Finite Group Databasebeta

← C24×C4×C389 #38733810

Subgroups — C24×C4×C389 #38733810

Order 24896.

1362 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C25×C389C211yesmaximal, characteristic
2C23×C4×C389C2130yesmaximal, direct product factor
3C24×C389C4116yesdirect product factor
4C24×C389C22115yes—
5C22×C4×C389C221140yesdirect product factor
6C23×C389C2×C41120yesdirect product factor
7C23×C389C23135yes—
8C2×C4×C389C231120yesdirect product factor
9C22×C389C22×C41140yesdirect product factor
10C22×C389C24115yes—
11C4×C389C24116yesdirect product factor
12C2×C389C23×C4130yesdirect product factor
13C2×C389C2511yescharacteristic
14C389C24×C411yescharacteristic, direct product factor, Sylow
15C24×C4C38911yesmaximal, characteristic, direct product factor, Sylow
16C25C2×C38911yescharacteristic
17C23×C4C2×C389130yesdirect product factor
18C24C4×C389116yesdirect product factor
19C24C22×C389115yes—
20C22×C4C22×C3891140yesdirect product factor
21C23C2×C4×C3891120yesdirect product factor
22C23C23×C389135yes—
23C2×C4C23×C3891120yesdirect product factor
24C22C22×C4×C3891140yesdirect product factor
25C22C24×C389115yes—
26C4C24×C389116yesdirect product factor
27C2C23×C4×C389130yesdirect product factor
28C2C25×C38911yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C25×C389
socle, prime radicalC25×C389C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C4×C389C2direct (N × H)
3. C24×C389C4direct (N × H)
5. C22×C4×C389C22direct (N × H)
6. C23×C389C2×C4direct (N × H)
8. C2×C4×C389C23direct (N × H)
9. C22×C389C22×C4direct (N × H)
11. C4×C389C24direct (N × H)
12. C2×C389C23×C4direct (N × H)
14. C389C24×C4direct (N × H)
15. C24×C4C389direct (N × H)
17. C23×C4C2×C389direct (N × H)
18. C24C4×C389direct (N × H)
20. C22×C4C22×C389direct (N × H)
21. C23C2×C4×C389direct (N × H)
23. C2×C4C23×C389direct (N × H)
24. C22C22×C4×C389direct (N × H)
26. C4C24×C389direct (N × H)
27. C2C23×C4×C389direct (N × H)

Maximal subgroups

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

subgroupindex
C25×C3892
C23×C4×C3892
C24×C4389