Finite Group Databasebeta

← #89046

Subgroups — #89046

Order 432.

218 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 47 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
1C3×#638C212yesmaximal, complemented
2C2×C3×C3⋊Dic3C211yesmaximal, characteristic, complemented
3#6296C211yesmaximal, characteristic, complemented
4#6295C211yesmaximal, characteristic, complemented
5#6294C212yesmaximal, complemented
6#3805—31nomaximal
7#3804—32nomaximal
8C22×C33C2211yescharacteristic
9C2×C3×C3⋊D3C2212yes—
10C3×C3⋊Dic3C2211yescharacteristic
11C3×C3⋊Dic3C2212yes—
12C3×C3⋊Dic3C2211yescharacteristic
13#638D312yescomplemented
14C2×C3⋊Dic3D311yescharacteristic, complemented
15C3×#67—32no—
16C3×#67—32no—
17C3×#67—62no—
18C2×C3×Dic3—32no—
19C2×C3×Dic3—61no—
20#627—32no—
21#627—31no—
22#626—32no—
23#625—31no—
24#624—32no—
25D3×Dic3—32no—
26D3×Dic3—32no—
27C2×C33—21no—
28C2×C33C2311yescharacteristic
29C3×C3⋊D3—22no—
30#237—92no—
31#235—91no—
32C22×C32—21no—
33C22×C32—22no—
34C22×C32—41no—
35C22×C32C2×D312yes—
36C22×C32C2×D311yescharacteristic
37C2×C3⋊D3C2×D312yes—
38C2×C3×D3—32no—
39C2×C3×D3—32no—
40C2×C3×D3—62no—
41C3⋊Dic3C2×D311yescharacteristic
42C3⋊Dic3C2×D312yes—
43C3⋊Dic3C2×D311yescharacteristic
44C3×Dic3—32no—
45C3×Dic3—32no—
46C3×Dic3—32no—
47C3×Dic3—32no—
48C3×Dic3—61no—
49C3×Dic3—61no—
50C3×Dic3—62no—
51C33#4111yescharacteristic, complemented, Sylow
52C3×D4—92no—
53C2×C3×C4—91no—
54#67—32no—
55#67—32no—
56#67—62no—
57#67—92no—
58C2×Dic3—32no—
59C2×Dic3—61no—
60C2×Dic3—92no—
61D12—91no—
62C4×D3—92no—
63C4×D3—92no—
64Dic6—91no—
65Dic6—92no—
66C2×C32—21no—
67C2×C32—22no—
68C2×C32—22no—
69C2×C32—21no—
70C2×C32—22no—
71C2×C32—41no—
72C2×C32—42no—
73C2×C32—42no—
74C2×C32C22×D311yescharacteristic
75C2×C32C22×D312yes—
76C3⋊D3—22no—
77C3×D3—62no—
78C3×D3—62no—
79C3×D3—122no—
80#41—271noSylow
81C22×C3—21no—
82C22×C3—22no—
83C22×C3—41no—
84C22×C3—92no—
85C22×C3D3212yes—
86C22×C3D3211yescharacteristic
87C2×D3—32no—
88C2×D3—32no—
89C2×D3—62no—
90C3×C4—92no—
91C3×C4—91no—
92C3×C4—91no—
93Dic3—32no—
94Dic3—32no—
95Dic3—32no—
96Dic3—32no—
97Dic3—61no—
98Dic3—61no—
99Dic3—62no—
100C32—22no—
101C32—21no—
102C32—41no—
103C32#23511yescharacteristic, complemented
104C32#23712yescomplemented
105Q8—271no—
106D4—92no—
107D4—271no—
108C2×C4—91no—
109C2×C4—272no—
110C2×C3—22no—
111C2×C3—22no—
112C2×C3—21no—
113C2×C3—21no—
114C2×C3—22no—
115C2×C3—42no—
116C2×C3—42no—
117C2×C3—41no—
118C2×C3—182no—
119C2×C3C2×D3212yes—
120C2×C3C2×D3211yescharacteristic
121D3—62no—
122D3—62no—
123D3—122no—
124C22—92no—
125C22#111311yescharacteristic
126C4—91no—
127C4—91no—
128C4—92no—
129C3—22no—
130C3—21no—
131C3—41no—
132C3#380412yescomplemented
133C3#380511yescharacteristic, complemented
134C2—21no—
135C2—182no—
136C2C2×#111311yescharacteristic
subgroupG/H
center, FrattiniC2C2×#1113
commutator, socle, cosocleC2×C33C23
FittingC22×C33C22
hypercenterC22#1113
hypocenterC33#41
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C3×#638C2semidirect
2. C2×C3×C3⋊Dic3C2semidirect
3. #6296C2semidirect
4. #6295C2semidirect
5. #6294C2semidirect
13. #638D3semidirect
14. C2×C3⋊Dic3D3semidirect
51. C33#41semidirect
103. C32#235semidirect
104. C32#237semidirect
132. C3#3804semidirect
133. C3#3805semidirect

Maximal subgroups

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

subgroupindex
C3×#6382
C2×C3×C3⋊Dic32
#62962
#62952
#62942
#38053
#38043