Finite Group Databasebeta

← #564×D43 #19148737

Subgroups — #564×D43 #19148737

Order 5504.

896 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43⋊#564C2115yesmaximal, complemented
2#125×D43C2115yesmaximal
3C43×#564C211yesmaximal, characteristic, complemented
4#13063317C22115yes—
5#13063316C22130yes—
6#13063315C22160yes—
7C4⋊C4×D43C22130yes—
8C42×D43C2215yes—
9#125×C43C22115yes—
10C2×C4×D43C23115yes—
11C4⋊C4×C43C23130yes—
12C42×C43C2315yes—
13C4⋊Dic43C23130yes—
14Dic43⋊C4C23160yes—
15C4×Dic43C23115yes—
16C22×D43C2411yescharacteristic
17C2×C4×C43C24115yes—
18C2×Dic43C24115yes—
19C4×D43—230no—
20C22×C43C2511yescharacteristic
21C2×D432−1+416yes—
22C4×C43—215no—
23Dic43—215no—
24C2×#564—431nomaximal, Sylow
25C2×C43C2×2−1+413yes—
26D43#56414yesdirect product factor
27#564—4315no—
28#564D4311yescharacteristic, direct product factor
29C2×#125—4315no—
30C43C2×#56411yescharacteristic, complemented, Sylow
31#125—4360no—
32#125—4330no—
33#125—4315no—
34#125C2×D43115yes—
35C2×C4⋊C4—4330no—
36C2×C42—435no—
37C22×C4—4315no—
38C4⋊C4—4360no—
39C4⋊C4—4330no—
40C4⋊C4C22×D43130yes—
41C42—4315no—
42C42C22×D4315yes—
43C23—431no—
44C2×C4—4315no—
45C2×C4—8630no—
46C2×C4C23×D43115yes—
47C22—436no—
48C22C24×D4311yescharacteristic
49C4—215no—
50C4—8615no—
51C2—434no—
52C22−1+4×D4313yes—
subgroupG/H
center, FrattiniC22C24×D43
commutator, socleC22×C43C25
FittingC43×#564C2
hypercenter#564D43
hypocenterC43C2×#564
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #564

Complements

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

NH ≅ G/Ntype
1. C43⋊#564C2semidirect
3. C43×#564C2semidirect
26. D43#564direct (N × H)
28. #564D43direct (N × H)
30. C43C2×#564semidirect