Finite Group Databasebeta

← C7×C11×C97⋊C3 #36375708

Subgroups — C7×C11×C97⋊C3 #36375708

Order 22407.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×C11×C97C311yesmaximal, characteristic, complemented, Hall
2C11×C97⋊C3C711yesmaximal, characteristic, direct product factor, Hall
3C7×C97⋊C3C1111yesmaximal, characteristic, direct product factor, Hall
4C11×C97C3×C711yescharacteristic, complemented, Hall
5C7×C97C3×C1111yescharacteristic, complemented, Hall
6C97⋊C3C7×C1111yescharacteristic, direct product factor, Hall
7C3×C7×C11—971nomaximal, Hall
8C97C3×C7×C1111yescharacteristic, complemented, Sylow
9C7×C11C97⋊C311yescharacteristic, direct product factor, Hall
10C3×C11—971noHall
11C3×C7—971noHall
12C11C7×C97⋊C311yescharacteristic, direct product factor, Sylow
13C7C11×C97⋊C311yescharacteristic, direct product factor, Sylow
14C3—971noSylow
subgroupG/H
center, hypercenterC7×C11C97⋊C3
commutator, cosocle, hypocenterC97C3×C7×C11
FrattiniC1G
Fitting, socleC7×C11×C97C3
LCSG ▷ C97
UCSC1 ◁ C7×C11

Complements

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

NH ≅ G/Ntype
1. C7×C11×C97C3semidirect
2. C11×C97⋊C3C7direct (N × H)
3. C7×C97⋊C3C11direct (N × H)
4. C11×C97C3×C7semidirect
5. C7×C97C3×C11semidirect
6. C97⋊C3C7×C11direct (N × H)
8. C97C3×C7×C11semidirect
9. C7×C11C97⋊C3direct (N × H)
12. C11C7×C97⋊C3direct (N × H)
13. C7C11×C97⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C7×C11×C973
C11×C97⋊C37
C7×C97⋊C311
C3×C7×C1197