Finite Group Databasebeta

← C2×C3×C4×C7×C193 #72209158

Subgroups — C2×C3×C4×C7×C193 #72209158

Order 32424.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C7×C193C311yesmaximal, characteristic, direct product factor, Hall
2C2×C3×C4×C193C711yesmaximal, characteristic, direct product factor, Hall
3C22×C3×C7×C193C211yesmaximal, characteristic
4C3×C4×C7×C193C212yesmaximal, direct product factor
5C2×C3×C7×C193C412yesdirect product factor
6C2×C3×C7×C193C2211yescharacteristic
7C22×C7×C193C2×C311yescharacteristic
8C4×C7×C193C2×C312yesdirect product factor
9C3×C7×C193C2×C411yescharacteristic, direct product factor, Hall
10C2×C7×C193C3×C412yesdirect product factor
11C2×C7×C193C22×C311yescharacteristic
12C22×C3×C193C2×C711yescharacteristic
13C3×C4×C193C2×C712yesdirect product factor
14C2×C4×C193C3×C711yescharacteristic, direct product factor, Hall
15C7×C193C2×C3×C411yescharacteristic, direct product factor, Hall
16C2×C3×C193C4×C712yesdirect product factor
17C2×C3×C193C22×C711yescharacteristic
18C22×C193C2×C3×C711yescharacteristic
19C4×C193C2×C3×C712yesdirect product factor
20C3×C193C2×C4×C711yescharacteristic, direct product factor, Hall
21C2×C193C3×C4×C712yesdirect product factor
22C2×C193C22×C3×C711yescharacteristic
23C193C2×C3×C4×C711yescharacteristic, direct product factor, Sylow
24C2×C3×C4×C7C19311yesmaximal, characteristic, direct product factor, Hall
25C22×C3×C7C2×C19311yescharacteristic
26C3×C4×C7C2×C19312yesdirect product factor
27C2×C4×C7C3×C19311yescharacteristic, direct product factor, Hall
28C2×C3×C7C4×C19312yesdirect product factor
29C2×C3×C7C22×C19311yescharacteristic
30C22×C7C2×C3×C19311yescharacteristic
31C4×C7C2×C3×C19312yesdirect product factor
32C2×C3×C4C7×C19311yescharacteristic, direct product factor, Hall
33C3×C7C2×C4×C19311yescharacteristic, direct product factor, Hall
34C2×C7C3×C4×C19312yesdirect product factor
35C2×C7C22×C3×C19311yescharacteristic
36C22×C3C2×C7×C19311yescharacteristic
37C3×C4C2×C7×C19312yesdirect product factor
38C2×C4C3×C7×C19311yescharacteristic, direct product factor, Sylow
39C7C2×C3×C4×C19311yescharacteristic, direct product factor, Sylow
40C2×C3C4×C7×C19312yesdirect product factor
41C2×C3C22×C7×C19311yescharacteristic
42C22C2×C3×C7×C19311yescharacteristic
43C4C2×C3×C7×C19312yesdirect product factor
44C3C2×C4×C7×C19311yescharacteristic, direct product factor, Sylow
45C2C3×C4×C7×C19312yesdirect product factor
46C2C22×C3×C7×C19311yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C22×C3×C7×C193
socle, prime radicalC22×C3×C7×C193C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C4×C7×C193C3direct (N × H)
2. C2×C3×C4×C193C7direct (N × H)
4. C3×C4×C7×C193C2direct (N × H)
5. C2×C3×C7×C193C4direct (N × H)
8. C4×C7×C193C2×C3direct (N × H)
9. C3×C7×C193C2×C4direct (N × H)
10. C2×C7×C193C3×C4direct (N × H)
13. C3×C4×C193C2×C7direct (N × H)
14. C2×C4×C193C3×C7direct (N × H)
15. C7×C193C2×C3×C4direct (N × H)
16. C2×C3×C193C4×C7direct (N × H)
19. C4×C193C2×C3×C7direct (N × H)
20. C3×C193C2×C4×C7direct (N × H)
21. C2×C193C3×C4×C7direct (N × H)
23. C193C2×C3×C4×C7direct (N × H)
24. C2×C3×C4×C7C193direct (N × H)
26. C3×C4×C7C2×C193direct (N × H)
27. C2×C4×C7C3×C193direct (N × H)
28. C2×C3×C7C4×C193direct (N × H)
31. C4×C7C2×C3×C193direct (N × H)
32. C2×C3×C4C7×C193direct (N × H)
33. C3×C7C2×C4×C193direct (N × H)
34. C2×C7C3×C4×C193direct (N × H)
37. C3×C4C2×C7×C193direct (N × H)
38. C2×C4C3×C7×C193direct (N × H)
39. C7C2×C3×C4×C193direct (N × H)
40. C2×C3C4×C7×C193direct (N × H)
43. C4C2×C3×C7×C193direct (N × H)
44. C3C2×C4×C7×C193direct (N × H)
45. C2C3×C4×C7×C193direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C7×C1933
C2×C3×C4×C1937
C22×C3×C7×C1932
C3×C4×C7×C1932
C2×C3×C4×C7193