Finite Group Databasebeta

← C24×C4×C3⋊D3 #11919146

Subgroups — C24×C4×C3⋊D3 #11919146

Order 1152.

31656 conjugacy classes of subgroups; only the 8681 normal subgroups are shown.

normal subgroups only

This group has 31656 conjugacy classes of subgroups — too many to draw. Only its 8681 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
1C25×C3⋊D3C211yesmaximal, characteristic
2C24×C32×C4C211yesmaximal, characteristic, complemented
3C24×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C23×C4×C3⋊D3C2160yesmaximal, direct product factor
5C24×C4×D3—34nomaximal
6C25×C32C2211yescharacteristic
7C24×C3⋊D3C4132yesdirect product factor
8C24×C3⋊D3C22130yes—
9C23×C32×C4C22130yescomplemented
10C23×C3⋊Dic3C22130yescomplemented
11C22×C4×C3⋊D3C221560yesdirect product factor
12C25×D3—34no—
13C24×C3×C4D314yescomplemented
14C24×Dic3—34no—
15C23×C4×D3—3240no—
16C24×C32C2×C4116yescomplemented
17C24×C32C23115yes—
18C23×C3⋊D3C2×C41480yesdirect product factor
19C23×C3⋊D3C231140yes—
20C22×C32×C4C231140yescomplemented
21C22×C3⋊Dic3C231140yescomplemented
22C2×C4×C3⋊D3C231960yesdirect product factor
23C25×C4—91noSylow
24C25×C3C2×D314yes—
25C24×D3—3128no—
26C24×D3—3120no—
27C23×C3×C4C2×D31120yescomplemented
28C23×Dic3—3120no—
29C22×C4×D3—32240no—
30C23×C32C22×C41120yescomplemented
31C23×C32C24135yes—
32C22×C3⋊D3C22×C411120yesdirect product factor
33C22×C3⋊D3C241120yes—
34C2×C32×C4C241120yescomplemented
35C2×C3⋊Dic3C241120yescomplemented
36C4×C3⋊D3C241256yesdirect product factor
37C26—91no—
38C24×C4—91no—
39C24×C4—960no—
40C24×C4C3⋊D311yescharacteristic, direct product factor
41C24×C3C4×D3164yescomplemented
42C24×C3C22×D3160yes—
43C23×D3—31920no—
44C23×D3—3560no—
45C22×C3×C4C22×D31560yescomplemented
46C22×Dic3—3560no—
47C2×C4×D3—33840no—
48C22×C32C23×C41140yescomplemented
49C22×C32C25115yes—
50C2×C3⋊D3C23×C41480yesdirect product factor
51C2×C3⋊D3C25116yes—
52C32×C4C25116yescomplemented
53C3⋊Dic3C25116yescomplemented
54C25—932no—
55C25—930no—
56C25C2×C3⋊D311yescharacteristic
57C23×C4—930no—
58C23×C4—9560no—
59C23×C4C2×C3⋊D3130yesdirect product factor
60C23×C3C2×C4×D31480yescomplemented
61C23×C3C23×D31140yes—
62C22×D3—34480no—
63C22×D3—3480no—
64C2×C3×C4C23×D31480yescomplemented
65C2×Dic3—3480no—
66C4×D3—31024no—
67C2×C32C24×C4130yescomplemented
68C2×C32C2611yescharacteristic
69C3⋊D3C24×C4132yesdirect product factor
70C24—9140no—
71C24—9480no—
72C24C4×C3⋊D3116yesdirect product factor
73C24C22×C3⋊D3115yes—
74C22×C4—9140no—
75C22×C4—9960no—
76C22×C4C22×C3⋊D31140yesdirect product factor
77C22×C3C22×C4×D31560yescomplemented
78C22×C3C24×D3160yes—
79C2×D3—31920no—
80C2×D3—364no—
81C3×C4C24×D3164yescomplemented
82Dic3—364no—
83C32C25×C411yescharacteristic, complemented, Sylow
84C23—91120no—
85C23—9120no—
86C23C2×C4×C3⋊D31120yesdirect product factor
87C23C23×C3⋊D3135yes—
88C2×C4—9120no—
89C2×C4—9256no—
90C2×C4C23×C3⋊D31120yesdirect product factor
91C2×C3C23×C4×D31120yescomplemented
92C2×C3C25×D314yes—
93D3—3128no—
94C22—9480no—
95C22—916no—
96C22C22×C4×C3⋊D31140yesdirect product factor
97C22C24×C3⋊D3115yes—
98C4—916no—
99C4C24×C3⋊D3116yesdirect product factor
100C3C24×C4×D314yescomplemented
101C2—932no—
102C2C23×C4×C3⋊D3130yesdirect product factor
103C2C25×C3⋊D311yescharacteristic
subgroupG/H
center, hypercenterC24×C4C3⋊D3
commutator, hypocenterC32C25×C4
FrattiniC2C25×C3⋊D3
FittingC24×C32×C4C2
socleC25×C32C22
prime radicalC25×C3⋊D3C2
cosocleC2×C32C26
LCSG ▷ C32
UCSC1 ◁ C24×C4

Complements

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

NH ≅ G/Ntype
2. C24×C32×C4C2semidirect
3. C24×C3⋊Dic3C2semidirect
4. C23×C4×C3⋊D3C2direct (N × H)
7. C24×C3⋊D3C4direct (N × H)
9. C23×C32×C4C22semidirect
10. C23×C3⋊Dic3C22semidirect
11. C22×C4×C3⋊D3C22direct (N × H)
13. C24×C3×C4D3semidirect
16. C24×C32C2×C4semidirect
18. C23×C3⋊D3C2×C4direct (N × H)
20. C22×C32×C4C23semidirect
21. C22×C3⋊Dic3C23semidirect
22. C2×C4×C3⋊D3C23direct (N × H)
27. C23×C3×C4C2×D3semidirect
30. C23×C32C22×C4semidirect
32. C22×C3⋊D3C22×C4direct (N × H)
34. C2×C32×C4C24semidirect
35. C2×C3⋊Dic3C24semidirect
36. C4×C3⋊D3C24direct (N × H)
40. C24×C4C3⋊D3direct (N × H)
41. C24×C3C4×D3semidirect
45. C22×C3×C4C22×D3semidirect
48. C22×C32C23×C4semidirect
50. C2×C3⋊D3C23×C4direct (N × H)
52. C32×C4C25semidirect
53. C3⋊Dic3C25semidirect
59. C23×C4C2×C3⋊D3direct (N × H)
60. C23×C3C2×C4×D3semidirect
64. C2×C3×C4C23×D3semidirect
67. C2×C32C24×C4semidirect
69. C3⋊D3C24×C4direct (N × H)
72. C24C4×C3⋊D3direct (N × H)
76. C22×C4C22×C3⋊D3direct (N × H)
77. C22×C3C22×C4×D3semidirect
81. C3×C4C24×D3semidirect
83. C32C25×C4semidirect
86. C23C2×C4×C3⋊D3direct (N × H)
90. C2×C4C23×C3⋊D3direct (N × H)
91. C2×C3C23×C4×D3semidirect
96. C22C22×C4×C3⋊D3direct (N × H)
99. C4C24×C3⋊D3direct (N × H)
100. C3C24×C4×D3semidirect
102. C2C23×C4×C3⋊D3direct (N × H)

Maximal subgroups

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

subgroupindex
C25×C3⋊D32
C24×C32×C42
C24×C3⋊Dic32
C23×C4×C3⋊D32
C24×C4×D33