Finite Group Databasebeta

← C3×#21462835 #37552876

Subgroups — C3×#21462835 #37552876

Order 23430.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#16840848C211yesmaximal, characteristic, complemented, Hall
2#21462835C311yesmaximal, characteristic, direct product factor, Hall
3C3×C11×D71C511yesmaximal, characteristic, complemented, Hall
4#16840848C2×C311yescharacteristic, complemented, Hall
5C3×C11×C71C2×C511yescharacteristic, complemented, Hall
6C3×D71⋊C5—111nomaximal, Hall
7C11×D71C3×C511yescharacteristic, complemented, Hall
8C3×C71⋊C5—111noHall
9C11×C71C2×C3×C511yescharacteristic, complemented, Hall
10D71⋊C5—111noHall
11C3×D71C11⋊C511yescharacteristic, complemented, Hall
12C71⋊C5—111noHall
13C2×C3×C11⋊C5—711nomaximal, Hall
14C3×C71C2×C11⋊C511yescharacteristic, complemented, Hall
15C3×C11⋊C5—711noHall
16D71C3×C11⋊C511yescharacteristic, complemented, Hall
17C2×C11⋊C5—711noHall
18C71C2×C3×C11⋊C511yescharacteristic, complemented, Sylow
19C2×C3×C11—3551noHall
20C11⋊C5—711noHall
21C3×C11D71⋊C511yescharacteristic, complemented, Hall
22C2×C3×C5—7811noHall
23C2×C11—3551noHall
24C3×C5—7811noHall
25C11C3×D71⋊C511yescharacteristic, complemented, Sylow
26C2×C5—7811noHall
27C2×C3—3551noHall
28C5—7811noSylow
29C3#2146283511yescharacteristic, direct product factor, Sylow
30C2—3551noSylow
subgroupG/H
center, hypercenterC3#21462835
commutator, cosocle, hypocenterC11×C71C2×C3×C5
FrattiniC1G
Fitting, socleC3×C11×C71C2×C5
LCSG ▷ C11×C71
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×#16840848C2semidirect
2. #21462835C3direct (N × H)
3. C3×C11×D71C5semidirect
4. #16840848C2×C3semidirect
5. C3×C11×C71C2×C5semidirect
7. C11×D71C3×C5semidirect
9. C11×C71C2×C3×C5semidirect
11. C3×D71C11⋊C5semidirect
14. C3×C71C2×C11⋊C5semidirect
16. D71C3×C11⋊C5semidirect
18. C71C2×C3×C11⋊C5semidirect
21. C3×C11D71⋊C5semidirect
25. C11C3×D71⋊C5semidirect
29. C3#21462835direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#168408482
#214628353
C3×C11×D715
C3×D71⋊C511
C2×C3×C11⋊C571