Finite Group Databasebeta

← C32×D3×D4 #89057

Subgroups — C32×D3×D4 #89057

Order 432.

388 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 150 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×D3C212yesmaximal, complemented
2C33×D4C211yesmaximal, characteristic, complemented
3C32×#67C212yesmaximal, complemented
4C32×D12C211yesmaximal, characteristic, complemented
5C32×C4×D3C211yesmaximal, characteristic, complemented
6C2×C32×D4—31nomaximal
7C3×D3×D4C314yesmaximal, direct product factor
8C22×C33C2212yescomplemented
9C2×C32×D3—24no—
10C2×C32×D3C2211yescharacteristic
11C2×C32×D3C2212yescomplemented
12C33×C4C2211yescharacteristic, complemented
13C32×Dic3C2211yescharacteristic, complemented
14C23×C32—32no—
15C22×C3×D3C2×C318yescomplemented
16C32×D4—24no—
17C32×D4—32no—
18C32×D4—31no—
19C32×D4D311yescharacteristic, direct product factor
20C32×D4C2×C314yescomplemented
21C2×C32×C4—31no—
22C3×#67C2×C318yescomplemented
23C3×D12C2×C314yescomplemented
24C3×C4×D3C2×C314yescomplemented
25C2×C33—22no—
26C2×C33C2311yescharacteristic
27C32×D3—22no—
28C32×D3D412yesdirect product factor
29C2×C3×D4—34no—
30D3×D4C3211yescharacteristic, direct product factor
31C22×C32—28no—
32C22×C32—31no—
33C22×C32—32no—
34C22×C32—64no—
35C22×C32C2×D312yescomplemented
36C22×C32C22×C318yescomplemented
37C2×C3×D3—216no—
38C2×C3×D3C22×C314yes—
39C2×C3×D3C22×C318yescomplemented
40C32×C4—24no—
41C32×C4—31no—
42C32×C4C2×D311yescharacteristic, complemented
43C32×C4C22×C314yescomplemented
44C3×Dic3C22×C314yescomplemented
45C33C2×D411yescharacteristic, complemented, Sylow
46C23×C3—38no—
47C22×D3C2×C3212yescomplemented
48C3×D4—24no—
49C3×D4—38no—
50C3×D4—34no—
51C3×D4C3×D314yesdirect product factor
52C3×D4C2×C3211yescharacteristic, complemented
53C2×C3×C4—34no—
54#67C2×C3212yescomplemented
55D12C2×C3211yescharacteristic, complemented
56C4×D3C2×C3211yescharacteristic, complemented
57C2×C32—22no—
58C2×C32—24no—
59C2×C32—28no—
60C2×C32—32no—
61C2×C32—48no—
62C2×C32—62no—
63C2×C32C22×D311yescharacteristic
64C2×C32C23×C314yes—
65C3×D3—28no—
66C3×D3C3×D418yesdirect product factor
67C2×D4—31noSylow
68C22×C3—28no—
69C22×C3—34no—
70C22×C3—38no—
71C22×C3—616no—
72C22×C3C2×C3×D318yescomplemented
73C22×C3C22×C3212yescomplemented
74C2×D3—24no—
75C2×D3C22×C3211yescharacteristic
76C2×D3C22×C3212yescomplemented
77C3×C4—24no—
78C3×C4—34no—
79C3×C4C2×C3×D314yescomplemented
80C3×C4C22×C3211yescharacteristic, complemented
81Dic3C22×C3211yescharacteristic, complemented
82C32—24no—
83C32D3×D411yescharacteristic, direct product factor
84C32C2×C3×D414yescomplemented
85C23—32no—
86D4—32no—
87D4—31no—
88D4C32×D311yescharacteristic, direct product factor
89C2×C4—31no—
90C2×C3—28no—
91C2×C3—22no—
92C2×C3—24no—
93C2×C3—38no—
94C2×C3—48no—
95C2×C3—68no—
96C2×C3C22×C3×D314yes—
97C2×C3C23×C3211yescharacteristic
98D3—22no—
99D3C32×D412yesdirect product factor
100C22—31no—
101C22—32no—
102C22—64no—
103C22C2×C32×D312yescomplemented
104C4—31no—
105C4C2×C32×D311yescharacteristic, complemented
106C3—24no—
107C3C3×D3×D414yesdirect product factor
108C3C2×C32×D411yescharacteristic, complemented
109C2—22no—
110C2—32no—
111C2—62no—
112C2C22×C32×D311yescharacteristic
subgroupG/H
centerC2×C32C22×D3
commutator, cosocleC2×C3C23×C32
FrattiniC2C22×C32×D3
FittingC33×D4C2
socleC2×C33C23
hypercenterC32×D4D3
hypocenterC3C2×C32×D4
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C32 ◁ C32×D4

Complements

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

NH ≅ G/Ntype
1. C22×C32×D3C2semidirect
2. C33×D4C2semidirect
3. C32×#67C2semidirect
4. C32×D12C2semidirect
5. C32×C4×D3C2semidirect
7. C3×D3×D4C3direct (N × H)
8. C22×C33C22semidirect
11. C2×C32×D3C22semidirect
12. C33×C4C22semidirect
13. C32×Dic3C22semidirect
15. C22×C3×D3C2×C3semidirect
19. C32×D4D3direct (N × H)
20. C32×D4C2×C3semidirect
22. C3×#67C2×C3semidirect
23. C3×D12C2×C3semidirect
24. C3×C4×D3C2×C3semidirect
28. C32×D3D4direct (N × H)
30. D3×D4C32direct (N × H)
35. C22×C32C2×D3semidirect
36. C22×C32C22×C3semidirect
39. C2×C3×D3C22×C3semidirect
42. C32×C4C2×D3semidirect
43. C32×C4C22×C3semidirect
44. C3×Dic3C22×C3semidirect
45. C33C2×D4semidirect
47. C22×D3C2×C32semidirect
51. C3×D4C3×D3direct (N × H)
52. C3×D4C2×C32semidirect
54. #67C2×C32semidirect
55. D12C2×C32semidirect
56. C4×D3C2×C32semidirect
66. C3×D3C3×D4direct (N × H)
72. C22×C3C2×C3×D3semidirect
73. C22×C3C22×C32semidirect
76. C2×D3C22×C32semidirect
79. C3×C4C2×C3×D3semidirect
80. C3×C4C22×C32semidirect
81. Dic3C22×C32semidirect
83. C32D3×D4direct (N × H)
84. C32C2×C3×D4semidirect
88. D4C32×D3direct (N × H)
99. D3C32×D4direct (N × H)
103. C22C2×C32×D3semidirect
105. C4C2×C32×D3semidirect
107. C3C3×D3×D4direct (N × H)
108. C3C2×C32×D4semidirect

Maximal subgroups

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

subgroupindex
C22×C32×D32
C33×D42
C32×#672
C32×D122
C32×C4×D32
C2×C32×D43
C3×D3×D43