Finite Group Databasebeta

← C17×#10587717 #22604652

Subgroups — C17×#10587717 #22604652

Order 9282.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#63271C211yesmaximal, characteristic, complemented, Hall
2C7×C17×D13C311yesmaximal, characteristic, complemented, Hall
3C7×C13×C17C2×C311yescharacteristic, complemented, Hall
4C17×D13⋊C3—71nomaximal, Hall
5C2×C17×ΓL(1,𝔽8)—131nomaximal, Hall
6C17×C13⋊C3—71noHall
7#10587717C1711yesmaximal, characteristic, direct product factor, Hall
8C17×D13ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
9C17×ΓL(1,𝔽8)—131noHall
10#63271C2×C1711yescharacteristic, complemented, Hall
11C2×C7×C17—131noHall
12C13×C17C2×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
13C7×D13C3×C1711yescharacteristic, complemented, Hall
14C7×C17D13⋊C311yescharacteristic, complemented, Hall
15C2×C3×C17—911noHall
16C7×C13C2×C3×C1711yescharacteristic, complemented, Hall
17D13⋊C3—71noHall
18C3×C17—911noHall
19C2×ΓL(1,𝔽8)—131noHall
20C13⋊C3—71noHall
21C2×C17—131noHall
22D13C17×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
23ΓL(1,𝔽8)—131noHall
24C17#1058771711yescharacteristic, direct product factor, Sylow
25C2×C7—131noHall
26C13C2×C17×ΓL(1,𝔽8)11yescharacteristic, complemented, Sylow
27C7C17×D13⋊C311yescharacteristic, complemented, Sylow
28C2×C3—911noHall
29C3—911noSylow
30C2—131noSylow
subgroupG/H
center, hypercenterC17#10587717
commutator, hypocenterC7×C13C2×C3×C17
FrattiniC1G
Fitting, socleC7×C13×C17C2×C3
LCSG ▷ C7×C13
UCSC1 ◁ C17

Complements

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

NH ≅ G/Ntype
1. C17×#63271C2semidirect
2. C7×C17×D13C3semidirect
3. C7×C13×C17C2×C3semidirect
7. #10587717C17direct (N × H)
8. C17×D13ΓL(1,𝔽8)semidirect
10. #63271C2×C17semidirect
12. C13×C17C2×ΓL(1,𝔽8)semidirect
13. C7×D13C3×C17semidirect
14. C7×C17D13⋊C3semidirect
16. C7×C13C2×C3×C17semidirect
22. D13C17×ΓL(1,𝔽8)semidirect
24. C17#10587717direct (N × H)
26. C13C2×C17×ΓL(1,𝔽8)semidirect
27. C7C17×D13⋊C3semidirect