Finite Group Databasebeta

← C7×C11⋊C5×D31 #37558828

Subgroups — C7×C11⋊C5×D31 #37558828

Order 23870.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×C31×C11⋊C5C211yesmaximal, characteristic, complemented, Hall
2C7×C11×D31C511yesmaximal, characteristic, complemented, Hall
3C11⋊C5×D31C711yesmaximal, characteristic, direct product factor, Hall
4C7×C11×C31C2×C511yescharacteristic, complemented, Hall
5C5×C7×D31—111nomaximal, Hall
6C31×C11⋊C5C2×C711yescharacteristic, complemented, Hall
7C5×C7×C31—111noHall
8C2×C7×C11⋊C5—311nomaximal, Hall
9C11×D31C5×C711yescharacteristic, complemented, Hall
10C7×D31C11⋊C511yescharacteristic, direct product factor, Hall
11C7×C11⋊C5D3111yescharacteristic, direct product factor, Hall
12C11×C31C2×C5×C711yescharacteristic, complemented, Hall
13C5×D31—111noHall
14C7×C31C2×C11⋊C511yescharacteristic, complemented, Hall
15C5×C31—111noHall
16C2×C7×C11—311noHall
17C2×C11⋊C5—311noHall
18C7×C11C5×D3111yescharacteristic, complemented, Hall
19C2×C5×C7—3411noHall
20D31C7×C11⋊C511yescharacteristic, direct product factor, Hall
21C11⋊C5C7×D3111yescharacteristic, direct product factor, Hall
22C5×C7—111noHall
23C31C2×C7×C11⋊C511yescharacteristic, complemented, Sylow
24C2×C11—311noHall
25C2×C7—311noHall
26C11C5×C7×D3111yescharacteristic, complemented, Sylow
27C2×C5—3411noHall
28C7C11⋊C5×D3111yescharacteristic, direct product factor, Sylow
29C5—111noSylow
30C2—311noSylow
subgroupG/H
center, hypercenterC7C11⋊C5×D31
commutator, cosocle, hypocenterC11×C31C2×C5×C7
FrattiniC1G
Fitting, socleC7×C11×C31C2×C5
LCSG ▷ C11×C31
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C7×C31×C11⋊C5C2semidirect
2. C7×C11×D31C5semidirect
3. C11⋊C5×D31C7direct (N × H)
4. C7×C11×C31C2×C5semidirect
6. C31×C11⋊C5C2×C7semidirect
9. C11×D31C5×C7semidirect
10. C7×D31C11⋊C5direct (N × H)
11. C7×C11⋊C5D31direct (N × H)
12. C11×C31C2×C5×C7semidirect
14. C7×C31C2×C11⋊C5semidirect
18. C7×C11C5×D31semidirect
20. D31C7×C11⋊C5direct (N × H)
21. C11⋊C5C7×D31direct (N × H)
23. C31C2×C7×C11⋊C5semidirect
26. C11C5×C7×D31semidirect
28. C7C11⋊C5×D31direct (N × H)

Maximal subgroups

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

subgroupindex
C7×C31×C11⋊C52
C7×C11×D315
C11⋊C5×D317
C5×C7×D3111
C2×C7×C11⋊C531