Finite Group Databasebeta

← C32×C9×D12 #14518877

Subgroups — C32×C9×D12 #14518877

Order 1944.

1244 conjugacy classes of subgroups; only the 450 normal subgroups are shown.

normal subgroups only

This group has 1244 conjugacy classes of subgroups — too many to draw. Only its 450 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
1C2×C32×D3×C9C212yesmaximal, complemented
2C33×C4×C9C211yesmaximal, characteristic, complemented
3C33×D12C311yesmaximal, characteristic
4C32×D4×C9—31nomaximal
5C3×C9×D12C3112yesmaximal, direct product factor
6C2×C33×C9C2211yescharacteristic
7C32×D3×C9—22no—
8C2×C33×D3C2×C312yes—
9C34×C4C2×C311yescharacteristic
10C22×C32×C9—32no—
11C2×C3×D3×C9C2×C3124yescomplemented
12C32×C4×C9—21no—
13C32×C4×C9—212no—
14C32×C4×C9D311yescharacteristic, complemented
15C32×C4×C9C2×C3112yescomplemented
16C33×C9D411yescharacteristic, complemented, Sylow
17C33×D4—31no—
18C32×D12C919yesdirect product factor
19C32×D12C3214yes—
20C3×D4×C9—312no—
21C9×D12C3219yesdirect product factor
22C2×C34C22×C311yescharacteristic
23C33×D3—22no—
24C2×C32×C9—21no—
25C2×C32×C9—212no—
26C2×C32×C9—62no—
27C2×C32×C9C2×D311yescharacteristic
28C2×C32×C9C22×C3112yes—
29C3×D3×C9—224no—
30C22×C33—32no—
31C2×C32×D3C2×C9118yescomplemented
32C2×C32×D3C2×C3218yes—
33C33×C4—29no—
34C33×C4—24no—
35C33×C4C2×C919yescomplemented
36C33×C4C3×D311yescharacteristic
37C33×C4C2×C3214yes—
38C22×C3×C9—324no—
39C2×D3×C9C2×C32118yescomplemented
40C3×C4×C9—212no—
41C3×C4×C9—236no—
42C3×C4×C9C3×D3112yescomplemented
43C3×C4×C9C2×C3219yescomplemented
44C34C3×D411yescharacteristic
45C32×C9—21no—
46C32×C9—212no—
47C32×C9D1211yescharacteristic, direct product factor
48C32×C9C3×D4112yescomplemented
49C32×D4—39no—
50C32×D4—34no—
51C3×D12C3×C9112yesdirect product factor
52C3×D12C3311yescharacteristic
53D4×C9—39no—
54C2×C33—29no—
55C2×C33—24no—
56C2×C33—62no—
57C2×C33C22×C919yes—
58C2×C33C2×C3×D311yescharacteristic
59C2×C33C22×C3214yes—
60C32×D3—218no—
61C32×D3—28no—
62C2×C3×C9—212no—
63C2×C3×C9—236no—
64C2×C3×C9—624no—
65C2×C3×C9C2×C3×D3112yes—
66C2×C3×C9C22×C3219yes—
67D3×C9—218no—
68C22×C32—318no—
69C22×C32—38no—
70C2×C3×D3C2×C3×C9124yescomplemented
71C2×C3×D3C2×C3312yes—
72C32×C4—236no—
73C32×C4—212no—
74C32×C4—24no—
75C32×C4D3×C919yescomplemented
76C32×C4C2×C3×C9112yescomplemented
77C32×C4C32×D314yes—
78C32×C4C2×C3311yescharacteristic
79C22×C9—318no—
80C4×C9—29no—
81C4×C9C32×D319yescomplemented
82C33—29no—
83C33—24no—
84C33D4×C919yescomplemented
85C33C3×D1211yescharacteristic
86C33C32×D414yes—
87C3×C9—212no—
88C3×C9—236no—
89C3×C9C3×D12112yesdirect product factor
90C3×C9C32×D419yescomplemented
91C3×D4—312no—
92C3×D4—31no—
93D12C32×C911yescharacteristic, direct product factor
94C2×C32—236no—
95C2×C32—212no—
96C2×C32—24no—
97C2×C32—618no—
98C2×C32—68no—
99C2×C32C2×D3×C919yes—
100C2×C32C22×C3×C9112yes—
101C2×C32C2×C32×D314yes—
102C2×C32C22×C3311yescharacteristic
103C3×D3—224no—
104C3×D3—22no—
105C2×C9—29no—
106C2×C9—618no—
107C2×C9C2×C32×D319yes—
108C22×C3—324no—
109C22×C3—32no—
110C2×D3C2×C32×C912yescomplemented
111C3×C4—212no—
112C3×C4—21no—
113C3×C4C3×D3×C9112yescomplemented
114C3×C4C2×C32×C911yescharacteristic, complemented
115C3×C4C33×D311yescharacteristic
116C32—24no—
117C32—236no—
118C32—212no—
119C32C9×D1219yesdirect product factor
120C32C3×D4×C9112yescomplemented
121C32C32×D1214yes—
122C32C33×D411yescharacteristic
123C9—29no—
124C9C32×D1219yesdirect product factor
125D4—31noSylow
126C2×C3—212no—
127C2×C3—21no—
128C2×C3—62no—
129C2×C3—624no—
130C2×C3C2×C3×D3×C9112yes—
131C2×C3C22×C32×C911yescharacteristic
132C2×C3C2×C33×D311yescharacteristic
133D3—22no—
134C22—32no—
135C4C32×D3×C911yescharacteristic, complemented
136C3—212no—
137C3—21no—
138C3C3×C9×D12112yesdirect product factor
139C3C32×D4×C911yescharacteristic, complemented
140C3C33×D1211yescharacteristic
141C2—62no—
142C2C2×C32×D3×C911yescharacteristic
subgroupG/H
centerC2×C32×C9C2×D3
commutatorC2×C3C22×C32×C9
FrattiniC2×C3C2×C33×D3
FittingC33×C4×C9C2
socleC2×C34C22×C3
prime radicalC33×D12C3
cosocleC2×C32C22×C33
hypercenterC32×C4×C9D3
hypocenterC3C32×D4×C9
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C32×C9 ◁ C32×C4×C9

Complements

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

NH ≅ G/Ntype
1. C2×C32×D3×C9C2semidirect
2. C33×C4×C9C2semidirect
5. C3×C9×D12C3direct (N × H)
11. C2×C3×D3×C9C2×C3semidirect
14. C32×C4×C9D3semidirect
15. C32×C4×C9C2×C3semidirect
16. C33×C9D4semidirect
18. C32×D12C9direct (N × H)
21. C9×D12C32direct (N × H)
31. C2×C32×D3C2×C9semidirect
35. C33×C4C2×C9semidirect
39. C2×D3×C9C2×C32semidirect
42. C3×C4×C9C3×D3semidirect
43. C3×C4×C9C2×C32semidirect
47. C32×C9D12direct (N × H)
48. C32×C9C3×D4semidirect
51. C3×D12C3×C9direct (N × H)
70. C2×C3×D3C2×C3×C9semidirect
75. C32×C4D3×C9semidirect
76. C32×C4C2×C3×C9semidirect
81. C4×C9C32×D3semidirect
84. C33D4×C9semidirect
89. C3×C9C3×D12direct (N × H)
90. C3×C9C32×D4semidirect
93. D12C32×C9direct (N × H)
110. C2×D3C2×C32×C9semidirect
113. C3×C4C3×D3×C9semidirect
114. C3×C4C2×C32×C9semidirect
119. C32C9×D12direct (N × H)
120. C32C3×D4×C9semidirect
124. C9C32×D12direct (N × H)
135. C4C32×D3×C9semidirect
138. C3C3×C9×D12direct (N × H)
139. C3C32×D4×C9semidirect

Maximal subgroups

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

subgroupindex
C2×C32×D3×C92
C33×C4×C92
C33×D123
C32×D4×C93
C3×C9×D123