Group #18087333 — subgroups

Subgroups — #18087333

Order 4864.

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

normal subgroups only

This group has 310 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	#14564455	C₂	1	1	yes	maximal, characteristic
2	#14562308	C₂	1	2	yes	maximal
3	#14561495	C₂	1	2	yes	maximal
4	#14561480	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1849	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597315	C₂²	1	1	yes	characteristic
7	#11926597	C₂²	1	2	yes	—
8	C₂×#10597273	—	2	1	no	—
9	C₂×#10597273	—	2	1	no	—
10	#11926410	C₂²	1	1	yes	characteristic
11	#11926291	—	2	4	no	—
12	C₂×C₁₉×#108	—	2	1	no	—
13	C₂×C₁₉×#108	—	2	1	no	—
14	C₁₉×#423	C₂²	1	2	yes	—
15	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
16	C₂²×Dic₃₈	—	2	1	no	—
17	C₂×M₁₆×C₁₉	—	2	2	no	—
18	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
20	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
21	C₂×C₄⋊Dic₁₉	—	2	2	no	—
22	C₂×C₄⋊Dic₁₉	—	2	1	no	—
23	#10597315	—	2	2	no	—
24	#10597315	—	2	1	no	—
25	#10597315	D₄	1	2	yes	—
26	C₁₉×#108	—	4	2	no	—
27	C₁₉×#108	—	4	2	no	—
28	C₁₉×C₄⋊C₈	—	2	2	no	—
29	C₁₉×C₄⋊C₈	—	2	2	no	—
30	C₁₉×#97	—	2	2	no	—
31	C₁₉⋊#95	—	2	2	no	—
32	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
33	#10597273	—	4	2	no	—
34	#10597273	—	4	2	no	—
35	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
36	C₄×C₁₉⋊C₈	—	2	2	no	—
37	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
38	C₂²×C₄×C₁₉	#41	1	2	yes	—
39	C₂²×Dic₁₉	—	4	1	no	—
40	C₂²×Dic₁₉	—	4	1	no	—
41	C₂×Dic₃₈	—	2	2	no	—
42	C₂×Dic₃₈	—	4	1	no	—
43	C₂×Dic₃₈	—	4	1	no	—
44	C₂×Dic₃₈	—	4	1	no	—
45	C₂×Dic₃₈	—	4	1	no	—
46	C₂×Dic₃₈	—	4	1	no	—
47	M₁₆×C₁₉	—	4	2	no	—
48	M₁₆×C₁₉	—	4	2	no	—
49	C₂×C₈×C₁₉	—	2	1	no	—
50	C₂×C₈×C₁₉	—	2	1	no	—
51	C₂×C₈×C₁₉	—	2	1	no	—
52	C₂×C₈×C₁₉	—	2	1	no	—
53	C₂×C₈×C₁₉	—	4	2	no	—
54	C₂×C₈×C₁₉	D₈	1	2	yes	—
55	C₂×C₈×C₁₉	SD₁₆	1	2	yes	—
56	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
57	C₄²×C₁₉	#41	1	2	yes	—
58	C₄²×C₁₉	#41	1	1	yes	characteristic
59	C₄⋊Dic₁₉	—	2	4	no	—
60	C₄⋊Dic₁₉	—	4	2	no	—
61	C₄⋊Dic₁₉	—	4	1	no	—
62	C₄⋊Dic₁₉	—	4	1	no	—
63	C₂×C₁₉⋊C₈	—	4	2	no	—
64	#10632	—	19	1	no	maximal, Sylow
65	C₂³×C₁₉	#124	1	1	yes	characteristic
66	C₂×C₄×C₁₉	—	4	2	no	—
67	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
68	C₂×C₄×C₁₉	#123	1	2	yes	—
69	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
70	C₂×C₄×C₁₉	#126	1	2	yes	—
71	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
72	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
73	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
74	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
75	C₂×Dic₁₉	—	4	2	no	—
76	C₂×Dic₁₉	—	8	1	no	—
77	C₂×Dic₁₉	—	8	1	no	—
78	C₂×Dic₁₉	—	8	2	no	—
79	C₂×Dic₁₉	—	8	1	no	—
80	Dic₃₈	—	4	2	no	—
81	Dic₃₈	—	4	2	no	—
82	Dic₃₈	—	8	1	no	—
83	Dic₃₈	—	8	1	no	—
84	C₈×C₁₉	—	2	2	no	—
85	C₈×C₁₉	—	2	2	no	—
86	C₈×C₁₉	—	8	2	no	—
87	C₁₉⋊C₈	—	8	2	no	—
88	#1960	—	19	1	no	—
89	#1849	D₁₉	1	1	yes	characteristic
90	#1546	—	19	2	no	—
91	#1286	—	19	2	no	—
92	#1281	—	19	1	no	—
93	C₂²×C₁₉	—	2	2	no	—
94	C₂²×C₁₉	#397	1	1	yes	characteristic
95	C₂²×C₁₉	#486	1	1	yes	characteristic
96	C₂²×C₁₉	#489	1	1	yes	characteristic
97	C₄×C₁₉	—	2	2	no	—
98	C₄×C₁₉	—	2	2	no	—
99	C₄×C₁₉	#459	1	1	yes	characteristic
100	C₄×C₁₉	#461	1	1	yes	characteristic
101	C₄×C₁₉	#480	1	1	yes	characteristic
102	C₄×C₁₉	#481	1	1	yes	characteristic
103	Dic₁₉	—	8	2	no	—
104	Dic₁₉	—	16	1	no	—
105	C₂×C₄⋊Q₈	—	19	1	no	—
106	#431	—	19	2	no	—
107	C₂×#108	—	2	1	no	—
108	C₂×#108	—	2	1	no	—
109	#423	C₂×D₁₉	1	2	yes	—
110	C₂×#103	—	38	1	no	—
111	C₂×#103	—	38	1	no	—
112	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
113	#382	—	19	1	no	—
114	#332	—	38	4	no	—
115	C₂×C₁₉	—	2	1	no	—
116	C₂×C₁₉	—	2	1	no	—
117	C₂×C₁₉	#2071	1	1	yes	characteristic
118	C₂×C₁₉	#2082	1	2	yes	—
119	C₂²×Q₈	—	38	1	no	—
120	C₂×M₁₆	—	2	2	no	—
121	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
122	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
123	C₄⋊Q₈	—	19	2	no	—
124	C₄⋊Q₈	—	38	2	no	—
125	C₄⋊Q₈	—	38	1	no	—
126	C₂×C₄⋊C₄	—	38	2	no	—
127	C₂×C₄⋊C₄	—	38	1	no	—
128	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
129	#108	—	4	2	no	—
130	#108	—	4	2	no	—
131	C₄⋊C₈	—	2	2	no	—
132	C₄⋊C₈	—	2	2	no	—
133	C₄⋊C₈	—	38	2	no	—
134	#103	—	76	2	no	—
135	#103	—	76	2	no	—
136	C₂²⋊C₈	—	38	2	no	—
137	#97	—	2	2	no	—
138	C₄×C₈	—	38	2	no	—
139	#95	—	38	2	no	—
140	C₁₉	#10632	1	1	yes	characteristic, complemented, Sylow
141	C₂×Q₈	—	38	2	no	—
142	C₂×Q₈	—	76	1	no	—
143	C₂×Q₈	—	76	1	no	—
144	C₂×Q₈	—	76	1	no	—
145	C₂×Q₈	—	76	1	no	—
146	C₂×Q₈	—	76	1	no	—
147	C₂²×C₄	—	76	1	no	—
148	C₂²×C₄	—	76	1	no	—
149	C₂²×C₄	#64545	1	2	yes	—
150	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
151	M₁₆	—	4	2	no	—
152	M₁₆	—	4	2	no	—
153	C₂×C₈	—	2	1	no	—
154	C₂×C₈	—	2	1	no	—
155	C₂×C₈	—	2	1	no	—
156	C₂×C₈	—	2	1	no	—
157	C₂×C₈	—	4	2	no	—
158	C₂×C₈	—	76	2	no	—
159	C₂×C₈	#64525	1	2	yes	—
160	C₂×C₈	#64527	1	2	yes	—
161	C₄⋊C₄	—	38	4	no	—
162	C₄⋊C₄	—	76	2	no	—
163	C₄⋊C₄	—	76	1	no	—
164	C₄⋊C₄	—	76	1	no	—
165	C₄²	#64541	1	2	yes	—
166	C₄²	D₄×D₁₉	1	1	yes	characteristic
167	C₄²	#64543	1	1	yes	characteristic
168	C₂³	#10597393	1	1	yes	characteristic
169	Q₈	—	76	2	no	—
170	Q₈	—	76	2	no	—
171	Q₈	—	152	1	no	—
172	Q₈	—	152	1	no	—
173	C₂×C₄	—	4	2	no	—
174	C₂×C₄	—	76	2	no	—
175	C₂×C₄	—	152	2	no	—
176	C₂×C₄	—	152	1	no	—
177	C₂×C₄	—	152	1	no	—
178	C₂×C₄	—	152	1	no	—
179	C₂×C₄	#10597340	1	2	yes	—
180	C₂×C₄	#10597344	1	2	yes	—
181	C₂×C₄	#10597375	1	1	yes	characteristic
182	C₂×C₄	C₂×#64525	1	1	yes	characteristic
183	C₂×C₄	#10597378	1	1	yes	characteristic
184	C₂×C₄	#10597384	1	1	yes	characteristic
185	C₂×C₄	C₂×#64527	1	1	yes	characteristic
186	C₂×C₄	#10597388	1	1	yes	characteristic
187	C₈	—	2	2	no	—
188	C₈	—	2	2	no	—
189	C₈	—	8	2	no	—
190	C₈	—	152	2	no	—
191	C₂²	—	2	2	no	—
192	C₂²	#11926470	1	1	yes	characteristic
193	C₂²	#11926892	1	1	yes	characteristic
194	C₂²	#11926906	1	1	yes	characteristic
195	C₄	—	2	2	no	—
196	C₄	—	2	2	no	—
197	C₄	—	304	1	no	—
198	C₄	—	152	2	no	—
199	C₄	#11926736	1	1	yes	characteristic
200	C₄	#11926746	1	1	yes	characteristic
201	C₄	#11926857	1	1	yes	characteristic
202	C₄	#11926862	1	1	yes	characteristic
203	C₂	—	2	1	no	—
204	C₂	—	2	1	no	—
205	C₂	#14565039	1	1	yes	characteristic
206	C₂	#14565100	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14564455

C₂

yes

maximal, characteristic

#14562308

C₂

yes

maximal

#14561495

C₂

yes

maximal

#14561480

C₂

yes

maximal, characteristic

C₁₉×#1849

C₂

yes

maximal, characteristic

C₂×#10597315

C₂²

yes

characteristic

#11926597

C₂²

yes

—

C₂×#10597273

—

C₂×#10597273

—

#11926410

C₂²

yes

characteristic

#11926291

—

C₂×C₁₉×#108

—

C₂×C₁₉×#108

—

C₁₉×#423

C₂²

yes

—

C₂×C₁₉×#97

C₂²

yes

characteristic

C₂²×Dic₃₈

—

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

#10597315

—

#10597315

—

#10597315

D₄

yes

—

C₁₉×#108

—

C₁₉×#108

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×#97

—

C₁₉⋊#95

—

C₂²⋊(C₁₉⋊C₈)

—

#10597273

—

#10597273

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₈

yes

—

C₂×C₈×C₁₉

SD₁₆

yes

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₄²×C₁₉

#41

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#121

yes

characteristic

C₂×C₄×C₁₉

#123

yes

—

C₂×C₄×C₁₉

#123

yes

characteristic

C₂×C₄×C₁₉

#126

yes

—

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

C₂×C₄×C₁₉

C₂×SD₁₆

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1960

—

#1849

D₁₉

yes

—

—

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#459

yes

characteristic

100

C₄×C₁₉

#461

yes

characteristic

101

C₄×C₁₉

#480

yes

characteristic

102

C₄×C₁₉

#481

yes

characteristic

103

Dic₁₉

—

104

Dic₁₉

—

105

C₂×C₄⋊Q₈

—

106

#431

—

107

C₂×#108

—

108

C₂×#108

—

109

#423

C₂×D₁₉

yes

—

110

C₂×#103

—

111

C₂×#103

—

112

C₂×#97

C₂×D₁₉

yes

characteristic

113

#382

—

114

#332

—

115

C₂×C₁₉

—

116

C₂×C₁₉

—

117

C₂×C₁₉

#2071

yes

characteristic

118

C₂×C₁₉

#2082

yes

—

119

C₂²×Q₈

—

120

C₂×M₁₆

—

121

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

122

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

123

C₄⋊Q₈

—

124

C₄⋊Q₈

—

125

C₄⋊Q₈

—

126

C₂×C₄⋊C₄

—

127

C₂×C₄⋊C₄

—

128

C₂×C₄²

C₂²×D₁₉

yes

characteristic

129

#108

—

130

#108

—

131

C₄⋊C₈

—

132

C₄⋊C₈

—

133

C₄⋊C₈

—

134

#103

—

135

#103

—

136

C₂²⋊C₈

—

137

#97

—

138

C₄×C₈

—

139

#95

—

140

C₁₉

#10632

yes

characteristic, complemented, Sylow

141

C₂×Q₈

—

142

C₂×Q₈

—

143

C₂×Q₈

—

144

C₂×Q₈

—

145

C₂×Q₈

—

146

C₂×Q₈

—

147

C₂²×C₄

—

148

C₂²×C₄

—

149

C₂²×C₄

#64545

yes

—

150

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

151

M₁₆

—

152

M₁₆

—

153

C₂×C₈

—

154

C₂×C₈

—

155

C₂×C₈

—

156

C₂×C₈

—

157

C₂×C₈

—

158

C₂×C₈

—

159

C₂×C₈

#64525

yes

—

160

C₂×C₈

#64527

yes

—

161

C₄⋊C₄

—

162

C₄⋊C₄

—

163

C₄⋊C₄

—

164

C₄⋊C₄

—

165

C₄²

#64541

yes

—

166

C₄²

D₄×D₁₉

yes

characteristic

167

C₄²

#64543

yes

characteristic

168

C₂³

#10597393

yes

characteristic

169

Q₈

—

170

Q₈

—

171

Q₈

—

152

—

172

Q₈

—

152

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

—

152

—

176

C₂×C₄

—

152

—

177

C₂×C₄

—

152

—

178

C₂×C₄

—

152

—

179

C₂×C₄

#10597340

yes

—

180

C₂×C₄

#10597344

yes

—

181

C₂×C₄

#10597375

yes

characteristic

182

C₂×C₄

C₂×#64525

yes

characteristic

183

C₂×C₄

#10597378

yes

characteristic

184

C₂×C₄

#10597384

yes

characteristic

185

C₂×C₄

C₂×#64527

yes

characteristic

186

C₂×C₄

#10597388

yes

characteristic

187

C₈

—

188

C₈

—

189

C₈

—

190

C₈

—

152

—

191

C₂²

—

192

C₂²

#11926470

yes

characteristic

193

C₂²

#11926892

yes

characteristic

194

C₂²

#11926906

yes

characteristic

195

C₄

—

196

C₄

—

197

C₄

—

304

—

198

C₄

—

152

—

199

C₄

#11926736

yes

characteristic

200

C₄

#11926746

yes

characteristic

201

C₄

#11926857

yes

characteristic

202

C₄

#11926862

yes

characteristic

203

C₂

—

204

C₂

—

205

C₂

#14565039

yes

characteristic

206

C₂

#14565100

yes

—

	subgroup	G/H
center	C₂²	#11926470
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1849	C₂
socle	C₂²×C₁₉	#397
prime radical	C₂³×C₁₉	#124
hypercenter	#1849	D₁₉
hypocenter	C₁₉	#10632
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1849

subgroup

G/H

center

C₂²

#11926470

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1849

C₂

C₂²×C₁₉

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1849

N	H ≅ G/N	type
140. C₁₉	#10632	semidirect

H ≅ G/N

type

140. C₁₉

#10632

semidirect

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

subgroup	index
#14564455	2
#14562308	2
#14561495	2
#14561480	2
C₁₉×#1849	2
#10632	19

subgroup

index

C₁₉×#1849

Subgroups — #18087333

Conjugacy classes of subgroups

Complements

Maximal subgroups