Finite Group Databasebeta

← C2×C3⋊(C3⋊#11925894) #36345255

Subgroups — C2×C3⋊(C3⋊#11925894) #36345255

Order 21780.

300 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#10597244C211yesmaximal, characteristic, complemented
2C3⋊(C3⋊#11925894)C212yesmaximal, direct product factor
3C2×C3⋊#11925894—34nomaximal
4C32×#10597244C2211yescharacteristic, complemented, Hall
5C2×C3⋊(C3⋊(C11⋊D11))C511yesmaximal, characteristic, complemented, Hall
6C2×C3×#10597244D314yescomplemented
7C3⋊#11925894—38no—
8C2×#11925894—91noHall
9C3⋊(C3⋊(C11⋊D11))C2×C512yescomplemented
10C2×C32×C112C2×C511yescharacteristic, complemented
11C2×C3⋊(C3⋊AGL(1,𝔽11))—112nomaximal
12C3×#10597244C2×D314yescomplemented
13C2×C3⋊(C11⋊D11)—34no—
14C2×#10597244C3⋊D311yescharacteristic, complemented
15#11925894—92no—
16C32×C112C22×C511yescharacteristic, complemented, Hall
17C2×C32×C11⋊C5—112no—
18C3⋊(C3⋊AGL(1,𝔽11))—114no—
19C2×C3×C112C5×D314yescomplemented
20C3⋊(C11⋊D11)—38no—
21C2×C3⋊AGL(1,𝔽11)—338no—
22#10597244C2×C3⋊D311yescharacteristic, complemented, Hall
23C32×C11⋊C5—112no—
24C2×C11⋊D11—91noHall
25C2×C3⋊D33—112no—
26C2×C3⋊D33—552no—
27C3×C112C2×C5×D314yescomplemented
28C2×C3×C11⋊C5—118no—
29C3⋊AGL(1,𝔽11)—3316no—
30C2×C112C5×C3⋊D311yescharacteristic, complemented
31C11⋊D11—92no—
32C2×AGL(1,𝔽11)—992no—
33C2×C32×C11—52no—
34C2×C32×C11AGL(1,𝔽11)12yescomplemented
35C3⋊D33—114no—
36C3⋊D33—554no—
37C2×C5×C3⋊D3—1211noHall
38C3×C11⋊C5—118no—
39C2×D33—338no—
40C2×D33—1658no—
41C112C2×C5×C3⋊D311yescharacteristic, complemented, Sylow
42C2×C11⋊C5—112no—
43AGL(1,𝔽11)—994no—
44C32×C11—52no—
45C32×C11C2×AGL(1,𝔽11)12yescomplemented
46C2×C32×C5—1211no—
47C5×C3⋊D3—1212no—
48C2×C3×C11—58no—
49C2×C3×C11C3⋊AGL(1,𝔽11)18yescomplemented
50D33—3316no—
51D33—16516no—
52C2×C5×D3—3634no—
53C11⋊C5—112no—
54C32×C5—1211noHall
55C2×D11—992no—
56C2×D11—4952no—
57C2×C3⋊D3—1211noHall
58C3×C11—58no—
59C3×C11C2×C3⋊AGL(1,𝔽11)18yescomplemented
60C2×C3×C5—1214no—
61C5×D3—3638no—
62C2×C11—52no—
63C2×C11C3⋊(C3⋊AGL(1,𝔽11))12yescomplemented
64D11—994no—
65D11—4954no—
66C22×C5—10891noHall
67C2×C32#1192589411yescharacteristic, complemented
68C3⋊D3—1212no—
69C3×C5—1214no—
70C2×D3—3634no—
71C11—52no—
72C11C2×C3⋊(C3⋊AGL(1,𝔽11))12yescomplemented
73C2×C5—10892no—
74C2×C5—1211no—
75C32C2×#1192589411yescharacteristic, complemented, Sylow
76C2×C3C3⋊#1192589414yescomplemented
77D3—3638no—
78C5—1211noSylow
79C22—10891noSylow
80C3C2×C3⋊#1192589414yescomplemented
81C2—10892no—
82C2C3⋊(C3⋊#11925894)11yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2C3⋊(C3⋊#11925894)
commutator, cosocle, hypocenterC32×C112C22×C5
FrattiniC1G
Fitting, socleC2×C32×C112C2×C5
LCSG ▷ C32×C112
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C32×#10597244C2semidirect
2. C3⋊(C3⋊#11925894)C2direct (N × H)
4. C32×#10597244C22semidirect
5. C2×C3⋊(C3⋊(C11⋊D11))C5semidirect
6. C2×C3×#10597244D3semidirect
9. C3⋊(C3⋊(C11⋊D11))C2×C5semidirect
10. C2×C32×C112C2×C5semidirect
12. C3×#10597244C2×D3semidirect
14. C2×#10597244C3⋊D3semidirect
16. C32×C112C22×C5semidirect
19. C2×C3×C112C5×D3semidirect
22. #10597244C2×C3⋊D3semidirect
27. C3×C112C2×C5×D3semidirect
30. C2×C112C5×C3⋊D3semidirect
34. C2×C32×C11AGL(1,𝔽11)semidirect
41. C112C2×C5×C3⋊D3semidirect
45. C32×C11C2×AGL(1,𝔽11)semidirect
49. C2×C3×C11C3⋊AGL(1,𝔽11)semidirect
59. C3×C11C2×C3⋊AGL(1,𝔽11)semidirect
63. C2×C11C3⋊(C3⋊AGL(1,𝔽11))semidirect
67. C2×C32#11925894semidirect
72. C11C2×C3⋊(C3⋊AGL(1,𝔽11))semidirect
75. C32C2×#11925894semidirect
76. C2×C3C3⋊#11925894semidirect
80. C3C2×C3⋊#11925894semidirect
82. C2C3⋊(C3⋊#11925894)direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#105972442
C3⋊(C3⋊#11925894)2
C2×C3⋊#119258943
C2×C3⋊(C3⋊(C11⋊D11))5
C2×C3⋊(C3⋊AGL(1,𝔽11))11