Finite Group Databasebeta

← #88957

Subgroups — #88957

Order 432.

198 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 50 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#6294C211yesmaximal, characteristic
2#6293C212yesmaximal, complemented
3Dic3×C3⋊D3C211yesmaximal, characteristic
4C3×#627C212yesmaximal, complemented
5C3×#624C211yesmaximal, characteristic
6#3797—31nomaximal
7D3×Dic6—32nomaximal
8C2×C3×C3⋊D3C2211yescharacteristic
9C3⋊(C3⋊Dic3)C2211yescharacteristic
10C3×C3⋊Dic3C2212yes—
11C32×Dic3C2212yes—
12C32×Dic3C2211yescharacteristic
13C4×C3⋊D3—31no—
14#634—32no—
15C3×C4×D3—32no—
16C3×Dic6—32no—
17C3×Dic6—32no—
18#627—32no—
19#627—32no—
20#627—62no—
21#627D312yescomplemented
22#624—31no—
23#624D311yescharacteristic
24D3×Dic3—32no—
25D3×Dic3—32no—
26D3×Dic3—61no—
27C2×C33C2311yescharacteristic
28C3×C3⋊D3Q812yescomplemented
29D3×Q8—92no—
30C2×Dic6—91no—
31C2×C3⋊D3C2×D311yescharacteristic
32C2×C3×D3—32no—
33C2×C3×D3—61no—
34C32×C4—31no—
35C32×C4—32no—
36C3⋊Dic3—32no—
37C3⋊Dic3—31no—
38C3⋊Dic3—61no—
39C3⋊Dic3—62no—
40C3⋊Dic3—121no—
41C3⋊Dic3C2×D312yes—
42C3×Dic3—21no—
43C3×Dic3—22no—
44C3×Dic3—32no—
45C3×Dic3—32no—
46C3×Dic3—62no—
47C3×Dic3C2×D312yes—
48C3×Dic3C2×D312yes—
49C3×Dic3C2×D312yes—
50C33C2×Q811yescharacteristic, complemented, Sylow
51C3×Q8—92no—
52C2×C3×C4—91no—
53C2×Dic3—91no—
54C2×Dic3—91no—
55C4×D3—32no—
56C4×D3—92no—
57C4×D3—92no—
58C4×D3—181no—
59Dic6—32no—
60Dic6—32no—
61Dic6—92no—
62Dic6—92no—
63Dic6—92no—
64Dic6—182no—
65C2×C32—22no—
66C2×C32—21no—
67C2×C32—41no—
68C2×C32C22×D311yescharacteristic
69C2×C32C22×D312yes—
70C3⋊D3Dic612yescomplemented
71C3×D3—34no—
72C3×D3—62no—
73C2×Q8—271noSylow
74C22×C3—91no—
75C2×D3—32no—
76C2×D3—61no—
77C3×C4—32no—
78C3×C4—32no—
79C3×C4—32no—
80C3×C4—62no—
81C3×C4—61no—
82C3×C4—92no—
83Dic3—32no—
84Dic3—32no—
85Dic3—62no—
86Dic3—92no—
87Dic3—91no—
88Dic3—182no—
89Dic3—181no—
90Dic3—361no—
91Dic3D3211yescharacteristic
92Dic3D3212yes—
93C32—22no—
94C32—21no—
95C32—41no—
96C32C2×Dic611yescharacteristic, complemented
97C32D3×Q812yescomplemented
98Q8—92no—
99Q8—272no—
100C2×C4—91no—
101C2×C4—271no—
102C2×C4—271no—
103C2×C3—22no—
104C2×C3—21no—
105C2×C3—41no—
106C2×C3—92no—
107C2×C3C2×D3212yes—
108C2×C3C2×D3211yescharacteristic
109D3—34no—
110D3—62no—
111C22—91no—
112C4—32no—
113C4—31no—
114C4—92no—
115C4—271no—
116C3—21no—
117C3—22no—
118C3—41no—
119C3D3×Dic612yescomplemented
120C3#379711yescharacteristic, complemented
121C2—92no—
122C2D3311yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2D33
commutator, Fitting, socle, cosocleC2×C33C23
prime radicalC2×C3×C3⋊D3C22
hypocenterC33C2×Q8
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. #6293C2semidirect
4. C3×#627C2semidirect
21. #627D3semidirect
28. C3×C3⋊D3Q8semidirect
50. C33C2×Q8semidirect
70. C3⋊D3Dic6semidirect
96. C32C2×Dic6semidirect
97. C32D3×Q8semidirect
119. C3D3×Dic6semidirect
120. C3#3797semidirect

Maximal subgroups

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

subgroupindex
#62942
#62932
Dic3×C3⋊D32
C3×#6272
C3×#6242
#37973
D3×Dic63