Finite Group Databasebeta

← C2×D33 #89112

Subgroups — C2×D33 #89112

Order 432.

642 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 642 conjugacy classes of subgroups — too many to draw. Only its 132 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×#1113C211yesmaximal, characteristic, complemented
2C2×D3×C3⋊D3C213yesmaximal, complemented
3C2×C3×D32C213yesmaximal, complemented
4D33C218yesmaximal, direct product factor
5C22×D32—33nomaximal
6C2×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
7C2×C3×C3⋊D3C2213yescomplemented
8C2×C32×D3C2213yescomplemented
9#1113C2214yescomplemented
10D3×C3⋊D3C22112yescomplemented
11C3×D32C22112yescomplemented
12C22×C3⋊D3—33no—
13C22×C3×D3—36no—
14C2×D32—33no—
15C2×D32—36no—
16C2×D32—324no—
17C2×D32—63no—
18C2×D32D313yesdirect product factor
19C2×C33C2311yescharacteristic, complemented
20C3⋊(C3⋊D3)C2312yescomplemented
21C3×C3⋊D3C2316yescomplemented
22C32×D3C2316yescomplemented
23C23×D3—93no—
24C22×C32—33no—
25C2×C3⋊D3—33no—
26C2×C3⋊D3—312no—
27C2×C3⋊D3—63no—
28C2×C3⋊D3—121no—
29C2×C3⋊D3C2×D313yescomplemented
30C2×C3×D3—23no—
31C2×C3×D3—36no—
32C2×C3×D3—324no—
33C2×C3×D3—63no—
34C2×C3×D3C2×D316yescomplemented
35D32—312no—
36D32—324no—
37D32—612no—
38D32C2×D3112yesdirect product factor
39C33C2411yescharacteristic, complemented, Sylow
40C23×C3—93no—
41C22×D3—36no—
42C22×D3—93no—
43C22×D3—924no—
44C22×D3—96no—
45C22×D3—93no—
46C22×D3—183no—
47C2×C32—23no—
48C2×C32—36no—
49C2×C32—41no—
50C2×C32C22×D313yescomplemented
51C3⋊D3—36no—
52C3⋊D3—66no—
53C3⋊D3—122no—
54C3⋊D3C22×D316yescomplemented
55C3×D3—26no—
56C3×D3—312no—
57C3×D3—66no—
58C3×D3C22×D3112yescomplemented
59C24—271noSylow
60C22×C3—36no—
61C22×C3—63no—
62C22×C3—912no—
63C22×C3—93no—
64C2×D3—36no—
65C2×D3—324no—
66C2×D3—63no—
67C2×D3—912no—
68C2×D3—924no—
69C2×D3—93no—
70C2×D3—912no—
71C2×D3—1812no—
72C2×D3—183no—
73C2×D3—361no—
74C2×D3D3213yesdirect product factor
75C32—23no—
76C32—41no—
77C32C23×D313yescomplemented
78C23—93no—
79C23—273no—
80C23—278no—
81C23—271no—
82C2×C3—23no—
83C2×C3—312no—
84C2×C3—41no—
85C2×C3—66no—
86C2×C3—96no—
87C2×C3C2×D3213yescomplemented
88D3—312no—
89D3—66no—
90D3—96no—
91D3—186no—
92D3—362no—
93D3C2×D3216yesdirect product factor
94C22—33no—
95C22—912no—
96C22—93no—
97C22—2712no—
98C22—274no—
99C22—271no—
100C3—23no—
101C3—41no—
102C3C22×D3213yescomplemented
103C2—36no—
104C2—96no—
105C2—272no—
106C2D3311yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2D33
commutator, cosocle, hypocenterC33C24
FrattiniC1G
Fitting, socleC2×C33C23
LCSG ▷ C33
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×#1113C2semidirect
2. C2×D3×C3⋊D3C2semidirect
3. C2×C3×D32C2semidirect
4. D33C2direct (N × H)
6. C2×C3⋊(C3⋊D3)C22semidirect
7. C2×C3×C3⋊D3C22semidirect
8. C2×C32×D3C22semidirect
9. #1113C22semidirect
10. D3×C3⋊D3C22semidirect
11. C3×D32C22semidirect
18. C2×D32D3direct (N × H)
19. C2×C33C23semidirect
20. C3⋊(C3⋊D3)C23semidirect
21. C3×C3⋊D3C23semidirect
22. C32×D3C23semidirect
29. C2×C3⋊D3C2×D3semidirect
34. C2×C3×D3C2×D3semidirect
38. D32C2×D3direct (N × H)
39. C33C24semidirect
50. C2×C32C22×D3semidirect
54. C3⋊D3C22×D3semidirect
58. C3×D3C22×D3semidirect
74. C2×D3D32direct (N × H)
77. C32C23×D3semidirect
87. C2×C3C2×D32semidirect
93. D3C2×D32direct (N × H)
102. C3C22×D32semidirect
106. C2D33direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#11132
C2×D3×C3⋊D32
C2×C3×D322
D332
C22×D323