Finite Group Databasebeta

← C22×C3×(C127⋊C3)⋊C7 #44544792

Subgroups — C22×C3×(C127⋊C3)⋊C7 #44544792

Order 32004.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×(C127⋊C3)⋊C7C213yesmaximal, direct product factor
2C22×C3×C127⋊C7C311yesmaximal, characteristic, complemented
3C22×(C127⋊C3)⋊C7C313yesmaximal, direct product factor
4C3×(C127⋊C3)⋊C7C2211yescharacteristic, direct product factor, Hall
5C2×(C127⋊C3)⋊C7C2×C319yesdirect product factor
6C2×C3×C127⋊C7C2×C313yescomplemented
7C22×C3×C127⋊C3C711yesmaximal, characteristic, complemented, Hall
8C22×C127⋊C7C3211yescharacteristic, complemented, Hall
9C3×C127⋊C7C22×C311yescharacteristic, complemented
10(C127⋊C3)⋊C7C22×C313yesdirect product factor
11C2×C3×C127⋊C3C2×C713yescomplemented
12C2×C127⋊C7C2×C3213yescomplemented
13C22×C3×C127C3×C711yescharacteristic, complemented
14C22×C127⋊C3C3×C713yescomplemented
15C3×C127⋊C3C22×C711yescharacteristic, complemented, Hall
16C127⋊C7C22×C3211yescharacteristic, complemented, Hall
17C2×C3×C127C2×C3×C713yescomplemented
18C2×C127⋊C3C2×C3×C719yescomplemented
19C22×C127C32×C711yescharacteristic, complemented, Hall
20C3×C127C22×C3×C711yescharacteristic, complemented
21C127⋊C3C22×C3×C713yescomplemented
22C2×C127C2×C32×C713yescomplemented
23C22×C32×C7—1271nomaximal, Hall
24C127C22×C32×C711yescharacteristic, complemented, Sylow
25C2×C32×C7—1273no—
26C22×C3×C7—1273no—
27C22×C3×C7—1271no—
28C32×C7—1271noHall
29C2×C3×C7—1279no—
30C2×C3×C7—1273no—
31C22×C32—1271noHall
32C22×C7—1271noHall
33C3×C7—1273no—
34C3×C7—1271no—
35C2×C32—1273no—
36C2×C7—1273no—
37C22×C3—1273no—
38C22×C3(C127⋊C3)⋊C711yescharacteristic, direct product factor
39C32—1271noSylow
40C7—1271noSylow
41C2×C3—1279no—
42C2×C3C2×(C127⋊C3)⋊C713yesdirect product factor
43C22C3×(C127⋊C3)⋊C711yescharacteristic, direct product factor, Sylow
44C3—1273no—
45C3C22×(C127⋊C3)⋊C711yescharacteristic, direct product factor
46C2C2×C3×(C127⋊C3)⋊C713yesdirect product factor
subgroupG/H
center, hypercenterC22×C3(C127⋊C3)⋊C7
commutator, cosocle, hypocenterC127C22×C32×C7
FrattiniC1G
Fitting, socleC22×C3×C127C3×C7
LCSG ▷ C127
UCSC1 ◁ C22×C3

Complements

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

NH ≅ G/Ntype
1. C2×C3×(C127⋊C3)⋊C7C2direct (N × H)
2. C22×C3×C127⋊C7C3semidirect
3. C22×(C127⋊C3)⋊C7C3direct (N × H)
4. C3×(C127⋊C3)⋊C7C22direct (N × H)
5. C2×(C127⋊C3)⋊C7C2×C3direct (N × H)
6. C2×C3×C127⋊C7C2×C3semidirect
7. C22×C3×C127⋊C3C7semidirect
8. C22×C127⋊C7C32semidirect
9. C3×C127⋊C7C22×C3semidirect
10. (C127⋊C3)⋊C7C22×C3direct (N × H)
11. C2×C3×C127⋊C3C2×C7semidirect
12. C2×C127⋊C7C2×C32semidirect
13. C22×C3×C127C3×C7semidirect
14. C22×C127⋊C3C3×C7semidirect
15. C3×C127⋊C3C22×C7semidirect
16. C127⋊C7C22×C32semidirect
17. C2×C3×C127C2×C3×C7semidirect
18. C2×C127⋊C3C2×C3×C7semidirect
19. C22×C127C32×C7semidirect
20. C3×C127C22×C3×C7semidirect
21. C127⋊C3C22×C3×C7semidirect
22. C2×C127C2×C32×C7semidirect
24. C127C22×C32×C7semidirect
38. C22×C3(C127⋊C3)⋊C7direct (N × H)
42. C2×C3C2×(C127⋊C3)⋊C7direct (N × H)
43. C22C3×(C127⋊C3)⋊C7direct (N × H)
45. C3C22×(C127⋊C3)⋊C7direct (N × H)
46. C2C2×C3×(C127⋊C3)⋊C7direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×(C127⋊C3)⋊C72
C22×C3×C127⋊C73
C22×(C127⋊C3)⋊C73
C22×C3×C127⋊C37
C22×C32×C7127