Finite Group Databasebeta

← C2×C3⋊#19153445 #46829426

Subgroups — C2×C3⋊#19153445 #46829426

Order 34596.

268 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#15668332C211yesmaximal, characteristic, complemented
2C3⋊#19153445C212yesmaximal, direct product factor
3C2×C31×D93C311yesmaximal, characteristic, complemented
4C2×#19153445—31nomaximal
5C3×#15668332C2211yescharacteristic, complemented, Hall
6C31×D93C2×C312yescomplemented
7C2×#15668332—21no—
8C2×#15668332D311yescharacteristic, complemented
9#19153445—32no—
10C2×C3×C312C2×C311yescharacteristic, complemented
11C2×C31×D31—31noHall
12C3×C312C22×C311yescharacteristic, complemented
13#15668332—21no—
14#15668332C2×D311yescharacteristic, complemented
15C2×C312C3×D311yescharacteristic, complemented
16C31×D31—32no—
17C2×C3⋊(D31⋊C3)—311nomaximal
18C2×D3×C31⋊C3—311nomaximal
19C312C2×C3×D311yescharacteristic, complemented, Sylow
20C2×C3×C31⋊C3—311no—
21C2×C3×C31⋊C3—311no—
22C2×C3×C31⋊C3—6215no—
23C3⋊(D31⋊C3)—312no—
24D3×C31⋊C3—312no—
25C2×D93C31⋊C311yescharacteristic, complemented
26C2×D3×C31—311no—
27C22×C31⋊C3—931no—
28C2×D31⋊C3—931no—
29C3×C31⋊C3—311no—
30C3×C31⋊C3—311no—
31C3×C31⋊C3—6215no—
32C2×C3×C31—215no—
33C2×C3×C31D31⋊C311yescharacteristic, complemented
34C2×C3×C31C2×C31⋊C311yescharacteristic, complemented
35D93C2×C31⋊C312yescomplemented
36D3×C31—312no—
37C2×C31⋊C3—311no—
38C2×C31⋊C3—311no—
39C2×C31⋊C3—6230no—
40C2×C31⋊C3—621no—
41C2×C31⋊C3—621no—
42C2×C31⋊C3—6215no—
43C2×C31⋊C3—932no—
44D31⋊C3—932no—
45C22×C31—931no—
46C2×D31—31no—
47C3×C31—215no—
48C3×C31C2×D31⋊C311yescharacteristic, complemented
49C3×C31C22×C31⋊C311yescharacteristic, complemented
50C31⋊C3—311no—
51C31⋊C3—311no—
52C31⋊C3—6230no—
53C31⋊C3—621no—
54C31⋊C3—621no—
55C31⋊C3—6215no—
56C2×C31—215no—
57C2×C31—932no—
58C2×C31D3×C31⋊C311yescharacteristic, complemented
59C2×C31C3⋊(D31⋊C3)11yescharacteristic, complemented
60D31—32no—
61C2×C3×D3—9611noHall
62C31—215no—
63C31C2×D3×C31⋊C311yescharacteristic, complemented
64C31C2×C3⋊(D31⋊C3)11yescharacteristic, complemented
65C2×C32—9611no—
66C3×D3—9612no—
67C22×C3—28831no—
68C2×D3—311no—
69C32—9611noSylow
70C2×C3—28832no—
71C2×C3—19221no—
72C2×C3—9611no—
73C2×C3#1915344511yescharacteristic, complemented
74D3—312no—
75C22—931noSylow
76C3—19221no—
77C3—9611no—
78C3C2×#1915344511yescharacteristic, complemented
79C2—932no—
80C2C3⋊#1915344511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2C3⋊#19153445
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×#15668332C2semidirect
2. C3⋊#19153445C2direct (N × H)
3. C2×C31×D93C3semidirect
5. C3×#15668332C22semidirect
6. C31×D93C2×C3semidirect
8. C2×#15668332D3semidirect
10. C2×C3×C312C2×C3semidirect
12. C3×C312C22×C3semidirect
14. #15668332C2×D3semidirect
15. C2×C312C3×D3semidirect
19. C312C2×C3×D3semidirect
25. C2×D93C31⋊C3semidirect
33. C2×C3×C31D31⋊C3semidirect
34. C2×C3×C31C2×C31⋊C3semidirect
35. D93C2×C31⋊C3semidirect
48. C3×C31C2×D31⋊C3semidirect
49. C3×C31C22×C31⋊C3semidirect
58. C2×C31D3×C31⋊C3semidirect
59. C2×C31C3⋊(D31⋊C3)semidirect
63. C31C2×D3×C31⋊C3semidirect
64. C31C2×C3⋊(D31⋊C3)semidirect
73. C2×C3#19153445semidirect
78. C3C2×#19153445semidirect
80. C2C3⋊#19153445direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#156683322
C3⋊#191534452
C2×C31×D933
C2×#191534453
C2×C3⋊(D31⋊C3)31
C2×D3×C31⋊C331