Finite Group Databasebeta

← #11925896⋊(C3⋊D3) #36345169

Subgroups — #11925896⋊(C3⋊D3) #36345169

Order 21780.

252 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 55 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
1C3⋊(C3⋊#11925896)C211yesmaximal, characteristic, complemented
2C3⋊(C3⋊#11925893)C211yesmaximal, characteristic, complemented
3C32×#11925896C211yesmaximal, characteristic, complemented
4#11925896⋊D3—34nomaximal
5C32×#10597245C2211yescharacteristic, complemented, Hall
6D11×C3⋊D33C511yesmaximal, characteristic, complemented, Hall
7C3⋊#11925896—34no—
8C3⋊#11925893—34no—
9C3×#11925896D314yescomplemented
10#11925896⋊C2—91noHall
11C3⋊(C3⋊(C11⋊D11))C2×C511yescharacteristic, complemented
12C11×C3⋊D33C2×C511yescharacteristic, complemented
13C32×C11×D11C2×C511yescharacteristic, complemented
14C2×C3⋊(C3⋊AGL(1,𝔽11))—111nomaximal
15C3⋊D3×AGL(1,𝔽11)—111nomaximal
16C3×#10597245C2×D314yescomplemented
17D11×D33—34no—
18#11925896—91no—
19#11925896C3⋊D311yescharacteristic, complemented
20#11925893—91no—
21C32×C112C22×C511yescharacteristic, complemented, Hall
22C2×C32×C11⋊C5—111no—
23C3⋊(C3⋊AGL(1,𝔽11))—111no—
24C3⋊(C3⋊AGL(1,𝔽11))—111no—
25C3⋊(C3⋊AGL(1,𝔽11))—111no—
26C3⋊D3×C11⋊C5—111no—
27C32×AGL(1,𝔽11)—111no—
28C3⋊(C11⋊D11)—34no—
29C11×D33—34no—
30C3×C11×D11C5×D314yescomplemented
31C2×C3⋊AGL(1,𝔽11)—334no—
32D3×AGL(1,𝔽11)—334no—
33#10597245C2×C3⋊D311yescharacteristic, complemented, Hall
34C32×C11⋊C5—111no—
35C32×C11⋊C5—111no—
36D112—91noHall
37C2×C3⋊D33—111no—
38C3⋊D3×D11—111no—
39C3×C112C2×C5×D314yescomplemented
40C2×C3×C11⋊C5—114no—
41C3⋊AGL(1,𝔽11)—334no—
42C3⋊AGL(1,𝔽11)—334no—
43C3⋊AGL(1,𝔽11)—334no—
44D3×C11⋊C5—334no—
45C3×AGL(1,𝔽11)—114no—
46C11⋊D11—91no—
47C11×D11—91no—
48C11×D11C5×C3⋊D311yescharacteristic, complemented
49C2×AGL(1,𝔽11)—991no—
50C2×AGL(1,𝔽11)—991no—
51C2×C32×C11—111no—
52C3⋊D33—111no—
53C3⋊D33—111no—
54C3⋊D33—1101no—
55C3⋊D33AGL(1,𝔽11)11yescharacteristic, complemented
56C11×C3⋊D3—111no—
57C32×D11AGL(1,𝔽11)11yescharacteristic, complemented
58C2×C5×C3⋊D3—1211noHall
59C3×C11⋊C5—114no—
60C3×C11⋊C5—114no—
61C2×D33—334no—
62D3×D11—334no—
63C112C2×C5×C3⋊D311yescharacteristic, complemented, Sylow
64C2×C11⋊C5—111no—
65C2×C11⋊C5—991no—
66AGL(1,𝔽11)—111no—
67AGL(1,𝔽11)—991no—
68AGL(1,𝔽11)—991no—
69AGL(1,𝔽11)—991no—
70C32×C11—101no—
71C32×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
72C32×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
73C2×C32×C5—1211no—
74C5×C3⋊D3—1211no—
75C5×C3⋊D3—1211no—
76C2×C3×C11—114no—
77D33—34no—
78D33—334no—
79D33—334no—
80D33—3304no—
81C3×D11C3⋊AGL(1,𝔽11)14yescomplemented
82D3×C11—334no—
83C2×C5×D3—3634no—
84C11⋊C5—111no—
85C11⋊C5—111no—
86C32×C5—1211noHall
87C2×D11—991no—
88C2×D11—991no—
89C2×C3⋊D3—1211noHall
90C3×C11—104no—
91C3×C11D3×AGL(1,𝔽11)14yescomplemented
92C3×C11C2×C3⋊AGL(1,𝔽11)14yescomplemented
93C2×C3×C5—1214no—
94C5×D3—3634no—
95C5×D3—3634no—
96C2×C11—111no—
97C2×C11—991no—
98D11—91no—
99D11—991no—
100D11—991no—
101D11—9901no—
102D11C3⋊(C3⋊AGL(1,𝔽11))11yescharacteristic, complemented
103C22×C5—10891noHall
104C2×C32—111no—
105C3⋊D3—111no—
106C3⋊D3—1211no—
107C3×C5—1214no—
108C2×D3—3634no—
109C11—101no—
110C11C3⋊D3×AGL(1,𝔽11)11yescharacteristic, complemented
111C11C2×C3⋊(C3⋊AGL(1,𝔽11))11yescharacteristic, complemented
112C2×C5—10891no—
113C2×C5—10891no—
114C2×C5—1211no—
115C32#11925896⋊C211yescharacteristic, complemented, Sylow
116C2×C3—114no—
117D3—334no—
118D3—3634no—
119C5—1211noSylow
120C22—10891noSylow
121C3#11925896⋊D314yescomplemented
122C2—111no—
123C2—10891no—
124C2—991no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C112C22×C5
LCSG ▷ C32×C112
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3⋊(C3⋊#11925896)C2semidirect
2. C3⋊(C3⋊#11925893)C2semidirect
3. C32×#11925896C2semidirect
5. C32×#10597245C22semidirect
6. D11×C3⋊D33C5semidirect
9. C3×#11925896D3semidirect
11. C3⋊(C3⋊(C11⋊D11))C2×C5semidirect
12. C11×C3⋊D33C2×C5semidirect
13. C32×C11×D11C2×C5semidirect
16. C3×#10597245C2×D3semidirect
19. #11925896C3⋊D3semidirect
21. C32×C112C22×C5semidirect
30. C3×C11×D11C5×D3semidirect
33. #10597245C2×C3⋊D3semidirect
39. C3×C112C2×C5×D3semidirect
48. C11×D11C5×C3⋊D3semidirect
55. C3⋊D33AGL(1,𝔽11)semidirect
57. C32×D11AGL(1,𝔽11)semidirect
63. C112C2×C5×C3⋊D3semidirect
71. C32×C11C2×AGL(1,𝔽11)semidirect
72. C32×C11C2×AGL(1,𝔽11)semidirect
81. C3×D11C3⋊AGL(1,𝔽11)semidirect
91. C3×C11D3×AGL(1,𝔽11)semidirect
92. C3×C11C2×C3⋊AGL(1,𝔽11)semidirect
102. D11C3⋊(C3⋊AGL(1,𝔽11))semidirect
110. C11C3⋊D3×AGL(1,𝔽11)semidirect
111. C11C2×C3⋊(C3⋊AGL(1,𝔽11))semidirect
115. C32#11925896⋊C2semidirect
121. C3#11925896⋊D3semidirect

Maximal subgroups

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

subgroupindex
C3⋊(C3⋊#11925896)2
C3⋊(C3⋊#11925893)2
C32×#119258962
#11925896⋊D33
D11×C3⋊D335
C2×C3⋊(C3⋊AGL(1,𝔽11))11
C3⋊D3×AGL(1,𝔽11)11