Finite Group Databasebeta

← #11925895⋊(C3⋊D3) #36345162

Subgroups — #11925895⋊(C3⋊D3) #36345162

Order 21780.

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

normal subgroups only

This group has 360 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⋊#11925895)C211yesmaximal, characteristic, complemented
2C3⋊(C3⋊#11925892)C211yesmaximal, characteristic, complemented
3C32×#11925895C211yesmaximal, characteristic, complemented
4#11925895⋊D3—34nomaximal
5C32×#10597243C2211yescharacteristic, complemented, Hall
6D11×C3⋊D33C511yesmaximal, characteristic, complemented, Hall
7C3⋊#11925895—34no—
8C3⋊#11925892—34no—
9C3×#11925895D314yescomplemented
10#11925892⋊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×#10597243C2×D314yescomplemented
17D11×D33—34no—
18#11925895—91no—
19#11925895C3⋊D311yescharacteristic, complemented
20#11925892—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⋊(C3⋊AGL(1,𝔽11))—225no—
27C3⋊D3×C11⋊C5—111no—
28C32×AGL(1,𝔽11)—111no—
29C3⋊(C11⋊D11)—34no—
30C11×D33—34no—
31C3×C11×D11C5×D314yescomplemented
32C2×C3⋊AGL(1,𝔽11)—334no—
33D3×AGL(1,𝔽11)—334no—
34#10597243C2×C3⋊D311yescharacteristic, complemented, Hall
35C32×C11⋊C5—111no—
36C32×C11⋊C5—111no—
37C32×C11⋊C5—225no—
38D112—91noHall
39C2×C3⋊D33—111no—
40C3⋊D3×D11—111no—
41C3×C112C2×C5×D314yescomplemented
42C2×C3×C11⋊C5—114no—
43C3⋊AGL(1,𝔽11)—334no—
44C3⋊AGL(1,𝔽11)—334no—
45C3⋊AGL(1,𝔽11)—334no—
46C3⋊AGL(1,𝔽11)—6620no—
47D3×C11⋊C5—334no—
48C3×AGL(1,𝔽11)—114no—
49C11⋊D11—91no—
50C11×D11—91no—
51C11×D11C5×C3⋊D311yescharacteristic, complemented
52C2×AGL(1,𝔽11)—991no—
53C2×AGL(1,𝔽11)—991no—
54C2×C32×C11—111no—
55C3⋊D33—111no—
56C3⋊D33—111no—
57C3⋊D33—225no—
58C3⋊D33AGL(1,𝔽11)11yescharacteristic, complemented
59C11×C3⋊D3—111no—
60C32×D11AGL(1,𝔽11)11yescharacteristic, complemented
61C2×C5×C3⋊D3—1211noHall
62C3×C11⋊C5—114no—
63C3×C11⋊C5—114no—
64C3×C11⋊C5—2220no—
65C2×D33—334no—
66D3×D11—334no—
67C112C2×C5×C3⋊D311yescharacteristic, complemented, Sylow
68C2×C11⋊C5—111no—
69C2×C11⋊C5—991no—
70AGL(1,𝔽11)—111no—
71AGL(1,𝔽11)—991no—
72AGL(1,𝔽11)—991no—
73AGL(1,𝔽11)—991no—
74AGL(1,𝔽11)—1985no—
75C32×C11—25no—
76C32×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
77C32×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
78C2×C32×C5—1211no—
79C5×C3⋊D3—1211no—
80C5×C3⋊D3—1211no—
81C2×C3×C11—114no—
82D33—34no—
83D33—334no—
84D33—334no—
85D33—6620no—
86C3×D11C3⋊AGL(1,𝔽11)14yescomplemented
87D3×C11—334no—
88C2×C5×D3—3634no—
89C11⋊C5—111no—
90C11⋊C5—111no—
91C11⋊C5—225no—
92C32×C5—1211noHall
93C2×D11—991no—
94C2×D11—991no—
95C2×C3⋊D3—1211noHall
96C3×C11—220no—
97C3×C11D3×AGL(1,𝔽11)14yescomplemented
98C3×C11C2×C3⋊AGL(1,𝔽11)14yescomplemented
99C2×C3×C5—1214no—
100C5×D3—3634no—
101C5×D3—3634no—
102C2×C11—111no—
103C2×C11—991no—
104D11—91no—
105D11—991no—
106D11—991no—
107D11—1985no—
108D11C3⋊(C3⋊AGL(1,𝔽11))11yescharacteristic, complemented
109C22×C5—10891noHall
110C2×C32—111no—
111C3⋊D3—111no—
112C3⋊D3—1211no—
113C3×C5—1214no—
114C2×D3—3634no—
115C11—25no—
116C11C3⋊D3×AGL(1,𝔽11)11yescharacteristic, complemented
117C11C2×C3⋊(C3⋊AGL(1,𝔽11))11yescharacteristic, complemented
118C2×C5—10891no—
119C2×C5—10891no—
120C2×C5—1211no—
121C32#11925892⋊C211yescharacteristic, complemented, Sylow
122C2×C3—114no—
123D3—334no—
124D3—3634no—
125C5—1211noSylow
126C22—10891noSylow
127C3#11925895⋊D314yescomplemented
128C2—111no—
129C2—10891no—
130C2—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⋊#11925895)C2semidirect
2. C3⋊(C3⋊#11925892)C2semidirect
3. C32×#11925895C2semidirect
5. C32×#10597243C22semidirect
6. D11×C3⋊D33C5semidirect
9. C3×#11925895D3semidirect
11. C3⋊(C3⋊(C11⋊D11))C2×C5semidirect
12. C11×C3⋊D33C2×C5semidirect
13. C32×C11×D11C2×C5semidirect
16. C3×#10597243C2×D3semidirect
19. #11925895C3⋊D3semidirect
21. C32×C112C22×C5semidirect
31. C3×C11×D11C5×D3semidirect
34. #10597243C2×C3⋊D3semidirect
41. C3×C112C2×C5×D3semidirect
51. C11×D11C5×C3⋊D3semidirect
58. C3⋊D33AGL(1,𝔽11)semidirect
60. C32×D11AGL(1,𝔽11)semidirect
67. C112C2×C5×C3⋊D3semidirect
76. C32×C11C2×AGL(1,𝔽11)semidirect
77. C32×C11C2×AGL(1,𝔽11)semidirect
86. C3×D11C3⋊AGL(1,𝔽11)semidirect
97. C3×C11D3×AGL(1,𝔽11)semidirect
98. C3×C11C2×C3⋊AGL(1,𝔽11)semidirect
108. D11C3⋊(C3⋊AGL(1,𝔽11))semidirect
116. C11C3⋊D3×AGL(1,𝔽11)semidirect
117. C11C2×C3⋊(C3⋊AGL(1,𝔽11))semidirect
121. C32#11925892⋊C2semidirect
127. C3#11925895⋊D3semidirect

Maximal subgroups

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

subgroupindex
C3⋊(C3⋊#11925895)2
C3⋊(C3⋊#11925892)2
C32×#119258952
#11925895⋊D33
D11×C3⋊D335
C2×C3⋊(C3⋊AGL(1,𝔽11))11
C3⋊D3×AGL(1,𝔽11)11