Finite Group Databasebeta

← C7×C11×D193 #44446152

Subgroups — C7×C11×D193 #44446152

Order 29722.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×C11×C193C211yesmaximal, characteristic, complemented, Hall
2C11×D193C711yesmaximal, characteristic, direct product factor, Hall
3C7×D193C1111yesmaximal, characteristic, direct product factor, Hall
4C11×C193C2×C711yescharacteristic, complemented, Hall
5C7×C193C2×C1111yescharacteristic, complemented, Hall
6D193C7×C1111yescharacteristic, direct product factor, Hall
7C193C2×C7×C1111yescharacteristic, complemented, Sylow
8C2×C7×C11—1931nomaximal, Hall
9C7×C11D19311yescharacteristic, direct product factor, Hall
10C2×C11—1931noHall
11C2×C7—1931noHall
12C11C7×D19311yescharacteristic, direct product factor, Sylow
13C7C11×D19311yescharacteristic, direct product factor, Sylow
14C2—1931noSylow
subgroupG/H
center, hypercenterC7×C11D193
commutator, cosocle, hypocenterC193C2×C7×C11
FrattiniC1G
Fitting, socleC7×C11×C193C2
LCSG ▷ C193
UCSC1 ◁ C7×C11

Complements

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

NH ≅ G/Ntype
1. C7×C11×C193C2semidirect
2. C11×D193C7direct (N × H)
3. C7×D193C11direct (N × H)
4. C11×C193C2×C7semidirect
5. C7×C193C2×C11semidirect
6. D193C7×C11direct (N × H)
7. C193C2×C7×C11semidirect
9. C7×C11D193direct (N × H)
12. C11C7×D193direct (N × H)
13. C7C11×D193direct (N × H)

Maximal subgroups

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

subgroupindex
C7×C11×C1932
C11×D1937
C7×D19311
C2×C7×C11193