Group #18082399 — subgroups

Subgroups — #18082399

Order 4864.

510 conjugacy classes of subgroups; only the 195 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 195 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	C₂×#11926942	C₂	1	1	yes	maximal, characteristic
2	#14564596	C₂	1	2	yes	maximal
3	#14564437	C₂	1	2	yes	maximal
4	#14563795	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×#322	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597315	C₂²	1	2	yes	—
7	#11926942	—	2	2	no	—
8	#11926942	C₄	1	4	yes	complemented
9	C₂×#10597275	—	2	2	no	—
10	C₂×#10597274	—	2	2	no	—
11	C₂×#10597273	—	2	4	no	—
12	#11926414	C₂²	1	1	yes	characteristic
13	#11926414	C₂²	1	1	yes	characteristic
14	#11926307	—	2	4	no	—
15	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
16	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#322	—	2	2	no	—
18	C₂²×Dic₃₈	—	2	2	no	—
19	C₂²×C₈×C₁₉	D₄	1	4	yes	—
20	C₂²×C₈×C₁₉	D₄	1	2	yes	—
21	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
22	C₂×C₄⋊Dic₁₉	—	2	2	no	—
23	C₂×C₄⋊Dic₁₉	—	2	2	no	—
24	C₂×C₄⋊Dic₁₉	—	2	2	no	—
25	C₂×C₄⋊Dic₁₉	—	2	2	no	—
26	C₂×C₄⋊Dic₁₉	—	2	1	no	—
27	C₂×C₄⋊Dic₁₉	—	2	1	no	—
28	#10597315	—	2	2	no	—
29	#10597315	—	2	2	no	—
30	#10597315	—	2	2	no	—
31	#10597315	C₂×C₄	1	4	yes	—
32	C₄×C₈×C₁₉	—	2	2	no	—
33	C₄×C₈×C₁₉	—	2	2	no	—
34	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
35	C₄×C₈×C₁₉	D₄	1	2	yes	—
36	#10597275	—	4	4	no	—
37	#10597274	—	2	8	no	—
38	#10597273	—	4	8	no	—
39	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
41	C₂²×Dic₁₉	—	4	2	no	—
42	C₂²×Dic₁₉	—	4	1	no	—
43	C₂²×Dic₁₉	—	4	1	no	—
44	C₂×Dic₃₈	—	2	4	no	—
45	C₂×Dic₃₈	—	4	4	no	—
46	C₂×Dic₃₈	—	4	4	no	—
47	C₂×Dic₃₈	—	4	2	no	—
48	C₂×C₈×C₁₉	—	2	4	no	—
49	C₂×C₈×C₁₉	—	2	4	no	—
50	C₂×C₈×C₁₉	—	2	4	no	—
51	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
52	C₂×C₈×C₁₉	SD₁₆	1	4	yes	—
53	C₂×C₈×C₁₉	Q₁₆	1	4	yes	—
54	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
55	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
56	C₄²×C₁₉	#41	1	2	yes	—
57	C₄⋊Dic₁₉	—	2	4	no	—
58	C₄⋊Dic₁₉	—	2	4	no	—
59	C₄⋊Dic₁₉	—	4	2	no	—
60	C₄⋊Dic₁₉	—	4	2	no	—
61	C₄⋊Dic₁₉	—	4	2	no	—
62	C₄⋊Dic₁₉	—	4	2	no	—
63	C₄⋊Dic₁₉	—	4	4	no	—
64	C₄⋊Dic₁₉	—	4	4	no	—
65	#9841	—	19	1	no	maximal, Sylow
66	C₂³×C₁₉	#127	1	1	yes	characteristic
67	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
68	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
69	C₂×C₄×C₁₉	#121	1	2	yes	—
70	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
71	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
72	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
73	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
74	C₂×C₄×C₁₉	#137	1	4	yes	—
75	C₂×Dic₁₉	—	4	4	no	—
76	C₂×Dic₁₉	—	8	2	no	—
77	C₂×Dic₁₉	—	8	2	no	—
78	C₂×Dic₁₉	—	8	1	no	—
79	C₂×Dic₁₉	—	8	1	no	—
80	C₂×Dic₁₉	—	8	2	no	—
81	C₂×Dic₁₉	—	8	2	no	—
82	Dic₃₈	—	4	8	no	—
83	Dic₃₈	—	8	4	no	—
84	C₈×C₁₉	—	4	4	no	—
85	C₈×C₁₉	#103	1	8	yes	complemented
86	C₂×#498	—	19	1	no	—
87	#1990	—	19	2	no	—
88	#1956	—	19	2	no	—
89	#1845	—	19	1	no	—
90	C₂×#322	D₁₉	1	1	yes	characteristic
91	C₂²×C₁₉	#390	1	1	yes	characteristic
92	C₂²×C₁₉	#492	1	1	yes	characteristic
93	C₂²×C₁₉	#494	1	1	yes	characteristic
94	C₂²×C₁₉	#496	1	2	yes	—
95	C₂²×C₁₉	#497	1	2	yes	—
96	C₄×C₁₉	C₂×#103	1	2	yes	—
97	C₄×C₁₉	#440	1	4	yes	—
98	C₄×C₁₉	#468	1	4	yes	—
99	C₄×C₁₉	#487	1	2	yes	—
100	Dic₁₉	—	8	4	no	—
101	Dic₁₉	—	16	1	no	—
102	Dic₁₉	—	16	1	no	—
103	C₂×C₄⋊Q₈	—	19	2	no	—
104	#498	—	19	4	no	—
105	#498	—	38	2	no	—
106	C₂×#107	—	38	2	no	—
107	C₂×#106	—	38	2	no	—
108	C₂×#103	—	38	4	no	—
109	C₂×C₄×C₈	C₂×D₁₉	1	2	yes	—
110	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
111	#384	—	19	1	no	—
112	#384	—	19	1	no	—
113	#340	—	38	4	no	—
114	#322	—	2	2	no	—
115	C₂×C₁₉	#1715	1	1	yes	characteristic
116	C₂×C₁₉	#1716	1	1	yes	characteristic
117	C₂×C₁₉	#1723	1	2	yes	—
118	C₂×C₁₉	#1956	1	1	yes	characteristic
119	C₂×C₁₉	#1973	1	2	yes	—
120	C₂²×Q₈	—	38	2	no	—
121	C₂²×C₈	D₇₆	1	4	yes	—
122	C₂²×C₈	D₇₆	1	2	yes	—
123	C₄⋊Q₈	—	19	4	no	—
124	C₄⋊Q₈	—	38	2	no	—
125	C₄⋊Q₈	—	38	2	no	—
126	C₄⋊Q₈	—	38	2	no	—
127	C₂×C₄⋊C₄	—	38	2	no	—
128	C₂×C₄⋊C₄	—	38	2	no	—
129	C₂×C₄⋊C₄	—	38	2	no	—
130	C₂×C₄⋊C₄	—	38	2	no	—
131	C₂×C₄⋊C₄	—	38	1	no	—
132	C₂×C₄⋊C₄	—	38	1	no	—
133	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
134	#107	—	76	4	no	—
135	#106	—	38	8	no	—
136	#103	—	76	8	no	—
137	C₄×C₈	—	2	2	no	—
138	C₄×C₈	—	2	2	no	—
139	C₄×C₈	C₄×D₁₉	1	2	yes	—
140	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
141	C₁₉	#9841	1	1	yes	characteristic, complemented, Sylow
142	C₂×Q₈	—	38	4	no	—
143	C₂×Q₈	—	76	2	no	—
144	C₂×Q₈	—	76	4	no	—
145	C₂×Q₈	—	76	4	no	—
146	C₂²×C₄	—	76	2	no	—
147	C₂²×C₄	—	76	1	no	—
148	C₂²×C₄	—	76	1	no	—
149	C₂²×C₄	C₂×D₇₆	1	2	yes	—
150	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
151	C₂×C₈	—	2	4	no	—
152	C₂×C₈	—	2	4	no	—
153	C₂×C₈	—	2	4	no	—
154	C₂×C₈	#64516	1	4	yes	—
155	C₂×C₈	Dic₇₆	1	4	yes	—
156	C₂×C₈	(C₂×D₁₉)⋊C₄	1	4	yes	—
157	C₄⋊C₄	—	38	4	no	—
158	C₄⋊C₄	—	38	4	no	—
159	C₄⋊C₄	—	76	2	no	—
160	C₄⋊C₄	—	76	2	no	—
161	C₄⋊C₄	—	76	2	no	—
162	C₄⋊C₄	—	76	2	no	—
163	C₄⋊C₄	—	76	4	no	—
164	C₄⋊C₄	—	76	4	no	—
165	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
166	C₄²	#64541	1	2	yes	—
167	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
168	C₂³	#10597320	1	1	yes	characteristic
169	Q₈	—	76	8	no	—
170	Q₈	—	152	4	no	—
171	C₂×C₄	—	76	4	no	—
172	C₂×C₄	—	152	1	no	—
173	C₂×C₄	—	152	1	no	—
174	C₂×C₄	—	152	2	no	—
175	C₂×C₄	—	152	2	no	—
176	C₂×C₄	—	152	2	no	—
177	C₂×C₄	—	152	2	no	—
178	C₂×C₄	C₄×D₇₆	1	2	yes	—
179	C₂×C₄	#10597321	1	1	yes	characteristic
180	C₂×C₄	C₂×#64516	1	2	yes	—
181	C₂×C₄	C₂×Dic₇₆	1	2	yes	—
182	C₂×C₄	#10597354	1	4	yes	—
183	C₂×C₄	#10597355	1	4	yes	—
184	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
185	C₂×C₄	#10597376	1	2	yes	—
186	C₈	—	4	4	no	—
187	C₈	#10597273	1	8	yes	complemented
188	C₂²	#11926446	1	1	yes	characteristic
189	C₂²	#11926917	1	1	yes	characteristic
190	C₂²	#11926924	1	1	yes	characteristic
191	C₂²	#11926933	1	2	yes	—
192	C₂²	#11926938	1	2	yes	—
193	C₄	—	304	1	no	—
194	C₄	—	304	1	no	—
195	C₄	—	152	4	no	—
196	C₄	C₂×#10597273	1	2	yes	—
197	C₄	#11926646	1	4	yes	—
198	C₄	#11926790	1	4	yes	—
199	C₄	#11926895	1	2	yes	—
200	C₂	#14563263	1	1	yes	characteristic
201	C₂	#14563268	1	1	yes	characteristic
202	C₂	#14563312	1	2	yes	—
203	C₂	#14564437	1	1	yes	characteristic
204	C₂	#14564516	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926942

C₂

yes

maximal, characteristic

#14564596

C₂

yes

maximal

#14564437

C₂

yes

maximal

#14563795

C₂

yes

maximal, characteristic

C₂×C₁₉×#322

C₂

yes

maximal, characteristic

C₂×#10597315

C₂²

yes

—

#11926942

—

#11926942

C₄

yes

—

—

—

C₂²

yes

characteristic

#11926414

C₂²

yes

characteristic

#11926307

—

C₂×C₄×C₈×C₁₉

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#322

—

C₂²×Dic₃₈

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

—

—

—

C₂×C₄

yes

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

D₄

yes

—

#10597275

—

#10597274

—

#10597273

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₂×C₈×C₁₉

SD₁₆

yes

—

C₂×C₈×C₁₉

Q₁₆

yes

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

#124

yes

characteristic

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₂×C₄×C₁₉

C₂×Q₁₆

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

yes

—

—

—

—

D₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

#497

yes

—

C₄×C₁₉

C₂×#103

yes

—

C₄×C₁₉

#440

yes

—

C₄×C₁₉

#468

yes

—

C₄×C₁₉

#487

yes

—

100

Dic₁₉

—

101

Dic₁₉

—

102

Dic₁₉

—

103

C₂×C₄⋊Q₈

—

104

#498

—

105

#498

—

106

C₂×#107

—

107

C₂×#106

—

108

C₂×#103

—

109

C₂×C₄×C₈

C₂×D₁₉

yes

—

110

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

111

#384

—

112

#384

—

113

#340

—

114

#322

—

115

C₂×C₁₉

#1715

yes

characteristic

116

C₂×C₁₉

#1716

yes

characteristic

117

C₂×C₁₉

#1723

yes

—

118

C₂×C₁₉

#1956

yes

characteristic

119

C₂×C₁₉

#1973

yes

—

120

C₂²×Q₈

—

121

C₂²×C₈

D₇₆

yes

—

122

C₂²×C₈

D₇₆

yes

—

123

C₄⋊Q₈

—

124

C₄⋊Q₈

—

125

C₄⋊Q₈

—

126

C₄⋊Q₈

—

127

C₂×C₄⋊C₄

—

128

C₂×C₄⋊C₄

—

129

C₂×C₄⋊C₄

—

130

C₂×C₄⋊C₄

—

131

C₂×C₄⋊C₄

—

132

C₂×C₄⋊C₄

—

133

C₂×C₄²

C₂²×D₁₉

yes

characteristic

134

#107

—

135

#106

—

136

#103

—

137

C₄×C₈

—

138

C₄×C₈

—

139

C₄×C₈

C₄×D₁₉

yes

—

140

C₄×C₈

C₂²⋊D₁₉

yes

—

141

C₁₉

#9841

yes

characteristic, complemented, Sylow

142

C₂×Q₈

—

143

C₂×Q₈

—

144

C₂×Q₈

—

145

C₂×Q₈

—

146

C₂²×C₄

—

147

C₂²×C₄

—

148

C₂²×C₄

—

149

C₂²×C₄

C₂×D₇₆

yes

—

150

C₂²×C₄

C₂×D₇₆

yes

characteristic

151

C₂×C₈

—

152

C₂×C₈

—

153

C₂×C₈

—

154

C₂×C₈

#64516

yes

—

155

C₂×C₈

Dic₇₆

yes

—

156

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

—

157

C₄⋊C₄

—

158

C₄⋊C₄

—

159

C₄⋊C₄

—

160

C₄⋊C₄

—

161

C₄⋊C₄

—

162

C₄⋊C₄

—

163

C₄⋊C₄

—

164

C₄⋊C₄

—

165

C₄²

C₂×C₄×D₁₉

yes

characteristic

166

C₄²

#64541

yes

—

167

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

168

C₂³

#10597320

yes

characteristic

169

Q₈

—

170

Q₈

—

152

—

171

C₂×C₄

—

172

C₂×C₄

—

152

—

173

C₂×C₄

—

152

—

174

C₂×C₄

—

152

—

175

C₂×C₄

—

152

—

176

C₂×C₄

—

152

—

177

C₂×C₄

—

152

—

178

C₂×C₄

C₄×D₇₆

yes

—

179

C₂×C₄

#10597321

yes

characteristic

180

C₂×C₄

C₂×#64516

yes

—

181

C₂×C₄

C₂×Dic₇₆

yes

—

182

C₂×C₄

#10597354

yes

—

183

C₂×C₄

#10597355

yes

—

184

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

185

C₂×C₄

#10597376

yes

—

186

C₈

—

187

C₈

#10597273

yes

complemented

188

C₂²

#11926446

yes

characteristic

189

C₂²

#11926917

yes

characteristic

190

C₂²

#11926924

yes

characteristic

191

C₂²

#11926933

yes

—

192

C₂²

#11926938

yes

—

193

C₄

—

304

—

194

C₄

—

304

—

195

C₄

—

152

—

196

C₄

C₂×#10597273

yes

—

197

C₄

#11926646

yes

—

198

C₄

#11926790

yes

—

199

C₄

#11926895

yes

—

200

C₂

#14563263

yes

characteristic

201

C₂

#14563268

yes

characteristic

202

C₂

#14563312

yes

—

203

C₂

#14564437

yes

characteristic

204

C₂

#14564516

yes

—

	subgroup	G/H
center	C₂³	#10597320
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#322	C₂
socle, prime radical	C₂³×C₁₉	#127
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#322	D₁₉
hypocenter	C₁₉	#9841
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#322

subgroup

G/H

center

C₂³

#10597320

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₂×C₁₉×#322

C₂

socle, prime radical

C₂³×C₁₉

#127

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#322

N	H ≅ G/N	type
8. #11926942	C₄	semidirect
85. C₈×C₁₉	#103	semidirect
141. C₁₉	#9841	semidirect
187. C₈	#10597273	semidirect

H ≅ G/N

type

8. #11926942

C₄

semidirect

85. C₈×C₁₉

#103

semidirect

141. C₁₉

#9841

semidirect

187. C₈

#10597273

semidirect

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

subgroup	index
C₂×#11926942	2
#14564596	2
#14564437	2
#14563795	2
C₂×C₁₉×#322	2
#9841	19

subgroup

index

C₂×C₁₉×#322

Subgroups — #18082399

Conjugacy classes of subgroups

Complements

Maximal subgroups