Finite Group Databasebeta

← AGL(1,𝔽11)×C3⋊D57 #49178558

Subgroups — AGL(1,𝔽11)×C3⋊D57 #49178558

Order 37620.

240 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 67 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
1C11⋊C5×C3⋊D57C211yesmaximal, characteristic, complemented
2C3⋊(C3⋊(C19⋊AGL(1,𝔽11)))C211yesmaximal, characteristic, complemented
3C32×C19×AGL(1,𝔽11)C211yesmaximal, characteristic, complemented
4AGL(1,𝔽11)×D57—34nomaximal
5C32×C19×C11⋊C5C2211yescharacteristic, complemented, Hall
6D11×C3⋊D57C511yesmaximal, characteristic, complemented, Hall
7C3⋊(C19⋊AGL(1,𝔽11))—34no—
8C11⋊C5×D57—34no—
9C3×C19×AGL(1,𝔽11)D314yescomplemented
10D19×AGL(1,𝔽11)—91noHall
11C3⋊D627C2×C511yescharacteristic, complemented
12C11×C3⋊D57C2×C511yescharacteristic, complemented
13C32×C19×D11C2×C511yescharacteristic, complemented
14C2×C5×C3⋊D57—111nomaximal, Hall
15C3×C19×C11⋊C5C2×D314yescomplemented
16D11×D57—34no—
17C19⋊AGL(1,𝔽11)—91no—
18C19×AGL(1,𝔽11)C3⋊D311yescharacteristic, complemented
19D19×C11⋊C5—91no—
20C3⋊D3×AGL(1,𝔽11)—191nomaximal, Hall
21C32×C11×C19C22×C511yescharacteristic, complemented, Hall
22C2×C32×C5×C19—111no—
23C5×C3⋊D57—111no—
24C5×C3⋊D57—111no—
25D627—34no—
26C11×D57—34no—
27C3×C19×D11C5×D314yescomplemented
28C2×C5×D57—334no—
29C19×C11⋊C5C2×C3⋊D311yescharacteristic, complemented, Hall
30C3⋊(C3⋊AGL(1,𝔽11))—191no—
31C3⋊D3×C11⋊C5—191no—
32C32×AGL(1,𝔽11)D1911yescharacteristic, complemented
33C32×C5×C19—111noHall
34D11×D19—91noHall
35C2×C3⋊D57—111noHall
36D3×AGL(1,𝔽11)—574no—
37C3×C11×C19C2×C5×D314yescomplemented
38C2×C3×C5×C19—114no—
39C5×D57—334no—
40C5×D57—334no—
41C32×C11⋊C5C2×D1911yescharacteristic, complemented, Hall
42D209—91no—
43C11×D19—91no—
44C19×D11C5×C3⋊D311yescharacteristic, complemented
45C3⋊D3×D11—191noHall
46C2×C5×D19—991noHall
47C2×C32×C19—111no—
48C3⋊D57—111no—
49C3⋊D57AGL(1,𝔽11)11yescharacteristic, direct product factor
50C3⋊AGL(1,𝔽11)—574no—
51D3×C11⋊C5—574no—
52C3×AGL(1,𝔽11)D5714yescomplemented
53C3×C5×C19—114no—
54C2×D57—334no—
55C2×AGL(1,𝔽11)—1711noHall
56C11×C19C2×C5×C3⋊D311yescharacteristic, complemented, Hall
57C3⋊D33—191no—
58C11×C3⋊D3—191no—
59C32×D11C5×D1911yescharacteristic, complemented
60C2×C5×C19—111no—
61C5×D19—991no—
62C5×D19—991no—
63C2×C5×C3⋊D3—2091noHall
64C32×C19C2×AGL(1,𝔽11)11yescharacteristic, complemented, Hall
65C3×C11⋊C5C2×D5714yescomplemented
66D3×D11—574no—
67C2×C3×C19—114no—
68D57—34no—
69D57—334no—
70C2×C11⋊C5—1711no—
71AGL(1,𝔽11)—1711no—
72AGL(1,𝔽11)C3⋊D5711yescharacteristic, direct product factor
73C32×C11C2×C5×D1911yescharacteristic, complemented, Hall
74C5×C19—111noHall
75C2×C32×C5—111no—
76C5×C3⋊D3—2091no—
77C5×C3⋊D3—2091no—
78C2×D19—991noHall
79D33—574no—
80C3×D11C5×D5714yescomplemented
81D3×C11—574no—
82C2×C5×D3—6274no—
83C3×C19D3×AGL(1,𝔽11)14yescomplemented
84C11⋊C5C2×C3⋊D5711yescharacteristic, complemented, Hall
85C32×C5—111noHall
86C2×D11—1711noHall
87C2×C19—111no—
88D19—91no—
89D19—991no—
90C2×C3⋊D3—2091noHall
91C3×C11C2×C5×D5714yescomplemented
92C2×C3×C5—114no—
93C5×D3—6274no—
94C5×D3—6274no—
95C2×C11—1711no—
96D11—1711no—
97D11C5×C3⋊D5711yescharacteristic, complemented
98C22×C5—18811noHall
99C19C3⋊D3×AGL(1,𝔽11)11yescharacteristic, complemented, Sylow
100C2×C32—111no—
101C3⋊D3—191no—
102C3⋊D3—2091no—
103C3×C5—114no—
104C2×D3—6274no—
105C11C2×C5×C3⋊D5711yescharacteristic, complemented, Sylow
106C2×C5—111no—
107C2×C5—18811no—
108C2×C5—18811no—
109C32D19×AGL(1,𝔽11)11yescharacteristic, complemented, Sylow
110C2×C3—114no—
111D3—574no—
112D3—6274no—
113C5—111noSylow
114C22—18811noSylow
115C3AGL(1,𝔽11)×D5714yescomplemented
116C2—111no—
117C2—18811no—
118C2—1711no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C11×C19C22×C5
LCSG ▷ C32×C11×C19
UCSC1

Complements

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

NH ≅ G/Ntype
1. C11⋊C5×C3⋊D57C2semidirect
2. C3⋊(C3⋊(C19⋊AGL(1,𝔽11)))C2semidirect
3. C32×C19×AGL(1,𝔽11)C2semidirect
5. C32×C19×C11⋊C5C22semidirect
6. D11×C3⋊D57C5semidirect
9. C3×C19×AGL(1,𝔽11)D3semidirect
11. C3⋊D627C2×C5semidirect
12. C11×C3⋊D57C2×C5semidirect
13. C32×C19×D11C2×C5semidirect
15. C3×C19×C11⋊C5C2×D3semidirect
18. C19×AGL(1,𝔽11)C3⋊D3semidirect
21. C32×C11×C19C22×C5semidirect
27. C3×C19×D11C5×D3semidirect
29. C19×C11⋊C5C2×C3⋊D3semidirect
32. C32×AGL(1,𝔽11)D19semidirect
37. C3×C11×C19C2×C5×D3semidirect
41. C32×C11⋊C5C2×D19semidirect
44. C19×D11C5×C3⋊D3semidirect
49. C3⋊D57AGL(1,𝔽11)direct (N × H)
52. C3×AGL(1,𝔽11)D57semidirect
56. C11×C19C2×C5×C3⋊D3semidirect
59. C32×D11C5×D19semidirect
64. C32×C19C2×AGL(1,𝔽11)semidirect
65. C3×C11⋊C5C2×D57semidirect
72. AGL(1,𝔽11)C3⋊D57direct (N × H)
73. C32×C11C2×C5×D19semidirect
80. C3×D11C5×D57semidirect
83. C3×C19D3×AGL(1,𝔽11)semidirect
84. C11⋊C5C2×C3⋊D57semidirect
91. C3×C11C2×C5×D57semidirect
97. D11C5×C3⋊D57semidirect
99. C19C3⋊D3×AGL(1,𝔽11)semidirect
105. C11C2×C5×C3⋊D57semidirect
109. C32D19×AGL(1,𝔽11)semidirect
115. C3AGL(1,𝔽11)×D57semidirect

Maximal subgroups

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

subgroupindex
C11⋊C5×C3⋊D572
C3⋊(C3⋊(C19⋊AGL(1,𝔽11)))2
C32×C19×AGL(1,𝔽11)2
AGL(1,𝔽11)×D573
D11×C3⋊D575
C2×C5×C3⋊D5711
C3⋊D3×AGL(1,𝔽11)19