Finite Group Databasebeta

← #20254991

Subgroups — #20254991

Order 6016.

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×#13094051C212yesmaximal, complemented
2#15689776C211yesmaximal, characteristic, complemented
3D4×D188C211yesmaximal, characteristic, complemented
4#15689497C211yesmaximal, characteristic, complemented
5#15689372C212yesmaximal, complemented
6#15689319C211yesmaximal, characteristic, complemented
7#15689272C212yesmaximal, complemented
8#15689271C212yesmaximal, complemented
9C4×#10625334C211yesmaximal, characteristic, complemented
10#15689200C211yesmaximal, characteristic, complemented
11C47×#461C211yesmaximal, characteristic, complemented
12C2×#10625354C2212yescomplemented
13C22×D188—21no—
14C2×D4×D47C2212yes—
15#13094051—28no—
16C2×#10625336C2212yescomplemented
17C2×#10625336C2212yescomplemented
18C2×D376C2212yescomplemented
19C2×#10625334C2211yescharacteristic
20C2×#10625324C2212yescomplemented
21#13094021C2211yescharacteristic
22#13094009—22no—
23#13094000C2212yescomplemented
24#13093999—21no—
25#13093999C2212yes—
26#13093998—21no—
27#13093994—22no—
28C4×D188C2211yescharacteristic
29C4×D188C2211yescharacteristic, complemented
30C4⋊C4×D47—21no—
31#13093957C2211yescharacteristic, complemented
32#13093946C2212yescomplemented
33#13093945C2211yescharacteristic
34#13093944C2211yescharacteristic, complemented
35(C2×D47)⋊C8C2212yescomplemented
36C4×C47⋊C8C2211yescharacteristic, complemented
37C2×SD16×C47C2212yes—
38C4⋊Q8×C47C2211yescharacteristic, complemented
39C4×D4×C47C2211yescharacteristic
40C4⋊C8×C47C2211yescharacteristic, complemented
41#103×C47C2212yescomplemented
42C23×D47—22no—
43C2×Q8×C47C2312yes—
44C2×D4×C47C2311yescharacteristic
45C22×C4×C47—21no—
46C2×C22⋊D47—22no—
47#10625354—24no—
48#10625354—42no—
49D4×D47—24no—
50D4×D47—42no—
51C2×D188—22no—
52C2×D188—22no—
53C2×D188—21no—
54C2×D188—21no—
55C2×D188—44no—
56C2×D188D411yescharacteristic
57C2×D188C2312yes—
58C2×D188C2311yescharacteristic
59C2×C4×D47—21no—
60C2×C4×D47—22no—
61C2×C4×D47C2312yes—
62SD16×C47—24no—
63C2×C8×C47C2312yes—
64C4⋊C4×C47—21no—
65C4⋊C4×C47—21no—
66C4⋊C4×C47C2311yescharacteristic
67C22⋊C4×C47—21no—
68C42×C47C2311yescharacteristic
69#10625336—24no—
70#10625336—42no—
71#10625334D414yescomplemented
72(C2×D47)⋊C4—22no—
73(C2×D47)⋊C4—21no—
74(C2×D47)⋊C4—22no—
75(C2×D47)⋊C4D412yes—
76C4⋊Dic47D411yescharacteristic
77C4⋊Dic47C2311yescharacteristic
78Dic47⋊C4—22no—
79C2×C47⋊C8C2311yescharacteristic
80C2×C47⋊C8C2311yescharacteristic
81D376—24no—
82#10625324—24no—
83C23×C47—21no—
84C22×D47—21no—
85C22×D47—22no—
86C22×D47—44no—
87C22×D47—44no—
88C22×D47—82no—
89C22×D47C2×D412yes—
90Q8×C47—22no—
91Q8×C47—22no—
92D4×C47—21no—
93D4×C47C2×D412yes—
94C2×C4×C47—22no—
95C2×C4×C47—21no—
96C2×C4×C47—42no—
97C2×C4×C47C2×D411yescharacteristic
98C2×C4×C47C2×D411yescharacteristic
99C2×C4×C47C2411yescharacteristic
100C22⋊D47—44no—
101C2×Dic47—21no—
102C2×Dic47C2×D412yes—
103D188—22no—
104D188—22no—
105D188—21no—
106D188—22no—
107D188—44no—
108D188—44no—
109D188—42no—
110D188—81no—
111D188C2×D412yescomplemented
112C4×D47—22no—
113C4×D47—22no—
114C4×D47—44no—
115C4×D47—42no—
116C8×C47—22no—
117C47⋊C8—21no—
118C47⋊C8C2×D412yescomplemented
119C22×C47—22no—
120C22×C47—41no—
121C22×C47—41no—
122C22×C47C22×D411yescharacteristic
123C2×D47—22no—
124C2×D47—22no—
125C2×D47—22no—
126C2×D47—22no—
127C2×D47—41no—
128C2×D47—41no—
129C2×D47—42no—
130C2×D47—42no—
131C2×D47—42no—
132C2×D47—88no—
133C4×C47—21no—
134C4×C47—42no—
135C4×C47—41no—
136C4×C47AGL(1,ℤ/8)12yescomplemented
137C4×C47C22×D411yescharacteristic
138C4×C47H(5,𝔽2)11yescharacteristic
139Dic47—22no—
140Dic47—41no—
141#3272—471nomaximal, Sylow
142C2×C47—42no—
143C2×C47D4211yescharacteristic
144C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
145C2×C47#57711yescharacteristic
146D47—42no—
147D47—42no—
148D47—82no—
149C2×AGL(1,ℤ/8)—472no—
150#547—471no—
151D42—471no—
152#492—471no—
153#468—472no—
154#461D4711yescharacteristic, complemented
155#459—471no—
156#450—472no—
157#449—472no—
158C4×D8—471no—
159#436—471no—
160C47#327211yescharacteristic, complemented, Sylow
161C2×#41—472no—
162C22×D4—472no—
163C22×D4—941no—
164AGL(1,ℤ/8)—948no—
165C2×SD16—472no—
166C2×SD16—472no—
167C2×SD16C2×D4712yes—
168C2×D8—471no—
169C2×D8—472no—
170C2×M16—472no—
171C4⋊Q8C2×D4711yescharacteristic, complemented
172#127—471no—
173#123—942no—
174C22⋊Q8—472no—
175#121—472no—
176#121—941no—
177#121—941no—
178#120—942no—
179C4×D4—471no—
180C4×D4—471no—
181C4×D4C2×D4711yescharacteristic
182C2×C4⋊C4—941no—
183#107—471no—
184C4⋊C8C2×D4711yescharacteristic, complemented
185#103C2×D4712yescomplemented
186#102—471no—
187#102—472no—
188#102—471no—
189C22⋊C8—472no—
190C4×C8—471no—
191C24—942no—
192#41—944no—
193#41—1882no—
194C2×Q8C22×D4712yes—
195C2×D4—471no—
196C2×D4—471no—
197C2×D4—472no—
198C2×D4—942no—
199C2×D4—942no—
200C2×D4—942no—
201C2×D4—944no—
202C2×D4—941no—
203C2×D4—941no—
204C2×D4—1884no—
205C2×D4—1882no—
206C2×D4C22×D4711yescharacteristic
207C22×C4—21no—
208C22×C4—472no—
209C22×C4—942no—
210C22×C4—941no—
211SD16—24no—
212SD16—944no—
213SD16—1882no—
214D8—474no—
215D8—944no—
216M16—944no—
217C2×C8—471no—
218C2×C8—471no—
219C2×C8C22×D4712yes—
220C4⋊C4—21no—
221C4⋊C4—21no—
222C4⋊C4—471no—
223C4⋊C4—471no—
224C4⋊C4—942no—
225C4⋊C4C22×D4711yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—472no—
228C22⋊C4—942no—
229C22⋊C4—942no—
230C22⋊C4—941no—
231C42C22×D4711yescharacteristic
232C23—21no—
233C23—472no—
234C23—941no—
235C23—942no—
236C23—3762no—
237C23—1884no—
238C23—1884no—
239Q8—22no—
240Q8—22no—
241D4—21no—
242D4—472no—
243D4—942no—
244D4—942no—
245D4—941no—
246D4—942no—
247D4—3761no—
248D4—1884no—
249D4—1884no—
250D4—1884no—
251D4—1882no—
252D4D4×D4712yes—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—42no—
256C2×C4—472no—
257C2×C4—942no—
258C2×C4—942no—
259C2×C4—941no—
260C2×C4—1884no—
261C2×C4—1882no—
262C2×C4D4×D4711yescharacteristic
263C2×C4D4×D4711yescharacteristic
264C2×C4C23×D4711yescharacteristic
265C8—22no—
266C8—472no—
267C8—941no—
268C22—22no—
269C22—41no—
270C22—41no—
271C22—942no—
272C22—942no—
273C22—942no—
274C22—942no—
275C22—3768no—
276C22—1882no—
277C22—1882no—
278C22—1882no—
279C22—1881no—
280C22—1881no—
281C22C2×D4×D4711yescharacteristic
282C4—21no—
283C4—42no—
284C4—41no—
285C4—942no—
286C4—1881no—
287C4#1309405112yescomplemented
288C4C2×D4×D4711yescharacteristic
289C4#1309407011yescharacteristic
290C2—42no—
291C2—3762no—
292C2—1882no—
293C2—1882no—
294C2#1568975711yescharacteristic
295C2C2×#1309405111yescharacteristic
296C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#461C2
socleC22×C47C22×D4
hypercenter#461D47
hypocenterC47#3272
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. C2×#13094051C2semidirect
2. #15689776C2semidirect
3. D4×D188C2semidirect
4. #15689497C2semidirect
5. #15689372C2semidirect
6. #15689319C2semidirect
7. #15689272C2semidirect
8. #15689271C2semidirect
9. C4×#10625334C2semidirect
10. #15689200C2semidirect
11. C47×#461C2semidirect
12. C2×#10625354C22semidirect
16. C2×#10625336C22semidirect
17. C2×#10625336C22semidirect
18. C2×D376C22semidirect
20. C2×#10625324C22semidirect
23. #13094000C22semidirect
29. C4×D188C22semidirect
31. #13093957C22semidirect
32. #13093946C22semidirect
34. #13093944C22semidirect
35. (C2×D47)⋊C8C22semidirect
36. C4×C47⋊C8C22semidirect
38. C4⋊Q8×C47C22semidirect
40. C4⋊C8×C47C22semidirect
41. #103×C47C22semidirect
71. #10625334D4semidirect
111. D188C2×D4semidirect
118. C47⋊C8C2×D4semidirect
136. C4×C47AGL(1,ℤ/8)semidirect
154. #461D47semidirect
160. C47#3272semidirect
171. C4⋊Q8C2×D47semidirect
184. C4⋊C8C2×D47semidirect
185. #103C2×D47semidirect
287. C4#13094051semidirect