Finite Group Databasebeta

← C22×C4×C11×C139 #72201737

Subgroups — C22×C4×C11×C139 #72201737

Order 24464.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C11×C139C211yesmaximal, characteristic
2C2×C4×C11×C139C216yesmaximal, direct product factor
3C22×C11×C139C414yesdirect product factor
4C22×C11×C139C2213yes—
5C4×C11×C139C2214yesdirect product factor
6C2×C11×C139C2×C416yesdirect product factor
7C2×C11×C139C2311yescharacteristic
8C22×C4×C139C1111yesmaximal, characteristic, direct product factor, Hall
9C11×C139C22×C411yescharacteristic, direct product factor, Hall
10C23×C139C2×C1111yescharacteristic
11C2×C4×C139C2×C1116yesdirect product factor
12C22×C139C4×C1114yesdirect product factor
13C22×C139C22×C1113yes—
14C4×C139C22×C1114yesdirect product factor
15C2×C139C2×C4×C1116yesdirect product factor
16C2×C139C23×C1111yescharacteristic
17C22×C4×C11C13911yesmaximal, characteristic, direct product factor, Hall
18C139C22×C4×C1111yescharacteristic, direct product factor, Sylow
19C23×C11C2×C13911yescharacteristic
20C2×C4×C11C2×C13916yesdirect product factor
21C22×C11C4×C13914yesdirect product factor
22C22×C11C22×C13913yes—
23C4×C11C22×C13914yesdirect product factor
24C2×C11C2×C4×C13916yesdirect product factor
25C2×C11C23×C13911yescharacteristic
26C22×C4C11×C13911yescharacteristic, direct product factor, Sylow
27C11C22×C4×C13911yescharacteristic, direct product factor, Sylow
28C23C2×C11×C13911yescharacteristic
29C2×C4C2×C11×C13916yesdirect product factor
30C22C4×C11×C13914yesdirect product factor
31C22C22×C11×C13913yes—
32C4C22×C11×C13914yesdirect product factor
33C2C2×C4×C11×C13916yesdirect product factor
34C2C23×C11×C13911yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C11×C139
socle, prime radicalC23×C11×C139C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×C11×C139C2direct (N × H)
3. C22×C11×C139C4direct (N × H)
5. C4×C11×C139C22direct (N × H)
6. C2×C11×C139C2×C4direct (N × H)
8. C22×C4×C139C11direct (N × H)
9. C11×C139C22×C4direct (N × H)
11. C2×C4×C139C2×C11direct (N × H)
12. C22×C139C4×C11direct (N × H)
14. C4×C139C22×C11direct (N × H)
15. C2×C139C2×C4×C11direct (N × H)
17. C22×C4×C11C139direct (N × H)
18. C139C22×C4×C11direct (N × H)
20. C2×C4×C11C2×C139direct (N × H)
21. C22×C11C4×C139direct (N × H)
23. C4×C11C22×C139direct (N × H)
24. C2×C11C2×C4×C139direct (N × H)
26. C22×C4C11×C139direct (N × H)
27. C11C22×C4×C139direct (N × H)
29. C2×C4C2×C11×C139direct (N × H)
30. C22C4×C11×C139direct (N × H)
32. C4C22×C11×C139direct (N × H)
33. C2C2×C4×C11×C139direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C11×C1392
C2×C4×C11×C1392
C22×C4×C13911
C22×C4×C11139