Group #18086711 — subgroups

Subgroups — #18086711

Order 4864.

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

normal subgroups only

This group has 402 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×#1848	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	C₂×C₁₉×#108	—	2	2	no	—
15	C₁₉×#423	C₂²	1	1	yes	characteristic
16	C₁₉×#423	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
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×#108	—	4	4	no	—
33	C₁₉×C₄⋊C₈	—	2	2	no	—
34	C₁₉×C₄⋊C₈	—	2	2	no	—
35	C₄×C₈×C₁₉	—	2	1	no	—
36	C₄×C₈×C₁₉	D₄	1	2	yes	—
37	#10597278	—	2	4	no	—
38	#10597274	—	2	2	no	—
39	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
40	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
41	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	#41	1	2	yes	—
43	C₂×C₂²⋊D₁₉	—	4	2	no	—
44	#64541	—	8	2	no	—
45	#64541	—	8	2	no	—
46	C₂×D₇₆	—	2	2	no	—
47	C₂×D₇₆	—	2	2	no	—
48	C₂×D₇₆	—	2	2	no	—
49	C₂×C₄×D₁₉	—	4	2	no	—
50	C₂×Dic₃₈	—	2	2	no	—
51	M₁₆×C₁₉	—	4	2	no	—
52	M₁₆×C₁₉	—	4	2	no	—
53	C₂×C₈×C₁₉	—	2	2	no	—
54	C₂×C₈×C₁₉	—	2	2	no	—
55	C₂×C₈×C₁₉	—	2	2	no	—
56	C₂×C₈×C₁₉	—	2	2	no	—
57	C₂×C₈×C₁₉	—	4	1	no	—
58	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
59	C₄²×C₁₉	C₂×D₄	1	2	yes	—
60	C₄²×C₁₉	#41	1	1	yes	characteristic
61	(C₂×D₁₉)⋊C₄	—	4	2	no	—
62	(C₂×D₁₉)⋊C₄	—	4	2	no	—
63	C₄⋊Dic₁₉	—	2	2	no	—
64	C₄⋊Dic₁₉	—	2	2	no	—
65	#64520	—	8	2	no	—
66	C₂×C₁₉⋊C₈	—	4	2	no	—
67	D₁₅₂	—	8	2	no	—
68	#10530	—	19	1	no	maximal, Sylow
69	C₂³×C₁₉	#124	1	1	yes	characteristic
70	C₂²×D₁₉	—	4	2	no	—
71	C₂×C₄×C₁₉	—	2	1	no	—
72	C₂×C₄×C₁₉	—	2	1	no	—
73	C₂×C₄×C₁₉	—	2	2	no	—
74	C₂×C₄×C₁₉	—	2	2	no	—
75	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
76	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
77	C₂×C₄×C₁₉	#121	1	2	yes	—
78	C₂×C₄×C₁₉	#123	1	2	yes	—
79	C₂²⋊D₁₉	—	8	4	no	—
80	C₂×Dic₁₉	—	4	2	no	—
81	D₇₆	—	4	2	no	—
82	D₇₆	—	4	2	no	—
83	D₇₆	—	4	2	no	—
84	D₇₆	—	4	2	no	—
85	D₇₆	—	8	2	no	—
86	C₄×D₁₉	—	8	2	no	—
87	C₄×D₁₉	—	8	2	no	—
88	Dic₃₈	—	8	2	no	—
89	C₈×C₁₉	—	2	4	no	—
90	C₈×C₁₉	—	4	2	no	—
91	C₈×C₁₉	—	8	1	no	—
92	C₁₉⋊C₈	—	8	2	no	—
93	#3253	—	19	1	no	—
94	#1848	D₁₉	1	1	yes	characteristic, complemented
95	#1560	—	19	2	no	—
96	#1492	—	19	2	no	—
97	#1309	—	19	1	no	—
98	C₂²×C₁₉	—	2	2	no	—
99	C₂²×C₁₉	—	2	1	no	—
100	C₂²×C₁₉	#394	1	1	yes	characteristic
101	C₂×D₁₉	—	8	2	no	—
102	C₂×D₁₉	—	8	2	no	—
103	C₂×D₁₉	—	8	2	no	—
104	C₄×C₁₉	—	2	2	no	—
105	C₄×C₁₉	—	2	1	no	—
106	C₄×C₁₉	#453	1	1	yes	characteristic
107	C₄×C₁₉	#456	1	1	yes	characteristic
108	C₄×C₁₉	#471	1	2	yes	—
109	C₄×C₁₉	#472	1	2	yes	—
110	Dic₁₉	—	8	2	no	—
111	#532	—	19	2	no	—
112	#476	—	38	2	no	—
113	#469	—	38	2	no	—
114	#459	—	38	2	no	—
115	C₂×#108	—	2	2	no	—
116	#423	—	19	2	no	—
117	#423	C₂×D₁₉	1	1	yes	characteristic
118	#423	C₂×D₁₉	1	1	yes	characteristic
119	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
120	#333	—	38	2	no	—
121	#331	—	38	2	no	—
122	D₄⋊C₈	—	38	4	no	—
123	C₂×C₁₉	—	4	1	no	—
124	C₂×C₁₉	#2039	1	1	yes	characteristic
125	C₂×C₁₉	#2051	1	2	yes	—
126	D₁₉	—	16	2	no	—
127	C₂×#41	—	38	2	no	—
128	C₂×D₈	—	38	2	no	—
129	C₂×M₁₆	—	2	1	no	—
130	C₂×M₁₆	—	38	2	no	—
131	C₂×M₁₆	C₂²⋊D₁₉	1	2	yes	—
132	C₂²×C₈	—	2	1	no	—
133	C₄⋊Q₈	—	19	2	no	—
134	#127	—	19	2	no	—
135	#124	—	38	2	no	—
136	#121	—	38	2	no	—
137	#121	—	38	2	no	—
138	C₄×D₄	—	38	2	no	—
139	C₄×D₄	—	38	2	no	—
140	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
141	#108	—	4	4	no	—
142	#106	—	38	2	no	—
143	C₄⋊C₈	—	2	2	no	—
144	C₄⋊C₈	—	2	2	no	—
145	C₄⋊C₈	—	38	2	no	—
146	C₄⋊C₈	—	38	2	no	—
147	#102	—	38	4	no	—
148	C₄×C₈	—	2	1	no	—
149	C₄×C₈	D₇₆	1	2	yes	—
150	C₁₉	#10530	1	1	yes	characteristic, complemented, Sylow
151	#41	—	152	2	no	—
152	#41	—	152	2	no	—
153	C₂×Q₈	—	38	2	no	—
154	C₂×D₄	—	38	2	no	—
155	C₂×D₄	—	38	2	no	—
156	C₂×D₄	—	38	2	no	—
157	C₂×D₄	—	76	2	no	—
158	C₂²×C₄	—	76	2	no	—
159	C₂²×C₄	#64545	1	2	yes	—
160	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
161	D₈	—	152	2	no	—
162	M₁₆	—	4	2	no	—
163	M₁₆	—	4	2	no	—
164	M₁₆	—	152	2	no	—
165	C₂×C₈	—	2	2	no	—
166	C₂×C₈	—	2	2	no	—
167	C₂×C₈	—	2	2	no	—
168	C₂×C₈	—	2	2	no	—
169	C₂×C₈	—	4	1	no	—
170	C₂×C₈	—	76	2	no	—
171	C₄⋊C₄	—	38	2	no	—
172	C₄⋊C₄	—	38	2	no	—
173	C₂²⋊C₄	—	76	2	no	—
174	C₂²⋊C₄	—	76	2	no	—
175	C₄²	C₂×D₇₆	1	1	yes	characteristic
176	C₄²	#64541	1	1	yes	characteristic
177	C₄²	D₄×D₁₉	1	2	yes	—
178	C₂³	—	76	2	no	—
179	C₂³	#10597393	1	1	yes	characteristic
180	Q₈	—	152	2	no	—
181	D₄	—	76	2	no	—
182	D₄	—	76	2	no	—
183	D₄	—	76	2	no	—
184	D₄	—	76	2	no	—
185	D₄	—	152	2	no	—
186	D₄	—	152	4	no	—
187	C₂×C₄	—	2	2	no	—
188	C₂×C₄	—	2	2	no	—
189	C₂×C₄	—	2	1	no	—
190	C₂×C₄	—	2	1	no	—
191	C₂×C₄	—	76	2	no	—
192	C₂×C₄	—	152	2	no	—
193	C₂×C₄	—	152	2	no	—
194	C₂×C₄	#10597340	1	2	yes	—
195	C₂×C₄	#10597341	1	2	yes	—
196	C₂×C₄	#10597376	1	1	yes	characteristic
197	C₂×C₄	#10597383	1	1	yes	characteristic
198	C₈	—	2	4	no	—
199	C₈	—	4	2	no	—
200	C₈	—	8	1	no	—
201	C₈	—	152	2	no	—
202	C₂²	—	2	2	no	—
203	C₂²	—	2	1	no	—
204	C₂²	—	152	2	no	—
205	C₂²	—	152	2	no	—
206	C₂²	—	152	2	no	—
207	C₂²	#11926461	1	1	yes	characteristic
208	C₄	—	2	2	no	—
209	C₄	—	2	1	no	—
210	C₄	—	152	2	no	—
211	C₄	#11926711	1	1	yes	characteristic
212	C₄	#11926726	1	1	yes	characteristic
213	C₄	#11926808	1	2	yes	—
214	C₄	#11926815	1	2	yes	—
215	C₂	—	4	1	no	—
216	C₂	—	304	2	no	—
217	C₂	#14564859	1	1	yes	characteristic
218	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×#1848

C₂

yes

maximal, characteristic, complemented

#11927094

C₂²

yes

—

—

—

—

C₂²

yes

—

#11926292

—

#11926287

—

#11926273

—

C₂×C₁₉×#108

—

C₁₉×#423

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

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×#108

—

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

—

#1848

D₁₉

yes

characteristic, complemented

#1560

—

#1492

—

#1309

—

C₂²×C₁₉

—

C₂²×C₁₉

—

100

C₂²×C₁₉

#394

yes

characteristic

101

C₂×D₁₉

—

102

C₂×D₁₉

—

103

C₂×D₁₉

—

104

C₄×C₁₉

—

105

C₄×C₁₉

—

106

C₄×C₁₉

#453

yes

characteristic

107

C₄×C₁₉

#456

yes

characteristic

108

C₄×C₁₉

#471

yes

—

109

C₄×C₁₉

#472

yes

—

110

Dic₁₉

—

111

#532

—

112

#476

—

113

#469

—

114

#459

—

115

C₂×#108

—

116

#423

—

117

#423

C₂×D₁₉

yes

characteristic

118

#423

C₂×D₁₉

yes

characteristic

119

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

120

#333

—

121

#331

—

122

D₄⋊C₈

—

123

C₂×C₁₉

—

124

C₂×C₁₉

#2039

yes

characteristic

125

C₂×C₁₉

#2051

yes

—

126

D₁₉

—

127

C₂×#41

—

128

C₂×D₈

—

129

C₂×M₁₆

—

130

C₂×M₁₆

—

131

C₂×M₁₆

C₂²⋊D₁₉

yes

—

132

C₂²×C₈

—

133

C₄⋊Q₈

—

134

#127

—

135

#124

—

136

#121

—

137

#121

—

138

C₄×D₄

—

139

C₄×D₄

—

140

C₂×C₄²

C₂²×D₁₉

yes

characteristic

141

#108

—

142

#106

—

143

C₄⋊C₈

—

144

C₄⋊C₈

—

145

C₄⋊C₈

—

146

C₄⋊C₈

—

147

#102

—

148

C₄×C₈

—

149

C₄×C₈

D₇₆

yes

—

150

C₁₉

#10530

yes

characteristic, complemented, Sylow

151

#41

—

152

—

152

#41

—

152

—

153

C₂×Q₈

—

154

C₂×D₄

—

155

C₂×D₄

—

156

C₂×D₄

—

157

C₂×D₄

—

158

C₂²×C₄

—

159

C₂²×C₄

#64545

yes

—

160

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

161

D₈

—

152

—

162

M₁₆

—

163

M₁₆

—

164

M₁₆

—

152

—

165

C₂×C₈

—

166

C₂×C₈

—

167

C₂×C₈

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₄⋊C₄

—

172

C₄⋊C₄

—

173

C₂²⋊C₄

—

174

C₂²⋊C₄

—

175

C₄²

C₂×D₇₆

yes

characteristic

176

C₄²

#64541

yes

characteristic

177

C₄²

D₄×D₁₉

yes

—

178

C₂³

—

179

C₂³

#10597393

yes

characteristic

180

Q₈

—

152

—

181

D₄

—

182

D₄

—

183

D₄

—

184

D₄

—

185

D₄

—

152

—

186

D₄

—

152

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

152

—

193

C₂×C₄

—

152

—

194

C₂×C₄

#10597340

yes

—

195

C₂×C₄

#10597341

yes

—

196

C₂×C₄

#10597376

yes

characteristic

197

C₂×C₄

#10597383

yes

characteristic

198

C₈

—

199

C₈

—

200

C₈

—

201

C₈

—

152

—

202

C₂²

—

203

C₂²

—

204

C₂²

—

152

—

205

C₂²

—

152

—

206

C₂²

—

152

—

207

C₂²

#11926461

yes

characteristic

208

C₄

—

209

C₄

—

210

C₄

—

152

—

211

C₄

#11926711

yes

characteristic

212

C₄

#11926726

yes

characteristic

213

C₄

#11926808

yes

—

214

C₄

#11926815

yes

—

215

C₂

—

216

C₂

—

304

—

217

C₂

#14564859

yes

characteristic

218

C₂

#14564929

yes

—

	subgroup	G/H
center	C₂²	#11926461
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1848	C₂
socle	C₂²×C₁₉	#394
prime radical	#14575016	C₂
hypercenter	#1848	D₁₉
hypocenter	C₁₉	#10530
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1848

subgroup

G/H

center

C₂²

#11926461

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1848

C₂

C₂²×C₁₉

C₂

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1848

N	H ≅ G/N	type
2. #14562368	C₂	semidirect
3. #14562087	C₂	semidirect
4. C₁₉⋊#1309	C₂	semidirect
5. C₁₉×#1848	C₂	semidirect
94. #1848	D₁₉	semidirect
150. C₁₉	#10530	semidirect

H ≅ G/N

type

2. #14562368

C₂

semidirect

3. #14562087

C₂

semidirect

4. C₁₉⋊#1309

C₂

semidirect

5. C₁₉×#1848

C₂

semidirect

94. #1848

D₁₉

semidirect

150. C₁₉

#10530

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×#1848	2
#10530	19

subgroup

index

#14575016

#14562368

#14562087

C₁₉⋊#1309

C₁₉×#1848

#10530

Subgroups — #18086711

Conjugacy classes of subgroups

Complements

Maximal subgroups