Finite Group Databasebeta

← C3×#3753 #88844

Subgroups — C3×#3753 #88844

Order 432.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C33×D4C211yesmaximal, characteristic, complemented
2C3×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
3C3×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
4#3753C311yesmaximal, characteristic, direct product factor
5C3×#213—34nomaximal
6C22×C33—21no—
7C2×C3×C3⋊D3—21no—
8C33×C4C2211yescharacteristic
9C32×D4—24no—
10C32×D4D314yescomplemented
11C32×D4C2×C311yescharacteristic, complemented
12C4⋊(C3⋊D3)C2×C311yescharacteristic, complemented
13C3×D12—34no—
14C3⋊(C3⋊C8)C2×C311yescharacteristic, complemented
15C3×C3⋊C8—34no—
16C2×C33—41no—
17C2×C33D411yescharacteristic
18C3×C3⋊D3—41no—
19C3×D8—91no—
20#213—34no—
21C22×C32—28no—
22C22×C32—24no—
23C22×C32—21no—
24C2×C3⋊D3—21no—
25C2×C3×D3—64no—
26C32×C4—24no—
27C32×C4C2×D314yes—
28C32×C4C22×C311yescharacteristic
29C33D811yescharacteristic, complemented, Sylow
30C3×D4—24no—
31C3×D4—91no—
32C3×D4C3×D314yescomplemented
33C3×D4C3⋊D311yescharacteristic, complemented
34D12—34no—
35C3×C8—91no—
36C3⋊C8—34no—
37C2×C32—24no—
38C2×C32—48no—
39C2×C32—44no—
40C2×C32—41no—
41C2×C32#6714yes—
42C2×C32C3×D411yescharacteristic
43C3⋊D3—41no—
44C3×D3—124no—
45D8—91noSylow
46C22×C3—28no—
47C22×C3—24no—
48C22×C3—21no—
49C22×C3—181no—
50C2×D3—64no—
51C3×C4—24no—
52C3×C4C2×C3×D314yes—
53C3×C4C2×C3⋊D311yescharacteristic
54C32—24no—
55C32#21314yescomplemented
56C32C3×D811yescharacteristic, complemented
57D4—91no—
58D4C3×C3⋊D311yescharacteristic, complemented
59C8—91no—
60C2×C3—24no—
61C2×C3—48no—
62C2×C3—44no—
63C2×C3—41no—
64C2×C3—361no—
65C2×C3C3×#6714yes—
66C2×C3#63811yescharacteristic
67D3—124no—
68C22—21no—
69C22—181no—
70C4C2×C3×C3⋊D311yescharacteristic
71C3—24no—
72C3C3×#21314yescomplemented
73C3#375311yescharacteristic, direct product factor
74C2—41no—
75C2—361no—
76C2C3×#63811yescharacteristic
subgroupG/H
centerC2×C3#638
commutator, cosocleC32×C4C22×C3
FrattiniC4C2×C3×C3⋊D3
FittingC33×D4C2
socleC2×C33D4
hypercenterC3×D4C3⋊D3
hypocenterC32C3×D8
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×D4

Complements

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

NH ≅ G/Ntype
1. C33×D4C2semidirect
2. C3×C4⋊(C3⋊D3)C2semidirect
3. C3×C3⋊(C3⋊C8)C2semidirect
4. #3753C3direct (N × H)
10. C32×D4D3semidirect
11. C32×D4C2×C3semidirect
12. C4⋊(C3⋊D3)C2×C3semidirect
14. C3⋊(C3⋊C8)C2×C3semidirect
29. C33D8semidirect
32. C3×D4C3×D3semidirect
33. C3×D4C3⋊D3semidirect
55. C32#213semidirect
56. C32C3×D8semidirect
58. D4C3×C3⋊D3semidirect
72. C3C3×#213semidirect
73. C3#3753direct (N × H)

Maximal subgroups

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

subgroupindex
C33×D42
C3×C4⋊(C3⋊D3)2
C3×C3⋊(C3⋊C8)2
#37533
C3×#2133