Finite Group Databasebeta

← (C3⋊S4)⋊C4 #64206

Subgroups — (C3⋊S4)⋊C4 #64206

Order 288.

122 conjugacy classes of subgroups; only the 21 normal subgroups are shown.

normal subgroups only

This group has 122 conjugacy classes of subgroups — too many to draw. Only its 21 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
2Dic3×A4C211yesmaximal, characteristic, complemented
3C3×SL(2,ℤ/4)C211yesmaximal, characteristic, complemented
4C4×S4—31nomaximal
5#67⋊C4—31nomaximal
6C2×C3×A4C2211yescharacteristic
7C3⋊S4C412yescomplemented
8#624—41nomaximal
9C2×S4—31no—
10C2×S4—61no—
11C2×#67—31no—
12C22×Dic3D311yescharacteristic, complemented
13C2×C4×D3—31no—
14C4×A4—31no—
15SL(2,ℤ/4)D311yescharacteristic, complemented
16C3×C22⋊C4—31no—
17(C2×D3)⋊C4—31no—
18Dic3⋊C4—31no—
19C4×Dic3—31no—
20C2×C3⋊D3—41no—
21C3×A4C2×C411yescharacteristic, complemented
22C3×Dic3—41no—
23C3×Dic3—41no—
24C4×D4—91noSylow
25C23×C3C2×D311yescharacteristic
26C22×D3—31no—
27C2×A4—21no—
28C2×A4C2×D311yescharacteristic
29S4—32no—
30S4—62no—
31C2×C3×C4—31no—
32C2×C3×C4—31no—
33#67—32no—
34#67—32no—
35C2×Dic3—31no—
36C2×Dic3—31no—
37C2×Dic3—31no—
38C4×D3—61no—
39C4×D3—61no—
40C4×D3—121no—
41C2×C32—41no—
42C3⋊D3—42no—
43C2×D4—91no—
44C22×C4—31no—
45C22×C4—91no—
46C4⋊C4—91no—
47C22⋊C4—31no—
48C22⋊C4—91no—
49C42—91no—
50C22×C3—31no—
51C22×C3—31no—
52C22×C3C4×D311yescharacteristic, complemented
53C2×D3—32no—
54C2×D3—61no—
55C2×D3—61no—
56C2×D3—121no—
57C2×D3—241no—
58A4—21no—
59A4C4×D311yescharacteristic, complemented
60C3×C4—61no—
61C3×C4—61no—
62C3×C4—121no—
63Dic3—32no—
64Dic3—31no—
65Dic3—41no—
66Dic3S411yescharacteristic, complemented
67C32—41noSylow
68C23—91no—
69C23D3211yescharacteristic
70D4—92no—
71D4—92no—
72C2×C4—31no—
73C2×C4—31no—
74C2×C4—91no—
75C2×C4—91no—
76C2×C4—91no—
77C2×C4—181no—
78C2×C4—181no—
79C2×C3—31no—
80C2×C3—31no—
81C2×C3—41no—
82C2×C3—81no—
83C2×C3C2×S411yescharacteristic
84D3—62no—
85D3—122no—
86D3—242no—
87C22—31no—
88C22—31no—
89C22—92no—
90C22—181no—
91C22—181no—
92C22#62411yescharacteristic, complemented
93C4—31no—
94C4—61no—
95C4—61no—
96C4—92no—
97C4—91no—
98C3—41no—
99C3—81no—
100C3C4×S411yescharacteristic, complemented
101C2—31no—
102C2—31no—
103C2—182no—
104C2D3×S411yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2D3×S4
commutator, hypocenterC3×A4C2×C4
Fitting, socleC23×C3C2×D3
prime radicalC2×C3⋊S4C2
cosocleC2×C3×A4C22
LCSG ▷ C3×A4
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. Dic3×A4C2semidirect
3. C3×SL(2,ℤ/4)C2semidirect
7. C3⋊S4C4semidirect
12. C22×Dic3D3semidirect
15. SL(2,ℤ/4)D3semidirect
21. C3×A4C2×C4semidirect
52. C22×C3C4×D3semidirect
59. A4C4×D3semidirect
66. Dic3S4semidirect
92. C22#624semidirect
100. C3C4×S4semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊S42
Dic3×A42
C3×SL(2,ℤ/4)2
C4×S43
#67⋊C43
#6244