Finite Group Databasebeta

← C27×C7×C27 #72201495

Subgroups — C27×C7×C27 #72201495

Order 24192.

233696 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C26×C7×C27C21127yesmaximal, direct product factor
2C27×C7×C9C311yesmaximal, characteristic
3C25×C7×C27C2212667yesdirect product factor
4C26×C7×C9C2×C31127yes—
5C27×C27C711yesmaximal, characteristic, direct product factor, Hall
6C24×C7×C27C23111811yesdirect product factor
7C27×C3×C7C911yescharacteristic
8C25×C7×C9C22×C312667yes—
9C26×C27C2×C71127yesdirect product factor
10C23×C7×C27C24111811yesdirect product factor
11C26×C3×C7C2×C91127yes—
12C27×C9C3×C711yescharacteristic
13C24×C7×C9C23×C3111811yes—
14C27×C7C2711yescharacteristic, direct product factor, Hall
15C25×C27C22×C712667yesdirect product factor
16C22×C7×C27C2512667yesdirect product factor
17C25×C3×C7C22×C912667yes—
18C26×C9C2×C3×C71127yes—
19C23×C7×C9C24×C3111811yes—
20C26×C7C2×C271127yesdirect product factor
21C24×C27C23×C7111811yesdirect product factor
22C27×C3C7×C911yescharacteristic
23C2×C7×C27C261127yesdirect product factor
24C24×C3×C7C23×C9111811yes—
25C25×C9C22×C3×C712667yes—
26C22×C7×C9C25×C312667yes—
27C25×C7C22×C2712667yesdirect product factor
28C23×C27C24×C7111811yesdirect product factor
29C26×C3C2×C7×C91127yes—
30C7×C27C2711yescharacteristic, direct product factor, Hall
31C23×C3×C7C24×C9111811yes—
32C24×C9C23×C3×C7111811yes—
33C27C7×C2711yescharacteristic, direct product factor, Sylow
34C2×C7×C9C26×C31127yes—
35C24×C7C23×C27111811yesdirect product factor
36C22×C27C25×C712667yesdirect product factor
37C25×C3C22×C7×C912667yes—
38C22×C3×C7C25×C912667yes—
39C23×C9C24×C3×C7111811yes—
40C26C2×C7×C271127yesdirect product factor
41C7×C9C27×C311yescharacteristic
42C23×C7C24×C27111811yesdirect product factor
43C2×C27C26×C71127yesdirect product factor
44C24×C3C23×C7×C9111811yes—
45C2×C3×C7C26×C91127yes—
46C22×C9C25×C3×C712667yes—
47C25C22×C7×C2712667yesdirect product factor
48C22×C7C25×C2712667yesdirect product factor
49C27C27×C711yescharacteristic, direct product factor, Sylow
50C23×C3C24×C7×C9111811yes—
51C3×C7C27×C911yescharacteristic
52C2×C9C26×C3×C71127yes—
53C24C23×C7×C27111811yesdirect product factor
54C2×C7C26×C271127yesdirect product factor
55C22×C3C25×C7×C912667yes—
56C9C27×C3×C711yescharacteristic
57C23C24×C7×C27111811yesdirect product factor
58C7C27×C2711yescharacteristic, direct product factor, Sylow
59C2×C3C26×C7×C91127yes—
60C22C25×C7×C2712667yesdirect product factor
61C3C27×C7×C911yescharacteristic
62C2C26×C7×C271127yesdirect product factor
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC9C27×C3×C7
socle, prime radicalC27×C3×C7C9
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
1. C26×C7×C27C2direct (N × H)
3. C25×C7×C27C22direct (N × H)
5. C27×C27C7direct (N × H)
6. C24×C7×C27C23direct (N × H)
9. C26×C27C2×C7direct (N × H)
10. C23×C7×C27C24direct (N × H)
14. C27×C7C27direct (N × H)
15. C25×C27C22×C7direct (N × H)
16. C22×C7×C27C25direct (N × H)
20. C26×C7C2×C27direct (N × H)
21. C24×C27C23×C7direct (N × H)
23. C2×C7×C27C26direct (N × H)
27. C25×C7C22×C27direct (N × H)
28. C23×C27C24×C7direct (N × H)
30. C7×C27C27direct (N × H)
33. C27C7×C27direct (N × H)
35. C24×C7C23×C27direct (N × H)
36. C22×C27C25×C7direct (N × H)
40. C26C2×C7×C27direct (N × H)
42. C23×C7C24×C27direct (N × H)
43. C2×C27C26×C7direct (N × H)
47. C25C22×C7×C27direct (N × H)
48. C22×C7C25×C27direct (N × H)
49. C27C27×C7direct (N × H)
53. C24C23×C7×C27direct (N × H)
54. C2×C7C26×C27direct (N × H)
57. C23C24×C7×C27direct (N × H)
58. C7C27×C27direct (N × H)
60. C22C25×C7×C27direct (N × H)
62. C2C26×C7×C27direct (N × H)

Maximal subgroups

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

subgroupindex
C26×C7×C272
C27×C7×C93
C27×C277