Finite Group Databasebeta

← D11×C5⋊AGL(1,𝔽11) #27130924

Subgroups — D11×C5⋊AGL(1,𝔽11) #27130924

Order 12100.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5⋊((C11⋊C5)⋊D11)C211yesmaximal, characteristic, complemented
2C11×C5⋊AGL(1,𝔽11)C211yesmaximal, characteristic, complemented
3C5×D11×C11⋊C5C211yesmaximal, characteristic, complemented
4C5×C11×C11⋊C5C2211yescharacteristic, complemented, Hall
5D11×D55C511yesmaximal, characteristic, complemented
6D11×AGL(1,𝔽11)—51nomaximal
7C5⋊(C11⋊D11)C2×C511yescharacteristic, complemented
8C11×D55C2×C511yescharacteristic, complemented
9C5×C11×D11C2×C511yescharacteristic, complemented
10D11×C11⋊C5—22no—
11D11×C11⋊C5D511yescharacteristic, complemented
12(C11⋊C5)⋊D11—51no—
13C11×AGL(1,𝔽11)—51no—
14C5×D5×D11—111nomaximal
15C2×C5⋊AGL(1,𝔽11)—111nomaximal
16C5×C112C22×C511yescharacteristic, complemented
17C11×C11⋊C5—22no—
18C11×C11⋊C5C2×D511yescharacteristic, complemented
19C5×D55—111no—
20C5×D5×C11—111no—
21C52×D11—111no—
22C2×C5×C11⋊C5—111no—
23C5⋊AGL(1,𝔽11)—111no—
24C5⋊AGL(1,𝔽11)D1111yescharacteristic, direct product factor
25D112—51noHall
26C52×C11—111no—
27C5×C11⋊C5C2×D1111yescharacteristic, complemented
28C11⋊D11—51no—
29C11×D11—51no—
30C11×D11C5×D511yescharacteristic, complemented
31C2×D55—111no—
32C2×C5×D11—551no—
33D5×D11—111no—
34C2×AGL(1,𝔽11)—551no—
35C112C2×C5×D511yescharacteristic, complemented, Sylow
36C2×C5×C11—111no—
37C2×C5×C11—551no—
38D55—111no—
39D55—111no—
40D55—1101no—
41D55C5×D1111yescharacteristic, complemented
42C5×D11—111no—
43C5×D11—222no—
44C5×D11—551no—
45C5×D11AGL(1,𝔽11)11yescharacteristic, complemented
46D5×C11—111no—
47C2×C11⋊C5—111no—
48C2×C11⋊C5—222no—
49AGL(1,𝔽11)—51no—
50AGL(1,𝔽11)—551no—
51C2×C5×D5—1211noHall
52C5×C11—101no—
53C5×C11—111no—
54C5×C11—222no—
55C5×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
56C5×C11C2×C5×D1111yescharacteristic, complemented
57C11⋊C5—22no—
58C11⋊C5D5×D1111yescharacteristic, complemented
59C2×C52—1211no—
60C5×D5—111no—
61C5×D5—1211no—
62C2×D11—551no—
63C2×D11—551no—
64C52—111noSylow
65C2×C11—111no—
66C2×C11—551no—
67D11—51no—
68D11—5501no—
69D11—551no—
70D11—551no—
71D11C5⋊AGL(1,𝔽11)11yescharacteristic, direct product factor
72C22×C5—6051no—
73C2×D5—1211no—
74C11—101no—
75C11C2×C5⋊AGL(1,𝔽11)11yescharacteristic, complemented
76C11C5×D5×D1111yescharacteristic, complemented
77C2×C5—111no—
78C2×C5—551no—
79C2×C5—6051no—
80C2×C5—1211no—
81C2×C5—2422no—
82D5—111no—
83D5—1211no—
84C5—111no—
85C5—222no—
86C5D11×AGL(1,𝔽11)11yescharacteristic, complemented
87C22—6051noSylow
88C2—111no—
89C2—551no—
90C2—6051no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C112C22×C5
LCSG ▷ C5×C112
UCSC1

Complements

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

NH ≅ G/Ntype
1. C5⋊((C11⋊C5)⋊D11)C2semidirect
2. C11×C5⋊AGL(1,𝔽11)C2semidirect
3. C5×D11×C11⋊C5C2semidirect
4. C5×C11×C11⋊C5C22semidirect
5. D11×D55C5semidirect
7. C5⋊(C11⋊D11)C2×C5semidirect
8. C11×D55C2×C5semidirect
9. C5×C11×D11C2×C5semidirect
11. D11×C11⋊C5D5semidirect
16. C5×C112C22×C5semidirect
18. C11×C11⋊C5C2×D5semidirect
24. C5⋊AGL(1,𝔽11)D11direct (N × H)
27. C5×C11⋊C5C2×D11semidirect
30. C11×D11C5×D5semidirect
35. C112C2×C5×D5semidirect
41. D55C5×D11semidirect
45. C5×D11AGL(1,𝔽11)semidirect
55. C5×C11C2×AGL(1,𝔽11)semidirect
56. C5×C11C2×C5×D11semidirect
58. C11⋊C5D5×D11semidirect
71. D11C5⋊AGL(1,𝔽11)direct (N × H)
75. C11C2×C5⋊AGL(1,𝔽11)semidirect
76. C11C5×D5×D11semidirect
86. C5D11×AGL(1,𝔽11)semidirect

Maximal subgroups

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

subgroupindex
C5⋊((C11⋊C5)⋊D11)2
C11×C5⋊AGL(1,𝔽11)2
C5×D11×C11⋊C52
D11×D555
D11×AGL(1,𝔽11)5
C5×D5×D1111
C2×C5⋊AGL(1,𝔽11)11