Finite Group Databasebeta

← (#19153449⋊C2)⋊C3 #46829375

Subgroups — (#19153449⋊C2)⋊C3 #46829375

Order 34596.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19153449⋊C3C212yesmaximal, complemented
2(C31⋊C3)⋊(D31⋊C3)C211yesmaximal, characteristic, complemented
3#19153449⋊C2C311yesmaximal, characteristic, complemented
4#19153443⋊C2—31nomaximal
5C31⋊C32C2211yescharacteristic, complemented, Hall
6#19153449C2×C312yescomplemented
7(C31⋊C3)⋊D31—21no—
8#19153445—32no—
9#19153444C2×C311yescharacteristic, complemented
10#19153443D311yescharacteristic, complemented
11D312—31noHall
12#15668333C22×C311yescharacteristic, complemented
13#15668332C2×D311yescharacteristic, complemented
14C31×C31⋊C3—21no—
15C31⋊D31C3×D311yescharacteristic, complemented
16C31×D31—32no—
17C312C2×C3×D311yescharacteristic, complemented, Sylow
18C3×D31⋊C3—621no—
19C2×D31⋊C3—932no—
20C3×C31⋊C3—621no—
21C3×D31—621no—
22C2×C31⋊C3—932no—
23D31⋊C3—621no—
24D31⋊C3—621no—
25D31⋊C3—621no—
26D31⋊C3—932no—
27D31⋊C3—932no—
28D31⋊C3—1864no—
29C2×D31—932no—
30C3×C31—621no—
31C31⋊C3—21no—
32C31⋊C3—621no—
33C31⋊C3—621no—
34C31⋊C3—932no—
35C31⋊C3—1864no—
36C2×C31—932no—
37D31—32no—
38D31—621no—
39D31—932no—
40D31—1864no—
41C2×C3×D3—9611nomaximal, Hall
42C31—21no—
43C31—32no—
44C31—64no—
45C2×C32—9611no—
46C3×D3—9612no—
47C22×C3—28831no—
48C2×D3—9611no—
49C32—9611noSylow
50C2×C3—28832no—
51C2×C3—19221no—
52C2×C3—9611no—
53C2×C3—9611no—
54D3—9612no—
55C22—28831noSylow
56C3—621no—
57C3—9611no—
58C3—9611no—
59C2—932no—
60C2—9611no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, cosocle, hypocenter#15668333C22×C3
Fitting, socleC312C2×C3×D3
LCSG ▷ #15668333
UCSC1

Complements

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

NH ≅ G/Ntype
1. #19153449⋊C3C2semidirect
2. (C31⋊C3)⋊(D31⋊C3)C2semidirect
3. #19153449⋊C2C3semidirect
5. C31⋊C32C22semidirect
6. #19153449C2×C3semidirect
9. #19153444C2×C3semidirect
10. #19153443D3semidirect
12. #15668333C22×C3semidirect
13. #15668332C2×D3semidirect
15. C31⋊D31C3×D3semidirect
17. C312C2×C3×D3semidirect

Maximal subgroups

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

subgroupindex
#19153449⋊C32
(C31⋊C3)⋊(D31⋊C3)2
#19153449⋊C23
#19153443⋊C23
C2×C3×D3961