Finite Group Databasebeta

← C22×C3×D32 #89120

Subgroups — C22×C3×D32 #89120

Order 432.

642 conjugacy classes of subgroups; only the 208 normal subgroups are shown.

normal subgroups only

This group has 642 conjugacy classes of subgroups — too many to draw. Only its 208 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×C3×C3⋊D3C211yesmaximal, characteristic, complemented
2C22×C32×D3C212yesmaximal, complemented
3C2×C3×D32C2112yesmaximal, direct product factor
4C23×C3×D3—32nomaximal
5C22×D32C311yesmaximal, characteristic, direct product factor
6C22×C33C2211yescharacteristic, complemented
7C2×C3×C3⋊D3C2216yescomplemented
8C2×C32×D3C22112yescomplemented
9C3×D32C22116yesdirect product factor
10C23×C32—32no—
11C22×C3⋊D3C2×C311yescharacteristic, complemented
12C22×C3×D3—22no—
13C22×C3×D3—32no—
14C22×C3×D3—324no—
15C22×C3×D3—61no—
16C22×C3×D3D312yesdirect product factor
17C22×C3×D3C2×C312yescomplemented
18C2×D32C2×C3112yesdirect product factor
19C2×C33C2313yescomplemented
20C3×C3⋊D3C2314yescomplemented
21C32×D3C2318yescomplemented
22C24×C3—91no—
23C23×D3—32no—
24C22×C32—21no—
25C22×C32—22no—
26C22×C32—312no—
27C22×C32—41no—
28C22×C32C2×D312yescomplemented
29C22×C32C22×C311yescharacteristic, complemented
30C2×C3⋊D3C22×C316yescomplemented
31C2×C3×D3—212no—
32C2×C3×D3—312no—
33C2×C3×D3—332no—
34C2×C3×D3—66no—
35C2×C3×D3C2×D3112yesdirect product factor
36C2×C3×D3C22×C3112yescomplemented
37D32C22×C3116yesdirect product factor
38C33C2411yescharacteristic, complemented, Sylow
39C23×C3—32no—
40C23×C3—32no—
41C23×C3—62no—
42C23×C3—912no—
43C23×C3—91no—
44C22×D3—32no—
45C22×D3—324no—
46C22×D3—61no—
47C22×D3C3×D312yesdirect product factor
48C2×C32—23no—
49C2×C32—26no—
50C2×C32—38no—
51C2×C32—43no—
52C2×C32C22×D316yescomplemented
53C2×C32C23×C313yescomplemented
54C3⋊D3C23×C314yescomplemented
55C3×D3—28no—
56C3×D3—38no—
57C3×D3—64no—
58C3×D3C22×D318yesdirect product factor
59C3×D3C23×C318yescomplemented
60C24—91noSylow
61C22×C3—21no—
62C22×C3—22no—
63C22×C3—312no—
64C22×C3—312no—
65C22×C3—41no—
66C22×C3—612no—
67C22×C3—916no—
68C22×C3—96no—
69C22×C3D3211yescharacteristic, direct product factor
70C22×C3C2×C3×D312yescomplemented
71C2×D3—312no—
72C2×D3—332no—
73C2×D3—66no—
74C2×D3C2×C3×D3112yesdirect product factor
75C32—21no—
76C32—22no—
77C32—41no—
78C32C23×D312yescomplemented
79C32C24×C311yescharacteristic, complemented
80C23—32no—
81C23—912no—
82C23—91no—
83C2×C3—23no—
84C2×C3—26no—
85C2×C3—38no—
86C2×C3—38no—
87C2×C3—43no—
88C2×C3—68no—
89C2×C3—94no—
90C2×C3C2×D3213yesdirect product factor
91C2×C3C22×C3×D316yescomplemented
92D3—38no—
93D3—64no—
94D3C22×C3×D318yesdirect product factor
95C22—312no—
96C22—916no—
97C22—96no—
98C22C3×D3211yescharacteristic, direct product factor
99C3—21no—
100C3—22no—
101C3—41no—
102C3C22×D3211yescharacteristic, direct product factor
103C3C23×C3×D312yescomplemented
104C2—38no—
105C2—94no—
106C2C2×C3×D3213yesdirect product factor
subgroupG/H
center, hypercenterC22×C3D32
commutator, cosocle, hypocenterC32C24×C3
FrattiniC1G
Fitting, socleC22×C33C22
LCSG ▷ C32
UCSC1 ◁ C22×C3

Complements

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

NH ≅ G/Ntype
1. C22×C3×C3⋊D3C2semidirect
2. C22×C32×D3C2semidirect
3. C2×C3×D32C2direct (N × H)
5. C22×D32C3direct (N × H)
6. C22×C33C22semidirect
7. C2×C3×C3⋊D3C22semidirect
8. C2×C32×D3C22semidirect
9. C3×D32C22direct (N × H)
11. C22×C3⋊D3C2×C3semidirect
16. C22×C3×D3D3direct (N × H)
17. C22×C3×D3C2×C3semidirect
18. C2×D32C2×C3direct (N × H)
19. C2×C33C23semidirect
20. C3×C3⋊D3C23semidirect
21. C32×D3C23semidirect
28. C22×C32C2×D3semidirect
29. C22×C32C22×C3semidirect
30. C2×C3⋊D3C22×C3semidirect
35. C2×C3×D3C2×D3direct (N × H)
36. C2×C3×D3C22×C3semidirect
37. D32C22×C3direct (N × H)
38. C33C24semidirect
47. C22×D3C3×D3direct (N × H)
52. C2×C32C22×D3semidirect
53. C2×C32C23×C3semidirect
54. C3⋊D3C23×C3semidirect
58. C3×D3C22×D3direct (N × H)
59. C3×D3C23×C3semidirect
69. C22×C3D32direct (N × H)
70. C22×C3C2×C3×D3semidirect
74. C2×D3C2×C3×D3direct (N × H)
78. C32C23×D3semidirect
79. C32C24×C3semidirect
90. C2×C3C2×D32direct (N × H)
91. C2×C3C22×C3×D3semidirect
94. D3C22×C3×D3direct (N × H)
98. C22C3×D32direct (N × H)
102. C3C22×D32direct (N × H)
103. C3C23×C3×D3semidirect
106. C2C2×C3×D32direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C3⋊D32
C22×C32×D32
C2×C3×D322
C23×C3×D33
C22×D323