Finite Group Databasebeta

← #564×D47 #20257530

Subgroups — #564×D47 #20257530

Order 6016.

896 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47⋊#564C2115yesmaximal, complemented
2#125×D47C2115yesmaximal
3C47×#564C211yesmaximal, characteristic, complemented
4#13094016C22115yes—
5#13094015C22130yes—
6#13094014C22160yes—
7C4⋊C4×D47C22130yes—
8C42×D47C2215yes—
9#125×C47C22115yes—
10C2×C4×D47C23115yes—
11C4⋊C4×C47C23130yes—
12C42×C47C2315yes—
13C4⋊Dic47C23130yes—
14Dic47⋊C4C23160yes—
15C4×Dic47C23115yes—
16C22×D47C2411yescharacteristic
17C2×C4×C47C24115yes—
18C2×Dic47C24115yes—
19C4×D47—230no—
20C22×C47C2511yescharacteristic
21C2×D472−1+416yes—
22C4×C47—215no—
23Dic47—215no—
24C2×#564—471nomaximal, Sylow
25C2×C47C2×2−1+413yes—
26D47#56414yesdirect product factor
27#564—4715no—
28#564D4711yescharacteristic, direct product factor
29C2×#125—4715no—
30C47C2×#56411yescharacteristic, complemented, Sylow
31#125—4760no—
32#125—4730no—
33#125—4715no—
34#125C2×D47115yes—
35C2×C4⋊C4—4730no—
36C2×C42—475no—
37C22×C4—4715no—
38C4⋊C4—4760no—
39C4⋊C4—4730no—
40C4⋊C4C22×D47130yes—
41C42—4715no—
42C42C22×D4715yes—
43C23—471no—
44C2×C4—4715no—
45C2×C4—9430no—
46C2×C4C23×D47115yes—
47C22—476no—
48C22C24×D4711yescharacteristic
49C4—215no—
50C4—9415no—
51C2—474no—
52C22−1+4×D4713yes—
subgroupG/H
center, FrattiniC22C24×D47
commutator, socleC22×C47C25
FittingC47×#564C2
hypercenter#564D47
hypocenterC47C2×#564
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #564

Complements

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

NH ≅ G/Ntype
1. C47⋊#564C2semidirect
3. C47×#564C2semidirect
26. D47#564direct (N × H)
28. #564D47direct (N × H)
30. C47C2×#564semidirect