Finite Group Databasebeta

← #19146191

Subgroups — #19146191

Order 5504.

546 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 133 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#14583554C211yesmaximal, characteristic, complemented
3#14583271C211yesmaximal, characteristic, complemented
4#14583143C212yesmaximal, complemented
5#14583104C211yesmaximal, characteristic, complemented
6#14583091C211yesmaximal, characteristic, complemented
7#14583050C212yesmaximal, complemented
8#14583042C212yesmaximal, complemented
9C4×#10621882C211yesmaximal, characteristic, complemented
10#14582977C211yesmaximal, characteristic, complemented
11D42×C43C211yesmaximal, characteristic, complemented
12C2×#10621898C2212yescomplemented
13#13063351—28no—
14C2×#10621883C2212yes—
15C2×#10621883C2212yescomplemented
16C2×#10621883C2212yescomplemented
17C2×#10621882C2211yescharacteristic
18C2×#10621882C2212yescomplemented
19C2×#10621877C2212yescomplemented
20#13063325C2211yescharacteristic, complemented
21#13063307—22no—
22#13063304C2212yescomplemented
23#13063296—21no—
24C4×D172C2211yescharacteristic, complemented
25C4⋊C4×D43—21no—
26#13063258C2211yescharacteristic, complemented
27C4⋊(C43⋊C8)C2211yescharacteristic, complemented
28#13063248C2212yescomplemented
29#13063246C2211yescharacteristic
30#13063246C2212yescomplemented
31#13063245C2211yescharacteristic, complemented
32C22⋊(C43⋊C8)C2212yescomplemented
33C4×C43⋊C8C2211yescharacteristic, complemented
34C22×D4×C43—21no—
35C22×D4×C43C2212yes—
36#127×C43C2211yescharacteristic
37#121×C43—21no—
38#121×C43C2212yes—
39#120×C43—22no—
40C4×D4×C43C2211yescharacteristic
41C4×D4×C43C2211yescharacteristic
42C24×C43—22no—
43C2×D4×C43—22no—
44C2×D4×C43—21no—
45C2×D4×C43—21no—
46C2×D4×C43—22no—
47C2×D4×C43—24no—
48C2×D4×C43—42no—
49C2×D4×C43—44no—
50C2×D4×C43D411yescharacteristic
51C2×D4×C43C2312yes—
52C2×D4×C43C2311yescharacteristic
53C22×C4×C43—21no—
54C22×C4×C43C2312yes—
55C2×C22⋊D43—22no—
56#10621898—24no—
57#10621898—42no—
58C2×D172C2311yescharacteristic
59C2×C4×D43—21no—
60C2×C4×D43—22no—
61C2×Dic86C2312yes—
62C4⋊C4×C43D411yescharacteristic
63C4⋊C4×C43C2311yescharacteristic
64C22⋊C4×C43—21no—
65C22⋊C4×C43—22no—
66C22⋊C4×C43D412yes—
67C42×C43C2311yescharacteristic
68C22⋊Dic43—22no—
69#10621883—24no—
70#10621883—24no—
71#10621883—42no—
72#10621882—24no—
73#10621882D414yescomplemented
74(C2×D43)⋊C4—21no—
75C4⋊Dic43—21no—
76C4⋊Dic43—21no—
77C4⋊Dic43C2311yescharacteristic
78Dic43⋊C4—22no—
79#10621877—24no—
80C2×C43⋊C8C2311yescharacteristic
81C2×C43⋊C8C2312yes—
82C2×C43⋊C8C2311yescharacteristic
83C23×C43—21no—
84C23×C43—22no—
85C23×C43—44no—
86C23×C43—44no—
87C23×C43—82no—
88C23×C43C2×D412yes—
89C22×D43—21no—
90D4×C43—22no—
91D4×C43—22no—
92D4×C43—21no—
93D4×C43—22no—
94D4×C43—44no—
95D4×C43—44no—
96D4×C43—42no—
97D4×C43—81no—
98D4×C43C2×D412yes—
99C2×C4×C43—22no—
100C2×C4×C43—22no—
101C2×C4×C43—21no—
102C2×C4×C43—42no—
103C2×C4×C43C2×D412yes—
104C2×C4×C43C2×D411yescharacteristic
105C2×C4×C43C2×D411yescharacteristic
106C2×C4×C43C2411yescharacteristic
107C22⋊D43—44no—
108C2×Dic43—21no—
109C2×Dic43—22no—
110D172—21no—
111D172C2×D412yescomplemented
112C4×D43—44no—
113C4×D43—42no—
114Dic86—22no—
115Dic86—22no—
116C43⋊C8—22no—
117C43⋊C8—21no—
118C43⋊C8C2×D412yescomplemented
119C22×C43—22no—
120C22×C43—22no—
121C22×C43—22no—
122C22×C43—22no—
123C22×C43—41no—
124C22×C43—41no—
125C22×C43—42no—
126C22×C43—42no—
127C22×C43—42no—
128C22×C43—88no—
129C22×C43C22×D411yescharacteristic
130C2×D43—22no—
131C2×D43—41no—
132C2×D43—41no—
133C4×C43—22no—
134C4×C43—21no—
135C4×C43—41no—
136C4×C43AGL(1,ℤ/8)12yescomplemented
137C4×C43C22×D411yescharacteristic
138C4×C43H(5,𝔽2)11yescharacteristic
139Dic43—42no—
140Dic43—41no—
141#3272—431nomaximal, Sylow
142C2×C43—42no—
143C2×C43—42no—
144C2×C43—82no—
145C2×C43D4211yescharacteristic
146C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
147C2×C43#57711yescharacteristic
148D43—42no—
149C2×AGL(1,ℤ/8)—432no—
150#547—431no—
151D42D4311yescharacteristic, complemented
152#492—431no—
153#468—432no—
154#461—431no—
155#459—431no—
156#450—432no—
157#449—432no—
158C4×D8—431no—
159#436—431no—
160C43#327211yescharacteristic, complemented, Sylow
161C2×#41—432no—
162C22×D4—21no—
163C22×D4C2×D4312yes—
164AGL(1,ℤ/8)—868no—
165C2×SD16—432no—
166C2×SD16—432no—
167C2×SD16—432no—
168C2×D8—431no—
169C2×D8—432no—
170C2×M16—432no—
171C4⋊Q8—431no—
172#127C2×D4311yescharacteristic
173#123—862no—
174C22⋊Q8—432no—
175#121—21no—
176#121—861no—
177#121C2×D4312yes—
178#120—22no—
179C4×D4—431no—
180C4×D4C2×D4311yescharacteristic
181C4×D4C2×D4311yescharacteristic
182C2×C4⋊C4—861no—
183#107—431no—
184C4⋊C8—431no—
185#103—432no—
186#102—431no—
187#102—432no—
188#102—431no—
189C22⋊C8—432no—
190C4×C8—431no—
191C24—22no—
192#41—864no—
193#41—1722no—
194C2×Q8—432no—
195C2×D4—24no—
196C2×D4—22no—
197C2×D4—22no—
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—42no—
201C2×D4—44no—
202C2×D4—431no—
203C2×D4—862no—
204C2×D4C22⋊D4311yescharacteristic
205C2×D4C22×D4312yes—
206C2×D4C22×D4311yescharacteristic
207C22×C4—21no—
208C22×C4—861no—
209C22×C4—862no—
210C22×C4C22×D4312yes—
211SD16—864no—
212SD16—864no—
213SD16—1722no—
214D8—434no—
215D8—864no—
216M16—864no—
217C2×C8—431no—
218C2×C8—431no—
219C2×C8—432no—
220C4⋊C4—431no—
221C4⋊C4—861no—
222C4⋊C4—862no—
223C4⋊C4—861no—
224C4⋊C4C22⋊D4311yescharacteristic
225C4⋊C4C22×D4311yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—22no—
228C22⋊C4—862no—
229C22⋊C4—861no—
230C22⋊C4C22⋊D4312yes—
231C42C22×D4311yescharacteristic
232C23—21no—
233C23—22no—
234C23—44no—
235C23—44no—
236C23—82no—
237C23—861no—
238C23C2×C22⋊D4312yes—
239Q8—862no—
240Q8—862no—
241D4—22no—
242D4—22no—
243D4—21no—
244D4—22no—
245D4—44no—
246D4—44no—
247D4—42no—
248D4—81no—
249D4—432no—
250D4—861no—
251D4—1724no—
252D4D4×D4312yes—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—42no—
257C2×C4—861no—
258C2×C4—862no—
259C2×C4—1724no—
260C2×C4—1722no—
261C2×C4C2×C22⋊D4311yescharacteristic
262C2×C4C2×C22⋊D4312yes—
263C2×C4C2×C22⋊D4311yescharacteristic
264C2×C4C23×D4311yescharacteristic
265C8—432no—
266C8—862no—
267C8—861no—
268C22—22no—
269C22—22no—
270C22—22no—
271C22—22no—
272C22—41no—
273C22—41no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—88no—
278C22—862no—
279C22—1721no—
280C22—1721no—
281C22C22×C22⋊D4311yescharacteristic
282C4—21no—
283C4—22no—
284C4—41no—
285C4—1721no—
286C4—1722no—
287C4#1306335112yescomplemented
288C4C2×D4×D4311yescharacteristic
289C4#1306337011yescharacteristic
290C2—42no—
291C2—42no—
292C2—82no—
293C2—1722no—
294C2D4×C22⋊D4311yescharacteristic
295C2C2×#1306335111yescharacteristic
296C2#1458371011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingD42×C43C2
socleC22×C43C22×D4
hypercenterD42D43
hypocenterC43#3272
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C2×#13063351C2semidirect
2. #14583554C2semidirect
3. #14583271C2semidirect
4. #14583143C2semidirect
5. #14583104C2semidirect
6. #14583091C2semidirect
7. #14583050C2semidirect
8. #14583042C2semidirect
9. C4×#10621882C2semidirect
10. #14582977C2semidirect
11. D42×C43C2semidirect
12. C2×#10621898C22semidirect
15. C2×#10621883C22semidirect
16. C2×#10621883C22semidirect
18. C2×#10621882C22semidirect
19. C2×#10621877C22semidirect
20. #13063325C22semidirect
22. #13063304C22semidirect
24. C4×D172C22semidirect
26. #13063258C22semidirect
27. C4⋊(C43⋊C8)C22semidirect
28. #13063248C22semidirect
30. #13063246C22semidirect
31. #13063245C22semidirect
32. C22⋊(C43⋊C8)C22semidirect
33. C4×C43⋊C8C22semidirect
73. #10621882D4semidirect
111. D172C2×D4semidirect
118. C43⋊C8C2×D4semidirect
136. C4×C43AGL(1,ℤ/8)semidirect
151. D42D43semidirect
160. C43#3272semidirect
287. C4#13063351semidirect