Finite Group Databasebeta

← AGL(1,𝔽11)×C97⋊C3 #44544985

Subgroups — AGL(1,𝔽11)×C97⋊C3 #44544985

Order 32010.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11⋊C5×C97⋊C3C211yesmaximal, characteristic, complemented, Hall
2C97×AGL(1,𝔽11)C311yesmaximal, characteristic, complemented, Hall
3D11×C97⋊C3C511yesmaximal, characteristic, complemented, Hall
4C11⋊C5×C97C2×C311yescharacteristic, complemented, Hall
5C11×C97⋊C3C2×C511yescharacteristic, complemented, Hall
6C2×C5×C97⋊C3—111nomaximal, Hall
7D11×C97C3×C511yescharacteristic, complemented, Hall
8C5×C97⋊C3—111noHall
9C11×C97C2×C3×C511yescharacteristic, complemented, Hall
10C2×C5×C97—111noHall
11C2×C97⋊C3—111noHall
12C5×C97—111noHall
13C3×AGL(1,𝔽11)—971nomaximal, Hall
14C97⋊C3AGL(1,𝔽11)11yescharacteristic, direct product factor, Hall
15C2×C97—111noHall
16C3×C11⋊C5—971noHall
17AGL(1,𝔽11)C97⋊C311yescharacteristic, direct product factor, Hall
18C97C3×AGL(1,𝔽11)11yescharacteristic, complemented, Sylow
19C3×D11—971noHall
20C11⋊C5C2×C97⋊C311yescharacteristic, complemented, Hall
21C3×C11—971noHall
22C2×C3×C5—10671noHall
23D11C5×C97⋊C311yescharacteristic, complemented, Hall
24C3×C5—10671noHall
25C11C2×C5×C97⋊C311yescharacteristic, complemented, Sylow
26C2×C5—111noHall
27C2×C3—10671noHall
28C5—111noSylow
29C3—971noSylow
30C2—111noSylow
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC11×C97C2×C3×C5
LCSG ▷ C11×C97
UCSC1

Complements

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

NH ≅ G/Ntype
1. C11⋊C5×C97⋊C3C2semidirect
2. C97×AGL(1,𝔽11)C3semidirect
3. D11×C97⋊C3C5semidirect
4. C11⋊C5×C97C2×C3semidirect
5. C11×C97⋊C3C2×C5semidirect
7. D11×C97C3×C5semidirect
9. C11×C97C2×C3×C5semidirect
14. C97⋊C3AGL(1,𝔽11)direct (N × H)
17. AGL(1,𝔽11)C97⋊C3direct (N × H)
18. C97C3×AGL(1,𝔽11)semidirect
20. C11⋊C5C2×C97⋊C3semidirect
23. D11C5×C97⋊C3semidirect
25. C11C2×C5×C97⋊C3semidirect

Maximal subgroups

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

subgroupindex
C11⋊C5×C97⋊C32
C97×AGL(1,𝔽11)3
D11×C97⋊C35
C2×C5×C97⋊C311
C3×AGL(1,𝔽11)97