Finite Group Databasebeta

← C33×C4×C13×C17 #72201162

Subgroups — C33×C4×C13×C17 #72201162

Order 23868.

336 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C33×C13×C17C211yesmaximal, characteristic
2C33×C13×C17C411yescharacteristic, direct product factor, Hall
3C32×C4×C13×C17C3113yesmaximal, direct product factor
4C2×C32×C13×C17C2×C3113yes—
5C3×C4×C13×C17C32113yesdirect product factor
6C32×C13×C17C3×C4113yesdirect product factor
7C33×C4×C17C1311yesmaximal, characteristic, direct product factor, Hall
8C33×C4×C13C1711yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C13×C17C2×C32113yes—
10C2×C33×C17C2×C1311yescharacteristic
11C4×C13×C17C3311yescharacteristic, direct product factor, Hall
12C2×C33×C13C2×C1711yescharacteristic
13C3×C13×C17C32×C4113yesdirect product factor
14C32×C4×C17C3×C13113yesdirect product factor
15C32×C4×C13C3×C17113yesdirect product factor
16C33×C17C4×C1311yescharacteristic, direct product factor, Hall
17C2×C13×C17C2×C3311yescharacteristic
18C33×C13C4×C1711yescharacteristic, direct product factor, Hall
19C2×C32×C17C2×C3×C13113yes—
20C2×C32×C13C2×C3×C17113yes—
21C13×C17C33×C411yescharacteristic, direct product factor, Hall
22C3×C4×C17C32×C13113yesdirect product factor
23C3×C4×C13C32×C17113yesdirect product factor
24C32×C17C3×C4×C13113yesdirect product factor
25C32×C13C3×C4×C17113yesdirect product factor
26C33×C4C13×C1711yescharacteristic, direct product factor, Hall
27C2×C3×C17C2×C32×C13113yes—
28C2×C3×C13C2×C32×C17113yes—
29C4×C17C33×C1311yescharacteristic, direct product factor, Hall
30C2×C33C2×C13×C1711yescharacteristic
31C4×C13C33×C1711yescharacteristic, direct product factor, Hall
32C3×C17C32×C4×C13113yesdirect product factor
33C3×C13C32×C4×C17113yesdirect product factor
34C32×C4C3×C13×C17113yesdirect product factor
35C2×C17C2×C33×C1311yescharacteristic
36C33C4×C13×C1711yescharacteristic, direct product factor, Sylow
37C2×C13C2×C33×C1711yescharacteristic
38C2×C32C2×C3×C13×C17113yes—
39C17C33×C4×C1311yescharacteristic, direct product factor, Sylow
40C13C33×C4×C1711yescharacteristic, direct product factor, Sylow
41C3×C4C32×C13×C17113yesdirect product factor
42C32C3×C4×C13×C17113yesdirect product factor
43C2×C3C2×C32×C13×C17113yes—
44C4C33×C13×C1711yescharacteristic, direct product factor, Sylow
45C3C32×C4×C13×C17113yesdirect product factor
46C2C2×C33×C13×C1711yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C2×C33×C13×C17
socle, prime radicalC2×C33×C13×C17C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C33×C13×C17C4direct (N × H)
3. C32×C4×C13×C17C3direct (N × H)
5. C3×C4×C13×C17C32direct (N × H)
6. C32×C13×C17C3×C4direct (N × H)
7. C33×C4×C17C13direct (N × H)
8. C33×C4×C13C17direct (N × H)
11. C4×C13×C17C33direct (N × H)
13. C3×C13×C17C32×C4direct (N × H)
14. C32×C4×C17C3×C13direct (N × H)
15. C32×C4×C13C3×C17direct (N × H)
16. C33×C17C4×C13direct (N × H)
18. C33×C13C4×C17direct (N × H)
21. C13×C17C33×C4direct (N × H)
22. C3×C4×C17C32×C13direct (N × H)
23. C3×C4×C13C32×C17direct (N × H)
24. C32×C17C3×C4×C13direct (N × H)
25. C32×C13C3×C4×C17direct (N × H)
26. C33×C4C13×C17direct (N × H)
29. C4×C17C33×C13direct (N × H)
31. C4×C13C33×C17direct (N × H)
32. C3×C17C32×C4×C13direct (N × H)
33. C3×C13C32×C4×C17direct (N × H)
34. C32×C4C3×C13×C17direct (N × H)
36. C33C4×C13×C17direct (N × H)
39. C17C33×C4×C13direct (N × H)
40. C13C33×C4×C17direct (N × H)
41. C3×C4C32×C13×C17direct (N × H)
42. C32C3×C4×C13×C17direct (N × H)
44. C4C33×C13×C17direct (N × H)
45. C3C32×C4×C13×C17direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C33×C13×C172
C32×C4×C13×C173
C33×C4×C1713
C33×C4×C1317