Finite Group Databasebeta

← C22×D3×C3⋊D3 #89121

Subgroups — C22×D3×C3⋊D3 #89121

Order 432.

932 conjugacy classes of subgroups; only the 188 normal subgroups are shown.

normal subgroups only

This group has 932 conjugacy classes of subgroups — too many to draw. Only its 188 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⋊D3)C211yesmaximal, characteristic, complemented
2C22×C3×C3⋊D3C211yesmaximal, characteristic, complemented
3C22×C32×D3C211yesmaximal, characteristic, complemented
4C2×D3×C3⋊D3C2112yesmaximal, direct product factor
5C23×C3⋊D3—31nomaximal
6C22×D32—34nomaximal
7C22×C33C2211yescharacteristic, complemented
8C2×C3⋊(C3⋊D3)C2216yescomplemented
9C2×C3×C3⋊D3C2216yescomplemented
10C2×C32×D3C2216yescomplemented
11D3×C3⋊D3C22116yesdirect product factor
12C23×C32—31no—
13C22×C3⋊D3—31no—
14C22×C3⋊D3—312no—
15C22×C3⋊D3—34no—
16C22×C3⋊D3—64no—
17C22×C3⋊D3D311yescharacteristic, direct product factor
18C22×C3×D3—34no—
19C22×C3×D3D314yescomplemented
20C2×D32—348no—
21C2×C33C2313yescomplemented
22C3⋊(C3⋊D3)C2314yescomplemented
23C3×C3⋊D3C2314yescomplemented
24C32×D3C2314yescomplemented
25C23×D3—94no—
26C23×D3—91no—
27C22×C32—24no—
28C22×C32—36no—
29C22×C32C2×D314yescomplemented
30C22×C32C2×D311yescharacteristic, complemented
31C2×C3⋊D3—36no—
32C2×C3⋊D3—316no—
33C2×C3⋊D3—324no—
34C2×C3⋊D3—624no—
35C2×C3⋊D3C2×D316yesdirect product factor
36C2×C3×D3—324no—
37C2×C3×D3C2×D3124yescomplemented
38D32—364no—
39C33C2411yescharacteristic, complemented, Sylow
40C23×C3—34no—
41C23×C3—91no—
42C22×D3—34no—
43C22×D3—948no—
44C22×D3—94no—
45C22×D3—91no—
46C22×D3—912no—
47C22×D3—184no—
48C22×D3C3⋊D311yescharacteristic, direct product factor
49C2×C32—212no—
50C2×C32—34no—
51C2×C32C22×D3112yescomplemented
52C2×C32C22×D313yescomplemented
53C3⋊D3—34no—
54C3⋊D3—316no—
55C3⋊D3—616no—
56C3⋊D3C22×D314yesdirect product factor
57C3×D3—316no—
58C3×D3C22×D3116yescomplemented
59C24—271noSylow
60C22×C3—24no—
61C22×C3—324no—
62C22×C3—96no—
63C22×C3D3214yescomplemented
64C22×C3C2×C3⋊D311yescharacteristic, complemented
65C2×D3—324no—
66C2×D3—964no—
67C2×D3—924no—
68C2×D3—96no—
69C2×D3—916no—
70C2×D3—1824no—
71C2×D3C2×C3⋊D316yesdirect product factor
72C32—24no—
73C32C23×D314yescomplemented
74C32C23×D311yescharacteristic, complemented
75C23—31no—
76C23—91no—
77C23—2712no—
78C23—271no—
79C2×C3—212no—
80C2×C3—316no—
81C2×C3—94no—
82C2×C3C2×D32112yescomplemented
83C2×C3C22×C3⋊D313yescomplemented
84D3—316no—
85D3—916no—
86D3—94no—
87D3—1816no—
88D3C22×C3⋊D314yesdirect product factor
89C22—36no—
90C22—96no—
91C22—2716no—
92C22—276no—
93C22D3×C3⋊D311yescharacteristic, direct product factor
94C3—24no—
95C3C22×D3214yescomplemented
96C3C23×C3⋊D311yescharacteristic, complemented
97C2—34no—
98C2—94no—
99C2—274no—
100C2C2×D3×C3⋊D313yesdirect product factor
subgroupG/H
center, hypercenterC22D3×C3⋊D3
commutator, cosocle, hypocenterC33C24
FrattiniC1G
Fitting, socleC22×C33C22
LCSG ▷ C33
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×C3⋊(C3⋊D3)C2semidirect
2. C22×C3×C3⋊D3C2semidirect
3. C22×C32×D3C2semidirect
4. C2×D3×C3⋊D3C2direct (N × H)
7. C22×C33C22semidirect
8. C2×C3⋊(C3⋊D3)C22semidirect
9. C2×C3×C3⋊D3C22semidirect
10. C2×C32×D3C22semidirect
11. D3×C3⋊D3C22direct (N × H)
17. C22×C3⋊D3D3direct (N × H)
19. C22×C3×D3D3semidirect
21. C2×C33C23semidirect
22. C3⋊(C3⋊D3)C23semidirect
23. C3×C3⋊D3C23semidirect
24. C32×D3C23semidirect
29. C22×C32C2×D3semidirect
30. C22×C32C2×D3semidirect
35. C2×C3⋊D3C2×D3direct (N × H)
37. C2×C3×D3C2×D3semidirect
39. C33C24semidirect
48. C22×D3C3⋊D3direct (N × H)
51. C2×C32C22×D3semidirect
52. C2×C32C22×D3semidirect
56. C3⋊D3C22×D3direct (N × H)
58. C3×D3C22×D3semidirect
63. C22×C3D32semidirect
64. C22×C3C2×C3⋊D3semidirect
71. C2×D3C2×C3⋊D3direct (N × H)
73. C32C23×D3semidirect
74. C32C23×D3semidirect
82. C2×C3C2×D32semidirect
83. C2×C3C22×C3⋊D3semidirect
88. D3C22×C3⋊D3direct (N × H)
93. C22D3×C3⋊D3direct (N × H)
95. C3C22×D32semidirect
96. C3C23×C3⋊D3semidirect
100. C2C2×D3×C3⋊D3direct (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⋊D3)2
C22×C3×C3⋊D32
C22×C32×D32
C2×D3×C3⋊D32
C23×C3⋊D33
C22×D323