Finite Group Databasebeta

← C11×C5⋊(C5⋊(C7⋊D7)) #41004012

Subgroups — C11×C5⋊(C5⋊(C7⋊D7)) #41004012

Order 26950.

320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C52×C72×C11C211yesmaximal, characteristic, complemented, Hall
2C11×C5⋊(C7⋊D7)—56nomaximal
3C11×C5⋊D35—78nomaximal
4C5×C72×C11D516yescomplemented
5C5⋊(C5⋊(C7⋊D7))C1111yesmaximal, characteristic, direct product factor, Hall
6C52×C7×C11D718yescomplemented
7C52×C72C2×C1111yescharacteristic, complemented, Hall
8C11×C7⋊D7—251noHall
9C11×D35—3548no—
10C11×C5⋊D5—491noHall
11C72×C11C5⋊D511yescharacteristic, complemented, Hall
12C5⋊(C7⋊D7)—56no—
13C5×C7×C11D35148yescomplemented
14C5⋊D35—78no—
15C52×C11C7⋊D711yescharacteristic, complemented, Hall
16C5×C72D5×C1116yescomplemented
17C52×C7C11×D718yescomplemented
18C11×D7—1758no—
19D5×C11—2456no—
20C7⋊D7—251noHall
21C7×C11C5⋊D3518yescomplemented
22D35—3548no—
23C5×C11C5⋊(C7⋊D7)16yescomplemented
24C5⋊D5—491noHall
25C72C11×C5⋊D511yescharacteristic, complemented, Sylow
26C5×C7C11×D35148yescomplemented
27C52C11×C7⋊D711yescharacteristic, complemented, Sylow
28C2×C11—12251noHall
29D7—1758no—
30C11C5⋊(C5⋊(C7⋊D7))11yescharacteristic, direct product factor, Sylow
31D5—2456no—
32C7C11×C5⋊D3518yescomplemented
33C5C11×C5⋊(C7⋊D7)16yescomplemented
34C2—12251noSylow
subgroupG/H
center, hypercenterC11C5⋊(C5⋊(C7⋊D7))
commutator, cosocle, hypocenterC52×C72C2×C11
FrattiniC1G
Fitting, socleC52×C72×C11C2
LCSG ▷ C52×C72
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C52×C72×C11C2semidirect
4. C5×C72×C11D5semidirect
5. C5⋊(C5⋊(C7⋊D7))C11direct (N × H)
6. C52×C7×C11D7semidirect
7. C52×C72C2×C11semidirect
11. C72×C11C5⋊D5semidirect
13. C5×C7×C11D35semidirect
15. C52×C11C7⋊D7semidirect
16. C5×C72D5×C11semidirect
17. C52×C7C11×D7semidirect
21. C7×C11C5⋊D35semidirect
23. C5×C11C5⋊(C7⋊D7)semidirect
25. C72C11×C5⋊D5semidirect
26. C5×C7C11×D35semidirect
27. C52C11×C7⋊D7semidirect
30. C11C5⋊(C5⋊(C7⋊D7))direct (N × H)
32. C7C11×C5⋊D35semidirect
33. C5C11×C5⋊(C7⋊D7)semidirect

Maximal subgroups

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

subgroupindex
C52×C72×C112
C11×C5⋊(C7⋊D7)5
C11×C5⋊D357
C5⋊(C5⋊(C7⋊D7))11