Finite Group Databasebeta

← C2×C17×#10620252 #36348980

Subgroups — C2×C17×#10620252 #36348980

Order 22134.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#10620252C211yesmaximal, characteristic, direct product factor, Hall
2C2×C7×C17×C31C311yesmaximal, characteristic, complemented, Hall
3C7×C17×C31C2×C311yescharacteristic, complemented, Hall
4C2×C17×C31⋊C3—71nomaximal, Hall
5C17×C31⋊C3—71noHall
6C2×#10620252C1711yesmaximal, characteristic, direct product factor, Hall
7C2×C17×C31ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
8C2×C17×ΓL(1,𝔽8)—311nomaximal, Hall
9#10620252C2×C1711yescharacteristic, direct product factor, Hall
10C17×C31C2×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
11C2×C7×C31C3×C1711yescharacteristic, complemented, Hall
12C17×ΓL(1,𝔽8)—311noHall
13C2×C7×C17C31⋊C311yescharacteristic, complemented, Hall
14C7×C31C2×C3×C1711yescharacteristic, complemented, Hall
15C2×C31⋊C3—71noHall
16C7×C17C2×C31⋊C311yescharacteristic, complemented, Hall
17C2×C3×C17—2171noHall
18C31⋊C3—71noHall
19C2×C31C17×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
20C3×C17—2171noHall
21C2×ΓL(1,𝔽8)—311noHall
22C2×C17#1062025211yescharacteristic, direct product factor, Hall
23C31C2×C17×ΓL(1,𝔽8)11yescharacteristic, complemented, Sylow
24ΓL(1,𝔽8)—311noHall
25C17C2×#1062025211yescharacteristic, direct product factor, Sylow
26C2×C7C17×C31⋊C311yescharacteristic, complemented, Hall
27C7C2×C17×C31⋊C311yescharacteristic, complemented, Sylow
28C2×C3—2171noHall
29C3—2171noSylow
30C2C17×#1062025211yescharacteristic, direct product factor, Sylow
subgroupG/H
center, hypercenterC2×C17#10620252
commutator, cosocle, hypocenterC7×C31C2×C3×C17
FrattiniC1G
Fitting, socleC2×C7×C17×C31C3
LCSG ▷ C7×C31
UCSC1 ◁ C2×C17

Complements

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

NH ≅ G/Ntype
1. C17×#10620252C2direct (N × H)
2. C2×C7×C17×C31C3semidirect
3. C7×C17×C31C2×C3semidirect
6. C2×#10620252C17direct (N × H)
7. C2×C17×C31ΓL(1,𝔽8)semidirect
9. #10620252C2×C17direct (N × H)
10. C17×C31C2×ΓL(1,𝔽8)semidirect
11. C2×C7×C31C3×C17semidirect
13. C2×C7×C17C31⋊C3semidirect
14. C7×C31C2×C3×C17semidirect
16. C7×C17C2×C31⋊C3semidirect
19. C2×C31C17×ΓL(1,𝔽8)semidirect
22. C2×C17#10620252direct (N × H)
23. C31C2×C17×ΓL(1,𝔽8)semidirect
25. C17C2×#10620252direct (N × H)
26. C2×C7C17×C31⋊C3semidirect
27. C7C2×C17×C31⋊C3semidirect
30. C2C17×#10620252direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#106202522
C2×C7×C17×C313
C2×C17×C31⋊C37
C2×#1062025217
C2×C17×ΓL(1,𝔽8)31