Finite Group Databasebeta

← #20252672

Subgroups — #20252672

Order 6016.

732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 732 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13094071C211yesmaximal, characteristic, complemented
2C2×#13094050C211yesmaximal, characteristic, complemented
3C22×#10625335C211yesmaximal, characteristic, complemented
4#15689266C214yesmaximal, complemented
5#15689261C214yesmaximal, complemented
6#15689131C211yesmaximal, characteristic, complemented
7#15689117C211yesmaximal, characteristic, complemented
8#15689090C211yesmaximal, characteristic, complemented
9C47×#535C211yesmaximal, characteristic, complemented
10#13094071—24no—
11#13094071—24no—
12C2×#10625350C2211yescharacteristic
13C2×#10625350C2212yescomplemented
14C2×#10625352—21no—
15C2×#10625352—22no—
16C22×Dic94C2211yescharacteristic
17C22×Dic94C2212yescomplemented
18C2×Q8×D47—21no—
19#13094050—24no—
20C2×#10625335—24no—
21C2×#10625335C2212yes—
22C2×#10625335C2214yes—
23C2×#10625334C2212yes—
24C2×#10625329C2211yescharacteristic
25C22×C47⋊C8C2211yescharacteristic
26#13093947C2212yescomplemented
27#13093947C2214yescomplemented
28#13093944C2212yescomplemented
29C22⋊(C47⋊C8)C2214yescomplemented
30C2×#41×C47C2211yescharacteristic
31C22×D4×C47C2211yescharacteristic
32#127×C47—21no—
33#124×C47—21no—
34#121×C47C2214yes—
35#120×C47—22no—
36#117×C47C2211yescharacteristic
37C24×C47—21no—
38#41×C47—22no—
39#41×C47—22no—
40C2×Q8×C47D411yescharacteristic
41C2×D4×C47—24no—
42C2×D4×C47—22no—
43C2×D4×C47—22no—
44C2×D4×C47—21no—
45C2×D4×C47D412yes—
46C2×D4×C47D411yescharacteristic
47C2×D4×C47C2312yes—
48C22×C4×C47C2312yes—
49C22×C4×C47C2311yescharacteristic
50C2×C22⋊D47—21no—
51C2×C22⋊D47—22no—
52C22×Dic47—21no—
53C22×Dic47—22no—
54Q8×D47—28no—
55#10625352—216no—
56#10625352—28no—
57#10625350—22no—
58#10625350—24no—
59#10625350—24no—
60#10625350D414yescomplemented
61C2×D188C2311yescharacteristic
62C2×C4×D47—21no—
63C2×C4×D47—22no—
64C2×Dic94—21no—
65C2×Dic94—22no—
66C2×Dic94—22no—
67C2×Dic94—24no—
68C2×Dic94—24no—
69C2×Dic94D414yescomplemented
70C2×Dic94C2312yes—
71C2×Dic94C2311yescharacteristic
72C4⋊C4×C47C2312yes—
73C22⋊C4×C47—21no—
74C22⋊C4×C47—24no—
75C42×C47—21no—
76#10625335—28no—
77#10625335—24no—
78#10625334—24no—
79#10625329—22no—
80C2×C47⋊C8—22no—
81C2×C47⋊C8C2312yes—
82C2×C47⋊C8C2312yes—
83C23×C47—22no—
84C23×C47—42no—
85C23×C47—82no—
86C23×C47C2×D412yes—
87C23×C47C2×D411yescharacteristic
88C22×D47—21no—
89Q8×C47—22no—
90D4×C47—24no—
91D4×C47—22no—
92D4×C47—22no—
93D4×C47—22no—
94D4×C47—42no—
95D4×C47—84no—
96C2×C4×C47—22no—
97C2×C4×C47—22no—
98C2×C4×C47—22no—
99C2×C4×C47C2×D412yes—
100C2×C4×C47C2×D412yes—
101C2×C4×C47C2×D412yes—
102C2×C4×C47C2×D411yescharacteristic
103C2×C4×C47C2411yescharacteristic
104C22⋊D47—28no—
105C22⋊D47—24no—
106C2×Dic47—28no—
107C2×Dic47—24no—
108C2×Dic47—22no—
109C2×Dic47—21no—
110D188—21no—
111D188C2×D412yes—
112C4×D47—28no—
113C4×D47—24no—
114Dic94—28no—
115Dic94—24no—
116Dic94—22no—
117Dic94—21no—
118Dic94C2×D412yes—
119Dic94C2×D414yes—
120C47⋊C8—22no—
121C47⋊C8—22no—
122C22×C47—22no—
123C22×C47—22no—
124C22×C47—24no—
125C22×C47—42no—
126C22×C47—44no—
127C22×C47—84no—
128C22×C47#12012yes—
129C22×C47C22×D411yescharacteristic
130C2×D47—22no—
131C2×D47—42no—
132C4×C47—22no—
133C4×C47—42no—
134C4×C47#12012yes—
135C4×C47C22×D411yescharacteristic
136C4×C47C22×D411yescharacteristic
137Dic47—22no—
138Dic47—24no—
139#3010—471nomaximal, Sylow
140C2×C47—22no—
141C2×C47—42no—
142C2×C47—82no—
143C2×C47C2×#12011yescharacteristic
144C2×C47#57712yes—
145D47—42no—
146C2×2−1+4—471no—
147C2×AGL(1,ℤ/8)—471no—
148C22×SD16—471no—
149#535D4711yescharacteristic, complemented
150#449—474no—
151#448—474no—
152#419—471no—
153#416—471no—
154#408—471no—
155C47#301011yescharacteristic, complemented, Sylow
1562−1+4—944no—
1572−1+4—944no—
158C2×#41—471no—
159C2×#41—472no—
160C2×#41—942no—
161C2×#41—941no—
162C2×#41C2×D4711yescharacteristic
163C22×Q8—471no—
164C22×Q8—472no—
165C22×Q8—941no—
166C22×D4C2×D4711yescharacteristic
167AGL(1,ℤ/8)—944no—
168C2×SD16—474no—
169C2×SD16—472no—
170C2×SD16—944no—
171C2×D8—472no—
172C2×M16—471no—
173C22×C8—471no—
174#127—21no—
175#124—21no—
176#121C2×D4714yes—
177#120—22no—
178#117C2×D4711yescharacteristic
179#103—472no—
180#103—474no—
181#102—472no—
182C22⋊C8—474no—
183C24—21no—
184#41—22no—
185#41—22no—
186#41—474no—
187#41—944no—
188#41—944no—
189#41—9416no—
190#41—948no—
191#41—942no—
192C2×Q8—474no—
193C2×Q8—472no—
194C2×Q8—471no—
195C2×Q8—944no—
196C2×Q8—944no—
197C2×Q8—948no—
198C2×Q8—942no—
199C2×Q8—942no—
200C2×Q8—941no—
201C2×Q8C22⋊D4711yescharacteristic
202C2×D4—24no—
203C2×D4—22no—
204C2×D4—22no—
205C2×D4—21no—
206C2×D4—471no—
207C2×D4—942no—
208C2×D4—941no—
209C2×D4C22⋊D4712yes—
210C2×D4C22⋊D4711yescharacteristic
211C2×D4C22×D4712yes—
212C22×C4—942no—
213C22×C4—941no—
214C22×C4—942no—
215C22×C4—941no—
216C22×C4C22×D4712yes—
217C22×C4C22×D4711yescharacteristic
218SD16—948no—
219SD16—944no—
220D8—944no—
221M16—942no—
222C2×C8—472no—
223C2×C8—472no—
224C2×C8—942no—
225C4⋊C4C22×D4712yes—
226C22⋊C4—21no—
227C22⋊C4—24no—
228C42—21no—
229C23—22no—
230C23—42no—
231C23—82no—
232C23—941no—
233C23C2×C22⋊D4712yes—
234C23C2×C22⋊D4711yescharacteristic
235Q8—22no—
236Q8—474no—
237Q8—472no—
238Q8—948no—
239Q8—944no—
240Q8—942no—
241Q8—941no—
242D4—24no—
243D4—22no—
244D4—22no—
245D4—22no—
246D4—42no—
247D4—84no—
248D4—472no—
249D4—948no—
250D4—944no—
251D4—941no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—948no—
256C2×C4—948no—
257C2×C4—944no—
258C2×C4—942no—
259C2×C4—941no—
260C2×C4—944no—
261C2×C4D4×D4712yes—
262C2×C4D4×D4712yes—
263C2×C4C2×C22⋊D4712yes—
264C2×C4C2×C22⋊D4711yescharacteristic
265C2×C4C23×D4711yescharacteristic
266C8—942no—
267C8—942no—
268C22—22no—
269C22—22no—
270C22—24no—
271C22—42no—
272C22—44no—
273C22—84no—
274C22—942no—
275C22—1882no—
276C22#1309399212yes—
277C22C22×C22⋊D4711yescharacteristic
278C4—22no—
279C4—42no—
280C4—944no—
281C4—942no—
282C4#1309399212yes—
283C4C2×D4×D4711yescharacteristic
284C4C2×D4×D4711yescharacteristic
285C2—22no—
286C2—42no—
287C2—82no—
288C2—1882no—
289C2C2×#1309399211yescharacteristic
290C2#1568993412yes—
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#535C2
socleC22×C47C22×D4
hypercenter#535D47
hypocenterC47#3010
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#13094071C2semidirect
2. C2×#13094050C2semidirect
3. C22×#10625335C2semidirect
4. #15689266C2semidirect
5. #15689261C2semidirect
6. #15689131C2semidirect
7. #15689117C2semidirect
8. #15689090C2semidirect
9. C47×#535C2semidirect
13. C2×#10625350C22semidirect
17. C22×Dic94C22semidirect
26. #13093947C22semidirect
27. #13093947C22semidirect
28. #13093944C22semidirect
29. C22⋊(C47⋊C8)C22semidirect
60. #10625350D4semidirect
69. C2×Dic94D4semidirect
149. #535D47semidirect
155. C47#3010semidirect