Finite Group Databasebeta

← #88959

Subgroups — #88959

Order 432.

218 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 46 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
1#6296C211yesmaximal, characteristic, complemented
2#6291C212yesmaximal, complemented
3#6289C211yesmaximal, characteristic, complemented
4C3×#625C211yesmaximal, characteristic, complemented
5C3×D3×Dic3C212yesmaximal, complemented
6#3804—32nomaximal
7#3798—31nomaximal
8C2×C3⋊(C3⋊D3)C2211yescharacteristic
9C2×C32×D3C2212yes—
10C3×C3⋊Dic3C2212yes—
11C3×C3⋊Dic3C2211yescharacteristic
12C32×Dic3C2211yescharacteristic
13#638—32no—
14C4×C3⋊D3—31no—
15C3×#67—32no—
16C2×C3×Dic3—32no—
17C3×C4×D3—32no—
18#627—31no—
19#627—32no—
20#626—32no—
21#626—32no—
22#626—62no—
23#625D311yescharacteristic, complemented
24#624—32no—
25#624—61no—
26D3×Dic3D312yescomplemented
27C2×C33C2311yescharacteristic
28C3⋊(C3⋊D3)—21no—
29C32×D3—22no—
30#237—91no—
31#235—92no—
32C22×C32—32no—
33C2×C3⋊D3—32no—
34C2×C3⋊D3—31no—
35C2×C3⋊D3—61no—
36C2×C3⋊D3—62no—
37C2×C3⋊D3—121no—
38C2×C3×D3—22no—
39C2×C3×D3C2×D312yes—
40C2×C3×D3C2×D312yes—
41C32×C4—31no—
42C3⋊Dic3C2×D312yes—
43C3⋊Dic3C2×D311yescharacteristic
44C3×Dic3—21no—
45C3×Dic3—32no—
46C3×Dic3—32no—
47C3×Dic3—32no—
48C3×Dic3—61no—
49C3×Dic3—62no—
50C3×Dic3C2×D312yes—
51C33#4111yescharacteristic, complemented, Sylow
52C3×D4—91no—
53C2×C3×C4—92no—
54#67—32no—
55#67—92no—
56#67—92no—
57#67—182no—
58C2×Dic3—32no—
59D12—92no—
60C4×D3—32no—
61C4×D3—92no—
62C4×D3—91no—
63C4×D3—181no—
64Dic6—92no—
65Dic6—91no—
66C2×C32—21no—
67C2×C32—22no—
68C2×C32—41no—
69C2×C32—62no—
70C2×C32C22×D312yes—
71C2×C32C22×D311yescharacteristic
72C3⋊D3—61no—
73C3⋊D3—62no—
74C3⋊D3—62no—
75C3⋊D3—122no—
76C3⋊D3—122no—
77C3×D3—22no—
78C3×D3—22no—
79C3×D3—42no—
80#41—271noSylow
81C22×C3—32no—
82C22×C3—32no—
83C22×C3—62no—
84C2×D3—92no—
85C2×D3—91no—
86C2×D3—181no—
87C2×D3—182no—
88C2×D3—361no—
89C2×D3D3212yes—
90C3×C4—32no—
91C3×C4—61no—
92C3×C4—91no—
93C3×C4—92no—
94Dic3—32no—
95Dic3—32no—
96Dic3—32no—
97Dic3—61no—
98Dic3—62no—
99Dic3D3211yescharacteristic
100C32—21no—
101C32—22no—
102C32—41no—
103C32#23512yescomplemented
104C32#23711yescharacteristic, complemented
105Q8—271no—
106D4—91no—
107D4—272no—
108C2×C4—92no—
109C2×C4—271no—
110C2×C3—21no—
111C2×C3—22no—
112C2×C3—41no—
113C2×C3—62no—
114C2×C3—62no—
115C2×C3—122no—
116C2×C3C2×D3211yescharacteristic
117C2×C3C2×D3212yes—
118D3—22no—
119D3—182no—
120D3—181no—
121D3—182no—
122D3—362no—
123D3—362no—
124C22—32no—
125C22—271no—
126C4—31no—
127C4—92no—
128C4—91no—
129C3—21no—
130C3—22no—
131C3—41no—
132C3#379811yescharacteristic, complemented
133C3#380412yescomplemented
134C2—62no—
135C2—541no—
136C2D3311yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2D33
commutator, Fitting, socle, cosocleC2×C33C23
hypocenterC33#41
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. #6296C2semidirect
2. #6291C2semidirect
3. #6289C2semidirect
4. C3×#625C2semidirect
5. C3×D3×Dic3C2semidirect
23. #625D3semidirect
26. D3×Dic3D3semidirect
51. C33#41semidirect
103. C32#235semidirect
104. C32#237semidirect
132. C3#3798semidirect
133. C3#3804semidirect

Maximal subgroups

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

subgroupindex
#62962
#62912
#62892
C3×#6252
C3×D3×Dic32
#38043
#37983