Finite Group Databasebeta

← C3×C4×C9⋊D9 #14517488

Subgroups — C3×C4×C9⋊D9 #14517488

Order 1944.

488 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 148 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×C3×C9⋊D9C211yesmaximal, characteristic
2C3×C4×C92C211yesmaximal, characteristic, complemented
3C3×C9⋊Dic9C211yesmaximal, characteristic, complemented
4C3×C4×C3⋊D9—34nomaximal
5C4×C9⋊D9C311yesmaximal, characteristic, direct product factor
6C2×C3×C92C2211yescharacteristic
7C3×C9⋊D9C412yesdirect product factor
8C2×C3×C3⋊D9—34no—
9C32×C4×C9D314yes—
10C3×C3⋊Dic9—34no—
11C2×C9⋊D9C2×C311yescharacteristic
12C4×C92—24no—
13C4×C92C2×C311yescharacteristic, complemented
14C9⋊Dic9C2×C311yescharacteristic, complemented
15C3×C92C2×C411yescharacteristic, complemented, Sylow
16C3×C4×C3⋊D3—91no—
17C4×C3⋊D9—34no—
18C3×C4×D9—912no—
19C2×C32×C9C2×D314yes—
20C3×C3⋊D9—38no—
21C2×C92—24no—
22C2×C92C22×C311yescharacteristic
23C9⋊D9C3×C412yesdirect product factor
24C2×C3×C3⋊D3—91no—
25C33×C4C3⋊D311yescharacteristic
26C3×C3⋊Dic3—91no—
27C2×C3⋊D9—34no—
28C2×C3×D9—912no—
29C3×C4×C9—24no—
30C3×C4×C9—212no—
31C3×C4×C9D9112yescomplemented
32C3×C4×C9C3×D314yes—
33C3⋊Dic9—34no—
34C3×Dic9—912no—
35C32×C9C4×D314yes—
36C92—24no—
37C92C2×C3×C411yescharacteristic, complemented
38C4×C3⋊D3—91no—
39C3×C4×D3—274no—
40C4×D9—912no—
41C2×C33C2×C3⋊D311yescharacteristic
42C3×C3⋊D3—92no—
43C2×C3×C9—24no—
44C2×C3×C9—212no—
45C2×C3×C9C2×D9112yes—
46C2×C3×C9C2×C3×D314yes—
47C3⋊D9—38no—
48C3×D9—924no—
49C2×C3⋊D3—91no—
50C2×C3×D3—274no—
51C32×C4—24no—
52C32×C4C3⋊D914yes—
53C32×C4C3×C3⋊D311yescharacteristic
54C3⋊Dic3—91no—
55C3×Dic3—274no—
56C2×D9—912no—
57C4×C9—212no—
58C4×C9C3×D9112yescomplemented
59Dic9—912no—
60C33C4×C3⋊D311yescharacteristic
61C3×C9—24no—
62C3×C9—212no—
63C3×C9C4×D9112yescomplemented
64C3×C9C3×C4×D314yes—
65C2×C3×C4—811no—
66C4×D3—274no—
67C2×C32—24no—
68C2×C32C2×C3⋊D914yes—
69C2×C32C2×C3×C3⋊D311yescharacteristic
70C3⋊D3—92no—
71C3×D3—278no—
72C2×C9—212no—
73C2×C9C2×C3×D9112yes—
74D9—924no—
75C22×C3—811no—
76C2×D3—274no—
77C3×C4—24no—
78C3×C4—811no—
79C3×C4C9⋊D911yescharacteristic, direct product factor
80C3×C4C3×C3⋊D914yes—
81Dic3—274no—
82C32—24no—
83C32C4×C3⋊D914yes—
84C32C3×C4×C3⋊D311yescharacteristic
85C9—212no—
86C9C3×C4×D9112yescomplemented
87C2×C4—811noSylow
88C2×C3—24no—
89C2×C3—812no—
90C2×C3C2×C9⋊D911yescharacteristic
91C2×C3C2×C3×C3⋊D914yes—
92D3—278no—
93C22—811no—
94C4—811no—
95C4C3×C9⋊D911yescharacteristic, direct product factor
96C3—24no—
97C3C4×C9⋊D911yescharacteristic, direct product factor
98C3C3×C4×C3⋊D914yes—
99C2—812no—
100C2C2×C3×C9⋊D911yescharacteristic
subgroupG/H
center, hypercenterC3×C4C9⋊D9
commutator, hypocenterC92C2×C3×C4
FrattiniC2×C32C2×C3×C3⋊D3
FittingC3×C4×C92C2
socleC2×C33C2×C3⋊D3
prime radicalC2×C3×C9⋊D9C2
cosocleC2×C92C22×C3
LCSG ▷ C92
UCSC1 ◁ C3×C4

Complements

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

NH ≅ G/Ntype
2. C3×C4×C92C2semidirect
3. C3×C9⋊Dic9C2semidirect
5. C4×C9⋊D9C3direct (N × H)
7. C3×C9⋊D9C4direct (N × H)
13. C4×C92C2×C3semidirect
14. C9⋊Dic9C2×C3semidirect
15. C3×C92C2×C4semidirect
23. C9⋊D9C3×C4direct (N × H)
31. C3×C4×C9D9semidirect
37. C92C2×C3×C4semidirect
58. C4×C9C3×D9semidirect
63. C3×C9C4×D9semidirect
79. C3×C4C9⋊D9direct (N × H)
86. C9C3×C4×D9semidirect
95. C4C3×C9⋊D9direct (N × H)
97. C3C4×C9⋊D9direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C9⋊D92
C3×C4×C922
C3×C9⋊Dic92
C3×C4×C3⋊D93
C4×C9⋊D93