Finite Group Databasebeta

← C23×C4×C7×C137 #72207448

Subgroups — C23×C4×C7×C137 #72207448

Order 30688.

472 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C7×C137C2114yesmaximal, direct product factor
2C24×C7×C137C211yesmaximal, characteristic
3C23×C7×C137C418yesdirect product factor
4C23×C7×C137C2217yes—
5C2×C4×C7×C137C22128yesdirect product factor
6C23×C4×C137C711yesmaximal, characteristic, direct product factor, Hall
7C22×C7×C137C2×C4128yesdirect product factor
8C22×C7×C137C2317yes—
9C4×C7×C137C2318yesdirect product factor
10C24×C137C2×C711yescharacteristic
11C22×C4×C137C2×C7114yesdirect product factor
12C2×C7×C137C22×C4114yesdirect product factor
13C2×C7×C137C2411yescharacteristic
14C23×C137C4×C718yesdirect product factor
15C23×C137C22×C717yes—
16C2×C4×C137C22×C7128yesdirect product factor
17C7×C137C23×C411yescharacteristic, direct product factor, Hall
18C22×C137C2×C4×C7128yesdirect product factor
19C22×C137C23×C717yes—
20C4×C137C23×C718yesdirect product factor
21C2×C137C22×C4×C7114yesdirect product factor
22C2×C137C24×C711yescharacteristic
23C23×C4×C7C13711yesmaximal, characteristic, direct product factor, Hall
24C137C23×C4×C711yescharacteristic, direct product factor, Sylow
25C24×C7C2×C13711yescharacteristic
26C22×C4×C7C2×C137114yesdirect product factor
27C23×C7C4×C13718yesdirect product factor
28C23×C7C22×C13717yes—
29C2×C4×C7C22×C137128yesdirect product factor
30C23×C4C7×C13711yescharacteristic, direct product factor, Sylow
31C22×C7C2×C4×C137128yesdirect product factor
32C22×C7C23×C13717yes—
33C4×C7C23×C13718yesdirect product factor
34C24C2×C7×C13711yescharacteristic
35C22×C4C2×C7×C137114yesdirect product factor
36C2×C7C22×C4×C137114yesdirect product factor
37C2×C7C24×C13711yescharacteristic
38C23C4×C7×C13718yesdirect product factor
39C23C22×C7×C13717yes—
40C2×C4C22×C7×C137128yesdirect product factor
41C7C23×C4×C13711yescharacteristic, direct product factor, Sylow
42C22C2×C4×C7×C137128yesdirect product factor
43C22C23×C7×C13717yes—
44C4C23×C7×C13718yesdirect product factor
45C2C24×C7×C13711yescharacteristic
46C2C22×C4×C7×C137114yesdirect product factor
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C24×C7×C137
socle, prime radicalC24×C7×C137C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C4×C7×C137C2direct (N × H)
3. C23×C7×C137C4direct (N × H)
5. C2×C4×C7×C137C22direct (N × H)
6. C23×C4×C137C7direct (N × H)
7. C22×C7×C137C2×C4direct (N × H)
9. C4×C7×C137C23direct (N × H)
11. C22×C4×C137C2×C7direct (N × H)
12. C2×C7×C137C22×C4direct (N × H)
14. C23×C137C4×C7direct (N × H)
16. C2×C4×C137C22×C7direct (N × H)
17. C7×C137C23×C4direct (N × H)
18. C22×C137C2×C4×C7direct (N × H)
20. C4×C137C23×C7direct (N × H)
21. C2×C137C22×C4×C7direct (N × H)
23. C23×C4×C7C137direct (N × H)
24. C137C23×C4×C7direct (N × H)
26. C22×C4×C7C2×C137direct (N × H)
27. C23×C7C4×C137direct (N × H)
29. C2×C4×C7C22×C137direct (N × H)
30. C23×C4C7×C137direct (N × H)
31. C22×C7C2×C4×C137direct (N × H)
33. C4×C7C23×C137direct (N × H)
35. C22×C4C2×C7×C137direct (N × H)
36. C2×C7C22×C4×C137direct (N × H)
38. C23C4×C7×C137direct (N × H)
40. C2×C4C22×C7×C137direct (N × H)
41. C7C23×C4×C137direct (N × H)
42. C22C2×C4×C7×C137direct (N × H)
44. C4C23×C7×C137direct (N × H)
46. C2C22×C4×C7×C137direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C7×C1372
C24×C7×C1372
C23×C4×C1377
C23×C4×C7137