Finite Group Databasebeta

← C4×ΓL(1,𝔽8)×C11⋊C5 #17987607

Subgroups — C4×ΓL(1,𝔽8)×C11⋊C5 #17987607

Order 4620.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×ΓL(1,𝔽8)×C11⋊C5C211yesmaximal, characteristic
2C4×C7×C11⋊C5C311yesmaximal, characteristic, complemented, Hall
3ΓL(1,𝔽8)×C11⋊C5C411yescharacteristic, direct product factor, Hall
4C4×C11×ΓL(1,𝔽8)C511yesmaximal, characteristic, complemented, Hall
5C2×C7×C11⋊C5C2×C311yescharacteristic
6C3×C4×C11⋊C5—71nomaximal, Hall
7C2×C11×ΓL(1,𝔽8)C2×C511yescharacteristic
8C4×C5×ΓL(1,𝔽8)—111nomaximal, Hall
9C7×C11⋊C5C3×C411yescharacteristic, complemented, Hall
10C2×C3×C11⋊C5—71no—
11C4×C7×C11C3×C511yescharacteristic, complemented, Hall
12C11×ΓL(1,𝔽8)C4×C511yescharacteristic, complemented, Hall
13C4×C11⋊C5ΓL(1,𝔽8)11yescharacteristic, direct product factor, Hall
14C2×C5×ΓL(1,𝔽8)—111no—
15C3×C11⋊C5—71noHall
16C2×C7×C11C2×C3×C511yescharacteristic
17C4×C5×C7—111noHall
18C3×C4×C11—71noHall
19C2×C11⋊C5C2×ΓL(1,𝔽8)11yescharacteristic
20C5×ΓL(1,𝔽8)—111noHall
21C4×ΓL(1,𝔽8)C11⋊C511yescharacteristic, direct product factor, Hall
22C7×C11C3×C4×C511yescharacteristic, complemented, Hall
23C2×C5×C7—111no—
24C2×C3×C11—71no—
25C3×C4×C5—771noHall
26C11⋊C5C4×ΓL(1,𝔽8)11yescharacteristic, direct product factor, Hall
27C4×C11C5×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
28C2×ΓL(1,𝔽8)C2×C11⋊C511yescharacteristic
29C5×C7—111noHall
30C3×C11—71noHall
31C2×C3×C5—771no—
32C4×C7C3×C11⋊C511yescharacteristic, complemented, Hall
33C2×C11C2×C5×ΓL(1,𝔽8)11yescharacteristic
34ΓL(1,𝔽8)C4×C11⋊C511yescharacteristic, direct product factor, Hall
35C4×C5—111noHall
36C3×C5—771noHall
37C2×C7C2×C3×C11⋊C511yescharacteristic
38C3×C4—71noHall
39C11C4×C5×ΓL(1,𝔽8)11yescharacteristic, complemented, Sylow
40C2×C5—111no—
41C7C3×C4×C11⋊C511yescharacteristic, complemented, Sylow
42C2×C3—71no—
43C5—111noSylow
44C4ΓL(1,𝔽8)×C11⋊C511yescharacteristic, direct product factor, Sylow
45C3—71noSylow
46C2C2×ΓL(1,𝔽8)×C11⋊C511yescharacteristic
subgroupG/H
center, hypercenterC4ΓL(1,𝔽8)×C11⋊C5
commutator, hypocenterC7×C11C3×C4×C5
FrattiniC2C2×ΓL(1,𝔽8)×C11⋊C5
FittingC4×C7×C11C3×C5
socle, cosocleC2×C7×C11C2×C3×C5
prime radicalC2×ΓL(1,𝔽8)×C11⋊C5C2
LCSG ▷ C7×C11
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
2. C4×C7×C11⋊C5C3semidirect
3. ΓL(1,𝔽8)×C11⋊C5C4direct (N × H)
4. C4×C11×ΓL(1,𝔽8)C5semidirect
9. C7×C11⋊C5C3×C4semidirect
11. C4×C7×C11C3×C5semidirect
12. C11×ΓL(1,𝔽8)C4×C5semidirect
13. C4×C11⋊C5ΓL(1,𝔽8)direct (N × H)
21. C4×ΓL(1,𝔽8)C11⋊C5direct (N × H)
22. C7×C11C3×C4×C5semidirect
26. C11⋊C5C4×ΓL(1,𝔽8)direct (N × H)
27. C4×C11C5×ΓL(1,𝔽8)semidirect
32. C4×C7C3×C11⋊C5semidirect
34. ΓL(1,𝔽8)C4×C11⋊C5direct (N × H)
39. C11C4×C5×ΓL(1,𝔽8)semidirect
41. C7C3×C4×C11⋊C5semidirect
44. C4ΓL(1,𝔽8)×C11⋊C5direct (N × H)

Maximal subgroups

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

subgroupindex
C2×ΓL(1,𝔽8)×C11⋊C52
C4×C7×C11⋊C53
C4×C11×ΓL(1,𝔽8)5
C3×C4×C11⋊C57
C4×C5×ΓL(1,𝔽8)11