Finite Group Databasebeta

← C2×C31×C3⋊(D31⋊C3) #46829422

Subgroups — C2×C31×C3⋊(D31⋊C3) #46829422

Order 34596.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C31×C31⋊C3C211yesmaximal, characteristic, complemented
2C31×C3⋊(D31⋊C3)C212yesmaximal, direct product factor
3C2×C31×D93C311yesmaximal, characteristic, complemented
4C2×C31×D31⋊C3—31nomaximal
5C3×C31×C31⋊C3C2211yescharacteristic, complemented, Hall
6C31×D93C2×C312yescomplemented
7C2×C31×C31⋊C3—21no—
8C2×C31×C31⋊C3D311yescharacteristic, complemented
9C31×D31⋊C3—32no—
10C2×C3×C312C2×C311yescharacteristic, complemented
11C2×C31×D31—31noHall
12C3×C312C22×C311yescharacteristic, complemented
13C31×C31⋊C3—21no—
14C31×C31⋊C3C2×D311yescharacteristic, complemented
15C2×C312C3×D311yescharacteristic, complemented
16C31×D31—32no—
17C2×C3×D3×C31—311nomaximal
18C2×C3⋊(D31⋊C3)C3111yesmaximal, characteristic, direct product factor
19C312C2×C3×D311yescharacteristic, complemented, Sylow
20C2×C32×C31—311no—
21C3×D3×C31—312no—
22C2×C3×C31⋊C3C2×C3111yescharacteristic, complemented
23C3⋊(D31⋊C3)C2×C3112yesdirect product factor
24C22×C3×C31—931no—
25C2×D93C3×C3111yescharacteristic, complemented
26C2×D3×C31—311no—
27C2×D31⋊C3—31no—
28C32×C31—311no—
29C3×C31⋊C3C22×C3111yescharacteristic, complemented
30C2×C3×C31—65no—
31C2×C3×C31—311no—
32C2×C3×C31—621no—
33C2×C3×C31—932no—
34C2×C3×C31D31⋊C311yescharacteristic, complemented
35C2×C3×C31C2×C3×C3111yescharacteristic, complemented
36D93C2×C3×C3112yescomplemented
37D3×C31—312no—
38C2×C31⋊C3—21no—
39C2×C31⋊C3D3×C3111yescharacteristic, complemented
40D31⋊C3—32no—
41C22×C31—931no—
42C2×D31—31no—
43C3×C31—65no—
44C3×C31—311no—
45C3×C31—621no—
46C3×C31C2×D31⋊C311yescharacteristic, complemented
47C3×C31C22×C3×C3111yescharacteristic, complemented
48C31⋊C3—21no—
49C31⋊C3C2×D3×C3111yescharacteristic, complemented
50C2×C31—65no—
51C2×C31—932no—
52C2×C31C3⋊(D31⋊C3)11yescharacteristic, direct product factor
53C2×C31C3×D3×C3111yescharacteristic, complemented
54D31—32no—
55C2×C3×D3—311noHall
56C31—65no—
57C31C2×C3⋊(D31⋊C3)11yescharacteristic, direct product factor
58C31C2×C3×D3×C3111yescharacteristic, complemented
59C2×C32—311no—
60C3×D3—312no—
61C22×C3—931no—
62C2×D3—311no—
63C32—311noSylow
64C2×C3—311no—
65C2×C3—621no—
66C2×C3—932no—
67C2×C3C31×D31⋊C311yescharacteristic, complemented
68D3—312no—
69C22—931noSylow
70C3—311no—
71C3—621no—
72C3C2×C31×D31⋊C311yescharacteristic, complemented
73C2—932no—
74C2C31×C3⋊(D31⋊C3)11yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C31C3⋊(D31⋊C3)
commutator, cosocle, hypocenterC3×C31C22×C3×C31
FrattiniC1G
Fitting, socleC2×C3×C312C2×C3
LCSG ▷ C3×C31
UCSC1 ◁ C2×C31

Complements

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

NH ≅ G/Ntype
1. C2×C3×C31×C31⋊C3C2semidirect
2. C31×C3⋊(D31⋊C3)C2direct (N × H)
3. C2×C31×D93C3semidirect
5. C3×C31×C31⋊C3C22semidirect
6. C31×D93C2×C3semidirect
8. C2×C31×C31⋊C3D3semidirect
10. C2×C3×C312C2×C3semidirect
12. C3×C312C22×C3semidirect
14. C31×C31⋊C3C2×D3semidirect
15. C2×C312C3×D3semidirect
18. C2×C3⋊(D31⋊C3)C31direct (N × H)
19. C312C2×C3×D3semidirect
22. C2×C3×C31⋊C3C2×C31semidirect
23. C3⋊(D31⋊C3)C2×C31direct (N × H)
25. C2×D93C3×C31semidirect
29. C3×C31⋊C3C22×C31semidirect
34. C2×C3×C31D31⋊C3semidirect
35. C2×C3×C31C2×C3×C31semidirect
36. D93C2×C3×C31semidirect
39. C2×C31⋊C3D3×C31semidirect
46. C3×C31C2×D31⋊C3semidirect
47. C3×C31C22×C3×C31semidirect
49. C31⋊C3C2×D3×C31semidirect
52. C2×C31C3⋊(D31⋊C3)direct (N × H)
53. C2×C31C3×D3×C31semidirect
57. C31C2×C3⋊(D31⋊C3)direct (N × H)
58. C31C2×C3×D3×C31semidirect
67. C2×C3C31×D31⋊C3semidirect
72. C3C2×C31×D31⋊C3semidirect
74. C2C31×C3⋊(D31⋊C3)direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C31×C31⋊C32
C31×C3⋊(D31⋊C3)2
C2×C31×D933
C2×C31×D31⋊C33
C2×C3×D3×C3131
C2×C3⋊(D31⋊C3)31