Finite Group Databasebeta

← C24×C4×C172 #72196306

Subgroups — C24×C4×C172 #72196306

Order 18496.

13620 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C25×C172C211yesmaximal, characteristic
2C23×C4×C172C2130yesmaximal, direct product factor
3C24×C172C4116yesdirect product factor
4C24×C172C22115yes—
5C22×C4×C172C221140yesdirect product factor
6C23×C172C2×C41120yesdirect product factor
7C23×C172C23135yes—
8C2×C4×C172C231120yesdirect product factor
9C22×C172C22×C41140yesdirect product factor
10C22×C172C24115yes—
11C4×C172C24116yesdirect product factor
12C24×C4×C17C17118yesmaximal, direct product factor
13C2×C172C23×C4130yesdirect product factor
14C2×C172C2511yescharacteristic
15C25×C17C2×C17118yes—
16C23×C4×C17C2×C171540yesdirect product factor
17C172C24×C411yescharacteristic, direct product factor, Sylow
18C24×C17C4×C171288yesdirect product factor
19C24×C17C22×C171270yes—
20C22×C4×C17C22×C1712520yesdirect product factor
21C23×C17C2×C4×C1712160yesdirect product factor
22C23×C17C23×C171630yes—
23C2×C4×C17C23×C1712160yesdirect product factor
24C22×C17C22×C4×C1712520yesdirect product factor
25C22×C17C24×C171270yes—
26C4×C17C24×C171288yesdirect product factor
27C24×C4C17211yescharacteristic, direct product factor, Sylow
28C2×C17C23×C4×C171540yesdirect product factor
29C2×C17C25×C17118yes—
30C25C2×C17211yescharacteristic
31C23×C4C2×C172130yesdirect product factor
32C17C24×C4×C17118yesdirect product factor
33C24C4×C172116yesdirect product factor
34C24C22×C172115yes—
35C22×C4C22×C1721140yesdirect product factor
36C23C2×C4×C1721120yesdirect product factor
37C23C23×C172135yes—
38C2×C4C23×C1721120yesdirect product factor
39C22C22×C4×C1721140yesdirect product factor
40C22C24×C172115yes—
41C4C24×C172116yesdirect product factor
42C2C23×C4×C172130yesdirect product factor
43C2C25×C17211yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C25×C172
socle, prime radicalC25×C172C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C4×C172C2direct (N × H)
3. C24×C172C4direct (N × H)
5. C22×C4×C172C22direct (N × H)
6. C23×C172C2×C4direct (N × H)
8. C2×C4×C172C23direct (N × H)
9. C22×C172C22×C4direct (N × H)
11. C4×C172C24direct (N × H)
12. C24×C4×C17C17direct (N × H)
13. C2×C172C23×C4direct (N × H)
16. C23×C4×C17C2×C17direct (N × H)
17. C172C24×C4direct (N × H)
18. C24×C17C4×C17direct (N × H)
20. C22×C4×C17C22×C17direct (N × H)
21. C23×C17C2×C4×C17direct (N × H)
23. C2×C4×C17C23×C17direct (N × H)
24. C22×C17C22×C4×C17direct (N × H)
26. C4×C17C24×C17direct (N × H)
27. C24×C4C172direct (N × H)
28. C2×C17C23×C4×C17direct (N × H)
31. C23×C4C2×C172direct (N × H)
32. C17C24×C4×C17direct (N × H)
33. C24C4×C172direct (N × H)
35. C22×C4C22×C172direct (N × H)
36. C23C2×C4×C172direct (N × H)
38. C2×C4C23×C172direct (N × H)
39. C22C22×C4×C172direct (N × H)
41. C4C24×C172direct (N × H)
42. C2C23×C4×C172direct (N × H)

Maximal subgroups

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

subgroupindex
C25×C1722
C23×C4×C1722
C24×C4×C1717