Group #18085289 — subgroups

Subgroups — #18085289

Order 4864.

576 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 113 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	#14574781	C₂	1	2	yes	maximal
2	#14572033	C₂	1	1	yes	maximal, characteristic
3	#14564612	C₂	1	1	yes	maximal, characteristic
4	#14562306	C₂	1	2	yes	maximal
5	C₁₉×#1276	C₂	1	1	yes	maximal, characteristic
6	#11927101	C₂²	1	1	yes	characteristic
7	C₂×#10597315	—	2	2	no	—
8	C₂×#10597315	C₂²	1	2	yes	—
9	#11926942	—	2	2	no	—
10	#11926895	—	2	2	no	—
11	#11926875	—	2	4	no	—
12	#11926830	—	2	4	no	—
13	#11926568	C₂²	1	1	yes	characteristic
14	#11926414	—	2	4	no	—
15	#11926304	—	2	2	no	—
16	#11926289	—	2	4	no	—
17	C₁₉×#431	C₂²	1	2	yes	—
18	C₄³×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×Dic₃₈	—	2	2	no	—
20	C₂×C₄²×C₁₉	—	2	2	no	—
21	C₂×C₄²×C₁₉	D₄	1	2	yes	—
22	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
23	#10597372	—	2	1	no	—
24	C₂×C₄⋊Dic₁₉	—	2	8	no	—
25	C₂×C₄⋊Dic₁₉	—	2	2	no	—
26	C₂×C₄⋊Dic₁₉	D₄	1	4	yes	—
27	#10597370	—	2	2	no	—
28	C₂×#64520	—	2	1	no	—
29	#10597316	—	2	1	no	—
30	#10597315	—	2	2	no	—
31	#10597315	—	2	2	no	—
32	#10597315	—	2	2	no	—
33	#10597315	—	2	2	no	—
34	#10597315	—	4	4	no	—
35	#10597315	—	4	4	no	—
36	#10597315	D₄	1	2	yes	—
37	C₄×Dic₃₈	—	2	2	no	—
38	C₁₉×C₄⋊C₈	D₄	1	4	yes	—
39	C₁₉×C₂²⋊C₈	—	2	2	no	—
40	C₄×C₈×C₁₉	—	2	2	no	—
41	#10597274	—	2	8	no	—
42	#10597273	—	2	8	no	—
43	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
44	C₂²×C₄×C₁₉	—	2	2	no	—
45	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
46	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
47	C₂²×Dic₁₉	—	2	4	no	—
48	C₂×Dic₃₈	—	2	2	no	—
49	C₂×Dic₃₈	—	4	2	no	—
50	C₂×Dic₃₈	—	4	2	no	—
51	C₂×Dic₃₈	—	4	4	no	—
52	C₂×Dic₃₈	—	4	4	no	—
53	C₂×C₈×C₁₉	—	2	4	no	—
54	C₄²×C₁₉	—	2	8	no	—
55	C₄²×C₁₉	—	2	2	no	—
56	C₄²×C₁₉	SD₁₆	1	4	yes	—
57	C₄²×C₁₉	C₂×D₄	1	2	yes	—
58	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
59	C₄²×C₁₉	#41	1	1	yes	characteristic
60	C₂²⋊Dic₁₉	—	4	1	no	—
61	C₄⋊Dic₁₉	—	2	4	no	—
62	C₄⋊Dic₁₉	—	2	2	no	—
63	C₄⋊Dic₁₉	—	2	4	no	—
64	C₄⋊Dic₁₉	—	2	2	no	—
65	C₄⋊Dic₁₉	—	4	16	no	—
66	C₄⋊Dic₁₉	—	4	2	no	—
67	C₄⋊Dic₁₉	—	4	2	no	—
68	Dic₁₉⋊C₄	—	4	2	no	—
69	C₄×Dic₁₉	—	4	1	no	—
70	#64520	—	4	2	no	—
71	C₂×C₁₉⋊C₈	—	4	1	no	—
72	#10299	—	19	1	no	maximal, Sylow
73	C₂³×C₁₉	#120	1	1	yes	characteristic
74	C₂×C₄×C₁₉	—	2	8	no	—
75	C₂×C₄×C₁₉	—	2	4	no	—
76	C₂×C₄×C₁₉	—	2	4	no	—
77	C₂×C₄×C₁₉	#120	1	2	yes	—
78	C₂×C₄×C₁₉	#121	1	2	yes	—
79	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
80	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
81	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
82	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
83	C₂×Dic₁₉	—	4	2	no	—
84	C₂×Dic₁₉	—	4	4	no	—
85	C₂×Dic₁₉	—	4	8	no	—
86	Dic₃₈	—	4	4	no	—
87	Dic₃₈	—	8	4	no	—
88	Dic₃₈	—	8	2	no	—
89	Dic₃₈	—	8	2	no	—
90	C₈×C₁₉	—	4	4	no	—
91	C₁₉⋊C₈	—	8	1	no	—
92	#3229	—	19	2	no	—
93	#2868	—	19	1	no	—
94	#1994	—	19	1	no	—
95	#1546	—	19	2	no	—
96	#1276	D₁₉	1	1	yes	characteristic
97	C₂²×C₁₉	—	2	2	no	—
98	C₂²×C₁₉	#392	1	1	yes	characteristic
99	C₂²×C₁₉	#450	1	2	yes	—
100	C₄×C₁₉	—	2	8	no	—
101	C₄×C₁₉	—	2	2	no	—
102	C₄×C₁₉	#456	1	4	yes	—
103	C₄×C₁₉	#460	1	2	yes	—
104	C₄×C₁₉	#492	1	1	yes	characteristic
105	C₄×C₁₉	#496	1	1	yes	characteristic
106	Dic₁₉	—	8	2	no	—
107	Dic₁₉	—	8	4	no	—
108	#533	—	19	1	no	—
109	C₂×C₄⋊Q₈	—	19	2	no	—
110	C₂×C₄⋊Q₈	—	38	2	no	—
111	#498	—	38	2	no	—
112	#487	—	38	2	no	—
113	#483	—	38	4	no	—
114	#475	—	38	4	no	—
115	#431	C₂×D₁₉	1	2	yes	—
116	#423	—	19	1	no	—
117	#384	—	38	4	no	—
118	C₄³	C₂×D₁₉	1	1	yes	characteristic
119	#339	—	38	2	no	—
120	#332	—	38	4	no	—
121	C₂×C₁₉	—	2	2	no	—
122	C₂×C₁₉	#2005	1	2	yes	—
123	C₂×C₁₉	#2014	1	1	yes	characteristic
124	C₂²×Q₈	—	38	2	no	—
125	C₂×M₁₆	—	38	1	no	—
126	C₄⋊Q₈	—	19	2	no	—
127	C₄⋊Q₈	—	38	2	no	—
128	C₄⋊Q₈	—	38	2	no	—
129	C₄⋊Q₈	—	38	2	no	—
130	C₄⋊Q₈	—	38	2	no	—
131	C₄⋊Q₈	—	76	4	no	—
132	C₄⋊Q₈	—	76	4	no	—
133	#125	—	38	1	no	—
134	C₂²⋊Q₈	—	38	2	no	—
135	C₄×Q₈	—	38	2	no	—
136	#117	—	38	1	no	—
137	C₂×C₄⋊C₄	—	19	4	no	—
138	C₂×C₄⋊C₄	—	38	8	no	—
139	C₂×C₄⋊C₄	—	38	2	no	—
140	C₂×C₄²	—	2	2	no	—
141	C₂×C₄²	D₇₆	1	2	yes	—
142	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
143	#106	—	38	8	no	—
144	C₄⋊C₈	—	38	2	no	—
145	C₄⋊C₈	D₇₆	1	4	yes	—
146	#103	—	38	8	no	—
147	C₂²⋊C₈	—	2	2	no	—
148	C₄×C₈	—	2	2	no	—
149	C₁₉	#10299	1	1	yes	characteristic, complemented, Sylow
150	C₂×Q₈	—	38	2	no	—
151	C₂×Q₈	—	76	2	no	—
152	C₂×Q₈	—	76	2	no	—
153	C₂×Q₈	—	76	4	no	—
154	C₂×Q₈	—	76	4	no	—
155	C₂²×C₄	—	2	2	no	—
156	C₂²×C₄	—	38	4	no	—
157	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
158	C₂²×C₄	D₄×D₁₉	1	2	yes	—
159	M₁₆	—	76	2	no	—
160	C₂×C₈	—	2	4	no	—
161	C₂×C₈	—	76	1	no	—
162	C₄⋊C₄	—	38	4	no	—
163	C₄⋊C₄	—	38	2	no	—
164	C₄⋊C₄	—	38	4	no	—
165	C₄⋊C₄	—	38	2	no	—
166	C₄⋊C₄	—	76	16	no	—
167	C₄⋊C₄	—	76	2	no	—
168	C₄⋊C₄	—	76	2	no	—
169	C₄⋊C₄	—	76	2	no	—
170	C₂²⋊C₄	—	76	1	no	—
171	C₄²	—	2	8	no	—
172	C₄²	—	2	2	no	—
173	C₄²	—	76	1	no	—
174	C₄²	#64516	1	4	yes	—
175	C₄²	C₂×D₇₆	1	2	yes	—
176	C₄²	D₄×D₁₉	1	1	yes	characteristic
177	C₄²	#64545	1	1	yes	characteristic
178	C₂³	#10597328	1	1	yes	characteristic
179	Q₈	—	76	4	no	—
180	Q₈	—	152	2	no	—
181	Q₈	—	152	2	no	—
182	Q₈	—	152	4	no	—
183	C₂×C₄	—	2	8	no	—
184	C₂×C₄	—	2	4	no	—
185	C₂×C₄	—	2	4	no	—
186	C₂×C₄	—	76	8	no	—
187	C₂×C₄	—	76	2	no	—
188	C₂×C₄	—	76	4	no	—
189	C₂×C₄	#10597320	1	1	yes	characteristic
190	C₂×C₄	#10597328	1	2	yes	—
191	C₂×C₄	#10597341	1	2	yes	—
192	C₂×C₄	#10597341	1	1	yes	characteristic
193	C₂×C₄	C₂×#64516	1	2	yes	—
194	C₂×C₄	#10597354	1	2	yes	—
195	C₈	—	4	4	no	—
196	C₈	—	152	1	no	—
197	C₂²	—	2	2	no	—
198	C₂²	#11926454	1	1	yes	characteristic
199	C₂²	#11926697	1	2	yes	—
200	C₄	—	2	8	no	—
201	C₄	—	2	2	no	—
202	C₄	—	152	2	no	—
203	C₄	—	152	4	no	—
204	C₄	#11926728	1	4	yes	—
205	C₄	#11926745	1	2	yes	—
206	C₄	#11926917	1	1	yes	characteristic
207	C₄	#11926933	1	1	yes	characteristic
208	C₂	—	2	2	no	—
209	C₂	#14564674	1	2	yes	—
210	C₂	#14564725	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14574781

C₂

yes

maximal

#14572033

C₂

yes

maximal, characteristic

#14564612

C₂

yes

maximal, characteristic

#14562306

C₂

yes

maximal

C₁₉×#1276

C₂

yes

maximal, characteristic

#11927101

C₂²

yes

characteristic

C₂×#10597315

—

C₂×#10597315

C₂²

yes

—

—

—

—

—

C₂²

yes

—

—

—

C₁₉×#431

C₂²

yes

—

C₄³×C₁₉

C₂²

yes

characteristic

C₂²×Dic₃₈

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

#10597372

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

D₄

yes

—

—

—

—

—

—

—

—

—

—

D₄

yes

—

C₄×Dic₃₈

—

C₁₉×C₄⋊C₈

D₄

yes

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

#10597274

—

#10597273

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

SD₁₆

yes

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

#41

yes

characteristic

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

#64520

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#120

yes

—

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

—

—

—

—

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

#392

yes

characteristic

C₂²×C₁₉

#450

yes

—

100

C₄×C₁₉

—

101

C₄×C₁₉

—

102

C₄×C₁₉

#456

yes

—

103

C₄×C₁₉

#460

yes

—

104

C₄×C₁₉

#492

yes

characteristic

105

C₄×C₁₉

#496

yes

characteristic

106

Dic₁₉

—

107

Dic₁₉

—

108

#533

—

109

C₂×C₄⋊Q₈

—

110

C₂×C₄⋊Q₈

—

111

#498

—

112

#487

—

113

#483

—

114

#475

—

115

#431

C₂×D₁₉

yes

—

116

#423

—

117

#384

—

118

C₄³

C₂×D₁₉

yes

characteristic

119

#339

—

120

#332

—

121

C₂×C₁₉

—

122

C₂×C₁₉

#2005

yes

—

123

C₂×C₁₉

#2014

yes

characteristic

124

C₂²×Q₈

—

125

C₂×M₁₆

—

126

C₄⋊Q₈

—

127

C₄⋊Q₈

—

128

C₄⋊Q₈

—

129

C₄⋊Q₈

—

130

C₄⋊Q₈

—

131

C₄⋊Q₈

—

132

C₄⋊Q₈

—

133

#125

—

134

C₂²⋊Q₈

—

135

C₄×Q₈

—

136

#117

—

137

C₂×C₄⋊C₄

—

138

C₂×C₄⋊C₄

—

139

C₂×C₄⋊C₄

—

140

C₂×C₄²

—

141

C₂×C₄²

D₇₆

yes

—

142

C₂×C₄²

C₂²×D₁₉

yes

characteristic

143

#106

—

144

C₄⋊C₈

—

145

C₄⋊C₈

D₇₆

yes

—

146

#103

—

147

C₂²⋊C₈

—

148

C₄×C₈

—

149

C₁₉

#10299

yes

characteristic, complemented, Sylow

150

C₂×Q₈

—

151

C₂×Q₈

—

152

C₂×Q₈

—

153

C₂×Q₈

—

154

C₂×Q₈

—

155

C₂²×C₄

—

156

C₂²×C₄

—

157

C₂²×C₄

C₂×D₇₆

yes

characteristic

158

C₂²×C₄

D₄×D₁₉

yes

—

159

M₁₆

—

160

C₂×C₈

—

161

C₂×C₈

—

162

C₄⋊C₄

—

163

C₄⋊C₄

—

164

C₄⋊C₄

—

165

C₄⋊C₄

—

166

C₄⋊C₄

—

167

C₄⋊C₄

—

168

C₄⋊C₄

—

169

C₄⋊C₄

—

170

C₂²⋊C₄

—

171

C₄²

—

172

C₄²

—

173

C₄²

—

174

C₄²

#64516

yes

—

175

C₄²

C₂×D₇₆

yes

—

176

C₄²

D₄×D₁₉

yes

characteristic

177

C₄²

#64545

yes

characteristic

178

C₂³

#10597328

yes

characteristic

179

Q₈

—

180

Q₈

—

152

—

181

Q₈

—

152

—

182

Q₈

—

152

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

#10597320

yes

characteristic

190

C₂×C₄

#10597328

yes

—

191

C₂×C₄

#10597341

yes

—

192

C₂×C₄

#10597341

yes

characteristic

193

C₂×C₄

C₂×#64516

yes

—

194

C₂×C₄

#10597354

yes

—

195

C₈

—

196

C₈

—

152

—

197

C₂²

—

198

C₂²

#11926454

yes

characteristic

199

C₂²

#11926697

yes

—

200

C₄

—

201

C₄

—

202

C₄

—

152

—

203

C₄

—

152

—

204

C₄

#11926728

yes

—

205

C₄

#11926745

yes

—

206

C₄

#11926917

yes

characteristic

207

C₄

#11926933

yes

characteristic

208

C₂

—

209

C₂

#14564674

yes

—

210

C₂

#14564725

yes

characteristic

	subgroup	G/H
center	C₂²	#11926454
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1276	C₂
socle	C₂²×C₁₉	#392
prime radical	C₂³×C₁₉	#120
hypercenter	#1276	D₁₉
hypocenter	C₁₉	#10299
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1276

subgroup

G/H

center

C₂²

#11926454

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1276

C₂

C₂²×C₁₉

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1276

N	H ≅ G/N	type
149. C₁₉	#10299	semidirect

H ≅ G/N

type

149. C₁₉

#10299

semidirect

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

subgroup	index
#14574781	2
#14572033	2
#14564612	2
#14562306	2
C₁₉×#1276	2
#10299	19

subgroup

index

C₁₉×#1276

Subgroups — #18085289

Conjugacy classes of subgroups

Complements

Maximal subgroups