Finite Group Databasebeta

← #36345367

Subgroups — #36345367

Order 21780.

360 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 61 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
1C32×C5⋊(C11⋊D11)C211yesmaximal, characteristic, complemented
2C5×C11×C3⋊D33C211yesmaximal, characteristic, complemented
3C11×C3⋊D165C211yesmaximal, characteristic, complemented
4D33⋊D55—34nomaximal
5C32×C5×C112C2211yescharacteristic, complemented, Hall
6#17983775—51nomaximal, Hall
7C11×D165—34no—
8C5×C11×D33—34no—
9C3×C5⋊(C11⋊D11)D314yescomplemented
10D11×D55—91noHall
11C11×C3⋊D33—51no—
12C11×C3⋊D33D511yescharacteristic, complemented
13C32×C11⋊D11—51no—
14D55⋊(C3⋊D3)—111nomaximal
15C3⋊D3×D55—111nomaximal
16C3×C5×C112C2×D314yescomplemented
17D33⋊D11—154no—
18C5⋊(C11⋊D11)C3⋊D311yescharacteristic, complemented
19C11×D55—91no—
20C5×C11×D11—91no—
21C32×C112C2×D511yescharacteristic, complemented, Hall
22C3⋊D165D1111yescharacteristic, complemented
23C11×C3⋊D15—111no—
24C5×C3⋊D33D1111yescharacteristic, complemented
25C5×C11×C3⋊D3—111no—
26C32×D55—111no—
27C32×D55—111no—
28C32×D55—225no—
29C11×D33—34no—
30C11×D33—154no—
31C3×C11⋊D11—54no—
32D15⋊D11—334no—
33D3×D55—334no—
34C5×C112C2×C3⋊D311yescharacteristic, complemented, Hall
35C32×C5×C11—25no—
36C32×C5×C11C2×D1111yescharacteristic, complemented
37C32×C5×C11C2×D1111yescharacteristic, complemented
38D112—451noHall
39C3⋊D3×D11—551no—
40C3⋊D3×D11—551no—
41C3×C112D3×D514yescomplemented
42D165—34no—
43C11×D15—334no—
44C5×D33—34no—
45C5×D3×C11—334no—
46C3×D55—114no—
47C3×D55—114no—
48C3×D55—2220no—
49C11⋊D11—51no—
50C11×D11—91no—
51C11×D11—451no—
52C2×D55—991no—
53D5×D11—991no—
54C3⋊D33—51no—
55C3⋊D33D5511yescharacteristic, complemented
56C11×C3⋊D3—111no—
57C11×C3⋊D3—551no—
58C32×D11—551no—
59C32×D11—551no—
60C32×D11—1105no—
61D5×C3⋊D3—1211noHall
62C3×C5×C11—220no—
63C3×C5×C11D3×D1114yescomplemented
64C3×C5×C11D3×D1114yescomplemented
65D3×D11—1654no—
66D3×D11—1654no—
67C112D5×C3⋊D311yescharacteristic, complemented, Sylow
68C2×C5×C11—991no—
69D55—91no—
70D55—111no—
71D55—111no—
72D55—225no—
73C5×D11—91no—
74D5×C11—991no—
75C32×C11—25no—
76C32×C11D5×D1111yescharacteristic, complemented
77C32×C11C2×D5511yescharacteristic, complemented
78C3⋊D15—111no—
79C5×C3⋊D3—111no—
80C32×D5—1211no—
81D33—34no—
82D33—154no—
83C3×D11—554no—
84C3×D11—554no—
85C3×D11—11020no—
86D3×C11—334no—
87D3×C11—1654no—
88D3×D5—3634no—
89C5×C11—25no—
90C5×C11C3⋊D3×D1111yescharacteristic, complemented
91C5×C11C3⋊D3×D1111yescharacteristic, complemented
92C32×C5D11211yescharacteristic, complemented, Hall
93C2×D11—4951no—
94C2×D11—4951no—
95C2×C3⋊D3—6051noHall
96C3×C11—220no—
97C3×C11D3×D5514yescomplemented
98C3×C11D15⋊D1114yescomplemented
99D15—334no—
100C3×D5—1214no—
101C5×D3—334no—
102C2×C11—991no—
103C2×C11—4951no—
104D11—91no—
105D11—451no—
106D11—551no—
107D11—551no—
108D11—1105no—
109C2×D5—10891noHall
110C2×C32—6051no—
111C3⋊D3—111no—
112C3⋊D3—551no—
113C3×C5D33⋊D1114yescomplemented
114C2×D3—18154no—
115C11—25no—
116C11C3⋊D3×D5511yescharacteristic, complemented
117C11D55⋊(C3⋊D3)11yescharacteristic, complemented
118C2×C5—991no—
119D5—991no—
120D5—1211no—
121C32D11×D5511yescharacteristic, complemented, Sylow
122C2×C3—6054no—
123D3—334no—
124D3—1654no—
125C5#1798377511yescharacteristic, complemented, Sylow
126C22—54451noSylow
127C3D33⋊D5514yescomplemented
128C2—6051no—
129C2—991no—
130C2—4951no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C112C22
LCSG ▷ C32×C5×C112
UCSC1

Complements

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

NH ≅ G/Ntype
1. C32×C5⋊(C11⋊D11)C2semidirect
2. C5×C11×C3⋊D33C2semidirect
3. C11×C3⋊D165C2semidirect
5. C32×C5×C112C22semidirect
9. C3×C5⋊(C11⋊D11)D3semidirect
12. C11×C3⋊D33D5semidirect
16. C3×C5×C112C2×D3semidirect
18. C5⋊(C11⋊D11)C3⋊D3semidirect
21. C32×C112C2×D5semidirect
22. C3⋊D165D11semidirect
24. C5×C3⋊D33D11semidirect
34. C5×C112C2×C3⋊D3semidirect
36. C32×C5×C11C2×D11semidirect
37. C32×C5×C11C2×D11semidirect
41. C3×C112D3×D5semidirect
55. C3⋊D33D55semidirect
63. C3×C5×C11D3×D11semidirect
64. C3×C5×C11D3×D11semidirect
67. C112D5×C3⋊D3semidirect
76. C32×C11D5×D11semidirect
77. C32×C11C2×D55semidirect
90. C5×C11C3⋊D3×D11semidirect
91. C5×C11C3⋊D3×D11semidirect
92. C32×C5D112semidirect
97. C3×C11D3×D55semidirect
98. C3×C11D15⋊D11semidirect
113. C3×C5D33⋊D11semidirect
116. C11C3⋊D3×D55semidirect
117. C11D55⋊(C3⋊D3)semidirect
121. C32D11×D55semidirect
125. C5#17983775semidirect
127. C3D33⋊D55semidirect

Maximal subgroups

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

subgroupindex
C32×C5⋊(C11⋊D11)2
C5×C11×C3⋊D332
C11×C3⋊D1652
D33⋊D553
#179837755
D55⋊(C3⋊D3)11
C3⋊D3×D5511