Finite Group Databasebeta

← C2×C17×(C43⋊C3)⋊C7 #44502014

Subgroups — C2×C17×(C43⋊C3)⋊C7 #44502014

Order 30702.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×(C43⋊C3)⋊C7C211yesmaximal, characteristic, direct product factor, Hall
2C2×C17×C43⋊C7C311yesmaximal, characteristic, complemented, Hall
3C17×C43⋊C7C2×C311yescharacteristic, complemented, Hall
4C2×C17×C43⋊C3C711yesmaximal, characteristic, complemented, Hall
5C17×C43⋊C3C2×C711yescharacteristic, complemented, Hall
6C2×(C43⋊C3)⋊C7C1711yesmaximal, characteristic, direct product factor, Hall
7C2×C17×C43C3×C711yescharacteristic, complemented, Hall
8(C43⋊C3)⋊C7C2×C1711yescharacteristic, direct product factor, Hall
9C17×C43C2×C3×C711yescharacteristic, complemented, Hall
10C2×C3×C7×C17—431nomaximal, Hall
11C2×C43⋊C7C3×C1711yescharacteristic, complemented, Hall
12C3×C7×C17—431noHall
13C43⋊C7C2×C3×C1711yescharacteristic, complemented, Hall
14C2×C43⋊C3C7×C1711yescharacteristic, complemented, Hall
15C2×C7×C17—431noHall
16C43⋊C3C2×C7×C1711yescharacteristic, complemented, Hall
17C7×C17—431noHall
18C2×C3×C17—431noHall
19C2×C43C3×C7×C1711yescharacteristic, complemented, Hall
20C3×C17—431noHall
21C43C2×C3×C7×C1711yescharacteristic, complemented, Sylow
22C2×C3×C7—431noHall
23C2×C17(C43⋊C3)⋊C711yescharacteristic, direct product factor, Hall
24C3×C7—431noHall
25C17C2×(C43⋊C3)⋊C711yescharacteristic, direct product factor, Sylow
26C2×C7—431noHall
27C7—431noSylow
28C2×C3—431noHall
29C3—431noSylow
30C2C17×(C43⋊C3)⋊C711yescharacteristic, direct product factor, Sylow
subgroupG/H
center, hypercenterC2×C17(C43⋊C3)⋊C7
commutator, cosocle, hypocenterC43C2×C3×C7×C17
FrattiniC1G
Fitting, socleC2×C17×C43C3×C7
LCSG ▷ C43
UCSC1 ◁ C2×C17

Complements

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

NH ≅ G/Ntype
1. C17×(C43⋊C3)⋊C7C2direct (N × H)
2. C2×C17×C43⋊C7C3semidirect
3. C17×C43⋊C7C2×C3semidirect
4. C2×C17×C43⋊C3C7semidirect
5. C17×C43⋊C3C2×C7semidirect
6. C2×(C43⋊C3)⋊C7C17direct (N × H)
7. C2×C17×C43C3×C7semidirect
8. (C43⋊C3)⋊C7C2×C17direct (N × H)
9. C17×C43C2×C3×C7semidirect
11. C2×C43⋊C7C3×C17semidirect
13. C43⋊C7C2×C3×C17semidirect
14. C2×C43⋊C3C7×C17semidirect
16. C43⋊C3C2×C7×C17semidirect
19. C2×C43C3×C7×C17semidirect
21. C43C2×C3×C7×C17semidirect
23. C2×C17(C43⋊C3)⋊C7direct (N × H)
25. C17C2×(C43⋊C3)⋊C7direct (N × H)
30. C2C17×(C43⋊C3)⋊C7direct (N × H)

Maximal subgroups

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

subgroupindex
C17×(C43⋊C3)⋊C72
C2×C17×C43⋊C73
C2×C17×C43⋊C37
C2×(C43⋊C3)⋊C717
C2×C3×C7×C1743