Group #18082517 — subgroups

Subgroups — #18082517

Order 4864.

412 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 127 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	#14563773	C₂	1	1	yes	maximal, characteristic, complemented
2	#14562090	C₂	1	2	yes	maximal, complemented
3	#14562086	C₂	1	2	yes	maximal
4	C₂×#11926265	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3131	C₂	1	1	yes	maximal, characteristic
6	#11926568	C₂²	1	2	yes	—
7	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
8	#11926309	—	2	2	no	—
9	Q₈⋊(C₁₉⋊C₈)	—	2	4	no	—
10	D₄⋊(C₁₉⋊C₈)	—	2	4	no	—
11	#11926265	—	2	2	no	—
12	C₁₉×#533	C₂²	1	1	yes	characteristic
13	C₁₉×#532	C₂²	1	1	yes	characteristic
14	C₁₉×#488	—	2	2	no	—
15	C₁₉×#487	C₄	1	2	yes	—
16	C₁₉×#486	C₄	1	2	yes	—
17	C₁₉×#416	—	2	2	no	—
18	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×#41×C₁₉	—	2	1	no	—
20	C₂²×C₈×C₁₉	D₄	1	2	yes	—
21	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
22	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
23	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
24	C₁₉×#125	—	2	1	no	—
25	C₁₉×#124	—	2	1	no	—
26	C₁₉×C₂²⋊Q₈	—	2	2	no	—
27	C₁₉×#121	—	2	2	no	—
28	C₄×Q₈×C₁₉	—	2	2	no	—
29	C₄×D₄×C₁₉	—	2	2	no	—
30	C₁₉×#117	—	2	1	no	—
31	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
32	C₂×#64520	—	2	2	no	—
33	C₂²×C₁₉⋊C₈	—	2	2	no	—
34	C₁₉×#103	—	2	4	no	—
35	C₁₉×#102	—	2	4	no	—
36	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
37	C₄×C₈×C₁₉	D₄	1	2	yes	—
38	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
39	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
40	C₄×C₁₉⋊C₈	—	2	2	no	—
41	C₄×C₁₉⋊C₈	D₄	1	4	yes	—
42	#41×C₁₉	—	4	4	no	—
43	C₂×Q₈×C₁₉	—	2	1	no	—
44	C₂×Q₈×C₁₉	—	2	2	no	—
45	C₂×D₄×C₁₉	—	2	1	no	—
46	C₂×D₄×C₁₉	—	2	2	no	—
47	C₂×D₄×C₁₉	—	4	1	no	—
48	C₂²×C₄×C₁₉	—	4	1	no	—
49	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₉	#41	1	2	yes	—
51	C₂×C₈×C₁₉	—	2	4	no	—
52	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
53	C₄⋊C₄×C₁₉	—	2	2	no	—
54	C₄⋊C₄×C₁₉	—	2	2	no	—
55	C₄⋊C₄×C₁₉	—	2	2	no	—
56	C₄⋊C₄×C₁₉	—	4	2	no	—
57	C₂²⋊C₄×C₁₉	—	4	1	no	—
58	C₂²⋊C₄×C₁₉	—	4	2	no	—
59	C₄²×C₁₉	—	4	1	no	—
60	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
61	C₄²×C₁₉	C₂×D₄	1	2	yes	—
62	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
63	#64520	—	4	4	no	—
64	C₂×C₁₉⋊C₈	—	2	4	no	—
65	C₂×C₁₉⋊C₈	—	4	4	no	—
66	C₂×C₁₉⋊C₈	—	4	2	no	—
67	#9863	—	19	1	no	maximal, Sylow
68	C₂³×C₁₉	—	4	1	no	—
69	C₂³×C₁₉	#124	1	1	yes	characteristic
70	Q₈×C₁₉	—	4	2	no	—
71	Q₈×C₁₉	—	4	4	no	—
72	D₄×C₁₉	—	4	2	no	—
73	D₄×C₁₉	—	4	4	no	—
74	D₄×C₁₉	—	8	2	no	—
75	C₂×C₄×C₁₉	—	2	4	no	—
76	C₂×C₄×C₁₉	—	4	2	no	—
77	C₂×C₄×C₁₉	—	4	1	no	—
78	C₂×C₄×C₁₉	—	8	2	no	—
79	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
80	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
81	C₂×C₄×C₁₉	#121	1	2	yes	—
82	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
83	C₂×C₄×C₁₉	#135	1	4	yes	—
84	C₈×C₁₉	—	2	4	no	—
85	C₁₉⋊C₈	—	4	4	no	—
86	C₁₉⋊C₈	—	8	2	no	—
87	#3131	D₁₉	1	1	yes	characteristic
88	#1837	—	19	1	no	—
89	#1493	—	19	2	no	—
90	#1492	—	19	2	no	—
91	C₂×#322	—	19	1	no	—
92	C₂²×C₁₉	—	2	2	no	—
93	C₂²×C₁₉	—	8	1	no	—
94	C₂²×C₁₉	—	8	2	no	—
95	C₂²×C₁₉	#390	1	1	yes	characteristic
96	C₂²×C₁₉	#488	1	2	yes	—
97	C₄×C₁₉	—	2	2	no	—
98	C₄×C₁₉	—	8	1	no	—
99	C₄×C₁₉	—	8	2	no	—
100	C₄×C₁₉	#416	1	2	yes	—
101	C₄×C₁₉	#444	1	4	yes	—
102	C₄×C₁₉	#495	1	2	yes	—
103	#533	C₂×D₁₉	1	1	yes	characteristic
104	#532	C₂×D₁₉	1	1	yes	characteristic
105	#488	—	2	2	no	—
106	#487	Dic₁₉	1	2	yes	—
107	#486	Dic₁₉	1	2	yes	—
108	#423	—	19	2	no	—
109	#416	—	2	2	no	—
110	C₂×C₄×C₈	—	19	2	no	—
111	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
112	#341	—	38	2	no	—
113	Q₈⋊C₈	—	38	4	no	—
114	D₄⋊C₈	—	38	4	no	—
115	#322	—	38	2	no	—
116	C₂×C₁₉	—	2	2	no	—
117	C₂×C₁₉	—	16	1	no	—
118	C₂×C₁₉	#1958	1	1	yes	characteristic
119	C₂×C₁₉	#1975	1	2	yes	—
120	C₂×#41	—	2	1	no	—
121	C₂×M₁₆	—	38	2	no	—
122	C₂²×C₈	—	38	2	no	—
123	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
124	C₄⋊Q₈	C₂×Dic₁₉	1	1	yes	characteristic
125	C₄⋊Q₈	C₂×Dic₁₉	1	2	yes	—
126	#127	C₂×Dic₁₉	1	1	yes	characteristic
127	#125	—	2	1	no	—
128	#124	—	2	1	no	—
129	C₂²⋊Q₈	—	2	2	no	—
130	#121	—	2	2	no	—
131	C₄×Q₈	—	2	2	no	—
132	C₄×D₄	—	2	2	no	—
133	#117	—	2	1	no	—
134	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
135	C₄⋊C₈	—	38	2	no	—
136	C₄⋊C₈	—	38	2	no	—
137	#103	—	2	4	no	—
138	#102	—	2	4	no	—
139	C₄×C₈	—	19	4	no	—
140	C₄×C₈	—	38	2	no	—
141	C₄×C₈	C₂×Dic₁₉	1	2	yes	—
142	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
143	C₁₉	#9863	1	1	yes	characteristic, complemented, Sylow
144	#41	—	4	4	no	—
145	C₂×Q₈	—	2	2	no	—
146	C₂×Q₈	—	2	1	no	—
147	C₂×D₄	—	2	2	no	—
148	C₂×D₄	—	2	1	no	—
149	C₂×D₄	—	4	1	no	—
150	C₂²×C₄	—	4	1	no	—
151	C₂²×C₄	#64543	1	2	yes	—
152	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
153	M₁₆	—	76	4	no	—
154	C₂×C₈	—	2	4	no	—
155	C₂×C₈	—	38	4	no	—
156	C₂×C₈	—	76	4	no	—
157	C₂×C₈	—	76	2	no	—
158	C₂×C₈	C₂²⋊Dic₁₉	1	4	yes	—
159	C₄⋊C₄	—	2	2	no	—
160	C₄⋊C₄	—	2	2	no	—
161	C₄⋊C₄	—	2	2	no	—
162	C₄⋊C₄	—	4	2	no	—
163	C₂²⋊C₄	—	4	1	no	—
164	C₂²⋊C₄	—	4	2	no	—
165	C₄²	—	4	1	no	—
166	C₄²	D₄×D₁₉	1	2	yes	—
167	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
168	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
169	C₂³	—	4	1	no	—
170	C₂³	#10597382	1	1	yes	characteristic
171	Q₈	—	4	2	no	—
172	Q₈	—	4	4	no	—
173	D₄	—	4	2	no	—
174	D₄	—	4	4	no	—
175	D₄	—	8	2	no	—
176	C₂×C₄	—	2	4	no	—
177	C₂×C₄	—	4	2	no	—
178	C₂×C₄	—	4	1	no	—
179	C₂×C₄	—	8	2	no	—
180	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
181	C₂×C₄	#10597384	1	2	yes	—
182	C₂×C₄	#10597386	1	1	yes	characteristic
183	C₂×C₄	#10597396	1	4	yes	—
184	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
185	C₈	—	2	4	no	—
186	C₈	—	76	4	no	—
187	C₈	—	152	2	no	—
188	C₂²	—	2	2	no	—
189	C₂²	—	8	1	no	—
190	C₂²	—	8	2	no	—
191	C₂²	#11926447	1	1	yes	characteristic
192	C₂²	#11926898	1	2	yes	—
193	C₄	—	2	2	no	—
194	C₄	—	8	1	no	—
195	C₄	—	8	2	no	—
196	C₄	#11926540	1	2	yes	—
197	C₄	#11926666	1	4	yes	—
198	C₄	#11926926	1	2	yes	—
199	C₂	—	2	2	no	—
200	C₂	—	16	1	no	—
201	C₂	#14564447	1	1	yes	characteristic
202	C₂	#14564529	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14563773

C₂

yes

maximal, characteristic, complemented

#14562090

C₂

yes

maximal, complemented

#14562086

C₂

yes

maximal

C₂×#11926265

C₂

yes

maximal, characteristic, complemented

C₁₉×#3131

C₂

yes

maximal, characteristic

#11926568

C₂²

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

#11926309

—

Q₈⋊(C₁₉⋊C₈)

—

D₄⋊(C₁₉⋊C₈)

—

#11926265

—

C₁₉×#533

C₂²

yes

characteristic

C₁₉×#532

C₂²

yes

characteristic

C₁₉×#488

—

C₁₉×#487

C₄

yes

—

C₁₉×#486

C₄

yes

—

C₁₉×#416

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂×#41×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

characteristic

C₁₉×#127

C₂×C₄

yes

characteristic

C₁₉×#125

—

C₁₉×#124

—

C₁₉×C₂²⋊Q₈

—

C₁₉×#121

—

C₄×Q₈×C₁₉

—

C₄×D₄×C₁₉

—

C₁₉×#117

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

C₂²×C₁₉⋊C₈

—

C₁₉×#103

—

C₁₉×#102

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

D₄

yes

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

D₄

yes

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#9863

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

#124

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×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

#121

yes

—

C₂×C₄×C₁₉

#127

yes

characteristic

C₂×C₄×C₁₉

#135

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#3131

D₁₉

yes

—

—

—

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#390

yes

characteristic

C₂²×C₁₉

#488

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

100

C₄×C₁₉

#416

yes

—

101

C₄×C₁₉

#444

yes

—

102

C₄×C₁₉

#495

yes

—

103

#533

C₂×D₁₉

yes

characteristic

104

#532

C₂×D₁₉

yes

characteristic

105

#488

—

106

#487

Dic₁₉

yes

—

107

#486

Dic₁₉

yes

—

108

#423

—

109

#416

—

110

C₂×C₄×C₈

—

111

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

112

#341

—

113

Q₈⋊C₈

—

114

D₄⋊C₈

—

115

#322

—

116

C₂×C₁₉

—

117

C₂×C₁₉

—

118

C₂×C₁₉

#1958

yes

characteristic

119

C₂×C₁₉

#1975

yes

—

120

C₂×#41

—

121

C₂×M₁₆

—

122

C₂²×C₈

—

123

C₂²×C₈

C₂²⋊D₁₉

yes

—

124

C₄⋊Q₈

C₂×Dic₁₉

yes

characteristic

125

C₄⋊Q₈

C₂×Dic₁₉

yes

—

126

#127

C₂×Dic₁₉

yes

characteristic

127

#125

—

128

#124

—

129

C₂²⋊Q₈

—

130

#121

—

131

C₄×Q₈

—

132

C₄×D₄

—

133

#117

—

134

C₂×C₄²

C₂²×D₁₉

yes

characteristic

135

C₄⋊C₈

—

136

C₄⋊C₈

—

137

#103

—

138

#102

—

139

C₄×C₈

—

140

C₄×C₈

—

141

C₄×C₈

C₂×Dic₁₉

yes

—

142

C₄×C₈

C₂²⋊D₁₉

yes

—

143

C₁₉

#9863

yes

characteristic, complemented, Sylow

144

#41

—

145

C₂×Q₈

—

146

C₂×Q₈

—

147

C₂×D₄

—

148

C₂×D₄

—

149

C₂×D₄

—

150

C₂²×C₄

—

151

C₂²×C₄

#64543

yes

—

152

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

153

M₁₆

—

154

C₂×C₈

—

155

C₂×C₈

—

156

C₂×C₈

—

157

C₂×C₈

—

158

C₂×C₈

C₂²⋊Dic₁₉

yes

—

159

C₄⋊C₄

—

160

C₄⋊C₄

—

161

C₄⋊C₄

—

162

C₄⋊C₄

—

163

C₂²⋊C₄

—

164

C₂²⋊C₄

—

165

C₄²

—

166

C₄²

D₄×D₁₉

yes

—

167

C₄²

C₂²×Dic₁₉

yes

characteristic

168

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

169

C₂³

—

170

C₂³

#10597382

yes

characteristic

171

Q₈

—

172

Q₈

—

173

D₄

—

174

D₄

—

175

D₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

D₄×Dic₁₉

yes

—

181

C₂×C₄

#10597384

yes

—

182

C₂×C₄

#10597386

yes

characteristic

183

C₂×C₄

#10597396

yes

—

184

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

185

C₈

—

186

C₈

—

187

C₈

—

152

—

188

C₂²

—

189

C₂²

—

190

C₂²

—

191

C₂²

#11926447

yes

characteristic

192

C₂²

#11926898

yes

—

193

C₄

—

194

C₄

—

195

C₄

—

196

C₄

#11926540

yes

—

197

C₄

#11926666

yes

—

198

C₄

#11926926

yes

—

199

C₂

—

200

C₂

—

201

C₂

#14564447

yes

characteristic

202

C₂

#14564529

yes

—

	subgroup	G/H
center	C₂×C₄	#10597386
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#3131	C₂
socle	C₂²×C₁₉	#390
prime radical	C₁₉×#532	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3131	D₁₉
hypocenter	C₁₉	#9863
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3131

subgroup

G/H

center

C₂×C₄

#10597386

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#3131

C₂

socle

C₂²×C₁₉

#390

prime radical

C₁₉×#532

C₂²

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3131

N	H ≅ G/N	type
1. #14563773	C₂	semidirect
2. #14562090	C₂	semidirect
4. C₂×#11926265	C₂	semidirect
143. C₁₉	#9863	semidirect

H ≅ G/N

type

1. #14563773

C₂

semidirect

2. #14562090

C₂

semidirect

4. C₂×#11926265

C₂

semidirect

143. C₁₉

#9863

semidirect

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

subgroup	index
#14563773	2
#14562090	2
#14562086	2
C₂×#11926265	2
C₁₉×#3131	2
#9863	19

subgroup

index

C₁₉×#3131

Subgroups — #18082517

Conjugacy classes of subgroups

Complements

Maximal subgroups