Finite Group Databasebeta

← D51⋊D49 #23756127

Subgroups — D51⋊D49 #23756127

Order 9996.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×D147C211yesmaximal, characteristic, complemented
2C49×D51C211yesmaximal, characteristic, complemented
3C3×D833C211yesmaximal, characteristic, complemented
4D17×D49—31nomaximal, Hall
5C3×C17×C49C2211yescharacteristic, complemented, Hall
6D833D311yescharacteristic, complemented
7D17×C49—31no—
8C17×D49—31no—
9D21⋊D17—71nomaximal
10C17×C49C2×D311yescharacteristic, complemented, Hall
11C17×D21—71no—
12C7×D51D711yescharacteristic
13C3×D119—71no—
14D3×D49—171nomaximal, Hall
15D7×D17—211no—
16C3×C7×C17C2×D711yescharacteristic
17D147D1711yescharacteristic, complemented
18C3×D49—171no—
19D3×C49—171no—
20D119—71no—
21C7×D17—31no—
22D7×C17—211no—
23D3×D17—491noHall
24C2×D49—511noHall
25C3×C49C2×D1711yescharacteristic, complemented, Hall
26C7×C17D3×D711yescharacteristic
27D51D4911yescharacteristic, complemented
28C3×D17—491no—
29D3×C17—491no—
30C2×C49—511no—
31D49—31no—
32D49—171no—
33D3×D7—1191no—
34C2×D17—1471noHall
35C3×C17C2×D4911yescharacteristic, complemented, Hall
36C49D3×D1711yescharacteristic, complemented, Sylow
37D21—71no—
38C3×D7—1191no—
39D3×C7—171no—
40C2×C17—1471no—
41D17—31no—
42D17—491no—
43C2×D7—3571no—
44C3×C7D7×D1711yescharacteristic
45C17D3×D4911yescharacteristic, complemented, Sylow
46C2×C7—511no—
47D7—211no—
48D7—1191no—
49C2×D3—8331noHall
50C7D21⋊D1711yescharacteristic
51C2×C3—8331no—
52D3—171no—
53D3—491no—
54C22—24991noSylow
55C3D17×D4911yescharacteristic, complemented, Sylow
56C2—511no—
57C2—8331no—
58C2—1471no—
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC3×C17×C49C22
FrattiniC7D21⋊D17
socleC3×C7×C17C2×D7
LCSG ▷ C3×C17×C49
UCSC1

Complements

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

NH ≅ G/Ntype
1. C17×D147C2semidirect
2. C49×D51C2semidirect
3. C3×D833C2semidirect
5. C3×C17×C49C22semidirect
6. D833D3semidirect
10. C17×C49C2×D3semidirect
17. D147D17semidirect
25. C3×C49C2×D17semidirect
27. D51D49semidirect
35. C3×C17C2×D49semidirect
36. C49D3×D17semidirect
45. C17D3×D49semidirect
55. C3D17×D49semidirect