Group #18077863 — subgroups

Subgroups — #18077863

Order 4864.

426 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 103 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	#14573960	C₂	1	1	yes	maximal, characteristic
2	#14572737	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562053	C₂	1	2	yes	maximal
4	#14561473	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1526	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927094	C₂²	1	1	yes	characteristic
7	#11926901	—	2	2	no	—
8	#11926896	C₄	1	2	yes	—
9	#11926892	C₄	1	2	yes	—
10	#11926675	—	2	2	no	—
11	Q₈×C₁₉⋊C₈	—	2	2	no	—
12	#11926605	—	2	2	no	—
13	#11926597	C₂²	1	2	yes	—
14	#11926538	—	2	2	no	—
15	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
16	#11926273	—	2	2	no	—
17	#11926273	—	2	2	no	—
18	C₁₉×#533	C₂²	1	1	yes	characteristic
19	C₄×M₁₆×C₁₉	C₂²	1	2	yes	—
20	C₁₉×#330	—	2	2	no	—
21	C₂×#64541	—	2	1	no	—
22	C₂×M₁₆×C₁₉	—	2	2	no	—
23	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
24	C₁₉×#125	D₄	1	2	yes	—
25	C₁₉×C₂²⋊Q₈	—	2	2	no	—
26	C₄×Q₈×C₁₉	—	2	2	no	—
27	C₁₉×#117	D₄	1	2	yes	—
28	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
29	#10597376	—	2	2	no	—
30	C₂²×C₁₉⋊C₈	—	2	1	no	—
31	#10597321	—	2	1	no	—
32	#10597320	C₂×C₄	1	1	yes	characteristic
33	C₄×D₇₆	—	2	2	no	—
34	#10597315	C₂×C₄	1	1	yes	characteristic
35	C₁₉×#97	—	2	2	no	—
36	C₄×C₈×C₁₉	—	2	2	no	—
37	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
38	#10597267	—	2	4	no	—
39	#10597266	—	2	4	no	—
40	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
41	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
42	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
43	#10597260	—	2	2	no	—
44	C₄×C₁₉⋊C₈	—	2	2	no	—
45	C₄×C₁₉⋊C₈	—	2	2	no	—
46	C₄×C₁₉⋊C₈	—	2	1	no	—
47	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
48	C₂×Q₈×C₁₉	—	2	2	no	—
49	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₉	#41	1	2	yes	—
51	C₂×C₂²⋊D₁₉	—	4	1	no	—
52	#64541	—	4	4	no	—
53	C₂×D₇₆	—	2	1	no	—
54	C₂×D₇₆	—	2	2	no	—
55	C₂×C₄×D₁₉	—	4	1	no	—
56	C₂×Dic₃₈	—	2	1	no	—
57	M₁₆×C₁₉	—	2	4	no	—
58	M₁₆×C₁₉	—	4	2	no	—
59	C₂×C₈×C₁₉	—	4	2	no	—
60	C₄⋊C₄×C₁₉	—	2	2	no	—
61	C₄⋊C₄×C₁₉	—	2	4	no	—
62	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
63	C₂²⋊C₄×C₁₉	—	2	2	no	—
64	C₄²×C₁₉	—	2	2	no	—
65	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
66	C₄²×C₁₉	C₂×D₄	1	2	yes	—
67	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
68	(C₂×D₁₉)⋊C₄	—	4	2	no	—
69	C₄⋊Dic₁₉	—	2	2	no	—
70	C₂×C₁₉⋊C₈	—	2	2	no	—
71	C₂×C₁₉⋊C₈	—	2	2	no	—
72	C₂×C₁₉⋊C₈	—	2	2	no	—
73	C₂×C₁₉⋊C₈	—	4	2	no	—
74	#9070	—	19	1	no	maximal, Sylow
75	C₂³×C₁₉	#123	1	1	yes	characteristic
76	C₂²×D₁₉	—	4	1	no	—
77	Q₈×C₁₉	—	4	2	no	—
78	Q₈×C₁₉	—	4	2	no	—
79	C₂×C₄×C₁₉	—	2	2	no	—
80	C₂×C₄×C₁₉	—	2	2	no	—
81	C₂×C₄×C₁₉	—	2	2	no	—
82	C₂×C₄×C₁₉	—	2	4	no	—
83	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
85	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
86	C₂×C₄×C₁₉	#121	1	2	yes	—
87	C₂²⋊D₁₉	—	8	2	no	—
88	C₂×Dic₁₉	—	4	1	no	—
89	D₇₆	—	4	2	no	—
90	D₇₆	—	4	2	no	—
91	D₇₆	—	4	2	no	—
92	C₄×D₁₉	—	8	2	no	—
93	Dic₃₈	—	4	2	no	—
94	C₈×C₁₉	—	4	4	no	—
95	C₁₉⋊C₈	—	4	2	no	—
96	C₁₉⋊C₈	—	4	2	no	—
97	C₁₉⋊C₈	—	4	2	no	—
98	#3131	—	19	1	no	—
99	#2986	—	19	1	no	—
100	#1526	D₁₉	1	1	yes	characteristic, complemented
101	#1484	—	19	2	no	—
102	#1278	—	19	2	no	—
103	C₂²×C₁₉	—	2	2	no	—
104	C₂²×C₁₉	—	2	1	no	—
105	C₂²×C₁₉	#386	1	1	yes	characteristic
106	C₂×D₁₉	—	8	2	no	—
107	C₂×D₁₉	—	8	1	no	—
108	C₄×C₁₉	—	2	2	no	—
109	C₄×C₁₉	—	2	1	no	—
110	C₄×C₁₉	—	4	4	no	—
111	C₄×C₁₉	#443	1	2	yes	—
112	C₄×C₁₉	#444	1	2	yes	—
113	C₄×C₁₉	#454	1	2	yes	—
114	Dic₁₉	—	8	1	no	—
115	#533	C₂×D₁₉	1	1	yes	characteristic
116	#532	—	19	1	no	—
117	#488	—	38	2	no	—
118	#487	—	19	2	no	—
119	#486	—	19	2	no	—
120	#446	—	38	2	no	—
121	C₈×Q₈	—	38	2	no	—
122	#433	—	38	2	no	—
123	#431	—	19	2	no	—
124	#416	—	38	2	no	—
125	C₄×M₁₆	C₂×D₁₉	1	2	yes	—
126	C₂×C₄×C₈	—	19	1	no	—
127	#330	—	2	2	no	—
128	D₄⋊C₈	—	38	2	no	—
129	D₄⋊C₈	—	38	2	no	—
130	C₂×C₁₉	—	4	1	no	—
131	C₂×C₁₉	#1876	1	2	yes	—
132	C₂×C₁₉	#1888	1	1	yes	characteristic
133	D₁₉	—	16	1	no	—
134	C₂×#41	—	38	1	no	—
135	C₂×M₁₆	—	2	2	no	—
136	C₂²×C₈	—	38	1	no	—
137	C₄⋊Q₈	—	19	1	no	—
138	C₄⋊Q₈	C₄×D₁₉	1	2	yes	—
139	#127	—	19	1	no	—
140	#125	C₂²⋊D₁₉	1	2	yes	—
141	#124	—	38	1	no	—
142	C₂²⋊Q₈	—	2	2	no	—
143	#121	—	38	2	no	—
144	C₄×Q₈	—	2	2	no	—
145	C₄×D₄	—	38	2	no	—
146	#117	D₇₆	1	2	yes	—
147	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
148	C₄⋊C₈	—	19	2	no	—
149	C₄⋊C₈	—	19	2	no	—
150	C₄⋊C₈	—	38	4	no	—
151	#103	—	38	4	no	—
152	#102	—	38	4	no	—
153	C₂²⋊C₈	—	38	2	no	—
154	#97	—	2	2	no	—
155	#97	—	38	2	no	—
156	C₄×C₈	—	2	2	no	—
157	C₄×C₈	—	19	2	no	—
158	C₄×C₈	—	38	2	no	—
159	C₄×C₈	—	38	2	no	—
160	C₄×C₈	—	38	1	no	—
161	C₁₉	#9070	1	1	yes	characteristic, complemented, Sylow
162	#41	—	76	4	no	—
163	C₂×Q₈	—	2	2	no	—
164	C₂×Q₈	—	38	1	no	—
165	C₂×D₄	—	38	2	no	—
166	C₂×D₄	—	38	1	no	—
167	C₂×D₄	—	76	1	no	—
168	C₂²×C₄	—	76	1	no	—
169	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
170	C₂²×C₄	#64543	1	2	yes	—
171	M₁₆	—	2	4	no	—
172	M₁₆	—	4	2	no	—
173	C₂×C₈	—	4	2	no	—
174	C₂×C₈	—	38	2	no	—
175	C₂×C₈	—	38	2	no	—
176	C₂×C₈	—	38	2	no	—
177	C₂×C₈	—	76	2	no	—
178	C₄⋊C₄	—	2	4	no	—
179	C₄⋊C₄	—	2	2	no	—
180	C₄⋊C₄	—	38	2	no	—
181	C₄⋊C₄	(C₂×D₁₉)⋊C₄	1	4	yes	—
182	C₂²⋊C₄	—	2	2	no	—
183	C₂²⋊C₄	—	76	2	no	—
184	C₄²	—	2	2	no	—
185	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
186	C₄²	D₄×D₁₉	1	2	yes	—
187	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
188	C₂³	—	76	1	no	—
189	C₂³	#10597332	1	1	yes	characteristic
190	Q₈	—	4	2	no	—
191	Q₈	—	4	2	no	—
192	Q₈	—	76	2	no	—
193	D₄	—	76	2	no	—
194	D₄	—	76	2	no	—
195	D₄	—	76	2	no	—
196	D₄	—	152	2	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	2	2	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	4	no	—
201	C₂×C₄	—	76	1	no	—
202	C₂×C₄	—	152	2	no	—
203	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
204	C₂×C₄	#10597328	1	1	yes	characteristic
205	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
206	C₂×C₄	#10597385	1	2	yes	—
207	C₈	—	4	4	no	—
208	C₈	—	76	2	no	—
209	C₈	—	76	2	no	—
210	C₈	—	76	2	no	—
211	C₂²	—	2	2	no	—
212	C₂²	—	2	1	no	—
213	C₂²	—	152	2	no	—
214	C₂²	—	152	1	no	—
215	C₂²	#11926421	1	1	yes	characteristic
216	C₄	—	2	2	no	—
217	C₄	—	2	1	no	—
218	C₄	—	4	4	no	—
219	C₄	—	152	1	no	—
220	C₄	#11926658	1	2	yes	—
221	C₄	#11926663	1	2	yes	—
222	C₄	#11926719	1	2	yes	—
223	C₂	—	4	1	no	—
224	C₂	—	304	1	no	—
225	C₂	#14563960	1	2	yes	—
226	C₂	#14564036	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14573960

C₂

yes

maximal, characteristic

#14572737

C₂

yes

maximal, characteristic, complemented

#14562053

C₂

yes

maximal

#14561473

C₂

yes

maximal, complemented

C₁₉×#1526

C₂

yes

maximal, characteristic, complemented

#11927094

C₂²

yes

characteristic

#11926901

—

#11926896

C₄

yes

—

#11926892

C₄

yes

—

#11926675

—

Q₈×C₁₉⋊C₈

—

#11926605

—

#11926597

C₂²

yes

—

#11926538

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

characteristic

#11926273

—

#11926273

—

C₁₉×#533

C₂²

yes

characteristic

C₄×M₁₆×C₁₉

C₂²

yes

—

C₁₉×#330

—

C₂×#64541

—

C₂×M₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

—

C₁₉×#125

D₄

yes

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₁₉×#117

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

#10597376

—

C₂²×C₁₉⋊C₈

—

#10597321

—

#10597320

C₂×C₄

yes

characteristic

C₄×D₇₆

—

#10597315

C₂×C₄

yes

characteristic

C₁₉×#97

—

C₄×C₈×C₁₉

—

C₂²⋊(C₁₉⋊C₈)

—

#10597267

—

#10597266

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂×C₂²⋊D₁₉

—

#64541

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

#120

yes

characteristic

C₂×C₄×C₁₉

#121

yes

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

D₇₆

—

C₄×D₁₉

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#3131

—

#2986

—

100

#1526

D₁₉

yes

characteristic, complemented

101

#1484

—

102

#1278

—

103

C₂²×C₁₉

—

104

C₂²×C₁₉

—

105

C₂²×C₁₉

#386

yes

characteristic

106

C₂×D₁₉

—

107

C₂×D₁₉

—

108

C₄×C₁₉

—

109

C₄×C₁₉

—

110

C₄×C₁₉

—

111

C₄×C₁₉

#443

yes

—

112

C₄×C₁₉

#444

yes

—

113

C₄×C₁₉

#454

yes

—

114

Dic₁₉

—

115

#533

C₂×D₁₉

yes

characteristic

116

#532

—

117

#488

—

118

#487

—

119

#486

—

120

#446

—

121

C₈×Q₈

—

122

#433

—

123

#431

—

124

#416

—

125

C₄×M₁₆

C₂×D₁₉

yes

—

126

C₂×C₄×C₈

—

127

#330

—

128

D₄⋊C₈

—

129

D₄⋊C₈

—

130

C₂×C₁₉

—

131

C₂×C₁₉

#1876

yes

—

132

C₂×C₁₉

#1888

yes

characteristic

133

D₁₉

—

134

C₂×#41

—

135

C₂×M₁₆

—

136

C₂²×C₈

—

137

C₄⋊Q₈

—

138

C₄⋊Q₈

C₄×D₁₉

yes

—

139

#127

—

140

#125

C₂²⋊D₁₉

yes

—

141

#124

—

142

C₂²⋊Q₈

—

143

#121

—

144

C₄×Q₈

—

145

C₄×D₄

—

146

#117

D₇₆

yes

—

147

C₂×C₄²

C₂²×D₁₉

yes

characteristic

148

C₄⋊C₈

—

149

C₄⋊C₈

—

150

C₄⋊C₈

—

151

#103

—

152

#102

—

153

C₂²⋊C₈

—

154

#97

—

155

#97

—

156

C₄×C₈

—

157

C₄×C₈

—

158

C₄×C₈

—

159

C₄×C₈

—

160

C₄×C₈

—

161

C₁₉

#9070

yes

characteristic, complemented, Sylow

162

#41

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×D₄

—

166

C₂×D₄

—

167

C₂×D₄

—

168

C₂²×C₄

—

169

C₂²×C₄

C₂×D₇₆

yes

characteristic

170

C₂²×C₄

#64543

yes

—

171

M₁₆

—

172

M₁₆

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

(C₂×D₁₉)⋊C₄

yes

—

182

C₂²⋊C₄

—

183

C₂²⋊C₄

—

184

C₄²

—

185

C₄²

C₂×C₄×D₁₉

yes

characteristic

186

C₄²

D₄×D₁₉

yes

—

187

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

188

C₂³

—

189

C₂³

#10597332

yes

characteristic

190

Q₈

—

191

Q₈

—

192

Q₈

—

193

D₄

—

194

D₄

—

195

D₄

—

196

D₄

—

152

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

152

—

203

C₂×C₄

(C₂²⋊D₁₉)⋊C₄

yes

—

204

C₂×C₄

#10597328

yes

characteristic

205

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

206

C₂×C₄

#10597385

yes

—

207

C₈

—

208

C₈

—

209

C₈

—

210

C₈

—

211

C₂²

—

212

C₂²

—

213

C₂²

—

152

—

214

C₂²

—

152

—

215

C₂²

#11926421

yes

characteristic

216

C₄

—

217

C₄

—

218

C₄

—

219

C₄

—

152

—

220

C₄

#11926658

yes

—

221

C₄

#11926663

yes

—

222

C₄

#11926719

yes

—

223

C₂

—

224

C₂

—

304

—

225

C₂

#14563960

yes

—

226

C₂

#14564036

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597328
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1526	C₂
socle	C₂²×C₁₉	#386
prime radical	#11927094	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1526	D₁₉
hypocenter	C₁₉	#9070
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1526

subgroup

G/H

center

C₂×C₄

#10597328

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1526

C₂

C₂²×C₁₉

C₂²

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1526

N	H ≅ G/N	type
2. #14572737	C₂	semidirect
4. #14561473	C₂	semidirect
5. C₁₉×#1526	C₂	semidirect
100. #1526	D₁₉	semidirect
161. C₁₉	#9070	semidirect

H ≅ G/N

type

2. #14572737

C₂

semidirect

4. #14561473

C₂

semidirect

5. C₁₉×#1526

C₂

semidirect

100. #1526

D₁₉

semidirect

161. C₁₉

#9070

semidirect

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

subgroup	index
#14573960	2
#14572737	2
#14562053	2
#14561473	2
C₁₉×#1526	2
#9070	19

subgroup

index

C₁₉×#1526

Subgroups — #18077863

Conjugacy classes of subgroups

Complements

Maximal subgroups