Finite Group Databasebeta

← C3×C11×Dic85 #26014331

Subgroups — C3×C11×Dic85 #26014331

Order 11220.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×C11×C17C211yesmaximal, characteristic
2C11×Dic85C311yesmaximal, characteristic, direct product factor, Hall
3C3×C5×C11×C17C411yescharacteristic, complemented, Hall
4C3×C11×Dic17—51nomaximal, Hall
5C2×C5×C11×C17C2×C311yescharacteristic
6C2×C3×C11×C17D511yescharacteristic
7C3×Dic85C1111yesmaximal, characteristic, direct product factor, Hall
8C5×C11×C17C3×C411yescharacteristic, complemented, Hall
9C11×Dic17—51noHall
10C3×C11×Dic5—171nomaximal, Hall
11C3×C11×C17Dic511yescharacteristic, complemented, Hall
12C2×C3×C5×C17C2×C1111yescharacteristic
13C2×C11×C17C3×D511yescharacteristic
14Dic85C3×C1111yescharacteristic, direct product factor, Hall
15C2×C3×C5×C11D1711yescharacteristic
16C3×C5×C17C4×C1111yescharacteristic, complemented, Hall
17C11×Dic5—171noHall
18C3×Dic17—51noHall
19C11×C17C3×Dic511yescharacteristic, complemented, Hall
20C2×C5×C17C2×C3×C1111yescharacteristic
21C3×C5×C11Dic1711yescharacteristic, complemented, Hall
22C3×C4×C11—851noHall
23C2×C5×C11C3×D1711yescharacteristic
24C2×C3×C17D5×C1111yescharacteristic
25C5×C17C3×C4×C1111yescharacteristic, complemented, Hall
26Dic17—51noHall
27C2×C3×C11D8511yescharacteristic
28C3×Dic5—171noHall
29C5×C11C3×Dic1711yescharacteristic, complemented, Hall
30C3×C17C11×Dic511yescharacteristic, complemented, Hall
31C4×C11—851noHall
32C2×C17C3×D5×C1111yescharacteristic
33C3×C11Dic8511yescharacteristic, direct product factor, Hall
34C2×C3×C5C11×D1711yescharacteristic
35C2×C11C3×D8511yescharacteristic
36Dic5—171noHall
37C17C3×C11×Dic511yescharacteristic, complemented, Sylow
38C3×C5C11×Dic1711yescharacteristic, complemented, Hall
39C3×C4—851noHall
40C11C3×Dic8511yescharacteristic, direct product factor, Sylow
41C2×C5C3×C11×D1711yescharacteristic
42C2×C3C11×D8511yescharacteristic
43C5C3×C11×Dic1711yescharacteristic, complemented, Sylow
44C4—851noSylow
45C3C11×Dic8511yescharacteristic, direct product factor, Sylow
46C2C3×C11×D8511yescharacteristic
subgroupG/H
center, hypercenterC2×C3×C11D85
commutator, hypocenterC5×C17C3×C4×C11
FrattiniC2C3×C11×D85
Fitting, socle, prime radicalC2×C3×C5×C11×C17C2
cosocleC2×C5×C17C2×C3×C11
LCSG ▷ C5×C17
UCSC1 ◁ C2×C3×C11

Complements

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

NH ≅ G/Ntype
2. C11×Dic85C3direct (N × H)
3. C3×C5×C11×C17C4semidirect
7. C3×Dic85C11direct (N × H)
8. C5×C11×C17C3×C4semidirect
11. C3×C11×C17Dic5semidirect
14. Dic85C3×C11direct (N × H)
16. C3×C5×C17C4×C11semidirect
19. C11×C17C3×Dic5semidirect
21. C3×C5×C11Dic17semidirect
25. C5×C17C3×C4×C11semidirect
29. C5×C11C3×Dic17semidirect
30. C3×C17C11×Dic5semidirect
33. C3×C11Dic85direct (N × H)
37. C17C3×C11×Dic5semidirect
38. C3×C5C11×Dic17semidirect
40. C11C3×Dic85direct (N × H)
43. C5C3×C11×Dic17semidirect
45. C3C11×Dic85direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×C11×C172
C11×Dic853
C3×C11×Dic175
C3×Dic8511
C3×C11×Dic517