Finite Group Databasebeta

← #20252966

Subgroups — #20252966

Order 6016.

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

normal subgroups only

This group has 520 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×#13094044C211yesmaximal, characteristic, complemented
2C23×C47⋊C8C211yesmaximal, characteristic, complemented
3#15689634C211yesmaximal, characteristic, complemented
4#15689362C212yesmaximal, complemented
5#15689357C212yesmaximal, complemented
6#15689354C212yesmaximal, complemented
7#15689350C212yesmaximal, complemented
8#15689159C211yesmaximal, characteristic, complemented
9#15689119C211yesmaximal, characteristic, complemented
10#15689117C211yesmaximal, characteristic, complemented
11C47×#525C211yesmaximal, characteristic, complemented
12C2×#10625350C2211yescharacteristic
13#13094044—24no—
14C2×#10625337C2211yescharacteristic, complemented
15C2×#10625335C2211yescharacteristic, complemented
16C2×#10625336C2211yescharacteristic, complemented
17C2×#10625334C2211yescharacteristic, complemented
18C22×C47⋊C8—24no—
19C22×C47⋊C8C2212yes—
20C22×C47⋊C8C2212yes—
21C22×C47⋊C8C2211yescharacteristic
22C22×C47⋊C8C2211yescharacteristic
23#13094007—21no—
24#13094003C2212yes—
25#13093998C2212yes—
26#13093993—21no—
27C4×C22⋊D47—22no—
28#13093983C2211yescharacteristic
29#13093957C2212yescomplemented
30#13093955C2212yescomplemented
31#13093948C2212yescomplemented
32#13093947C2212yescomplemented
33#13093945C2212yescomplemented
34#13093944C2212yescomplemented
35C2×#41×C47C2211yescharacteristic
36C23×C4×C47C2211yescharacteristic
37#123×C47—21no—
38C22⋊Q8×C47C2212yes—
39#121×C47C2212yes—
40#120×C47—21no—
41C4×D4×C47—22no—
42#117×C47C2211yescharacteristic
43C24×C47D411yescharacteristic
44#41×C47—22no—
45#41×C47—22no—
46C2×Q8×C47C2311yescharacteristic
47C2×D4×C47—22no—
48C2×D4×C47—21no—
49C2×D4×C47C2311yescharacteristic
50C22×C4×C47—22no—
51C22×C4×C47—22no—
52C22×C4×C47—21no—
53C22×C4×C47D412yes—
54C22×C4×C47D411yescharacteristic
55C22×C4×C47C2312yes—
56C22×C4×C47C2311yescharacteristic
57C2×C22⋊D47—22no—
58C2×C22⋊D47—21no—
59#10625350—22no—
60#10625350—22no—
61C2×D188C2311yescharacteristic
62C2×C4×D47—21no—
63C2×Dic94C2311yescharacteristic
64C4⋊C4×C47—22no—
65C4⋊C4×C47C2312yes—
66C22⋊C4×C47—21no—
67C22⋊C4×C47—22no—
68C22⋊C4×C47—22no—
69C42×C47—21no—
70C22⋊Dic47—21no—
71C22⋊Dic47—22no—
72#10625337—22no—
73#10625336—22no—
74#10625335—22no—
75#10625334—22no—
76(C2×D47)⋊C4—22no—
77C4⋊Dic47C2312yes—
78Dic47⋊C4—22no—
79C4×Dic47—21no—
80C2×C47⋊C8—22no—
81C2×C47⋊C8—24no—
82C2×C47⋊C8—24no—
83C2×C47⋊C8D414yescomplemented
84C2×C47⋊C8C2312yes—
85C2×C47⋊C8C2311yescharacteristic
86C2×C47⋊C8C2311yescharacteristic
87C23×C47—22no—
88C23×C47—24no—
89C23×C47—21no—
90C23×C47C2×D411yescharacteristic
91C23×C47C2×D412yes—
92C22×D47—21no—
93Q8×C47—21no—
94Q8×C47—21no—
95D4×C47—21no—
96D4×C47—21no—
97D4×C47—42no—
98D4×C47—44no—
99C2×C4×C47—22no—
100C2×C4×C47—24no—
101C2×C4×C47—22no—
102C2×C4×C47—22no—
103C2×C4×C47—22no—
104C2×C4×C47—21no—
105C2×C4×C47—42no—
106C2×C4×C47C2×D412yes—
107C2×C4×C47C2×D412yes—
108C2×C4×C47C2×D411yescharacteristic
109C2×C4×C47#4112yes—
110C2×C4×C47C2411yescharacteristic
111C22⋊D47—42no—
112C22⋊D47—44no—
113C2×Dic47—22no—
114C2×Dic47—21no—
115D188—21no—
116D188—21no—
117C4×D47—42no—
118Dic94—21no—
119Dic94—21no—
120C47⋊C8—22no—
121C47⋊C8C2×D412yes—
122C47⋊C8C2×D412yes—
123C22×C47—28no—
124C22×C47—22no—
125C22×C47—22no—
126C22×C47—22no—
127C22×C47—41no—
128C22×C47—42no—
129C22×C47#12112yes—
130C22×C47#13514yescomplemented
131C22×C47C22×D411yescharacteristic
132C2×D47—41no—
133C2×D47—42no—
134C4×C47—22no—
135C4×C47—41no—
136C4×C47—42no—
137C4×C47#12112yes—
138C4×C47C22×D411yescharacteristic
139C4×C47C2×#4111yescharacteristic
140Dic47—41no—
141Dic47—42no—
142#3050—471nomaximal, Sylow
143C2×C47—22no—
144C2×C47—24no—
145C2×C47—81no—
146C2×C47C2×#12111yescharacteristic
147C2×C47C2×#13512yes—
148D47—81no—
149C2×#135—471no—
150C23×C8—471no—
151#525—471no—
152#525D4711yescharacteristic, complemented
153#467—472no—
154#466—472no—
155#465—472no—
156#465—472no—
157#427—471no—
158#416—471no—
159#416—471no—
160C47#305011yescharacteristic, complemented, Sylow
161C2×#41—471no—
162C2×#41C2×D4711yescharacteristic
163C23×C4C2×D4711yescharacteristic
164#135—944no—
165C2×Q16—471no—
166C2×SD16—471no—
167C2×SD16—471no—
168C2×D8—471no—
169C22×C8—471no—
170C22×C8—471no—
171C22×C8—472no—
172C22×C8—472no—
173C22×C8—944no—
174#123—21no—
175#123—941no—
176C22⋊Q8—472no—
177C22⋊Q8C2×D4712yes—
178#121—472no—
179#121C2×D4712yes—
180#120—21no—
181#120—941no—
182C4×D4—22no—
183C4×D4—942no—
184#117—471no—
185#117C2×D4711yescharacteristic
186#107—472no—
187#106—472no—
188#103—472no—
189#103—472no—
190#102—472no—
191#102—472no—
192C24C22⋊D4711yescharacteristic
193#41—22no—
194#41—22no—
195#41—942no—
196#41—942no—
197C2×Q8—471no—
198C2×Q8C22×D4711yescharacteristic
199C2×D4—22no—
200C2×D4—21no—
201C2×D4—471no—
202C2×D4—942no—
203C2×D4—941no—
204C2×D4C22×D4711yescharacteristic
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—21no—
208C22×C4—941no—
209C22×C4C22⋊D4711yescharacteristic
210C22×C4C22⋊D4712yes—
211C22×C4C22×D4712yes—
212C22×C4C22×D4711yescharacteristic
213Q16—942no—
214SD16—942no—
215SD16—942no—
216D8—942no—
217C2×C8—474no—
218C2×C8—471no—
219C2×C8—471no—
220C2×C8—472no—
221C2×C8—944no—
222C2×C8—944no—
223C2×C8—942no—
224C4⋊C4—22no—
225C4⋊C4—472no—
226C4⋊C4—942no—
227C4⋊C4C22×D4712yes—
228C22⋊C4—21no—
229C22⋊C4—22no—
230C22⋊C4—22no—
231C22⋊C4—941no—
232C22⋊C4—942no—
233C22⋊C4—942no—
234C42—21no—
235C42—941no—
236C23—22no—
237C23—24no—
238C23—21no—
239C23—941no—
240C23C2×C22⋊D4711yescharacteristic
241C23C2×C22⋊D4712yes—
242Q8—21no—
243Q8—21no—
244Q8—941no—
245Q8—941no—
246D4—21no—
247D4—21no—
248D4—42no—
249D4—44no—
250D4—941no—
251D4—941no—
252D4—1882no—
253D4—1884no—
254C2×C4—22no—
255C2×C4—24no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—42no—
261C2×C4—942no—
262C2×C4—941no—
263C2×C4—1882no—
264C2×C4D4×D4712yes—
265C2×C4#1062535212yes—
266C2×C4C2×C22⋊D4712yes—
267C2×C4C2×C22⋊D4711yescharacteristic
268C2×C4C23×D4711yescharacteristic
269C8—472no—
270C8—472no—
271C8—942no—
272C22—28no—
273C22—22no—
274C22—22no—
275C22—22no—
276C22—41no—
277C22—42no—
278C22—1881no—
279C22—1882no—
280C22#1309399612yes—
281C22#1309404414yescomplemented
282C22C22×C22⋊D4711yescharacteristic
283C4—22no—
284C4—41no—
285C4—42no—
286C4—1881no—
287C4—1882no—
288C4#1309399612yes—
289C4C2×D4×D4711yescharacteristic
290C4C2×#1062535211yescharacteristic
291C2—22no—
292C2—24no—
293C2—81no—
294C2—3761no—
295C2C2×#1309399611yescharacteristic
296C2C2×#1309404412yes—
subgroupG/H
centerC2×C4C2×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#525C2
socleC22×C47C22×D4
hypercenter#525D47
hypocenterC47#3050
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C2×#13094044C2semidirect
2. C23×C47⋊C8C2semidirect
3. #15689634C2semidirect
4. #15689362C2semidirect
5. #15689357C2semidirect
6. #15689354C2semidirect
7. #15689350C2semidirect
8. #15689159C2semidirect
9. #15689119C2semidirect
10. #15689117C2semidirect
11. C47×#525C2semidirect
14. C2×#10625337C22semidirect
15. C2×#10625335C22semidirect
16. C2×#10625336C22semidirect
17. C2×#10625334C22semidirect
29. #13093957C22semidirect
30. #13093955C22semidirect
31. #13093948C22semidirect
32. #13093947C22semidirect
33. #13093945C22semidirect
34. #13093944C22semidirect
83. C2×C47⋊C8D4semidirect
130. C22×C47#135semidirect
152. #525D47semidirect
160. C47#3050semidirect
281. C22#13094044semidirect