Finite Group Databasebeta

← C2×C3×D3×A4 #89116

Subgroups — C2×C3×D3×A4 #89116

Order 432.

232 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 56 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
1C2×C32×A4C211yesmaximal, characteristic, complemented
2C3×D3×A4C212yesmaximal, direct product factor
3C23×C3×D3C311yesmaximal, characteristic, complemented
4C22×C3×A4—31nomaximal
5C2×D3×A4C313yesmaximal, direct product factor
6C2×C32×D3—41nomaximal
7C32×A4C2211yescharacteristic, complemented
8C23×C32C2×C311yescharacteristic, complemented
9C22×C3×D3—31no—
10C22×C3×D3—31no—
11C22×C3×D3—32no—
12C22×C3×D3C2×C312yescomplemented
13C2×C3×A4—21no—
14C2×C3×A4—23no—
15C2×C3×A4—32no—
16C2×C3×A4D311yescharacteristic, direct product factor
17C2×C3×A4C2×C313yescomplemented
18D3×A4C2×C316yesdirect product factor
19C2×C33—41no—
20C32×D3—42no—
21C24×C3—31no—
22C23×D3C3211yescharacteristic, complemented
23C22×A4—33no—
24C22×C32—31no—
25C22×C32—31no—
26C22×C32—121no—
27C22×C32C22×C311yescharacteristic, complemented
28C2×C3×D3—32no—
29C2×C3×D3—31no—
30C2×C3×D3—32no—
31C2×C3×D3—32no—
32C2×C3×D3—32no—
33C2×C3×D3—43no—
34C2×C3×D3A411yescharacteristic, direct product factor
35C3×A4—21no—
36C3×A4—23no—
37C3×A4C2×D311yescharacteristic, direct product factor
38C3×A4C22×C313yescomplemented
39C33—41noSylow
40C23×C3—21no—
41C23×C3—32no—
42C23×C3—91no—
43C23×C3—92no—
44C23×C3—91no—
45C23×C3C3×D311yescharacteristic, complemented
46C23×C3C2×C3211yescharacteristic, complemented
47C22×D3—31no—
48C22×D3—31no—
49C22×D3—32no—
50C22×D3C2×C3212yescomplemented
51C2×A4—23no—
52C2×A4—36no—
53C2×A4C3×D313yesdirect product factor
54C2×C32—31no—
55C2×C32—31no—
56C2×C32—41no—
57C2×C32—43no—
58C2×C32—83no—
59C2×C32—81no—
60C2×C32—122no—
61C2×C32C2×A411yescharacteristic, complemented
62C3×D3—32no—
63C3×D3—46no—
64C3×D3C2×A412yesdirect product factor
65C24—31noSylow
66C22×C3—21no—
67C22×C3—31no—
68C22×C3—31no—
69C22×C3—31no—
70C22×C3—31no—
71C22×C3—31no—
72C22×C3—61no—
73C22×C3—61no—
74C22×C3—92no—
75C22×C3—92no—
76C22×C3—92no—
77C22×C3—92no—
78C22×C3—91no—
79C22×C3—123no—
80C22×C3C2×C3×D311yescharacteristic, complemented
81C22×C3C22×C3211yescharacteristic, complemented
82C2×D3—32no—
83C2×D3—31no—
84C2×D3—32no—
85C2×D3—32no—
86C2×D3—32no—
87C2×D3C3×A411yescharacteristic, direct product factor
88A4—23no—
89A4C2×C3×D313yesdirect product factor
90C32—41no—
91C32—43no—
92C32—83no—
93C32—81no—
94C32C22×A411yescharacteristic, complemented
95C23—32no—
96C23—91no—
97C23—92no—
98C23—91no—
99C23C32×D311yescharacteristic, complemented
100C2×C3—21no—
101C2×C3—31no—
102C2×C3—31no—
103C2×C3—32no—
104C2×C3—31no—
105C2×C3—31no—
106C2×C3—43no—
107C2×C3—61no—
108C2×C3—61no—
109C2×C3—83no—
110C2×C3—92no—
111C2×C3—126no—
112C2×C3D3×A411yescharacteristic, direct product factor
113C2×C3C2×C3×A411yescharacteristic, complemented
114D3—32no—
115D3C2×C3×A412yesdirect product factor
116C22—31no—
117C22—31no—
118C22—31no—
119C22—92no—
120C22—92no—
121C22—92no—
122C22—92no—
123C22—91no—
124C22C2×C32×D311yescharacteristic, complemented
125C3—21no—
126C3—43no—
127C3—83no—
128C3C2×D3×A411yescharacteristic, direct product factor
129C3C22×C3×A411yescharacteristic, complemented
130C2—31no—
131C2—31no—
132C2—32no—
133C2—92no—
134C2C3×D3×A411yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3D3×A4
commutator, cosocle, hypocenterC22×C3C22×C32
FrattiniC1G
Fitting, socleC23×C32C2×C3
LCSG ▷ C22×C3
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C2×C32×A4C2semidirect
2. C3×D3×A4C2direct (N × H)
3. C23×C3×D3C3semidirect
5. C2×D3×A4C3direct (N × H)
7. C32×A4C22semidirect
8. C23×C32C2×C3semidirect
12. C22×C3×D3C2×C3semidirect
16. C2×C3×A4D3direct (N × H)
17. C2×C3×A4C2×C3semidirect
18. D3×A4C2×C3direct (N × H)
22. C23×D3C32semidirect
27. C22×C32C22×C3semidirect
34. C2×C3×D3A4direct (N × H)
37. C3×A4C2×D3direct (N × H)
38. C3×A4C22×C3semidirect
45. C23×C3C3×D3semidirect
46. C23×C3C2×C32semidirect
50. C22×D3C2×C32semidirect
53. C2×A4C3×D3direct (N × H)
61. C2×C32C2×A4semidirect
64. C3×D3C2×A4direct (N × H)
80. C22×C3C2×C3×D3semidirect
81. C22×C3C22×C32semidirect
87. C2×D3C3×A4direct (N × H)
89. A4C2×C3×D3direct (N × H)
94. C32C22×A4semidirect
99. C23C32×D3semidirect
112. C2×C3D3×A4direct (N × H)
113. C2×C3C2×C3×A4semidirect
115. D3C2×C3×A4direct (N × H)
124. C22C2×C32×D3semidirect
128. C3C2×D3×A4direct (N × H)
129. C3C22×C3×A4semidirect
134. C2C3×D3×A4direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×A42
C3×D3×A42
C23×C3×D33
C22×C3×A43
C2×D3×A43
C2×C32×D34