Finite Group Databasebeta

← C2×C3⋊(C3⋊(3−1+2⋊C4)) #14519001

Subgroups — C2×C3⋊(C3⋊(3−1+2⋊C4)) #14519001

Order 1944.

1270 conjugacy classes of subgroups; only the 396 normal subgroups are shown.

normal subgroups only

This group has 1270 conjugacy classes of subgroups — too many to draw. Only its 396 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
1C22×C32×3−1+2C211yesmaximal, characteristic
2C3⋊(C3⋊(3−1+2⋊C4))C212yesmaximal, direct product factor
3C2×C3×C3⋊(C3⋊Dic3)—31nomaximal
4C2×C3⋊(C3⋊Dic9)C311yesmaximal, characteristic, complemented
5C2×C3⋊(3−1+2⋊C4)—312nomaximal
6C2×C32×3−1+2C412yescomplemented
7C2×C32×3−1+2C2211yescharacteristic
8C22×C34D311yescharacteristic
9C3×C3⋊(C3⋊Dic3)—32no—
10C22×C3×3−1+2—212no—
11C22×C3×3−1+2D3112yes—
12C22×C32×C9—21no—
13C22×C32×C9C2×C311yescharacteristic
14C3⋊(C3⋊Dic9)C2×C312yescomplemented
15C3⋊(3−1+2⋊C4)—324no—
16C32×3−1+2C2×C411yescharacteristic, complemented, Sylow
17C2×C3⋊(C3⋊Dic3)—31no—
18C2×C3×C3⋊Dic3—99no—
19C2×C3×C3⋊Dic3—94no—
20C2×C3⋊Dic9—312no—
21C2×3−1+2⋊C4—99no—
22C2×C34Dic312yes—
23C2×C34C2×D311yescharacteristic
24C2×C3×3−1+2—224no—
25C2×C3×3−1+2—212no—
26C2×C3×3−1+2Dic3124yescomplemented
27C2×C3×3−1+2C2×D3112yes—
28C2×C32×C9—22no—
29C2×C32×C9—21no—
30C2×C32×C9C3×C412yescomplemented
31C2×C32×C9C22×C311yescharacteristic
32C22×C33—24no—
33C22×C33—39no—
34C22×C33C3×D311yescharacteristic
35C22×C33C3⋊D314yes—
36C3⋊(C3⋊Dic3)—32no—
37C3×C3⋊Dic3—918no—
38C3×C3⋊Dic3—98no—
39C22×3−1+2—236no—
40C22×3−1+2C3⋊D319yes—
41C22×C3×C9—212no—
42C22×C3×C9C3×D3112yes—
43C3⋊Dic9—324no—
443−1+2⋊C4—918no—
45C34C2×Dic311yescharacteristic
46C3×3−1+2—212no—
47C3×3−1+2C2×Dic3112yescomplemented
48C32×C9—21no—
49C32×C9C2×C3×C411yescharacteristic, complemented
50C2×C3⋊Dic3—99no—
51C2×C3⋊Dic3—94no—
52C2×C3×Dic3—2712no—
53C2×C3×Dic3—271no—
54C2×Dic9—99no—
55C2×C33—28no—
56C2×C33—24no—
57C2×C33—318no—
58C2×C33—39no—
59C2×C33C3×Dic312yes—
60C2×C33C3⋊Dic318yes—
61C2×C33C2×C3×D311yescharacteristic
62C2×C33C2×C3⋊D314yes—
63C2×3−1+2—272no—
64C2×3−1+2—236no—
65C2×3−1+2C3⋊Dic3118yescomplemented
66C2×3−1+2C2×C3⋊D319yes—
67C2×C3×C9—224no—
68C2×C3×C9—212no—
69C2×C3×C9C3×Dic3124yescomplemented
70C2×C3×C9C2×C3×D3112yes—
71C22×C32—24no—
72C22×C32—312no—
73C22×C32—612no—
74C22×C32AGL(1,ℤ/9)19yes—
75C22×C32C3×C3⋊D314yes—
76C22×C32C3⋊(C3⋊D3)11yescharacteristic
77C3⋊Dic3—918no—
78C3⋊Dic3—98no—
79C3×Dic3—2724no—
80C3×Dic3—272no—
81C22×C9—29no—
82C22×C9C3×C3⋊D319yes—
83Dic9—918no—
84C33—24no—
85C33—39no—
86C33C2×C3×Dic311yescharacteristic
87C33C2×C3⋊Dic314yes—
883−1+2—236no—
893−1+2C2×C3⋊Dic319yescomplemented
90C3×C9—212no—
91C3×C9C2×C3×Dic3112yescomplemented
92C2×C3×C4—811no—
93C2×Dic3—2712no—
94C2×Dic3—271no—
95C2×C32—28no—
96C2×C32—24no—
97C2×C32—324no—
98C2×C32—312no—
99C2×C32—624no—
100C2×C32—612no—
101C2×C323−1+2⋊C4118yescomplemented
102C2×C32C2×AGL(1,ℤ/9)19yes—
103C2×C32C3×C3⋊Dic318yes—
104C2×C32C3⋊(C3⋊Dic3)12yes—
105C2×C32C2×C3×C3⋊D314yes—
106C2×C32C2×C3⋊(C3⋊D3)11yescharacteristic
107C2×C9—218no—
108C2×C9—29no—
109C2×C9C3×C3⋊Dic3118yescomplemented
110C2×C9C2×C3×C3⋊D319yes—
111C22×C3—31no—
112C22×C3—64no—
113C22×C3C3⋊AGL(1,ℤ/9)112yes—
114C22×C3C3×C3⋊(C3⋊D3)11yescharacteristic
115C3×C4—812no—
116Dic3—2724no—
117Dic3—272no—
118C32—24no—
119C32—312no—
120C32—612no—
121C32C2×3−1+2⋊C419yescomplemented
122C32C2×C3×C3⋊Dic314yes—
123C32C2×C3⋊(C3⋊Dic3)11yescharacteristic
124C9—29no—
125C9C2×C3×C3⋊Dic319yescomplemented
126C2×C4—811noSylow
127C2×C3—31no—
128C2×C3—32no—
129C2×C3—64no—
130C2×C3—68no—
131C2×C3C3⋊(3−1+2⋊C4)124yescomplemented
132C2×C3C2×C3⋊AGL(1,ℤ/9)112yes—
133C2×C3C3×C3⋊(C3⋊Dic3)12yes—
134C2×C3C2×C3×C3⋊(C3⋊D3)11yescharacteristic
135C22C3⋊(C3⋊AGL(1,ℤ/9))11yescharacteristic
136C4—812no—
137C3—31no—
138C3—64no—
139C3C2×C3⋊(3−1+2⋊C4)112yescomplemented
140C3C2×C3×C3⋊(C3⋊Dic3)11yescharacteristic
141C2C3⋊(C3⋊(3−1+2⋊C4))12yesdirect product factor
142C2C2×C3⋊(C3⋊AGL(1,ℤ/9))11yescharacteristic
subgroupG/H
center, hypercenterC22C3⋊(C3⋊AGL(1,ℤ/9))
commutator, hypocenterC32×C9C2×C3×C4
FrattiniC2×C3C2×C3×C3⋊(C3⋊D3)
FittingC22×C32×3−1+2C2
socleC22×C33C3×D3
prime radicalC22×C34D3
cosocleC2×C32×C9C22×C3
LCSG ▷ C32×C9
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
2. C3⋊(C3⋊(3−1+2⋊C4))C2direct (N × H)
4. C2×C3⋊(C3⋊Dic9)C3semidirect
6. C2×C32×3−1+2C4semidirect
14. C3⋊(C3⋊Dic9)C2×C3semidirect
16. C32×3−1+2C2×C4semidirect
26. C2×C3×3−1+2Dic3semidirect
30. C2×C32×C9C3×C4semidirect
47. C3×3−1+2C2×Dic3semidirect
49. C32×C9C2×C3×C4semidirect
65. C2×3−1+2C3⋊Dic3semidirect
69. C2×C3×C9C3×Dic3semidirect
89. 3−1+2C2×C3⋊Dic3semidirect
91. C3×C9C2×C3×Dic3semidirect
101. C2×C323−1+2⋊C4semidirect
109. C2×C9C3×C3⋊Dic3semidirect
121. C32C2×3−1+2⋊C4semidirect
125. C9C2×C3×C3⋊Dic3semidirect
131. C2×C3C3⋊(3−1+2⋊C4)semidirect
139. C3C2×C3⋊(3−1+2⋊C4)semidirect
141. C2C3⋊(C3⋊(3−1+2⋊C4))direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C32×3−1+22
C3⋊(C3⋊(3−1+2⋊C4))2
C2×C3×C3⋊(C3⋊Dic3)3
C2×C3⋊(C3⋊Dic9)3
C2×C3⋊(3−1+2⋊C4)3