Finite Group Databasebeta

← C7×Dic5×C43⋊C3 #31825366

Subgroups — C7×Dic5×C43⋊C3 #31825366

Order 18060.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×C7×C43⋊C3C211yesmaximal, characteristic
2C7×Dic5×C43C311yesmaximal, characteristic, complemented, Hall
3C5×C7×C43⋊C3C411yescharacteristic, complemented, Hall
4C4×C7×C43⋊C3—51nomaximal, Hall
5C2×C5×C7×C43C2×C311yescharacteristic
6Dic5×C43⋊C3C711yesmaximal, characteristic, direct product factor, Hall
7C2×C7×C43⋊C3D511yescharacteristic
8C5×C7×C43C3×C411yescharacteristic, complemented, Hall
9C2×C5×C43⋊C3C2×C711yescharacteristic
10C4×C7×C43—51noHall
11C7×C43⋊C3Dic511yescharacteristic, direct product factor, Hall
12Dic5×C43C3×C711yescharacteristic, complemented, Hall
13C5×C43⋊C3C4×C711yescharacteristic, complemented, Hall
14C2×C7×C43C3×D511yescharacteristic
15C4×C43⋊C3—51noHall
16C2×C5×C43C2×C3×C711yescharacteristic
17C3×C7×Dic5—431nomaximal, Hall
18C7×C43C3×Dic511yescharacteristic, complemented, Hall
19C2×C43⋊C3C7×D511yescharacteristic
20C5×C43C3×C4×C711yescharacteristic, complemented, Hall
21C2×C3×C5×C7—431no—
22C4×C43—51noHall
23C7×Dic5C43⋊C311yescharacteristic, direct product factor, Hall
24C43⋊C3C7×Dic511yescharacteristic, direct product factor, Hall
25C3×C5×C7—431noHall
26C2×C43C3×C7×D511yescharacteristic
27C3×C4×C7—2151noHall
28C2×C5×C7C2×C43⋊C311yescharacteristic
29C3×Dic5—431noHall
30C43C3×C7×Dic511yescharacteristic, complemented, Sylow
31C2×C3×C7—431no—
32C5×C7C4×C43⋊C311yescharacteristic, complemented, Hall
33C2×C3×C5—431no—
34C4×C7—51noHall
35C3×C7—431noHall
36Dic5C7×C43⋊C311yescharacteristic, direct product factor, Hall
37C3×C5—431noHall
38C2×C7D5×C43⋊C311yescharacteristic
39C3×C4—2151noHall
40C2×C5C2×C7×C43⋊C311yescharacteristic
41C7Dic5×C43⋊C311yescharacteristic, direct product factor, Sylow
42C2×C3—431no—
43C5C4×C7×C43⋊C311yescharacteristic, complemented, Sylow
44C4—51noSylow
45C3—431noSylow
46C2C7×D5×C43⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2×C7D5×C43⋊C3
commutator, hypocenterC5×C43C3×C4×C7
FrattiniC2C7×D5×C43⋊C3
Fitting, socleC2×C5×C7×C43C2×C3
prime radicalC2×C5×C7×C43⋊C3C2
cosocleC2×C5×C43C2×C3×C7
LCSG ▷ C5×C43
UCSC1 ◁ C2×C7

Complements

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

NH ≅ G/Ntype
2. C7×Dic5×C43C3semidirect
3. C5×C7×C43⋊C3C4semidirect
6. Dic5×C43⋊C3C7direct (N × H)
8. C5×C7×C43C3×C4semidirect
11. C7×C43⋊C3Dic5direct (N × H)
12. Dic5×C43C3×C7semidirect
13. C5×C43⋊C3C4×C7semidirect
18. C7×C43C3×Dic5semidirect
20. C5×C43C3×C4×C7semidirect
23. C7×Dic5C43⋊C3direct (N × H)
24. C43⋊C3C7×Dic5direct (N × H)
30. C43C3×C7×Dic5semidirect
32. C5×C7C4×C43⋊C3semidirect
36. Dic5C7×C43⋊C3direct (N × H)
41. C7Dic5×C43⋊C3direct (N × H)
43. C5C4×C7×C43⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×C5×C7×C43⋊C32
C7×Dic5×C433
C4×C7×C43⋊C35
Dic5×C43⋊C37
C3×C7×Dic543