Finite Group Databasebeta

← #11925894⋊(C3⋊D3) #36345166

Subgroups — #11925894⋊(C3⋊D3) #36345166

Order 21780.

252 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 50 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⋊#11925898)C211yesmaximal, characteristic, complemented
2C3⋊(C3⋊#11925897)C211yesmaximal, characteristic, complemented
3C32×#11925894C211yesmaximal, characteristic, complemented
4#11925894⋊D3—34nomaximal
5C32×#10597244C2211yescharacteristic, complemented, Hall
6#17983775C511yesmaximal, characteristic, complemented, Hall
7C3⋊#11925898—34no—
8C3⋊#11925897—34no—
9C3×#11925894D314yescomplemented
10#11925894⋊C2—91noHall
11C11×C3⋊D33C2×C511yescharacteristic, complemented
12C11×C3⋊D33C2×C511yescharacteristic, complemented
13C32×C11⋊D11C2×C511yescharacteristic, complemented
14C3⋊D3×AGL(1,𝔽11)—111nomaximal
15C3⋊D3×AGL(1,𝔽11)—111nomaximal
16C3×#10597244C2×D314yescomplemented
17D33⋊D11—34no—
18#11925898—91no—
19#11925897—91no—
20#11925894C3⋊D311yescharacteristic, complemented
21C32×C112C22×C511yescharacteristic, complemented, Hall
22C3⋊(C3⋊AGL(1,𝔽11))—111no—
23C3⋊(C3⋊AGL(1,𝔽11))—111no—
24C3⋊D3×C11⋊C5—111no—
25C3⋊D3×C11⋊C5—111no—
26C32×AGL(1,𝔽11)—111no—
27C32×AGL(1,𝔽11)—111no—
28C11×D33—34no—
29C11×D33—34no—
30C3×C11⋊D11C5×D314yescomplemented
31D3×AGL(1,𝔽11)—334no—
32D3×AGL(1,𝔽11)—334no—
33#10597244C2×C3⋊D311yescharacteristic, complemented, Hall
34C32×C11⋊C5—111no—
35C32×C11⋊C5—111no—
36D112—91noHall
37C3⋊D3×D11—111no—
38C3⋊D3×D11—111no—
39C3×C112C2×C5×D314yescomplemented
40C3⋊AGL(1,𝔽11)—334no—
41C3⋊AGL(1,𝔽11)—334no—
42D3×C11⋊C5—334no—
43D3×C11⋊C5—334no—
44C3×AGL(1,𝔽11)—114no—
45C3×AGL(1,𝔽11)—114no—
46C11⋊D11C5×C3⋊D311yescharacteristic, complemented
47C11×D11—91no—
48C11×D11—91no—
49C2×AGL(1,𝔽11)—991no—
50C2×AGL(1,𝔽11)—991no—
51C3⋊D33AGL(1,𝔽11)11yescharacteristic, complemented
52C3⋊D33AGL(1,𝔽11)11yescharacteristic, complemented
53C11×C3⋊D3—111no—
54C11×C3⋊D3—111no—
55C32×D11—111no—
56C32×D11—111no—
57C32×D11—1101no—
58C2×C5×C3⋊D3—1211noHall
59C3×C11⋊C5—114no—
60C3×C11⋊C5—114no—
61D3×D11—334no—
62D3×D11—334no—
63C112C2×C5×C3⋊D311yescharacteristic, complemented, Sylow
64C2×C11⋊C5—991no—
65C2×C11⋊C5—991no—
66AGL(1,𝔽11)—111no—
67AGL(1,𝔽11)—111no—
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—
76D33—34no—
77D33—34no—
78C3×D11—114no—
79C3×D11—114no—
80C3×D11—1104no—
81D3×C11—334no—
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×C11D3×AGL(1,𝔽11)14yescomplemented
93C2×C3×C5—1214no—
94C5×D3—3634no—
95C5×D3—3634no—
96C2×C11—991no—
97C2×C11—991no—
98D11—91no—
99D11—91no—
100D11—111no—
101D11—111no—
102D11—1101no—
103C22×C5—10891noHall
104C2×C32—1211no—
105C3⋊D3—111no—
106C3⋊D3—111no—
107C3×C5—1214no—
108C2×D3—3634no—
109C11—101no—
110C11C3⋊D3×AGL(1,𝔽11)11yescharacteristic, complemented
111C11C3⋊D3×AGL(1,𝔽11)11yescharacteristic, complemented
112C2×C5—10891no—
113C2×C5—10891no—
114C2×C5—1211no—
115C32#11925894⋊C211yescharacteristic, complemented, Sylow
116C2×C3—1214no—
117D3—334no—
118D3—334no—
119C5—1211noSylow
120C22—10891noSylow
121C3#11925894⋊D314yescomplemented
122C2—991no—
123C2—991no—
124C2—1211no—
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⋊#11925898)C2semidirect
2. C3⋊(C3⋊#11925897)C2semidirect
3. C32×#11925894C2semidirect
5. C32×#10597244C22semidirect
6. #17983775C5semidirect
9. C3×#11925894D3semidirect
11. C11×C3⋊D33C2×C5semidirect
12. C11×C3⋊D33C2×C5semidirect
13. C32×C11⋊D11C2×C5semidirect
16. C3×#10597244C2×D3semidirect
20. #11925894C3⋊D3semidirect
21. C32×C112C22×C5semidirect
30. C3×C11⋊D11C5×D3semidirect
33. #10597244C2×C3⋊D3semidirect
39. C3×C112C2×C5×D3semidirect
46. C11⋊D11C5×C3⋊D3semidirect
51. C3⋊D33AGL(1,𝔽11)semidirect
52. C3⋊D33AGL(1,𝔽11)semidirect
63. C112C2×C5×C3⋊D3semidirect
71. C32×C11C2×AGL(1,𝔽11)semidirect
72. C32×C11C2×AGL(1,𝔽11)semidirect
91. C3×C11D3×AGL(1,𝔽11)semidirect
92. C3×C11D3×AGL(1,𝔽11)semidirect
110. C11C3⋊D3×AGL(1,𝔽11)semidirect
111. C11C3⋊D3×AGL(1,𝔽11)semidirect
115. C32#11925894⋊C2semidirect
121. C3#11925894⋊D3semidirect

Maximal subgroups

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

subgroupindex
C3⋊(C3⋊#11925898)2
C3⋊(C3⋊#11925897)2
C32×#119258942
#11925894⋊D33
#179837755
C3⋊D3×AGL(1,𝔽11)11