Finite Group Databasebeta

← #20254984

Subgroups — #20254984

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×#13094050C212yesmaximal, complemented
2#15689778C211yesmaximal, characteristic, complemented
3#15689495C211yesmaximal, characteristic, complemented
4#15689367C212yesmaximal, complemented
5#15689328C211yesmaximal, characteristic, complemented
6#15689315C211yesmaximal, characteristic, complemented
7#15689274C212yesmaximal, complemented
8#15689266C212yesmaximal, complemented
9C4×#10625334C211yesmaximal, characteristic, complemented
10#15689201C211yesmaximal, characteristic, complemented
11D42×C47C211yesmaximal, characteristic, complemented
12C2×#10625350C2212yescomplemented
13#13094050—28no—
14C2×#10625335C2212yes—
15C2×#10625335C2212yescomplemented
16C2×#10625335C2212yescomplemented
17C2×#10625334C2211yescharacteristic
18C2×#10625334C2212yescomplemented
19C2×#10625329C2212yescomplemented
20#13094024C2211yescharacteristic, complemented
21#13094006—22no—
22#13094003C2212yescomplemented
23#13093995—21no—
24C4×D188C2211yescharacteristic, complemented
25C4⋊C4×D47—21no—
26#13093957C2211yescharacteristic, complemented
27C4⋊(C47⋊C8)C2211yescharacteristic, complemented
28#13093947C2212yescomplemented
29#13093945C2211yescharacteristic
30#13093945C2212yescomplemented
31#13093944C2211yescharacteristic, complemented
32C22⋊(C47⋊C8)C2212yescomplemented
33C4×C47⋊C8C2211yescharacteristic, complemented
34C22×D4×C47—21no—
35C22×D4×C47C2212yes—
36#127×C47C2211yescharacteristic
37#121×C47—21no—
38#121×C47C2212yes—
39#120×C47—22no—
40C4×D4×C47C2211yescharacteristic
41C4×D4×C47C2211yescharacteristic
42C24×C47—22no—
43C2×D4×C47—24no—
44C2×D4×C47—22no—
45C2×D4×C47—22no—
46C2×D4×C47—21no—
47C2×D4×C47—21no—
48C2×D4×C47—42no—
49C2×D4×C47—44no—
50C2×D4×C47D411yescharacteristic
51C2×D4×C47C2312yes—
52C2×D4×C47C2311yescharacteristic
53C22×C4×C47—21no—
54C22×C4×C47C2312yes—
55C2×C22⋊D47—22no—
56#10625350—24no—
57#10625350—42no—
58C2×D188C2311yescharacteristic
59C2×C4×D47—21no—
60C2×C4×D47—22no—
61C2×Dic94C2312yes—
62C4⋊C4×C47D411yescharacteristic
63C4⋊C4×C47C2311yescharacteristic
64C22⋊C4×C47—21no—
65C22⋊C4×C47—22no—
66C22⋊C4×C47D412yes—
67C42×C47C2311yescharacteristic
68C22⋊Dic47—22no—
69#10625335—24no—
70#10625335—24no—
71#10625335—42no—
72#10625334—24no—
73#10625334D414yescomplemented
74(C2×D47)⋊C4—21no—
75C4⋊Dic47—21no—
76C4⋊Dic47—21no—
77C4⋊Dic47C2311yescharacteristic
78Dic47⋊C4—22no—
79#10625329—24no—
80C2×C47⋊C8C2311yescharacteristic
81C2×C47⋊C8C2312yes—
82C2×C47⋊C8C2311yescharacteristic
83C23×C47—21no—
84C23×C47—22no—
85C23×C47—44no—
86C23×C47—44no—
87C23×C47—82no—
88C23×C47C2×D412yes—
89C22×D47—21no—
90D4×C47—22no—
91D4×C47—22no—
92D4×C47—21no—
93D4×C47—22no—
94D4×C47—44no—
95D4×C47—44no—
96D4×C47—42no—
97D4×C47—81no—
98D4×C47C2×D412yes—
99C2×C4×C47—22no—
100C2×C4×C47—22no—
101C2×C4×C47—21no—
102C2×C4×C47—42no—
103C2×C4×C47C2×D412yes—
104C2×C4×C47C2×D411yescharacteristic
105C2×C4×C47C2×D411yescharacteristic
106C2×C4×C47C2411yescharacteristic
107C22⋊D47—44no—
108C2×Dic47—21no—
109C2×Dic47—22no—
110D188—21no—
111D188C2×D412yescomplemented
112C4×D47—44no—
113C4×D47—42no—
114Dic94—22no—
115Dic94—22no—
116C47⋊C8—22no—
117C47⋊C8—21no—
118C47⋊C8C2×D412yescomplemented
119C22×C47—22no—
120C22×C47—22no—
121C22×C47—22no—
122C22×C47—22no—
123C22×C47—41no—
124C22×C47—41no—
125C22×C47—42no—
126C22×C47—42no—
127C22×C47—42no—
128C22×C47—88no—
129C22×C47C22×D411yescharacteristic
130C2×D47—22no—
131C2×D47—41no—
132C2×D47—41no—
133C4×C47—22no—
134C4×C47—21no—
135C4×C47—41no—
136C4×C47AGL(1,ℤ/8)12yescomplemented
137C4×C47C22×D411yescharacteristic
138C4×C47H(5,𝔽2)11yescharacteristic
139Dic47—42no—
140Dic47—41no—
141#3272—471nomaximal, Sylow
142C2×C47—42no—
143C2×C47—42no—
144C2×C47—82no—
145C2×C47D4211yescharacteristic
146C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
147C2×C47#57711yescharacteristic
148D47—42no—
149C2×AGL(1,ℤ/8)—472no—
150#547—471no—
151D42D4711yescharacteristic, complemented
152#492—471no—
153#468—472no—
154#461—471no—
155#459—471no—
156#450—472no—
157#449—472no—
158C4×D8—471no—
159#436—471no—
160C47#327211yescharacteristic, complemented, Sylow
161C2×#41—472no—
162C22×D4—21no—
163C22×D4C2×D4712yes—
164AGL(1,ℤ/8)—948no—
165C2×SD16—472no—
166C2×SD16—472no—
167C2×SD16—472no—
168C2×D8—471no—
169C2×D8—472no—
170C2×M16—472no—
171C4⋊Q8—471no—
172#127C2×D4711yescharacteristic
173#123—942no—
174C22⋊Q8—472no—
175#121—21no—
176#121—941no—
177#121C2×D4712yes—
178#120—22no—
179C4×D4—471no—
180C4×D4C2×D4711yescharacteristic
181C4×D4C2×D4711yescharacteristic
182C2×C4⋊C4—941no—
183#107—471no—
184C4⋊C8—471no—
185#103—472no—
186#102—471no—
187#102—472no—
188#102—471no—
189C22⋊C8—472no—
190C4×C8—471no—
191C24—22no—
192#41—944no—
193#41—1882no—
194C2×Q8—472no—
195C2×D4—24no—
196C2×D4—22no—
197C2×D4—22no—
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—42no—
201C2×D4—44no—
202C2×D4—471no—
203C2×D4—942no—
204C2×D4C22⋊D4711yescharacteristic
205C2×D4C22×D4712yes—
206C2×D4C22×D4711yescharacteristic
207C22×C4—21no—
208C22×C4—941no—
209C22×C4—942no—
210C22×C4C22×D4712yes—
211SD16—944no—
212SD16—944no—
213SD16—1882no—
214D8—474no—
215D8—944no—
216M16—944no—
217C2×C8—471no—
218C2×C8—471no—
219C2×C8—472no—
220C4⋊C4—471no—
221C4⋊C4—942no—
222C4⋊C4—941no—
223C4⋊C4—941no—
224C4⋊C4C22⋊D4711yescharacteristic
225C4⋊C4C22×D4711yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—22no—
228C22⋊C4—942no—
229C22⋊C4—941no—
230C22⋊C4C22⋊D4712yes—
231C42C22×D4711yescharacteristic
232C23—21no—
233C23—22no—
234C23—44no—
235C23—44no—
236C23—82no—
237C23—941no—
238C23C2×C22⋊D4712yes—
239Q8—942no—
240Q8—942no—
241D4—22no—
242D4—22no—
243D4—21no—
244D4—22no—
245D4—44no—
246D4—44no—
247D4—42no—
248D4—81no—
249D4—472no—
250D4—941no—
251D4—1884no—
252D4D4×D4712yes—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—42no—
257C2×C4—941no—
258C2×C4—942no—
259C2×C4—1884no—
260C2×C4—1882no—
261C2×C4C2×C22⋊D4711yescharacteristic
262C2×C4C2×C22⋊D4712yes—
263C2×C4C2×C22⋊D4711yescharacteristic
264C2×C4C23×D4711yescharacteristic
265C8—472no—
266C8—942no—
267C8—941no—
268C22—22no—
269C22—22no—
270C22—22no—
271C22—22no—
272C22—41no—
273C22—41no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—88no—
278C22—942no—
279C22—1881no—
280C22—1881no—
281C22C22×C22⋊D4711yescharacteristic
282C4—22no—
283C4—21no—
284C4—41no—
285C4—1882no—
286C4—1881no—
287C4#1309405012yescomplemented
288C4C2×D4×D4711yescharacteristic
289C4#1309406911yescharacteristic
290C2—42no—
291C2—42no—
292C2—82no—
293C2—1882no—
294C2D4×C22⋊D4711yescharacteristic
295C2C2×#1309405011yescharacteristic
296C2#1568993411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingD42×C47C2
socleC22×C47C22×D4
hypercenterD42D47
hypocenterC47#3272
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C2×#13094050C2semidirect
2. #15689778C2semidirect
3. #15689495C2semidirect
4. #15689367C2semidirect
5. #15689328C2semidirect
6. #15689315C2semidirect
7. #15689274C2semidirect
8. #15689266C2semidirect
9. C4×#10625334C2semidirect
10. #15689201C2semidirect
11. D42×C47C2semidirect
12. C2×#10625350C22semidirect
15. C2×#10625335C22semidirect
16. C2×#10625335C22semidirect
18. C2×#10625334C22semidirect
19. C2×#10625329C22semidirect
20. #13094024C22semidirect
22. #13094003C22semidirect
24. C4×D188C22semidirect
26. #13093957C22semidirect
27. C4⋊(C47⋊C8)C22semidirect
28. #13093947C22semidirect
30. #13093945C22semidirect
31. #13093944C22semidirect
32. C22⋊(C47⋊C8)C22semidirect
33. C4×C47⋊C8C22semidirect
73. #10625334D4semidirect
111. D188C2×D4semidirect
118. C47⋊C8C2×D4semidirect
136. C4×C47AGL(1,ℤ/8)semidirect
151. D42D47semidirect
160. C47#3272semidirect
287. C4#13094050semidirect