Group #18085638 — subgroups

Subgroups — #18085638

Order 4864.

438 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 97 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	#14571998	C₂	1	1	yes	maximal, characteristic, complemented
2	#14564463	C₂	1	1	yes	maximal, characteristic
3	#14562196	C₂	1	2	yes	maximal
4	#14561494	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1276	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927094	C₂²	1	1	yes	characteristic
7	C₂×#10597316	—	2	1	no	—
8	#11926568	C₂²	1	1	yes	characteristic
9	C₂×#10597262	—	2	1	no	—
10	C₂×#10597262	—	2	1	no	—
11	#11926442	—	2	4	no	—
12	#11926414	—	2	1	no	—
13	#11926410	C₂²	1	2	yes	—
14	#11926279	—	2	4	no	—
15	C₁₉×#431	C₂²	1	2	yes	—
16	C₄³×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×#64541	—	2	1	no	—
18	C₂×C₄²×C₁₉	—	2	2	no	—
19	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
20	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
21	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
22	#10597376	—	2	2	no	—
23	C₂×C₄⋊Dic₁₉	—	2	4	no	—
24	C₂×C₄⋊Dic₁₉	—	2	2	no	—
25	C₂×Dic₁₉⋊C₄	—	2	4	no	—
26	C₂×#64520	—	2	1	no	—
27	#10597321	—	2	1	no	—
28	#10597320	Q₈	1	1	yes	characteristic
29	C₄×D₇₆	—	2	2	no	—
30	#10597316	—	4	2	no	—
31	#10597316	—	4	2	no	—
32	#10597315	Q₈	1	1	yes	characteristic
33	C₁₉×C₄⋊C₈	—	2	2	no	—
34	C₁₉×C₂²⋊C₈	—	2	2	no	—
35	C₄×C₈×C₁₉	—	2	2	no	—
36	C₁₉⋊#95	—	2	2	no	—
37	C₁₉⋊#95	D₄	1	4	yes	—
38	#10597262	—	4	2	no	—
39	#10597262	—	4	2	no	—
40	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
41	C₂²×C₄×C₁₉	—	2	1	no	—
42	C₂²×C₄×C₁₉	—	2	1	no	—
43	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
44	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
45	C₂×C₂²⋊D₁₉	—	4	1	no	—
46	C₂²×Dic₁₉	—	2	4	no	—
47	#64541	—	4	1	no	—
48	#64541	—	4	1	no	—
49	#64541	—	4	1	no	—
50	#64541	—	4	1	no	—
51	C₂×D₇₆	—	2	1	no	—
52	C₂×D₇₆	—	2	2	no	—
53	C₂×C₄×D₁₉	—	4	1	no	—
54	C₂×Dic₃₈	—	2	1	no	—
55	C₂×C₈×C₁₉	—	4	2	no	—
56	C₄²×C₁₉	—	2	1	no	—
57	C₄²×C₁₉	—	2	1	no	—
58	C₄²×C₁₉	—	4	4	no	—
59	C₄²×C₁₉	D₈	1	2	yes	—
60	C₄²×C₁₉	SD₁₆	1	2	yes	—
61	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
62	C₄²×C₁₉	#41	1	2	yes	—
63	C₄²×C₁₉	#41	1	1	yes	characteristic
64	(C₂×D₁₉)⋊C₄	—	4	2	no	—
65	C₄⋊Dic₁₉	—	2	2	no	—
66	C₄⋊Dic₁₉	—	4	8	no	—
67	C₄⋊Dic₁₉	—	4	2	no	—
68	C₄⋊Dic₁₉	—	4	2	no	—
69	Dic₁₉⋊C₄	—	4	8	no	—
70	#64520	—	4	1	no	—
71	#64520	—	4	1	no	—
72	C₂×C₁₉⋊C₈	—	4	1	no	—
73	#10364	—	19	1	no	maximal, Sylow
74	C₂³×C₁₉	#120	1	1	yes	characteristic
75	C₂²×D₁₉	—	4	1	no	—
76	C₂×C₄×C₁₉	—	2	4	no	—
77	C₂×C₄×C₁₉	—	2	2	no	—
78	C₂×C₄×C₁₉	—	2	2	no	—
79	C₂×C₄×C₁₉	—	4	2	no	—
80	C₂×C₄×C₁₉	—	4	2	no	—
81	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
82	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
83	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
84	C₂×C₄×C₁₉	#124	1	2	yes	—
85	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
86	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
87	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
88	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
89	C₂²⋊D₁₉	—	8	1	no	—
90	C₂²⋊D₁₉	—	8	1	no	—
91	C₂×Dic₁₉	—	4	8	no	—
92	C₂×Dic₁₉	—	4	1	no	—
93	C₂×Dic₁₉	—	4	4	no	—
94	D₇₆	—	4	1	no	—
95	D₇₆	—	4	1	no	—
96	D₇₆	—	8	2	no	—
97	C₄×D₁₉	—	8	1	no	—
98	C₄×D₁₉	—	8	1	no	—
99	Dic₃₈	—	4	1	no	—
100	Dic₃₈	—	4	1	no	—
101	C₈×C₁₉	—	8	2	no	—
102	C₁₉⋊C₈	—	8	1	no	—
103	#2859	—	19	1	no	—
104	#1962	—	19	1	no	—
105	#1517	—	19	2	no	—
106	#1286	—	19	2	no	—
107	#1276	D₁₉	1	1	yes	characteristic, complemented
108	C₂²×C₁₉	—	2	2	no	—
109	C₂²×C₁₉	#393	1	1	yes	characteristic
110	C₂²×C₁₉	#447	1	1	yes	characteristic
111	C₂²×C₁₉	#448	1	1	yes	characteristic
112	C₂×D₁₉	—	8	1	no	—
113	C₂×D₁₉	—	8	2	no	—
114	C₄×C₁₉	—	2	4	no	—
115	C₄×C₁₉	—	2	2	no	—
116	C₄×C₁₉	—	2	2	no	—
117	C₄×C₁₉	—	4	2	no	—
118	C₄×C₁₉	#474	1	1	yes	characteristic
119	C₄×C₁₉	#476	1	1	yes	characteristic
120	C₄×C₁₉	#486	1	1	yes	characteristic
121	C₄×C₁₉	#489	1	1	yes	characteristic
122	Dic₁₉	—	8	4	no	—
123	Dic₁₉	—	8	1	no	—
124	#532	—	19	1	no	—
125	C₂×#125	—	38	1	no	—
126	#431	C₂×D₁₉	1	2	yes	—
127	#423	—	19	1	no	—
128	C₂×#104	—	38	1	no	—
129	C₂×#104	—	38	1	no	—
130	#389	—	38	4	no	—
131	#384	—	38	1	no	—
132	#382	—	19	2	no	—
133	C₄³	C₂×D₁₉	1	1	yes	characteristic
134	#327	—	38	4	no	—
135	C₂×C₁₉	—	2	1	no	—
136	C₂×C₁₉	—	2	1	no	—
137	C₂×C₁₉	#2023	1	1	yes	characteristic
138	C₂×C₁₉	#2031	1	2	yes	—
139	D₁₉	—	16	1	no	—
140	C₂×#41	—	38	1	no	—
141	C₂×M₁₆	—	38	1	no	—
142	C₄⋊Q₈	—	19	1	no	—
143	#127	—	19	1	no	—
144	#125	—	76	2	no	—
145	#125	—	76	2	no	—
146	#124	—	38	1	no	—
147	#121	—	38	2	no	—
148	C₄×D₄	—	38	2	no	—
149	C₂×C₄⋊C₄	—	38	4	no	—
150	C₂×C₄⋊C₄	—	38	4	no	—
151	C₂×C₄⋊C₄	—	38	2	no	—
152	C₂×C₄²	—	2	2	no	—
153	C₂×C₄²	D₇₆	1	1	yes	characteristic
154	C₂×C₄²	D₇₆	1	1	yes	characteristic
155	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
156	C₄⋊C₈	—	2	2	no	—
157	C₄⋊C₈	—	38	2	no	—
158	#104	—	76	2	no	—
159	#104	—	76	2	no	—
160	C₂²⋊C₈	—	2	2	no	—
161	C₄×C₈	—	2	2	no	—
162	#95	—	19	4	no	—
163	#95	—	38	2	no	—
164	C₁₉	#10364	1	1	yes	characteristic, complemented, Sylow
165	#41	—	76	1	no	—
166	#41	—	76	1	no	—
167	#41	—	76	1	no	—
168	#41	—	76	1	no	—
169	C₂×Q₈	—	38	1	no	—
170	C₂×D₄	—	38	2	no	—
171	C₂×D₄	—	38	1	no	—
172	C₂×D₄	—	76	1	no	—
173	C₂²×C₄	—	2	1	no	—
174	C₂²×C₄	—	2	1	no	—
175	C₂²×C₄	—	38	4	no	—
176	C₂²×C₄	—	76	1	no	—
177	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
178	C₂²×C₄	D₄×D₁₉	1	2	yes	—
179	M₁₆	—	76	1	no	—
180	M₁₆	—	76	1	no	—
181	C₂×C₈	—	4	2	no	—
182	C₂×C₈	—	76	1	no	—
183	C₄⋊C₄	—	38	2	no	—
184	C₄⋊C₄	—	76	8	no	—
185	C₄⋊C₄	—	76	8	no	—
186	C₄⋊C₄	—	76	2	no	—
187	C₄⋊C₄	—	76	2	no	—
188	C₂²⋊C₄	—	76	2	no	—
189	C₄²	—	2	1	no	—
190	C₄²	—	2	1	no	—
191	C₄²	—	4	4	no	—
192	C₄²	#64516	1	2	yes	—
193	C₄²	D₁₅₂	1	2	yes	—
194	C₄²	#64541	1	2	yes	—
195	C₄²	#64543	1	1	yes	characteristic
196	C₄²	Q₈×D₁₉	1	1	yes	characteristic
197	C₂³	—	76	1	no	—
198	C₂³	#10597328	1	1	yes	characteristic
199	Q₈	—	76	1	no	—
200	Q₈	—	76	1	no	—
201	D₄	—	76	1	no	—
202	D₄	—	76	1	no	—
203	D₄	—	152	2	no	—
204	D₄	—	152	1	no	—
205	D₄	—	152	1	no	—
206	C₂×C₄	—	2	4	no	—
207	C₂×C₄	—	2	2	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	4	2	no	—
210	C₂×C₄	—	4	2	no	—
211	C₂×C₄	—	76	8	no	—
212	C₂×C₄	—	76	4	no	—
213	C₂×C₄	—	76	1	no	—
214	C₂×C₄	—	152	1	no	—
215	C₂×C₄	—	152	1	no	—
216	C₂×C₄	#10597321	1	1	yes	characteristic
217	C₂×C₄	#10597331	1	2	yes	—
218	C₂×C₄	#10597342	1	2	yes	—
219	C₂×C₄	#10597343	1	1	yes	characteristic
220	C₂×C₄	C₂×#64516	1	1	yes	characteristic
221	C₂×C₄	C₂×D₁₅₂	1	1	yes	characteristic
222	C₂×C₄	#10597354	1	1	yes	characteristic
223	C₂×C₄	#10597355	1	1	yes	characteristic
224	C₈	—	8	2	no	—
225	C₈	—	152	1	no	—
226	C₂²	—	2	2	no	—
227	C₂²	—	152	1	no	—
228	C₂²	—	152	2	no	—
229	C₂²	#11926457	1	1	yes	characteristic
230	C₂²	#11926680	1	1	yes	characteristic
231	C₂²	#11926685	1	1	yes	characteristic
232	C₄	—	2	4	no	—
233	C₄	—	2	2	no	—
234	C₄	—	2	2	no	—
235	C₄	—	4	2	no	—
236	C₄	—	152	4	no	—
237	C₄	—	152	1	no	—
238	C₄	#11926825	1	1	yes	characteristic
239	C₄	#11926835	1	1	yes	characteristic
240	C₄	#11926891	1	1	yes	characteristic
241	C₄	#11926904	1	1	yes	characteristic
242	C₂	—	2	1	no	—
243	C₂	—	2	1	no	—
244	C₂	—	304	1	no	—
245	C₂	#14564772	1	1	yes	characteristic
246	C₂	#14564808	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14571998

C₂

yes

maximal, characteristic, complemented

#14564463

C₂

yes

maximal, characteristic

#14562196

C₂

yes

maximal

#14561494

C₂

yes

maximal, complemented

C₁₉×#1276

C₂

yes

maximal, characteristic, complemented

#11927094

C₂²

yes

characteristic

C₂×#10597316

—

#11926568

C₂²

yes

—

—

—

—

C₂²

yes

—

#11926279

—

C₁₉×#431

C₂²

yes

—

C₄³×C₁₉

C₂²

yes

characteristic

C₂×#64541

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

#10597376

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×Dic₁₉⋊C₄

—

C₂×#64520

—

#10597321

—

#10597320

Q₈

yes

characteristic

C₄×D₇₆

—

#10597316

—

#10597316

—

#10597315

Q₈

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

C₁₉⋊#95

—

C₁₉⋊#95

D₄

yes

—

#10597262

—

#10597262

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₂²⋊D₁₉

—

C₂²×Dic₁₉

—

—

—

—

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

D₈

yes

—

C₄²×C₁₉

SD₁₆

yes

—

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₄²×C₁₉

#41

yes

characteristic

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

C₂×C₄×C₁₉

C₂×SD₁₆

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂²⋊D₁₉

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

D₇₆

—

C₄×D₁₉

—

C₄×D₁₉

—

Dic₃₈

—

100

Dic₃₈

—

101

C₈×C₁₉

—

102

C₁₉⋊C₈

—

103

#2859

—

104

#1962

—

105

#1517

—

106

#1286

—

107

#1276

D₁₉

yes

characteristic, complemented

108

C₂²×C₁₉

—

109

C₂²×C₁₉

#393

yes

characteristic

110

C₂²×C₁₉

#447

yes

characteristic

111

C₂²×C₁₉

#448

yes

characteristic

112

C₂×D₁₉

—

113

C₂×D₁₉

—

114

C₄×C₁₉

—

115

C₄×C₁₉

—

116

C₄×C₁₉

—

117

C₄×C₁₉

—

118

C₄×C₁₉

#474

yes

characteristic

119

C₄×C₁₉

#476

yes

characteristic

120

C₄×C₁₉

#486

yes

characteristic

121

C₄×C₁₉

#489

yes

characteristic

122

Dic₁₉

—

123

Dic₁₉

—

124

#532

—

125

C₂×#125

—

126

#431

C₂×D₁₉

yes

—

127

#423

—

128

C₂×#104

—

129

C₂×#104

—

130

#389

—

131

#384

—

132

#382

—

133

C₄³

C₂×D₁₉

yes

characteristic

134

#327

—

135

C₂×C₁₉

—

136

C₂×C₁₉

—

137

C₂×C₁₉

#2023

yes

characteristic

138

C₂×C₁₉

#2031

yes

—

139

D₁₉

—

140

C₂×#41

—

141

C₂×M₁₆

—

142

C₄⋊Q₈

—

143

#127

—

144

#125

—

145

#125

—

146

#124

—

147

#121

—

148

C₄×D₄

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

—

152

C₂×C₄²

—

153

C₂×C₄²

D₇₆

yes

characteristic

154

C₂×C₄²

D₇₆

yes

characteristic

155

C₂×C₄²

C₂²×D₁₉

yes

characteristic

156

C₄⋊C₈

—

157

C₄⋊C₈

—

158

#104

—

159

#104

—

160

C₂²⋊C₈

—

161

C₄×C₈

—

162

#95

—

163

#95

—

164

C₁₉

#10364

yes

characteristic, complemented, Sylow

165

#41

—

166

#41

—

167

#41

—

168

#41

—

169

C₂×Q₈

—

170

C₂×D₄

—

171

C₂×D₄

—

172

C₂×D₄

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

—

176

C₂²×C₄

—

177

C₂²×C₄

C₂×D₇₆

yes

characteristic

178

C₂²×C₄

D₄×D₁₉

yes

—

179

M₁₆

—

180

M₁₆

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₂²⋊C₄

—

189

C₄²

—

190

C₄²

—

191

C₄²

—

192

C₄²

#64516

yes

—

193

C₄²

D₁₅₂

yes

—

194

C₄²

#64541

yes

—

195

C₄²

#64543

yes

characteristic

196

C₄²

Q₈×D₁₉

yes

characteristic

197

C₂³

—

198

C₂³

#10597328

yes

characteristic

199

Q₈

—

200

Q₈

—

201

D₄

—

202

D₄

—

203

D₄

—

152

—

204

D₄

—

152

—

205

D₄

—

152

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

152

—

215

C₂×C₄

—

152

—

216

C₂×C₄

#10597321

yes

characteristic

217

C₂×C₄

#10597331

yes

—

218

C₂×C₄

#10597342

yes

—

219

C₂×C₄

#10597343

yes

characteristic

220

C₂×C₄

C₂×#64516

yes

characteristic

221

C₂×C₄

C₂×D₁₅₂

yes

characteristic

222

C₂×C₄

#10597354

yes

characteristic

223

C₂×C₄

#10597355

yes

characteristic

224

C₈

—

225

C₈

—

152

—

226

C₂²

—

227

C₂²

—

152

—

228

C₂²

—

152

—

229

C₂²

#11926457

yes

characteristic

230

C₂²

#11926680

yes

characteristic

231

C₂²

#11926685

yes

characteristic

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

—

152

—

237

C₄

—

152

—

238

C₄

#11926825

yes

characteristic

239

C₄

#11926835

yes

characteristic

240

C₄

#11926891

yes

characteristic

241

C₄

#11926904

yes

characteristic

242

C₂

—

243

C₂

—

244

C₂

—

304

—

245

C₂

#14564772

yes

characteristic

246

C₂

#14564808

yes

—

	subgroup	G/H
center	C₂²	#11926457
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1276	C₂
socle	C₂²×C₁₉	#393
prime radical	#11927094	C₂²
hypercenter	#1276	D₁₉
hypocenter	C₁₉	#10364
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1276

subgroup

G/H

center

C₂²

#11926457

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1276

C₂

C₂²×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1276

N	H ≅ G/N	type
1. #14571998	C₂	semidirect
4. #14561494	C₂	semidirect
5. C₁₉×#1276	C₂	semidirect
107. #1276	D₁₉	semidirect
164. C₁₉	#10364	semidirect

H ≅ G/N

type

1. #14571998

C₂

semidirect

4. #14561494

C₂

semidirect

5. C₁₉×#1276

C₂

semidirect

107. #1276

D₁₉

semidirect

164. C₁₉

#10364

semidirect

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

subgroup	index
#14571998	2
#14564463	2
#14562196	2
#14561494	2
C₁₉×#1276	2
#10364	19

subgroup

index

C₁₉×#1276

Subgroups — #18085638

Conjugacy classes of subgroups

Complements

Maximal subgroups