Finite Group Databasebeta

← AGL(1,𝔽11)×C49⋊C3 #30633489

Subgroups — AGL(1,𝔽11)×C49⋊C3 #30633489

Order 16170.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11⋊C5×C49⋊C3C211yesmaximal, characteristic, complemented, Hall
2C49×AGL(1,𝔽11)C311yesmaximal, characteristic, complemented, Hall
3D11×C49⋊C3C511yesmaximal, characteristic, complemented, Hall
4C49×C11⋊C5C2×C311yescharacteristic, complemented, Hall
5ΓL(1,𝔽8)×AGL(1,𝔽11)—71nomaximal
6C11×C49⋊C3C2×C511yescharacteristic, complemented, Hall
7C2×C5×C49⋊C3—111nomaximal, Hall
8ΓL(1,𝔽8)×C11⋊C5—71no—
9D11×C49C3×C511yescharacteristic, complemented, Hall
10C7×AGL(1,𝔽11)ΓL(1,𝔽8)11yescharacteristic
11C5×C49⋊C3—111noHall
12C11×C49C2×C3×C511yescharacteristic, complemented, Hall
13C2×C5×C49—111noHall
14ΓL(1,𝔽8)×D11—71no—
15C7×C11⋊C5C2×ΓL(1,𝔽8)11yescharacteristic
16C3×AGL(1,𝔽11)—491noHall
17C2×C49⋊C3—551noHall
18C5×C49—111noHall
19C11×ΓL(1,𝔽8)—71no—
20C2×C5×ΓL(1,𝔽8)—771no—
21C3×C11⋊C5—491noHall
22C7×D11C5×ΓL(1,𝔽8)11yescharacteristic
23C49⋊C3AGL(1,𝔽11)11yescharacteristic, direct product factor, Hall
24AGL(1,𝔽11)C49⋊C311yescharacteristic, direct product factor, Hall
25C5×ΓL(1,𝔽8)—771no—
26C2×C49—551noHall
27C7×C11C2×C5×ΓL(1,𝔽8)11yescharacteristic
28C2×C5×C7—111no—
29C3×D11—491noHall
30C11⋊C5C2×C49⋊C311yescharacteristic, complemented, Hall
31C49C3×AGL(1,𝔽11)11yescharacteristic, complemented, Sylow
32C2×ΓL(1,𝔽8)—3851no—
33C5×C7—111no—
34C3×C11—491noHall
35C2×C3×C5—5391noHall
36D11C5×C49⋊C311yescharacteristic, complemented, Hall
37ΓL(1,𝔽8)—71no—
38C3×C5—5391noHall
39C2×C7—551no—
40C11C2×C5×C49⋊C311yescharacteristic, complemented, Sylow
41C2×C5—111noHall
42C7ΓL(1,𝔽8)×AGL(1,𝔽11)11yescharacteristic
43C2×C3—5391noHall
44C5—111noSylow
45C3—491noSylow
46C2—111noSylow
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC11×C49C2×C3×C5
FrattiniC7ΓL(1,𝔽8)×AGL(1,𝔽11)
socleC7×C11C2×C5×ΓL(1,𝔽8)
LCSG ▷ C11×C49
UCSC1

Complements

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

NH ≅ G/Ntype
1. C11⋊C5×C49⋊C3C2semidirect
2. C49×AGL(1,𝔽11)C3semidirect
3. D11×C49⋊C3C5semidirect
4. C49×C11⋊C5C2×C3semidirect
6. C11×C49⋊C3C2×C5semidirect
9. D11×C49C3×C5semidirect
12. C11×C49C2×C3×C5semidirect
23. C49⋊C3AGL(1,𝔽11)direct (N × H)
24. AGL(1,𝔽11)C49⋊C3direct (N × H)
30. C11⋊C5C2×C49⋊C3semidirect
31. C49C3×AGL(1,𝔽11)semidirect
36. D11C5×C49⋊C3semidirect
40. C11C2×C5×C49⋊C3semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C11⋊C5×C49⋊C32
C49×AGL(1,𝔽11)3
D11×C49⋊C35
ΓL(1,𝔽8)×AGL(1,𝔽11)7
C2×C5×C49⋊C311