Finite Group Databasebeta

← D7×(C67⋊C3)⋊C11 #44526284

Subgroups — D7×(C67⋊C3)⋊C11 #44526284

Order 30954.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×(C67⋊C3)⋊C11C211yesmaximal, characteristic, complemented, Hall
2D7×C67⋊C11C311yesmaximal, characteristic, complemented, Hall
3C7×C67⋊C11C2×C311yescharacteristic, complemented, Hall
4C2×(C67⋊C3)⋊C11—71nomaximal, Hall
5D7×C67⋊C3C1111yesmaximal, characteristic, complemented, Hall
6(C67⋊C3)⋊C11D711yescharacteristic, direct product factor, Hall
7C2×C67⋊C11—71noHall
8C7×C67⋊C3C2×C1111yescharacteristic, complemented, Hall
9D7×C67C3×C1111yescharacteristic, complemented, Hall
10C67⋊C11C3×D711yescharacteristic, complemented, Hall
11C7×C67C2×C3×C1111yescharacteristic, complemented, Hall
12C3×C11×D7—671nomaximal, Hall
13C2×C67⋊C3—71noHall
14C3×C7×C11—671noHall
15C67⋊C3C11×D711yescharacteristic, complemented, Hall
16C11×D7—671noHall
17C2×C67—71noHall
18C7×C11—671noHall
19C67C3×C11×D711yescharacteristic, complemented, Sylow
20C2×C3×C11—4691noHall
21C3×D7—671noHall
22C3×C11—671noHall
23C2×C11—4691noHall
24C3×C7—671noHall
25D7(C67⋊C3)⋊C1111yescharacteristic, direct product factor, Hall
26C11—671noSylow
27C7C2×(C67⋊C3)⋊C1111yescharacteristic, complemented, Sylow
28C2×C3—4691noHall
29C3—671noSylow
30C2—71noSylow
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C67C2×C3×C11
LCSG ▷ C7×C67
UCSC1

Complements

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

NH ≅ G/Ntype
1. C7×(C67⋊C3)⋊C11C2semidirect
2. D7×C67⋊C11C3semidirect
3. C7×C67⋊C11C2×C3semidirect
5. D7×C67⋊C3C11semidirect
6. (C67⋊C3)⋊C11D7direct (N × H)
8. C7×C67⋊C3C2×C11semidirect
9. D7×C67C3×C11semidirect
10. C67⋊C11C3×D7semidirect
11. C7×C67C2×C3×C11semidirect
15. C67⋊C3C11×D7semidirect
19. C67C3×C11×D7semidirect
25. D7(C67⋊C3)⋊C11direct (N × H)
27. C7C2×(C67⋊C3)⋊C11semidirect

Maximal subgroups

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

subgroupindex
C7×(C67⋊C3)⋊C112
D7×C67⋊C113
C2×(C67⋊C3)⋊C117
D7×C67⋊C311
C3×C11×D767