Group #18087565 — subgroups

Subgroups — #18087565

Order 4864.

296 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 93 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	#14564616	C₂	1	1	yes	maximal, characteristic
2	#14563755	C₂	1	1	yes	maximal, characteristic
3	#14562410	C₂	1	1	yes	maximal, characteristic
4	#14562406	C₂	1	1	yes	maximal, characteristic
5	#14562039	C₂	1	1	yes	maximal, characteristic
6	#14562039	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1274	C₂	1	1	yes	maximal, characteristic
8	#11927101	C₂²	1	1	yes	characteristic
9	#11926568	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
12	#11926304	—	2	2	no	—
13	#11926299	—	2	2	no	—
14	#11926297	—	2	2	no	—
15	#11926295	—	2	2	no	—
16	#11926276	—	2	2	no	—
17	#11926276	—	2	2	no	—
18	C₁₉×#431	C₂²	1	1	yes	characteristic
19	C₁₉×#431	C₂²	1	1	yes	characteristic
20	C₁₉×#376	C₂²	1	1	yes	characteristic
21	C₂×C₄²×C₁₉	D₄	1	2	yes	—
22	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
23	#10597372	—	2	1	no	—
24	#10597370	—	2	1	no	—
25	#10597370	—	2	1	no	—
26	C₂×#64520	—	2	1	no	—
27	C₂²×C₁₉⋊C₈	—	2	1	no	—
28	C₂²×C₁₉⋊C₈	—	2	1	no	—
29	#10597316	—	2	1	no	—
30	#10597315	Q₈	1	1	yes	characteristic
31	#10597315	Q₈	1	1	yes	characteristic
32	C₄×Dic₃₈	—	2	1	no	—
33	C₄×Dic₃₈	—	2	1	no	—
34	C₁₉×C₄⋊C₈	—	2	1	no	—
35	C₁₉×C₄⋊C₈	—	2	1	no	—
36	C₁₉×C₂²⋊C₈	—	2	1	no	—
37	C₁₉×C₂²⋊C₈	—	2	1	no	—
38	C₄×C₈×C₁₉	D₄	1	2	yes	—
39	C₄×C₈×C₁₉	D₄	1	2	yes	—
40	C₁₉×#95	—	2	1	no	—
41	C₁₉×#95	—	2	1	no	—
42	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
43	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
44	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
45	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
46	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
47	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
48	C₂²×C₄×C₁₉	—	2	2	no	—
49	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
52	C₂×Dic₃₈	—	2	1	no	—
53	C₂×Dic₃₈	—	2	1	no	—
54	C₂×C₈×C₁₉	—	2	2	no	—
55	C₂×C₈×C₁₉	—	2	2	no	—
56	C₄²×C₁₉	—	2	2	no	—
57	C₄²×C₁₉	—	2	2	no	—
58	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
59	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
60	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
61	C₄²×C₁₉	#41	1	1	yes	characteristic
62	C₂²⋊Dic₁₉	—	4	1	no	—
63	C₄⋊Dic₁₉	—	2	1	no	—
64	C₄⋊Dic₁₉	—	2	1	no	—
65	C₄⋊Dic₁₉	—	2	1	no	—
66	C₄⋊Dic₁₉	—	2	1	no	—
67	Dic₁₉⋊C₄	—	4	1	no	—
68	Dic₁₉⋊C₄	—	4	1	no	—
69	C₄×Dic₁₉	—	4	1	no	—
70	#64520	—	4	2	no	—
71	C₂×C₁₉⋊C₈	—	4	1	no	—
72	C₂×C₁₉⋊C₈	—	4	1	no	—
73	C₂×C₁₉⋊C₈	—	4	1	no	—
74	C₂×C₁₉⋊C₈	—	4	2	no	—
75	C₂×C₁₉⋊C₈	—	4	2	no	—
76	#10669	—	19	1	no	maximal, Sylow
77	C₂³×C₁₉	#123	1	1	yes	characteristic
78	C₂×C₄×C₁₉	—	4	1	no	—
79	C₂×C₄×C₁₉	—	4	1	no	—
80	C₂×C₄×C₁₉	—	4	2	no	—
81	C₂×C₄×C₁₉	—	4	2	no	—
82	C₂×C₄×C₁₉	—	4	2	no	—
83	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
84	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
85	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
86	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
87	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
88	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
89	C₂×C₄×C₁₉	#135	1	2	yes	—
90	C₂×C₄×C₁₉	#137	1	2	yes	—
91	C₂×Dic₁₉	—	4	1	no	—
92	C₂×Dic₁₉	—	4	1	no	—
93	Dic₃₈	—	4	2	no	—
94	Dic₃₈	—	4	2	no	—
95	C₈×C₁₉	—	4	2	no	—
96	C₈×C₁₉	—	4	2	no	—
97	C₁₉⋊C₈	—	8	1	no	—
98	C₁₉⋊C₈	—	8	1	no	—
99	C₁₉⋊C₈	—	8	1	no	—
100	#1995	—	19	1	no	—
101	#1832	—	19	1	no	—
102	#1571	—	19	1	no	—
103	#1570	—	19	1	no	—
104	#1481	—	19	1	no	—
105	#1481	—	19	1	no	—
106	#1274	D₁₉	1	1	yes	characteristic
107	C₂²×C₁₉	—	2	1	no	—
108	C₂²×C₁₉	—	2	1	no	—
109	C₂²×C₁₉	#399	1	1	yes	characteristic
110	C₂²×C₁₉	#485	1	2	yes	—
111	C₄×C₁₉	—	2	1	no	—
112	C₄×C₁₉	—	2	1	no	—
113	C₄×C₁₉	—	2	1	no	—
114	C₄×C₁₉	—	2	1	no	—
115	C₄×C₁₉	—	8	2	no	—
116	C₄×C₁₉	#479	1	2	yes	—
117	C₄×C₁₉	#495	1	1	yes	characteristic
118	C₄×C₁₉	#497	1	1	yes	characteristic
119	Dic₁₉	—	8	1	no	—
120	Dic₁₉	—	8	1	no	—
121	#533	—	19	1	no	—
122	#431	C₂×D₁₉	1	1	yes	characteristic
123	#431	C₂×D₁₉	1	1	yes	characteristic
124	#423	—	19	1	no	—
125	C₂×C₄⋊C₈	—	19	1	no	—
126	C₂×C₄⋊C₈	—	19	1	no	—
127	#376	C₂×D₁₉	1	1	yes	characteristic
128	#339	—	38	2	no	—
129	#336	—	38	2	no	—
130	#335	—	38	2	no	—
131	#334	—	38	2	no	—
132	Q₈⋊C₈	—	38	2	no	—
133	Q₈⋊C₈	—	38	2	no	—
134	C₂×C₁₉	—	2	2	no	—
135	C₂×C₁₉	#2097	1	1	yes	characteristic
136	C₂×C₁₉	#2098	1	1	yes	characteristic
137	C₂×C₁₉	#2098	1	1	yes	characteristic
138	C₂×M₁₆	—	38	1	no	—
139	C₂²×C₈	—	38	1	no	—
140	C₂²×C₈	—	38	1	no	—
141	C₄⋊Q₈	—	19	1	no	—
142	C₄⋊Q₈	—	19	1	no	—
143	#125	—	38	1	no	—
144	C₂²⋊Q₈	—	38	1	no	—
145	C₂²⋊Q₈	—	38	1	no	—
146	C₄×Q₈	—	38	1	no	—
147	C₄×Q₈	—	38	1	no	—
148	#117	—	38	1	no	—
149	C₂×C₄²	D₇₆	1	2	yes	—
150	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
151	C₄⋊C₈	—	2	1	no	—
152	C₄⋊C₈	—	2	1	no	—
153	C₄⋊C₈	—	38	1	no	—
154	C₄⋊C₈	—	38	1	no	—
155	C₄⋊C₈	—	38	1	no	—
156	C₄⋊C₈	—	38	1	no	—
157	C₄⋊C₈	—	38	1	no	—
158	C₄⋊C₈	—	38	1	no	—
159	C₂²⋊C₈	—	2	1	no	—
160	C₂²⋊C₈	—	2	1	no	—
161	C₄×C₈	D₇₆	1	2	yes	—
162	C₄×C₈	D₇₆	1	2	yes	—
163	#95	—	2	1	no	—
164	#95	—	2	1	no	—
165	C₁₉	#10669	1	1	yes	characteristic, complemented, Sylow
166	C₂×Q₈	—	38	1	no	—
167	C₂×Q₈	—	38	1	no	—
168	C₂²×C₄	—	2	2	no	—
169	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
170	C₂²×C₄	#64543	1	1	yes	characteristic
171	C₂²×C₄	#64543	1	1	yes	characteristic
172	M₁₆	—	76	2	no	—
173	C₂×C₈	—	2	2	no	—
174	C₂×C₈	—	2	2	no	—
175	C₂×C₈	—	76	1	no	—
176	C₂×C₈	—	76	1	no	—
177	C₂×C₈	—	76	1	no	—
178	C₂×C₈	—	76	2	no	—
179	C₂×C₈	—	76	2	no	—
180	C₄⋊C₄	—	38	1	no	—
181	C₄⋊C₄	—	38	1	no	—
182	C₄⋊C₄	—	38	1	no	—
183	C₄⋊C₄	—	38	1	no	—
184	C₄⋊C₄	—	76	1	no	—
185	C₄⋊C₄	—	76	1	no	—
186	C₂²⋊C₄	—	76	1	no	—
187	C₄²	—	2	2	no	—
188	C₄²	—	2	2	no	—
189	C₄²	—	76	1	no	—
190	C₄²	C₂×D₇₆	1	1	yes	characteristic
191	C₄²	C₂×D₇₆	1	1	yes	characteristic
192	C₄²	#64543	1	1	yes	characteristic
193	C₄²	Q₈×D₁₉	1	1	yes	characteristic
194	C₂³	#10597332	1	1	yes	characteristic
195	Q₈	—	76	2	no	—
196	Q₈	—	76	2	no	—
197	C₂×C₄	—	4	1	no	—
198	C₂×C₄	—	4	1	no	—
199	C₂×C₄	—	4	2	no	—
200	C₂×C₄	—	4	2	no	—
201	C₂×C₄	—	4	2	no	—
202	C₂×C₄	—	76	1	no	—
203	C₂×C₄	—	76	1	no	—
204	C₂×C₄	#10597320	1	1	yes	characteristic
205	C₂×C₄	#10597332	1	1	yes	characteristic
206	C₂×C₄	#10597332	1	1	yes	characteristic
207	C₂×C₄	#10597343	1	1	yes	characteristic
208	C₂×C₄	#10597343	1	1	yes	characteristic
209	C₂×C₄	#10597343	1	1	yes	characteristic
210	C₂×C₄	#10597350	1	2	yes	—
211	C₂×C₄	#10597355	1	2	yes	—
212	C₈	—	4	2	no	—
213	C₈	—	4	2	no	—
214	C₈	—	152	1	no	—
215	C₈	—	152	1	no	—
216	C₈	—	152	1	no	—
217	C₂²	—	2	1	no	—
218	C₂²	—	2	1	no	—
219	C₂²	#11926481	1	1	yes	characteristic
220	C₂²	#11926886	1	2	yes	—
221	C₄	—	2	1	no	—
222	C₄	—	2	1	no	—
223	C₄	—	2	1	no	—
224	C₄	—	2	1	no	—
225	C₄	—	8	2	no	—
226	C₄	—	152	1	no	—
227	C₄	—	152	1	no	—
228	C₄	#11926852	1	2	yes	—
229	C₄	#11926928	1	1	yes	characteristic
230	C₄	#11926938	1	1	yes	characteristic
231	C₂	—	2	2	no	—
232	C₂	#14565182	1	1	yes	characteristic
233	C₂	#14565189	1	1	yes	characteristic
234	C₂	#14565189	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14564616

C₂

yes

maximal, characteristic

#14563755

C₂

yes

maximal, characteristic

#14562410

C₂

yes

maximal, characteristic

#14562406

C₂

yes

maximal, characteristic

#14562039

C₂

yes

maximal, characteristic

#14562039

C₂

yes

maximal, characteristic

C₁₉×#1274

C₂

yes

maximal, characteristic

#11927101

C₂²

yes

characteristic

#11926568

C₂²

yes

characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

—

—

—

—

—

C₁₉×#431

C₂²

yes

characteristic

C₁₉×#431

C₂²

yes

characteristic

C₁₉×#376

C₂²

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

—

—

—

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

#10597316

—

#10597315

Q₈

yes

characteristic

#10597315

Q₈

yes

characteristic

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

D₄

yes

—

C₄×C₈×C₁₉

D₄

yes

—

C₁₉×#95

—

C₁₉×#95

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

C₂²×C₄×C₁₉

yes

C₂²×C₄×C₁₉

yes

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

#41

yes

characteristic

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

100

#1995

—

101

#1832

—

102

#1571

—

103

#1570

—

104

#1481

—

105

#1481

—

106

#1274

D₁₉

yes

characteristic

107

C₂²×C₁₉

—

108

C₂²×C₁₉

—

109

C₂²×C₁₉

#399

yes

characteristic

110

C₂²×C₁₉

#485

yes

—

111

C₄×C₁₉

—

112

C₄×C₁₉

—

113

C₄×C₁₉

—

114

C₄×C₁₉

—

115

C₄×C₁₉

—

116

C₄×C₁₉

#479

yes

—

117

C₄×C₁₉

#495

yes

characteristic

118

C₄×C₁₉

#497

yes

characteristic

119

Dic₁₉

—

120

Dic₁₉

—

121

#533

—

122

#431

C₂×D₁₉

yes

characteristic

123

#431

C₂×D₁₉

yes

characteristic

124

#423

—

125

C₂×C₄⋊C₈

—

126

C₂×C₄⋊C₈

—

127

#376

C₂×D₁₉

yes

characteristic

128

#339

—

129

#336

—

130

#335

—

131

#334

—

132

Q₈⋊C₈

—

133

Q₈⋊C₈

—

134

C₂×C₁₉

—

135

C₂×C₁₉

#2097

yes

characteristic

136

C₂×C₁₉

#2098

yes

characteristic

137

C₂×C₁₉

#2098

yes

characteristic

138

C₂×M₁₆

—

139

C₂²×C₈

—

140

C₂²×C₈

—

141

C₄⋊Q₈

—

142

C₄⋊Q₈

—

143

#125

—

144

C₂²⋊Q₈

—

145

C₂²⋊Q₈

—

146

C₄×Q₈

—

147

C₄×Q₈

—

148

#117

—

149

C₂×C₄²

D₇₆

yes

—

150

C₂×C₄²

C₂²×D₁₉

yes

characteristic

151

C₄⋊C₈

—

152

C₄⋊C₈

—

153

C₄⋊C₈

—

154

C₄⋊C₈

—

155

C₄⋊C₈

—

156

C₄⋊C₈

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₂²⋊C₈

—

160

C₂²⋊C₈

—

161

C₄×C₈

D₇₆

yes

—

162

C₄×C₈

D₇₆

yes

—

163

#95

—

164

#95

—

165

C₁₉

#10669

yes

characteristic, complemented, Sylow

166

C₂×Q₈

—

167

C₂×Q₈

—

168

C₂²×C₄

—

169

C₂²×C₄

C₂×D₇₆

yes

characteristic

170

C₂²×C₄

#64543

yes

characteristic

171

C₂²×C₄

#64543

yes

characteristic

172

M₁₆

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₂²⋊C₄

—

187

C₄²

—

188

C₄²

—

189

C₄²

—

190

C₄²

C₂×D₇₆

yes

characteristic

191

C₄²

C₂×D₇₆

yes

characteristic

192

C₄²

#64543

yes

characteristic

193

C₄²

Q₈×D₁₉

yes

characteristic

194

C₂³

#10597332

yes

characteristic

195

Q₈

—

196

Q₈

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

#10597320

yes

characteristic

205

C₂×C₄

#10597332

yes

characteristic

206

C₂×C₄

#10597332

yes

characteristic

207

C₂×C₄

#10597343

yes

characteristic

208

C₂×C₄

#10597343

yes

characteristic

209

C₂×C₄

#10597343

yes

characteristic

210

C₂×C₄

#10597350

yes

—

211

C₂×C₄

#10597355

yes

—

212

C₈

—

213

C₈

—

214

C₈

—

152

—

215

C₈

—

152

—

216

C₈

—

152

—

217

C₂²

—

218

C₂²

—

219

C₂²

#11926481

yes

characteristic

220

C₂²

#11926886

yes

—

221

C₄

—

222

C₄

—

223

C₄

—

224

C₄

—

225

C₄

—

226

C₄

—

152

—

227

C₄

—

152

—

228

C₄

#11926852

yes

—

229

C₄

#11926928

yes

characteristic

230

C₄

#11926938

yes

characteristic

231

C₂

—

232

C₂

#14565182

yes

characteristic

233

C₂

#14565189

yes

characteristic

234

C₂

#14565189

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597320
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1274	C₂
socle	C₂²×C₁₉	#399
prime radical	C₂³×C₁₉	#123
hypercenter	#1274	D₁₉
hypocenter	C₁₉	#10669
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1274

subgroup

G/H

center

C₂×C₄

#10597320

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1274

C₂

C₂²×C₁₉

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1274

N	H ≅ G/N	type
165. C₁₉	#10669	semidirect

H ≅ G/N

type

165. C₁₉

#10669

semidirect

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

subgroup	index
#14564616	2
#14563755	2
#14562410	2
#14562406	2
#14562039	2
C₁₉×#1274	2
#10669	19

subgroup

index

C₁₉×#1274

Subgroups — #18087565

Conjugacy classes of subgroups

Complements

Maximal subgroups