Finite Group Databasebeta

← C2×C3⋊(C3⋊#11925898) #36345254

Subgroups — C2×C3⋊(C3⋊#11925898) #36345254

Order 21780.

252 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 69 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
1C2×C32×#10597244C211yesmaximal, characteristic, complemented
2C3⋊(C3⋊#11925898)C212yesmaximal, direct product factor
3C2×C3⋊#11925898—34nomaximal
4C32×#10597244C2211yescharacteristic, complemented, Hall
5C2×C11×C3⋊D33C511yesmaximal, characteristic, complemented, Hall
6C2×C3×#10597244D314yescomplemented
7C3⋊#11925898—38no—
8C2×#11925898—91noHall
9C11×C3⋊D33C2×C512yescomplemented
10C2×C32×C112C2×C511yescharacteristic, complemented
11C2×C3⋊(C3⋊AGL(1,𝔽11))—111nomaximal
12C2×C3⋊D3×C11⋊C5—111nomaximal
13C3×#10597244C2×D314yescomplemented
14C2×C11×D33—34no—
15C2×#10597244C3⋊D311yescharacteristic, complemented
16#11925898—92no—
17C32×C112C22×C511yescharacteristic, complemented, Hall
18C2×C32×C11⋊C5—111no—
19C2×C32×C11⋊C5—111no—
20C3⋊(C3⋊AGL(1,𝔽11))—112no—
21C3⋊D3×C11⋊C5—112no—
22C2×C3×C112C5×D314yescomplemented
23C11×D33—38no—
24C2×C3⋊AGL(1,𝔽11)—334no—
25C2×D3×C11⋊C5—334no—
26#10597244C2×C3⋊D311yescharacteristic, complemented, Hall
27C32×C11⋊C5—111no—
28C32×C11⋊C5—111no—
29C2×C11×D11—91noHall
30C2×C3⋊D33C11⋊C511yescharacteristic, complemented
31C2×C11×C3⋊D3—111no—
32C3×C112C2×C5×D314yescomplemented
33C2×C3×C11⋊C5—114no—
34C2×C3×C11⋊C5—114no—
35C3⋊AGL(1,𝔽11)—338no—
36D3×C11⋊C5—338no—
37C2×C112C5×C3⋊D311yescharacteristic, complemented
38C11×D11—92no—
39C22×C11⋊C5—991no—
40C2×AGL(1,𝔽11)—991no—
41C2×C32×C11—101no—
42C2×C32×C11AGL(1,𝔽11)11yescharacteristic, complemented
43C2×C32×C11C2×C11⋊C511yescharacteristic, complemented
44C3⋊D33C2×C11⋊C512yescomplemented
45C11×C3⋊D3—112no—
46C2×C5×C3⋊D3—1211noHall
47C3×C11⋊C5—114no—
48C3×C11⋊C5—114no—
49C2×D33—34no—
50C2×D3×C11—334no—
51C112C2×C5×C3⋊D311yescharacteristic, complemented, Sylow
52C2×C11⋊C5—111no—
53C2×C11⋊C5—111no—
54C2×C11⋊C5—992no—
55AGL(1,𝔽11)—992no—
56C32×C11—101no—
57C32×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
58C32×C11C22×C11⋊C511yescharacteristic, complemented
59C2×C32×C5—1211no—
60C5×C3⋊D3—1212no—
61C2×C3×C11—104no—
62C2×C3×C11D3×C11⋊C514yescomplemented
63C2×C3×C11C3⋊AGL(1,𝔽11)14yescomplemented
64D33—38no—
65D3×C11—338no—
66C2×C5×D3—3634no—
67C11⋊C5—111no—
68C11⋊C5—111no—
69C32×C5—1211noHall
70C22×C11—991no—
71C2×D11—91no—
72C2×C3⋊D3—111noHall
73C3×C11—104no—
74C3×C11C2×D3×C11⋊C514yescomplemented
75C3×C11C2×C3⋊AGL(1,𝔽11)14yescomplemented
76C2×C3×C5—1214no—
77C5×D3—3638no—
78C2×C11—101no—
79C2×C11—992no—
80C2×C11C3⋊D3×C11⋊C511yescharacteristic, complemented
81C2×C11C3⋊(C3⋊AGL(1,𝔽11))11yescharacteristic, complemented
82D11—92no—
83C22×C5—10891noHall
84C2×C32#1192589811yescharacteristic, complemented
85C3⋊D3—112no—
86C3×C5—1214no—
87C2×D3—334no—
88C11—101no—
89C11C2×C3⋊D3×C11⋊C511yescharacteristic, complemented
90C11C2×C3⋊(C3⋊AGL(1,𝔽11))11yescharacteristic, complemented
91C2×C5—10892no—
92C2×C5—1211no—
93C32C2×#1192589811yescharacteristic, complemented, Sylow
94C2×C3C3⋊#1192589814yescomplemented
95D3—338no—
96C5—1211noSylow
97C22—991noSylow
98C3C2×C3⋊#1192589814yescomplemented
99C2—992no—
100C2C3⋊(C3⋊#11925898)11yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2C3⋊(C3⋊#11925898)
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⋊#11925898)C2direct (N × H)
4. C32×#10597244C22semidirect
5. C2×C11×C3⋊D33C5semidirect
6. C2×C3×#10597244D3semidirect
9. C11×C3⋊D33C2×C5semidirect
10. C2×C32×C112C2×C5semidirect
13. C3×#10597244C2×D3semidirect
15. C2×#10597244C3⋊D3semidirect
17. C32×C112C22×C5semidirect
22. C2×C3×C112C5×D3semidirect
26. #10597244C2×C3⋊D3semidirect
30. C2×C3⋊D33C11⋊C5semidirect
32. C3×C112C2×C5×D3semidirect
37. C2×C112C5×C3⋊D3semidirect
42. C2×C32×C11AGL(1,𝔽11)semidirect
43. C2×C32×C11C2×C11⋊C5semidirect
44. C3⋊D33C2×C11⋊C5semidirect
51. C112C2×C5×C3⋊D3semidirect
57. C32×C11C2×AGL(1,𝔽11)semidirect
58. C32×C11C22×C11⋊C5semidirect
62. C2×C3×C11D3×C11⋊C5semidirect
63. C2×C3×C11C3⋊AGL(1,𝔽11)semidirect
74. C3×C11C2×D3×C11⋊C5semidirect
75. C3×C11C2×C3⋊AGL(1,𝔽11)semidirect
80. C2×C11C3⋊D3×C11⋊C5semidirect
81. C2×C11C3⋊(C3⋊AGL(1,𝔽11))semidirect
84. C2×C32#11925898semidirect
89. C11C2×C3⋊D3×C11⋊C5semidirect
90. C11C2×C3⋊(C3⋊AGL(1,𝔽11))semidirect
93. C32C2×#11925898semidirect
94. C2×C3C3⋊#11925898semidirect
98. C3C2×C3⋊#11925898semidirect
100. C2C3⋊(C3⋊#11925898)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⋊#11925898)2
C2×C3⋊#119258983
C2×C11×C3⋊D335
C2×C3⋊(C3⋊AGL(1,𝔽11))11
C2×C3⋊D3×C11⋊C511