Finite Group Databasebeta

← #13091471

Subgroups — #13091471

Order 1458.

551 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 551 conjugacy classes of subgroups — too many to draw. Only its 66 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
2C32×AGL(1,ℤ/9)—33nomaximal
3C32×(C3⋊D3)⋊C3—31nomaximal
4#92304C313yesmaximal, complemented
5#92302C311yesmaximal, characteristic, complemented
6C32×3−1+2D313yescomplemented
7C32×H(3,𝔽3)D311yescharacteristic
8#6893—26no—
9#6893—23no—
10#6893—23no—
11#6893C2×C313yescomplemented
12#6891—21no—
13#6891—23no—
14#6891C2×C311yescharacteristic, complemented
15C32×C3⋊D3—31no—
16C33×D3—91no—
17C3×AGL(1,ℤ/9)—327no—
18C3×AGL(1,ℤ/9)—33no—
19C3×AGL(1,ℤ/9)—36no—
20C3×(C3⋊D3)⋊C3—39no—
21C3×(C3⋊D3)⋊C3—33no—
22C32×D9—33no—
23#4181C3211yescharacteristic, complemented
24C34—21no—
25C34C3×D311yescharacteristic
26C34C3⋊D311yescharacteristic
27C3×3−1+2—23no—
28C3×3−1+2—26no—
29C3×3−1+2—327no—
30C3×3−1+2C3×D313yes—
31C3×3−1+2C3×D316yescomplemented
32C3×H(3,𝔽3)—23no—
33C3×H(3,𝔽3)—39no—
34C3×H(3,𝔽3)C3×D313yes—
35C32×C9—23no—
36C32×C9C3×D313yescomplemented
37C32⋊C9—29no—
38C32⋊C9—26no—
39C32⋊C9—23no—
40C32⋊C9—22no—
41C32⋊C9—23no—
42C32⋊C9—21no—
43C32⋊C9—23no—
44C32⋊C9—21no—
45C32⋊C9—23no—
46C32⋊C9—26no—
47C32⋊C9—23no—
48C32⋊C9C2×C3211yescharacteristic, complemented
49C2×C33—271no—
50C3×C3⋊D3—33no—
51C3×C3⋊D3—31no—
52C32×D3—99no—
53C32×D3—93no—
54C32×D3—91no—
55C32×D3—271no—
56AGL(1,ℤ/9)—318no—
57AGL(1,ℤ/9)—39no—
58(C3⋊D3)⋊C3—39no—
59C3×D9—39no—
60C3×D9—33no—
61C33—21no—
62C33—23no—
63C33—33no—
64C33—63no—
65C33—91no—
66C33—91no—
67C33—181no—
68C33—181no—
69C33—181no—
70C33—182no—
71C33#27219yes—
72C33C32×D311yescharacteristic
73C33C3×C3⋊D313yes—
74C33C3×C3⋊D311yescharacteristic
753−1+2—39no—
763−1+2—318no—
773−1+2—618no—
783−1+2—69no—
79H(3,𝔽3)—39no—
80H(3,𝔽3)—69no—
81C3×C9—23no—
82C3×C9—26no—
83C3×C9—23no—
84C3×C9—39no—
85C3×C9—69no—
86C3×C9C32×D313yes—
87C2×C32—271no—
88C2×C32—273no—
89C2×C32—279no—
90C3⋊D3—31no—
91C3×D3—99no—
92C3×D3—93no—
93C3×D3—91no—
94C3×D3—271no—
95C3×D3—273no—
96D9—33no—
97C32—31no—
98C32—33no—
99C32—31no—
100C32—31no—
101C32—61no—
102C32—63no—
103C32—61no—
104C32—62no—
105C32—66no—
106C32—63no—
107C32—61no—
108C32—61no—
109C32—63no—
110C32—99no—
111C32—93no—
112C32—183no—
113C32—189no—
114C32C3×#27219yes—
115C32C3×#27213yes—
116C32C32×C3⋊D311yescharacteristic
117C9—33no—
118C9—63no—
119C9—63no—
120C9—66no—
121C2×C3—273no—
122C2×C3—279no—
123C2×C3—271no—
124D3—91no—
125D3—271no—
126C3—21no—
127C3—33no—
128C3—39no—
129C3—91no—
130C3—181no—
131C3—183no—
132C3C32×#27211yescharacteristic
133C3#4207⋊C311yescharacteristic
134C2—271noSylow
subgroupG/H
center, hypercenterC3#4207⋊C3
commutator, cosocle, hypocenterC32⋊C9C2×C32
Frattini, socleC32C32×C3⋊D3
Fitting#10624881C2
LCSG ▷ C32⋊C9
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. #10624881C2semidirect
4. #92304C3semidirect
5. #92302C3semidirect
6. C32×3−1+2D3semidirect
11. #6893C2×C3semidirect
14. #6891C2×C3semidirect
23. #4181C32semidirect
31. C3×3−1+2C3×D3semidirect
36. C32×C9C3×D3semidirect
48. C32⋊C9C2×C32semidirect

Maximal subgroups

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

subgroupindex
#106248812
C32×AGL(1,ℤ/9)3
C32×(C3⋊D3)⋊C33
#923043
#923023