Finite Group Databasebeta

← C2×C3⋊(C3⋊#11925895) #36345252

Subgroups — C2×C3⋊(C3⋊#11925895) #36345252

Order 21780.

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

normal subgroups only

This group has 360 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×#10597243C211yesmaximal, characteristic, complemented
2C3⋊(C3⋊#11925895)C212yesmaximal, direct product factor
3C2×C3⋊#11925895—34nomaximal
4C32×#10597243C2211yescharacteristic, complemented, Hall
5C2×C11×C3⋊D33C511yesmaximal, characteristic, complemented, Hall
6C2×C3×#10597243D314yescomplemented
7C3⋊#11925895—38no—
8C2×#11925895—91noHall
9C11×C3⋊D33C2×C512yescomplemented
10C2×C32×C112C2×C511yescharacteristic, complemented
11C2×C3⋊(C3⋊AGL(1,𝔽11))—111nomaximal
12C2×C3⋊D3×C11⋊C5—111nomaximal
13C3×#10597243C2×D314yescomplemented
14C2×C11×D33—34no—
15C2×#10597243C3⋊D311yescharacteristic, complemented
16#11925895—92no—
17C32×C112C22×C511yescharacteristic, complemented, Hall
18C2×C32×C11⋊C5—111no—
19C2×C32×C11⋊C5—111no—
20C2×C32×C11⋊C5—225no—
21C3⋊(C3⋊AGL(1,𝔽11))—112no—
22C3⋊D3×C11⋊C5—112no—
23C2×C3×C112C5×D314yescomplemented
24C11×D33—38no—
25C2×C3⋊AGL(1,𝔽11)—334no—
26C2×D3×C11⋊C5—334no—
27#10597243C2×C3⋊D311yescharacteristic, complemented, Hall
28C32×C11⋊C5—111no—
29C32×C11⋊C5—111no—
30C32×C11⋊C5—225no—
31C2×C11×D11—91noHall
32C2×C3⋊D33C11⋊C511yescharacteristic, complemented
33C2×C11×C3⋊D3—111no—
34C3×C112C2×C5×D314yescomplemented
35C2×C3×C11⋊C5—114no—
36C2×C3×C11⋊C5—114no—
37C2×C3×C11⋊C5—2220no—
38C3⋊AGL(1,𝔽11)—338no—
39D3×C11⋊C5—338no—
40C2×C112C5×C3⋊D311yescharacteristic, complemented
41C11×D11—92no—
42C22×C11⋊C5—991no—
43C2×AGL(1,𝔽11)—991no—
44C2×C32×C11—25no—
45C2×C32×C11AGL(1,𝔽11)11yescharacteristic, complemented
46C2×C32×C11C2×C11⋊C511yescharacteristic, complemented
47C3⋊D33C2×C11⋊C512yescomplemented
48C11×C3⋊D3—112no—
49C2×C5×C3⋊D3—1211noHall
50C3×C11⋊C5—114no—
51C3×C11⋊C5—114no—
52C3×C11⋊C5—2220no—
53C2×D33—34no—
54C2×D3×C11—334no—
55C112C2×C5×C3⋊D311yescharacteristic, complemented, Sylow
56C2×C11⋊C5—111no—
57C2×C11⋊C5—111no—
58C2×C11⋊C5—225no—
59C2×C11⋊C5—992no—
60AGL(1,𝔽11)—992no—
61C32×C11—25no—
62C32×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
63C32×C11C22×C11⋊C511yescharacteristic, complemented
64C2×C32×C5—1211no—
65C5×C3⋊D3—1212no—
66C2×C3×C11—220no—
67C2×C3×C11D3×C11⋊C514yescomplemented
68C2×C3×C11C3⋊AGL(1,𝔽11)14yescomplemented
69D33—38no—
70D3×C11—338no—
71C2×C5×D3—3634no—
72C11⋊C5—111no—
73C11⋊C5—111no—
74C11⋊C5—225no—
75C32×C5—1211noHall
76C22×C11—991no—
77C2×D11—91no—
78C2×C3⋊D3—111noHall
79C3×C11—220no—
80C3×C11C2×D3×C11⋊C514yescomplemented
81C3×C11C2×C3⋊AGL(1,𝔽11)14yescomplemented
82C2×C3×C5—1214no—
83C5×D3—3638no—
84C2×C11—25no—
85C2×C11—992no—
86C2×C11C3⋊D3×C11⋊C511yescharacteristic, complemented
87C2×C11C3⋊(C3⋊AGL(1,𝔽11))11yescharacteristic, complemented
88D11—92no—
89C22×C5—10891noHall
90C2×C32#1192589511yescharacteristic, complemented
91C3⋊D3—112no—
92C3×C5—1214no—
93C2×D3—334no—
94C11—25no—
95C11C2×C3⋊D3×C11⋊C511yescharacteristic, complemented
96C11C2×C3⋊(C3⋊AGL(1,𝔽11))11yescharacteristic, complemented
97C2×C5—10892no—
98C2×C5—1211no—
99C32C2×#1192589511yescharacteristic, complemented, Sylow
100C2×C3C3⋊#1192589514yescomplemented
101D3—338no—
102C5—1211noSylow
103C22—991noSylow
104C3C2×C3⋊#1192589514yescomplemented
105C2—992no—
106C2C3⋊(C3⋊#11925895)11yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2C3⋊(C3⋊#11925895)
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×#10597243C2semidirect
2. C3⋊(C3⋊#11925895)C2direct (N × H)
4. C32×#10597243C22semidirect
5. C2×C11×C3⋊D33C5semidirect
6. C2×C3×#10597243D3semidirect
9. C11×C3⋊D33C2×C5semidirect
10. C2×C32×C112C2×C5semidirect
13. C3×#10597243C2×D3semidirect
15. C2×#10597243C3⋊D3semidirect
17. C32×C112C22×C5semidirect
23. C2×C3×C112C5×D3semidirect
27. #10597243C2×C3⋊D3semidirect
32. C2×C3⋊D33C11⋊C5semidirect
34. C3×C112C2×C5×D3semidirect
40. C2×C112C5×C3⋊D3semidirect
45. C2×C32×C11AGL(1,𝔽11)semidirect
46. C2×C32×C11C2×C11⋊C5semidirect
47. C3⋊D33C2×C11⋊C5semidirect
55. C112C2×C5×C3⋊D3semidirect
62. C32×C11C2×AGL(1,𝔽11)semidirect
63. C32×C11C22×C11⋊C5semidirect
67. C2×C3×C11D3×C11⋊C5semidirect
68. C2×C3×C11C3⋊AGL(1,𝔽11)semidirect
80. C3×C11C2×D3×C11⋊C5semidirect
81. C3×C11C2×C3⋊AGL(1,𝔽11)semidirect
86. C2×C11C3⋊D3×C11⋊C5semidirect
87. C2×C11C3⋊(C3⋊AGL(1,𝔽11))semidirect
90. C2×C32#11925895semidirect
95. C11C2×C3⋊D3×C11⋊C5semidirect
96. C11C2×C3⋊(C3⋊AGL(1,𝔽11))semidirect
99. C32C2×#11925895semidirect
100. C2×C3C3⋊#11925895semidirect
104. C3C2×C3⋊#11925895semidirect
106. C2C3⋊(C3⋊#11925895)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×#105972432
C3⋊(C3⋊#11925895)2
C2×C3⋊#119258953
C2×C11×C3⋊D335
C2×C3⋊(C3⋊AGL(1,𝔽11))11
C2×C3⋊D3×C11⋊C511