Finite Group Databasebeta

← C2×C3×#16840849 #37552856

Subgroups — C2×C3×#16840849 #37552856

Order 23430.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#16840849C211yesmaximal, characteristic, direct product factor, Hall
2C2×#16840849C311yesmaximal, characteristic, direct product factor, Hall
3C2×C3×C11×C71C511yesmaximal, characteristic, complemented, Hall
4#16840849C2×C311yescharacteristic, direct product factor, Hall
5C3×C11×C71C2×C511yescharacteristic, complemented, Hall
6C2×C3×C71⋊C5—111nomaximal, Hall
7C2×C11×C71C3×C511yescharacteristic, complemented, Hall
8C3×C71⋊C5—111noHall
9C11×C71C2×C3×C511yescharacteristic, complemented, Hall
10C2×C71⋊C5—111noHall
11C2×C3×C71C11⋊C511yescharacteristic, complemented, Hall
12C71⋊C5—111noHall
13C2×C3×C11⋊C5—711nomaximal, Hall
14C3×C71C2×C11⋊C511yescharacteristic, complemented, Hall
15C3×C11⋊C5—711noHall
16C2×C71C3×C11⋊C511yescharacteristic, complemented, Hall
17C2×C11⋊C5—711noHall
18C71C2×C3×C11⋊C511yescharacteristic, complemented, Sylow
19C2×C3×C11C71⋊C511yescharacteristic, complemented, Hall
20C11⋊C5—711noHall
21C3×C11C2×C71⋊C511yescharacteristic, complemented, Hall
22C2×C3×C5—7811noHall
23C2×C11C3×C71⋊C511yescharacteristic, complemented, Hall
24C3×C5—7811noHall
25C11C2×C3×C71⋊C511yescharacteristic, complemented, Sylow
26C2×C5—7811noHall
27C2×C3#1684084911yescharacteristic, direct product factor, Hall
28C5—7811noSylow
29C3C2×#1684084911yescharacteristic, direct product factor, Sylow
30C2C3×#1684084911yescharacteristic, direct product factor, Sylow
subgroupG/H
center, hypercenterC2×C3#16840849
commutator, cosocle, hypocenterC11×C71C2×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C11×C71C5
LCSG ▷ C11×C71
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C3×#16840849C2direct (N × H)
2. C2×#16840849C3direct (N × H)
3. C2×C3×C11×C71C5semidirect
4. #16840849C2×C3direct (N × H)
5. C3×C11×C71C2×C5semidirect
7. C2×C11×C71C3×C5semidirect
9. C11×C71C2×C3×C5semidirect
11. C2×C3×C71C11⋊C5semidirect
14. C3×C71C2×C11⋊C5semidirect
16. C2×C71C3×C11⋊C5semidirect
18. C71C2×C3×C11⋊C5semidirect
19. C2×C3×C11C71⋊C5semidirect
21. C3×C11C2×C71⋊C5semidirect
23. C2×C11C3×C71⋊C5semidirect
25. C11C2×C3×C71⋊C5semidirect
27. C2×C3#16840849direct (N × H)
29. C3C2×#16840849direct (N × H)
30. C2C3×#16840849direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#168408492
C2×#168408493
C2×C3×C11×C715
C2×C3×C71⋊C511
C2×C3×C11⋊C571