Finite Group Databasebeta

← C3⋊(C3⋊(((C22⋊C9)⋊C2)⋊C3)) #14519224

Subgroups — C3⋊(C3⋊(((C22⋊C9)⋊C2)⋊C3)) #14519224

Order 1944.

834 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 834 conjugacy classes of subgroups — too many to draw. Only its 114 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
1C32×#1094C211yesmaximal, characteristic, complemented
2C3×#6312—31nomaximal
3C3⋊(C3⋊((C22⋊C9)⋊C2))C311yesmaximal, characteristic, complemented
4C3⋊(((C22⋊C9)⋊C2)⋊C3)—312nomaximal
5C3⋊(C3⋊AGL(1,ℤ/9))—41nomaximal
6C22×C34D311yescharacteristic
7C2×C3×C3⋊(C3⋊D3)—31no—
8C3×C3⋊(C3⋊Dic3)—31no—
9C3×#1094—212no—
10C3×#1094D3112yescomplemented
11C32×C22⋊C9—21no—
12C32×C22⋊C9C2×C311yescharacteristic, complemented
13C32×3−1+2—41noSylow
14#6312—31no—
15C3×#638—99no—
16C3×#638—94no—
17C3⋊((C22⋊C9)⋊C2)—312no—
18((C22⋊C9)⋊C2)⋊C3—99no—
19C2×C34—31no—
20C3×C3⋊(C3⋊D3)—61no—
21C3⋊(C3⋊D9)—41no—
22C3⋊AGL(1,ℤ/9)—1212no—
23C22×C33—24no—
24C22×C33—39no—
25C22×C33C3×D311yescharacteristic
26C22×C33C3⋊D314yes—
27C2×C3⋊(C3⋊D3)—31no—
28C2×C3×C3⋊D3—99no—
29C2×C3×C3⋊D3—94no—
30C3⋊(C3⋊Dic3)—31no—
31C3×C3⋊Dic3—99no—
32C3×C3⋊Dic3—94no—
33#1094—236no—
34#1094C3⋊D319yescomplemented
35C3×C22⋊C9—212no—
36C3×C22⋊C9C3×D3112yescomplemented
37C34S411yescharacteristic
38C3×3−1+2—412no—
39C3×3−1+2—812no—
40C32×C9—41no—
41C32×C9—81no—
42#638—99no—
43#638—94no—
44C3×#67—2712no—
45C3×#67—271no—
46(C22⋊C9)⋊C2—99no—
47C2×C33—31no—
48C2×C33—39no—
49C2×C33—34no—
50C2×C33—64no—
51C2×C33—69no—
52C3⋊(C3⋊D3)—61no—
53C3×C3⋊D3—189no—
54C3×C3⋊D3—184no—
55C3⋊D9—1212no—
56AGL(1,ℤ/9)—369no—
57C22×C32—24no—
58C22×C32—312no—
59C22×C32—612no—
60C22×C32AGL(1,ℤ/9)19yescomplemented
61C22×C32C3×C3⋊D314yes—
62C22×C32C3⋊(C3⋊D3)11yescharacteristic
63C2×C3⋊D3—99no—
64C2×C3⋊D3—94no—
65C2×C3×D3—2712no—
66C2×C3×D3—271no—
67C3⋊Dic3—99no—
68C3⋊Dic3—94no—
69C3×Dic3—2712no—
70C3×Dic3—271no—
71C22⋊C9—29no—
72C22⋊C9C3×C3⋊D319yescomplemented
73C33—24no—
74C33—39no—
75C33C3×S411yescharacteristic
76C33C3⋊S414yes—
773−1+2—49no—
783−1+2—836no—
79C3×C9—412no—
80C3×C9—812no—
81C3×D4—811no—
82#67—2712no—
83#67—271no—
84C2×C32—39no—
85C2×C32—34no—
86C2×C32—312no—
87C2×C32—31no—
88C2×C32—64no—
89C2×C32—612no—
90C2×C32—636no—
91C3⋊D3—189no—
92C3⋊D3—184no—
93C3×D3—5412no—
94C3×D3—541no—
95D9—369no—
96C22×C3—31no—
97C22×C3—64no—
98C22×C3—811no—
99C22×C3C3⋊AGL(1,ℤ/9)112yescomplemented
100C22×C3C3×C3⋊(C3⋊D3)11yescharacteristic
101C2×D3—271no—
102C2×D3—2712no—
103C3×C4—811no—
104Dic3—271no—
105Dic3—2712no—
106C32—24no—
107C32—312no—
108C32—612no—
109C32((C22⋊C9)⋊C2)⋊C319yescomplemented
110C32C3×C3⋊S414yes—
111C32C3⋊(C3⋊S4)11yescharacteristic
112C9—49no—
113C9—89no—
114D4—811noSylow
115C2×C3—31no—
116C2×C3—31no—
117C2×C3—312no—
118C2×C3—61no—
119C2×C3—612no—
120C2×C3—1621no—
121D3—541no—
122D3—5412no—
123C22—811no—
124C22C3⋊(C3⋊AGL(1,ℤ/9))11yescharacteristic, complemented
125C4—811no—
126C3—31no—
127C3—64no—
128C3C3⋊(((C22⋊C9)⋊C2)⋊C3)112yescomplemented
129C3C3×C3⋊(C3⋊S4)11yescharacteristic
130C2—31no—
131C2—1621no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC32×C22⋊C9C2×C3
FrattiniC3C3×C3⋊(C3⋊S4)
FittingC22×C34D3
socleC22×C33C3×D3
LCSG ▷ C32×C22⋊C9
UCSC1

Complements

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

NH ≅ G/Ntype
1. C32×#1094C2semidirect
3. C3⋊(C3⋊((C22⋊C9)⋊C2))C3semidirect
10. C3×#1094D3semidirect
12. C32×C22⋊C9C2×C3semidirect
34. #1094C3⋊D3semidirect
36. C3×C22⋊C9C3×D3semidirect
60. C22×C32AGL(1,ℤ/9)semidirect
72. C22⋊C9C3×C3⋊D3semidirect
99. C22×C3C3⋊AGL(1,ℤ/9)semidirect
109. C32((C22⋊C9)⋊C2)⋊C3semidirect
124. C22C3⋊(C3⋊AGL(1,ℤ/9))semidirect
128. C3C3⋊(((C22⋊C9)⋊C2)⋊C3)semidirect

Maximal subgroups

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

subgroupindex
C32×#10942
C3×#63123
C3⋊(C3⋊((C22⋊C9)⋊C2))3
C3⋊(((C22⋊C9)⋊C2)⋊C3)3
C3⋊(C3⋊AGL(1,ℤ/9))4