Finite Group Databasebeta

← D4×C3⋊D9 #88741

Subgroups — D4×C3⋊D9 #88741

Order 432.

270 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 73 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⋊D9C212yesmaximal, complemented
2C3×D4×C9C211yesmaximal, characteristic, complemented
3#6233C212yesmaximal, complemented
4C4⋊(C3⋊D9)C211yesmaximal, characteristic, complemented
5C4×C3⋊D9C211yesmaximal, characteristic, complemented
6D4×C3⋊D3—31nomaximal
7D4×D9—33nomaximal
8C22×C3×C9C2212yescomplemented
9C2×C3⋊D9—24no—
10C2×C3⋊D9C2211yescharacteristic
11C2×C3⋊D9C2212yescomplemented
12C3×C4×C9C2211yescharacteristic, complemented
13C3⋊Dic9C2211yescharacteristic, complemented
14C22×C3⋊D3—32no—
15C32×D4D311yescharacteristic
16#638—32no—
17C4⋊(C3⋊D3)—31no—
18C4×C3⋊D3—31no—
19C22×D9—36no—
20D4×C9D313yescomplemented
21#611—36no—
22D36—33no—
23C4×D9—33no—
24C2×C3×C9—22no—
25C2×C3×C9C2311yescharacteristic
26C3⋊D9—22no—
27C3⋊D9D412yesdirect product factor
28D3×D4—93no—
29D3×D4—91no—
30C22×C32C2×D312yes—
31C2×C3⋊D3—31no—
32C2×C3⋊D3—32no—
33C2×C3⋊D3—64no—
34C32×C4C2×D311yescharacteristic
35C3⋊Dic3—31no—
36C22×C9C2×D316yescomplemented
37C2×D9—33no—
38C2×D9—36no—
39C2×D9—612no—
40C4×C9C2×D313yescomplemented
41Dic9—33no—
42C3×C9C2×D411yescharacteristic, complemented, Sylow
43C22×D3—96no—
44C22×D3—92no—
45C3×D4D913yescomplemented
46C3×D4C3⋊D311yescharacteristic
47#67—96no—
48#67—92no—
49D12—93no—
50D12—91no—
51C4×D3—93no—
52C4×D3—91no—
53C2×C32—22no—
54C2×C32C22×D311yescharacteristic
55C3⋊D3—32no—
56C3⋊D3—62no—
57C2×C9—26no—
58C2×C9C22×D313yes—
59D9—36no—
60D9—66no—
61C2×D4—271noSylow
62C22×C3C2×D916yescomplemented
63C22×C3C2×C3⋊D312yes—
64C2×D3—93no—
65C2×D3—91no—
66C2×D3—96no—
67C2×D3—92no—
68C2×D3—184no—
69C2×D3—1812no—
70C3×C4C2×D913yescomplemented
71C3×C4C2×C3⋊D311yescharacteristic
72Dic3—93no—
73Dic3—91no—
74C32D3×D411yescharacteristic
75C9D3×D413yescomplemented
76C23—272no—
77D4—272no—
78D4—271no—
79D4C3⋊D911yescharacteristic, direct product factor
80C2×C4—271no—
81C2×C3—26no—
82C2×C3—22no—
83C2×C3C22×D913yes—
84C2×C3C22×C3⋊D311yescharacteristic
85D3—96no—
86D3—92no—
87D3—186no—
88D3—182no—
89C22—271no—
90C22—272no—
91C22—544no—
92C22C2×C3⋊D912yescomplemented
93C4—271no—
94C4C2×C3⋊D911yescharacteristic, complemented
95C3D4×D913yescomplemented
96C3D4×C3⋊D311yescharacteristic
97C2—22no—
98C2—272no—
99C2—542no—
100C2C22×C3⋊D911yescharacteristic
subgroupG/H
centerC2C22×C3⋊D9
commutator, cosocleC2×C3×C9C23
FrattiniC2×C3C22×C3⋊D3
FittingC3×D4×C9C2
socleC2×C32C22×D3
hypercenterD4C3⋊D9
hypocenterC3×C9C2×D4
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2 ◁ D4

Complements

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

NH ≅ G/Ntype
1. C22×C3⋊D9C2semidirect
2. C3×D4×C9C2semidirect
3. #6233C2semidirect
4. C4⋊(C3⋊D9)C2semidirect
5. C4×C3⋊D9C2semidirect
8. C22×C3×C9C22semidirect
11. C2×C3⋊D9C22semidirect
12. C3×C4×C9C22semidirect
13. C3⋊Dic9C22semidirect
20. D4×C9D3semidirect
27. C3⋊D9D4direct (N × H)
36. C22×C9C2×D3semidirect
40. C4×C9C2×D3semidirect
42. C3×C9C2×D4semidirect
45. C3×D4D9semidirect
62. C22×C3C2×D9semidirect
70. C3×C4C2×D9semidirect
75. C9D3×D4semidirect
79. D4C3⋊D9direct (N × H)
92. C22C2×C3⋊D9semidirect
94. C4C2×C3⋊D9semidirect
95. C3D4×D9semidirect

Maximal subgroups

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

subgroupindex
C22×C3⋊D92
C3×D4×C92
#62332
C4⋊(C3⋊D9)2
C4×C3⋊D92
D4×C3⋊D33
D4×D93