Group #18089111 — subgroups

Subgroups — #18089111

Order 4864.

1318 conjugacy classes of subgroups; only the 267 normal subgroups are shown.

normal subgroups only

This group has 1318 conjugacy classes of subgroups — too many to draw. Only its 267 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	C₂²×#10597293	C₂	1	4	yes	maximal
2	#14563329	C₂	1	2	yes	maximal
3	C₂²×C₁₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
4	C₂²×#64520	C₂²	1	4	yes	—
5	C₂×#10597293	—	2	16	no	—
6	C₂×#10597293	—	2	8	no	—
7	#11926299	—	2	4	no	—
8	C₂³×Q₈×C₁₉	C₂²	1	2	yes	—
9	C₂×C₁₉×C₄⋊Q₈	—	2	8	no	—
10	C₂×C₁₉×C₄⋊Q₈	—	2	4	no	—
11	C₂²×C₄⋊C₄×C₁₉	C₄	1	4	yes	—
12	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×Q₈×C₁₉	—	2	4	no	—
14	C₂²×Q₈×C₁₉	—	2	4	no	—
15	C₂²×Q₈×C₁₉	—	2	8	no	—
16	C₂²×Q₈×C₁₉	—	2	8	no	—
17	C₂²×Q₈×C₁₉	D₄	1	8	yes	—
18	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
19	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
20	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
21	C₁₉×C₄⋊Q₈	—	2	32	no	—
22	C₂×C₄⋊C₄×C₁₉	—	2	16	no	—
23	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
24	C₂×C₄²×C₁₉	—	2	4	no	—
25	C₂×C₄²×C₁₉	D₄	1	4	yes	—
26	C₂×#64520	—	2	4	no	—
27	C₂×#64520	—	2	8	no	—
28	C₂×#64520	—	2	8	no	—
29	C₂×#64520	D₄	1	8	yes	—
30	C₂²×C₁₉⋊C₈	—	2	4	no	—
31	#10597293	—	2	32	no	—
32	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
33	C₂×Q₈×C₁₉	—	2	16	no	—
34	C₂×Q₈×C₁₉	—	2	8	no	—
35	C₂×Q₈×C₁₉	—	2	16	no	—
36	C₂×Q₈×C₁₉	—	2	8	no	—
37	C₂×Q₈×C₁₉	—	4	4	no	—
38	C₂×Q₈×C₁₉	—	4	8	no	—
39	C₂×Q₈×C₁₉	—	4	8	no	—
40	C₂×Q₈×C₁₉	—	4	4	no	—
41	C₂×Q₈×C₁₉	—	4	4	no	—
42	C₂×Q₈×C₁₉	—	4	4	no	—
43	C₂²×C₄×C₁₉	—	2	4	no	—
44	C₂²×C₄×C₁₉	—	2	8	no	—
45	C₂²×C₄×C₁₉	—	2	4	no	—
46	C₂²×C₄×C₁₉	—	2	4	no	—
47	C₂²×C₄×C₁₉	—	2	16	no	—
48	C₂²×C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
49	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
50	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
51	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
52	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
53	C₂²×C₄×C₁₉	#41	1	4	yes	—
54	C₄⋊C₄×C₁₉	—	2	32	no	—
55	C₄²×C₁₉	—	2	8	no	—
56	#64520	—	2	16	no	—
57	#64520	—	4	8	no	—
58	C₂×C₁₉⋊C₈	—	2	8	no	—
59	C₂×C₁₉⋊C₈	—	4	4	no	—
60	C₂×C₁₉⋊C₈	—	4	4	no	—
61	#10983	—	19	1	no	maximal, Sylow
62	C₂³×C₁₉	—	2	4	no	—
63	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
64	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
65	C₂³×C₁₉	C₄×D₄	1	4	yes	—
66	Q₈×C₁₉	—	4	16	no	—
67	Q₈×C₁₉	—	4	16	no	—
68	C₂×C₄×C₁₉	—	2	16	no	—
69	C₂×C₄×C₁₉	—	2	4	no	—
70	C₂×C₄×C₁₉	—	2	4	no	—
71	C₂×C₄×C₁₉	—	2	8	no	—
72	C₂×C₄×C₁₉	—	2	16	no	—
73	C₂×C₄×C₁₉	—	4	8	no	—
74	C₂×C₄×C₁₉	—	4	8	no	—
75	C₂×C₄×C₁₉	#101	1	8	yes	complemented
76	C₂×C₄×C₁₉	#120	1	4	yes	—
77	C₂×C₄×C₁₉	#120	1	4	yes	—
78	C₂×C₄×C₁₉	#121	1	4	yes	—
79	C₂×C₄×C₁₉	#121	1	8	yes	—
80	C₂×C₄×C₁₉	#123	1	4	yes	—
81	C₂×C₄×C₁₉	#124	1	2	yes	—
82	C₂×C₄×C₁₉	#127	1	2	yes	—
83	C₁₉⋊C₈	—	4	8	no	—
84	C₂²×C₄⋊Q₈	D₁₉	1	1	yes	characteristic
85	C₂²×#101	—	19	4	no	—
86	#1728	—	19	2	no	—
87	C₂²×C₁₉	—	2	8	no	—
88	C₂²×C₁₉	—	2	4	no	—
89	C₂²×C₁₉	#379	1	1	yes	characteristic
90	C₂²×C₁₉	#386	1	4	yes	—
91	C₂²×C₁₉	#390	1	2	yes	—
92	C₂²×C₁₉	C₂×#101	1	4	yes	—
93	C₄×C₁₉	—	2	8	no	—
94	C₄×C₁₉	—	4	8	no	—
95	C₄×C₁₉	#392	1	4	yes	—
96	C₄×C₁₉	#394	1	4	yes	—
97	C₂³×Q₈	C₂×D₁₉	1	2	yes	—
98	C₂²×M₁₆	—	19	4	no	—
99	C₂×C₄⋊Q₈	—	2	8	no	—
100	C₂×C₄⋊Q₈	—	2	4	no	—
101	C₂²×C₄⋊C₄	Dic₁₉	1	4	yes	—
102	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
103	C₂×#101	—	38	16	no	—
104	C₂×#101	—	38	8	no	—
105	#336	—	38	4	no	—
106	C₂×C₁₉	—	2	4	no	—
107	C₂×C₁₉	#1438	1	1	yes	characteristic
108	C₂×C₁₉	#1784	1	2	yes	—
109	C₂×C₁₉	#1966	1	4	yes	—
110	C₂²×Q₈	—	2	8	no	—
111	C₂²×Q₈	—	2	8	no	—
112	C₂²×Q₈	—	2	4	no	—
113	C₂²×Q₈	—	2	4	no	—
114	C₂²×Q₈	C₂²⋊D₁₉	1	8	yes	—
115	C₂³×C₄	C₂×Dic₁₉	1	4	yes	—
116	C₂³×C₄	C₂×Dic₁₉	1	2	yes	—
117	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
118	C₂×M₁₆	—	19	8	no	—
119	C₂×M₁₆	—	38	4	no	—
120	C₂×M₁₆	—	38	8	no	—
121	C₂×M₁₆	—	38	8	no	—
122	C₂²×C₈	—	38	4	no	—
123	C₄⋊Q₈	—	2	32	no	—
124	C₂×C₄⋊C₄	—	2	16	no	—
125	C₂×C₄⋊C₄	—	2	8	no	—
126	C₂×C₄²	—	2	4	no	—
127	C₂×C₄²	C₂²⋊D₁₉	1	4	yes	—
128	#101	—	38	32	no	—
129	C₁₉	#10983	1	1	yes	characteristic, complemented, Sylow
130	C₂⁴	C₂²×Dic₁₉	1	1	yes	characteristic
131	C₂×Q₈	—	2	8	no	—
132	C₂×Q₈	—	2	8	no	—
133	C₂×Q₈	—	2	16	no	—
134	C₂×Q₈	—	2	16	no	—
135	C₂×Q₈	—	4	4	no	—
136	C₂×Q₈	—	4	4	no	—
137	C₂×Q₈	—	4	4	no	—
138	C₂×Q₈	—	4	8	no	—
139	C₂×Q₈	—	4	8	no	—
140	C₂×Q₈	—	4	4	no	—
141	C₂²×C₄	—	2	4	no	—
142	C₂²×C₄	—	2	8	no	—
143	C₂²×C₄	—	2	16	no	—
144	C₂²×C₄	—	2	4	no	—
145	C₂²×C₄	—	2	4	no	—
146	C₂²×C₄	C₂²⋊Dic₁₉	1	8	yes	—
147	C₂²×C₄	C₂²⋊Dic₁₉	1	4	yes	—
148	C₂²×C₄	D₄×D₁₉	1	4	yes	—
149	C₂²×C₄	#64543	1	4	yes	—
150	C₂²×C₄	C₂×C₂²⋊D₁₉	1	4	yes	—
151	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
152	M₁₆	—	38	16	no	—
153	M₁₆	—	76	8	no	—
154	C₂×C₈	—	38	8	no	—
155	C₂×C₈	—	76	4	no	—
156	C₂×C₈	—	76	4	no	—
157	C₄⋊C₄	—	2	32	no	—
158	C₄²	—	2	8	no	—
159	C₂³	—	2	4	no	—
160	C₂³	D₄×Dic₁₉	1	4	yes	—
161	C₂³	C₂×C₂²⋊Dic₁₉	1	2	yes	—
162	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
163	Q₈	—	4	16	no	—
164	Q₈	—	4	16	no	—
165	C₂×C₄	—	2	16	no	—
166	C₂×C₄	—	2	4	no	—
167	C₂×C₄	—	2	4	no	—
168	C₂×C₄	—	2	8	no	—
169	C₂×C₄	—	2	16	no	—
170	C₂×C₄	—	4	8	no	—
171	C₂×C₄	—	4	8	no	—
172	C₂×C₄	#10597293	1	8	yes	complemented
173	C₂×C₄	#10597381	1	4	yes	—
174	C₂×C₄	#10597382	1	2	yes	—
175	C₂×C₄	#10597383	1	4	yes	—
176	C₂×C₄	#10597384	1	4	yes	—
177	C₂×C₄	#10597385	1	8	yes	—
178	C₂×C₄	#10597386	1	2	yes	—
179	C₂×C₄	#10597399	1	4	yes	—
180	C₈	—	76	8	no	—
181	C₂²	—	2	8	no	—
182	C₂²	—	2	4	no	—
183	C₂²	#11926400	1	1	yes	characteristic
184	C₂²	#11926424	1	4	yes	—
185	C₂²	#11926447	1	2	yes	—
186	C₂²	C₂×#10597293	1	4	yes	—
187	C₄	—	2	8	no	—
188	C₄	—	4	8	no	—
189	C₄	#11926452	1	4	yes	—
190	C₄	#11926458	1	4	yes	—
191	C₂	—	2	4	no	—
192	C₂	#14561876	1	1	yes	characteristic
193	C₂	#14563559	1	2	yes	—
194	C₂	#14564480	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#10597293

C₂

yes

maximal

#14563329

C₂

yes

maximal

C₂²×C₁₉×C₄⋊Q₈

C₂

yes

maximal, characteristic

C₂²×#64520

C₂²

yes

—

C₂×#10597293

—

C₂×#10597293

—

#11926299

—

C₂³×Q₈×C₁₉

C₂²

yes

—

C₂×C₁₉×C₄⋊Q₈

—

C₂×C₁₉×C₄⋊Q₈

—

C₂²×C₄⋊C₄×C₁₉

C₄

yes

—

C₂²×C₄²×C₁₉

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

D₄

yes

—

C₂³×C₄×C₁₉

C₂×C₄

yes

—

C₂³×C₄×C₁₉

C₂×C₄

yes

—

C₂³×C₄×C₁₉

C₂³

yes

characteristic

C₁₉×C₄⋊Q₈

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

D₄

yes

—

—

—

—

D₄

yes

—

C₂²×C₁₉⋊C₈

—

#10597293

—

C₂⁴×C₁₉

C₂²×C₄

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

#41

yes

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#10983

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂³×C₁₉

C₄×D₄

yes

—

Q₈×C₁₉

—

Q₈×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

#101

yes

complemented

C₂×C₄×C₁₉

#120

yes

—

C₂×C₄×C₁₉

#120

yes

—

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

#123

yes

—

C₂×C₄×C₁₉

#124

yes

—

C₂×C₄×C₁₉

#127

yes

—

C₁₉⋊C₈

—

C₂²×C₄⋊Q₈

D₁₉

yes

characteristic

C₂²×#101

—

#1728

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#379

yes

characteristic

C₂²×C₁₉

#386

yes

—

C₂²×C₁₉

#390

yes

—

C₂²×C₁₉

C₂×#101

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#392

yes

—

C₄×C₁₉

#394

yes

—

C₂³×Q₈

C₂×D₁₉

yes

—

C₂²×M₁₆

—

C₂×C₄⋊Q₈

—

100

C₂×C₄⋊Q₈

—

101

C₂²×C₄⋊C₄

Dic₁₉

yes

—

102

C₂²×C₄²

C₂×D₁₉

yes

characteristic

103

C₂×#101

—

104

C₂×#101

—

105

#336

—

106

C₂×C₁₉

—

107

C₂×C₁₉

#1438

yes

characteristic

108

C₂×C₁₉

#1784

yes

—

109

C₂×C₁₉

#1966

yes

—

110

C₂²×Q₈

—

111

C₂²×Q₈

—

112

C₂²×Q₈

—

113

C₂²×Q₈

—

114

C₂²×Q₈

C₂²⋊D₁₉

yes

—

115

C₂³×C₄

C₂×Dic₁₉

yes

—

116

C₂³×C₄

C₂×Dic₁₉

yes

—

117

C₂³×C₄

C₂²×D₁₉

yes

characteristic

118

C₂×M₁₆

—

119

C₂×M₁₆

—

120

C₂×M₁₆

—

121

C₂×M₁₆

—

122

C₂²×C₈

—

123

C₄⋊Q₈

—

124

C₂×C₄⋊C₄

—

125

C₂×C₄⋊C₄

—

126

C₂×C₄²

—

127

C₂×C₄²

C₂²⋊D₁₉

yes

—

128

#101

—

129

C₁₉

#10983

yes

characteristic, complemented, Sylow

130

C₂⁴

C₂²×Dic₁₉

yes

characteristic

131

C₂×Q₈

—

132

C₂×Q₈

—

133

C₂×Q₈

—

134

C₂×Q₈

—

135

C₂×Q₈

—

136

C₂×Q₈

—

137

C₂×Q₈

—

138

C₂×Q₈

—

139

C₂×Q₈

—

140

C₂×Q₈

—

141

C₂²×C₄

—

142

C₂²×C₄

—

143

C₂²×C₄

—

144

C₂²×C₄

—

145

C₂²×C₄

—

146

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

147

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

148

C₂²×C₄

D₄×D₁₉

yes

—

149

C₂²×C₄

#64543

yes

—

150

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

151

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

152

M₁₆

—

153

M₁₆

—

154

C₂×C₈

—

155

C₂×C₈

—

156

C₂×C₈

—

157

C₄⋊C₄

—

158

C₄²

—

159

C₂³

—

160

C₂³

D₄×Dic₁₉

yes

—

161

C₂³

C₂×C₂²⋊Dic₁₉

yes

—

162

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

163

Q₈

—

164

Q₈

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

#10597293

yes

complemented

173

C₂×C₄

#10597381

yes

—

174

C₂×C₄

#10597382

yes

—

175

C₂×C₄

#10597383

yes

—

176

C₂×C₄

#10597384

yes

—

177

C₂×C₄

#10597385

yes

—

178

C₂×C₄

#10597386

yes

—

179

C₂×C₄

#10597399

yes

—

180

C₈

—

181

C₂²

—

182

C₂²

—

183

C₂²

#11926400

yes

characteristic

184

C₂²

#11926424

yes

—

185

C₂²

#11926447

yes

—

186

C₂²

C₂×#10597293

yes

—

187

C₄

—

188

C₄

—

189

C₄

#11926452

yes

—

190

C₄

#11926458

yes

—

191

C₂

—

192

C₂

#14561876

yes

characteristic

193

C₂

#14563559

yes

—

194

C₂

#14564480

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator, prime radical	C₂⁴×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂²×C₁₉×C₄⋊Q₈	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂²×C₄⋊Q₈	D₁₉
hypocenter	C₁₉	#10983
LCS	G ▷ C₂⁴×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂²×C₄⋊Q₈

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₁₉

commutator, prime radical

C₂⁴×C₁₉

C₂²×C₄

Frattini

C₂³×C₄

C₂²×D₁₉

Fitting

C₂²×C₁₉×C₄⋊Q₈

C₂

socle

C₂³×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂³×C₄×C₁₉

C₂³

hypercenter

C₂²×C₄⋊Q₈

D₁₉

hypocenter

C₁₉

#10983

LCS

G ▷ C₂⁴×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂²×C₄⋊Q₈

N	H ≅ G/N	type
75. C₂×C₄×C₁₉	#101	semidirect
129. C₁₉	#10983	semidirect
172. C₂×C₄	#10597293	semidirect

H ≅ G/N

type

75. C₂×C₄×C₁₉

#101

semidirect

129. C₁₉

#10983

semidirect

172. C₂×C₄

#10597293

semidirect

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

subgroup	index
C₂²×#10597293	2
#14563329	2
C₂²×C₁₉×C₄⋊Q₈	2
#10983	19

subgroup

index

C₂²×#10597293

#14563329

C₂²×C₁₉×C₄⋊Q₈

#10983

Subgroups — #18089111

Conjugacy classes of subgroups

Complements

Maximal subgroups