Finite Group Databasebeta

← A4×C49×C11⋊C5 #44568348

Subgroups — A4×C49×C11⋊C5 #44568348

Order 32340.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C49×C11⋊C5C311yesmaximal, characteristic, complemented, Hall
2C3×C49×C11⋊C5—41nomaximal, Hall
3C11×A4×C49C511yesmaximal, characteristic, complemented, Hall
4C2×C49×C11⋊C5—31no—
5C7×A4×C11⋊C5C711yesmaximal, characteristic
6C5×A4×C49—111nomaximal, Hall
7C49×C11⋊C5A411yescharacteristic, direct product factor, Hall
8C22×C11×C49C3×C511yescharacteristic, complemented, Hall
9C3×C11×C49—41noHall
10C22×C7×C11⋊C5C3×C711yescharacteristic
11C3×C7×C11⋊C5—41no—
12C2×C11×C49—31no—
13C22×C5×C49—111noHall
14C7×C11×A4C5×C711yescharacteristic
15C2×C7×C11⋊C5—31no—
16C3×C5×C49—441noHall
17A4×C11⋊C5C4911yescharacteristic, direct product factor, Hall
18A4×C49C11⋊C511yescharacteristic, direct product factor, Hall
19C11×C49C5×A411yescharacteristic, complemented, Hall
20C2×C5×C49—331no—
21C5×C7×A4—111no—
22C7×C11⋊C5C7×A411yescharacteristic
23C22×C7×C11C3×C5×C711yescharacteristic
24C5×C49—111noHall
25C3×C7×C11—41no—
26C22×C11⋊C5C3×C4911yescharacteristic, complemented, Hall
27C22×C49C3×C11⋊C511yescharacteristic, complemented, Hall
28C3×C11⋊C5—41noHall
29C2×C7×C11—31no—
30C3×C49—41noHall
31C22×C5×C7—111no—
32C11×A4C5×C4911yescharacteristic, complemented, Hall
33C2×C11⋊C5—31no—
34C3×C5×C7—441no—
35C2×C49—31no—
36C7×A4C7×C11⋊C511yescharacteristic
37C7×C11C5×C7×A411yescharacteristic
38C2×C5×C7—331no—
39C5×A4—111noHall
40C11⋊C5A4×C4911yescharacteristic, direct product factor, Hall
41C49A4×C11⋊C511yescharacteristic, direct product factor, Sylow
42C22×C11C3×C5×C4911yescharacteristic, complemented, Hall
43C5×C7—111no—
44C3×C11—41noHall
45C22×C7C3×C7×C11⋊C511yescharacteristic
46C2×C11—31no—
47C3×C7—41no—
48C22×C5—111noHall
49C3×C5—441noHall
50C2×C7—31no—
51A4C49×C11⋊C511yescharacteristic, direct product factor, Hall
52C11C5×A4×C4911yescharacteristic, complemented, Sylow
53C2×C5—331no—
54C7C7×A4×C11⋊C511yescharacteristic
55C5—111noSylow
56C22C3×C49×C11⋊C511yescharacteristic, complemented, Sylow
57C3—41noSylow
58C2—31no—
subgroupG/H
center, hypercenterC49A4×C11⋊C5
commutator, hypocenterC22×C11C3×C5×C49
FrattiniC7C7×A4×C11⋊C5
FittingC22×C11×C49C3×C5
socle, cosocleC22×C7×C11C3×C5×C7
prime radicalC7×A4×C11⋊C5C7
LCSG ▷ C22×C11
UCSC1 ◁ C49

Complements

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

NH ≅ G/Ntype
1. C22×C49×C11⋊C5C3semidirect
3. C11×A4×C49C5semidirect
7. C49×C11⋊C5A4direct (N × H)
8. C22×C11×C49C3×C5semidirect
17. A4×C11⋊C5C49direct (N × H)
18. A4×C49C11⋊C5direct (N × H)
19. C11×C49C5×A4semidirect
26. C22×C11⋊C5C3×C49semidirect
27. C22×C49C3×C11⋊C5semidirect
32. C11×A4C5×C49semidirect
40. C11⋊C5A4×C49direct (N × H)
41. C49A4×C11⋊C5direct (N × H)
42. C22×C11C3×C5×C49semidirect
51. A4C49×C11⋊C5direct (N × H)
52. C11C5×A4×C49semidirect
56. C22C3×C49×C11⋊C5semidirect

Maximal subgroups

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

subgroupindex
C22×C49×C11⋊C53
C3×C49×C11⋊C54
C11×A4×C495
C7×A4×C11⋊C57
C5×A4×C4911