Group #18077041 — subgroups

Subgroups — #18077041

Order 4864.

412 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 103 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	#14572702	C₂	1	1	yes	maximal, characteristic
2	#14562426	C₂	1	2	yes	maximal, complemented
3	#14562297	C₂	1	1	yes	maximal, characteristic
4	#14561468	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1962	C₂	1	1	yes	maximal, characteristic
6	#11926622	—	2	2	no	—
7	D₄×C₁₉⋊C₈	—	2	2	no	—
8	#11926597	C₂²	1	2	yes	—
9	#11926597	C₂²	1	2	yes	—
10	#11926511	—	2	2	no	—
11	#11926296	—	2	2	no	—
12	#11926294	—	2	2	no	—
13	#11926293	C₄	1	2	yes	complemented
14	#11926288	C₄	1	1	yes	characteristic, complemented
15	#11926288	C₄	1	1	yes	characteristic, complemented
16	C₁₉×#532	C₂²	1	1	yes	characteristic
17	C₁₉×#423	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#104	—	2	2	no	—
19	C₄³×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×#41×C₁₉	D₄	1	2	yes	—
21	C₂×M₁₆×C₁₉	—	2	1	no	—
22	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
23	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
24	C₁₉×#124	Q₈	1	2	yes	—
25	C₁₉×#121	—	2	2	no	—
26	C₄×D₄×C₁₉	—	2	2	no	—
27	C₂×C₄²×C₁₉	—	2	1	no	—
28	C₂×C₄²×C₁₉	—	2	2	no	—
29	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
30	C₂×#64520	—	2	2	no	—
31	C₂²×C₁₉⋊C₈	—	2	2	no	—
32	C₁₉×C₄⋊C₈	—	2	2	no	—
33	C₁₉×#104	—	4	4	no	—
34	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
35	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
36	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
37	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
38	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
39	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
40	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
41	C₄×C₁₉⋊C₈	—	2	2	no	—
42	C₄×C₁₉⋊C₈	—	2	2	no	—
43	#41×C₁₉	—	4	2	no	—
44	#41×C₁₉	—	4	2	no	—
45	C₂×Q₈×C₁₉	C₄⋊C₄	1	2	yes	—
46	C₂×D₄×C₁₉	—	2	2	no	—
47	C₂×D₄×C₁₉	—	2	2	no	—
48	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
49	C₂²×C₄×C₁₉	—	2	2	no	—
50	C₂²×C₄×C₁₉	—	4	1	no	—
51	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	#41	1	2	yes	—
53	M₁₆×C₁₉	—	4	2	no	—
54	C₂×C₈×C₁₉	—	4	1	no	—
55	C₄⋊C₄×C₁₉	—	2	2	no	—
56	C₂²⋊C₄×C₁₉	—	2	4	no	—
57	C₄²×C₁₉	—	2	4	no	—
58	C₄²×C₁₉	—	2	2	no	—
59	C₄²×C₁₉	—	4	2	no	—
60	C₄²×C₁₉	—	4	1	no	—
61	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
62	C₄²×C₁₉	C₂×D₄	1	2	yes	—
63	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
64	#64520	—	8	2	no	—
65	C₂×C₁₉⋊C₈	—	2	2	no	—
66	C₂×C₁₉⋊C₈	—	2	2	no	—
67	C₂×C₁₉⋊C₈	—	2	2	no	—
68	C₂×C₁₉⋊C₈	—	2	2	no	—
69	C₂×C₁₉⋊C₈	—	8	2	no	—
70	#8934	—	19	1	no	maximal, Sylow
71	C₂³×C₁₉	—	2	2	no	—
72	C₂³×C₁₉	#123	1	1	yes	characteristic
73	Q₈×C₁₉	—	4	2	no	—
74	D₄×C₁₉	—	4	2	no	—
75	D₄×C₁₉	—	4	2	no	—
76	D₄×C₁₉	—	4	2	no	—
77	D₄×C₁₉	—	8	2	no	—
78	C₂×C₄×C₁₉	—	2	2	no	—
79	C₂×C₄×C₁₉	—	2	2	no	—
80	C₂×C₄×C₁₉	—	2	1	no	—
81	C₂×C₄×C₁₉	—	2	1	no	—
82	C₂×C₄×C₁₉	—	2	2	no	—
83	C₂×C₄×C₁₉	—	4	2	no	—
84	C₂×C₄×C₁₉	—	4	4	no	—
85	C₂×C₄×C₁₉	—	4	2	no	—
86	C₂×C₄×C₁₉	—	4	2	no	—
87	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
88	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
89	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
90	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
91	C₈×C₁₉	—	8	1	no	—
92	C₁₉⋊C₈	—	4	2	no	—
93	C₁₉⋊C₈	—	4	2	no	—
94	C₁₉⋊C₈	—	4	2	no	—
95	C₁₉⋊C₈	—	4	2	no	—
96	#2979	—	19	1	no	—
97	#1962	D₁₉	1	1	yes	characteristic
98	#1574	—	19	2	no	—
99	#1543	—	19	1	no	—
100	#1276	—	19	2	no	—
101	C₂²×C₁₉	—	2	1	no	—
102	C₂²×C₁₉	—	2	2	no	—
103	C₂²×C₁₉	—	4	2	no	—
104	C₂²×C₁₉	—	4	4	no	—
105	C₂²×C₁₉	#385	1	1	yes	characteristic
106	C₄×C₁₉	—	2	1	no	—
107	C₄×C₁₉	—	2	2	no	—
108	C₄×C₁₉	—	4	4	no	—
109	C₄×C₁₉	—	4	2	no	—
110	C₄×C₁₉	#443	1	2	yes	—
111	C₄×C₁₉	#444	1	2	yes	—
112	C₄×C₁₉	#453	1	1	yes	characteristic
113	C₄×C₁₉	#455	1	1	yes	characteristic
114	#532	C₂×D₁₉	1	1	yes	characteristic
115	#436	—	38	2	no	—
116	C₈×D₄	—	38	2	no	—
117	#431	—	19	2	no	—
118	#431	—	19	2	no	—
119	#423	C₂×D₁₉	1	1	yes	characteristic
120	C₂×#104	—	2	2	no	—
121	#408	—	38	2	no	—
122	C₄³	C₂×D₁₉	1	1	yes	characteristic
123	#335	—	38	2	no	—
124	#334	—	38	2	no	—
125	#333	—	19	2	no	—
126	#331	—	19	1	no	—
127	#331	—	19	1	no	—
128	C₂×C₁₉	—	4	1	no	—
129	C₂×C₁₉	—	8	2	no	—
130	C₂×C₁₉	#1856	1	1	yes	characteristic
131	C₂×C₁₉	#1866	1	2	yes	—
132	C₂×#41	C₂²⋊D₁₉	1	2	yes	—
133	C₂×M₁₆	—	2	1	no	—
134	C₂×M₁₆	—	38	2	no	—
135	C₂²×C₈	—	38	2	no	—
136	C₄⋊Q₈	C₄×D₁₉	1	1	yes	characteristic
137	#127	C₄×D₁₉	1	1	yes	characteristic
138	#124	Dic₃₈	1	2	yes	—
139	#121	—	2	2	no	—
140	C₄×D₄	—	2	2	no	—
141	C₂×C₄²	—	2	2	no	—
142	C₂×C₄²	—	2	1	no	—
143	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
144	C₄⋊C₈	—	2	2	no	—
145	C₄⋊C₈	—	19	2	no	—
146	C₄⋊C₈	—	19	2	no	—
147	C₄⋊C₈	—	19	2	no	—
148	C₄⋊C₈	—	19	2	no	—
149	#104	—	4	4	no	—
150	C₂²⋊C₈	—	38	4	no	—
151	C₂²⋊C₈	—	38	2	no	—
152	C₂²⋊C₈	—	38	2	no	—
153	C₄×C₈	—	38	2	no	—
154	C₄×C₈	—	38	2	no	—
155	C₁₉	#8934	1	1	yes	characteristic, complemented, Sylow
156	#41	—	4	2	no	—
157	#41	—	4	2	no	—
158	C₂×Q₈	Dic₁₉⋊C₄	1	2	yes	—
159	C₂×D₄	—	2	2	no	—
160	C₂×D₄	—	2	2	no	—
161	C₂×D₄	Dic₁₉⋊C₄	1	2	yes	—
162	C₂²×C₄	—	2	2	no	—
163	C₂²×C₄	—	4	1	no	—
164	C₂²×C₄	#64543	1	2	yes	—
165	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
166	M₁₆	—	4	2	no	—
167	M₁₆	—	152	2	no	—
168	C₂×C₈	—	4	1	no	—
169	C₂×C₈	—	38	2	no	—
170	C₂×C₈	—	38	2	no	—
171	C₂×C₈	—	38	2	no	—
172	C₂×C₈	—	38	2	no	—
173	C₂×C₈	—	152	2	no	—
174	C₄⋊C₄	—	2	2	no	—
175	C₂²⋊C₄	—	2	4	no	—
176	C₄²	—	2	2	no	—
177	C₄²	—	2	4	no	—
178	C₄²	—	4	2	no	—
179	C₄²	—	4	1	no	—
180	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
181	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
182	C₄²	D₄×D₁₉	1	2	yes	—
183	C₂³	—	2	2	no	—
184	C₂³	#10597381	1	1	yes	characteristic
185	Q₈	—	4	2	no	—
186	D₄	—	4	2	no	—
187	D₄	—	4	2	no	—
188	D₄	—	4	2	no	—
189	D₄	—	8	2	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	2	2	no	—
192	C₂×C₄	—	2	1	no	—
193	C₂×C₄	—	2	1	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	4	2	no	—
196	C₂×C₄	—	4	4	no	—
197	C₂×C₄	—	4	2	no	—
198	C₂×C₄	—	4	2	no	—
199	C₂×C₄	#10597324	1	2	yes	—
200	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
201	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
202	C₂×C₄	#10597383	1	1	yes	characteristic
203	C₈	—	8	1	no	—
204	C₈	—	76	2	no	—
205	C₈	—	76	2	no	—
206	C₈	—	76	2	no	—
207	C₈	—	76	2	no	—
208	C₂²	—	2	1	no	—
209	C₂²	—	2	2	no	—
210	C₂²	—	4	2	no	—
211	C₂²	—	4	4	no	—
212	C₂²	#11926416	1	1	yes	characteristic
213	C₄	—	2	1	no	—
214	C₄	—	2	2	no	—
215	C₄	—	4	4	no	—
216	C₄	—	4	2	no	—
217	C₄	#11926658	1	2	yes	—
218	C₄	#11926663	1	2	yes	—
219	C₄	#11926711	1	1	yes	characteristic
220	C₄	#11926721	1	1	yes	characteristic
221	C₂	—	4	1	no	—
222	C₂	—	8	2	no	—
223	C₂	#14563844	1	1	yes	characteristic
224	C₂	#14563908	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14572702

C₂

yes

maximal, characteristic

#14562426

C₂

yes

maximal, complemented

#14562297

C₂

yes

maximal, characteristic

#14561468

C₂

yes

maximal, complemented

C₁₉×#1962

C₂

yes

maximal, characteristic

#11926622

—

D₄×C₁₉⋊C₈

—

#11926597

C₂²

yes

—

#11926597

C₂²

yes

—

—

—

—

C₄

yes

complemented

#11926288

C₄

yes

characteristic, complemented

#11926288

C₄

yes

characteristic, complemented

C₁₉×#532

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₂×C₁₉×#104

—

C₄³×C₁₉

C₂²

yes

characteristic

C₂×#41×C₁₉

D₄

yes

—

C₂×M₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

characteristic

C₁₉×#127

C₂×C₄

yes

characteristic

C₁₉×#124

Q₈

yes

—

C₁₉×#121

—

C₄×D₄×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

C₂²×C₁₉⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×#104

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

C₂×C₄

yes

—

C₄⋊(C₁₉⋊C₈)

C₂×C₄

yes

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

C₄⋊C₄

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×Q₈

yes

characteristic

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8934

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

#123

yes

characteristic

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

#120

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2979

—

#1962

D₁₉

yes

characteristic

#1574

—

#1543

—

100

#1276

—

101

C₂²×C₁₉

—

102

C₂²×C₁₉

—

103

C₂²×C₁₉

—

104

C₂²×C₁₉

—

105

C₂²×C₁₉

#385

yes

characteristic

106

C₄×C₁₉

—

107

C₄×C₁₉

—

108

C₄×C₁₉

—

109

C₄×C₁₉

—

110

C₄×C₁₉

#443

yes

—

111

C₄×C₁₉

#444

yes

—

112

C₄×C₁₉

#453

yes

characteristic

113

C₄×C₁₉

#455

yes

characteristic

114

#532

C₂×D₁₉

yes

characteristic

115

#436

—

116

C₈×D₄

—

117

#431

—

118

#431

—

119

#423

C₂×D₁₉

yes

characteristic

120

C₂×#104

—

121

#408

—

122

C₄³

C₂×D₁₉

yes

characteristic

123

#335

—

124

#334

—

125

#333

—

126

#331

—

127

#331

—

128

C₂×C₁₉

—

129

C₂×C₁₉

—

130

C₂×C₁₉

#1856

yes

characteristic

131

C₂×C₁₉

#1866

yes

—

132

C₂×#41

C₂²⋊D₁₉

yes

—

133

C₂×M₁₆

—

134

C₂×M₁₆

—

135

C₂²×C₈

—

136

C₄⋊Q₈

C₄×D₁₉

yes

characteristic

137

#127

C₄×D₁₉

yes

characteristic

138

#124

Dic₃₈

yes

—

139

#121

—

140

C₄×D₄

—

141

C₂×C₄²

—

142

C₂×C₄²

—

143

C₂×C₄²

C₂²×D₁₉

yes

characteristic

144

C₄⋊C₈

—

145

C₄⋊C₈

—

146

C₄⋊C₈

—

147

C₄⋊C₈

—

148

C₄⋊C₈

—

149

#104

—

150

C₂²⋊C₈

—

151

C₂²⋊C₈

—

152

C₂²⋊C₈

—

153

C₄×C₈

—

154

C₄×C₈

—

155

C₁₉

#8934

yes

characteristic, complemented, Sylow

156

#41

—

157

#41

—

158

C₂×Q₈

Dic₁₉⋊C₄

yes

—

159

C₂×D₄

—

160

C₂×D₄

—

161

C₂×D₄

Dic₁₉⋊C₄

yes

—

162

C₂²×C₄

—

163

C₂²×C₄

—

164

C₂²×C₄

#64543

yes

—

165

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

166

M₁₆

—

167

M₁₆

—

152

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

152

—

174

C₄⋊C₄

—

175

C₂²⋊C₄

—

176

C₄²

—

177

C₄²

—

178

C₄²

—

179

C₄²

—

180

C₄²

C₂×Dic₃₈

yes

characteristic

181

C₄²

C₂×C₄×D₁₉

yes

characteristic

182

C₄²

D₄×D₁₉

yes

—

183

C₂³

—

184

C₂³

#10597381

yes

characteristic

185

Q₈

—

186

D₄

—

187

D₄

—

188

D₄

—

189

D₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

#10597324

yes

—

200

C₂×C₄

(C₂²⋊D₁₉)⋊C₄

yes

—

201

C₂×C₄

C₂×Dic₁₉⋊C₄

yes

characteristic

202

C₂×C₄

#10597383

yes

characteristic

203

C₈

—

204

C₈

—

205

C₈

—

206

C₈

—

207

C₈

—

208

C₂²

—

209

C₂²

—

210

C₂²

—

211

C₂²

—

212

C₂²

#11926416

yes

characteristic

213

C₄

—

214

C₄

—

215

C₄

—

216

C₄

—

217

C₄

#11926658

yes

—

218

C₄

#11926663

yes

—

219

C₄

#11926711

yes

characteristic

220

C₄

#11926721

yes

characteristic

221

C₂

—

222

C₂

—

223

C₂

#14563844

yes

characteristic

224

C₂

#14563908

yes

—

	subgroup	G/H
center	C₂×C₄	#10597383
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1962	C₂
socle	C₂²×C₁₉	#385
prime radical	C₁₉×#532	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1962	D₁₉
hypocenter	C₁₉	#8934
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1962

subgroup

G/H

center

C₂×C₄

#10597383

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1962

C₂

socle

C₂²×C₁₉

#385

prime radical

C₁₉×#532

C₂²

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1962

N	H ≅ G/N	type
2. #14562426	C₂	semidirect
4. #14561468	C₂	semidirect
13. #11926293	C₄	semidirect
14. #11926288	C₄	semidirect
15. #11926288	C₄	semidirect
155. C₁₉	#8934	semidirect

H ≅ G/N

type

2. #14562426

C₂

semidirect

4. #14561468

C₂

semidirect

13. #11926293

C₄

semidirect

14. #11926288

C₄

semidirect

15. #11926288

C₄

semidirect

155. C₁₉

#8934

semidirect

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

subgroup	index
#14572702	2
#14562426	2
#14562297	2
#14561468	2
C₁₉×#1962	2
#8934	19

subgroup

index

C₁₉×#1962

Subgroups — #18077041

Conjugacy classes of subgroups

Complements

Maximal subgroups