Finite Group Databasebeta

← #20252737

Subgroups — #20252737

Order 6016.

724 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 724 conjugacy classes of subgroups — too many to draw. Only its 161 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
1#15689921C212yesmaximal, complemented
2#15689669C211yesmaximal, characteristic, complemented
3#15689306C212yesmaximal, complemented
4#15689301C212yesmaximal, complemented
5#15689296C212yesmaximal, complemented
6#15689291C212yesmaximal, complemented
7C2×#13093951C212yesmaximal, complemented
8#15689107C211yesmaximal, characteristic, complemented
9C47×#585C211yesmaximal, characteristic, complemented
10C2×#10625350C2211yescharacteristic, complemented
11#13094055—22no—
12#13094054C2214yescomplemented
13#13094050—22no—
14#13094049C2214yescomplemented
15#13094044—24no—
16C2×#10625329C2212yescomplemented
17#13094022C2211yescharacteristic, complemented
18#13094020C2211yescharacteristic, complemented
19#13094013C2211yescharacteristic, complemented
20#13094011C2211yescharacteristic, complemented
21#13093996—22no—
22C4×C22⋊D47—22no—
23C2×C4×Dic47C2211yescharacteristic, complemented
24#13093951C2214yescomplemented
25#13093951C2214yescomplemented
26#13093943C2212yescomplemented
27#13093941C2212yescomplemented
282−1+4×C47—22no—
292−1+4×C47C2212yes—
30H(5,𝔽2)×C47—22no—
31H(5,𝔽2)×C47—22no—
32H(5,𝔽2)×C47C2212yes—
33C2×#41×C47—24no—
34C2×#41×C47—22no—
35C2×#41×C47C2212yes—
36C2×#41×C47C2211yescharacteristic
37#41×C47—24no—
38#41×C47—28no—
39#41×C47—24no—
40#41×C47—24no—
41#41×C47—24no—
42#41×C47—22no—
43#41×C47—22no—
44#41×C47—24no—
45#41×C47—22no—
46#41×C47—22no—
47#41×C47D414yescomplemented
48#41×C47C2314yes—
49C2×Q8×C47—22no—
50C2×Q8×C47—24no—
51C2×Q8×C47D412yescomplemented
52C2×Q8×C47C2311yescharacteristic
53C2×D4×C47—28no—
54C2×D4×C47—22no—
55C2×D4×C47—24no—
56C2×D4×C47—22no—
57C2×D4×C47—24no—
58C2×D4×C47D412yes—
59C2×D4×C47D412yescomplemented
60C2×D4×C47C2311yescharacteristic
61C22×C4×C47—24no—
62C22×C4×C47—22no—
63C22×C4×C47D412yes—
64C22×C4×C47C2311yescharacteristic
65C2×C22⋊D47—22no—
66C2×C22⋊D47—21no—
67C22×Dic47—21no—
68#10625350—22no—
69#10625350—22no—
70C2×D188C2311yescharacteristic
71C2×C4×D47—21no—
72C2×Dic94C2311yescharacteristic
73C22⋊Dic47—22no—
74#10625337—24no—
75#10625336—24no—
76#10625335—24no—
77#10625334—24no—
78(C2×D47)⋊C4—22no—
79Dic47⋊C4—22no—
80C4×Dic47—21no—
81C4×Dic47C2311yescharacteristic
82C4×Dic47C2311yescharacteristic
83#10625329—22no—
84#10625329C2314yes—
85C2×C47⋊C8—22no—
86C23×C47—24no—
87C23×C47—22no—
88C23×C47C2×D412yes—
89C23×C47C2×D411yescharacteristic
90C22×D47—21no—
91Q8×C47—24no—
92Q8×C47—22no—
93Q8×C47—22no—
94Q8×C47C2×D414yes—
95D4×C47—28no—
96D4×C47—24no—
97D4×C47—24no—
98D4×C47—24no—
99D4×C47—24no—
100D4×C47—22no—
101D4×C47—22no—
102D4×C47C2×D414yes—
103C2×C4×C47—24no—
104C2×C4×C47—28no—
105C2×C4×C47—22no—
106C2×C4×C47—24no—
107C2×C4×C47—22no—
108C2×C4×C47—22no—
109C2×C4×C47—24no—
110C2×C4×C47C2×D412yes—
111C2×C4×C47C2×D411yescharacteristic
112C2×C4×C47C2×D412yes—
113C2×C4×C47C2×D412yes—
114C2×C4×C47C2411yescharacteristic
115C22⋊D47—44no—
116C22⋊D47—42no—
117C2×Dic47—21no—
118C2×Dic47—21no—
119C2×Dic47—21no—
120C2×Dic47—42no—
121D188—22no—
122C4×D47—41no—
123C4×D47—41no—
124Dic94—22no—
125C47⋊C8—24no—
126C22×C47—22no—
127C22×C47—24no—
128C22×C47—41no—
129C22×C47—42no—
130C22×C47—82no—
131C22×C47—84no—
132C22×C47#12012yes—
133C22×C47C22×D411yescharacteristic
134C2×D47—42no—
135C2×D47—41no—
136C4×C47—24no—
137C4×C47—22no—
138C4×C47#12011yescharacteristic
139C4×C47#12011yescharacteristic
140C4×C47C22×D412yes—
141Dic47—22no—
142Dic47—41no—
143Dic47—41no—
144#3018—471nomaximal, Sylow
145C2×C47—21no—
146C2×C47—22no—
147C2×C47—42no—
148C2×C47—44no—
149C2×C47C2×#12011yescharacteristic
150D47—81no—
151#585D4711yescharacteristic, complemented
152#575—472no—
153#532—471no—
154#456—472no—
155#455—472no—
156#454—472no—
157#453—472no—
158C2×#104—472no—
159#413—471no—
160C47#301811yescharacteristic, complemented, Sylow
1612−1+4—22no—
1622−1+4C2×D4712yes—
163H(5,𝔽2)—22no—
164H(5,𝔽2)—22no—
165H(5,𝔽2)C2×D4712yes—
166C2×#41—24no—
167C2×#41—22no—
168C2×#41—471no—
169C2×#41C2×D4712yes—
170C2×#41C2×D4711yescharacteristic
171#137—474no—
172#137—942no—
173AGL(1,ℤ/8)—474no—
174AGL(1,ℤ/8)—942no—
175#135—944no—
176C2×M16—472no—
177C4⋊Q8—471no—
178#127—471no—
179#124—471no—
180#124—471no—
181#121—942no—
182C4×D4—942no—
183C2×C42—471no—
184#104—474no—
185#104—474no—
186#101—472no—
187#100—472no—
188#41—24no—
189#41—28no—
190#41—24no—
191#41—24no—
192#41—24no—
193#41—22no—
194#41—22no—
195#41—24no—
196#41—22no—
197#41—22no—
198#41—942no—
199#41—942no—
200#41C22⋊D4714yescomplemented
201#41C22×D4714yes—
202C2×Q8—22no—
203C2×Q8—24no—
204C2×Q8—471no—
205C2×Q8C22⋊D4712yescomplemented
206C2×Q8C22×D4711yescharacteristic
207C2×D4—28no—
208C2×D4—22no—
209C2×D4—24no—
210C2×D4—22no—
211C2×D4—24no—
212C2×D4—471no—
213C2×D4—942no—
214C2×D4—941no—
215C2×D4C22⋊D4712yes—
216C2×D4C22⋊D4712yescomplemented
217C2×D4C22×D4711yescharacteristic
218C22×C4—24no—
219C22×C4—22no—
220C22×C4—941no—
221C22×C4—941no—
222C22×C4C22⋊D4712yes—
223C22×C4C22×D4711yescharacteristic
224Q16—944no—
225SD16—944no—
226SD16—944no—
227D8—944no—
228M16—474no—
229M16—942no—
230C2×C8—942no—
231C4⋊C4—942no—
232C22⋊C4—942no—
233C22⋊C4—942no—
234C42—471no—
235C42—471no—
236C42—941no—
237C23—24no—
238C23—22no—
239C23—941no—
240C23C2×C22⋊D4712yes—
241C23C2×C22⋊D4711yescharacteristic
242Q8—24no—
243Q8—22no—
244Q8—22no—
245Q8—942no—
246Q8C2×C22⋊D4714yes—
247D4—28no—
248D4—24no—
249D4—24no—
250D4—24no—
251D4—24no—
252D4—22no—
253D4—22no—
254D4—942no—
255D4—1884no—
256D4—1882no—
257D4C2×C22⋊D4714yes—
258C2×C4—24no—
259C2×C4—28no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—24no—
263C2×C4—22no—
264C2×C4—24no—
265C2×C4—941no—
266C2×C4—941no—
267C2×C4—941no—
268C2×C4—1882no—
269C2×C4—1881no—
270C2×C4—1881no—
271C2×C4C2×C22⋊D4712yes—
272C2×C4C2×C22⋊D4711yescharacteristic
273C2×C4C2×C22⋊D4712yes—
274C2×C4C2×C22⋊D4712yes—
275C2×C4C23×D4711yescharacteristic
276C8—944no—
277C22—22no—
278C22—24no—
279C22—41no—
280C22—42no—
281C22—82no—
282C22—84no—
283C22—1882no—
284C22—1881no—
285C22#1309399312yes—
286C22C22×C22⋊D4711yescharacteristic
287C4—24no—
288C4—22no—
289C4—942no—
290C4—1881no—
291C4—1881no—
292C4#1309399311yescharacteristic
293C4#1309399311yescharacteristic
294C4C22×C22⋊D4712yes—
295C2—21no—
296C2—22no—
297C2—42no—
298C2—44no—
299C2—3761no—
300C2C2×#1309399311yescharacteristic
subgroupG/H
centerC4#13093993
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#585C2
socleC2×C47C2×#120
hypercenter#585D47
hypocenterC47#3018
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ #585

Complements

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

NH ≅ G/Ntype
1. #15689921C2semidirect
2. #15689669C2semidirect
3. #15689306C2semidirect
4. #15689301C2semidirect
5. #15689296C2semidirect
6. #15689291C2semidirect
7. C2×#13093951C2semidirect
8. #15689107C2semidirect
9. C47×#585C2semidirect
10. C2×#10625350C22semidirect
12. #13094054C22semidirect
14. #13094049C22semidirect
16. C2×#10625329C22semidirect
17. #13094022C22semidirect
18. #13094020C22semidirect
19. #13094013C22semidirect
20. #13094011C22semidirect
23. C2×C4×Dic47C22semidirect
24. #13093951C22semidirect
25. #13093951C22semidirect
26. #13093943C22semidirect
27. #13093941C22semidirect
47. #41×C47D4semidirect
51. C2×Q8×C47D4semidirect
59. C2×D4×C47D4semidirect
151. #585D47semidirect
160. C47#3018semidirect
200. #41C22⋊D47semidirect
205. C2×Q8C22⋊D47semidirect
216. C2×D4C22⋊D47semidirect