Finite Group Databasebeta

← #88640

Subgroups — #88640

Order 432.

136 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 41 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
1C4×C3⋊D9C211yesmaximal, characteristic, complemented
2C4×D3×C9C211yesmaximal, characteristic, complemented
3C3×C4×D9C211yesmaximal, characteristic, complemented
4#6195C211yesmaximal, characteristic, complemented
5#6194C211yesmaximal, characteristic, complemented
6#6192C211yesmaximal, characteristic, complemented
7#6189C211yesmaximal, characteristic, complemented
8#3798—31nomaximal
9#3697—31nomaximal
10C2×C3⋊D9C2211yescharacteristic
11C2×D3×C9C2211yescharacteristic
12C2×C3×D9C2211yescharacteristic
13C3×C4×C9C2211yescharacteristic
14C3⋊Dic9C2211yescharacteristic
15C9×Dic3C2211yescharacteristic
16C3×Dic9C2211yescharacteristic
17C4×C3⋊D3—31no—
18C3×C4×D3—31no—
19C3×C4×D3D311yescharacteristic
20#627—31no—
21#626—31no—
22#626—31no—
23#625—31no—
24C2×C4×C9—31no—
25#611—31no—
26#611—31no—
27D36—31no—
28C4×D9—31no—
29C4×D9—61no—
30C4×D9D311yescharacteristic, complemented
31Dic18—31no—
32C2×C3×C9C2311yescharacteristic
33C3⋊D9—21no—
34D3×C9—21no—
35C3×D9—21no—
36#235—91no—
37#235—91no—
38C2×C3⋊D3—31no—
39C2×C3×D3—31no—
40C2×C3×D3C2×D311yescharacteristic
41C32×C4C2×D311yescharacteristic
42C3⋊Dic3—31no—
43C3×Dic3—31no—
44C3×Dic3C2×D311yescharacteristic
45C22×C9—31no—
46C2×D9—31no—
47C2×D9—61no—
48C2×D9C2×D311yescharacteristic
49C4×C9—21no—
50C4×C9—31no—
51C4×C9C2×D311yescharacteristic
52Dic9—31no—
53Dic9—61no—
54Dic9C2×D311yescharacteristic
55C3×C9#4111yescharacteristic, complemented, Sylow
56C2×C3×C4—31no—
57C2×C3×C4—91no—
58#67—91no—
59#67—91no—
60#67—91no—
61#67—91no—
62D12—91no—
63D12—91no—
64C4×D3—31no—
65C4×D3—91no—
66C4×D3—91no—
67C4×D3—181no—
68C4×D3D911yescharacteristic, complemented
69Dic6—91no—
70Dic6—91no—
71C2×C32C22×D311yescharacteristic
72C3⋊D3—61no—
73C3×D3—21no—
74C3×D3—61no—
75C2×C9—21no—
76C2×C9—61no—
77C2×C9C22×D311yescharacteristic
78D9—21no—
79D9—62no—
80D9—61no—
81#41—271noSylow
82C22×C3—31no—
83C22×C3—91no—
84C2×D3—31no—
85C2×D3—91no—
86C2×D3—91no—
87C2×D3—181no—
88C2×D3C2×D911yescharacteristic
89C3×C4—21no—
90C3×C4—31no—
91C3×C4—91no—
92C3×C4C2×D911yescharacteristic
93C3×C4D3211yescharacteristic
94Dic3—31no—
95Dic3—91no—
96Dic3—91no—
97Dic3—181no—
98Dic3C2×D911yescharacteristic
99C32#23511yescharacteristic
100C9—21no—
101C9#23511yescharacteristic, complemented
102Q8—271no—
103D4—271no—
104D4—271no—
105D4—271no—
106C2×C4—31no—
107C2×C4—91no—
108C2×C4—271no—
109C2×C3—21no—
110C2×C3—61no—
111C2×C3—181no—
112C2×C3C22×D911yescharacteristic
113C2×C3C2×D3211yescharacteristic
114D3—21no—
115D3—61no—
116D3—182no—
117D3—181no—
118D3—181no—
119C22—31no—
120C22—91no—
121C22—271no—
122C4—31no—
123C4—91no—
124C4—271no—
125C4D3×D911yescharacteristic
126C3—21no—
127C3#369711yescharacteristic, complemented
128C3#379811yescharacteristic
129C2—61no—
130C2—181no—
131C2—541no—
132C2C2×D3×D911yescharacteristic
subgroupG/H
center, hypercenterC4D3×D9
commutator, cosocleC2×C3×C9C23
FrattiniC2×C3C2×D32
FittingC3×C4×C9C22
socleC2×C32C22×D3
hypocenterC3×C9#41
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
1. C4×C3⋊D9C2semidirect
2. C4×D3×C9C2semidirect
3. C3×C4×D9C2semidirect
4. #6195C2semidirect
5. #6194C2semidirect
6. #6192C2semidirect
7. #6189C2semidirect
30. C4×D9D3semidirect
55. C3×C9#41semidirect
68. C4×D3D9semidirect
101. C9#235semidirect
127. C3#3697semidirect

Maximal subgroups

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

subgroupindex
C4×C3⋊D92
C4×D3×C92
C3×C4×D92
#61952
#61942
#61922
#61892
#37983
#36973