Group #18086610 — subgroups

Subgroups — #18086610

Order 4864.

408 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 77 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	#14574945	C₂	1	1	yes	maximal, characteristic
2	#14563788	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562331	C₂	1	2	yes	maximal, complemented
4	#14562144	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1290	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927094	C₂²	1	2	yes	—
7	#11926825	—	2	2	no	—
8	#11926780	—	2	2	no	—
9	#11926740	—	2	2	no	—
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×Dic₁₉⋊C₈	—	2	2	no	—
12	#11926390	C₂²	1	1	yes	characteristic
13	#11926292	—	2	2	no	—
14	#11926287	—	2	2	no	—
15	#11926279	—	2	4	no	—
16	C₁₉×#432	C₂²	1	2	yes	—
17	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×#64541	—	2	2	no	—
19	C₂²×C₈×C₁₉	D₄	1	2	yes	—
20	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
21	#10597376	—	2	2	no	—
22	#10597376	—	2	2	no	—
23	C₂×C₄×Dic₁₉	—	2	1	no	—
24	C₂²×C₁₉⋊C₈	—	2	1	no	—
25	C₂×D₁₅₂	—	2	2	no	—
26	#10597321	—	2	2	no	—
27	#10597320	D₄	1	2	yes	—
28	C₄×D₇₆	—	2	2	no	—
29	C₄×D₇₆	—	2	2	no	—
30	#10597315	D₄	1	2	yes	—
31	C₁₉×C₄⋊C₈	—	2	2	no	—
32	C₁₉×C₄⋊C₈	—	2	2	no	—
33	C₁₉×C₂²⋊C₈	—	2	2	no	—
34	C₁₉×#97	—	2	2	no	—
35	C₁₉⋊#95	—	2	1	no	—
36	C₁₉⋊#95	D₄	1	2	yes	—
37	#10597278	—	2	4	no	—
38	#10597275	—	2	2	no	—
39	Dic₁₉⋊C₈	—	4	4	no	—
40	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
41	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
44	C₂×C₂²⋊D₁₉	—	4	2	no	—
45	C₂²×Dic₁₉	—	2	2	no	—
46	#64541	—	8	4	no	—
47	C₂×D₇₆	—	2	2	no	—
48	C₂×D₇₆	—	2	2	no	—
49	C₂×D₇₆	—	2	2	no	—
50	C₂×C₄×D₁₉	—	4	2	no	—
51	C₂×Dic₃₈	—	2	2	no	—
52	C₂×C₈×C₁₉	—	2	2	no	—
53	C₂×C₈×C₁₉	—	4	2	no	—
54	C₂×C₈×C₁₉	—	4	2	no	—
55	C₄²×C₁₉	C₂×D₄	1	2	yes	—
56	C₄²×C₁₉	#41	1	2	yes	—
57	(C₂×D₁₉)⋊C₄	—	4	2	no	—
58	(C₂×D₁₉)⋊C₄	—	4	2	no	—
59	C₄⋊Dic₁₉	—	2	2	no	—
60	C₄⋊Dic₁₉	—	2	2	no	—
61	C₄×Dic₁₉	—	2	2	no	—
62	C₄×Dic₁₉	—	2	2	no	—
63	C₂×C₁₉⋊C₈	—	4	2	no	—
64	C₂×C₁₉⋊C₈	—	4	1	no	—
65	D₁₅₂	—	8	2	no	—
66	#10512	—	19	1	no	maximal, Sylow
67	C₂³×C₁₉	#121	1	1	yes	characteristic
68	C₂²×D₁₉	—	4	2	no	—
69	C₂×C₄×C₁₉	—	2	2	no	—
70	C₂×C₄×C₁₉	—	2	1	no	—
71	C₂×C₄×C₁₉	—	2	1	no	—
72	C₂×C₄×C₁₉	—	4	1	no	—
73	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
74	C₂×C₄×C₁₉	#121	1	2	yes	—
75	C₂×C₄×C₁₉	#123	1	2	yes	—
76	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
77	C₂²⋊D₁₉	—	8	4	no	—
78	C₂×Dic₁₉	—	2	4	no	—
79	C₂×Dic₁₉	—	4	2	no	—
80	C₂×Dic₁₉	—	4	2	no	—
81	C₂×Dic₁₉	—	4	2	no	—
82	D₇₆	—	4	2	no	—
83	D₇₆	—	4	2	no	—
84	D₇₆	—	8	2	no	—
85	D₇₆	—	8	2	no	—
86	C₄×D₁₉	—	8	4	no	—
87	Dic₃₈	—	8	2	no	—
88	C₈×C₁₉	—	4	2	no	—
89	C₈×C₁₉	—	8	2	no	—
90	C₁₉⋊C₈	—	8	1	no	—
91	#3245	—	19	1	no	—
92	#1843	—	19	1	no	—
93	#1551	—	19	2	no	—
94	#1505	—	19	2	no	—
95	#1290	D₁₉	1	1	yes	characteristic, complemented
96	C₂²×C₁₉	—	2	1	no	—
97	C₂²×C₁₉	—	2	1	no	—
98	C₂²×C₁₉	#394	1	1	yes	characteristic
99	C₂²×C₁₉	#472	1	2	yes	—
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	—	2	2	no	—
106	C₄×C₁₉	#453	1	1	yes	characteristic
107	C₄×C₁₉	#456	1	1	yes	characteristic
108	Dic₁₉	—	4	4	no	—
109	Dic₁₉	—	8	2	no	—
110	#532	—	19	2	no	—
111	#474	—	38	2	no	—
112	#466	—	38	2	no	—
113	#459	—	38	2	no	—
114	#432	C₂×D₁₉	1	2	yes	—
115	C₂×C₄⋊C₈	—	19	1	no	—
116	C₂×C₄⋊C₈	—	38	2	no	—
117	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
118	#376	—	19	1	no	—
119	#333	—	38	2	no	—
120	#331	—	38	2	no	—
121	#327	—	38	4	no	—
122	C₂×C₁₉	—	2	2	no	—
123	C₂×C₁₉	#2039	1	1	yes	characteristic
124	C₂×C₁₉	#2045	1	1	yes	characteristic
125	C₂×C₁₉	#2053	1	1	yes	characteristic
126	D₁₉	—	16	2	no	—
127	C₂×#41	—	38	2	no	—
128	C₂×D₈	—	38	2	no	—
129	C₂²×C₈	—	38	1	no	—
130	C₂²×C₈	D₇₆	1	2	yes	—
131	C₄⋊Q₈	—	19	2	no	—
132	#127	—	19	2	no	—
133	#124	—	38	2	no	—
134	#121	—	38	2	no	—
135	#121	—	38	2	no	—
136	C₄×D₄	—	38	2	no	—
137	C₄×D₄	—	38	2	no	—
138	C₂×C₄²	—	38	1	no	—
139	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
140	#107	—	38	2	no	—
141	C₄⋊C₈	—	2	2	no	—
142	C₄⋊C₈	—	2	2	no	—
143	C₄⋊C₈	—	38	2	no	—
144	C₄⋊C₈	—	76	4	no	—
145	#102	—	38	4	no	—
146	C₂²⋊C₈	—	2	2	no	—
147	#97	—	2	2	no	—
148	#95	—	19	2	no	—
149	#95	—	38	1	no	—
150	C₁₉	#10512	1	1	yes	characteristic, complemented, Sylow
151	#41	—	152	4	no	—
152	C₂×Q₈	—	38	2	no	—
153	C₂×D₄	—	38	2	no	—
154	C₂×D₄	—	38	2	no	—
155	C₂×D₄	—	38	2	no	—
156	C₂×D₄	—	76	2	no	—
157	C₂²×C₄	—	38	2	no	—
158	C₂²×C₄	—	76	2	no	—
159	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
160	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
161	C₂²×C₄	#64545	1	1	yes	characteristic
162	D₈	—	152	2	no	—
163	C₂×C₈	—	2	2	no	—
164	C₂×C₈	—	4	2	no	—
165	C₂×C₈	—	4	2	no	—
166	C₂×C₈	—	76	2	no	—
167	C₂×C₈	—	76	1	no	—
168	C₄⋊C₄	—	38	2	no	—
169	C₄⋊C₄	—	38	2	no	—
170	C₂²⋊C₄	—	76	2	no	—
171	C₂²⋊C₄	—	76	2	no	—
172	C₄²	—	38	2	no	—
173	C₄²	—	38	2	no	—
174	C₄²	#64541	1	2	yes	—
175	C₄²	D₄×D₁₉	1	2	yes	—
176	C₂³	—	76	2	no	—
177	C₂³	#10597341	1	1	yes	characteristic
178	Q₈	—	152	2	no	—
179	D₄	—	76	2	no	—
180	D₄	—	76	2	no	—
181	D₄	—	152	2	no	—
182	D₄	—	152	2	no	—
183	D₄	—	152	4	no	—
184	C₂×C₄	—	2	2	no	—
185	C₂×C₄	—	2	1	no	—
186	C₂×C₄	—	2	1	no	—
187	C₂×C₄	—	4	1	no	—
188	C₂×C₄	—	38	4	no	—
189	C₂×C₄	—	76	2	no	—
190	C₂×C₄	—	76	2	no	—
191	C₂×C₄	—	76	2	no	—
192	C₂×C₄	—	152	4	no	—
193	C₂×C₄	#10597321	1	1	yes	characteristic
194	C₂×C₄	#10597328	1	1	yes	characteristic
195	C₂×C₄	#10597330	1	2	yes	—
196	C₂×C₄	#10597340	1	2	yes	—
197	C₈	—	4	2	no	—
198	C₈	—	8	2	no	—
199	C₈	—	152	1	no	—
200	C₂²	—	2	1	no	—
201	C₂²	—	2	1	no	—
202	C₂²	—	152	2	no	—
203	C₂²	—	152	2	no	—
204	C₂²	—	152	2	no	—
205	C₂²	#11926462	1	1	yes	characteristic
206	C₂²	#11926815	1	2	yes	—
207	C₄	—	2	2	no	—
208	C₄	—	2	2	no	—
209	C₄	—	2	1	no	—
210	C₄	—	76	4	no	—
211	C₄	—	152	2	no	—
212	C₄	#11926714	1	1	yes	characteristic
213	C₄	#11926729	1	1	yes	characteristic
214	C₂	—	2	2	no	—
215	C₂	—	304	2	no	—
216	C₂	#14564860	1	1	yes	characteristic
217	C₂	#14564892	1	1	yes	characteristic
218	C₂	#14564942	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14574945

C₂

yes

maximal, characteristic

#14563788

C₂

yes

maximal, characteristic, complemented

#14562331

C₂

yes

maximal, complemented

#14562144

C₂

yes

maximal, complemented

C₁₉×#1290

C₂

yes

maximal, characteristic, complemented

#11927094

C₂²

yes

—

#11926825

—

#11926780

—

#11926740

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×Dic₁₉⋊C₈

—

#11926390

C₂²

yes

—

—

—

C₁₉×#432

C₂²

yes

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₂×#64541

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

#10597376

—

#10597376

—

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₂×D₁₅₂

—

#10597321

—

#10597320

D₄

yes

—

C₄×D₇₆

—

C₄×D₇₆

—

#10597315

D₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₁₉⋊#95

—

C₁₉⋊#95

D₄

yes

—

#10597278

—

#10597275

—

Dic₁₉⋊C₈

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂×C₂²⋊D₁₉

—

C₂²×Dic₁₉

—

#64541

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

D₁₅₂

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#120

yes

characteristic

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

#123

yes

—

C₂×C₄×C₁₉

#124

yes

characteristic

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

C₄×D₁₉

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

—

—

—

—

D₁₉

yes

characteristic, complemented

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#394

yes

characteristic

C₂²×C₁₉

#472

yes

—

100

C₂×D₁₉

—

101

C₂×D₁₉

—

102

C₂×D₁₉

—

103

C₄×C₁₉

—

104

C₄×C₁₉

—

105

C₄×C₁₉

—

106

C₄×C₁₉

#453

yes

characteristic

107

C₄×C₁₉

#456

yes

characteristic

108

Dic₁₉

—

109

Dic₁₉

—

110

#532

—

111

#474

—

112

#466

—

113

#459

—

114

#432

C₂×D₁₉

yes

—

115

C₂×C₄⋊C₈

—

116

C₂×C₄⋊C₈

—

117

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

118

#376

—

119

#333

—

120

#331

—

121

#327

—

122

C₂×C₁₉

—

123

C₂×C₁₉

#2039

yes

characteristic

124

C₂×C₁₉

#2045

yes

characteristic

125

C₂×C₁₉

#2053

yes

characteristic

126

D₁₉

—

127

C₂×#41

—

128

C₂×D₈

—

129

C₂²×C₈

—

130

C₂²×C₈

D₇₆

yes

—

131

C₄⋊Q₈

—

132

#127

—

133

#124

—

134

#121

—

135

#121

—

136

C₄×D₄

—

137

C₄×D₄

—

138

C₂×C₄²

—

139

C₂×C₄²

C₂²×D₁₉

yes

characteristic

140

#107

—

141

C₄⋊C₈

—

142

C₄⋊C₈

—

143

C₄⋊C₈

—

144

C₄⋊C₈

—

145

#102

—

146

C₂²⋊C₈

—

147

#97

—

148

#95

—

149

#95

—

150

C₁₉

#10512

yes

characteristic, complemented, Sylow

151

#41

—

152

—

152

C₂×Q₈

—

153

C₂×D₄

—

154

C₂×D₄

—

155

C₂×D₄

—

156

C₂×D₄

—

157

C₂²×C₄

—

158

C₂²×C₄

—

159

C₂²×C₄

C₂×D₇₆

yes

characteristic

160

C₂²×C₄

D₄×D₁₉

yes

characteristic

161

C₂²×C₄

#64545

yes

characteristic

162

D₈

—

152

—

163

C₂×C₈

—

164

C₂×C₈

—

165

C₂×C₈

—

166

C₂×C₈

—

167

C₂×C₈

—

168

C₄⋊C₄

—

169

C₄⋊C₄

—

170

C₂²⋊C₄

—

171

C₂²⋊C₄

—

172

C₄²

—

173

C₄²

—

174

C₄²

#64541

yes

—

175

C₄²

D₄×D₁₉

yes

—

176

C₂³

—

177

C₂³

#10597341

yes

characteristic

178

Q₈

—

152

—

179

D₄

—

180

D₄

—

181

D₄

—

152

—

182

D₄

—

152

—

183

D₄

—

152

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

152

—

193

C₂×C₄

#10597321

yes

characteristic

194

C₂×C₄

#10597328

yes

characteristic

195

C₂×C₄

#10597330

yes

—

196

C₂×C₄

#10597340

yes

—

197

C₈

—

198

C₈

—

199

C₈

—

152

—

200

C₂²

—

201

C₂²

—

202

C₂²

—

152

—

203

C₂²

—

152

—

204

C₂²

—

152

—

205

C₂²

#11926462

yes

characteristic

206

C₂²

#11926815

yes

—

207

C₄

—

208

C₄

—

209

C₄

—

210

C₄

—

211

C₄

—

152

—

212

C₄

#11926714

yes

characteristic

213

C₄

#11926729

yes

characteristic

214

C₂

—

215

C₂

—

304

—

216

C₂

#14564860

yes

characteristic

217

C₂

#14564892

yes

characteristic

218

C₂

#14564942

yes

characteristic

	subgroup	G/H
center	C₂²	#11926462
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1290	C₂
socle	C₂²×C₁₉	#394
prime radical	#14574945	C₂
hypercenter	#1290	D₁₉
hypocenter	C₁₉	#10512
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1290

subgroup

G/H

center

C₂²

#11926462

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1290

C₂

C₂²×C₁₉

C₂

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1290

N	H ≅ G/N	type
2. #14563788	C₂	semidirect
3. #14562331	C₂	semidirect
4. #14562144	C₂	semidirect
5. C₁₉×#1290	C₂	semidirect
95. #1290	D₁₉	semidirect
150. C₁₉	#10512	semidirect

H ≅ G/N

type

2. #14563788

C₂

semidirect

3. #14562331

C₂

semidirect

4. #14562144

C₂

semidirect

5. C₁₉×#1290

C₂

semidirect

95. #1290

D₁₉

semidirect

150. C₁₉

#10512

semidirect

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

subgroup	index
#14574945	2
#14563788	2
#14562331	2
#14562144	2
C₁₉×#1290	2
#10512	19

subgroup

index

C₁₉×#1290

Subgroups — #18086610

Conjugacy classes of subgroups

Complements

Maximal subgroups