Group #18075496 — subgroups

Subgroups — #18075496

Order 4864.

362 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 101 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	C₂×#11926668	C₂	1	1	yes	maximal, characteristic
2	#14562396	C₂	1	2	yes	maximal
3	#14561978	C₂	1	2	yes	maximal
4	#14561505	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1290	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Dic₃₈	C₂²	1	1	yes	characteristic
7	#11926668	—	2	2	no	—
8	#11926668	—	2	2	no	—
9	#11926601	C₂²	1	2	yes	—
10	C₂×Dic₁₉⋊C₈	C₄	1	2	yes	—
11	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×C₈×Dic₁₉	C₄	1	2	yes	—
13	#11926296	—	2	2	no	—
14	#11926294	—	2	2	no	—
15	#11926269	—	2	4	no	—
16	C₁₉×#432	C₂²	1	2	yes	—
17	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂²×Dic₃₈	Q₈	1	1	yes	characteristic
19	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
20	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
21	C₂×C₄⋊Dic₁₉	Q₈	1	1	yes	characteristic
22	C₂×Dic₁₉⋊C₄	D₄	1	2	yes	—
23	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
24	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
26	C₄×Dic₃₈	—	2	2	no	—
27	C₄×Dic₃₈	—	2	2	no	—
28	C₁₉×C₄⋊C₈	—	2	2	no	—
29	C₁₉×C₄⋊C₈	—	2	2	no	—
30	C₁₉×C₂²⋊C₈	—	2	2	no	—
31	C₁₉×#97	—	2	2	no	—
32	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
33	Dic₁₉⋊C₈	—	2	4	no	—
34	C₈×Dic₁₉	—	2	2	no	—
35	C₈×Dic₁₉	—	2	2	no	—
36	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
37	#10597260	—	2	2	no	—
38	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
39	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
40	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
43	C₂²×Dic₁₉	C₄⋊C₄	1	2	yes	—
44	C₂²×Dic₁₉	C₄⋊C₄	1	2	yes	—
45	C₂×Dic₃₈	—	2	2	no	—
46	C₂×Dic₃₈	—	2	4	no	—
47	C₂×C₈×C₁₉	—	2	2	no	—
48	C₂×C₈×C₁₉	—	4	2	no	—
49	C₂×C₈×C₁₉	—	4	2	no	—
50	C₄²×C₁₉	C₂×D₄	1	2	yes	—
51	C₄²×C₁₉	#41	1	2	yes	—
52	C₄⋊Dic₁₉	—	2	2	no	—
53	Dic₁₉⋊C₄	—	2	4	no	—
54	C₄×Dic₁₉	—	2	2	no	—
55	C₄×Dic₁₉	—	2	2	no	—
56	C₂×C₁₉⋊C₈	—	2	2	no	—
57	C₂×C₁₉⋊C₈	—	4	1	no	—
58	C₂×C₁₉⋊C₈	—	4	2	no	—
59	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
60	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
61	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
62	#8623	—	19	1	no	maximal, Sylow
63	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
64	C₂×C₄×C₁₉	—	2	2	no	—
65	C₂×C₄×C₁₉	—	2	1	no	—
66	C₂×C₄×C₁₉	—	2	1	no	—
67	C₂×C₄×C₁₉	—	4	1	no	—
68	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
69	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
70	C₂×C₄×C₁₉	#121	1	2	yes	—
71	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
72	C₂×Dic₁₉	—	2	2	no	—
73	C₂×Dic₁₉	—	2	2	no	—
74	C₂×Dic₁₉	—	2	2	no	—
75	C₂×Dic₁₉	—	4	2	no	—
76	C₂×Dic₁₉	#108	1	4	yes	—
77	Dic₃₈	—	2	8	no	—
78	C₈×C₁₉	—	4	2	no	—
79	C₈×C₁₉	—	8	2	no	—
80	C₁₉⋊C₈	—	2	1	no	—
81	C₁₉⋊C₈	—	2	2	no	—
82	C₁₉⋊C₈	—	8	2	no	—
83	C₁₉⋊C₈	#101	1	2	yes	—
84	C₂×C₈×Q₈	—	19	1	no	—
85	#1568	—	19	2	no	—
86	#1467	—	19	2	no	—
87	#1290	—	19	1	no	—
88	#1290	D₁₉	1	1	yes	characteristic
89	C₂²×C₁₉	—	2	1	no	—
90	C₂²×C₁₉	—	2	1	no	—
91	C₂²×C₁₉	#380	1	1	yes	characteristic
92	C₂²×C₁₉	C₂×#108	1	2	yes	—
93	C₄×C₁₉	—	2	1	no	—
94	C₄×C₁₉	—	2	2	no	—
95	C₄×C₁₉	—	2	2	no	—
96	C₄×C₁₉	C₂×#101	1	1	yes	characteristic
97	C₄×C₁₉	#413	1	1	yes	characteristic
98	Dic₁₉	—	2	4	no	—
99	Dic₁₉	—	4	2	no	—
100	C₂×C₄×Q₈	—	19	1	no	—
101	C₈×Q₈	—	38	2	no	—
102	C₈×Q₈	—	38	2	no	—
103	#432	—	19	2	no	—
104	#432	C₂×D₁₉	1	2	yes	—
105	C₂×C₄⋊C₈	—	19	2	no	—
106	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
107	C₂×C₄×C₈	—	19	1	no	—
108	C₂×C₄×C₈	—	19	2	no	—
109	#335	—	38	2	no	—
110	#334	—	38	2	no	—
111	#324	—	38	4	no	—
112	C₂×C₁₉	—	2	2	no	—
113	C₂×C₁₉	#1801	1	1	yes	characteristic
114	C₂×C₁₉	#1810	1	1	yes	characteristic
115	C₂×C₁₉	#1812	1	1	yes	characteristic
116	C₂²×Q₈	—	19	1	no	—
117	C₂²×C₈	—	19	1	no	—
118	C₂²×C₈	—	19	1	no	—
119	C₂²×C₈	C₄×D₁₉	1	2	yes	—
120	C₄×Q₈	—	38	2	no	—
121	C₄×Q₈	—	38	2	no	—
122	C₂×C₄⋊C₄	—	19	2	no	—
123	C₂×C₄⋊C₄	—	19	1	no	—
124	C₂×C₄²	—	19	2	no	—
125	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
126	C₄⋊C₈	—	2	2	no	—
127	C₄⋊C₈	—	2	2	no	—
128	C₄⋊C₈	—	38	4	no	—
129	C₄⋊C₈	—	38	2	no	—
130	C₂²⋊C₈	—	2	2	no	—
131	C₂²⋊C₈	—	38	2	no	—
132	#97	—	2	2	no	—
133	#97	—	38	2	no	—
134	C₄×C₈	—	19	2	no	—
135	C₄×C₈	—	19	2	no	—
136	C₄×C₈	—	38	2	no	—
137	C₄×C₈	—	38	2	no	—
138	C₁₉	#8623	1	1	yes	characteristic, complemented, Sylow
139	C₂×Q₈	—	38	4	no	—
140	C₂×Q₈	—	38	2	no	—
141	C₂²×C₄	—	19	2	no	—
142	C₂²×C₄	—	19	2	no	—
143	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
144	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
145	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
146	C₂×C₈	—	2	2	no	—
147	C₂×C₈	—	4	2	no	—
148	C₂×C₈	—	4	2	no	—
149	C₂×C₈	—	19	1	no	—
150	C₂×C₈	—	19	1	no	—
151	C₂×C₈	—	19	2	no	—
152	C₂×C₈	—	38	2	no	—
153	C₂×C₈	—	76	1	no	—
154	C₂×C₈	—	76	2	no	—
155	C₄⋊C₄	—	38	4	no	—
156	C₄⋊C₄	—	38	2	no	—
157	C₄²	—	38	2	no	—
158	C₄²	—	38	2	no	—
159	C₄²	#64541	1	2	yes	—
160	C₄²	D₄×D₁₉	1	2	yes	—
161	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
162	Q₈	—	38	8	no	—
163	C₂×C₄	—	2	2	no	—
164	C₂×C₄	—	2	1	no	—
165	C₂×C₄	—	2	1	no	—
166	C₂×C₄	—	4	1	no	—
167	C₂×C₄	—	19	4	no	—
168	C₂×C₄	—	38	2	no	—
169	C₂×C₄	—	38	2	no	—
170	C₂×C₄	—	38	2	no	—
171	C₂×C₄	—	76	2	no	—
172	C₂×C₄	#10597318	1	1	yes	characteristic
173	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
174	C₂×C₄	#10597330	1	2	yes	—
175	C₂×C₄	#10597342	1	2	yes	—
176	C₈	—	4	2	no	—
177	C₈	—	8	2	no	—
178	C₈	—	19	2	no	—
179	C₈	—	38	1	no	—
180	C₈	—	38	2	no	—
181	C₈	—	152	2	no	—
182	C₂²	—	2	1	no	—
183	C₂²	—	2	1	no	—
184	C₂²	#11926403	1	1	yes	characteristic
185	C₂²	#108×D₁₉	1	2	yes	—
186	C₄	—	2	1	no	—
187	C₄	—	2	2	no	—
188	C₄	—	2	2	no	—
189	C₄	—	38	4	no	—
190	C₄	—	76	2	no	—
191	C₄	#101×D₁₉	1	1	yes	characteristic
192	C₄	#11926525	1	1	yes	characteristic
193	C₂	—	2	2	no	—
194	C₂	#14563630	1	1	yes	characteristic
195	C₂	#14563672	1	1	yes	characteristic
196	C₂	#14563680	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926668

C₂

yes

maximal, characteristic

#14562396

C₂

yes

maximal

#14561978

C₂

yes

maximal

#14561505

C₂

yes

maximal, characteristic

C₁₉×#1290

C₂

yes

maximal, characteristic

C₂×C₄×Dic₃₈

C₂²

yes

—

—

C₂²

yes

—

C₂×Dic₁₉⋊C₈

C₄

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×C₈×Dic₁₉

C₄

yes

—

#11926296

—

#11926294

—

#11926269

—

C₁₉×#432

C₂²

yes

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₂²×Dic₃₈

Q₈

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

Q₈

yes

characteristic

C₂×Dic₁₉⋊C₄

D₄

yes

—

C₂×C₄×Dic₁₉

C₂×C₄

yes

—

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₂²⋊(C₁₉⋊C₈)

—

Dic₁₉⋊C₈

—

C₈×Dic₁₉

—

C₈×Dic₁₉

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂²×Dic₁₉

C₄⋊C₄

yes

—

C₂²×Dic₁₉

C₄⋊C₄

yes

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

characteristic

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

—

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

characteristic

#8623

—

maximal, Sylow

C₂³×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

#108

yes

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

#101

yes

—

C₂×C₈×Q₈

—

—

—

—

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#380

yes

characteristic

C₂²×C₁₉

C₂×#108

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

100

C₂×C₄×Q₈

—

101

C₈×Q₈

—

102

C₈×Q₈

—

103

#432

—

104

#432

C₂×D₁₉

yes

—

105

C₂×C₄⋊C₈

—

106

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

107

C₂×C₄×C₈

—

108

C₂×C₄×C₈

—

109

#335

—

110

#334

—

111

#324

—

112

C₂×C₁₉

—

113

C₂×C₁₉

#1801

yes

characteristic

114

C₂×C₁₉

#1810

yes

characteristic

115

C₂×C₁₉

#1812

yes

characteristic

116

C₂²×Q₈

—

117

C₂²×C₈

—

118

C₂²×C₈

—

119

C₂²×C₈

C₄×D₁₉

yes

—

120

C₄×Q₈

—

121

C₄×Q₈

—

122

C₂×C₄⋊C₄

—

123

C₂×C₄⋊C₄

—

124

C₂×C₄²

—

125

C₂×C₄²

C₂²×D₁₉

yes

characteristic

126

C₄⋊C₈

—

127

C₄⋊C₈

—

128

C₄⋊C₈

—

129

C₄⋊C₈

—

130

C₂²⋊C₈

—

131

C₂²⋊C₈

—

132

#97

—

133

#97

—

134

C₄×C₈

—

135

C₄×C₈

—

136

C₄×C₈

—

137

C₄×C₈

—

138

C₁₉

#8623

yes

characteristic, complemented, Sylow

139

C₂×Q₈

—

140

C₂×Q₈

—

141

C₂²×C₄

—

142

C₂²×C₄

—

143

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

144

C₂²×C₄

D₄×D₁₉

yes

characteristic

145

C₂²×C₄

Q₈×D₁₉

yes

characteristic

146

C₂×C₈

—

147

C₂×C₈

—

148

C₂×C₈

—

149

C₂×C₈

—

150

C₂×C₈

—

151

C₂×C₈

—

152

C₂×C₈

—

153

C₂×C₈

—

154

C₂×C₈

—

155

C₄⋊C₄

—

156

C₄⋊C₄

—

157

C₄²

—

158

C₄²

—

159

C₄²

#64541

yes

—

160

C₄²

D₄×D₁₉

yes

—

161

C₂³

C₄⋊C₄×D₁₉

yes

characteristic

162

Q₈

—

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

#10597318

yes

characteristic

173

C₂×C₄

C₂²⋊C₄×D₁₉

yes

characteristic

174

C₂×C₄

#10597330

yes

—

175

C₂×C₄

#10597342

yes

—

176

C₈

—

177

C₈

—

178

C₈

—

179

C₈

—

180

C₈

—

181

C₈

—

152

—

182

C₂²

—

183

C₂²

—

184

C₂²

#11926403

yes

characteristic

185

C₂²

#108×D₁₉

yes

—

186

C₄

—

187

C₄

—

188

C₄

—

189

C₄

—

190

C₄

—

191

C₄

#101×D₁₉

yes

characteristic

192

C₄

#11926525

yes

characteristic

193

C₂

—

194

C₂

#14563630

yes

characteristic

195

C₂

#14563672

yes

characteristic

196

C₂

#14563680

yes

characteristic

	subgroup	G/H
center	C₂²	#11926403
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1290	C₂
socle	C₂²×C₁₉	#380
prime radical	C₂³×C₁₉	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1290	D₁₉
hypocenter	C₁₉	#8623
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1290

subgroup

G/H

center

C₂²

#11926403

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1290

C₂

socle

C₂²×C₁₉

#380

prime radical

C₂³×C₁₉

C₂×C₄⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1290

N	H ≅ G/N	type
138. C₁₉	#8623	semidirect

H ≅ G/N

type

138. C₁₉

#8623

semidirect

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

subgroup	index
C₂×#11926668	2
#14562396	2
#14561978	2
#14561505	2
C₁₉×#1290	2
#8623	19

subgroup

index

C₁₉×#1290

Subgroups — #18075496

Conjugacy classes of subgroups

Complements

Maximal subgroups