Finite Group Databasebeta

← #88646

Subgroups — #88646

Order 432.

178 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 43 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×D3×D9C212yesmaximal, complemented
2C4×C3⋊D9C211yesmaximal, characteristic, complemented
3C9×D12C211yesmaximal, characteristic, complemented
4C3×D36C211yesmaximal, characteristic, complemented
5#6194C212yesmaximal, complemented
6#3802—31nomaximal
7D4×D9—31nomaximal
8C2×C3⋊D9C2211yescharacteristic
9C2×D3×C9C2212yescomplemented
10C2×C3×D9C2212yescomplemented
11D3×D9—24no—
12C3×C4×C9C2211yescharacteristic, complemented
13C3⋊Dic9C2211yescharacteristic, complemented
14C2×D32—32no—
15C4×C3⋊D3—31no—
16C3×D12—31no—
17C3×D12D311yescharacteristic
18#625—32no—
19C22×D9—32no—
20D4×C9—31no—
21#611—32no—
22D36D311yescharacteristic, complemented
23C4×D9—31no—
24C4×D9—61no—
25C2×C3×C9C2311yescharacteristic
26C3⋊D9D412yescomplemented
27D3×C9—22no—
28C3×D9—22no—
29D3×D4—91no—
30D3×D4—91no—
31C2×C3⋊D3—31no—
32C2×C3×D3—32no—
33C2×C3×D3C2×D312yes—
34D32—64no—
35C32×C4C2×D311yescharacteristic
36C3⋊Dic3—31no—
37C22×C9—32no—
38C2×D9—31no—
39C2×D9—61no—
40C2×D9—64no—
41C2×D9C2×D312yescomplemented
42C4×C9—21no—
43C4×C9C2×D311yescharacteristic, complemented
44Dic9—31no—
45Dic9—61no—
46C3×C9C2×D411yescharacteristic, complemented, Sylow
47C22×D3—92no—
48C22×D3—92no—
49C3×D4—31no—
50C3×D4—91no—
51#67—92no—
52#67—92no—
53D12—31no—
54D12D911yescharacteristic, complemented
55C4×D3—91no—
56C4×D3—91no—
57C4×D3—181no—
58C2×C32C22×D311yescharacteristic
59C3⋊D3—32no—
60C3×D3—22no—
61C3×D3—62no—
62C2×C9—21no—
63C2×C9—62no—
64C2×C9C22×D311yescharacteristic
65D9—22no—
66D9—32no—
67D9—62no—
68C2×D4—271noSylow
69C22×C3—32no—
70C22×C3—92no—
71C2×D3—32no—
72C2×D3—91no—
73C2×D3—91no—
74C2×D3—181no—
75C2×D3—184no—
76C2×D3—184no—
77C2×D3C2×D912yescomplemented
78C3×C4—21no—
79C3×C4C2×D911yescharacteristic, complemented
80C3×C4D3211yescharacteristic
81Dic3—91no—
82Dic3—91no—
83Dic3—181no—
84C32D3×D411yescharacteristic
85C9—21no—
86C9D3×D411yescharacteristic, complemented
87C23—272no—
88D4—31no—
89D4—91no—
90D4—272no—
91C2×C4—271no—
92C2×C3—21no—
93C2×C3—62no—
94C2×C3—182no—
95C2×C3C22×D911yescharacteristic
96C2×C3C2×D3211yescharacteristic
97D3—22no—
98D3—62no—
99D3—92no—
100D3—92no—
101D3—182no—
102C22—32no—
103C22—92no—
104C22—271no—
105C22—544no—
106C4—271no—
107C4D3×D911yescharacteristic, complemented
108C3—21no—
109C3D4×D911yescharacteristic, complemented
110C3#380211yescharacteristic
111C2—62no—
112C2—182no—
113C2—272no—
114C2C2×D3×D911yescharacteristic
subgroupG/H
centerC2C2×D3×D9
commutator, cosocleC2×C3×C9C23
FrattiniC2×C3C2×D32
FittingC3×C4×C9C22
socleC2×C32C22×D3
hypercenterC4D3×D9
hypocenterC3×C9C2×D4
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
1. C2×D3×D9C2semidirect
2. C4×C3⋊D9C2semidirect
3. C9×D12C2semidirect
4. C3×D36C2semidirect
5. #6194C2semidirect
9. C2×D3×C9C22semidirect
10. C2×C3×D9C22semidirect
12. C3×C4×C9C22semidirect
13. C3⋊Dic9C22semidirect
22. D36D3semidirect
26. C3⋊D9D4semidirect
41. C2×D9C2×D3semidirect
43. C4×C9C2×D3semidirect
46. C3×C9C2×D4semidirect
54. D12D9semidirect
77. C2×D3C2×D9semidirect
79. C3×C4C2×D9semidirect
86. C9D3×D4semidirect
107. C4D3×D9semidirect
109. C3D4×D9semidirect

Maximal subgroups

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

subgroupindex
C2×D3×D92
C4×C3⋊D92
C9×D122
C3×D362
#61942
#38023
D4×D93