Group #18069318 — subgroups

Subgroups — #18069318

Order 4864.

230 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 67 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	#14561715	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1375	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597315	C₄	1	1	yes	characteristic
5	C₂×#10597269	—	2	1	no	—
6	C₂×#10597273	—	2	1	no	—
7	C₂×#10597273	—	2	1	no	—
8	#11926410	C₄	1	1	yes	characteristic
9	C₂×C₁₉×M₃₂	—	2	1	no	—
10	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
11	C₂²×Dic₃₈	—	2	1	no	—
12	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
13	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
14	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄⋊Dic₁₉	—	2	1	no	—
16	C₂×C₄⋊Dic₁₉	—	4	1	no	—
17	#10597315	—	2	1	no	—
18	#10597315	—	4	1	no	—
19	#10597315	C₈	1	2	yes	—
20	C₁₉×M₃₂	—	4	1	no	—
21	C₁₉×M₃₂	—	4	1	no	—
22	C₂×C₁₆×C₁₉	—	2	2	no	—
23	C₁₉×#97	—	4	1	no	—
24	C₁₉⋊#95	—	4	1	no	—
25	#10597273	—	4	1	no	—
26	#10597273	—	4	1	no	—
27	#10597273	—	4	1	no	—
28	#10597273	—	4	1	no	—
29	#10597269	—	4	1	no	—
30	#10597269	—	4	1	no	—
31	C₂×C₁₉⋊C₁₆	—	2	2	no	—
32	C₂²×C₄×C₁₉	—	2	1	no	—
33	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
34	C₂²×Dic₁₉	—	4	1	no	—
35	C₂²×Dic₁₉	—	4	1	no	—
36	C₂×Dic₃₈	—	2	2	no	—
37	C₂×Dic₃₈	—	4	1	no	—
38	C₂×Dic₃₈	—	4	1	no	—
39	C₂×Dic₃₈	—	4	1	no	—
40	C₂×Dic₃₈	—	4	1	no	—
41	C₂×Dic₃₈	—	4	1	no	—
42	C₂×C₈×C₁₉	—	2	1	no	—
43	C₂×C₈×C₁₉	—	2	1	no	—
44	C₂×C₈×C₁₉	—	2	1	no	—
45	C₂×C₈×C₁₉	—	2	1	no	—
46	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
47	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
48	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
49	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
50	C₄²×C₁₉	—	2	1	no	—
51	C₄²×C₁₉	C₂×C₈	1	1	yes	characteristic
52	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
53	C₄⋊Dic₁₉	—	4	2	no	—
54	C₄⋊Dic₁₉	—	4	2	no	—
55	C₄⋊Dic₁₉	—	4	1	no	—
56	C₄⋊Dic₁₉	—	4	1	no	—
57	C₁₆×C₁₉	—	4	2	no	—
58	C₁₉⋊C₁₆	—	4	2	no	—
59	#7117	—	19	1	no	maximal, Sylow
60	C₂³×C₁₉	#100	1	1	yes	characteristic
61	C₂×C₄×C₁₉	—	2	1	no	—
62	C₂×C₄×C₁₉	—	2	1	no	—
63	C₂×C₄×C₁₉	—	4	2	no	—
64	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
65	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
66	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
67	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
68	C₂×C₄×C₁₉	#104	1	1	yes	characteristic
69	C₂×C₄×C₁₉	#104	1	1	yes	characteristic
70	C₂×Dic₁₉	—	4	2	no	—
71	C₂×Dic₁₉	—	8	1	no	—
72	C₂×Dic₁₉	—	8	1	no	—
73	C₂×Dic₁₉	—	8	2	no	—
74	C₂×Dic₁₉	—	8	1	no	—
75	Dic₃₈	—	4	2	no	—
76	Dic₃₈	—	4	2	no	—
77	Dic₃₈	—	8	1	no	—
78	Dic₃₈	—	8	1	no	—
79	C₈×C₁₉	—	2	1	no	—
80	C₈×C₁₉	—	2	1	no	—
81	C₈×C₁₉	—	2	1	no	—
82	C₈×C₁₉	—	2	1	no	—
83	#1960	—	19	1	no	—
84	#1375	—	19	1	no	—
85	#1375	D₁₉	1	1	yes	characteristic
86	C₂²×C₁₉	—	2	2	no	—
87	C₂²×C₁₉	#323	1	1	yes	characteristic
88	C₂²×C₁₉	#329	1	1	yes	characteristic
89	C₂²×C₁₉	#331	1	1	yes	characteristic
90	C₄×C₁₉	—	4	1	no	—
91	C₄×C₁₉	—	4	1	no	—
92	C₄×C₁₉	D₄⋊C₈	1	1	yes	characteristic
93	C₄×C₁₉	D₄⋊C₈	1	1	yes	characteristic
94	C₄×C₁₉	#327	1	1	yes	characteristic
95	C₄×C₁₉	#327	1	1	yes	characteristic
96	Dic₁₉	—	8	2	no	—
97	Dic₁₉	—	16	1	no	—
98	C₂×C₄⋊Q₈	—	19	1	no	—
99	C₂×M₃₂	—	2	1	no	—
100	C₂×M₃₂	—	38	1	no	—
101	C₂×#103	—	38	1	no	—
102	C₂×#103	—	38	1	no	—
103	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
104	#382	—	19	1	no	—
105	C₂×C₁₉	—	2	1	no	—
106	C₂×C₁₉	—	2	1	no	—
107	C₂×C₁₉	#1270	1	1	yes	characteristic
108	C₂×C₁₉	#1356	1	2	yes	—
109	C₂²×Q₈	—	38	1	no	—
110	C₂²×C₈	D₇₆	1	1	yes	characteristic
111	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
112	C₄⋊Q₈	—	19	2	no	—
113	C₄⋊Q₈	—	38	1	no	—
114	C₄⋊Q₈	—	76	1	no	—
115	C₂×C₄⋊C₄	—	38	1	no	—
116	C₂×C₄⋊C₄	—	76	1	no	—
117	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
118	M₃₂	—	4	1	no	—
119	M₃₂	—	4	1	no	—
120	M₃₂	—	76	1	no	—
121	M₃₂	—	76	1	no	—
122	C₂×C₁₆	—	2	2	no	—
123	C₂×C₁₆	—	38	2	no	—
124	#103	—	76	1	no	—
125	#103	—	76	1	no	—
126	#103	—	76	1	no	—
127	#103	—	76	1	no	—
128	#97	—	4	1	no	—
129	#95	—	76	1	no	—
130	C₁₉	#7117	1	1	yes	characteristic, complemented, Sylow
131	C₂×Q₈	—	38	2	no	—
132	C₂×Q₈	—	76	1	no	—
133	C₂×Q₈	—	76	1	no	—
134	C₂×Q₈	—	76	1	no	—
135	C₂×Q₈	—	76	1	no	—
136	C₂×Q₈	—	76	1	no	—
137	C₂²×C₄	—	2	1	no	—
138	C₂²×C₄	—	76	1	no	—
139	C₂²×C₄	—	76	1	no	—
140	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
141	C₂×C₈	—	2	1	no	—
142	C₂×C₈	—	2	1	no	—
143	C₂×C₈	—	2	1	no	—
144	C₂×C₈	—	2	1	no	—
145	C₂×C₈	#64516	1	1	yes	characteristic
146	C₂×C₈	D₁₅₂	1	1	yes	characteristic
147	C₂×C₈	#64525	1	1	yes	characteristic
148	C₂×C₈	#64527	1	1	yes	characteristic
149	C₄⋊C₄	—	76	2	no	—
150	C₄⋊C₄	—	76	2	no	—
151	C₄⋊C₄	—	76	1	no	—
152	C₄⋊C₄	—	76	1	no	—
153	C₄²	—	2	1	no	—
154	C₄²	C₈×D₁₉	1	1	yes	characteristic
155	C₄²	#64515	1	1	yes	characteristic
156	C₁₆	—	4	2	no	—
157	C₁₆	—	76	2	no	—
158	C₂³	#10597280	1	1	yes	characteristic
159	Q₈	—	76	2	no	—
160	Q₈	—	76	2	no	—
161	Q₈	—	152	1	no	—
162	Q₈	—	152	1	no	—
163	C₂×C₄	—	2	1	no	—
164	C₂×C₄	—	2	1	no	—
165	C₂×C₄	—	4	2	no	—
166	C₂×C₄	—	76	2	no	—
167	C₂×C₄	—	152	2	no	—
168	C₂×C₄	—	152	1	no	—
169	C₂×C₄	—	152	1	no	—
170	C₂×C₄	—	152	1	no	—
171	C₂×C₄	#10597262	1	1	yes	characteristic
172	C₂×C₄	#10597263	1	1	yes	characteristic
173	C₂×C₄	#10597266	1	1	yes	characteristic
174	C₂×C₄	(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
175	C₂×C₄	#10597278	1	1	yes	characteristic
176	C₂×C₄	#10597282	1	1	yes	characteristic
177	C₈	—	2	1	no	—
178	C₈	—	2	1	no	—
179	C₈	—	2	1	no	—
180	C₈	—	2	1	no	—
181	C₂²	—	2	2	no	—
182	C₂²	#11926267	1	1	yes	characteristic
183	C₂²	#11926283	1	1	yes	characteristic
184	C₂²	#11926287	1	1	yes	characteristic
185	C₄	—	4	1	no	—
186	C₄	—	4	1	no	—
187	C₄	—	304	1	no	—
188	C₄	—	152	2	no	—
189	C₄	#11926271	1	1	yes	characteristic
190	C₄	#11926273	1	1	yes	characteristic
191	C₄	#11926277	1	1	yes	characteristic
192	C₄	#11926279	1	1	yes	characteristic
193	C₂	—	2	1	no	—
194	C₂	—	2	1	no	—
195	C₂	#14561455	1	1	yes	characteristic
196	C₂	#14561669	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14564455

C₂

yes

maximal, characteristic

#14561715

C₂

yes

maximal, characteristic

C₁₉×#1375

C₂

yes

maximal, characteristic

C₂×#10597315

C₄

yes

—

—

—

C₄

yes

characteristic

C₂×C₁₉×M₃₂

—

C₂×C₁₉×#97

C₂²

yes

characteristic

C₂²×Dic₃₈

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

#10597315

—

#10597315

—

#10597315

C₈

yes

—

C₁₉×M₃₂

—

C₁₉×M₃₂

—

C₂×C₁₆×C₁₉

—

C₁₉×#97

—

C₁₉⋊#95

—

—

—

—

—

—

—

C₂×C₁₉⋊C₁₆

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₈

yes

characteristic

C₂×C₈×C₁₉

D₈

yes

characteristic

C₂×C₈×C₁₉

SD₁₆

yes

characteristic

C₂×C₈×C₁₉

SD₁₆

yes

characteristic

C₄²×C₁₉

—

C₄²×C₁₉

C₂×C₈

yes

characteristic

C₄²×C₁₉

M₁₆

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₁₆×C₁₉

—

C₁₉⋊C₁₆

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

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

—

C₈×C₁₉

—

#1960

—

#1375

—

#1375

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

D₄⋊C₈

yes

characteristic

C₄×C₁₉

D₄⋊C₈

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

C₂×C₄⋊Q₈

—

C₂×M₃₂

—

100

C₂×M₃₂

—

101

C₂×#103

—

102

C₂×#103

—

103

C₂×#97

C₂×D₁₉

yes

characteristic

104

#382

—

105

C₂×C₁₉

—

106

C₂×C₁₉

—

107

C₂×C₁₉

#1270

yes

characteristic

108

C₂×C₁₉

#1356

yes

—

109

C₂²×Q₈

—

110

C₂²×C₈

D₇₆

yes

characteristic

111

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

112

C₄⋊Q₈

—

113

C₄⋊Q₈

—

114

C₄⋊Q₈

—

115

C₂×C₄⋊C₄

—

116

C₂×C₄⋊C₄

—

117

C₂×C₄²

C₄×D₁₉

yes

characteristic

118

M₃₂

—

119

M₃₂

—

120

M₃₂

—

121

M₃₂

—

122

C₂×C₁₆

—

123

C₂×C₁₆

—

124

#103

—

125

#103

—

126

#103

—

127

#103

—

128

#97

—

129

#95

—

130

C₁₉

#7117

yes

characteristic, complemented, Sylow

131

C₂×Q₈

—

132

C₂×Q₈

—

133

C₂×Q₈

—

134

C₂×Q₈

—

135

C₂×Q₈

—

136

C₂×Q₈

—

137

C₂²×C₄

—

138

C₂²×C₄

—

139

C₂²×C₄

—

140

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

141

C₂×C₈

—

142

C₂×C₈

—

143

C₂×C₈

—

144

C₂×C₈

—

145

C₂×C₈

#64516

yes

characteristic

146

C₂×C₈

D₁₅₂

yes

characteristic

147

C₂×C₈

#64525

yes

characteristic

148

C₂×C₈

#64527

yes

characteristic

149

C₄⋊C₄

—

150

C₄⋊C₄

—

151

C₄⋊C₄

—

152

C₄⋊C₄

—

153

C₄²

—

154

C₄²

C₈×D₁₉

yes

characteristic

155

C₄²

#64515

yes

characteristic

156

C₁₆

—

157

C₁₆

—

158

C₂³

#10597280

yes

characteristic

159

Q₈

—

160

Q₈

—

161

Q₈

—

152

—

162

Q₈

—

152

—

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

152

—

168

C₂×C₄

—

152

—

169

C₂×C₄

—

152

—

170

C₂×C₄

—

152

—

171

C₂×C₄

#10597262

yes

characteristic

172

C₂×C₄

#10597263

yes

characteristic

173

C₂×C₄

#10597266

yes

characteristic

174

C₂×C₄

(C₂×D₁₉)⋊C₈

yes

characteristic

175

C₂×C₄

#10597278

yes

characteristic

176

C₂×C₄

#10597282

yes

characteristic

177

C₈

—

178

C₈

—

179

C₈

—

180

C₈

—

181

C₂²

—

182

C₂²

#11926267

yes

characteristic

183

C₂²

#11926283

yes

characteristic

184

C₂²

#11926287

yes

characteristic

185

C₄

—

186

C₄

—

187

C₄

—

304

—

188

C₄

—

152

—

189

C₄

#11926271

yes

characteristic

190

C₄

#11926273

yes

characteristic

191

C₄

#11926277

yes

characteristic

192

C₄

#11926279

yes

characteristic

193

C₂

—

194

C₂

—

195

C₂

#14561455

yes

characteristic

196

C₂

#14561669

yes

—

	subgroup	G/H
center	C₂²	#11926283
commutator	C₄²×C₁₉	C₂×C₈
Frattini	C₂×#97	C₂×D₁₉
Fitting	C₁₉×#1375	C₂
socle	C₂²×C₁₉	#329
prime radical	C₂³×C₁₉	#100
cosocle	C₂×C₁₉×#97	C₂²
hypercenter	#1375	D₁₉
hypocenter	C₁₉	#7117
LCS	G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#97 ◁ #1375

subgroup

G/H

center

C₂²

#11926283

commutator

C₄²×C₁₉

C₂×C₈

Frattini

C₂×#97

C₂×D₁₉

Fitting

C₁₉×#1375

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₁₉×#97

C₂²

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#97 ◁ #1375

N	H ≅ G/N	type
130. C₁₉	#7117	semidirect

H ≅ G/N

type

130. C₁₉

#7117

semidirect

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

subgroup	index
#14564455	2
#14561715	2
C₁₉×#1375	2
#7117	19

subgroup

index

#14564455

#14561715

C₁₉×#1375

#7117

Subgroups — #18069318

Conjugacy classes of subgroups

Complements

Maximal subgroups