Finite Group Databasebeta

← C2×D4×C3⋊D3 #64359

Subgroups — C2×D4×C3⋊D3 #64359

Order 288.

708 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 173 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
1C23×C3⋊D3C212yesmaximal, complemented
2C2×C32×D4C211yesmaximal, characteristic, complemented
3C2×#638C212yesmaximal, complemented
4D4×C3⋊D3C218yesmaximal, direct product factor
5C2×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
6C2×C4×C3⋊D3C211yesmaximal, characteristic, complemented
7C2×D3×D4—34nomaximal
8C23×C32C2212yescomplemented
9C22×C3⋊D3—28no—
10C22×C3⋊D3C2211yescharacteristic
11C22×C3⋊D3C2218yescomplemented
12C22×C3⋊D3C2212yescomplemented
13C32×D4C2214yescomplemented
14C2×C32×C4C2211yescharacteristic, complemented
15#638C2218yescomplemented
16C2×C3⋊Dic3C2211yescharacteristic, complemented
17C4⋊(C3⋊D3)C2214yescomplemented
18C4×C3⋊D3C2214yescomplemented
19C23×D3—38no—
20C2×C3×D4D314yescomplemented
21C2×#67—38no—
22D3×D4—332no—
23C2×D12—34no—
24C2×C4×D3—34no—
25C22×C32—24no—
26C22×C32C2311yescharacteristic
27C22×C32C2314yescomplemented
28C2×C3⋊D3—24no—
29C2×C3⋊D3—216no—
30C2×C3⋊D3D414yesdirect product factor
31C2×C3⋊D3C2312yes—
32C2×C3⋊D3C2314yescomplemented
33C32×C4C2312yescomplemented
34C3⋊Dic3C2312yescomplemented
35C22×D4—91noSylow
36C23×C3C2×D318yescomplemented
37C22×D3—34no—
38C22×D3—38no—
39C22×D3—332no—
40C22×D3—632no—
41C3×D4C2×D3116yescomplemented
42C2×C3×C4C2×D314yescomplemented
43#67—332no—
44C2×Dic3—34no—
45D12—316no—
46C4×D3—316no—
47C2×C32—24no—
48C2×C32C2×D412yescomplemented
49C2×C32C2411yescharacteristic
50C3⋊D3—24no—
51C3⋊D3C2×D414yesdirect product factor
52C24—92no—
53C2×D4—92no—
54C2×D4—98no—
55C2×D4—91no—
56C2×D4C3⋊D311yescharacteristic, direct product factor
57C22×C4—91no—
58C22×C3—216no—
59C22×C3C22×D314yes—
60C22×C3C22×D3116yescomplemented
61C2×D3—316no—
62C2×D3—38no—
63C2×D3—316no—
64C2×D3—664no—
65C2×D3—616no—
66C3×C4C22×D318yescomplemented
67Dic3—38no—
68C32C22×D411yescharacteristic, complemented, Sylow
69C23—91no—
70C23—92no—
71C23—98no—
72C23—188no—
73C23C2×C3⋊D312yescomplemented
74D4—98no—
75D4—94no—
76D4C2×C3⋊D314yesdirect product factor
77C2×C4—91no—
78C2×C4—94no—
79C2×C4C2×C3⋊D311yescharacteristic, complemented
80C2×C3—216no—
81C2×C3D3×D418yescomplemented
82C2×C3C23×D314yes—
83D3—316no—
84D3—616no—
85C22—24no—
86C22—92no—
87C22—94no—
88C22—94no—
89C22—1816no—
90C22—184no—
91C22C22×C3⋊D311yescharacteristic
92C22C22×C3⋊D314yescomplemented
93C4—92no—
94C4C22×C3⋊D312yescomplemented
95C3C2×D3×D414yescomplemented
96C2—24no—
97C2—94no—
98C2—184no—
99C2D4×C3⋊D312yesdirect product factor
100C2C23×C3⋊D311yescharacteristic
subgroupG/H
centerC22C22×C3⋊D3
commutator, cosocleC2×C32C24
FrattiniC2C23×C3⋊D3
FittingC2×C32×D4C2
socleC22×C32C23
hypercenterC2×D4C3⋊D3
hypocenterC32C22×D4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C23×C3⋊D3C2semidirect
2. C2×C32×D4C2semidirect
3. C2×#638C2semidirect
4. D4×C3⋊D3C2direct (N × H)
5. C2×C4⋊(C3⋊D3)C2semidirect
6. C2×C4×C3⋊D3C2semidirect
8. C23×C32C22semidirect
11. C22×C3⋊D3C22semidirect
12. C22×C3⋊D3C22semidirect
13. C32×D4C22semidirect
14. C2×C32×C4C22semidirect
15. #638C22semidirect
16. C2×C3⋊Dic3C22semidirect
17. C4⋊(C3⋊D3)C22semidirect
18. C4×C3⋊D3C22semidirect
20. C2×C3×D4D3semidirect
27. C22×C32C23semidirect
30. C2×C3⋊D3D4direct (N × H)
32. C2×C3⋊D3C23semidirect
33. C32×C4C23semidirect
34. C3⋊Dic3C23semidirect
36. C23×C3C2×D3semidirect
41. C3×D4C2×D3semidirect
42. C2×C3×C4C2×D3semidirect
48. C2×C32C2×D4semidirect
51. C3⋊D3C2×D4direct (N × H)
56. C2×D4C3⋊D3direct (N × H)
60. C22×C3C22×D3semidirect
66. C3×C4C22×D3semidirect
68. C32C22×D4semidirect
73. C23C2×C3⋊D3semidirect
76. D4C2×C3⋊D3direct (N × H)
79. C2×C4C2×C3⋊D3semidirect
81. C2×C3D3×D4semidirect
92. C22C22×C3⋊D3semidirect
94. C4C22×C3⋊D3semidirect
95. C3C2×D3×D4semidirect
99. C2D4×C3⋊D3direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3⋊D32
C2×C32×D42
C2×#6382
D4×C3⋊D32
C2×C4⋊(C3⋊D3)2
C2×C4×C3⋊D32
C2×D3×D43