Finite Group Databasebeta

← C11×ΓL(1,𝔽8)⋊D25 #26040468

Subgroups — C11×ΓL(1,𝔽8)⋊D25 #26040468

Order 11550.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×ΓL(1,𝔽8)×C25C211yesmaximal, characteristic, complemented, Hall
2C11×D175C311yesmaximal, characteristic, complemented, Hall
3C11×C5⋊AGL(1,𝔽7)—51nomaximal
4C7×C11×C25C2×C311yescharacteristic, complemented, Hall
5C3×C11×D25—71nomaximal, Hall
6C5×C11×ΓL(1,𝔽8)D511yescharacteristic
7ΓL(1,𝔽8)⋊D25C1111yesmaximal, characteristic, direct product factor, Hall
8C3×C11×C25—71noHall
9C11×D35—51no—
10C11×D25—71noHall
11ΓL(1,𝔽8)×C25C2×C1111yescharacteristic, complemented, Hall
12C11×AGL(1,𝔽7)—251noHall
13C5×C7×C11C3×D511yescharacteristic
14D175C3×C1111yescharacteristic, complemented, Hall
15C3×D5×C11—351no—
16C11×C25AGL(1,𝔽7)11yescharacteristic, complemented, Hall
17C11×ΓL(1,𝔽8)D2511yescharacteristic, complemented, Hall
18C5⋊AGL(1,𝔽7)—51no—
19C7×C25C2×C3×C1111yescharacteristic, complemented, Hall
20C3×C5×C11—71no—
21C11×D7—251noHall
22C3×D25—71noHall
23D5×C11—351no—
24C5×ΓL(1,𝔽8)D5×C1111yescharacteristic
25C7×C11C3×D2511yescharacteristic, complemented, Hall
26C3×C25—71noHall
27D35—51no—
28C2×C3×C11—1751noHall
29C5×C11C5⋊AGL(1,𝔽7)11yescharacteristic
30D25—71noHall
31AGL(1,𝔽7)—251noHall
32C5×C7C3×D5×C1111yescharacteristic
33C3×C11—71noHall
34C3×D5—351no—
35C25C11×AGL(1,𝔽7)11yescharacteristic, complemented, Sylow
36C2×C11—1751noHall
37ΓL(1,𝔽8)C11×D2511yescharacteristic, complemented, Hall
38C3×C5—71no—
39D7—251noHall
40C11ΓL(1,𝔽8)⋊D2511yescharacteristic, direct product factor, Sylow
41D5—351no—
42C7C3×C11×D2511yescharacteristic, complemented, Sylow
43C2×C3—1751noHall
44C5C11×C5⋊AGL(1,𝔽7)11yescharacteristic
45C3—71noSylow
46C2—1751noSylow
subgroupG/H
center, hypercenterC11ΓL(1,𝔽8)⋊D25
commutator, cosocle, hypocenterC7×C25C2×C3×C11
FrattiniC5C11×C5⋊AGL(1,𝔽7)
FittingC7×C11×C25C2×C3
socleC5×C7×C11C3×D5
LCSG ▷ C7×C25
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C11×ΓL(1,𝔽8)×C25C2semidirect
2. C11×D175C3semidirect
4. C7×C11×C25C2×C3semidirect
7. ΓL(1,𝔽8)⋊D25C11direct (N × H)
11. ΓL(1,𝔽8)×C25C2×C11semidirect
14. D175C3×C11semidirect
16. C11×C25AGL(1,𝔽7)semidirect
17. C11×ΓL(1,𝔽8)D25semidirect
19. C7×C25C2×C3×C11semidirect
25. C7×C11C3×D25semidirect
35. C25C11×AGL(1,𝔽7)semidirect
37. ΓL(1,𝔽8)C11×D25semidirect
40. C11ΓL(1,𝔽8)⋊D25direct (N × H)
42. C7C3×C11×D25semidirect

Maximal subgroups

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

subgroupindex
C11×ΓL(1,𝔽8)×C252
C11×D1753
C11×C5⋊AGL(1,𝔽7)5
C3×C11×D257
ΓL(1,𝔽8)⋊D2511