Finite Group Databasebeta

← C4×C13×ΓL(1,𝔽8)×C31 #46799211

Subgroups — C4×C13×ΓL(1,𝔽8)×C31 #46799211

Order 33852.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×ΓL(1,𝔽8)×C31C211yesmaximal, characteristic
2C4×C7×C13×C31C311yesmaximal, characteristic, complemented, Hall
3C13×ΓL(1,𝔽8)×C31C411yescharacteristic, direct product factor, Hall
4C2×C7×C13×C31C2×C311yescharacteristic
5C3×C4×C13×C31—71nomaximal, Hall
6C7×C13×C31C3×C411yescharacteristic, complemented, Hall
7C4×ΓL(1,𝔽8)×C31C1311yesmaximal, characteristic, direct product factor, Hall
8C2×C3×C13×C31—71no—
9C4×C13×C31ΓL(1,𝔽8)11yescharacteristic, direct product factor, Hall
10C2×ΓL(1,𝔽8)×C31C2×C1311yescharacteristic
11C3×C13×C31—71noHall
12C4×C13×ΓL(1,𝔽8)C3111yesmaximal, characteristic, direct product factor, Hall
13C4×C7×C31C3×C1311yescharacteristic, complemented, Hall
14C2×C13×C31C2×ΓL(1,𝔽8)11yescharacteristic
15ΓL(1,𝔽8)×C31C4×C1311yescharacteristic, direct product factor, Hall
16C2×C13×ΓL(1,𝔽8)C2×C3111yescharacteristic
17C2×C7×C31C2×C3×C1311yescharacteristic
18C13×C31C4×ΓL(1,𝔽8)11yescharacteristic, direct product factor, Hall
19C3×C4×C31—71noHall
20C4×C7×C13C3×C3111yescharacteristic, complemented, Hall
21C13×ΓL(1,𝔽8)C4×C3111yescharacteristic, direct product factor, Hall
22C7×C31C3×C4×C1311yescharacteristic, complemented, Hall
23C2×C3×C31—71no—
24C2×C7×C13C2×C3×C3111yescharacteristic
25C3×C4×C13—71noHall
26C4×C31C13×ΓL(1,𝔽8)11yescharacteristic, direct product factor, Hall
27C3×C31—71noHall
28C7×C13C3×C4×C3111yescharacteristic, complemented, Hall
29C4×ΓL(1,𝔽8)C13×C3111yescharacteristic, direct product factor, Hall
30C2×C3×C13—71no—
31C2×C31C2×C13×ΓL(1,𝔽8)11yescharacteristic
32C4×C13ΓL(1,𝔽8)×C3111yescharacteristic, direct product factor, Hall
33C2×ΓL(1,𝔽8)C2×C13×C3111yescharacteristic
34C3×C13—71noHall
35C31C4×C13×ΓL(1,𝔽8)11yescharacteristic, direct product factor, Sylow
36C4×C7C3×C13×C3111yescharacteristic, complemented, Hall
37C2×C13C2×ΓL(1,𝔽8)×C3111yescharacteristic
38ΓL(1,𝔽8)C4×C13×C3111yescharacteristic, direct product factor, Hall
39C2×C7C2×C3×C13×C3111yescharacteristic
40C13C4×ΓL(1,𝔽8)×C3111yescharacteristic, direct product factor, Sylow
41C3×C4—71noHall
42C7C3×C4×C13×C3111yescharacteristic, complemented, Sylow
43C2×C3—71no—
44C4C13×ΓL(1,𝔽8)×C3111yescharacteristic, direct product factor, Sylow
45C3—71noSylow
46C2C2×C13×ΓL(1,𝔽8)×C3111yescharacteristic
subgroupG/H
center, hypercenterC4×C13×C31ΓL(1,𝔽8)
commutator, hypocenterC7C3×C4×C13×C31
FrattiniC2C2×C13×ΓL(1,𝔽8)×C31
FittingC4×C7×C13×C31C3
socleC2×C7×C13×C31C2×C3
prime radicalC2×C13×ΓL(1,𝔽8)×C31C2
cosocleC2×C7C2×C3×C13×C31
LCSG ▷ C7
UCSC1 ◁ C4×C13×C31

Complements

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

NH ≅ G/Ntype
2. C4×C7×C13×C31C3semidirect
3. C13×ΓL(1,𝔽8)×C31C4direct (N × H)
6. C7×C13×C31C3×C4semidirect
7. C4×ΓL(1,𝔽8)×C31C13direct (N × H)
9. C4×C13×C31ΓL(1,𝔽8)direct (N × H)
12. C4×C13×ΓL(1,𝔽8)C31direct (N × H)
13. C4×C7×C31C3×C13semidirect
15. ΓL(1,𝔽8)×C31C4×C13direct (N × H)
18. C13×C31C4×ΓL(1,𝔽8)direct (N × H)
20. C4×C7×C13C3×C31semidirect
21. C13×ΓL(1,𝔽8)C4×C31direct (N × H)
22. C7×C31C3×C4×C13semidirect
26. C4×C31C13×ΓL(1,𝔽8)direct (N × H)
28. C7×C13C3×C4×C31semidirect
29. C4×ΓL(1,𝔽8)C13×C31direct (N × H)
32. C4×C13ΓL(1,𝔽8)×C31direct (N × H)
35. C31C4×C13×ΓL(1,𝔽8)direct (N × H)
36. C4×C7C3×C13×C31semidirect
38. ΓL(1,𝔽8)C4×C13×C31direct (N × H)
40. C13C4×ΓL(1,𝔽8)×C31direct (N × H)
42. C7C3×C4×C13×C31semidirect
44. C4C13×ΓL(1,𝔽8)×C31direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×ΓL(1,𝔽8)×C312
C4×C7×C13×C313
C3×C4×C13×C317
C4×ΓL(1,𝔽8)×C3113
C4×C13×ΓL(1,𝔽8)31