Finite Group Databasebeta

← D13×(C43⋊C3)⋊C7 #37553548

Subgroups — D13×(C43⋊C3)⋊C7 #37553548

Order 23478.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×(C43⋊C3)⋊C7C211yesmaximal, characteristic, complemented, Hall
2D13×C43⋊C7C311yesmaximal, characteristic, complemented, Hall
3C13×C43⋊C7C2×C311yescharacteristic, complemented, Hall
4D13×C43⋊C3C711yesmaximal, characteristic, complemented, Hall
5C2×(C43⋊C3)⋊C7—131nomaximal, Hall
6C13×C43⋊C3C2×C711yescharacteristic, complemented, Hall
7D13×C43C3×C711yescharacteristic, complemented, Hall
8(C43⋊C3)⋊C7D1311yescharacteristic, direct product factor, Hall
9C2×C43⋊C7—131noHall
10C13×C43C2×C3×C711yescharacteristic, complemented, Hall
11C3×C7×D13—431nomaximal, Hall
12C43⋊C7C3×D1311yescharacteristic, complemented, Hall
13C3×C7×C13—431noHall
14C2×C43⋊C3—131noHall
15C7×D13—431noHall
16C43⋊C3C7×D1311yescharacteristic, complemented, Hall
17C7×C13—431noHall
18C2×C43—131noHall
19C3×D13—3011noHall
20C43C3×C7×D1311yescharacteristic, complemented, Sylow
21C2×C3×C7—5591noHall
22C3×C13—3011noHall
23D13(C43⋊C3)⋊C711yescharacteristic, direct product factor, Hall
24C3×C7—431noHall
25C2×C7—5591noHall
26C13C2×(C43⋊C3)⋊C711yescharacteristic, complemented, Sylow
27C7—431noSylow
28C2×C3—39131noHall
29C3—3011noSylow
30C2—131noSylow
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC13×C43C2×C3×C7
LCSG ▷ C13×C43
UCSC1

Complements

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

NH ≅ G/Ntype
1. C13×(C43⋊C3)⋊C7C2semidirect
2. D13×C43⋊C7C3semidirect
3. C13×C43⋊C7C2×C3semidirect
4. D13×C43⋊C3C7semidirect
6. C13×C43⋊C3C2×C7semidirect
7. D13×C43C3×C7semidirect
8. (C43⋊C3)⋊C7D13direct (N × H)
10. C13×C43C2×C3×C7semidirect
12. C43⋊C7C3×D13semidirect
16. C43⋊C3C7×D13semidirect
20. C43C3×C7×D13semidirect
23. D13(C43⋊C3)⋊C7direct (N × H)
26. C13C2×(C43⋊C3)⋊C7semidirect

Maximal subgroups

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

subgroupindex
C13×(C43⋊C3)⋊C72
D13×C43⋊C73
D13×C43⋊C37
C2×(C43⋊C3)⋊C713
C3×C7×D1343