Group #18086716 — subgroups

Subgroups — #18086716

Order 4864.

386 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 83 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	#14575016	C₂	1	1	yes	maximal, characteristic
2	#14562368	C₂	1	2	yes	maximal, complemented
3	#14562087	C₂	1	2	yes	maximal, complemented
4	C₁₉⋊#1309	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1837	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927094	C₂²	1	2	yes	—
7	#11926835	—	2	2	no	—
8	#11926797	—	2	2	no	—
9	#11926740	—	2	2	no	—
10	#11926568	C₂²	1	2	yes	—
11	#11926292	—	2	2	no	—
12	#11926287	—	2	2	no	—
13	#11926273	—	2	4	no	—
14	C₁₉×#423	C₂²	1	1	yes	characteristic
15	C₁₉×#423	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#341	—	2	2	no	—
18	C₂×#64541	—	2	2	no	—
19	C₂×M₁₆×C₁₉	—	2	1	no	—
20	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
21	C₂²×C₈×C₁₉	—	2	1	no	—
22	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
23	#10597376	—	2	2	no	—
24	#10597376	—	2	2	no	—
25	C₂×#64520	—	2	2	no	—
26	C₂×D₁₅₂	—	2	2	no	—
27	#10597321	—	2	2	no	—
28	#10597320	D₄	1	2	yes	—
29	C₄×D₇₆	—	2	2	no	—
30	C₄×D₇₆	—	2	2	no	—
31	#10597315	D₄	1	2	yes	—
32	C₁₉×C₄⋊C₈	—	2	2	no	—
33	C₁₉×C₄⋊C₈	—	2	2	no	—
34	C₄×C₈×C₁₉	—	2	1	no	—
35	C₄×C₈×C₁₉	D₄	1	2	yes	—
36	#10597278	—	2	4	no	—
37	#10597274	—	2	2	no	—
38	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
39	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
40	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	#41	1	2	yes	—
42	C₂×C₂²⋊D₁₉	—	4	2	no	—
43	#64541	—	8	2	no	—
44	#64541	—	8	2	no	—
45	C₂×D₇₆	—	2	2	no	—
46	C₂×D₇₆	—	2	2	no	—
47	C₂×D₇₆	—	2	2	no	—
48	C₂×C₄×D₁₉	—	4	2	no	—
49	C₂×Dic₃₈	—	2	2	no	—
50	M₁₆×C₁₉	—	4	2	no	—
51	M₁₆×C₁₉	—	4	2	no	—
52	C₂×C₈×C₁₉	—	2	2	no	—
53	C₂×C₈×C₁₉	—	2	2	no	—
54	C₂×C₈×C₁₉	—	4	1	no	—
55	C₂×C₈×C₁₉	—	4	1	no	—
56	C₂×C₈×C₁₉	—	4	1	no	—
57	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₄²×C₁₉	C₂×D₄	1	2	yes	—
59	C₄²×C₁₉	#41	1	1	yes	characteristic
60	(C₂×D₁₉)⋊C₄	—	4	2	no	—
61	(C₂×D₁₉)⋊C₄	—	4	2	no	—
62	C₄⋊Dic₁₉	—	2	2	no	—
63	C₄⋊Dic₁₉	—	2	2	no	—
64	#64520	—	8	2	no	—
65	C₂×C₁₉⋊C₈	—	4	2	no	—
66	D₁₅₂	—	8	2	no	—
67	#10531	—	19	1	no	maximal, Sylow
68	C₂³×C₁₉	#124	1	1	yes	characteristic
69	C₂²×D₁₉	—	4	2	no	—
70	C₂×C₄×C₁₉	—	2	1	no	—
71	C₂×C₄×C₁₉	—	2	1	no	—
72	C₂×C₄×C₁₉	—	2	2	no	—
73	C₂×C₄×C₁₉	—	2	2	no	—
74	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
75	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
76	C₂×C₄×C₁₉	#121	1	2	yes	—
77	C₂×C₄×C₁₉	#123	1	2	yes	—
78	C₂²⋊D₁₉	—	8	4	no	—
79	C₂×Dic₁₉	—	4	2	no	—
80	D₇₆	—	4	2	no	—
81	D₇₆	—	4	2	no	—
82	D₇₆	—	4	2	no	—
83	D₇₆	—	4	2	no	—
84	D₇₆	—	8	2	no	—
85	C₄×D₁₉	—	8	2	no	—
86	C₄×D₁₉	—	8	2	no	—
87	Dic₃₈	—	8	2	no	—
88	C₈×C₁₉	—	4	2	no	—
89	C₈×C₁₉	—	4	2	no	—
90	C₈×C₁₉	—	8	1	no	—
91	C₁₉⋊C₈	—	8	2	no	—
92	#3253	—	19	1	no	—
93	#1837	D₁₉	1	1	yes	characteristic, complemented
94	#1560	—	19	2	no	—
95	#1492	—	19	2	no	—
96	#1309	—	19	1	no	—
97	C₂²×C₁₉	—	2	2	no	—
98	C₂²×C₁₉	—	2	1	no	—
99	C₂²×C₁₉	#394	1	1	yes	characteristic
100	C₂×D₁₉	—	8	2	no	—
101	C₂×D₁₉	—	8	2	no	—
102	C₂×D₁₉	—	8	2	no	—
103	C₄×C₁₉	—	2	2	no	—
104	C₄×C₁₉	—	2	1	no	—
105	C₄×C₁₉	#454	1	1	yes	characteristic
106	C₄×C₁₉	#455	1	1	yes	characteristic
107	C₄×C₁₉	#471	1	2	yes	—
108	C₄×C₁₉	#472	1	2	yes	—
109	Dic₁₉	—	8	2	no	—
110	#532	—	19	2	no	—
111	#476	—	38	2	no	—
112	#469	—	38	2	no	—
113	#459	—	38	2	no	—
114	#423	—	19	2	no	—
115	#423	C₂×D₁₉	1	1	yes	characteristic
116	#423	C₂×D₁₉	1	1	yes	characteristic
117	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
118	#341	—	2	2	no	—
119	#333	—	38	2	no	—
120	#331	—	38	2	no	—
121	D₄⋊C₈	—	38	4	no	—
122	C₂×C₁₉	—	4	1	no	—
123	C₂×C₁₉	#2040	1	1	yes	characteristic
124	C₂×C₁₉	#2051	1	2	yes	—
125	D₁₉	—	16	2	no	—
126	C₂×#41	—	38	2	no	—
127	C₂×D₈	—	38	2	no	—
128	C₂×M₁₆	—	2	1	no	—
129	C₂×M₁₆	—	38	2	no	—
130	C₂×M₁₆	C₂²⋊D₁₉	1	2	yes	—
131	C₂²×C₈	—	2	1	no	—
132	C₄⋊Q₈	—	19	2	no	—
133	#127	—	19	2	no	—
134	#124	—	38	2	no	—
135	#121	—	38	2	no	—
136	#121	—	38	2	no	—
137	C₄×D₄	—	38	2	no	—
138	C₄×D₄	—	38	2	no	—
139	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
140	#106	—	38	2	no	—
141	C₄⋊C₈	—	2	2	no	—
142	C₄⋊C₈	—	2	2	no	—
143	C₄⋊C₈	—	38	2	no	—
144	C₄⋊C₈	—	38	2	no	—
145	#102	—	38	4	no	—
146	C₄×C₈	—	2	1	no	—
147	C₄×C₈	D₇₆	1	2	yes	—
148	C₁₉	#10531	1	1	yes	characteristic, complemented, Sylow
149	#41	—	152	2	no	—
150	#41	—	152	2	no	—
151	C₂×Q₈	—	38	2	no	—
152	C₂×D₄	—	38	2	no	—
153	C₂×D₄	—	38	2	no	—
154	C₂×D₄	—	38	2	no	—
155	C₂×D₄	—	76	2	no	—
156	C₂²×C₄	—	76	2	no	—
157	C₂²×C₄	#64545	1	2	yes	—
158	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
159	D₈	—	152	2	no	—
160	M₁₆	—	4	2	no	—
161	M₁₆	—	4	2	no	—
162	M₁₆	—	152	2	no	—
163	C₂×C₈	—	2	2	no	—
164	C₂×C₈	—	2	2	no	—
165	C₂×C₈	—	4	1	no	—
166	C₂×C₈	—	4	1	no	—
167	C₂×C₈	—	4	1	no	—
168	C₂×C₈	—	76	2	no	—
169	C₄⋊C₄	—	38	2	no	—
170	C₄⋊C₄	—	38	2	no	—
171	C₂²⋊C₄	—	76	2	no	—
172	C₂²⋊C₄	—	76	2	no	—
173	C₄²	C₂×D₇₆	1	1	yes	characteristic
174	C₄²	#64541	1	1	yes	characteristic
175	C₄²	D₄×D₁₉	1	2	yes	—
176	C₂³	—	76	2	no	—
177	C₂³	#10597393	1	1	yes	characteristic
178	Q₈	—	152	2	no	—
179	D₄	—	76	2	no	—
180	D₄	—	76	2	no	—
181	D₄	—	76	2	no	—
182	D₄	—	76	2	no	—
183	D₄	—	152	2	no	—
184	D₄	—	152	4	no	—
185	C₂×C₄	—	2	2	no	—
186	C₂×C₄	—	2	2	no	—
187	C₂×C₄	—	2	1	no	—
188	C₂×C₄	—	2	1	no	—
189	C₂×C₄	—	76	2	no	—
190	C₂×C₄	—	152	2	no	—
191	C₂×C₄	—	152	2	no	—
192	C₂×C₄	#10597340	1	2	yes	—
193	C₂×C₄	#10597341	1	2	yes	—
194	C₂×C₄	#10597376	1	1	yes	characteristic
195	C₂×C₄	#10597383	1	1	yes	characteristic
196	C₈	—	4	2	no	—
197	C₈	—	4	2	no	—
198	C₈	—	8	1	no	—
199	C₈	—	152	2	no	—
200	C₂²	—	2	1	no	—
201	C₂²	—	2	2	no	—
202	C₂²	—	152	2	no	—
203	C₂²	—	152	2	no	—
204	C₂²	—	152	2	no	—
205	C₂²	#11926461	1	1	yes	characteristic
206	C₄	—	2	1	no	—
207	C₄	—	2	2	no	—
208	C₄	—	152	2	no	—
209	C₄	#11926716	1	1	yes	characteristic
210	C₄	#11926721	1	1	yes	characteristic
211	C₄	#11926808	1	2	yes	—
212	C₄	#11926815	1	2	yes	—
213	C₂	—	4	1	no	—
214	C₂	—	304	2	no	—
215	C₂	#14564864	1	1	yes	characteristic
216	C₂	#14564929	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14575016

C₂

yes

maximal, characteristic

#14562368

C₂

yes

maximal, complemented

#14562087

C₂

yes

maximal, complemented

C₁₉⋊#1309

C₂

yes

maximal, characteristic, complemented

C₁₉×#1837

C₂

yes

maximal, characteristic, complemented

#11927094

C₂²

yes

—

—

—

—

C₂²

yes

—

#11926292

—

#11926287

—

#11926273

—

C₁₉×#423

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#341

—

C₂×#64541

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

D₄

yes

—

C₂²×C₈×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

—

—

—

C₂×D₁₅₂

—

#10597321

—

#10597320

D₄

yes

—

C₄×D₇₆

—

C₄×D₇₆

—

#10597315

D₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

D₄

yes

—

#10597278

—

#10597274

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂×C₂²⋊D₁₉

—

#64541

—

#64541

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

characteristic

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

#64520

—

C₂×C₁₉⋊C₈

—

D₁₅₂

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#123

yes

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

C₄×D₁₉

—

C₄×D₁₉

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#3253

—

#1837

D₁₉

yes

characteristic, complemented

#1560

—

#1492

—

#1309

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#394

yes

characteristic

100

C₂×D₁₉

—

101

C₂×D₁₉

—

102

C₂×D₁₉

—

103

C₄×C₁₉

—

104

C₄×C₁₉

—

105

C₄×C₁₉

#454

yes

characteristic

106

C₄×C₁₉

#455

yes

characteristic

107

C₄×C₁₉

#471

yes

—

108

C₄×C₁₉

#472

yes

—

109

Dic₁₉

—

110

#532

—

111

#476

—

112

#469

—

113

#459

—

114

#423

—

115

#423

C₂×D₁₉

yes

characteristic

116

#423

C₂×D₁₉

yes

characteristic

117

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

118

#341

—

119

#333

—

120

#331

—

121

D₄⋊C₈

—

122

C₂×C₁₉

—

123

C₂×C₁₉

#2040

yes

characteristic

124

C₂×C₁₉

#2051

yes

—

125

D₁₉

—

126

C₂×#41

—

127

C₂×D₈

—

128

C₂×M₁₆

—

129

C₂×M₁₆

—

130

C₂×M₁₆

C₂²⋊D₁₉

yes

—

131

C₂²×C₈

—

132

C₄⋊Q₈

—

133

#127

—

134

#124

—

135

#121

—

136

#121

—

137

C₄×D₄

—

138

C₄×D₄

—

139

C₂×C₄²

C₂²×D₁₉

yes

characteristic

140

#106

—

141

C₄⋊C₈

—

142

C₄⋊C₈

—

143

C₄⋊C₈

—

144

C₄⋊C₈

—

145

#102

—

146

C₄×C₈

—

147

C₄×C₈

D₇₆

yes

—

148

C₁₉

#10531

yes

characteristic, complemented, Sylow

149

#41

—

152

—

150

#41

—

152

—

151

C₂×Q₈

—

152

C₂×D₄

—

153

C₂×D₄

—

154

C₂×D₄

—

155

C₂×D₄

—

156

C₂²×C₄

—

157

C₂²×C₄

#64545

yes

—

158

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

159

D₈

—

152

—

160

M₁₆

—

161

M₁₆

—

162

M₁₆

—

152

—

163

C₂×C₈

—

164

C₂×C₈

—

165

C₂×C₈

—

166

C₂×C₈

—

167

C₂×C₈

—

168

C₂×C₈

—

169

C₄⋊C₄

—

170

C₄⋊C₄

—

171

C₂²⋊C₄

—

172

C₂²⋊C₄

—

173

C₄²

C₂×D₇₆

yes

characteristic

174

C₄²

#64541

yes

characteristic

175

C₄²

D₄×D₁₉

yes

—

176

C₂³

—

177

C₂³

#10597393

yes

characteristic

178

Q₈

—

152

—

179

D₄

—

180

D₄

—

181

D₄

—

182

D₄

—

183

D₄

—

152

—

184

D₄

—

152

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

152

—

191

C₂×C₄

—

152

—

192

C₂×C₄

#10597340

yes

—

193

C₂×C₄

#10597341

yes

—

194

C₂×C₄

#10597376

yes

characteristic

195

C₂×C₄

#10597383

yes

characteristic

196

C₈

—

197

C₈

—

198

C₈

—

199

C₈

—

152

—

200

C₂²

—

201

C₂²

—

202

C₂²

—

152

—

203

C₂²

—

152

—

204

C₂²

—

152

—

205

C₂²

#11926461

yes

characteristic

206

C₄

—

207

C₄

—

208

C₄

—

152

—

209

C₄

#11926716

yes

characteristic

210

C₄

#11926721

yes

characteristic

211

C₄

#11926808

yes

—

212

C₄

#11926815

yes

—

213

C₂

—

214

C₂

—

304

—

215

C₂

#14564864

yes

characteristic

216

C₂

#14564929

yes

—

	subgroup	G/H
center	C₂²	#11926461
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1837	C₂
socle	C₂²×C₁₉	#394
prime radical	#14575016	C₂
hypercenter	#1837	D₁₉
hypocenter	C₁₉	#10531
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1837

subgroup

G/H

center

C₂²

#11926461

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1837

C₂

C₂²×C₁₉

C₂

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1837

N	H ≅ G/N	type
2. #14562368	C₂	semidirect
3. #14562087	C₂	semidirect
4. C₁₉⋊#1309	C₂	semidirect
5. C₁₉×#1837	C₂	semidirect
93. #1837	D₁₉	semidirect
148. C₁₉	#10531	semidirect

H ≅ G/N

type

2. #14562368

C₂

semidirect

3. #14562087

C₂

semidirect

4. C₁₉⋊#1309

C₂

semidirect

5. C₁₉×#1837

C₂

semidirect

93. #1837

D₁₉

semidirect

148. C₁₉

#10531

semidirect

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

subgroup	index
#14575016	2
#14562368	2
#14562087	2
C₁₉⋊#1309	2
C₁₉×#1837	2
#10531	19

subgroup

index

#14575016

#14562368

#14562087

C₁₉⋊#1309

C₁₉×#1837

#10531

Subgroups — #18086716

Conjugacy classes of subgroups

Complements

Maximal subgroups