Finite Group Databasebeta

← C3⋊(C3⋊(C3⋊((C3⋊D3)⋊C3))) #13091684

Subgroups — C3⋊(C3⋊(C3⋊((C3⋊D3)⋊C3))) #13091684

Order 1458.

5258 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C33×H(3,𝔽3)C211yesmaximal, characteristic, complemented, Sylow
2C3⋊(C3⋊(C3⋊(C3⋊D3)))C311yesmaximal, characteristic, complemented
3C3×C3⋊(C3⋊(C3⋊D3))—31nomaximal
4C3⋊(C3⋊((C3⋊D3)⋊C3))—339nomaximal
5C35—21no—
6C35D311yescharacteristic, complemented
7C35C2×C311yescharacteristic, complemented
8C32×H(3,𝔽3)—239no—
9C32×H(3,𝔽3)D3139yescomplemented
10C3⋊(C3⋊(C3⋊D3))—31no—
11C3⋊(C3⋊(C3⋊D3))—339no—
12C3⋊(C3⋊(C3⋊D3))—927no—
13C3×C3⋊(C3⋊D3)—927no—
14C3×C3⋊(C3⋊D3)—913no—
15C3⋊((C3⋊D3)⋊C3)—9117no—
16C34—213no—
17C34—239no—
18C34—327no—
19C34—327no—
20C34—627no—
21C34C3×D311yescharacteristic
22C34C3×D3139yescomplemented
23C34C3⋊D3113yescomplemented
24C3×H(3,𝔽3)—2468no—
25C3×H(3,𝔽3)C3⋊D31117yescomplemented
26C3⋊(C3⋊D3)—927no—
27C3⋊(C3⋊D3)—913no—
28C3⋊(C3⋊D3)—9117no—
29C3⋊(C3⋊D3)—27351no—
30C3×C3⋊D3—27117no—
31C3×C3⋊D3—2713no—
32(C3⋊D3)⋊C3—2727no—
33C33—252no—
34C33—2117no—
35C33—3351no—
36C33—3117no—
37C33—6117no—
38C33—6351no—
39C33(C3⋊D3)⋊C3127yescomplemented
40C33C3×C3⋊D3113yes—
41C33C3×C3⋊D31117yescomplemented
42C33C3⋊(C3⋊D3)113yescomplemented
43H(3,𝔽3)—2351no—
44H(3,𝔽3)C3⋊(C3⋊D3)127yescomplemented
45C3⋊D3—27117no—
46C3⋊D3—2713no—
47C3⋊D3—2727no—
48C3⋊D3—81351no—
49C3×D3—8139no—
50C3×D3—811no—
51C32—213no—
52C32—227no—
53C32—3351no—
54C32—339no—
55C32—6156no—
56C32—6351no—
57C32C3⋊((C3⋊D3)⋊C3)1117yescomplemented
58C32C3×C3⋊(C3⋊D3)113yes—
59C32C3×C3⋊(C3⋊D3)127yescomplemented
60C32C3⋊(C3⋊(C3⋊D3))11yescharacteristic, complemented
61C2×C3—2431no—
62D3—8139no—
63D3—811no—
64D3—24327no—
65C3—327no—
66C3—31no—
67C3—613no—
68C3—627no—
69C3C3⋊(C3⋊((C3⋊D3)⋊C3))139yescomplemented
70C3C3×C3⋊(C3⋊(C3⋊D3))11yescharacteristic
71C2—2431noSylow
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC35C2×C3
FrattiniC3C3×C3⋊(C3⋊(C3⋊D3))
FittingC33×H(3,𝔽3)C2
socleC34C3×D3
LCSG ▷ C35
UCSC1

Complements

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

NH ≅ G/Ntype
1. C33×H(3,𝔽3)C2semidirect
2. C3⋊(C3⋊(C3⋊(C3⋊D3)))C3semidirect
6. C35D3semidirect
7. C35C2×C3semidirect
9. C32×H(3,𝔽3)D3semidirect
22. C34C3×D3semidirect
23. C34C3⋊D3semidirect
25. C3×H(3,𝔽3)C3⋊D3semidirect
39. C33(C3⋊D3)⋊C3semidirect
41. C33C3×C3⋊D3semidirect
42. C33C3⋊(C3⋊D3)semidirect
44. H(3,𝔽3)C3⋊(C3⋊D3)semidirect
57. C32C3⋊((C3⋊D3)⋊C3)semidirect
59. C32C3×C3⋊(C3⋊D3)semidirect
60. C32C3⋊(C3⋊(C3⋊D3))semidirect
69. C3C3⋊(C3⋊((C3⋊D3)⋊C3))semidirect

Maximal subgroups

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

subgroupindex
C33×H(3,𝔽3)2
C3⋊(C3⋊(C3⋊(C3⋊D3)))3
C3×C3⋊(C3⋊(C3⋊D3))3
C3⋊(C3⋊((C3⋊D3)⋊C3))3