Finite Group Databasebeta

← C2×C3×C3⋊S4 #89114

Subgroups — C2×C3×C3⋊S4 #89114

Order 432.

208 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 38 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×C3⋊S4C212yesmaximal, direct product factor
3C2×C3⋊S4C311yesmaximal, characteristic, direct product factor
4C2×C3×S4—33nomaximal
5C2×C3×#67—31nomaximal
6C2×C3×C3⋊D3—41nomaximal
7C32×A4C2211yescharacteristic, complemented
8C23×C32D311yescharacteristic, complemented
9C22×C3×D3—31no—
10C2×C3×A4—21no—
11C2×C3×A4—23no—
12C2×C3×A4D313yescomplemented
13C2×C3×A4C2×C311yescharacteristic, complemented
14C3⋊S4C2×C312yesdirect product factor
15C3×S4—36no—
16C3×#67—32no—
17C3×#67—32no—
18C2×C3×Dic3—31no—
19C2×C33—41no—
20C3×C3⋊D3—42no—
21C2×S4—33no—
22C2×C3×D4—91no—
23C2×#67—31no—
24C22×C32—31no—
25C22×C32—31no—
26C22×C32C2×D311yescharacteristic, complemented
27C2×C3⋊D3—41no—
28C2×C3×D3—32no—
29C2×C3×D3—61no—
30C2×C3×D3—61no—
31C2×C3×D3—123no—
32C3×A4—21no—
33C3×A4—23no—
34C3×A4C2×D313yescomplemented
35C3×A4C22×C311yescharacteristic, complemented
36C3×Dic3—32no—
37C33—41noSylow
38C23×C3—21no—
39C23×C3—91no—
40C23×C3C3×D311yescharacteristic, complemented
41C23×C3C3⋊D311yescharacteristic, complemented
42C22×D3—31no—
43C2×A4—23no—
44C2×A4C3×D313yescomplemented
45S4—36no—
46C3×D4—92no—
47C3×D4—92no—
48C2×C3×C4—91no—
49#67—32no—
50#67—32no—
51C2×Dic3—31no—
52C2×C32—31no—
53C2×C32—31no—
54C2×C32—41no—
55C2×C32—43no—
56C2×C32—83no—
57C2×C32—81no—
58C2×C32S411yescharacteristic, complemented
59C3⋊D3—42no—
60C3×D3—62no—
61C3×D3—126no—
62C2×D4—91noSylow
63C22×C3—21no—
64C22×C3—31no—
65C22×C3—31no—
66C22×C3—31no—
67C22×C3—31no—
68C22×C3—61no—
69C22×C3—61no—
70C22×C3—92no—
71C22×C3—181no—
72C22×C3—181no—
73C22×C3C2×C3×D311yescharacteristic, complemented
74C22×C3C2×C3⋊D311yescharacteristic, complemented
75C2×D3—32no—
76C2×D3—61no—
77C2×D3—61no—
78C2×D3—123no—
79A4—23no—
80A4C2×C3×D313yescomplemented
81C3×C4—92no—
82Dic3—32no—
83C32—41no—
84C32—43no—
85C32—83no—
86C32—81no—
87C32C2×S411yescharacteristic, complemented
88C23—91no—
89C23C3×C3⋊D311yescharacteristic, complemented
90D4—92no—
91D4—92no—
92C2×C4—91no—
93C2×C3—21no—
94C2×C3—31no—
95C2×C3—31no—
96C2×C3—31no—
97C2×C3—31no—
98C2×C3—43no—
99C2×C3—61no—
100C2×C3—61no—
101C2×C3—83no—
102C2×C3—182no—
103C2×C3C3×S411yescharacteristic, complemented
104C2×C3C3⋊S411yescharacteristic, direct product factor
105D3—62no—
106D3—126no—
107C22—31no—
108C22—31no—
109C22—92no—
110C22—181no—
111C22—181no—
112C22C2×C3×C3⋊D311yescharacteristic, complemented
113C4—92no—
114C3—21no—
115C3—43no—
116C3—83no—
117C3C2×C3×S411yescharacteristic, complemented
118C3C2×C3⋊S411yescharacteristic, direct product factor
119C2—31no—
120C2—31no—
121C2—182no—
122C2C3×C3⋊S411yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3C3⋊S4
commutator, cosocle, hypocenterC3×A4C22×C3
FrattiniC1G
Fitting, socleC23×C32D3
LCSG ▷ C3×A4
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C2×C32×A4C2semidirect
2. C3×C3⋊S4C2direct (N × H)
3. C2×C3⋊S4C3direct (N × H)
7. C32×A4C22semidirect
8. C23×C32D3semidirect
12. C2×C3×A4D3semidirect
13. C2×C3×A4C2×C3semidirect
14. C3⋊S4C2×C3direct (N × H)
26. C22×C32C2×D3semidirect
34. C3×A4C2×D3semidirect
35. C3×A4C22×C3semidirect
40. C23×C3C3×D3semidirect
41. C23×C3C3⋊D3semidirect
44. C2×A4C3×D3semidirect
58. C2×C32S4semidirect
73. C22×C3C2×C3×D3semidirect
74. C22×C3C2×C3⋊D3semidirect
80. A4C2×C3×D3semidirect
87. C32C2×S4semidirect
89. C23C3×C3⋊D3semidirect
103. C2×C3C3×S4semidirect
104. C2×C3C3⋊S4direct (N × H)
112. C22C2×C3×C3⋊D3semidirect
117. C3C2×C3×S4semidirect
118. C3C2×C3⋊S4direct (N × H)
122. C2C3×C3⋊S4direct (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×C3⋊S42
C2×C3⋊S43
C2×C3×S43
C2×C3×#673
C2×C3×C3⋊D34