Finite Group Databasebeta

← ΓL(1,𝔽8)×AGL(1,𝔽23) #24922326

Subgroups — ΓL(1,𝔽8)×AGL(1,𝔽23) #24922326

Order 10626.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1ΓL(1,𝔽8)×C23⋊C11C211yesmaximal, characteristic, complemented, Hall
2C7×AGL(1,𝔽23)C311yesmaximal, characteristic, complemented, Hall
3C7×C23⋊C11C2×C311yescharacteristic, complemented, Hall
4C3×AGL(1,𝔽23)—71nomaximal, Hall
5ΓL(1,𝔽8)×D23C1111yesmaximal, characteristic, complemented, Hall
6C3×C23⋊C11—71noHall
7AGL(1,𝔽23)ΓL(1,𝔽8)11yescharacteristic, direct product factor, Hall
8ΓL(1,𝔽8)×C23C2×C1111yescharacteristic, complemented, Hall
9C2×C11×ΓL(1,𝔽8)—231nomaximal, Hall
10C7×D23C3×C1111yescharacteristic, complemented, Hall
11C23⋊C11C2×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
12C11×ΓL(1,𝔽8)—231noHall
13C7×C23C2×C3×C1111yescharacteristic, complemented, Hall
14C2×C7×C11—231noHall
15C3×D23—71noHall
16C7×C11—231noHall
17C3×C23—71noHall
18C2×C3×C11—1611noHall
19D23C11×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
20C2×ΓL(1,𝔽8)—231noHall
21C3×C11—1611noHall
22C23C2×C11×ΓL(1,𝔽8)11yescharacteristic, complemented, Sylow
23C2×C11—231noHall
24ΓL(1,𝔽8)AGL(1,𝔽23)11yescharacteristic, direct product factor, Hall
25C2×C7—231noHall
26C11—231noSylow
27C7C3×AGL(1,𝔽23)11yescharacteristic, complemented, Sylow
28C2×C3—1611noHall
29C3—71noSylow
30C2—231noSylow
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C23C2×C3×C11
LCSG ▷ C7×C23
UCSC1

Complements

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

NH ≅ G/Ntype
1. ΓL(1,𝔽8)×C23⋊C11C2semidirect
2. C7×AGL(1,𝔽23)C3semidirect
3. C7×C23⋊C11C2×C3semidirect
5. ΓL(1,𝔽8)×D23C11semidirect
7. AGL(1,𝔽23)ΓL(1,𝔽8)direct (N × H)
8. ΓL(1,𝔽8)×C23C2×C11semidirect
10. C7×D23C3×C11semidirect
11. C23⋊C11C2×ΓL(1,𝔽8)semidirect
13. C7×C23C2×C3×C11semidirect
19. D23C11×ΓL(1,𝔽8)semidirect
22. C23C2×C11×ΓL(1,𝔽8)semidirect
24. ΓL(1,𝔽8)AGL(1,𝔽23)direct (N × H)
27. C7C3×AGL(1,𝔽23)semidirect