Finite Group Databasebeta

← D3×#11925898 #20300017

Subgroups — D3×#11925898 #20300017

Order 7260.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#10597244C211yesmaximal, characteristic, complemented
2C3⋊#11925898C211yesmaximal, characteristic, complemented
3C3×#11925898C211yesmaximal, characteristic, complemented
4C2×#11925898—31nomaximal, Hall
5C3×#10597244C2211yescharacteristic, complemented, Hall
6D3×C11×D11C511yesmaximal, characteristic, complemented, Hall
7C2×#10597244—31no—
8#11925898—31no—
9#11925898D311yescharacteristic, direct product factor
10C11×D33C2×C511yescharacteristic, complemented
11D3×C112C2×C511yescharacteristic, complemented
12C3×C11×D11C2×C511yescharacteristic, complemented
13C2×D3×C11⋊C5—111nomaximal
14D3×AGL(1,𝔽11)—111nomaximal
15#10597244C2×D311yescharacteristic, complemented, Hall
16C2×C11×D11—31noHall
17C3×C112C22×C511yescharacteristic, complemented, Hall
18C2×C3×C11⋊C5—111no—
19C3⋊AGL(1,𝔽11)—111no—
20D3×C11⋊C5—111no—
21D3×C11⋊C5—111no—
22D3×C11⋊C5—111no—
23C3×AGL(1,𝔽11)—111no—
24C2×C112—31no—
25C11×D11—31no—
26C11×D11C5×D311yescharacteristic, complemented
27C22×C11⋊C5—331no—
28C2×AGL(1,𝔽11)—331no—
29C3×C11⋊C5—111no—
30C3×C11⋊C5—111no—
31C2×D3×C11—111no—
32D3×D11C11⋊C511yescharacteristic, complemented
33C112C2×C5×D311yescharacteristic, complemented, Sylow
34C2×C11⋊C5—111no—
35C2×C11⋊C5—331no—
36C2×C11⋊C5—331no—
37C2×C11⋊C5—331no—
38AGL(1,𝔽11)—111no—
39AGL(1,𝔽11)—331no—
40C2×C3×C11—111no—
41D33C2×C11⋊C511yescharacteristic, complemented
42C3×D11C2×C11⋊C511yescharacteristic, complemented
43D3×C11—101no—
44D3×C11—111no—
45D3×C11AGL(1,𝔽11)11yescharacteristic, complemented
46D3×C11C2×C11⋊C511yescharacteristic, complemented
47C2×C5×D3—1211noHall
48C11⋊C5—111no—
49C11⋊C5—111no—
50C22×C11—331no—
51C2×D11—31no—
52C3×C11—101no—
53C3×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
54C3×C11C22×C11⋊C511yescharacteristic, complemented
55C2×C3×C5—1211no—
56C5×D3—1211no—
57C5×D3—1211no—
58C2×C11—31no—
59C2×C11—31no—
60C2×C11—111no—
61C2×C11—301no—
62C2×C11—331no—
63D11—31no—
64D11D3×C11⋊C511yescharacteristic, complemented
65C22×C5—3631noHall
66C3×C5—1211noHall
67C2×D3—111noHall
68C11—101no—
69C11D3×AGL(1,𝔽11)11yescharacteristic, complemented
70C11C2×D3×C11⋊C511yescharacteristic, complemented
71C2×C5—3631no—
72C2×C5—3631no—
73C2×C5—1211no—
74C2×C3—111no—
75D3—111no—
76D3#1192589811yescharacteristic, direct product factor
77C5—1211noSylow
78C22—331noSylow
79C3C2×#1192589811yescharacteristic, complemented, Sylow
80C2—31no—
81C2—111no—
82C2—331no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C112C22×C5
LCSG ▷ C3×C112
UCSC1

Complements

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

NH ≅ G/Ntype
1. D3×#10597244C2semidirect
2. C3⋊#11925898C2semidirect
3. C3×#11925898C2semidirect
5. C3×#10597244C22semidirect
6. D3×C11×D11C5semidirect
9. #11925898D3direct (N × H)
10. C11×D33C2×C5semidirect
11. D3×C112C2×C5semidirect
12. C3×C11×D11C2×C5semidirect
15. #10597244C2×D3semidirect
17. C3×C112C22×C5semidirect
26. C11×D11C5×D3semidirect
32. D3×D11C11⋊C5semidirect
33. C112C2×C5×D3semidirect
41. D33C2×C11⋊C5semidirect
42. C3×D11C2×C11⋊C5semidirect
45. D3×C11AGL(1,𝔽11)semidirect
46. D3×C11C2×C11⋊C5semidirect
53. C3×C11C2×AGL(1,𝔽11)semidirect
54. C3×C11C22×C11⋊C5semidirect
64. D11D3×C11⋊C5semidirect
69. C11D3×AGL(1,𝔽11)semidirect
70. C11C2×D3×C11⋊C5semidirect
76. D3#11925898direct (N × H)
79. C3C2×#11925898semidirect