Finite Group Databasebeta

← C2×C32×C9×A4 #14519337

Subgroups — C2×C32×C9×A4 #14519337

Order 1944.

1784 conjugacy classes of subgroups; only the 892 normal subgroups are shown.

normal subgroups only

This group has 1784 conjugacy classes of subgroups — too many to draw. Only its 892 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×C9×A4C211yesmaximal, characteristic, direct product factor
2C2×C33×A4C311yesmaximal, characteristic
3C23×C32×C9C311yesmaximal, characteristic, complemented
4C2×C32×C22⋊C9C312yesmaximal, complemented
5C2×C3×C9×A4C3136yesmaximal, direct product factor
6C2×C33×C9—41nomaximal
7C33×A4C2×C311yescharacteristic
8C22×C32×C9—31no—
9C22×C32×C9—31no—
10C22×C32×C9C2×C311yescharacteristic, complemented
11C32×C22⋊C9C2×C312yescomplemented
12C3×C9×A4C2×C3136yesdirect product factor
13C33×C9—41noSylow
14C23×C33C3211yescharacteristic
15C2×C32×A4C9127yesdirect product factor
16C2×C32×A4C32112yes—
17C23×C3×C9C32112yescomplemented
18C2×C3×C22⋊C9C32124yescomplemented
19C2×C9×A4C32181yesdirect product factor
20C2×C34—41no—
21C2×C32×C9—31no—
22C2×C32×C9—31no—
23C2×C32×C9—42no—
24C2×C32×C9—436no—
25C2×C32×C9A411yescharacteristic, direct product factor
26C22×C33—31no—
27C22×C33—31no—
28C22×C33C2×C3211yescharacteristic
29C32×A4C2×C9127yesdirect product factor
30C32×A4C2×C32112yes—
31C22×C3×C9—312no—
32C22×C3×C9—312no—
33C22×C3×C9C2×C32112yescomplemented
34C3×C22⋊C9C2×C32124yescomplemented
35C9×A4C2×C32181yesdirect product factor
36C34—41no—
37C32×C9—42no—
38C32×C9—436no—
39C32×C9C2×A411yescharacteristic, direct product factor
40C23×C32C3×C919yescomplemented
41C23×C32C3314yes—
42C2×C3×A4C3×C91108yesdirect product factor
43C2×C3×A4C3319yes—
44C23×C9C3319yescomplemented
45C2×C22⋊C9C33118yescomplemented
46C2×C33—31no—
47C2×C33—31no—
48C2×C33—427no—
49C2×C33—412no—
50C2×C33C3×A411yescharacteristic
51C2×C3×C9—312no—
52C2×C3×C9—312no—
53C2×C3×C9—424no—
54C2×C3×C9—481no—
55C2×C3×C9C3×A4112yesdirect product factor
56C22×C32—34no—
57C22×C32—39no—
58C22×C32—39no—
59C22×C32—34no—
60C22×C32C2×C3×C919yescomplemented
61C22×C32C2×C3314yes—
62C3×A4C2×C3×C91108yesdirect product factor
63C3×A4C2×C3319yes—
64C22×C9—39no—
65C22×C9—39no—
66C22×C9C2×C3319yescomplemented
67C22⋊C9C2×C33118yescomplemented
68C33—427no—
69C33—412no—
70C33C2×C3×A411yescharacteristic
71C3×C9—424no—
72C3×C9—481no—
73C3×C9C2×C3×A4112yesdirect product factor
74C23×C3C32×C9112yescomplemented
75C23×C3C3411yescharacteristic
76C2×A4C32×C9127yesdirect product factor
77C2×C32—39no—
78C2×C32—39no—
79C2×C32—34no—
80C2×C32—34no—
81C2×C32—4108no—
82C2×C32—49no—
83C2×C32C9×A419yesdirect product factor
84C2×C32C32×A414yes—
85C2×C9—39no—
86C2×C9—39no—
87C2×C9—418no—
88C2×C9C32×A419yesdirect product factor
89C22×C3—312no—
90C22×C3—31no—
91C22×C3—312no—
92C22×C3—31no—
93C22×C3C2×C32×C9112yescomplemented
94C22×C3C2×C3411yescharacteristic
95A4C2×C32×C9127yesdirect product factor
96C32—49no—
97C32—4108no—
98C32C2×C9×A419yesdirect product factor
99C32C2×C32×A414yes—
100C9—418no—
101C9C2×C32×A419yesdirect product factor
102C23C33×C911yescharacteristic, complemented, Sylow
103C2×C3—31no—
104C2×C3—31no—
105C2×C3—312no—
106C2×C3—312no—
107C2×C3—427no—
108C2×C3C3×C9×A4112yesdirect product factor
109C2×C3C33×A411yescharacteristic
110C22—31no—
111C22—31no—
112C22C2×C33×C911yescharacteristic, complemented
113C3—427no—
114C3C2×C3×C9×A4112yesdirect product factor
115C3C2×C33×A411yescharacteristic
116C2—31no—
117C2—31no—
118C2C32×C9×A411yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C32×C9A4
commutator, hypocenterC22C2×C33×C9
FrattiniC3C2×C33×A4
FittingC23×C32×C9C3
socleC23×C33C32
prime radicalC2×C33×A4C3
cosocleC22×C3C2×C34
LCSG ▷ C22
UCSC1 ◁ C2×C32×C9

Complements

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

NH ≅ G/Ntype
1. C32×C9×A4C2direct (N × H)
3. C23×C32×C9C3semidirect
4. C2×C32×C22⋊C9C3semidirect
5. C2×C3×C9×A4C3direct (N × H)
10. C22×C32×C9C2×C3semidirect
11. C32×C22⋊C9C2×C3semidirect
12. C3×C9×A4C2×C3direct (N × H)
15. C2×C32×A4C9direct (N × H)
17. C23×C3×C9C32semidirect
18. C2×C3×C22⋊C9C32semidirect
19. C2×C9×A4C32direct (N × H)
25. C2×C32×C9A4direct (N × H)
29. C32×A4C2×C9direct (N × H)
33. C22×C3×C9C2×C32semidirect
34. C3×C22⋊C9C2×C32semidirect
35. C9×A4C2×C32direct (N × H)
39. C32×C9C2×A4direct (N × H)
40. C23×C32C3×C9semidirect
42. C2×C3×A4C3×C9direct (N × H)
44. C23×C9C33semidirect
45. C2×C22⋊C9C33semidirect
55. C2×C3×C9C3×A4direct (N × H)
60. C22×C32C2×C3×C9semidirect
62. C3×A4C2×C3×C9direct (N × H)
66. C22×C9C2×C33semidirect
67. C22⋊C9C2×C33semidirect
73. C3×C9C2×C3×A4direct (N × H)
74. C23×C3C32×C9semidirect
76. C2×A4C32×C9direct (N × H)
83. C2×C32C9×A4direct (N × H)
88. C2×C9C32×A4direct (N × H)
93. C22×C3C2×C32×C9semidirect
95. A4C2×C32×C9direct (N × H)
98. C32C2×C9×A4direct (N × H)
101. C9C2×C32×A4direct (N × H)
102. C23C33×C9semidirect
108. C2×C3C3×C9×A4direct (N × H)
112. C22C2×C33×C9semidirect
114. C3C2×C3×C9×A4direct (N × H)
118. C2C32×C9×A4direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C9×A42
C2×C33×A43
C23×C32×C93
C2×C32×C22⋊C93
C2×C3×C9×A43
C2×C33×C94