Finite Group Databasebeta

← #19143822

Subgroups — #19143822

Order 5504.

994 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 994 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063351C212yesmaximal, complemented
2#14583410C211yesmaximal, characteristic, complemented
3#14583050C214yesmaximal, complemented
4#14583033C214yesmaximal, complemented
5#14582904C212yesmaximal, complemented
6#14582863C211yesmaximal, characteristic, complemented
7C23×D4×C43C211yesmaximal, characteristic, complemented
8C2×#10621898C2211yescharacteristic, complemented
9#13063351—28no—
10C2×#10621883C2214yescomplemented
11C2×#10621882C2214yescomplemented
12C2×#10621877C2212yescomplemented
13#13063308—21no—
14#13063304C2212yescomplemented
15#13063299C2212yescomplemented
16#13063294—21no—
17C4×C22⋊D43—22no—
18#13063284C2211yescharacteristic, complemented
19#13063246C2218yescomplemented
20C22⋊(C43⋊C8)C2214yescomplemented
21C25×C43—21no—
22C22×D4×C43—28no—
23C22×D4×C43—22no—
24C22×D4×C43—21no—
25C22×D4×C43C2214yes—
26C22×D4×C43C2212yes—
27C23×C4×C43C2211yescharacteristic
28C24×C43—28no—
29C24×C43—24no—
30C24×C43—22no—
31C24×C43—48no—
32C24×C43D411yescharacteristic
33C2×D4×C43—216no—
34C2×D4×C43—28no—
35C2×D4×C43—216no—
36C2×D4×C43—24no—
37C2×D4×C43—24no—
38C2×D4×C43—22no—
39C2×D4×C43D418yescomplemented
40C2×D4×C43C2314yes—
41C22×C4×C43—24no—
42C22×C4×C43D412yes—
43C22×C4×C43D411yescharacteristic
44C22×C4×C43C2312yes—
45C22×C4×C43C2311yescharacteristic
46C2×C22⋊D43—22no—
47C2×C22⋊D43—21no—
48#10621898—24no—
49C2×D172C2311yescharacteristic, complemented
50C2×C4×D43—21no—
51C2×Dic86C2311yescharacteristic, complemented
52C22⋊Dic43—21no—
53C22⋊Dic43—22no—
54#10621883—28no—
55#10621882—28no—
56(C2×D43)⋊C4—22no—
57C4⋊Dic43C2312yescomplemented
58Dic43⋊C4—22no—
59C4×Dic43—21no—
60#10621877—24no—
61C2×C43⋊C8C2314yescomplemented
62C23×C43—22no—
63C23×C43—24no—
64C23×C43—216no—
65C23×C43—28no—
66C23×C43—24no—
67C23×C43—432no—
68C23×C43—48no—
69C23×C43—48no—
70C23×C43—48no—
71C23×C43C2×D411yescharacteristic
72C23×C43C2×D412yes—
73C22×D43—21no—
74D4×C43—216no—
75D4×C43—28no—
76D4×C43—24no—
77D4×C43C2×D418yes—
78C2×C4×C43—22no—
79C2×C4×C43—24no—
80C2×C4×C43—24no—
81C2×C4×C43C2×D412yes—
82C2×C4×C43C2×D411yescharacteristic
83C2×C4×C43C2×D414yes—
84C2×C4×C43C2411yescharacteristic
85C22⋊D43—42no—
86C22⋊D43—44no—
87C2×Dic43—22no—
88C2×Dic43—21no—
89D172—22no—
90C4×D43—42no—
91Dic86—22no—
92C43⋊C8—24no—
93C22×C43—28no—
94C22×C43—22no—
95C22×C43—22no—
96C22×C43—22no—
97C22×C43—28no—
98C22×C43—416no—
99C22×C43—432no—
100C22×C43—48no—
101C22×C43#12012yes—
102C22×C43AGL(1,ℤ/8)14yescomplemented
103C22×C43C22×D411yescharacteristic
104C2×D43—41no—
105C2×D43—42no—
106C4×C43—22no—
107C4×C43#12012yes—
108C4×C43C22×D412yes—
109Dic43—41no—
110Dic43—42no—
111#3003—431nomaximal, Sylow
112C2×C43—22no—
113C2×C43—24no—
114C2×C43—48no—
115C2×C43C2×#12011yescharacteristic
116C2×C43C2×AGL(1,ℤ/8)12yes—
117D43—81no—
118C23×D4D4311yescharacteristic, complemented
119C2×AGL(1,ℤ/8)—432no—
120#525—431no—
121#450—434no—
122#447—434no—
123#418—432no—
124#407—431no—
125C43#300311yescharacteristic, complemented, Sylow
126C25—21no—
127C2×#41—431no—
128C22×D4—28no—
129C22×D4—22no—
130C22×D4—21no—
131C22×D4C2×D4314yes—
132C22×D4C2×D4312yes—
133C23×C4C2×D4311yescharacteristic
134AGL(1,ℤ/8)—868no—
135C2×SD16—434no—
136C2×D8—434no—
137C2×M16—432no—
138#123—861no—
139C22⋊Q8—432no—
140#121—432no—
141#120—861no—
142C4×D4—862no—
143#117—431no—
144#102—438no—
145C22⋊C8—434no—
146C24—28no—
147C24—24no—
148C24—22no—
149C24—48no—
150C24C22⋊D4311yescharacteristic
151#41—864no—
152C2×Q8—431no—
153C2×D4—28no—
154C2×D4—216no—
155C2×D4—216no—
156C2×D4—24no—
157C2×D4—22no—
158C2×D4—24no—
159C2×D4—431no—
160C2×D4—862no—
161C2×D4—861no—
162C2×D4C22⋊D4318yescomplemented
163C2×D4C22×D4314yes—
164C22×C4—24no—
165C22×C4—861no—
166C22×C4C22⋊D4312yes—
167C22×C4C22⋊D4311yescharacteristic
168C22×C4C22×D4312yes—
169C22×C4C22×D4311yescharacteristic
170SD16—868no—
171D8—868no—
172M16—864no—
173C2×C8—434no—
174C4⋊C4—432no—
175C4⋊C4—862no—
176C22⋊C4—861no—
177C22⋊C4—862no—
178C22⋊C4—862no—
179C42—861no—
180C23—22no—
181C23—24no—
182C23—216no—
183C23—28no—
184C23—24no—
185C23—432no—
186C23—48no—
187C23—48no—
188C23—48no—
189C23—861no—
190C23C2×C22⋊D4311yescharacteristic
191C23C2×C22⋊D4312yes—
192Q8—862no—
193D4—216no—
194D4—28no—
195D4—24no—
196D4—862no—
197D4—1722no—
198D4—1724no—
199D4C2×C22⋊D4318yes—
200C2×C4—22no—
201C2×C4—24no—
202C2×C4—24no—
203C2×C4—862no—
204C2×C4—861no—
205C2×C4—1722no—
206C2×C4C2×C22⋊D4312yes—
207C2×C4C2×C22⋊D4311yescharacteristic
208C2×C4C2×C22⋊D4314yes—
209C2×C4C23×D4311yescharacteristic
210C8—864no—
211C22—28no—
212C22—22no—
213C22—22no—
214C22—22no—
215C22—28no—
216C22—416no—
217C22—432no—
218C22—48no—
219C22—1721no—
220C22—1722no—
221C22#1306329412yes—
222C22#1306335114yescomplemented
223C22C22×C22⋊D4311yescharacteristic
224C4—22no—
225C4—1721no—
226C4—1722no—
227C4#1306329412yes—
228C4C22×C22⋊D4312yes—
229C2—22no—
230C2—24no—
231C2—48no—
232C2—3441no—
233C2C2×#1306329411yescharacteristic
234C2C2×#1306335112yes—
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC23×D4×C43C2
socleC22×C43C22×D4
hypercenterC23×D4D43
hypocenterC43#3003
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#13063351C2semidirect
2. #14583410C2semidirect
3. #14583050C2semidirect
4. #14583033C2semidirect
5. #14582904C2semidirect
6. #14582863C2semidirect
7. C23×D4×C43C2semidirect
8. C2×#10621898C22semidirect
10. C2×#10621883C22semidirect
11. C2×#10621882C22semidirect
12. C2×#10621877C22semidirect
14. #13063304C22semidirect
15. #13063299C22semidirect
18. #13063284C22semidirect
19. #13063246C22semidirect
20. C22⋊(C43⋊C8)C22semidirect
39. C2×D4×C43D4semidirect
49. C2×D172C23semidirect
51. C2×Dic86C23semidirect
57. C4⋊Dic43C23semidirect
61. C2×C43⋊C8C23semidirect
102. C22×C43AGL(1,ℤ/8)semidirect
118. C23×D4D43semidirect
125. C43#3003semidirect
162. C2×D4C22⋊D43semidirect
222. C22#13063351semidirect