Finite Group Databasebeta

← C3×(C11⋊C5)⋊D97 #44544972

Subgroups — C3×(C11⋊C5)⋊D97 #44544972

Order 32010.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C11⋊C5×C97C211yesmaximal, characteristic, complemented, Hall
2(C11⋊C5)⋊D97C311yesmaximal, characteristic, direct product factor, Hall
3C3×D1067C511yesmaximal, characteristic, complemented, Hall
4C11⋊C5×C97C2×C311yescharacteristic, complemented, Hall
5C3×C11×C97C2×C511yescharacteristic, complemented, Hall
6C3×C5×D97—111nomaximal, Hall
7D1067C3×C511yescharacteristic, complemented, Hall
8C3×C5×C97—111noHall
9C11×C97C2×C3×C511yescharacteristic, complemented, Hall
10C5×D97—111noHall
11C3×D97—111noHall
12C5×C97—111noHall
13C3×AGL(1,𝔽11)—971nomaximal, Hall
14C3×C97AGL(1,𝔽11)11yescharacteristic, complemented, Hall
15D97—111noHall
16C3×C11⋊C5D9711yescharacteristic, complemented, Hall
17AGL(1,𝔽11)—971noHall
18C97C3×AGL(1,𝔽11)11yescharacteristic, complemented, Sylow
19C3×D11—971noHall
20C11⋊C5C3×D9711yescharacteristic, complemented, Hall
21C3×C11C5×D9711yescharacteristic, complemented, Hall
22C2×C3×C5—10671noHall
23D11—971noHall
24C3×C5—111noHall
25C11C3×C5×D9711yescharacteristic, complemented, Sylow
26C2×C5—10671noHall
27C2×C3—10671noHall
28C5—111noSylow
29C3(C11⋊C5)⋊D9711yescharacteristic, direct product factor, Sylow
30C2—10671noSylow
subgroupG/H
center, hypercenterC3(C11⋊C5)⋊D97
commutator, cosocle, hypocenterC11×C97C2×C3×C5
FrattiniC1G
Fitting, socleC3×C11×C97C2×C5
LCSG ▷ C11×C97
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×C11⋊C5×C97C2semidirect
2. (C11⋊C5)⋊D97C3direct (N × H)
3. C3×D1067C5semidirect
4. C11⋊C5×C97C2×C3semidirect
5. C3×C11×C97C2×C5semidirect
7. D1067C3×C5semidirect
9. C11×C97C2×C3×C5semidirect
14. C3×C97AGL(1,𝔽11)semidirect
16. C3×C11⋊C5D97semidirect
18. C97C3×AGL(1,𝔽11)semidirect
20. C11⋊C5C3×D97semidirect
21. C3×C11C5×D97semidirect
25. C11C3×C5×D97semidirect
29. C3(C11⋊C5)⋊D97direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C11⋊C5×C972
(C11⋊C5)⋊D973
C3×D10675
C3×C5×D9711
C3×AGL(1,𝔽11)97