Finite Group Databasebeta

← C3×D4×D9 #88709

Subgroups — C3×D4×D9 #88709

Order 432.

178 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 62 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
3C3×#611C212yesmaximal, complemented
4C3×D36C211yesmaximal, characteristic, complemented
5C3×C4×D9C211yesmaximal, characteristic, complemented
6C3×D3×D4—31nomaximal
7D4×D9C311yesmaximal, characteristic, direct product factor
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
16C3×#67—32no—
17C3×D12—31no—
18C3×C4×D3—31no—
19C22×D9C2×C312yescomplemented
20D4×C9—21no—
21D4×C9C2×C311yescharacteristic, complemented
22#611C2×C312yescomplemented
23D36C2×C311yescharacteristic, complemented
24C4×D9C2×C311yescharacteristic, complemented
25C2×C3×C9—22no—
26C2×C3×C9C2311yescharacteristic
27C3×D9—22no—
28C3×D9D412yesdirect product factor
29C2×C3×D4—91no—
30D3×D4—31no—
31C22×C32C2×D312yes—
32C2×C3×D3—31no—
33C2×C3×D3—32no—
34C2×C3×D3—64no—
35C32×C4C2×D311yescharacteristic
36C3×Dic3—31no—
37C22×C9—22no—
38C22×C9C22×C312yescomplemented
39C2×D9—24no—
40C2×D9C22×C311yescharacteristic
41C2×D9C22×C312yescomplemented
42C4×C9—21no—
43C4×C9C22×C311yescharacteristic, complemented
44Dic9C22×C311yescharacteristic, complemented
45C3×C9C2×D411yescharacteristic, complemented, Sylow
46C23×C3—92no—
47C22×D3—32no—
48C3×D4—21no—
49C3×D4—92no—
50C3×D4—91no—
51C3×D4D911yescharacteristic, direct product factor
52C3×D4C3×D311yescharacteristic
53C2×C3×C4—91no—
54#67—32no—
55D12—31no—
56C4×D3—31no—
57C2×C32—22no—
58C2×C32C22×D311yescharacteristic
59C3×D3—32no—
60C3×D3—62no—
61C2×C9—22no—
62C2×C9—21no—
63C2×C9—42no—
64C2×C9C23×C311yescharacteristic
65D9—22no—
66D9C3×D412yesdirect product factor
67C2×D4—91noSylow
68C22×C3—22no—
69C22×C3—91no—
70C22×C3—92no—
71C22×C3—184no—
72C22×C3C2×D912yescomplemented
73C22×C3C2×C3×D312yes—
74C2×D3—31no—
75C2×D3—32no—
76C2×D3—64no—
77C3×C4—21no—
78C3×C4—91no—
79C3×C4C2×D911yescharacteristic, complemented
80C3×C4C2×C3×D311yescharacteristic
81Dic3—31no—
82C32D3×D411yescharacteristic
83C9—21no—
84C9C2×C3×D411yescharacteristic, complemented
85C23—92no—
86D4—92no—
87D4—91no—
88D4C3×D911yescharacteristic, direct product factor
89C2×C4—91no—
90C2×C3—22no—
91C2×C3—22no—
92C2×C3—21no—
93C2×C3—42no—
94C2×C3—92no—
95C2×C3—182no—
96C2×C3C22×D911yescharacteristic
97C2×C3C22×C3×D311yescharacteristic
98D3—32no—
99D3—62no—
100C22—91no—
101C22—92no—
102C22—184no—
103C22C2×C3×D912yescomplemented
104C4—91no—
105C4C2×C3×D911yescharacteristic, complemented
106C3—21no—
107C3D4×D911yescharacteristic, direct product factor
108C3C3×D3×D411yescharacteristic
109C2—22no—
110C2—92no—
111C2—182no—
112C2C22×C3×D911yescharacteristic
subgroupG/H
centerC2×C3C22×D9
commutator, cosocleC2×C9C23×C3
FrattiniC2×C3C22×C3×D3
FittingC3×D4×C9C2
socleC2×C32C22×D3
hypercenterC3×D4D9
hypocenterC9C2×C3×D4
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C3 ◁ C3×D4

Complements

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

NH ≅ G/Ntype
1. C22×C3×D9C2semidirect
2. C3×D4×C9C2semidirect
3. C3×#611C2semidirect
4. C3×D36C2semidirect
5. C3×C4×D9C2semidirect
7. D4×D9C3direct (N × H)
8. C22×C3×C9C22semidirect
11. C2×C3×D9C22semidirect
12. C3×C4×C9C22semidirect
13. C3×Dic9C22semidirect
19. C22×D9C2×C3semidirect
21. D4×C9C2×C3semidirect
22. #611C2×C3semidirect
23. D36C2×C3semidirect
24. C4×D9C2×C3semidirect
28. C3×D9D4direct (N × H)
38. C22×C9C22×C3semidirect
41. C2×D9C22×C3semidirect
43. C4×C9C22×C3semidirect
44. Dic9C22×C3semidirect
45. C3×C9C2×D4semidirect
51. C3×D4D9direct (N × H)
66. D9C3×D4direct (N × H)
72. C22×C3C2×D9semidirect
79. C3×C4C2×D9semidirect
84. C9C2×C3×D4semidirect
88. D4C3×D9direct (N × H)
103. C22C2×C3×D9semidirect
105. C4C2×C3×D9semidirect
107. C3D4×D9direct (N × H)

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
C3×#6112
C3×D362
C3×C4×D92
C3×D3×D43
D4×D93