Finite Group Databasebeta

← C2×C11×ΓL(1,𝔽8)×C53 #37587486

Subgroups — C2×C11×ΓL(1,𝔽8)×C53 #37587486

Order 24486.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×ΓL(1,𝔽8)×C53C211yesmaximal, characteristic, direct product factor, Hall
2C2×C7×C11×C53C311yesmaximal, characteristic, complemented, Hall
3C7×C11×C53C2×C311yescharacteristic, complemented, Hall
4C2×C3×C11×C53—71nomaximal, Hall
5C2×ΓL(1,𝔽8)×C53C1111yesmaximal, characteristic, direct product factor, Hall
6C3×C11×C53—71noHall
7C2×C11×C53ΓL(1,𝔽8)11yescharacteristic, direct product factor, Hall
8ΓL(1,𝔽8)×C53C2×C1111yescharacteristic, direct product factor, Hall
9C2×C7×C53C3×C1111yescharacteristic, complemented, Hall
10C11×C53C2×ΓL(1,𝔽8)11yescharacteristic, direct product factor, Hall
11C2×C11×ΓL(1,𝔽8)C5311yesmaximal, characteristic, direct product factor, Hall
12C7×C53C2×C3×C1111yescharacteristic, complemented, Hall
13C2×C3×C53—71noHall
14C11×ΓL(1,𝔽8)C2×C5311yescharacteristic, direct product factor, Hall
15C3×C53—71noHall
16C2×C7×C11C3×C5311yescharacteristic, complemented, Hall
17C2×C53C11×ΓL(1,𝔽8)11yescharacteristic, direct product factor, Hall
18C7×C11C2×C3×C5311yescharacteristic, complemented, Hall
19C2×C3×C11—71noHall
20C53C2×C11×ΓL(1,𝔽8)11yescharacteristic, direct product factor, Sylow
21C2×ΓL(1,𝔽8)C11×C5311yescharacteristic, direct product factor, Hall
22C3×C11—71noHall
23C2×C11ΓL(1,𝔽8)×C5311yescharacteristic, direct product factor, Hall
24ΓL(1,𝔽8)C2×C11×C5311yescharacteristic, direct product factor, Hall
25C2×C7C3×C11×C5311yescharacteristic, complemented, Hall
26C11C2×ΓL(1,𝔽8)×C5311yescharacteristic, direct product factor, Sylow
27C7C2×C3×C11×C5311yescharacteristic, complemented, Sylow
28C2×C3—71noHall
29C3—71noSylow
30C2C11×ΓL(1,𝔽8)×C5311yescharacteristic, direct product factor, Sylow
subgroupG/H
center, hypercenterC2×C11×C53ΓL(1,𝔽8)
commutator, cosocle, hypocenterC7C2×C3×C11×C53
FrattiniC1G
Fitting, socleC2×C7×C11×C53C3
LCSG ▷ C7
UCSC1 ◁ C2×C11×C53

Complements

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

NH ≅ G/Ntype
1. C11×ΓL(1,𝔽8)×C53C2direct (N × H)
2. C2×C7×C11×C53C3semidirect
3. C7×C11×C53C2×C3semidirect
5. C2×ΓL(1,𝔽8)×C53C11direct (N × H)
7. C2×C11×C53ΓL(1,𝔽8)direct (N × H)
8. ΓL(1,𝔽8)×C53C2×C11direct (N × H)
9. C2×C7×C53C3×C11semidirect
10. C11×C53C2×ΓL(1,𝔽8)direct (N × H)
11. C2×C11×ΓL(1,𝔽8)C53direct (N × H)
12. C7×C53C2×C3×C11semidirect
14. C11×ΓL(1,𝔽8)C2×C53direct (N × H)
16. C2×C7×C11C3×C53semidirect
17. C2×C53C11×ΓL(1,𝔽8)direct (N × H)
18. C7×C11C2×C3×C53semidirect
20. C53C2×C11×ΓL(1,𝔽8)direct (N × H)
21. C2×ΓL(1,𝔽8)C11×C53direct (N × H)
23. C2×C11ΓL(1,𝔽8)×C53direct (N × H)
24. ΓL(1,𝔽8)C2×C11×C53direct (N × H)
25. C2×C7C3×C11×C53semidirect
26. C11C2×ΓL(1,𝔽8)×C53direct (N × H)
27. C7C2×C3×C11×C53semidirect
30. C2C11×ΓL(1,𝔽8)×C53direct (N × H)

Maximal subgroups

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

subgroupindex
C11×ΓL(1,𝔽8)×C532
C2×C7×C11×C533
C2×C3×C11×C537
C2×ΓL(1,𝔽8)×C5311
C2×C11×ΓL(1,𝔽8)53