Finite Group Databasebeta

← C49×Dic11⋊C5 #24924689

Subgroups — C49×Dic11⋊C5 #24924689

Order 10780.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C49×C11⋊C5C211yesmaximal, characteristic
2C49×C11⋊C5C411yescharacteristic, complemented, Hall
3Dic11×C49C511yesmaximal, characteristic, complemented, Hall
4C7×Dic11⋊C5C711yesmaximal, characteristic
5C2×C11×C49C2×C511yescharacteristic
6C4×C5×C49—111nomaximal, Hall
7C2×C7×C11⋊C5C2×C711yescharacteristic
8C11×C49C4×C511yescharacteristic, complemented, Hall
9C2×C5×C49—111no—
10C7×C11⋊C5C4×C711yescharacteristic
11C7×Dic11C5×C711yescharacteristic
12C5×C49—111noHall
13Dic11⋊C5C4911yescharacteristic, direct product factor, Hall
14C4×C49—111noHall
15C2×C7×C11C2×C5×C711yescharacteristic
16C4×C5×C7—111no—
17C2×C11⋊C5C2×C4911yescharacteristic
18C2×C49AGL(1,𝔽11)11yescharacteristic
19C7×C11C4×C5×C711yescharacteristic
20C2×C5×C7—111no—
21C11⋊C5C4×C4911yescharacteristic, complemented, Hall
22C49Dic11⋊C511yescharacteristic, direct product factor, Sylow
23Dic11C5×C4911yescharacteristic, complemented, Hall
24C5×C7—111no—
25C4×C7—111no—
26C2×C11C2×C5×C4911yescharacteristic
27C4×C5—111noHall
28C2×C7C7×AGL(1,𝔽11)11yescharacteristic
29C11C4×C5×C4911yescharacteristic, complemented, Sylow
30C2×C5—111no—
31C7C7×Dic11⋊C511yescharacteristic
32C5—111noSylow
33C4—111noSylow
34C2C49×AGL(1,𝔽11)11yescharacteristic
subgroupG/H
center, hypercenterC2×C49AGL(1,𝔽11)
commutator, hypocenterC11C4×C5×C49
FrattiniC2×C7C7×AGL(1,𝔽11)
FittingC2×C11×C49C2×C5
socle, cosocleC2×C7×C11C2×C5×C7
prime radicalC2×C7×C11⋊C5C2×C7
LCSG ▷ C11
UCSC1 ◁ C2×C49

Complements

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

NH ≅ G/Ntype
2. C49×C11⋊C5C4semidirect
3. Dic11×C49C5semidirect
8. C11×C49C4×C5semidirect
13. Dic11⋊C5C49direct (N × H)
21. C11⋊C5C4×C49semidirect
22. C49Dic11⋊C5direct (N × H)
23. Dic11C5×C49semidirect
29. C11C4×C5×C49semidirect