Finite Group Databasebeta

← C23×(C11⋊C5)⋊D11 #42123713

Subgroups — C23×(C11⋊C5)⋊D11 #42123713

Order 27830.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×C23×C11⋊C5C211yesmaximal, characteristic, complemented, Hall
2C23×C11⋊D11C511yesmaximal, characteristic, complemented, Hall
3C112×C23C2×C511yescharacteristic, complemented, Hall
4C23×AGL(1,𝔽11)—111nomaximal
5C5×D11×C23—111nomaximal
6C5×C11×C23—111no—
7C23×C11⋊C5D1111yescharacteristic, complemented
8(C11⋊C5)⋊D11C2311yesmaximal, characteristic, direct product factor, Hall
9C11×C11⋊C5C2×C2311yescharacteristic, complemented, Hall
10D11×C23—111no—
11D11×C23—111no—
12D11×C23—552no—
13C11×C23—52no—
14C11×C23AGL(1,𝔽11)11yescharacteristic, complemented
15C11×C23C5×D1111yescharacteristic, complemented
16C11⋊D11C5×C2311yescharacteristic, complemented, Hall
17C2×C5×C23—1211noHall
18C112C2×C5×C2311yescharacteristic, complemented, Sylow
19C5×C23—111noHall
20C5×D11—111no—
21AGL(1,𝔽11)—111no—
22C5×C11—111no—
23C11⋊C5D11×C2311yescharacteristic, complemented
24C2×C23—1211noHall
25C23(C11⋊C5)⋊D1111yescharacteristic, direct product factor, Sylow
26D11—111no—
27D11—111no—
28D11—552no—
29C11—52no—
30C11C5×D11×C2311yescharacteristic, complemented
31C11C23×AGL(1,𝔽11)11yescharacteristic, complemented
32C2×C5—1211noHall
33C5—111noSylow
34C2—1211noSylow
subgroupG/H
center, hypercenterC23(C11⋊C5)⋊D11
commutator, cosocle, hypocenterC112C2×C5×C23
FrattiniC1G
Fitting, socleC112×C23C2×C5
LCSG ▷ C112
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C11×C23×C11⋊C5C2semidirect
2. C23×C11⋊D11C5semidirect
3. C112×C23C2×C5semidirect
7. C23×C11⋊C5D11semidirect
8. (C11⋊C5)⋊D11C23direct (N × H)
9. C11×C11⋊C5C2×C23semidirect
14. C11×C23AGL(1,𝔽11)semidirect
15. C11×C23C5×D11semidirect
16. C11⋊D11C5×C23semidirect
18. C112C2×C5×C23semidirect
23. C11⋊C5D11×C23semidirect
25. C23(C11⋊C5)⋊D11direct (N × H)
30. C11C5×D11×C23semidirect
31. C11C23×AGL(1,𝔽11)semidirect

Maximal subgroups

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

subgroupindex
C11×C23×C11⋊C52
C23×C11⋊D115
C23×AGL(1,𝔽11)11
C5×D11×C2311
(C11⋊C5)⋊D1123