Finite Group Databasebeta

← C2×C11×C211⋊C7 #44570646

Subgroups — C2×C11×C211⋊C7 #44570646

Order 32494.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×C211⋊C7C211yesmaximal, characteristic, direct product factor, Hall
2C2×C11×C211C711yesmaximal, characteristic, complemented, Hall
3C2×C211⋊C7C1111yesmaximal, characteristic, direct product factor, Hall
4C11×C211C2×C711yescharacteristic, complemented, Hall
5C211⋊C7C2×C1111yescharacteristic, direct product factor, Hall
6C2×C211C7×C1111yescharacteristic, complemented, Hall
7C211C2×C7×C1111yescharacteristic, complemented, Sylow
8C2×C7×C11—2111nomaximal, Hall
9C7×C11—2111noHall
10C2×C11C211⋊C711yescharacteristic, direct product factor, Hall
11C2×C7—2111noHall
12C11C2×C211⋊C711yescharacteristic, direct product factor, Sylow
13C7—2111noSylow
14C2C11×C211⋊C711yescharacteristic, direct product factor, Sylow
subgroupG/H
center, hypercenterC2×C11C211⋊C7
commutator, cosocle, hypocenterC211C2×C7×C11
FrattiniC1G
Fitting, socleC2×C11×C211C7
LCSG ▷ C211
UCSC1 ◁ C2×C11

Complements

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

NH ≅ G/Ntype
1. C11×C211⋊C7C2direct (N × H)
2. C2×C11×C211C7semidirect
3. C2×C211⋊C7C11direct (N × H)
4. C11×C211C2×C7semidirect
5. C211⋊C7C2×C11direct (N × H)
6. C2×C211C7×C11semidirect
7. C211C2×C7×C11semidirect
10. C2×C11C211⋊C7direct (N × H)
12. C11C2×C211⋊C7direct (N × H)
14. C2C11×C211⋊C7direct (N × H)

Maximal subgroups

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

subgroupindex
C11×C211⋊C72
C2×C11×C2117
C2×C211⋊C711
C2×C7×C11211