Finite Group Databasebeta

← C4×C11×C13×ΓL(1,𝔽8) #26046413

Subgroups — C4×C11×C13×ΓL(1,𝔽8) #26046413

Order 12012.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×C13×ΓL(1,𝔽8)C211yesmaximal, characteristic
2C4×C7×C11×C13C311yesmaximal, characteristic, complemented, Hall
3C11×C13×ΓL(1,𝔽8)C411yescharacteristic, direct product factor, Hall
4C2×C7×C11×C13C2×C311yescharacteristic
5C3×C4×C11×C13—71nomaximal, Hall
6C4×C13×ΓL(1,𝔽8)C1111yesmaximal, characteristic, direct product factor, Hall
7C7×C11×C13C3×C411yescharacteristic, complemented, Hall
8C4×C11×ΓL(1,𝔽8)C1311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C11×C13—71no—
10C4×C11×C13ΓL(1,𝔽8)11yescharacteristic, direct product factor, Hall
11C2×C13×ΓL(1,𝔽8)C2×C1111yescharacteristic
12C2×C11×ΓL(1,𝔽8)C2×C1311yescharacteristic
13C3×C11×C13—71noHall
14C4×C7×C13C3×C1111yescharacteristic, complemented, Hall
15C4×C7×C11C3×C1311yescharacteristic, complemented, Hall
16C2×C11×C13C2×ΓL(1,𝔽8)11yescharacteristic
17C13×ΓL(1,𝔽8)C4×C1111yescharacteristic, direct product factor, Hall
18C11×ΓL(1,𝔽8)C4×C1311yescharacteristic, direct product factor, Hall
19C2×C7×C13C2×C3×C1111yescharacteristic
20C3×C4×C13—71noHall
21C2×C7×C11C2×C3×C1311yescharacteristic
22C11×C13C4×ΓL(1,𝔽8)11yescharacteristic, direct product factor, Hall
23C3×C4×C11—71noHall
24C7×C13C3×C4×C1111yescharacteristic, complemented, Hall
25C4×ΓL(1,𝔽8)C11×C1311yescharacteristic, direct product factor, Hall
26C2×C3×C13—71no—
27C7×C11C3×C4×C1311yescharacteristic, complemented, Hall
28C2×C3×C11—71no—
29C4×C13C11×ΓL(1,𝔽8)11yescharacteristic, direct product factor, Hall
30C4×C11C13×ΓL(1,𝔽8)11yescharacteristic, direct product factor, Hall
31C2×ΓL(1,𝔽8)C2×C11×C1311yescharacteristic
32C3×C13—71noHall
33C3×C11—71noHall
34C4×C7C3×C11×C1311yescharacteristic, complemented, Hall
35C2×C13C2×C11×ΓL(1,𝔽8)11yescharacteristic
36C2×C11C2×C13×ΓL(1,𝔽8)11yescharacteristic
37ΓL(1,𝔽8)C4×C11×C1311yescharacteristic, direct product factor, Hall
38C2×C7C2×C3×C11×C1311yescharacteristic
39C13C4×C11×ΓL(1,𝔽8)11yescharacteristic, direct product factor, Sylow
40C3×C4—71noHall
41C11C4×C13×ΓL(1,𝔽8)11yescharacteristic, direct product factor, Sylow
42C7C3×C4×C11×C1311yescharacteristic, complemented, Sylow
43C2×C3—71no—
44C4C11×C13×ΓL(1,𝔽8)11yescharacteristic, direct product factor, Sylow
45C3—71noSylow
46C2C2×C11×C13×ΓL(1,𝔽8)11yescharacteristic
subgroupG/H
center, hypercenterC4×C11×C13ΓL(1,𝔽8)
commutator, hypocenterC7C3×C4×C11×C13
FrattiniC2C2×C11×C13×ΓL(1,𝔽8)
FittingC4×C7×C11×C13C3
socleC2×C7×C11×C13C2×C3
prime radicalC2×C11×C13×ΓL(1,𝔽8)C2
cosocleC2×C7C2×C3×C11×C13
LCSG ▷ C7
UCSC1 ◁ C4×C11×C13

Complements

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

NH ≅ G/Ntype
2. C4×C7×C11×C13C3semidirect
3. C11×C13×ΓL(1,𝔽8)C4direct (N × H)
6. C4×C13×ΓL(1,𝔽8)C11direct (N × H)
7. C7×C11×C13C3×C4semidirect
8. C4×C11×ΓL(1,𝔽8)C13direct (N × H)
10. C4×C11×C13ΓL(1,𝔽8)direct (N × H)
14. C4×C7×C13C3×C11semidirect
15. C4×C7×C11C3×C13semidirect
17. C13×ΓL(1,𝔽8)C4×C11direct (N × H)
18. C11×ΓL(1,𝔽8)C4×C13direct (N × H)
22. C11×C13C4×ΓL(1,𝔽8)direct (N × H)
24. C7×C13C3×C4×C11semidirect
25. C4×ΓL(1,𝔽8)C11×C13direct (N × H)
27. C7×C11C3×C4×C13semidirect
29. C4×C13C11×ΓL(1,𝔽8)direct (N × H)
30. C4×C11C13×ΓL(1,𝔽8)direct (N × H)
34. C4×C7C3×C11×C13semidirect
37. ΓL(1,𝔽8)C4×C11×C13direct (N × H)
39. C13C4×C11×ΓL(1,𝔽8)direct (N × H)
41. C11C4×C13×ΓL(1,𝔽8)direct (N × H)
42. C7C3×C4×C11×C13semidirect
44. C4C11×C13×ΓL(1,𝔽8)direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×C13×ΓL(1,𝔽8)2
C4×C7×C11×C133
C3×C4×C11×C137
C4×C13×ΓL(1,𝔽8)11
C4×C11×ΓL(1,𝔽8)13