Finite Group Databasebeta

← C3×C4×S4 #64249

Subgroups — C3×C4×S4 #64249

Order 288.

118 conjugacy classes of subgroups; only the 28 normal subgroups are shown.

normal subgroups only

This group has 118 conjugacy classes of subgroups — too many to draw. Only its 28 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×C3×S4C211yesmaximal, characteristic
2C3×C4×A4C211yesmaximal, characteristic, complemented
3C3×SL(2,ℤ/4)C211yesmaximal, characteristic, complemented
4C4×S4C311yesmaximal, characteristic, direct product factor
5C3×C4×D4—31nomaximal
6C2×C3×A4C2211yescharacteristic
7C3×S4C412yesdirect product factor
8C3×C4×D3—41nomaximal
9C2×S4C2×C311yescharacteristic
10C2×C3×D4—31no—
11C22×C3×C4—31no—
12C22×C3×C4D311yescharacteristic, complemented
13C4×A4—21no—
14C4×A4C2×C311yescharacteristic, complemented
15SL(2,ℤ/4)C2×C311yescharacteristic, complemented
16C3×C4⋊C4—31no—
17C3×C22⋊C4—31no—
18C3×C22⋊C4—31no—
19C3×C42—31no—
20C2×C3×D3—41no—
21C3×A4C2×C411yescharacteristic, complemented
22C32×C4—41no—
23C3×Dic3—41no—
24C4×D4—31noSylow
25C23×C3—31no—
26C23×C3C2×D311yescharacteristic
27C2×A4—21no—
28C2×A4C22×C311yescharacteristic
29S4C3×C412yesdirect product factor
30C3×D4—32no—
31C3×D4—32no—
32C2×C3×C4—31no—
33C2×C3×C4—31no—
34C2×C3×C4—31no—
35C2×C3×C4—31no—
36C2×C3×C4—31no—
37C2×C3×C4—61no—
38C2×C3×C4—61no—
39C4×D3—41no—
40C2×C32—41no—
41C3×D3—42no—
42C2×D4—31no—
43C22×C4—31no—
44C22×C4C3×D311yescharacteristic, complemented
45C4⋊C4—31no—
46C22⋊C4—31no—
47C22⋊C4—31no—
48C42—31no—
49C22×C3—31no—
50C22×C3—31no—
51C22×C3—32no—
52C22×C3—61no—
53C22×C3—61no—
54C22×C3C4×D311yescharacteristic, complemented
55C2×D3—41no—
56A4—21no—
57A4C2×C3×C411yescharacteristic, complemented
58C3×C4—32no—
59C3×C4—31no—
60C3×C4—41no—
61C3×C4—61no—
62C3×C4—61no—
63C3×C4—81no—
64C3×C4S411yescharacteristic, direct product factor
65Dic3—41no—
66C32—41noSylow
67C23—31no—
68C23C2×C3×D311yescharacteristic
69D4—32no—
70D4—32no—
71C2×C4—31no—
72C2×C4—31no—
73C2×C4—31no—
74C2×C4—31no—
75C2×C4—31no—
76C2×C4—61no—
77C2×C4—61no—
78C2×C3—31no—
79C2×C3—31no—
80C2×C3—41no—
81C2×C3—62no—
82C2×C3—81no—
83C2×C3C2×S411yescharacteristic
84D3—42no—
85C22—31no—
86C22—31no—
87C22—32no—
88C22—61no—
89C22—61no—
90C22C3×C4×D311yescharacteristic, complemented
91C4—32no—
92C4—31no—
93C4—61no—
94C4—61no—
95C4C3×S411yescharacteristic, direct product factor
96C3—41no—
97C3—81no—
98C3C4×S411yescharacteristic, direct product factor
99C2—31no—
100C2—31no—
101C2—62no—
102C2C2×C3×S411yescharacteristic
subgroupG/H
center, hypercenterC3×C4S4
commutator, hypocenterA4C2×C3×C4
FrattiniC2C2×C3×S4
FittingC22×C3×C4D3
socleC23×C3C2×D3
prime radicalC2×C3×S4C2
cosocleC2×A4C22×C3
LCSG ▷ A4
UCSC1 ◁ C3×C4

Complements

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

NH ≅ G/Ntype
2. C3×C4×A4C2semidirect
3. C3×SL(2,ℤ/4)C2semidirect
4. C4×S4C3direct (N × H)
7. C3×S4C4direct (N × H)
12. C22×C3×C4D3semidirect
14. C4×A4C2×C3semidirect
15. SL(2,ℤ/4)C2×C3semidirect
21. C3×A4C2×C4semidirect
29. S4C3×C4direct (N × H)
44. C22×C4C3×D3semidirect
54. C22×C3C4×D3semidirect
57. A4C2×C3×C4semidirect
64. C3×C4S4direct (N × H)
90. C22C3×C4×D3semidirect
95. C4C3×S4direct (N × H)
98. C3C4×S4direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×S42
C3×C4×A42
C3×SL(2,ℤ/4)2
C4×S43
C3×C4×D43
C3×C4×D34