Group #18084785 — subgroups

Subgroups — #18084785

Order 4864.

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

normal subgroups only

This group has 542 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	#14574576	C₂	1	2	yes	maximal
2	#14574159	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562198	C₂	1	2	yes	maximal, complemented
4	#14561480	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1961	C₂	1	1	yes	maximal, characteristic
6	#11927101	C₂²	1	2	yes	—
7	#11926953	—	2	2	no	—
8	#11926953	—	2	2	no	—
9	#11926916	—	2	2	no	—
10	#11926890	—	2	2	no	—
11	#11926741	—	2	4	no	—
12	#11926695	—	2	4	no	—
13	#11926597	C₂²	1	2	yes	—
14	#11926582	—	2	2	no	—
15	#11926280	—	2	4	no	—
16	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#102	—	2	2	no	—
18	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
19	C₁₉×#382	C₂²	1	1	yes	characteristic
20	C₂²×D₄×C₁₉	—	2	1	no	—
21	C₂²×D₄×C₁₉	—	2	2	no	—
22	C₂²×C₈×C₁₉	D₄	1	2	yes	—
23	C₁₉×#127	—	2	2	no	—
24	C₁₉×#127	—	2	1	no	—
25	C₁₉×#127	D₄	1	2	yes	—
26	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
27	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
28	C₂×#64526	—	2	8	no	—
29	#10597372	—	2	2	no	—
30	#10597370	—	2	2	no	—
31	#10597370	—	2	2	no	—
32	#10597316	—	2	2	no	—
33	#10597315	D₄	1	2	yes	—
34	#10597315	D₄	1	2	yes	—
35	C₄×Dic₃₈	—	2	2	no	—
36	C₄×Dic₃₈	—	2	2	no	—
37	C₁₉×#102	—	4	4	no	—
38	C₁₉×#97	—	2	2	no	—
39	C₁₉×#95	—	2	2	no	—
40	#10597289	—	2	8	no	—
41	C₂²⋊(C₁₉⋊C₈)	D₄	1	4	yes	—
42	#10597275	—	2	4	no	—
43	#10597274	—	2	2	no	—
44	#10597274	—	2	2	no	—
45	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
46	C₄×C₁₉⋊C₈	—	2	2	no	—
47	C₂⁴×C₁₉	—	4	1	no	—
48	C₂×D₄×C₁₉	—	2	4	no	—
49	C₂×D₄×C₁₉	—	2	2	no	—
50	C₂×D₄×C₁₉	—	4	1	no	—
51	C₂×D₄×C₁₉	—	4	2	no	—
52	C₂×D₄×C₁₉	—	4	2	no	—
53	C₂×D₄×C₁₉	—	4	2	no	—
54	C₂×D₄×C₁₉	—	8	4	no	—
55	C₂²×C₄×C₁₉	—	4	1	no	—
56	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
57	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₂×Dic₃₈	—	2	2	no	—
59	C₂×Dic₃₈	—	2	2	no	—
60	C₂×C₈×C₁₉	—	2	2	no	—
61	C₂×C₈×C₁₉	—	2	2	no	—
62	C₂×C₈×C₁₉	SD₁₆	1	4	yes	complemented
63	C₄⋊C₄×C₁₉	—	4	2	no	—
64	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
65	C₄²×C₁₉	C₂×D₄	1	2	yes	—
66	C₄²×C₁₉	#41	1	1	yes	characteristic
67	C₂²⋊Dic₁₉	—	4	2	no	—
68	#64526	—	8	8	no	—
69	C₄⋊Dic₁₉	—	2	2	no	—
70	C₄⋊Dic₁₉	—	2	2	no	—
71	C₄⋊Dic₁₉	—	2	2	no	—
72	C₄⋊Dic₁₉	—	2	2	no	—
73	Dic₁₉⋊C₄	—	4	2	no	—
74	Dic₁₉⋊C₄	—	4	2	no	—
75	C₄×Dic₁₉	—	4	2	no	—
76	C₂×C₁₉⋊C₈	—	2	4	no	—
77	#10220	—	19	1	no	maximal, Sylow
78	C₂³×C₁₉	—	4	2	no	—
79	C₂³×C₁₉	—	8	4	no	—
80	C₂³×C₁₉	—	8	1	no	—
81	C₂³×C₁₉	—	8	1	no	—
82	C₂³×C₁₉	#127	1	1	yes	characteristic
83	D₄×C₁₉	—	4	8	no	—
84	D₄×C₁₉	—	4	4	no	—
85	D₄×C₁₉	—	8	4	no	—
86	D₄×C₁₉	—	8	2	no	—
87	C₂×C₄×C₁₉	—	4	2	no	—
88	C₂×C₄×C₁₉	—	8	2	no	—
89	C₂×C₄×C₁₉	—	8	1	no	—
90	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
91	C₂×C₄×C₁₉	#120	1	2	yes	—
92	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
93	C₂×C₄×C₁₉	#121	1	2	yes	—
94	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
95	C₂×C₄×C₁₉	#137	1	2	yes	—
96	C₂×Dic₁₉	—	4	2	no	—
97	C₂×Dic₁₉	—	4	2	no	—
98	Dic₃₈	—	4	4	no	—
99	Dic₃₈	—	8	2	no	—
100	C₈×C₁₉	—	2	4	no	—
101	C₁₉⋊C₈	—	4	4	no	—
102	#3208	—	19	2	no	—
103	#3162	—	19	1	no	—
104	#1961	D₁₉	1	1	yes	characteristic
105	#1518	—	19	2	no	—
106	#1281	—	19	1	no	—
107	C₂²×C₁₉	—	2	2	no	—
108	C₂²×C₁₉	—	8	4	no	—
109	C₂²×C₁₉	—	8	2	no	—
110	C₂²×C₁₉	—	16	2	no	—
111	C₂²×C₁₉	—	16	2	no	—
112	C₂²×C₁₉	#392	1	1	yes	characteristic
113	C₂²×C₁₉	#492	1	1	yes	characteristic
114	C₂²×C₁₉	#497	1	1	yes	characteristic
115	C₄×C₁₉	—	2	2	no	—
116	C₄×C₁₉	—	2	2	no	—
117	C₄×C₁₉	—	16	1	no	—
118	C₄×C₁₉	#448	1	2	yes	—
119	C₄×C₁₉	#461	1	2	yes	—
120	Dic₁₉	—	8	2	no	—
121	Dic₁₉	—	8	2	no	—
122	#533	—	19	2	no	—
123	C₂×#127	C₂×D₁₉	1	1	yes	characteristic
124	#501	—	38	2	no	—
125	#501	—	38	2	no	—
126	#492	—	38	2	no	—
127	#486	—	38	2	no	—
128	#460	—	38	4	no	—
129	#450	—	38	4	no	—
130	#431	—	19	2	no	—
131	#427	—	38	2	no	—
132	C₂×#102	—	2	2	no	—
133	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
134	#382	C₂×D₁₉	1	1	yes	characteristic
135	#328	—	38	4	no	—
136	C₂×C₁₉	—	2	1	no	—
137	C₂×C₁₉	—	2	1	no	—
138	C₂×C₁₉	—	16	2	no	—
139	C₂×C₁₉	#2008	1	2	yes	—
140	C₂×C₁₉	#2013	1	1	yes	characteristic
141	C₂²×D₄	—	2	2	no	—
142	C₂²×D₄	—	2	1	no	—
143	C₂×SD₁₆	—	38	8	no	—
144	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
145	C₄⋊Q₈	—	19	2	no	—
146	C₄⋊Q₈	—	19	2	no	—
147	#127	—	2	1	no	—
148	#127	—	2	2	no	—
149	#127	D₇₆	1	2	yes	—
150	#125	—	38	2	no	—
151	C₂²⋊Q₈	—	38	2	no	—
152	C₂²⋊Q₈	—	38	2	no	—
153	C₄×Q₈	—	38	2	no	—
154	C₄×Q₈	—	38	2	no	—
155	#117	—	38	2	no	—
156	C₂×C₄⋊C₄	—	2	1	no	—
157	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
158	#107	—	38	4	no	—
159	#106	—	38	2	no	—
160	#106	—	38	2	no	—
161	C₄⋊C₈	—	38	2	no	—
162	#102	—	4	4	no	—
163	#102	—	38	8	no	—
164	C₂²⋊C₈	—	19	4	no	—
165	#97	—	2	2	no	—
166	C₄×C₈	—	38	2	no	—
167	#95	—	2	2	no	—
168	C₁₉	#10220	1	1	yes	characteristic, complemented, Sylow
169	C₂⁴	—	4	1	no	—
170	C₂×Q₈	—	38	2	no	—
171	C₂×Q₈	—	38	2	no	—
172	C₂×D₄	—	2	2	no	—
173	C₂×D₄	—	2	4	no	—
174	C₂×D₄	—	4	2	no	—
175	C₂×D₄	—	4	1	no	—
176	C₂×D₄	—	4	2	no	—
177	C₂×D₄	—	4	2	no	—
178	C₂×D₄	—	8	4	no	—
179	C₂²×C₄	—	4	1	no	—
180	C₂²×C₄	D₄×D₁₉	1	2	yes	—
181	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
182	SD₁₆	—	152	8	no	—
183	C₂×C₈	—	2	2	no	—
184	C₂×C₈	—	2	2	no	—
185	C₂×C₈	—	38	4	no	—
186	C₂×C₈	#64526	1	4	yes	complemented
187	C₄⋊C₄	—	4	2	no	—
188	C₄⋊C₄	—	38	2	no	—
189	C₄⋊C₄	—	38	2	no	—
190	C₄⋊C₄	—	38	2	no	—
191	C₄⋊C₄	—	38	2	no	—
192	C₄⋊C₄	—	76	2	no	—
193	C₄⋊C₄	—	76	2	no	—
194	C₂²⋊C₄	—	76	2	no	—
195	C₄²	—	76	2	no	—
196	C₄²	C₂×D₇₆	1	1	yes	characteristic
197	C₄²	#64541	1	1	yes	characteristic
198	C₄²	D₄×D₁₉	1	2	yes	—
199	C₂³	—	4	2	no	—
200	C₂³	—	8	4	no	—
201	C₂³	—	8	1	no	—
202	C₂³	—	8	1	no	—
203	C₂³	#10597386	1	1	yes	characteristic
204	Q₈	—	76	4	no	—
205	Q₈	—	152	2	no	—
206	D₄	—	4	8	no	—
207	D₄	—	4	4	no	—
208	D₄	—	8	4	no	—
209	D₄	—	8	2	no	—
210	C₂×C₄	—	4	2	no	—
211	C₂×C₄	—	8	2	no	—
212	C₂×C₄	—	8	1	no	—
213	C₂×C₄	—	76	2	no	—
214	C₂×C₄	—	76	2	no	—
215	C₂×C₄	#10597328	1	2	yes	—
216	C₂×C₄	#10597330	1	2	yes	—
217	C₂×C₄	#10597376	1	1	yes	characteristic
218	C₂×C₄	C₂×#64526	1	2	yes	—
219	C₂×C₄	#10597383	1	1	yes	characteristic
220	C₂×C₄	#10597397	1	2	yes	—
221	C₈	—	2	4	no	—
222	C₈	—	76	4	no	—
223	C₂²	—	2	2	no	—
224	C₂²	—	8	4	no	—
225	C₂²	—	8	2	no	—
226	C₂²	—	16	2	no	—
227	C₂²	—	16	2	no	—
228	C₂²	#11926453	1	1	yes	characteristic
229	C₂²	#11926916	1	1	yes	characteristic
230	C₂²	#11926939	1	1	yes	characteristic
231	C₄	—	2	2	no	—
232	C₄	—	2	2	no	—
233	C₄	—	16	1	no	—
234	C₄	—	152	2	no	—
235	C₄	—	152	2	no	—
236	C₄	#11926682	1	2	yes	—
237	C₄	#11926749	1	2	yes	—
238	C₂	—	2	1	no	—
239	C₂	—	2	1	no	—
240	C₂	—	16	2	no	—
241	C₂	#14564690	1	2	yes	—
242	C₂	#14564717	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14574576

C₂

yes

maximal

#14574159

C₂

yes

maximal, characteristic, complemented

#14562198

C₂

yes

maximal, complemented

#14561480

C₂

yes

maximal, characteristic, complemented

C₁₉×#1961

C₂

yes

maximal, characteristic

#11927101

C₂²

yes

—

—

—

—

—

—

—

C₂²

yes

—

#11926582

—

#11926280

—

C₂×C₁₉×#127

C₂²

yes

characteristic

C₂×C₁₉×#102

—

C₂×C₁₉×#97

C₂²

yes

characteristic

C₁₉×#382

C₂²

yes

characteristic

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₁₉×#127

—

C₁₉×#127

—

C₁₉×#127

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

—

—

—

—

—

D₄

yes

—

#10597315

D₄

yes

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₁₉×#102

—

C₁₉×#97

—

C₁₉×#95

—

#10597289

—

C₂²⋊(C₁₉⋊C₈)

D₄

yes

—

#10597275

—

#10597274

—

#10597274

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₂⁴×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

SD₁₆

yes

complemented

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

characteristic

C₂²⋊Dic₁₉

—

#64526

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

#10220

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#127

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#120

yes

characteristic

C₂×C₄×C₁₉

#120

yes

—

C₂×C₄×C₁₉

#121

yes

characteristic

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

100

C₈×C₁₉

—

101

C₁₉⋊C₈

—

102

#3208

—

103

#3162

—

104

#1961

D₁₉

yes

characteristic

105

#1518

—

106

#1281

—

107

C₂²×C₁₉

—

108

C₂²×C₁₉

—

109

C₂²×C₁₉

—

110

C₂²×C₁₉

—

111

C₂²×C₁₉

—

112

C₂²×C₁₉

#392

yes

characteristic

113

C₂²×C₁₉

#492

yes

characteristic

114

C₂²×C₁₉

#497

yes

characteristic

115

C₄×C₁₉

—

116

C₄×C₁₉

—

117

C₄×C₁₉

—

118

C₄×C₁₉

#448

yes

—

119

C₄×C₁₉

#461

yes

—

120

Dic₁₉

—

121

Dic₁₉

—

122

#533

—

123

C₂×#127

C₂×D₁₉

yes

characteristic

124

#501

—

125

#501

—

126

#492

—

127

#486

—

128

#460

—

129

#450

—

130

#431

—

131

#427

—

132

C₂×#102

—

133

C₂×#97

C₂×D₁₉

yes

characteristic

134

#382

C₂×D₁₉

yes

characteristic

135

#328

—

136

C₂×C₁₉

—

137

C₂×C₁₉

—

138

C₂×C₁₉

—

139

C₂×C₁₉

#2008

yes

—

140

C₂×C₁₉

#2013

yes

characteristic

141

C₂²×D₄

—

142

C₂²×D₄

—

143

C₂×SD₁₆

—

144

C₂²×C₈

C₂²⋊D₁₉

yes

—

145

C₄⋊Q₈

—

146

C₄⋊Q₈

—

147

#127

—

148

#127

—

149

#127

D₇₆

yes

—

150

#125

—

151

C₂²⋊Q₈

—

152

C₂²⋊Q₈

—

153

C₄×Q₈

—

154

C₄×Q₈

—

155

#117

—

156

C₂×C₄⋊C₄

—

157

C₂×C₄²

C₂²×D₁₉

yes

characteristic

158

#107

—

159

#106

—

160

#106

—

161

C₄⋊C₈

—

162

#102

—

163

#102

—

164

C₂²⋊C₈

—

165

#97

—

166

C₄×C₈

—

167

#95

—

168

C₁₉

#10220

yes

characteristic, complemented, Sylow

169

C₂⁴

—

170

C₂×Q₈

—

171

C₂×Q₈

—

172

C₂×D₄

—

173

C₂×D₄

—

174

C₂×D₄

—

175

C₂×D₄

—

176

C₂×D₄

—

177

C₂×D₄

—

178

C₂×D₄

—

179

C₂²×C₄

—

180

C₂²×C₄

D₄×D₁₉

yes

—

181

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

182

SD₁₆

—

152

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

#64526

yes

complemented

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₂²⋊C₄

—

195

C₄²

—

196

C₄²

C₂×D₇₆

yes

characteristic

197

C₄²

#64541

yes

characteristic

198

C₄²

D₄×D₁₉

yes

—

199

C₂³

—

200

C₂³

—

201

C₂³

—

202

C₂³

—

203

C₂³

#10597386

yes

characteristic

204

Q₈

—

205

Q₈

—

152

—

206

D₄

—

207

D₄

—

208

D₄

—

209

D₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

#10597328

yes

—

216

C₂×C₄

#10597330

yes

—

217

C₂×C₄

#10597376

yes

characteristic

218

C₂×C₄

C₂×#64526

yes

—

219

C₂×C₄

#10597383

yes

characteristic

220

C₂×C₄

#10597397

yes

—

221

C₈

—

222

C₈

—

223

C₂²

—

224

C₂²

—

225

C₂²

—

226

C₂²

—

227

C₂²

—

228

C₂²

#11926453

yes

characteristic

229

C₂²

#11926916

yes

characteristic

230

C₂²

#11926939

yes

characteristic

231

C₄

—

232

C₄

—

233

C₄

—

234

C₄

—

152

—

235

C₄

—

152

—

236

C₄

#11926682

yes

—

237

C₄

#11926749

yes

—

238

C₂

—

239

C₂

—

240

C₂

—

241

C₂

#14564690

yes

—

242

C₂

#14564717

yes

characteristic

	subgroup	G/H
center	C₂²	#11926453
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1961	C₂
socle	C₂²×C₁₉	#392
prime radical	C₂×C₁₉×#127	C₂²
hypercenter	#1961	D₁₉
hypocenter	C₁₉	#10220
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1961

subgroup

G/H

center

C₂²

#11926453

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1961

C₂

socle

C₂²×C₁₉

#392

prime radical

C₂×C₁₉×#127

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1961

N	H ≅ G/N	type
2. #14574159	C₂	semidirect
3. #14562198	C₂	semidirect
4. #14561480	C₂	semidirect
62. C₂×C₈×C₁₉	SD₁₆	semidirect
168. C₁₉	#10220	semidirect
186. C₂×C₈	#64526	semidirect

H ≅ G/N

type

2. #14574159

C₂

semidirect

3. #14562198

C₂

semidirect

4. #14561480

C₂

semidirect

62. C₂×C₈×C₁₉

SD₁₆

semidirect

168. C₁₉

#10220

semidirect

186. C₂×C₈

#64526

semidirect

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

subgroup	index
#14574576	2
#14574159	2
#14562198	2
#14561480	2
C₁₉×#1961	2
#10220	19

subgroup

index

C₁₉×#1961

Subgroups — #18084785

Conjugacy classes of subgroups

Complements

Maximal subgroups