Finite Group Databasebeta

← D32×A4 #89102

Subgroups — D32×A4 #89102

Order 432.

188 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 30 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
1A4×C3⋊D3C211yesmaximal, characteristic, complemented
2C3×D3×A4C212yesmaximal, complemented
3C22×D32C311yesmaximal, characteristic, complemented
4C2×D3×A4—32nomaximal
5C32×A4C2211yescharacteristic, complemented
6C3×D32—41nomaximal
7C22×C3⋊D3C2×C311yescharacteristic, complemented
8C22×C3×D3C2×C312yescomplemented
9C2×C3×A4—32no—
10C2×D32—31no—
11C2×D32—31no—
12C2×D32—32no—
13D3×A4—22no—
14D3×A4—32no—
15D3×A4—61no—
16D3×A4D312yesdirect product factor
17C3×C3⋊D3—41no—
18C32×D3—42no—
19C23×D3—32no—
20C22×A4—91no—
21C22×C32C22×C311yescharacteristic, complemented
22C2×C3⋊D3—31no—
23C2×C3⋊D3—31no—
24C2×C3×D3—32no—
25C2×C3×D3—32no—
26C2×C3×D3—122no—
27C3×A4—22no—
28C3×A4—21no—
29C3×A4—41no—
30C3×A4C2×D312yescomplemented
31D32—32no—
32D32—31no—
33D32—32no—
34D32A411yescharacteristic, direct product factor
35C33—41noSylow
36C23×C3—32no—
37C22×D3—32no—
38C22×D3—61no—
39C22×D3—92no—
40C22×D3—92no—
41C22×D3—92no—
42C22×D3—92no—
43C22×D3C3×D312yescomplemented
44C2×A4—32no—
45C2×A4—62no—
46C2×A4—91no—
47C2×C32—31no—
48C2×C32—122no—
49C3⋊D3—31no—
50C3⋊D3C2×A411yescharacteristic, complemented
51C3×D3—32no—
52C3×D3—42no—
53C3×D3—82no—
54C3×D3—122no—
55C3×D3—241no—
56C3×D3C2×A412yescomplemented
57C24—91noSylow
58C22×C3—21no—
59C22×C3—92no—
60C22×C3—92no—
61C22×C3—361no—
62C22×C3C2×C3×D312yescomplemented
63C2×D3—32no—
64C2×D3—32no—
65C2×D3—32no—
66C2×D3—92no—
67C2×D3—92no—
68C2×D3—92no—
69C2×D3—94no—
70C2×D3—92no—
71C2×D3—92no—
72C2×D3—181no—
73C2×D3—181no—
74A4—22no—
75A4—41no—
76A4D3211yescharacteristic, direct product factor
77C32—42no—
78C32—81no—
79C32—82no—
80C32—161no—
81C32C22×A411yescharacteristic, complemented
82C23—32no—
83C23—91no—
84C23—271no—
85C23—272no—
86C23—271no—
87C2×C3—32no—
88C2×C3—32no—
89C2×C3—61no—
90C2×C3—92no—
91C2×C3—122no—
92C2×C3—242no—
93C2×C3—361no—
94D3—32no—
95D3—32no—
96D3—61no—
97D3—92no—
98D3—181no—
99D3D3×A412yesdirect product factor
100C22—92no—
101C22—91no—
102C22—92no—
103C22—271no—
104C22—272no—
105C22—271no—
106C22—271no—
107C22—272no—
108C22C3×D3211yescharacteristic, complemented
109C3—21no—
110C3—41no—
111C3—82no—
112C3—161no—
113C3C2×D3×A412yescomplemented
114C2—31no—
115C2—32no—
116C2—92no—
117C2—91no—
118C2—271no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC22×C32C22×C3
LCSG ▷ C22×C32
UCSC1

Complements

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

NH ≅ G/Ntype
1. A4×C3⋊D3C2semidirect
2. C3×D3×A4C2semidirect
3. C22×D32C3semidirect
5. C32×A4C22semidirect
7. C22×C3⋊D3C2×C3semidirect
8. C22×C3×D3C2×C3semidirect
16. D3×A4D3direct (N × H)
21. C22×C32C22×C3semidirect
30. C3×A4C2×D3semidirect
34. D32A4direct (N × H)
43. C22×D3C3×D3semidirect
50. C3⋊D3C2×A4semidirect
56. C3×D3C2×A4semidirect
62. C22×C3C2×C3×D3semidirect
76. A4D32direct (N × H)
81. C32C22×A4semidirect
99. D3D3×A4direct (N × H)
108. C22C3×D32semidirect
113. C3C2×D3×A4semidirect

Maximal subgroups

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

subgroupindex
A4×C3⋊D32
C3×D3×A42
C22×D323
C2×D3×A43
C3×D324