Group #18080066 — subgroups

Subgroups — #18080066

Order 4864.

540 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 99 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	#14574088	C₂	1	1	yes	maximal, characteristic
2	#14562348	C₂	1	2	yes	maximal, complemented
3	#14562270	C₂	1	1	yes	maximal, characteristic, complemented
4	#14561506	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2980	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10597395	—	2	2	no	—
7	C₂×#10597320	C₂²	1	1	yes	characteristic
8	#11926934	—	2	2	no	—
9	#11926920	C₄	1	2	yes	—
10	#11926918	C₄	1	2	yes	—
11	#11926601	C₂²	1	2	yes	—
12	C₄×#64520	C₂²	1	1	yes	characteristic
13	#11926287	—	2	4	no	—
14	#11926284	—	2	2	no	—
15	C₁₉×#532	C₂²	1	1	yes	characteristic
16	C₁₉×#435	—	2	4	no	—
17	C₁₉×#432	C₂²	1	2	yes	—
18	C₁₉×#408	—	2	2	no	—
19	C₂×#41×C₁₉	D₄	1	2	yes	—
20	C₂²×D₇₆	—	2	1	no	—
21	C₂²×D₇₆	—	2	2	no	—
22	C₂×M₁₆×C₁₉	—	2	2	no	—
23	C₂²×C₈×C₁₉	—	2	2	no	—
24	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
25	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
26	C₁₉×#124	D₄	1	2	yes	—
27	C₁₉×#121	—	2	2	no	—
28	C₄×D₄×C₁₉	—	2	2	no	—
29	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
30	#10597395	—	4	4	no	—
31	#10597395	—	4	4	no	—
32	C₂×#64527	—	2	4	no	—
33	C₂×#64525	—	2	4	no	—
34	C₂×#64520	—	2	1	no	—
35	#10597320	—	2	2	no	—
36	#10597320	—	2	1	no	—
37	#10597320	C₂×C₄	1	2	yes	—
38	C₁₉×C₄⋊C₈	D₄	1	4	yes	—
39	C₁₉×C₂²⋊C₈	—	2	4	no	—
40	C₁₉×C₂²⋊C₈	—	2	2	no	—
41	C₁₉×#97	—	2	2	no	—
42	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
43	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
44	#10597260	—	2	1	no	—
45	#10597260	—	2	2	no	—
46	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
47	C₂³×D₁₉	—	4	1	no	—
48	#41×C₁₉	—	4	2	no	—
49	#41×C₁₉	—	4	2	no	—
50	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
51	C₂×D₄×C₁₉	—	2	2	no	—
52	C₂×D₄×C₁₉	—	2	2	no	—
53	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
54	C₂²×C₄×C₁₉	—	2	2	no	—
55	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	#41	1	2	yes	—
57	C₂×D₇₆	—	2	2	no	—
58	C₂×D₇₆	—	2	4	no	—
59	C₂×D₇₆	—	4	2	no	—
60	C₂×D₇₆	—	4	2	no	—
61	C₂×D₇₆	—	4	1	no	—
62	C₂×D₇₆	—	4	2	no	—
63	C₂×D₇₆	—	8	4	no	—
64	M₁₆×C₁₉	—	8	2	no	—
65	C₂×C₈×C₁₉	—	2	4	no	—
66	C₂×C₈×C₁₉	—	8	2	no	—
67	C₄⋊C₄×C₁₉	—	2	2	no	—
68	C₂²⋊C₄×C₁₉	—	2	4	no	—
69	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
70	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
71	C₄²×C₁₉	C₂×D₄	1	2	yes	—
72	#64527	—	4	8	no	—
73	#64525	—	4	8	no	—
74	#64520	—	2	4	no	—
75	C₂×C₁₉⋊C₈	—	2	2	no	—
76	C₂×C₁₉⋊C₈	—	4	2	no	—
77	#9423	—	19	1	no	maximal, Sylow
78	C₂³×C₁₉	—	2	2	no	—
79	C₂³×C₁₉	#123	1	1	yes	characteristic
80	C₂²×D₁₉	—	4	2	no	—
81	C₂²×D₁₉	—	8	1	no	—
82	C₂²×D₁₉	—	8	1	no	—
83	C₂²×D₁₉	—	8	4	no	—
84	Q₈×C₁₉	—	4	2	no	—
85	D₄×C₁₉	—	4	2	no	—
86	D₄×C₁₉	—	8	2	no	—
87	D₄×C₁₉	—	8	2	no	—
88	C₂×C₄×C₁₉	—	2	2	no	—
89	C₂×C₄×C₁₉	—	2	2	no	—
90	C₂×C₄×C₁₉	—	4	2	no	—
91	C₂×C₄×C₁₉	—	4	2	no	—
92	C₂×C₄×C₁₉	—	4	2	no	—
93	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
95	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
96	C₂×C₄×C₁₉	#121	1	2	yes	—
97	D₇₆	—	4	4	no	—
98	D₇₆	—	8	4	no	—
99	D₇₆	—	8	4	no	—
100	D₇₆	—	8	2	no	—
101	C₈×C₁₉	—	4	4	no	—
102	C₁₉⋊C₈	—	2	4	no	—
103	C₁₉⋊C₈	—	8	2	no	—
104	#3151	—	19	1	no	—
105	#2980	D₁₉	1	1	yes	characteristic, complemented
106	#1555	—	19	2	no	—
107	#1536	—	19	1	no	—
108	#1291	—	19	2	no	—
109	C₂²×C₁₉	—	2	1	no	—
110	C₂²×C₁₉	—	2	2	no	—
111	C₂²×C₁₉	—	4	2	no	—
112	C₂²×C₁₉	—	4	4	no	—
113	C₂²×C₁₉	#386	1	1	yes	characteristic
114	C₂×D₁₉	—	8	2	no	—
115	C₂×D₁₉	—	8	4	no	—
116	C₂×D₁₉	—	16	2	no	—
117	C₂×D₁₉	—	16	2	no	—
118	C₄×C₁₉	—	2	1	no	—
119	C₄×C₁₉	—	2	2	no	—
120	C₄×C₁₉	—	2	2	no	—
121	C₄×C₁₉	—	4	2	no	—
122	C₄×C₁₉	#453	1	2	yes	—
123	C₂×AGL(1,ℤ/8)	—	38	2	no	—
124	#532	C₂×D₁₉	1	1	yes	characteristic
125	C₂×#127	—	19	1	no	—
126	#496	—	38	2	no	—
127	#493	—	19	2	no	—
128	#492	—	19	2	no	—
129	#435	—	2	4	no	—
130	#432	—	19	2	no	—
131	#432	C₂×D₁₉	1	2	yes	—
132	#408	—	2	2	no	—
133	C₄×M₁₆	—	19	1	no	—
134	#331	—	38	4	no	—
135	#329	—	38	2	no	—
136	C₂×C₁₉	—	4	1	no	—
137	C₂×C₁₉	—	8	2	no	—
138	C₂×C₁₉	#1887	1	1	yes	characteristic
139	C₂×C₁₉	#1903	1	2	yes	—
140	D₁₉	—	16	2	no	—
141	C₂×#41	C₂²⋊D₁₉	1	2	yes	—
142	C₂²×D₄	—	38	2	no	—
143	C₂²×D₄	—	38	1	no	—
144	AGL(1,ℤ/8)	—	76	4	no	—
145	AGL(1,ℤ/8)	—	76	4	no	—
146	C₂×SD₁₆	—	38	4	no	—
147	C₂×D₈	—	38	4	no	—
148	C₂×M₁₆	—	2	2	no	—
149	C₂×M₁₆	—	38	1	no	—
150	C₂²×C₈	—	2	2	no	—
151	C₄⋊Q₈	C₄×D₁₉	1	1	yes	characteristic
152	#127	—	19	2	no	—
153	#127	—	38	1	no	—
154	#127	—	38	2	no	—
155	#127	C₄×D₁₉	1	1	yes	characteristic
156	#124	D₇₆	1	2	yes	—
157	#121	—	2	2	no	—
158	C₄×D₄	—	2	2	no	—
159	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
160	C₄⋊C₈	—	38	2	no	—
161	C₄⋊C₈	C₂²⋊D₁₉	1	4	yes	—
162	C₂²⋊C₈	—	2	4	no	—
163	C₂²⋊C₈	—	2	2	no	—
164	C₂²⋊C₈	—	38	2	no	—
165	#97	—	2	2	no	—
166	#97	—	38	1	no	—
167	#97	—	38	2	no	—
168	C₄×C₈	—	19	2	no	—
169	C₁₉	#9423	1	1	yes	characteristic, complemented, Sylow
170	C₂⁴	—	76	1	no	—
171	#41	—	4	2	no	—
172	#41	—	4	2	no	—
173	C₂×Q₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
174	C₂×D₄	—	2	2	no	—
175	C₂×D₄	—	2	2	no	—
176	C₂×D₄	—	38	2	no	—
177	C₂×D₄	—	38	4	no	—
178	C₂×D₄	—	76	2	no	—
179	C₂×D₄	—	76	2	no	—
180	C₂×D₄	—	76	2	no	—
181	C₂×D₄	—	76	1	no	—
182	C₂×D₄	—	152	4	no	—
183	C₂×D₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
184	C₂²×C₄	—	2	2	no	—
185	C₂²×C₄	#64541	1	2	yes	—
186	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
187	SD₁₆	—	76	8	no	—
188	D₈	—	76	8	no	—
189	M₁₆	—	8	2	no	—
190	M₁₆	—	38	4	no	—
191	C₂×C₈	—	2	4	no	—
192	C₂×C₈	—	8	2	no	—
193	C₂×C₈	—	38	2	no	—
194	C₂×C₈	—	76	2	no	—
195	C₄⋊C₄	—	2	2	no	—
196	C₂²⋊C₄	—	2	4	no	—
197	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
198	C₄²	C₂×D₇₆	1	1	yes	characteristic
199	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
200	C₂³	—	2	2	no	—
201	C₂³	—	76	2	no	—
202	C₂³	—	152	1	no	—
203	C₂³	—	152	1	no	—
204	C₂³	—	152	4	no	—
205	C₂³	#10597375	1	1	yes	characteristic
206	Q₈	—	4	2	no	—
207	D₄	—	4	2	no	—
208	D₄	—	8	2	no	—
209	D₄	—	8	2	no	—
210	D₄	—	76	4	no	—
211	D₄	—	152	4	no	—
212	D₄	—	152	4	no	—
213	D₄	—	152	2	no	—
214	C₂×C₄	—	2	2	no	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	4	2	no	—
217	C₂×C₄	—	4	2	no	—
218	C₂×C₄	—	4	2	no	—
219	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
220	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
221	C₂×C₄	#10597376	1	2	yes	—
222	C₂×C₄	#10597399	1	1	yes	characteristic
223	C₈	—	4	4	no	—
224	C₈	—	38	4	no	—
225	C₈	—	152	2	no	—
226	C₂²	—	2	2	no	—
227	C₂²	—	2	1	no	—
228	C₂²	—	4	4	no	—
229	C₂²	—	4	2	no	—
230	C₂²	—	304	2	no	—
231	C₂²	—	304	2	no	—
232	C₂²	—	152	4	no	—
233	C₂²	—	152	2	no	—
234	C₂²	#11926423	1	1	yes	characteristic
235	C₄	—	2	2	no	—
236	C₄	—	2	2	no	—
237	C₄	—	2	1	no	—
238	C₄	—	4	2	no	—
239	C₄	#11926712	1	2	yes	—
240	C₂	—	4	1	no	—
241	C₂	—	8	2	no	—
242	C₂	—	304	2	no	—
243	C₂	#14564033	1	1	yes	characteristic
244	C₂	#14564115	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14574088

C₂

yes

maximal, characteristic

#14562348

C₂

yes

maximal, complemented

#14562270

C₂

yes

maximal, characteristic, complemented

#14561506

C₂

yes

maximal, complemented

C₁₉×#2980

C₂

yes

maximal, characteristic, complemented

C₂×#10597395

—

C₂×#10597320

C₂²

yes

characteristic

#11926934

—

#11926920

C₄

yes

—

#11926918

C₄

yes

—

#11926601

C₂²

yes

—

C₄×#64520

C₂²

yes

characteristic

#11926287

—

#11926284

—

C₁₉×#532

C₂²

yes

characteristic

C₁₉×#435

—

C₁₉×#432

C₂²

yes

—

C₁₉×#408

—

C₂×#41×C₁₉

D₄

yes

—

C₂²×D₇₆

—

C₂²×D₇₆

—

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

characteristic

C₁₉×#127

C₂×C₄

yes

characteristic

C₁₉×#124

D₄

yes

—

C₁₉×#121

—

C₄×D₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

—

—

—

—

—

—

—

C₂×C₄

yes

—

C₁₉×C₄⋊C₈

D₄

yes

—

C₁₉×C₂²⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

#10597260

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

—

C₂³×D₁₉

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

C₂²⋊C₄

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

#64527

—

#64525

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#9423

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

#123

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

Q₈×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×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

#120

yes

characteristic

C₂×C₄×C₁₉

#121

yes

—

D₇₆

—

D₇₆

—

D₇₆

—

100

D₇₆

—

101

C₈×C₁₉

—

102

C₁₉⋊C₈

—

103

C₁₉⋊C₈

—

104

#3151

—

105

#2980

D₁₉

yes

characteristic, complemented

106

#1555

—

107

#1536

—

108

#1291

—

109

C₂²×C₁₉

—

110

C₂²×C₁₉

—

111

C₂²×C₁₉

—

112

C₂²×C₁₉

—

113

C₂²×C₁₉

#386

yes

characteristic

114

C₂×D₁₉

—

115

C₂×D₁₉

—

116

C₂×D₁₉

—

117

C₂×D₁₉

—

118

C₄×C₁₉

—

119

C₄×C₁₉

—

120

C₄×C₁₉

—

121

C₄×C₁₉

—

122

C₄×C₁₉

#453

yes

—

123

C₂×AGL(1,ℤ/8)

—

124

#532

C₂×D₁₉

yes

characteristic

125

C₂×#127

—

126

#496

—

127

#493

—

128

#492

—

129

#435

—

130

#432

—

131

#432

C₂×D₁₉

yes

—

132

#408

—

133

C₄×M₁₆

—

134

#331

—

135

#329

—

136

C₂×C₁₉

—

137

C₂×C₁₉

—

138

C₂×C₁₉

#1887

yes

characteristic

139

C₂×C₁₉

#1903

yes

—

140

D₁₉

—

141

C₂×#41

C₂²⋊D₁₉

yes

—

142

C₂²×D₄

—

143

C₂²×D₄

—

144

AGL(1,ℤ/8)

—

145

AGL(1,ℤ/8)

—

146

C₂×SD₁₆

—

147

C₂×D₈

—

148

C₂×M₁₆

—

149

C₂×M₁₆

—

150

C₂²×C₈

—

151

C₄⋊Q₈

C₄×D₁₉

yes

characteristic

152

#127

—

153

#127

—

154

#127

—

155

#127

C₄×D₁₉

yes

characteristic

156

#124

D₇₆

yes

—

157

#121

—

158

C₄×D₄

—

159

C₂×C₄²

C₂²×D₁₉

yes

characteristic

160

C₄⋊C₈

—

161

C₄⋊C₈

C₂²⋊D₁₉

yes

—

162

C₂²⋊C₈

—

163

C₂²⋊C₈

—

164

C₂²⋊C₈

—

165

#97

—

166

#97

—

167

#97

—

168

C₄×C₈

—

169

C₁₉

#9423

yes

characteristic, complemented, Sylow

170

C₂⁴

—

171

#41

—

172

#41

—

173

C₂×Q₈

(C₂×D₁₉)⋊C₄

yes

—

174

C₂×D₄

—

175

C₂×D₄

—

176

C₂×D₄

—

177

C₂×D₄

—

178

C₂×D₄

—

179

C₂×D₄

—

180

C₂×D₄

—

181

C₂×D₄

—

182

C₂×D₄

—

152

—

183

C₂×D₄

(C₂×D₁₉)⋊C₄

yes

—

184

C₂²×C₄

—

185

C₂²×C₄

#64541

yes

—

186

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

187

SD₁₆

—

188

D₈

—

189

M₁₆

—

190

M₁₆

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₄⋊C₄

—

196

C₂²⋊C₄

—

197

C₄²

C₂×C₄×D₁₉

yes

characteristic

198

C₄²

C₂×D₇₆

yes

characteristic

199

C₄²

C₂×C₂²⋊D₁₉

yes

—

200

C₂³

—

201

C₂³

—

202

C₂³

—

152

—

203

C₂³

—

152

—

204

C₂³

—

152

—

205

C₂³

#10597375

yes

characteristic

206

Q₈

—

207

D₄

—

208

D₄

—

209

D₄

—

210

D₄

—

211

D₄

—

152

—

212

D₄

—

152

—

213

D₄

—

152

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

220

C₂×C₄

C₄×C₂²⋊D₁₉

yes

—

221

C₂×C₄

#10597376

yes

—

222

C₂×C₄

#10597399

yes

characteristic

223

C₈

—

224

C₈

—

225

C₈

—

152

—

226

C₂²

—

227

C₂²

—

228

C₂²

—

229

C₂²

—

230

C₂²

—

304

—

231

C₂²

—

304

—

232

C₂²

—

152

—

233

C₂²

—

152

—

234

C₂²

#11926423

yes

characteristic

235

C₄

—

236

C₄

—

237

C₄

—

238

C₄

—

239

C₄

#11926712

yes

—

240

C₂

—

241

C₂

—

242

C₂

—

304

—

243

C₂

#14564033

yes

characteristic

244

C₂

#14564115

yes

—

	subgroup	G/H
center	C₂²	#11926423
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2980	C₂
socle	C₂²×C₁₉	#386
prime radical	#14574088	C₂
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2980	D₁₉
hypocenter	C₁₉	#9423
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2980

subgroup

G/H

center

C₂²

#11926423

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2980

C₂

C₂²×C₁₉

C₂

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2980

N	H ≅ G/N	type
2. #14562348	C₂	semidirect
3. #14562270	C₂	semidirect
4. #14561506	C₂	semidirect
5. C₁₉×#2980	C₂	semidirect
105. #2980	D₁₉	semidirect
169. C₁₉	#9423	semidirect

H ≅ G/N

type

2. #14562348

C₂

semidirect

3. #14562270

C₂

semidirect

4. #14561506

C₂

semidirect

5. C₁₉×#2980

C₂

semidirect

105. #2980

D₁₉

semidirect

169. C₁₉

#9423

semidirect

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

subgroup	index
#14574088	2
#14562348	2
#14562270	2
#14561506	2
C₁₉×#2980	2
#9423	19

subgroup

index

C₁₉×#2980

Subgroups — #18080066

Conjugacy classes of subgroups

Complements

Maximal subgroups