Finite Group Databasebeta

← #88964

Subgroups — #88964

Order 432.

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

normal subgroups only

This group has 214 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#6295C211yesmaximal, characteristic, complemented
2Dic3×C3⋊D3C212yesmaximal, complemented
3D3×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C3×#627C211yesmaximal, characteristic, complemented
5C3×#626C212yesmaximal, complemented
6#3805—31nomaximal
7#3796—32nomaximal
8C2×C3×C3⋊D3C2212yes—
9C2×C32×D3C2211yescharacteristic
10C3⋊(C3⋊Dic3)C2211yescharacteristic
11C3×C3⋊Dic3C2211yescharacteristic
12C32×Dic3C2212yes—
13C2×C3⋊Dic3—31no—
14C4×C3⋊D3—32no—
15C3×#67—32no—
16C3×D12—32no—
17C3×Dic6—32no—
18#627D311yescharacteristic, complemented
19#626—32no—
20#626D312yescomplemented
21#625—31no—
22D3×Dic3—32no—
23D3×Dic3—32no—
24D3×Dic3—32no—
25D3×Dic3—61no—
26D3×Dic3—62no—
27C2×C33C2311yescharacteristic
28C3×C3⋊D3—22no—
29C32×D3—21no—
30#239—91no—
31#237—92no—
32C22×C32—31no—
33C2×C3⋊D3C2×D312yes—
34C2×C3×D3—21no—
35C2×C3×D3—32no—
36C2×C3×D3—32no—
37C2×C3×D3—62no—
38C2×C3×D3C2×D312yes—
39C32×C4—32no—
40C3⋊Dic3—32no—
41C3⋊Dic3—31no—
42C3⋊Dic3—61no—
43C3⋊Dic3—62no—
44C3⋊Dic3—121no—
45C3⋊Dic3C2×D311yescharacteristic
46C3×Dic3—22no—
47C3×Dic3—32no—
48C3×Dic3—61no—
49C3×Dic3C2×D312yes—
50C3×Dic3C2×D312yes—
51C33#4111yescharacteristic, complemented, Sylow
52C3×Q8—91no—
53C3×D4—92no—
54#67—32no—
55#67—92no—
56C2×Dic3—92no—
57C2×Dic3—92no—
58C2×Dic3—181no—
59D12—32no—
60D12—91no—
61C4×D3—92no—
62C4×D3—92no—
63C4×D3—91no—
64C4×D3—182no—
65Dic6—32no—
66C2×C32—22no—
67C2×C32—21no—
68C2×C32—41no—
69C2×C32—61no—
70C2×C32C22×D312yes—
71C2×C32C22×D311yescharacteristic
72C3⋊D3—22no—
73C3×D3—22no—
74C3×D3—22no—
75C3×D3—64no—
76C3×D3—62no—
77C3×D3—62no—
78#41—271noSylow
79C22×C3—32no—
80C22×C3—61no—
81C22×C3—92no—
82C2×D3—32no—
83C2×D3—32no—
84C2×D3—62no—
85C2×D3D3211yescharacteristic
86C3×C4—32no—
87C3×C4—32no—
88C3×C4—62no—
89C3×C4—91no—
90Dic3—32no—
91Dic3—61no—
92Dic3—91no—
93Dic3—92no—
94Dic3—182no—
95Dic3—181no—
96Dic3—361no—
97Dic3D3212yes—
98C32—22no—
99C32—21no—
100C32—41no—
101C32#23712yescomplemented
102C32#23911yescharacteristic, complemented
103Q8—91no—
104D4—92no—
105D4—271no—
106C2×C4—272no—
107C2×C4—271no—
108C2×C3—21no—
109C2×C3—22no—
110C2×C3—41no—
111C2×C3—62no—
112C2×C3—62no—
113C2×C3—182no—
114C2×C3C2×D3212yes—
115C2×C3C2×D3211yescharacteristic
116D3—21no—
117D3—64no—
118D3—62no—
119D3—62no—
120C22—31no—
121C22—92no—
122C4—32no—
123C4—91no—
124C4—271no—
125C3—22no—
126C3—21no—
127C3—41no—
128C3#379612yescomplemented
129C3#380511yescharacteristic, complemented
130C2—61no—
131C2—182no—
132C2D3311yescharacteristic
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. #6295C2semidirect
2. Dic3×C3⋊D3C2semidirect
3. D3×C3⋊Dic3C2semidirect
4. C3×#627C2semidirect
5. C3×#626C2semidirect
18. #627D3semidirect
20. #626D3semidirect
51. C33#41semidirect
101. C32#237semidirect
102. C32#239semidirect
128. C3#3796semidirect
129. C3#3805semidirect

Maximal subgroups

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

subgroupindex
#62952
Dic3×C3⋊D32
D3×C3⋊Dic32
C3×#6272
C3×#6262
#38053
#37963