Finite Group Databasebeta

← C24×C3×C4×C109 #72198525

Subgroups — C24×C3×C4×C109 #72198525

Order 20928.

2724 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C4×C109C2130yesmaximal, direct product factor
2C25×C3×C109C211yesmaximal, characteristic
3C24×C3×C109C4116yesdirect product factor
4C24×C3×C109C22115yes—
5C22×C3×C4×C109C221140yesdirect product factor
6C23×C3×C109C2×C41120yesdirect product factor
7C23×C3×C109C23135yes—
8C2×C3×C4×C109C231120yesdirect product factor
9C24×C4×C109C311yesmaximal, characteristic, direct product factor, Hall
10C25×C109C2×C311yescharacteristic
11C23×C4×C109C2×C3130yesdirect product factor
12C24×C109C3×C4116yesdirect product factor
13C24×C109C22×C3115yes—
14C22×C4×C109C22×C31140yesdirect product factor
15C22×C3×C109C22×C41140yesdirect product factor
16C22×C3×C109C24115yes—
17C3×C4×C109C24116yesdirect product factor
18C23×C109C2×C3×C41120yesdirect product factor
19C23×C109C23×C3135yes—
20C2×C4×C109C23×C31120yesdirect product factor
21C2×C3×C109C23×C4130yesdirect product factor
22C2×C3×C109C2511yescharacteristic
23C22×C109C22×C3×C41140yesdirect product factor
24C22×C109C24×C3115yes—
25C4×C109C24×C3116yesdirect product factor
26C3×C109C24×C411yescharacteristic, direct product factor, Hall
27C2×C109C23×C3×C4130yesdirect product factor
28C2×C109C25×C311yescharacteristic
29C24×C3×C4C10911yesmaximal, characteristic, direct product factor, Hall
30C109C24×C3×C411yescharacteristic, direct product factor, Sylow
31C25×C3C2×C10911yescharacteristic
32C23×C3×C4C2×C109130yesdirect product factor
33C24×C4C3×C10911yescharacteristic, direct product factor, Sylow
34C24×C3C4×C109116yesdirect product factor
35C24×C3C22×C109115yes—
36C22×C3×C4C22×C1091140yesdirect product factor
37C25C2×C3×C10911yescharacteristic
38C23×C4C2×C3×C109130yesdirect product factor
39C23×C3C2×C4×C1091120yesdirect product factor
40C23×C3C23×C109135yes—
41C2×C3×C4C23×C1091120yesdirect product factor
42C24C3×C4×C109116yesdirect product factor
43C24C22×C3×C109115yes—
44C22×C4C22×C3×C1091140yesdirect product factor
45C22×C3C22×C4×C1091140yesdirect product factor
46C22×C3C24×C109115yes—
47C3×C4C24×C109116yesdirect product factor
48C23C2×C3×C4×C1091120yesdirect product factor
49C23C23×C3×C109135yes—
50C2×C4C23×C3×C1091120yesdirect product factor
51C2×C3C23×C4×C109130yesdirect product factor
52C2×C3C25×C10911yescharacteristic
53C22C22×C3×C4×C1091140yesdirect product factor
54C22C24×C3×C109115yes—
55C4C24×C3×C109116yesdirect product factor
56C3C24×C4×C10911yescharacteristic, direct product factor, Sylow
57C2C25×C3×C10911yescharacteristic
58C2C23×C3×C4×C109130yesdirect product factor
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C25×C3×C109
socle, prime radicalC25×C3×C109C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×C3×C4×C109C2direct (N × H)
3. C24×C3×C109C4direct (N × H)
5. C22×C3×C4×C109C22direct (N × H)
6. C23×C3×C109C2×C4direct (N × H)
8. C2×C3×C4×C109C23direct (N × H)
9. C24×C4×C109C3direct (N × H)
11. C23×C4×C109C2×C3direct (N × H)
12. C24×C109C3×C4direct (N × H)
14. C22×C4×C109C22×C3direct (N × H)
15. C22×C3×C109C22×C4direct (N × H)
17. C3×C4×C109C24direct (N × H)
18. C23×C109C2×C3×C4direct (N × H)
20. C2×C4×C109C23×C3direct (N × H)
21. C2×C3×C109C23×C4direct (N × H)
23. C22×C109C22×C3×C4direct (N × H)
25. C4×C109C24×C3direct (N × H)
26. C3×C109C24×C4direct (N × H)
27. C2×C109C23×C3×C4direct (N × H)
29. C24×C3×C4C109direct (N × H)
30. C109C24×C3×C4direct (N × H)
32. C23×C3×C4C2×C109direct (N × H)
33. C24×C4C3×C109direct (N × H)
34. C24×C3C4×C109direct (N × H)
36. C22×C3×C4C22×C109direct (N × H)
38. C23×C4C2×C3×C109direct (N × H)
39. C23×C3C2×C4×C109direct (N × H)
41. C2×C3×C4C23×C109direct (N × H)
42. C24C3×C4×C109direct (N × H)
44. C22×C4C22×C3×C109direct (N × H)
45. C22×C3C22×C4×C109direct (N × H)
47. C3×C4C24×C109direct (N × H)
48. C23C2×C3×C4×C109direct (N × H)
50. C2×C4C23×C3×C109direct (N × H)
51. C2×C3C23×C4×C109direct (N × H)
53. C22C22×C3×C4×C109direct (N × H)
55. C4C24×C3×C109direct (N × H)
56. C3C24×C4×C109direct (N × H)
58. C2C23×C3×C4×C109direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C4×C1092
C25×C3×C1092
C24×C4×C1093
C24×C3×C4109