Group #18085677 — subgroups

Subgroups — #18085677

Order 4864.

402 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 91 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	#14566940	C₂	1	1	yes	maximal, characteristic, complemented
2	#14562130	C₂	1	2	yes	maximal
3	#14561536	C₂	1	2	yes	maximal, complemented
4	#14561464	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1963	C₂	1	1	yes	maximal, characteristic
6	#11926597	C₂²	1	2	yes	—
7	#11926486	—	2	2	no	—
8	#11926478	—	2	2	no	—
9	C₄×Dic₁₉⋊C₄	—	2	2	no	—
10	C₄×C₄⋊Dic₁₉	C₂²	1	2	yes	—
11	#11926278	—	2	2	no	—
12	#11926278	—	2	2	no	—
13	C₁₉×#532	C₂²	1	1	yes	characteristic
14	C₁₉×#423	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#104	—	2	2	no	—
16	C₁₉×#376	C₂²	1	1	yes	characteristic
17	C₂×#41×C₁₉	—	2	1	no	—
18	C₂×M₁₆×C₁₉	—	2	1	no	—
19	C₁₉×C₄⋊Q₈	Q₈	1	1	yes	characteristic
20	C₁₉×#127	Q₈	1	1	yes	characteristic
21	C₁₉×#124	—	2	1	no	—
22	C₁₉×#121	—	2	2	no	—
23	C₄×D₄×C₁₉	—	2	2	no	—
24	C₂×C₄²×C₁₉	D₄	1	2	yes	—
25	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
26	C₂×C₄⋊Dic₁₉	—	2	2	no	—
27	C₂×Dic₁₉⋊C₄	—	2	2	no	—
28	C₂×Dic₁₉⋊C₄	—	2	2	no	—
29	C₂×C₄×Dic₁₉	—	2	2	no	—
30	C₁₉×C₄⋊C₈	—	2	2	no	—
31	C₁₉×#104	—	4	4	no	—
32	C₁₉×#95	—	2	2	no	—
33	C₁₉⋊#95	—	2	2	no	—
34	C₁₉⋊#95	—	2	2	no	—
35	C₁₉⋊#95	D₄	1	2	yes	—
36	C₁₉⋊#95	D₄	1	2	yes	—
37	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
38	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
39	C₄×C₁₉⋊C₈	—	2	2	no	—
40	#41×C₁₉	—	4	2	no	—
41	#41×C₁₉	—	4	2	no	—
42	C₂×Q₈×C₁₉	—	2	1	no	—
43	C₂×D₄×C₁₉	—	2	1	no	—
44	C₂×D₄×C₁₉	—	2	2	no	—
45	C₂×D₄×C₁₉	—	4	1	no	—
46	C₂²×C₄×C₁₉	—	2	2	no	—
47	C₂²×C₄×C₁₉	—	4	1	no	—
48	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
49	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
50	C₂²×Dic₁₉	—	2	2	no	—
51	C₂²×Dic₁₉	—	2	2	no	—
52	M₁₆×C₁₉	—	4	2	no	—
53	C₂×C₈×C₁₉	—	4	1	no	—
54	C₄⋊C₄×C₁₉	—	2	2	no	—
55	C₂²⋊C₄×C₁₉	—	4	2	no	—
56	C₄²×C₁₉	—	2	2	no	—
57	C₄²×C₁₉	—	2	2	no	—
58	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
59	C₄²×C₁₉	#41	1	1	yes	characteristic
60	C₄²×C₁₉	#41	1	2	yes	—
61	C₄⋊Dic₁₉	—	4	4	no	—
62	Dic₁₉⋊C₄	—	4	4	no	—
63	Dic₁₉⋊C₄	—	4	4	no	—
64	C₄×Dic₁₉	—	4	2	no	—
65	C₄×Dic₁₉	—	4	2	no	—
66	C₂×C₁₉⋊C₈	—	4	2	no	—
67	#10372	—	19	1	no	maximal, Sylow
68	C₂³×C₁₉	—	4	1	no	—
69	C₂³×C₁₉	#120	1	1	yes	characteristic
70	Q₈×C₁₉	—	4	2	no	—
71	D₄×C₁₉	—	4	2	no	—
72	D₄×C₁₉	—	8	2	no	—
73	D₄×C₁₉	—	8	2	no	—
74	C₂×C₄×C₁₉	—	4	2	no	—
75	C₂×C₄×C₁₉	—	4	2	no	—
76	C₂×C₄×C₁₉	—	4	2	no	—
77	C₂×C₄×C₁₉	—	4	1	no	—
78	C₂×C₄×C₁₉	—	4	2	no	—
79	C₂×C₄×C₁₉	—	8	1	no	—
80	C₂×C₄×C₁₉	—	8	1	no	—
81	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
82	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
83	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
84	C₂×C₄×C₁₉	#124	1	2	yes	—
85	C₂×C₄×C₁₉	#135	1	2	yes	—
86	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
87	C₂×Dic₁₉	—	2	4	no	—
88	C₂×Dic₁₉	—	4	2	no	—
89	C₂×Dic₁₉	—	4	2	no	—
90	C₂×Dic₁₉	—	4	2	no	—
91	C₂×Dic₁₉	—	4	2	no	—
92	C₂×Dic₁₉	—	4	2	no	—
93	C₈×C₁₉	—	8	1	no	—
94	C₁₉⋊C₈	—	8	2	no	—
95	#2402	—	19	1	no	—
96	#1963	D₁₉	1	1	yes	characteristic
97	#1502	—	19	2	no	—
98	#1303	—	19	2	no	—
99	#1274	—	19	1	no	—
100	C₂²×C₁₉	—	2	2	no	—
101	C₂²×C₁₉	—	8	1	no	—
102	C₂²×C₁₉	—	8	2	no	—
103	C₂²×C₁₉	#393	1	1	yes	characteristic
104	C₂²×C₁₉	#449	1	2	yes	—
105	C₄×C₁₉	—	2	2	no	—
106	C₄×C₁₉	—	2	2	no	—
107	C₄×C₁₉	—	8	2	no	—
108	C₄×C₁₉	—	8	1	no	—
109	C₄×C₁₉	#478	1	2	yes	—
110	C₄×C₁₉	#488	1	1	yes	characteristic
111	C₄×C₁₉	#490	1	1	yes	characteristic
112	Dic₁₉	—	4	4	no	—
113	Dic₁₉	—	8	2	no	—
114	#532	C₂×D₁₉	1	1	yes	characteristic
115	#431	—	19	2	no	—
116	#423	C₂×D₁₉	1	1	yes	characteristic
117	C₂×#104	—	2	2	no	—
118	#400	—	38	2	no	—
119	#398	—	38	2	no	—
120	C₄×C₄⋊C₄	—	19	2	no	—
121	C₄×C₄⋊C₄	—	38	2	no	—
122	#376	C₂×D₁₉	1	1	yes	characteristic
123	#327	—	38	2	no	—
124	#327	—	38	2	no	—
125	C₂×C₁₉	—	2	2	no	—
126	C₂×C₁₉	—	16	1	no	—
127	C₂×C₁₉	#2025	1	1	yes	characteristic
128	C₂×C₁₉	#2031	1	2	yes	—
129	C₂×#41	—	2	1	no	—
130	C₂×M₁₆	—	2	1	no	—
131	C₄⋊Q₈	Dic₃₈	1	1	yes	characteristic
132	#127	Dic₃₈	1	1	yes	characteristic
133	#124	—	2	1	no	—
134	#121	—	2	2	no	—
135	C₄×D₄	—	2	2	no	—
136	C₂×C₄⋊C₄	—	38	2	no	—
137	C₂×C₄⋊C₄	—	38	2	no	—
138	C₂×C₄⋊C₄	—	38	2	no	—
139	C₂×C₄²	—	38	2	no	—
140	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
141	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
142	C₄⋊C₈	—	2	2	no	—
143	C₄⋊C₈	—	38	2	no	—
144	#104	—	4	4	no	—
145	C₂²⋊C₈	—	38	2	no	—
146	C₄×C₈	—	38	2	no	—
147	#95	—	2	2	no	—
148	#95	—	19	2	no	—
149	#95	—	19	2	no	—
150	#95	—	38	2	no	—
151	#95	—	38	2	no	—
152	C₁₉	#10372	1	1	yes	characteristic, complemented, Sylow
153	#41	—	4	2	no	—
154	#41	—	4	2	no	—
155	C₂×Q₈	—	2	1	no	—
156	C₂×D₄	—	2	2	no	—
157	C₂×D₄	—	2	1	no	—
158	C₂×D₄	—	4	1	no	—
159	C₂²×C₄	—	2	2	no	—
160	C₂²×C₄	—	4	1	no	—
161	C₂²×C₄	—	38	2	no	—
162	C₂²×C₄	—	38	2	no	—
163	C₂²×C₄	D₄×D₁₉	1	2	yes	—
164	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
165	M₁₆	—	4	2	no	—
166	C₂×C₈	—	4	1	no	—
167	C₂×C₈	—	76	2	no	—
168	C₄⋊C₄	—	2	2	no	—
169	C₄⋊C₄	—	76	4	no	—
170	C₄⋊C₄	—	76	4	no	—
171	C₄⋊C₄	—	76	4	no	—
172	C₂²⋊C₄	—	4	2	no	—
173	C₄²	—	2	2	no	—
174	C₄²	—	2	2	no	—
175	C₄²	—	76	2	no	—
176	C₄²	—	76	2	no	—
177	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
178	C₄²	#64541	1	1	yes	characteristic
179	C₄²	#64543	1	2	yes	—
180	C₂³	—	4	1	no	—
181	C₂³	#10597383	1	1	yes	characteristic
182	Q₈	—	4	2	no	—
183	D₄	—	4	2	no	—
184	D₄	—	8	2	no	—
185	D₄	—	8	2	no	—
186	C₂×C₄	—	4	2	no	—
187	C₂×C₄	—	4	2	no	—
188	C₂×C₄	—	4	2	no	—
189	C₂×C₄	—	4	2	no	—
190	C₂×C₄	—	4	1	no	—
191	C₂×C₄	—	8	1	no	—
192	C₂×C₄	—	8	1	no	—
193	C₂×C₄	—	38	4	no	—
194	C₂×C₄	—	76	2	no	—
195	C₂×C₄	—	76	2	no	—
196	C₂×C₄	—	76	2	no	—
197	C₂×C₄	—	76	2	no	—
198	C₂×C₄	—	76	2	no	—
199	C₂×C₄	#10597324	1	2	yes	—
200	C₂×C₄	#10597331	1	2	yes	—
201	C₂×C₄	#10597370	1	1	yes	characteristic
202	C₂×C₄	#10597378	1	2	yes	—
203	C₂×C₄	#10597382	1	1	yes	characteristic
204	C₂×C₄	#10597396	1	2	yes	—
205	C₈	—	8	1	no	—
206	C₈	—	152	2	no	—
207	C₂²	—	2	2	no	—
208	C₂²	—	8	1	no	—
209	C₂²	—	8	2	no	—
210	C₂²	#11926456	1	1	yes	characteristic
211	C₂²	#11926687	1	2	yes	—
212	C₄	—	2	2	no	—
213	C₄	—	2	2	no	—
214	C₄	—	8	2	no	—
215	C₄	—	8	1	no	—
216	C₄	—	76	4	no	—
217	C₄	—	152	2	no	—
218	C₄	#11926844	1	2	yes	—
219	C₄	#11926898	1	1	yes	characteristic
220	C₄	#11926908	1	1	yes	characteristic
221	C₂	—	2	2	no	—
222	C₂	—	16	1	no	—
223	C₂	#14564781	1	1	yes	characteristic
224	C₂	#14564805	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14566940

C₂

yes

maximal, characteristic, complemented

#14562130

C₂

yes

maximal

#14561536

C₂

yes

maximal, complemented

#14561464

C₂

yes

maximal, characteristic, complemented

C₁₉×#1963

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

—

#11926486

—

#11926478

—

C₄×Dic₁₉⋊C₄

—

C₄×C₄⋊Dic₁₉

C₂²

yes

—

#11926278

—

#11926278

—

C₁₉×#532

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₂×C₁₉×#104

—

C₁₉×#376

C₂²

yes

characteristic

C₂×#41×C₁₉

—

C₂×M₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

Q₈

yes

characteristic

C₁₉×#127

Q₈

yes

characteristic

C₁₉×#124

—

C₁₉×#121

—

C₄×D₄×C₁₉

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×Dic₁₉⋊C₄

—

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

—

C₁₉×C₄⋊C₈

—

C₁₉×#104

—

C₁₉×#95

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₁₉⋊#95

D₄

yes

—

C₁₉⋊#95

D₄

yes

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×Q₈

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

#10372

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

#120

yes

characteristic

Q₈×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

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#2402

—

#1963

D₁₉

yes

—

—

—

100

C₂²×C₁₉

—

101

C₂²×C₁₉

—

102

C₂²×C₁₉

—

103

C₂²×C₁₉

#393

yes

characteristic

104

C₂²×C₁₉

#449

yes

—

105

C₄×C₁₉

—

106

C₄×C₁₉

—

107

C₄×C₁₉

—

108

C₄×C₁₉

—

109

C₄×C₁₉

#478

yes

—

110

C₄×C₁₉

#488

yes

characteristic

111

C₄×C₁₉

#490

yes

characteristic

112

Dic₁₉

—

113

Dic₁₉

—

114

#532

C₂×D₁₉

yes

characteristic

115

#431

—

116

#423

C₂×D₁₉

yes

characteristic

117

C₂×#104

—

118

#400

—

119

#398

—

120

C₄×C₄⋊C₄

—

121

C₄×C₄⋊C₄

—

122

#376

C₂×D₁₉

yes

characteristic

123

#327

—

124

#327

—

125

C₂×C₁₉

—

126

C₂×C₁₉

—

127

C₂×C₁₉

#2025

yes

characteristic

128

C₂×C₁₉

#2031

yes

—

129

C₂×#41

—

130

C₂×M₁₆

—

131

C₄⋊Q₈

Dic₃₈

yes

characteristic

132

#127

Dic₃₈

yes

characteristic

133

#124

—

134

#121

—

135

C₄×D₄

—

136

C₂×C₄⋊C₄

—

137

C₂×C₄⋊C₄

—

138

C₂×C₄⋊C₄

—

139

C₂×C₄²

—

140

C₂×C₄²

C₂²⋊D₁₉

yes

—

141

C₂×C₄²

C₂²×D₁₉

yes

characteristic

142

C₄⋊C₈

—

143

C₄⋊C₈

—

144

#104

—

145

C₂²⋊C₈

—

146

C₄×C₈

—

147

#95

—

148

#95

—

149

#95

—

150

#95

—

151

#95

—

152

C₁₉

#10372

yes

characteristic, complemented, Sylow

153

#41

—

154

#41

—

155

C₂×Q₈

—

156

C₂×D₄

—

157

C₂×D₄

—

158

C₂×D₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

—

163

C₂²×C₄

D₄×D₁₉

yes

—

164

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

165

M₁₆

—

166

C₂×C₈

—

167

C₂×C₈

—

168

C₄⋊C₄

—

169

C₄⋊C₄

—

170

C₄⋊C₄

—

171

C₄⋊C₄

—

172

C₂²⋊C₄

—

173

C₄²

—

174

C₄²

—

175

C₄²

—

176

C₄²

—

177

C₄²

C₂×Dic₃₈

yes

characteristic

178

C₄²

#64541

yes

characteristic

179

C₄²

#64543

yes

—

180

C₂³

—

181

C₂³

#10597383

yes

characteristic

182

Q₈

—

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

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

#10597324

yes

—

200

C₂×C₄

#10597331

yes

—

201

C₂×C₄

#10597370

yes

characteristic

202

C₂×C₄

#10597378

yes

—

203

C₂×C₄

#10597382

yes

characteristic

204

C₂×C₄

#10597396

yes

—

205

C₈

—

206

C₈

—

152

—

207

C₂²

—

208

C₂²

—

209

C₂²

—

210

C₂²

#11926456

yes

characteristic

211

C₂²

#11926687

yes

—

212

C₄

—

213

C₄

—

214

C₄

—

215

C₄

—

216

C₄

—

217

C₄

—

152

—

218

C₄

#11926844

yes

—

219

C₄

#11926898

yes

characteristic

220

C₄

#11926908

yes

characteristic

221

C₂

—

222

C₂

—

223

C₂

#14564781

yes

characteristic

224

C₂

#14564805

yes

—

	subgroup	G/H
center	C₂×C₄	#10597382
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1963	C₂
socle	C₂²×C₁₉	#393
prime radical	C₁₉×#532	C₂²
hypercenter	#1963	D₁₉
hypocenter	C₁₉	#10372
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1963

subgroup

G/H

center

C₂×C₄

#10597382

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1963

C₂

socle

C₂²×C₁₉

#393

prime radical

C₁₉×#532

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1963

N	H ≅ G/N	type
1. #14566940	C₂	semidirect
3. #14561536	C₂	semidirect
4. #14561464	C₂	semidirect
152. C₁₉	#10372	semidirect

H ≅ G/N

type

1. #14566940

C₂

semidirect

3. #14561536

C₂

semidirect

4. #14561464

C₂

semidirect

152. C₁₉

#10372

semidirect

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

subgroup	index
#14566940	2
#14562130	2
#14561536	2
#14561464	2
C₁₉×#1963	2
#10372	19

subgroup

index

C₁₉×#1963

Subgroups — #18085677

Conjugacy classes of subgroups

Complements

Maximal subgroups