Group #18086992 — subgroups

Subgroups — #18086992

Order 4864.

406 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 129 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	#14568877	C₂	1	1	yes	maximal, characteristic
2	#14564399	C₂	1	2	yes	maximal
3	#14563794	C₂	1	1	yes	maximal, characteristic
4	#14561474	C₂	1	2	yes	maximal
5	C₁₉×#1296	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597264	—	2	2	no	—
7	C₂×#10597274	—	2	2	no	—
8	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
9	#11926483	—	2	2	no	—
10	#11926443	—	2	2	no	—
11	#11926414	C₂²	1	1	yes	characteristic
12	#11926409	—	2	2	no	—
13	C₄×C₄⋊Dic₁₉	C₂²	1	2	yes	—
14	#11926307	—	2	2	no	—
15	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
16	C₁₉×#384	C₂²	1	1	yes	characteristic
17	C₂²×C₈×C₁₉	—	2	2	no	—
18	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
19	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
20	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
21	C₂×C₄⋊Dic₁₉	—	2	2	no	—
22	C₂×C₄⋊Dic₁₉	—	2	1	no	—
23	C₂×C₄⋊Dic₁₉	—	2	2	no	—
24	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
25	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
26	C₂×C₄×Dic₁₉	—	2	2	no	—
27	C₂²×C₁₉⋊C₈	—	2	1	no	—
28	C₁₉×C₄⋊C₈	—	2	2	no	—
29	C₁₉×C₄⋊C₈	Q₈	1	4	yes	—
30	C₁₉⋊#95	—	2	2	no	—
31	C₁₉⋊#95	—	2	4	no	—
32	C₁₉⋊#95	—	2	2	no	—
33	#10597274	—	4	4	no	—
34	#10597264	—	4	4	no	—
35	C₄×C₁₉⋊C₈	—	2	1	no	—
36	C₄×C₁₉⋊C₈	Q₈	1	2	yes	—
37	C₂²×C₄×C₁₉	—	2	2	no	—
38	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
39	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
40	C₂²×Dic₁₉	—	2	2	no	—
41	C₂²×Dic₁₉	—	2	2	no	—
42	C₂²×Dic₁₉	—	4	1	no	—
43	C₂×C₈×C₁₉	—	2	4	no	—
44	C₂×C₈×C₁₉	—	4	2	no	—
45	C₂×C₈×C₁₉	—	4	2	no	—
46	C₄⋊C₄×C₁₉	—	4	2	no	—
47	C₄⋊C₄×C₁₉	—	4	2	no	—
48	C₄⋊C₄×C₁₉	—	4	2	no	—
49	C₄²×C₁₉	C₂×Q₈	1	2	yes	—
50	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
51	C₄²×C₁₉	#41	1	1	yes	characteristic
52	C₄⋊Dic₁₉	—	2	2	no	—
53	C₄⋊Dic₁₉	—	2	2	no	—
54	C₄⋊Dic₁₉	—	2	2	no	—
55	C₄⋊Dic₁₉	—	2	2	no	—
56	C₄⋊Dic₁₉	—	4	2	no	—
57	C₄⋊Dic₁₉	—	4	2	no	—
58	C₄⋊Dic₁₉	—	4	2	no	—
59	C₄⋊Dic₁₉	—	8	2	no	—
60	C₄×Dic₁₉	—	4	2	no	—
61	C₄×Dic₁₉	—	4	2	no	—
62	C₂×C₁₉⋊C₈	—	2	2	no	—
63	C₂×C₁₉⋊C₈	—	2	2	no	—
64	C₂×C₁₉⋊C₈	—	2	2	no	—
65	#10576	—	19	1	no	maximal, Sylow
66	C₂³×C₁₉	#120	1	1	yes	characteristic
67	C₂×C₄×C₁₉	—	2	1	no	—
68	C₂×C₄×C₁₉	—	2	1	no	—
69	C₂×C₄×C₁₉	—	4	4	no	—
70	C₂×C₄×C₁₉	—	4	2	no	—
71	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
72	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
73	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
74	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
75	C₂×C₄×C₁₉	#135	1	2	yes	—
76	C₂×C₄×C₁₉	#135	1	2	yes	—
77	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
78	C₂×C₄×C₁₉	#137	1	2	yes	—
79	C₂×Dic₁₉	—	4	2	no	—
80	C₂×Dic₁₉	—	4	2	no	—
81	C₂×Dic₁₉	—	4	2	no	—
82	C₂×Dic₁₉	—	4	2	no	—
83	C₂×Dic₁₉	—	4	2	no	—
84	C₂×Dic₁₉	—	4	2	no	—
85	C₂×Dic₁₉	—	8	2	no	—
86	C₂×Dic₁₉	—	8	1	no	—
87	C₈×C₁₉	—	4	4	no	—
88	C₁₉⋊C₈	—	2	4	no	—
89	#2571	—	19	1	no	—
90	#1948	—	19	2	no	—
91	#1845	—	19	1	no	—
92	#1296	D₁₉	1	1	yes	characteristic
93	#1279	—	19	2	no	—
94	C₂²×C₁₉	#395	1	1	yes	characteristic
95	C₂²×C₁₉	#449	1	2	yes	—
96	C₂²×C₁₉	#452	1	2	yes	—
97	C₂²×C₁₉	#453	1	1	yes	characteristic
98	C₂²×C₁₉	#456	1	1	yes	characteristic
99	C₄×C₁₉	—	2	1	no	—
100	C₄×C₁₉	—	2	1	no	—
101	C₄×C₁₉	—	8	2	no	—
102	C₄×C₁₉	#478	1	2	yes	—
103	C₄×C₁₉	#479	1	2	yes	—
104	C₄×C₁₉	#499	1	2	yes	—
105	C₄×C₁₉	#501	1	2	yes	—
106	Dic₁₉	—	8	2	no	—
107	Dic₁₉	—	8	2	no	—
108	Dic₁₉	—	16	1	no	—
109	C₂×#107	—	38	2	no	—
110	C₂×#106	—	38	2	no	—
111	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
112	C₂×C₄×C₈	—	19	1	no	—
113	#400	—	38	2	no	—
114	#389	—	38	2	no	—
115	#384	—	19	1	no	—
116	#384	C₂×D₁₉	1	1	yes	characteristic
117	#382	—	38	2	no	—
118	C₄×C₄⋊C₄	—	19	2	no	—
119	#340	—	38	2	no	—
120	C₂×C₁₉	#1620	1	1	yes	characteristic
121	C₂×C₁₉	#1634	1	1	yes	characteristic
122	C₂×C₁₉	#1650	1	2	yes	—
123	C₂×C₁₉	#2059	1	2	yes	—
124	C₂×C₁₉	#2060	1	1	yes	characteristic
125	C₂²×C₈	—	2	2	no	—
126	C₂²×C₈	—	38	1	no	—
127	C₂×C₄⋊C₄	—	2	2	no	—
128	C₂×C₄⋊C₄	—	19	2	no	—
129	C₂×C₄⋊C₄	—	19	2	no	—
130	C₂×C₄⋊C₄	—	38	1	no	—
131	C₂×C₄⋊C₄	—	38	2	no	—
132	C₂×C₄⋊C₄	—	38	2	no	—
133	C₂×C₄⋊C₄	D₇₆	1	2	yes	—
134	C₂×C₄²	—	38	2	no	—
135	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
136	#107	—	76	4	no	—
137	#106	—	76	4	no	—
138	C₄⋊C₈	—	2	2	no	—
139	C₄⋊C₈	Dic₃₈	1	4	yes	—
140	C₄×C₈	—	19	2	no	—
141	C₄×C₈	—	38	1	no	—
142	#95	—	38	2	no	—
143	#95	—	38	4	no	—
144	#95	—	38	2	no	—
145	C₁₉	#10576	1	1	yes	characteristic, complemented, Sylow
146	C₂²×C₄	—	2	2	no	—
147	C₂²×C₄	—	38	2	no	—
148	C₂²×C₄	—	38	2	no	—
149	C₂²×C₄	—	76	1	no	—
150	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
151	C₂²×C₄	D₄×D₁₉	1	2	yes	—
152	C₂×C₈	—	2	4	no	—
153	C₂×C₈	—	4	2	no	—
154	C₂×C₈	—	4	2	no	—
155	C₂×C₈	—	38	2	no	—
156	C₂×C₈	—	38	2	no	—
157	C₂×C₈	—	38	2	no	—
158	C₄⋊C₄	—	4	2	no	—
159	C₄⋊C₄	—	4	2	no	—
160	C₄⋊C₄	—	4	2	no	—
161	C₄⋊C₄	—	38	2	no	—
162	C₄⋊C₄	—	38	2	no	—
163	C₄⋊C₄	—	38	2	no	—
164	C₄⋊C₄	—	38	2	no	—
165	C₄⋊C₄	—	76	2	no	—
166	C₄⋊C₄	—	76	2	no	—
167	C₄⋊C₄	—	76	2	no	—
168	C₄⋊C₄	—	152	2	no	—
169	C₄²	—	76	2	no	—
170	C₄²	—	76	2	no	—
171	C₄²	C₂×Dic₃₈	1	2	yes	—
172	C₄²	#64543	1	1	yes	characteristic
173	C₄²	Q₈×D₁₉	1	1	yes	characteristic
174	C₂³	#10597328	1	1	yes	characteristic
175	C₂×C₄	—	2	1	no	—
176	C₂×C₄	—	2	1	no	—
177	C₂×C₄	—	4	4	no	—
178	C₂×C₄	—	4	2	no	—
179	C₂×C₄	—	76	2	no	—
180	C₂×C₄	—	76	2	no	—
181	C₂×C₄	—	76	2	no	—
182	C₂×C₄	—	76	2	no	—
183	C₂×C₄	—	76	2	no	—
184	C₂×C₄	—	76	2	no	—
185	C₂×C₄	—	152	2	no	—
186	C₂×C₄	—	152	1	no	—
187	C₂×C₄	#10597315	1	1	yes	characteristic
188	C₂×C₄	#10597324	1	2	yes	—
189	C₂×C₄	#10597334	1	2	yes	—
190	C₂×C₄	#10597343	1	1	yes	characteristic
191	C₂×C₄	#10597357	1	2	yes	—
192	C₂×C₄	#10597362	1	2	yes	—
193	C₂×C₄	#10597362	1	2	yes	—
194	C₂×C₄	#10597364	1	2	yes	—
195	C₈	—	4	4	no	—
196	C₈	—	38	4	no	—
197	C₂²	#11926465	1	1	yes	characteristic
198	C₂²	#11926690	1	2	yes	—
199	C₂²	#11926709	1	2	yes	—
200	C₂²	#11926714	1	1	yes	characteristic
201	C₂²	#11926729	1	1	yes	characteristic
202	C₄	—	2	1	no	—
203	C₄	—	2	1	no	—
204	C₄	—	8	2	no	—
205	C₄	—	304	1	no	—
206	C₄	—	152	2	no	—
207	C₄	—	152	2	no	—
208	C₄	#11926846	1	2	yes	—
209	C₄	#11926849	1	2	yes	—
210	C₄	#11926944	1	2	yes	—
211	C₄	#11926952	1	2	yes	—
212	C₂	#14562695	1	1	yes	characteristic
213	C₂	#14562781	1	1	yes	characteristic
214	C₂	#14562892	1	2	yes	—
215	C₂	#14564972	1	2	yes	—
216	C₂	#14564981	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14568877

C₂

yes

maximal, characteristic

#14564399

C₂

yes

maximal

#14563794

C₂

yes

maximal, characteristic

#14561474

C₂

yes

maximal

C₁₉×#1296

C₂

yes

maximal, characteristic

C₂×#10597264

—

C₂×#10597274

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

—

C₂²

yes

characteristic

#11926409

—

C₄×C₄⋊Dic₁₉

C₂²

yes

—

#11926307

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

—

C₁₉×#384

C₂²

yes

characteristic

C₂²×C₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

D₄

yes

—

C₂×C₄⋊Dic₁₉

D₄

yes

—

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

Q₈

yes

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₁₉⋊#95

—

#10597274

—

#10597264

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

Q₈

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×Q₈

yes

—

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

#41

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

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

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

C₄⋊Q₈

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

#135

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

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

—

—

—

D₁₉

yes

characteristic

#1279

—

C₂²×C₁₉

#395

yes

characteristic

C₂²×C₁₉

#449

yes

—

C₂²×C₁₉

#452

yes

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

100

C₄×C₁₉

—

101

C₄×C₁₉

—

102

C₄×C₁₉

#478

yes

—

103

C₄×C₁₉

#479

yes

—

104

C₄×C₁₉

#499

yes

—

105

C₄×C₁₉

#501

yes

—

106

Dic₁₉

—

107

Dic₁₉

—

108

Dic₁₉

—

109

C₂×#107

—

110

C₂×#106

—

111

C₂×C₄⋊C₈

C₂×D₁₉

yes

—

112

C₂×C₄×C₈

—

113

#400

—

114

#389

—

115

#384

—

116

#384

C₂×D₁₉

yes

characteristic

117

#382

—

118

C₄×C₄⋊C₄

—

119

#340

—

120

C₂×C₁₉

#1620

yes

characteristic

121

C₂×C₁₉

#1634

yes

characteristic

122

C₂×C₁₉

#1650

yes

—

123

C₂×C₁₉

#2059

yes

—

124

C₂×C₁₉

#2060

yes

characteristic

125

C₂²×C₈

—

126

C₂²×C₈

—

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×C₄⋊C₄

D₇₆

yes

—

134

C₂×C₄²

—

135

C₂×C₄²

C₂²×D₁₉

yes

characteristic

136

#107

—

137

#106

—

138

C₄⋊C₈

—

139

C₄⋊C₈

Dic₃₈

yes

—

140

C₄×C₈

—

141

C₄×C₈

—

142

#95

—

143

#95

—

144

#95

—

145

C₁₉

#10576

yes

characteristic, complemented, Sylow

146

C₂²×C₄

—

147

C₂²×C₄

—

148

C₂²×C₄

—

149

C₂²×C₄

—

150

C₂²×C₄

C₂×D₇₆

yes

characteristic

151

C₂²×C₄

D₄×D₁₉

yes

—

152

C₂×C₈

—

153

C₂×C₈

—

154

C₂×C₈

—

155

C₂×C₈

—

156

C₂×C₈

—

157

C₂×C₈

—

158

C₄⋊C₄

—

159

C₄⋊C₄

—

160

C₄⋊C₄

—

161

C₄⋊C₄

—

162

C₄⋊C₄

—

163

C₄⋊C₄

—

164

C₄⋊C₄

—

165

C₄⋊C₄

—

166

C₄⋊C₄

—

167

C₄⋊C₄

—

168

C₄⋊C₄

—

152

—

169

C₄²

—

170

C₄²

—

171

C₄²

C₂×Dic₃₈

yes

—

172

C₄²

#64543

yes

characteristic

173

C₄²

Q₈×D₁₉

yes

characteristic

174

C₂³

#10597328

yes

characteristic

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

152

—

186

C₂×C₄

—

152

—

187

C₂×C₄

#10597315

yes

characteristic

188

C₂×C₄

#10597324

yes

—

189

C₂×C₄

#10597334

yes

—

190

C₂×C₄

#10597343

yes

characteristic

191

C₂×C₄

#10597357

yes

—

192

C₂×C₄

#10597362

yes

—

193

C₂×C₄

#10597362

yes

—

194

C₂×C₄

#10597364

yes

—

195

C₈

—

196

C₈

—

197

C₂²

#11926465

yes

characteristic

198

C₂²

#11926690

yes

—

199

C₂²

#11926709

yes

—

200

C₂²

#11926714

yes

characteristic

201

C₂²

#11926729

yes

characteristic

202

C₄

—

203

C₄

—

204

C₄

—

205

C₄

—

304

—

206

C₄

—

152

—

207

C₄

—

152

—

208

C₄

#11926846

yes

—

209

C₄

#11926849

yes

—

210

C₄

#11926944

yes

—

211

C₄

#11926952

yes

—

212

C₂

#14562695

yes

characteristic

213

C₂

#14562781

yes

characteristic

214

C₂

#14562892

yes

—

215

C₂

#14564972

yes

—

216

C₂

#14564981

yes

characteristic

	subgroup	G/H
center	C₂³	#10597328
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1296	C₂
socle, prime radical	C₂³×C₁₉	#120
hypercenter	#1296	D₁₉
hypocenter	C₁₉	#10576
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

subgroup

G/H

center

C₂³

#10597328

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1296

C₂

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

N	H ≅ G/N	type
145. C₁₉	#10576	semidirect

H ≅ G/N

type

145. C₁₉

#10576

semidirect

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

subgroup	index
#14568877	2
#14564399	2
#14563794	2
#14561474	2
C₁₉×#1296	2
#10576	19

subgroup

index

C₁₉×#1296

Subgroups — #18086992

Conjugacy classes of subgroups

Complements

Maximal subgroups