Finite Group Databasebeta

← #20254990

Subgroups — #20254990

Order 6016.

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×#13094052C212yesmaximal, complemented
2#15689778C211yesmaximal, characteristic, complemented
3D4×D188C211yesmaximal, characteristic, complemented
4#15689496C211yesmaximal, characteristic, complemented
5#15689369C212yesmaximal, complemented
6#15689329C211yesmaximal, characteristic, complemented
7#15689319C211yesmaximal, characteristic, complemented
8#15689276C212yesmaximal, complemented
9#15689270C212yesmaximal, complemented
10C4×D376C211yesmaximal, characteristic, complemented
11C47×#436C211yesmaximal, characteristic, complemented
12C2×#10625350C2212yescomplemented
13C22×D188C2212yes—
14C2×D4×D47—21no—
15#13094052—28no—
16C2×#10625325C2212yes—
17C2×#10625325C2212yescomplemented
18C2×#10625325C2212yescomplemented
19C2×D376C2211yescharacteristic
20C2×D376C2212yescomplemented
21#13094024C2211yescharacteristic, complemented
22#13094021C2211yescharacteristic
23#13094006—22no—
24#13094003C2212yescomplemented
25#13093999—21no—
26#13093998C2212yes—
27#13093995—21no—
28#13093994—22no—
29C4×D188C2211yescharacteristic
30C4×D188C2211yescharacteristic, complemented
31C4⋊C4×D47—21no—
32#13093958C2211yescharacteristic, complemented
33#13093949C2212yescomplemented
34#13093946C2211yescharacteristic
35#13093946C2211yescharacteristic, complemented
36#13093946C2212yescomplemented
37C2×M16×C47C2212yescomplemented
38C4×D4×C47C2211yescharacteristic
39C4⋊C8×C47C2211yescharacteristic, complemented
40C22⋊C8×C47C2212yescomplemented
41C4×C8×C47C2211yescharacteristic, complemented
42C23×D47—22no—
43C2×D4×C47D411yescharacteristic
44C22×C4×C47C2312yes—
45C2×C22⋊D47—22no—
46C2×C22⋊D47—22no—
47D4×D47—44no—
48#10625350—24no—
49#10625350—42no—
50C2×D188—24no—
51C2×D188—22no—
52C2×D188—21no—
53C2×D188—21no—
54C2×D188—42no—
55C2×D188C2312yes—
56C2×D188C2311yescharacteristic
57C2×D188C2311yescharacteristic
58C2×C4×D47—21no—
59C2×C4×D47—22no—
60C2×C4×D47—21no—
61C2×Dic94C2312yes—
62M16×C47—24no—
63C2×C8×C47C2312yes—
64C2×C8×C47C2311yescharacteristic
65C2×C8×C47C2311yescharacteristic
66C4⋊C4×C47D411yescharacteristic
67C22⋊C4×C47D412yes—
68C42×C47C2311yescharacteristic
69C22⋊Dic47—22no—
70(C2×D47)⋊C4—21no—
71(C2×D47)⋊C4—21no—
72(C2×D47)⋊C4—22no—
73C4⋊Dic47—21no—
74C4⋊Dic47—21no—
75C4⋊Dic47C2311yescharacteristic
76C4⋊Dic47C2311yescharacteristic
77Dic47⋊C4—22no—
78D376—24no—
79D376D414yescomplemented
80#10625325—24no—
81#10625325—24no—
82#10625325—42no—
83C23×C47C2×D412yes—
84C22×D47—21no—
85C22×D47—21no—
86C22×D47—22no—
87C22×D47—44no—
88C22×D47—44no—
89C22×D47—82no—
90D4×C47—22no—
91C2×C4×C47—22no—
92C2×C4×C47—22no—
93C2×C4×C47C2×D412yes—
94C2×C4×C47C2×D411yescharacteristic
95C2×C4×C47C2×D411yescharacteristic
96C2×C4×C47C2411yescharacteristic
97C22⋊D47—44no—
98C22⋊D47—44no—
99C2×Dic47—21no—
100C2×Dic47—22no—
101C2×Dic47—21no—
102D188—22no—
103D188—21no—
104D188—21no—
105D188—22no—
106D188—44no—
107D188—42no—
108D188—81no—
109D188C2×D412yes—
110D188C2×D412yescomplemented
111C4×D47—44no—
112C4×D47—42no—
113C4×D47—42no—
114Dic94—22no—
115Dic94—22no—
116C8×C47—22no—
117C8×C47—21no—
118C8×C47C2×D412yescomplemented
119C22×C47—22no—
120C22×C47—22no—
121C22×C47—22no—
122C22×C47C22×D411yescharacteristic
123C2×D47—22no—
124C2×D47—22no—
125C2×D47—41no—
126C2×D47—41no—
127C2×D47—41no—
128C2×D47—41no—
129C2×D47—42no—
130C2×D47—42no—
131C2×D47—42no—
132C2×D47—88no—
133C4×C47—22no—
134C4×C47—21no—
135C4×C47AGL(1,ℤ/8)12yescomplemented
136C4×C47C22×D411yescharacteristic
137C4×C47H(5,𝔽2)11yescharacteristic
138Dic47—42no—
139Dic47—41no—
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#461—471no—
155#459—471no—
156#450—472no—
157#449—472no—
158C4×D8—471no—
159#436D4711yescharacteristic, complemented
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×SD16—472no—
168C2×D8—471no—
169C2×D8—472no—
170C2×M16C2×D4712yescomplemented
171C4⋊Q8—471no—
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#103—472no—
186#102—471no—
187#102—471no—
188#102—472no—
189C22⋊C8C2×D4712yescomplemented
190C4×C8C2×D4711yescharacteristic, complemented
191C24—942no—
192#41—944no—
193#41—1882no—
194C2×Q8—472no—
195C2×D4—471no—
196C2×D4—471no—
197C2×D4—472no—
198C2×D4—944no—
199C2×D4—942no—
200C2×D4—942no—
201C2×D4—941no—
202C2×D4—942no—
203C2×D4—941no—
204C2×D4—1882no—
205C2×D4—1884no—
206C2×D4D18811yescharacteristic
207C22×C4—941no—
208C22×C4—942no—
209C22×C4—941no—
210C22×C4C22×D4712yes—
211SD16—944no—
212SD16—944no—
213SD16—1882no—
214D8—474no—
215D8—944no—
216M16—24no—
217C2×C8C22×D4711yescharacteristic
218C2×C8C22×D4712yes—
219C2×C8C22×D4711yescharacteristic
220C4⋊C4—471no—
221C4⋊C4—471no—
222C4⋊C4—942no—
223C4⋊C4—941no—
224C4⋊C4—941no—
225C4⋊C4D18811yescharacteristic
226C22⋊C4—942no—
227C22⋊C4—941no—
228C22⋊C4—941no—
229C22⋊C4—942no—
230C22⋊C4D18812yes—
231C42C22×D4711yescharacteristic
232C23—941no—
233C23—941no—
234C23—942no—
235C23—3762no—
236C23—1884no—
237C23—1884no—
238C23C2×D18812yes—
239Q8—942no—
240Q8—942no—
241D4—22no—
242D4—472no—
243D4—472no—
244D4—942no—
245D4—941no—
246D4—941no—
247D4—942no—
248D4—3761no—
249D4—1884no—
250D4—1884no—
251D4—1884no—
252D4—1882no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—941no—
256C2×C4—941no—
257C2×C4—942no—
258C2×C4—1884no—
259C2×C4—1882no—
260C2×C4—1882no—
261C2×C4C2×D18811yescharacteristic
262C2×C4C2×D18812yes—
263C2×C4C2×D18811yescharacteristic
264C2×C4C23×D4711yescharacteristic
265C8—22no—
266C8—21no—
267C8D4×D4712yescomplemented
268C22—22no—
269C22—22no—
270C22—22no—
271C22—942no—
272C22—942no—
273C22—3768no—
274C22—1882no—
275C22—1882no—
276C22—1882no—
277C22—1881no—
278C22—1881no—
279C22—1881no—
280C22—1881no—
281C22C22×D18811yescharacteristic
282C4—22no—
283C4—21no—
284C4—1882no—
285C4—1881no—
286C4—1881no—
287C4#1309405212yescomplemented
288C4C2×D4×D4711yescharacteristic
289C4#1309407011yescharacteristic
290C2—42no—
291C2—3762no—
292C2—1882no—
293C2—1882no—
294C2D4×D18811yescharacteristic
295C2C2×#1309405211yescharacteristic
296C2#1568993511yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#436C2
socleC22×C47C22×D4
hypercenter#436D47
hypocenterC47#3272
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. C2×#13094052C2semidirect
2. #15689778C2semidirect
3. D4×D188C2semidirect
4. #15689496C2semidirect
5. #15689369C2semidirect
6. #15689329C2semidirect
7. #15689319C2semidirect
8. #15689276C2semidirect
9. #15689270C2semidirect
10. C4×D376C2semidirect
11. C47×#436C2semidirect
12. C2×#10625350C22semidirect
17. C2×#10625325C22semidirect
18. C2×#10625325C22semidirect
20. C2×D376C22semidirect
21. #13094024C22semidirect
24. #13094003C22semidirect
30. C4×D188C22semidirect
32. #13093958C22semidirect
33. #13093949C22semidirect
35. #13093946C22semidirect
36. #13093946C22semidirect
37. C2×M16×C47C22semidirect
39. C4⋊C8×C47C22semidirect
40. C22⋊C8×C47C22semidirect
41. C4×C8×C47C22semidirect
79. D376D4semidirect
110. D188C2×D4semidirect
118. C8×C47C2×D4semidirect
135. C4×C47AGL(1,ℤ/8)semidirect
159. #436D47semidirect
160. C47#3272semidirect
170. C2×M16C2×D47semidirect
184. C4⋊C8C2×D47semidirect
189. C22⋊C8C2×D47semidirect
190. C4×C8C2×D47semidirect
267. C8D4×D47semidirect
287. C4#13094052semidirect