Finite Group Databasebeta

← #19146198

Subgroups — #19146198

Order 5504.

546 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 125 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×#13063352C212yesmaximal, complemented
2#14583552C211yesmaximal, characteristic, complemented
3D4×D172C211yesmaximal, characteristic, complemented
4#14583273C211yesmaximal, characteristic, complemented
5#14583148C212yesmaximal, complemented
6#14583095C211yesmaximal, characteristic, complemented
7#14583048C212yesmaximal, complemented
8#14583047C212yesmaximal, complemented
9C4×#10621882C211yesmaximal, characteristic, complemented
10#14582976C211yesmaximal, characteristic, complemented
11C43×#461C211yesmaximal, characteristic, complemented
12C2×#10621902C2212yescomplemented
13C22×D172—21no—
14C2×D4×D43C2212yes—
15#13063352—28no—
16C2×#10621884C2212yescomplemented
17C2×#10621884C2212yescomplemented
18C2×D344C2212yescomplemented
19C2×#10621882C2211yescharacteristic
20C2×#10621872C2212yescomplemented
21#13063322C2211yescharacteristic
22#13063310—22no—
23#13063301C2212yescomplemented
24#13063300—21no—
25#13063300C2212yes—
26#13063299—21no—
27#13063295—22no—
28C4×D172C2211yescharacteristic
29C4×D172C2211yescharacteristic, complemented
30C4⋊C4×D43—21no—
31#13063258C2211yescharacteristic, complemented
32#13063247C2212yescomplemented
33#13063246C2211yescharacteristic
34#13063245C2211yescharacteristic, complemented
35(C2×D43)⋊C8C2212yescomplemented
36C4×C43⋊C8C2211yescharacteristic, complemented
37C2×SD16×C43C2212yes—
38C4⋊Q8×C43C2211yescharacteristic, complemented
39C4×D4×C43C2211yescharacteristic
40C4⋊C8×C43C2211yescharacteristic, complemented
41#103×C43C2212yescomplemented
42C23×D43—22no—
43C2×Q8×C43C2312yes—
44C2×D4×C43C2311yescharacteristic
45C22×C4×C43—21no—
46C2×C22⋊D43—22no—
47#10621902—24no—
48#10621902—42no—
49D4×D43—24no—
50D4×D43—42no—
51C2×D172—21no—
52C2×D172—21no—
53C2×D172—22no—
54C2×D172—22no—
55C2×D172—44no—
56C2×D172D411yescharacteristic
57C2×D172C2312yes—
58C2×D172C2311yescharacteristic
59C2×C4×D43—21no—
60C2×C4×D43—22no—
61C2×C4×D43C2312yes—
62SD16×C43—24no—
63C2×C8×C43C2312yes—
64C4⋊C4×C43—21no—
65C4⋊C4×C43—21no—
66C4⋊C4×C43C2311yescharacteristic
67C22⋊C4×C43—21no—
68C42×C43C2311yescharacteristic
69#10621884—24no—
70#10621884—42no—
71#10621882D414yescomplemented
72(C2×D43)⋊C4—21no—
73(C2×D43)⋊C4—22no—
74(C2×D43)⋊C4—22no—
75(C2×D43)⋊C4D412yes—
76C4⋊Dic43D411yescharacteristic
77C4⋊Dic43C2311yescharacteristic
78Dic43⋊C4—22no—
79C2×C43⋊C8C2311yescharacteristic
80C2×C43⋊C8C2311yescharacteristic
81D344—24no—
82#10621872—24no—
83C23×C43—21no—
84C22×D43—21no—
85C22×D43—22no—
86C22×D43—44no—
87C22×D43—44no—
88C22×D43—82no—
89C22×D43C2×D412yes—
90Q8×C43—22no—
91Q8×C43—22no—
92D4×C43—21no—
93D4×C43C2×D412yes—
94C2×C4×C43—22no—
95C2×C4×C43—21no—
96C2×C4×C43—42no—
97C2×C4×C43C2×D411yescharacteristic
98C2×C4×C43C2×D411yescharacteristic
99C2×C4×C43C2411yescharacteristic
100C22⋊D43—44no—
101C2×Dic43—21no—
102C2×Dic43C2×D412yes—
103D172—22no—
104D172—22no—
105D172—21no—
106D172—22no—
107D172—44no—
108D172—44no—
109D172—42no—
110D172—81no—
111D172C2×D412yescomplemented
112C4×D43—22no—
113C4×D43—22no—
114C4×D43—44no—
115C4×D43—42no—
116C8×C43—22no—
117C43⋊C8—21no—
118C43⋊C8C2×D412yescomplemented
119C22×C43—22no—
120C22×C43—41no—
121C22×C43—41no—
122C22×C43C22×D411yescharacteristic
123C2×D43—22no—
124C2×D43—22no—
125C2×D43—22no—
126C2×D43—22no—
127C2×D43—41no—
128C2×D43—41no—
129C2×D43—42no—
130C2×D43—42no—
131C2×D43—42no—
132C2×D43—88no—
133C4×C43—21no—
134C4×C43—42no—
135C4×C43—41no—
136C4×C43AGL(1,ℤ/8)12yescomplemented
137C4×C43C22×D411yescharacteristic
138C4×C43H(5,𝔽2)11yescharacteristic
139Dic43—22no—
140Dic43—41no—
141#3272—431nomaximal, Sylow
142C2×C43—42no—
143C2×C43D4211yescharacteristic
144C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
145C2×C43#57711yescharacteristic
146D43—42no—
147D43—42no—
148D43—82no—
149C2×AGL(1,ℤ/8)—432no—
150#547—431no—
151D42—431no—
152#492—431no—
153#468—432no—
154#461D4311yescharacteristic, complemented
155#459—431no—
156#450—432no—
157#449—432no—
158C4×D8—431no—
159#436—431no—
160C43#327211yescharacteristic, complemented, Sylow
161C2×#41—432no—
162C22×D4—432no—
163C22×D4—861no—
164AGL(1,ℤ/8)—868no—
165C2×SD16—432no—
166C2×SD16—432no—
167C2×SD16C2×D4312yes—
168C2×D8—431no—
169C2×D8—432no—
170C2×M16—432no—
171C4⋊Q8C2×D4311yescharacteristic, complemented
172#127—431no—
173#123—862no—
174C22⋊Q8—432no—
175#121—432no—
176#121—861no—
177#121—861no—
178#120—862no—
179C4×D4—431no—
180C4×D4—431no—
181C4×D4C2×D4311yescharacteristic
182C2×C4⋊C4—861no—
183#107—431no—
184C4⋊C8C2×D4311yescharacteristic, complemented
185#103C2×D4312yescomplemented
186#102—431no—
187#102—432no—
188#102—431no—
189C22⋊C8—432no—
190C4×C8—431no—
191C24—862no—
192#41—864no—
193#41—1722no—
194C2×Q8C22×D4312yes—
195C2×D4—431no—
196C2×D4—431no—
197C2×D4—432no—
198C2×D4—862no—
199C2×D4—862no—
200C2×D4—862no—
201C2×D4—864no—
202C2×D4—861no—
203C2×D4—861no—
204C2×D4—1724no—
205C2×D4—1722no—
206C2×D4C22×D4311yescharacteristic
207C22×C4—21no—
208C22×C4—432no—
209C22×C4—862no—
210C22×C4—861no—
211SD16—24no—
212SD16—864no—
213SD16—1722no—
214D8—434no—
215D8—864no—
216M16—864no—
217C2×C8—431no—
218C2×C8—431no—
219C2×C8C22×D4312yes—
220C4⋊C4—21no—
221C4⋊C4—21no—
222C4⋊C4—431no—
223C4⋊C4—431no—
224C4⋊C4—862no—
225C4⋊C4C22×D4311yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—432no—
228C22⋊C4—862no—
229C22⋊C4—862no—
230C22⋊C4—861no—
231C42C22×D4311yescharacteristic
232C23—21no—
233C23—432no—
234C23—861no—
235C23—862no—
236C23—3442no—
237C23—1724no—
238C23—1724no—
239Q8—22no—
240Q8—22no—
241D4—21no—
242D4—432no—
243D4—862no—
244D4—862no—
245D4—861no—
246D4—862no—
247D4—3441no—
248D4—1724no—
249D4—1724no—
250D4—1724no—
251D4—1722no—
252D4D4×D4312yes—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—42no—
256C2×C4—432no—
257C2×C4—862no—
258C2×C4—862no—
259C2×C4—861no—
260C2×C4—1724no—
261C2×C4—1722no—
262C2×C4D4×D4311yescharacteristic
263C2×C4D4×D4311yescharacteristic
264C2×C4C23×D4311yescharacteristic
265C8—22no—
266C8—432no—
267C8—861no—
268C22—22no—
269C22—41no—
270C22—41no—
271C22—862no—
272C22—862no—
273C22—862no—
274C22—862no—
275C22—3448no—
276C22—1722no—
277C22—1722no—
278C22—1722no—
279C22—1721no—
280C22—1721no—
281C22C2×D4×D4311yescharacteristic
282C4—21no—
283C4—41no—
284C4—42no—
285C4—862no—
286C4—1721no—
287C4#1306335212yescomplemented
288C4C2×D4×D4311yescharacteristic
289C4#1306337111yescharacteristic
290C2—42no—
291C2—3442no—
292C2—1722no—
293C2—1722no—
294C2#1458353311yescharacteristic
295C2C2×#1306335211yescharacteristic
296C2#1458370811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#461C2
socleC22×C43C22×D4
hypercenter#461D43
hypocenterC43#3272
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. C2×#13063352C2semidirect
2. #14583552C2semidirect
3. D4×D172C2semidirect
4. #14583273C2semidirect
5. #14583148C2semidirect
6. #14583095C2semidirect
7. #14583048C2semidirect
8. #14583047C2semidirect
9. C4×#10621882C2semidirect
10. #14582976C2semidirect
11. C43×#461C2semidirect
12. C2×#10621902C22semidirect
16. C2×#10621884C22semidirect
17. C2×#10621884C22semidirect
18. C2×D344C22semidirect
20. C2×#10621872C22semidirect
23. #13063301C22semidirect
29. C4×D172C22semidirect
31. #13063258C22semidirect
32. #13063247C22semidirect
34. #13063245C22semidirect
35. (C2×D43)⋊C8C22semidirect
36. C4×C43⋊C8C22semidirect
38. C4⋊Q8×C43C22semidirect
40. C4⋊C8×C43C22semidirect
41. #103×C43C22semidirect
71. #10621882D4semidirect
111. D172C2×D4semidirect
118. C43⋊C8C2×D4semidirect
136. C4×C43AGL(1,ℤ/8)semidirect
154. #461D43semidirect
160. C43#3272semidirect
171. C4⋊Q8C2×D43semidirect
184. C4⋊C8C2×D43semidirect
185. #103C2×D43semidirect
287. C4#13063352semidirect