Finite Group Databasebeta

← C22×C3×C4×C383 #72196113

Subgroups — C22×C3×C4×C383 #72196113

Order 18384.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C383C211yesmaximal, characteristic
2C2×C3×C4×C383C216yesmaximal, direct product factor
3C22×C4×C383C311yesmaximal, characteristic, direct product factor, Hall
4C22×C3×C383C414yesdirect product factor
5C22×C3×C383C2213yes—
6C3×C4×C383C2214yesdirect product factor
7C23×C383C2×C311yescharacteristic
8C2×C4×C383C2×C316yesdirect product factor
9C2×C3×C383C2×C416yesdirect product factor
10C2×C3×C383C2311yescharacteristic
11C22×C383C3×C414yesdirect product factor
12C22×C383C22×C313yes—
13C4×C383C22×C314yesdirect product factor
14C3×C383C22×C411yescharacteristic, direct product factor, Hall
15C2×C383C2×C3×C416yesdirect product factor
16C2×C383C23×C311yescharacteristic
17C383C22×C3×C411yescharacteristic, direct product factor, Sylow
18C22×C3×C4C38311yesmaximal, characteristic, direct product factor, Hall
19C23×C3C2×C38311yescharacteristic
20C2×C3×C4C2×C38316yesdirect product factor
21C22×C4C3×C38311yescharacteristic, direct product factor, Sylow
22C22×C3C4×C38314yesdirect product factor
23C22×C3C22×C38313yes—
24C3×C4C22×C38314yesdirect product factor
25C23C2×C3×C38311yescharacteristic
26C2×C4C2×C3×C38316yesdirect product factor
27C2×C3C2×C4×C38316yesdirect product factor
28C2×C3C23×C38311yescharacteristic
29C22C3×C4×C38314yesdirect product factor
30C22C22×C3×C38313yes—
31C4C22×C3×C38314yesdirect product factor
32C3C22×C4×C38311yescharacteristic, direct product factor, Sylow
33C2C2×C3×C4×C38316yesdirect product factor
34C2C23×C3×C38311yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C3×C383
socle, prime radicalC23×C3×C383C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×C383C2direct (N × H)
3. C22×C4×C383C3direct (N × H)
4. C22×C3×C383C4direct (N × H)
6. C3×C4×C383C22direct (N × H)
8. C2×C4×C383C2×C3direct (N × H)
9. C2×C3×C383C2×C4direct (N × H)
11. C22×C383C3×C4direct (N × H)
13. C4×C383C22×C3direct (N × H)
14. C3×C383C22×C4direct (N × H)
15. C2×C383C2×C3×C4direct (N × H)
17. C383C22×C3×C4direct (N × H)
18. C22×C3×C4C383direct (N × H)
20. C2×C3×C4C2×C383direct (N × H)
21. C22×C4C3×C383direct (N × H)
22. C22×C3C4×C383direct (N × H)
24. C3×C4C22×C383direct (N × H)
26. C2×C4C2×C3×C383direct (N × H)
27. C2×C3C2×C4×C383direct (N × H)
29. C22C3×C4×C383direct (N × H)
31. C4C22×C3×C383direct (N × H)
32. C3C22×C4×C383direct (N × H)
33. C2C2×C3×C4×C383direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C3832
C2×C3×C4×C3832
C22×C4×C3833
C22×C3×C4383