Finite Group Databasebeta

← C22×(C11⋊C5)⋊C8 #13182521

Subgroups — C22×(C11⋊C5)⋊C8 #13182521

Order 1760.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C11⋊C5C211yesmaximal, characteristic
2C2×(C11⋊C5)⋊C8C216yesmaximal, direct product factor
3C23×C11⋊C5C411yescharacteristic
4C2×C4×C11⋊C5C413yes—
5C2×C4×C11⋊C5C2213yes—
6(C11⋊C5)⋊C8C2214yesdirect product factor
7C22×C11⋊C8C511yesmaximal, characteristic, complemented, Hall
8C22×C11⋊C5C814yescomplemented
9C22×C11⋊C5C2×C413yes—
10C4×C11⋊C5C2×C413yes—
11C4×C11⋊C5C2311yescharacteristic
12C22×C4×C11C2×C511yescharacteristic
13C2×C11⋊C8C2×C516yescomplemented
14C22×C5×C8—111nomaximal, Hall
15C2×C11⋊C5C2×C816yescomplemented
16C2×C11⋊C5C22×C411yescharacteristic
17C23×C11C4×C511yescharacteristic
18C2×C4×C11C4×C513yes—
19C2×C4×C11C22×C513yes—
20C11⋊C8C22×C514yescomplemented
21C22×C4×C5—111no—
22C2×C5×C8—116no—
23C11⋊C5C22×C811yescharacteristic, complemented, Hall
24C22×C11C5×C814yescomplemented
25C22×C11C2×C4×C513yes—
26C4×C11C2×C4×C513yes—
27C4×C11C23×C511yescharacteristic
28C23×C5—111no—
29C2×C4×C5—113no—
30C2×C4×C5—113no—
31C5×C8—114no—
32C22×C8—111noSylow
33C2×C11C2×C5×C816yescomplemented
34C2×C11C22×C4×C511yescharacteristic
35C22×C5—114no—
36C22×C5—113no—
37C4×C5—113no—
38C4×C5—111no—
39C22×C4AGL(1,𝔽11)11yescharacteristic
40C2×C8—116no—
41C11C22×C5×C811yescharacteristic, complemented, Sylow
42C2×C5—116no—
43C2×C5—111no—
44C23Dic11⋊C511yescharacteristic
45C2×C4Dic11⋊C513yes—
46C2×C4C2×AGL(1,𝔽11)13yes—
47C8—114no—
48C5—111noSylow
49C22(C11⋊C5)⋊C814yesdirect product factor
50C22C2×Dic11⋊C513yes—
51C4C2×Dic11⋊C513yes—
52C4C22×AGL(1,𝔽11)11yescharacteristic
53C2C2×(C11⋊C5)⋊C816yesdirect product factor
54C2C22×Dic11⋊C511yescharacteristic
subgroupG/H
center, hypercenterC22×C4AGL(1,𝔽11)
commutator, hypocenterC11C22×C5×C8
FrattiniC4C22×AGL(1,𝔽11)
FittingC22×C4×C11C2×C5
socleC23×C11C4×C5
prime radicalC23×C11⋊C5C4
cosocleC4×C11C23×C5
LCSG ▷ C11
UCSC1 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×(C11⋊C5)⋊C8C2direct (N × H)
6. (C11⋊C5)⋊C8C22direct (N × H)
7. C22×C11⋊C8C5semidirect
8. C22×C11⋊C5C8semidirect
13. C2×C11⋊C8C2×C5semidirect
15. C2×C11⋊C5C2×C8semidirect
20. C11⋊C8C22×C5semidirect
23. C11⋊C5C22×C8semidirect
24. C22×C11C5×C8semidirect
33. C2×C11C2×C5×C8semidirect
41. C11C22×C5×C8semidirect
49. C22(C11⋊C5)⋊C8direct (N × H)
53. C2C2×(C11⋊C5)⋊C8direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C11⋊C52
C2×(C11⋊C5)⋊C82
C22×C11⋊C85
C22×C5×C811