Finite Group Databasebeta

← #88965

Subgroups — #88965

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#6295C211yesmaximal, characteristic, complemented
2#6292C212yesmaximal, complemented
3#6289C211yesmaximal, characteristic, complemented
4C3×#627C211yesmaximal, characteristic, complemented
5C3×#624C212yesmaximal, complemented
6#3799—32nomaximal
7#3798—31nomaximal
8C2×C3⋊(C3⋊D3)C2211yescharacteristic
9C2×C3×C3⋊D3C2212yes—
10C3×C3⋊Dic3C2211yescharacteristic
11C32×Dic3C2211yescharacteristic
12C32×Dic3C2212yes—
13C4⋊(C3⋊D3)—32no—
14C4×C3⋊D3—31no—
15C3×C4×D3—32no—
16C3×C4×D3—32no—
17C3×Dic6—32no—
18#627D311yescharacteristic, complemented
19#626—32no—
20#626—32no—
21#626—32no—
22#626—62no—
23#625—31no—
24#624—32no—
25#624—61no—
26#624D312yescomplemented
27C2×C33C2311yescharacteristic
28C3⋊(C3⋊D3)—21no—
29C3×C3⋊D3—22no—
30#239—91no—
31#235—92no—
32C2×C3⋊D3—32no—
33C2×C3⋊D3—31no—
34C2×C3⋊D3—61no—
35C2×C3⋊D3—62no—
36C2×C3⋊D3—121no—
37C2×C3⋊D3C2×D312yes—
38C2×C3×D3—32no—
39C2×C3×D3—32no—
40C2×C3×D3—62no—
41C32×C4—32no—
42C32×C4—31no—
43C3⋊Dic3C2×D311yescharacteristic
44C3×Dic3—21no—
45C3×Dic3—22no—
46C3×Dic3—32no—
47C3×Dic3—61no—
48C3×Dic3C2×D312yes—
49C3×Dic3C2×D312yes—
50C3×Dic3C2×D312yes—
51C33#4111yescharacteristic, complemented, Sylow
52C3×Q8—91no—
53C2×C3×C4—92no—
54#67—92no—
55#67—92no—
56D12—92no—
57D12—92no—
58D12—91no—
59D12—182no—
60C4×D3—32no—
61C4×D3—32no—
62C4×D3—92no—
63C4×D3—91no—
64C4×D3—181no—
65Dic6—32no—
66C2×C32—21no—
67C2×C32—22no—
68C2×C32—41no—
69C2×C32C22×D312yes—
70C2×C32C22×D311yescharacteristic
71C3⋊D3—22no—
72C3⋊D3—61no—
73C3⋊D3—62no—
74C3⋊D3—62no—
75C3⋊D3—122no—
76C3⋊D3—122no—
77C3×D3—62no—
78C3×D3—62no—
79C3×D3—122no—
80#41—271noSylow
81C22×C3—92no—
82C2×D3—32no—
83C2×D3—32no—
84C2×D3—62no—
85C2×D3—91no—
86C2×D3—92no—
87C2×D3—181no—
88C2×D3—182no—
89C2×D3—361no—
90C3×C4—32no—
91C3×C4—32no—
92C3×C4—32no—
93C3×C4—61no—
94C3×C4—62no—
95C3×C4—91no—
96Dic3—32no—
97Dic3—61no—
98Dic3D3212yes—
99Dic3D3211yescharacteristic
100C32—21no—
101C32—22no—
102C32—41no—
103C32#23512yescomplemented
104C32#23911yescharacteristic, complemented
105Q8—91no—
106D4—272no—
107D4—271no—
108C2×C4—92no—
109C2×C4—271no—
110C2×C3—21no—
111C2×C3—22no—
112C2×C3—41no—
113C2×C3—182no—
114C2×C3C2×D3211yescharacteristic
115C2×C3C2×D3212yes—
116D3—62no—
117D3—62no—
118D3—122no—
119D3—182no—
120D3—181no—
121D3—182no—
122D3—362no—
123D3—362no—
124C22—92no—
125C22—271no—
126C4—31no—
127C4—32no—
128C4—91no—
129C3—22no—
130C3—21no—
131C3—41no—
132C3#379811yescharacteristic, complemented
133C3#379912yescomplemented
134C2—182no—
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. #6295C2semidirect
2. #6292C2semidirect
3. #6289C2semidirect
4. C3×#627C2semidirect
5. C3×#624C2semidirect
18. #627D3semidirect
26. #624D3semidirect
51. C33#41semidirect
103. C32#235semidirect
104. C32#239semidirect
132. C3#3798semidirect
133. C3#3799semidirect

Maximal subgroups

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

subgroupindex
#62952
#62922
#62892
C3×#6272
C3×#6242
#37993
#37983