Finite Group Databasebeta

← (C3⋊D3)⋊((C11⋊C5)⋊D11) #36345117

Subgroups — (C3⋊D3)⋊((C11⋊C5)⋊D11) #36345117

Order 21780.

220 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 40 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
1C11×C3⋊D3×C11⋊C5C211yesmaximal, characteristic, complemented
2C3×C3⋊((C11⋊C5)⋊D11)C212yesmaximal, complemented
3D3×(C11⋊C5)⋊D11—32nomaximal
4C32×C11×C11⋊C5C2211yescharacteristic, complemented, Hall
5(C3⋊D3)⋊(C11⋊D11)C511yesmaximal, characteristic, complemented, Hall
6C3⋊((C11⋊C5)⋊D11)D312yescomplemented
7D3×C11×C11⋊C5—32no—
8D3×C11×C11⋊C5—61no—
9C3×(C11⋊C5)⋊D11—32no—
10C2×(C11⋊C5)⋊D11—91noHall
11C112×C3⋊D3C2×C511yescharacteristic, complemented
12C3×C3⋊(C11⋊D11)C2×C512yescomplemented
13C5×(C3⋊D3)⋊D11—111nomaximal
14(C3⋊D3)⋊AGL(1,𝔽11)—111nomaximal
15C3×C11×C11⋊C5—21no—
16C3×C11×C11⋊C5C2×D312yescomplemented
17D3×C11⋊D11—32no—
18C2×C11×C11⋊C5—91no—
19(C11⋊C5)⋊D11—32no—
20C32×C112C22×C511yescharacteristic, complemented, Hall
21C5×C11×C3⋊D3—111no—
22C3×C5×D33—112no—
23C3⋊D3×C11⋊C5D1111yescharacteristic, complemented
24C3×C3⋊AGL(1,𝔽11)—112no—
25C3⋊(C11⋊D11)C5×D312yescomplemented
26D3×C112—32no—
27D3×C112—61no—
28C3×C11⋊D11—32no—
29C5×D3×D11—332no—
30D3×AGL(1,𝔽11)—332no—
31C11×C11⋊C5D3211yescharacteristic, complemented, Hall
32C32×C5×C11—111no—
33C32×C11⋊C5C2×D1111yescharacteristic, complemented
34C2×C11⋊D11—91noHall
35(C3⋊D3)⋊D11—111no—
36(C3⋊D3)⋊D11—111no—
37(C3⋊D3)⋊D11—552no—
38C3×C112—21no—
39C3×C112C2×C5×D312yescomplemented
40C5×D33—112no—
41C5×D3×C11—332no—
42C5×D3×C11—661no—
43C3×C5×D11—332no—
44C3⋊AGL(1,𝔽11)—112no—
45D3×C11⋊C5—32no—
46D3×C11⋊C5—61no—
47C3×AGL(1,𝔽11)—332no—
48C2×C112—91no—
49C11⋊D11—32no—
50C2×C5×D11—991no—
51C2×AGL(1,𝔽11)—991no—
52C11×C3⋊D3—52no—
53C11×C3⋊D3AGL(1,𝔽11)11yescharacteristic, complemented
54C11×C3⋊D3C5×D1111yescharacteristic, complemented
55C3×D33—112no—
56C3×D33—112no—
57C3×D33—554no—
58C5×D32—1211noHall
59C3×C5×C11—112no—
60C3×C5×C11—221no—
61C3×C11⋊C5—21no—
62C3×C11⋊C5D3×D1112yescomplemented
63D3×D11—332no—
64D3×D11—332no—
65D3×D11—1654no—
66C112C5×D3211yescharacteristic, complemented, Sylow
67C2×C5×C11—991no—
68C5×D11—332no—
69C2×C11⋊C5—91no—
70AGL(1,𝔽11)—332no—
71C32×C11—52no—
72C32×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
73C32×C11C2×C5×D1111yescharacteristic, complemented
74C5×C3⋊D3—111no—
75C3×C5×D3—1212no—
76D33—112no—
77D33—112no—
78D33—554no—
79C3×D11—332no—
80C3×D11—332no—
81C3×D11—1654no—
82D3×C11—32no—
83D3×C11—32no—
84D3×C11—61no—
85D3×C11—61no—
86D3×C11—154no—
87D3×C11—302no—
88C2×C5×D3—3632no—
89C5×C11—111no—
90C11⋊C5(C3⋊D3)⋊D1111yescharacteristic, complemented
91C32×C5—111noHall
92C2×D11—991no—
93C2×D11—991no—
94C2×D11—4952no—
95D32—1211noHall
96C3×C11—21no—
97C3×C11—21no—
98C3×C11—54no—
99C3×C11—102no—
100C3×C11D3×AGL(1,𝔽11)12yescomplemented
101C3×C11C5×D3×D1112yescomplemented
102C2×C3×C5—3632no—
103C5×D3—332no—
104C5×D3—661no—
105C5×D3—1212no—
106C2×C11—91no—
107C2×C11—91no—
108C2×C11—452no—
109D11—332no—
110D11—332no—
111D11—1654no—
112C22×C5—10891noHall
113C3⋊D3(C11⋊C5)⋊D1111yescharacteristic, complemented
114C3×D3—1212no—
115C3×C5—112no—
116C3×C5—221no—
117C2×D3—3632no—
118C11—52no—
119C11(C3⋊D3)⋊AGL(1,𝔽11)11yescharacteristic, complemented
120C11C5×(C3⋊D3)⋊D1111yescharacteristic, complemented
121C2×C5—991no—
122C2×C5—3632no—
123C32C2×(C11⋊C5)⋊D1111yescharacteristic, complemented, Sylow
124C2×C3—3632no—
125D3—32no—
126D3—61no—
127D3—1212no—
128C5—111noSylow
129C22—10891noSylow
130C3—21no—
131C3D3×(C11⋊C5)⋊D1112yescomplemented
132C2—91no—
133C2—3632no—
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. C11×C3⋊D3×C11⋊C5C2semidirect
2. C3×C3⋊((C11⋊C5)⋊D11)C2semidirect
4. C32×C11×C11⋊C5C22semidirect
5. (C3⋊D3)⋊(C11⋊D11)C5semidirect
6. C3⋊((C11⋊C5)⋊D11)D3semidirect
11. C112×C3⋊D3C2×C5semidirect
12. C3×C3⋊(C11⋊D11)C2×C5semidirect
16. C3×C11×C11⋊C5C2×D3semidirect
20. C32×C112C22×C5semidirect
23. C3⋊D3×C11⋊C5D11semidirect
25. C3⋊(C11⋊D11)C5×D3semidirect
31. C11×C11⋊C5D32semidirect
33. C32×C11⋊C5C2×D11semidirect
39. C3×C112C2×C5×D3semidirect
53. C11×C3⋊D3AGL(1,𝔽11)semidirect
54. C11×C3⋊D3C5×D11semidirect
62. C3×C11⋊C5D3×D11semidirect
66. C112C5×D32semidirect
72. C32×C11C2×AGL(1,𝔽11)semidirect
73. C32×C11C2×C5×D11semidirect
90. C11⋊C5(C3⋊D3)⋊D11semidirect
100. C3×C11D3×AGL(1,𝔽11)semidirect
101. C3×C11C5×D3×D11semidirect
113. C3⋊D3(C11⋊C5)⋊D11semidirect
119. C11(C3⋊D3)⋊AGL(1,𝔽11)semidirect
120. C11C5×(C3⋊D3)⋊D11semidirect
123. C32C2×(C11⋊C5)⋊D11semidirect
131. C3D3×(C11⋊C5)⋊D11semidirect

Maximal subgroups

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

subgroupindex
C11×C3⋊D3×C11⋊C52
C3×C3⋊((C11⋊C5)⋊D11)2
D3×(C11⋊C5)⋊D113
(C3⋊D3)⋊(C11⋊D11)5
C5×(C3⋊D3)⋊D1111
(C3⋊D3)⋊AGL(1,𝔽11)11