561467

C₂

semidirect

17. C₁₉×#333

C₄

semidirect

18. C₁₉×#333

C₄

semidirect

19. C₁₉×#331

C₄

semidirect

125. #333

Dic₁₉

semidirect

126. #333

Dic₁₉

semidirect

127. #331

Dic₁₉

semidirect

155. C₁₉

#8935

semidirect

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

subgroup	index
#14572702	2
#14564464	2
#14562424	2
#14561467	2
C₁₉×#1543	2
#8935	19

subgroup

index

C₁₉×#1543

Subgroups — #18077049

Conjugacy classes of subgroups

Complements

Maximal subgroups