Finite Group Databasebeta

← C9×(C3⋊D3)⋊C9 #13090612

Subgroups — C9×(C3⋊D3)⋊C9 #13090612

Order 1458.

284 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×C32⋊C9C211yesmaximal, characteristic, complemented, Sylow
2C3×C9×C3⋊D3C311yesmaximal, characteristic
3C3×(C3⋊D3)⋊C9C313yesmaximal
4D3×C92—31nomaximal
5C33×C9C2×C311yescharacteristic
6C3×C32⋊C9C2×C313yes—
7C3×C92—21no—
8C3×C92D311yescharacteristic, complemented
9#6855—23no—
10C32×C3⋊D3C3211yescharacteristic
11C9×C3⋊D3C913yescomplemented
12C3×D3×C9—33no—
13C3×D3×C9—31no—
14C3×D3×C9—91no—
15C2×C92—91no—
16(C3⋊D3)⋊C9C919yesdirect product factor
17C34C2×C3211yescharacteristic
18C32×C9—21no—
19C32×C9—23no—
20C32×C9—23no—
21C32×C9—31no—
22C32×C9—63no—
23C32×C9—61no—
24C32×C9C2×C913yescomplemented
25C32×C9C3×D311yescharacteristic
26C32×C9C3×D313yes—
27C32⋊C9—29no—
28C32⋊C9C2×C919yescomplemented
29C92—31no—
30C92—61no—
31C92—62no—
32C92—61no—
33C3×C3⋊D3C3×C913yes—
34C3×C3⋊D3C3×C911yescharacteristic
35C32×D3—31no—
36C32×D3—91no—
37C2×C3×C9—93no—
38C2×C3×C9—91no—
39D3×C9—33no—
40D3×C9—39no—
41D3×C9—93no—
42C33—23no—
43C33—21no—
44C33—31no—
45C33—61no—
46C33—63no—
47C33C2×C3×C913yes—
48C33C2×C3×C911yescharacteristic
49C33C32×D311yescharacteristic
50C3×C9—21no—
51C3×C9—23no—
52C3×C9—29no—
53C3×C9—23no—
54C3×C9—33no—
55C3×C9—33no—
56C3×C9—66no—
57C3×C9—63no—
58C3×C9—63no—
59C3×C9—66no—
60C3×C9—62no—
61C3×C9—63no—
62C3×C9—61no—
63C3×C9—63no—
64C3×C9D3×C913yes—
65C3×C9D3×C919yescomplemented
66C3×C9(C3⋊D3)⋊C311yescharacteristic
67C2×C32—91no—
68C3⋊D3C9211yescharacteristic, complemented
69C3×D3—31no—
70C3×D3—33no—
71C3×D3—91no—
72C3×D3—93no—
73C2×C9—99no—
74C2×C9—93no—
75C32—21no—
76C32—23no—
77C32—21no—
78C32—23no—
79C32—31no—
80C32—33no—
81C32—63no—
82C32—61no—
83C32—66no—
84C32—62no—
85C32—61no—
86C32—63no—
87C32C2×C9211yescharacteristic, complemented
88C32C3×D3×C911yescharacteristic
89C32C3×D3×C913yes—
90C32C3×(C3⋊D3)⋊C311yescharacteristic
91C9—23no—
92C9—39no—
93C9—63no—
94C9—69no—
95C9(C3⋊D3)⋊C913yesdirect product factor
96C2×C3—91no—
97C2×C3—93no—
98D3—31no—
99D3—91no—
100C3—23no—
101C3—21no—
102C3—31no—
103C3—61no—
104C3—63no—
105C3D3×C9211yescharacteristic
106C3C3×(C3⋊D3)⋊C911yescharacteristic
107C3C9×(C3⋊D3)⋊C313yes—
108C2—91noSylow
subgroupG/H
center, hypercenterC3×C9(C3⋊D3)⋊C3
commutator, hypocenterC32C2×C92
Frattini, socleC33C32×D3
FittingC9×C32⋊C9C2
prime radicalC32×C3⋊D3C32
cosocleC34C2×C32
LCSG ▷ C32
UCSC1 ◁ C3×C9

Complements

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

NH ≅ G/Ntype
1. C9×C32⋊C9C2semidirect
8. C3×C92D3semidirect
11. C9×C3⋊D3C9semidirect
16. (C3⋊D3)⋊C9C9direct (N × H)
24. C32×C9C2×C9semidirect
28. C32⋊C9C2×C9semidirect
65. C3×C9D3×C9semidirect
68. C3⋊D3C92semidirect
87. C32C2×C92semidirect
95. C9(C3⋊D3)⋊C9direct (N × H)

Maximal subgroups

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

subgroupindex
C9×C32⋊C92
C3×C9×C3⋊D33
C3×(C3⋊D3)⋊C93
D3×C923