Finite Group Databasebeta

← C24×C4×C271 #31773608

Subgroups — C24×C4×C271 #31773608

Order 17344.

1362 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C25×C271C211yesmaximal, characteristic
2C23×C4×C271C2130yesmaximal, direct product factor
3C24×C271C4116yesdirect product factor
4C24×C271C22115yes—
5C22×C4×C271C221140yesdirect product factor
6C23×C271C2×C41120yesdirect product factor
7C23×C271C23135yes—
8C2×C4×C271C231120yesdirect product factor
9C22×C271C22×C41140yesdirect product factor
10C22×C271C24115yes—
11C4×C271C24116yesdirect product factor
12C2×C271C23×C4130yesdirect product factor
13C2×C271C2511yescharacteristic
14C271C24×C411yescharacteristic, direct product factor, Sylow
15C24×C4C27111yesmaximal, characteristic, direct product factor, Sylow
16C25C2×C27111yescharacteristic
17C23×C4C2×C271130yesdirect product factor
18C24C4×C271116yesdirect product factor
19C24C22×C271115yes—
20C22×C4C22×C2711140yesdirect product factor
21C23C2×C4×C2711120yesdirect product factor
22C23C23×C271135yes—
23C2×C4C23×C2711120yesdirect product factor
24C22C22×C4×C2711140yesdirect product factor
25C22C24×C271115yes—
26C4C24×C271116yesdirect product factor
27C2C23×C4×C271130yesdirect product factor
28C2C25×C27111yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C25×C271
socle, prime radicalC25×C271C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C4×C271C2direct (N × H)
3. C24×C271C4direct (N × H)
5. C22×C4×C271C22direct (N × H)
6. C23×C271C2×C4direct (N × H)
8. C2×C4×C271C23direct (N × H)
9. C22×C271C22×C4direct (N × H)
11. C4×C271C24direct (N × H)
12. C2×C271C23×C4direct (N × H)
14. C271C24×C4direct (N × H)
15. C24×C4C271direct (N × H)
17. C23×C4C2×C271direct (N × H)
18. C24C4×C271direct (N × H)
20. C22×C4C22×C271direct (N × H)
21. C23C2×C4×C271direct (N × H)
23. C2×C4C23×C271direct (N × H)
24. C22C22×C4×C271direct (N × H)
26. C4C24×C271direct (N × H)
27. C2C23×C4×C271direct (N × H)

Maximal subgroups

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

subgroupindex
C25×C2712
C23×C4×C2712
C24×C4271