Finite Group Databasebeta

← C2×C3⋊((C31⋊C3)⋊D31) #46829423

Subgroups — C2×C3⋊((C31⋊C3)⋊D31) #46829423

Order 34596.

188 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C31×C31⋊C3C211yesmaximal, characteristic, complemented
2C3⋊((C31⋊C3)⋊D31)C212yesmaximal, direct product factor
3C2×C3⋊(C31⋊D31)C311yesmaximal, characteristic, complemented
4C2×(C31⋊C3)⋊D31—31nomaximal
5C3×C31×C31⋊C3C2211yescharacteristic, complemented, Hall
6C3⋊(C31⋊D31)C2×C312yescomplemented
7C2×C31×C31⋊C3—21no—
8C2×C31×C31⋊C3D311yescharacteristic, complemented
9(C31⋊C3)⋊D31—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×D93—311nomaximal
18C2×C3⋊(D31⋊C3)—311nomaximal
19C312C2×C3×D311yescharacteristic, complemented, Sylow
20C2×C32×C31—311no—
21C3×D93—312no—
22C2×C3×C31⋊C3D3111yescharacteristic, complemented
23C3⋊(D31⋊C3)—312no—
24C2×D93—311no—
25C2×D93—311no—
26C2×D93—9310no—
27C2×C3×D31—931no—
28C2×D31⋊C3—931no—
29C32×C31—311no—
30C3×C31⋊C3C2×D3111yescharacteristic, complemented
31C2×C3×C31—310no—
32C2×C3×C31—311no—
33C2×C3×C31—621no—
34C2×C3×C31D31⋊C311yescharacteristic, complemented
35C2×C3×C31C3×D3111yescharacteristic, complemented
36D93—312no—
37D93—312no—
38D93—9320no—
39C3×D31—932no—
40C2×C31⋊C3—21no—
41C2×C31⋊C3D9311yescharacteristic, complemented
42D31⋊C3—932no—
43C2×D31—27910no—
44C2×D31—931no—
45C2×D31—931no—
46C3×C31—310no—
47C3×C31—311no—
48C3×C31—621no—
49C3×C31C2×D31⋊C311yescharacteristic, complemented
50C3×C31C2×C3×D3111yescharacteristic, complemented
51C31⋊C3—21no—
52C31⋊C3C2×D9311yescharacteristic, complemented
53C2×C31—310no—
54C2×C31C3⋊(D31⋊C3)11yescharacteristic, complemented
55C2×C31C3×D9311yescharacteristic, complemented
56D31—27920no—
57D31—932no—
58D31—932no—
59C2×C3×D3—9611noHall
60C31—310no—
61C31C2×C3⋊(D31⋊C3)11yescharacteristic, complemented
62C31C2×C3×D9311yescharacteristic, complemented
63C2×C32—311no—
64C3×D3—9612no—
65C22×C3—28831no—
66C2×D3—9611no—
67C32—311noSylow
68C2×C3—311no—
69C2×C3—621no—
70C2×C3—28832no—
71C2×C3(C31⋊C3)⋊D3111yescharacteristic, complemented
72D3—9612no—
73C22—28831noSylow
74C3—311no—
75C3—621no—
76C3C2×(C31⋊C3)⋊D3111yescharacteristic, complemented
77C2—28832no—
78C2C3⋊((C31⋊C3)⋊D31)11yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2C3⋊((C31⋊C3)⋊D31)
commutator, cosocle, hypocenterC3×C312C22×C3
FrattiniC1G
Fitting, socleC2×C3×C312C2×C3
LCSG ▷ C3×C312
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3×C31×C31⋊C3C2semidirect
2. C3⋊((C31⋊C3)⋊D31)C2direct (N × H)
3. C2×C3⋊(C31⋊D31)C3semidirect
5. C3×C31×C31⋊C3C22semidirect
6. C3⋊(C31⋊D31)C2×C3semidirect
8. C2×C31×C31⋊C3D3semidirect
10. C2×C3×C312C2×C3semidirect
12. C3×C312C22×C3semidirect
14. C31×C31⋊C3C2×D3semidirect
15. C2×C312C3×D3semidirect
19. C312C2×C3×D3semidirect
22. C2×C3×C31⋊C3D31semidirect
30. C3×C31⋊C3C2×D31semidirect
34. C2×C3×C31D31⋊C3semidirect
35. C2×C3×C31C3×D31semidirect
41. C2×C31⋊C3D93semidirect
49. C3×C31C2×D31⋊C3semidirect
50. C3×C31C2×C3×D31semidirect
52. C31⋊C3C2×D93semidirect
54. C2×C31C3⋊(D31⋊C3)semidirect
55. C2×C31C3×D93semidirect
61. C31C2×C3⋊(D31⋊C3)semidirect
62. C31C2×C3×D93semidirect
71. C2×C3(C31⋊C3)⋊D31semidirect
76. C3C2×(C31⋊C3)⋊D31semidirect
78. C2C3⋊((C31⋊C3)⋊D31)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
C3⋊((C31⋊C3)⋊D31)2
C2×C3⋊(C31⋊D31)3
C2×(C31⋊C3)⋊D313
C2×C3×D9331
C2×C3⋊(D31⋊C3)31