Finite Group Databasebeta

← #13091472

Subgroups — #13091472

Order 1458.

443 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 443 conjugacy classes of subgroups — too many to draw. Only its 54 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
1#10624881C211yesmaximal, characteristic, complemented, Sylow
2C3⋊(C3⋊AGL(1,ℤ/9))C311yesmaximal, characteristic, complemented
3C3×C3⋊((C3⋊D3)⋊C3)—31nomaximal
4#92306C313yesmaximal, complemented
5#4169⋊C3—33nomaximal
6C32×3−1+2—21no—
7C32×3−1+2C2×C311yescharacteristic, complemented
8C32×H(3,𝔽3)D311yescharacteristic
9#6893—23no—
10#6893—29no—
11#6893C2×C313yescomplemented
12#6891—23no—
13#6891D313yescomplemented
14C3×C3⋊(C3⋊D3)—31no—
15C32×C3⋊D3—91no—
16C3⋊(C3⋊D9)C3211yescharacteristic, complemented
17C3⋊AGL(1,ℤ/9)—33no—
18C3⋊AGL(1,ℤ/9)—93no—
19C3⋊((C3⋊D3)⋊C3)—33no—
20C3×(C3⋊D3)⋊C3—93no—
21#4169—39no—
22C34—21no—
23C34C3×D311yescharacteristic
24C34C3⋊D311yescharacteristic
25C3×3−1+2—23no—
26C3×3−1+2—23no—
27C3×3−1+2—23no—
28C3×3−1+2—23no—
29C3×3−1+2—33no—
30C3×3−1+2—63no—
31C3×3−1+2—66no—
32C3×3−1+2—63no—
33C3×3−1+2C3×D313yes—
34C3×H(3,𝔽3)—23no—
35C3×H(3,𝔽3)—33no—
36C3×H(3,𝔽3)—63no—
37C3×H(3,𝔽3)C3×D313yes—
38C32×C9—23no—
39C32×C9—21no—
40C32×C9C2×C3211yescharacteristic, complemented
41C32⋊C9—218no—
42C32⋊C9—29no—
43C32⋊C9—29no—
44C32⋊C9C3×D319yescomplemented
45C3⋊(C3⋊D3)—31no—
46C3×C3⋊D3—93no—
47C3×C3⋊D3—91no—
48C3×C3⋊D3—93no—
49C3×C3⋊D3—273no—
50C32×D3—271no—
51C32×D3—273no—
52C3⋊D9—33no—
53C3⋊D9—93no—
54AGL(1,ℤ/9)—273no—
55(C3⋊D3)⋊C3—99no—
56C33—21no—
57C33—23no—
58C33—23no—
59C33—31no—
60C33—61no—
61C33—62no—
62C33—61no—
63C33—93no—
64C33—93no—
65C33—183no—
66C33(C3⋊D3)⋊C313yes—
67C33C32×D311yescharacteristic
68C33C3×C3⋊D311yescharacteristic
69C33C3×C3⋊D313yes—
703−1+2—33no—
713−1+2—69no—
723−1+2—63no—
733−1+2—69no—
743−1+2—66no—
753−1+2—69no—
763−1+2—63no—
77H(3,𝔽3)—39no—
78H(3,𝔽3)—69no—
79C3×C9—23no—
80C3×C9—29no—
81C3×C9—33no—
82C3×C9—69no—
83C3×C9—63no—
84C3×C9C32×D313yes—
85C2×C32—811no—
86C3⋊D3—91no—
87C3⋊D3—93no—
88C3⋊D3—273no—
89C3×D3—273no—
90C3×D3—279no—
91C3×D3—273no—
92C3×D3—271no—
93C3×D3—813no—
94D9—273no—
95C32—23no—
96C32—21no—
97C32—33no—
98C32—33no—
99C32—33no—
100C32—39no—
101C32—63no—
102C32—63no—
103C32—69no—
104C32—93no—
105C32—91no—
106C32—183no—
107C32—181no—
108C32—183no—
109C32—183no—
110C32—186no—
111C32C3×(C3⋊D3)⋊C313yes—
112C32C3⋊((C3⋊D3)⋊C3)11yescharacteristic
113C32C32×C3⋊D311yescharacteristic
114C9—33no—
115C9—63no—
116C9—69no—
117C2×C3—811no—
118C2×C3—813no—
119D3—271no—
120D3—273no—
121D3—813no—
122C3—33no—
123C3—31no—
124C3—61no—
125C3—63no—
126C3—93no—
127C3—183no—
128C3C3×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
129C3#4207⋊C313yes—
130C2—811noSylow
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC32×C9C2×C32
Frattini, socleC32C32×C3⋊D3
Fitting#10624881C2
LCSG ▷ C32×C9
UCSC1

Complements

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

NH ≅ G/Ntype
1. #10624881C2semidirect
2. C3⋊(C3⋊AGL(1,ℤ/9))C3semidirect
4. #92306C3semidirect
7. C32×3−1+2C2×C3semidirect
11. #6893C2×C3semidirect
13. #6891D3semidirect
16. C3⋊(C3⋊D9)C32semidirect
40. C32×C9C2×C32semidirect
44. C32⋊C9C3×D3semidirect

Maximal subgroups

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

subgroupindex
#106248812
C3⋊(C3⋊AGL(1,ℤ/9))3
C3×C3⋊((C3⋊D3)⋊C3)3
#923063
#4169⋊C33