Finite Group Databasebeta

← D55⋊(C3⋊D51) #46778190

Subgroups — D55⋊(C3⋊D51) #46778190

Order 33660.

240 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 65 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×C17×D55C211yesmaximal, characteristic, complemented
2C5×C3⋊D561C211yesmaximal, characteristic, complemented
3C11×C3⋊D255C211yesmaximal, characteristic, complemented
4D55⋊D51—34nomaximal
5C32×C5×C11×C17C2211yescharacteristic, complemented, Hall
6D11×C3⋊D51—51nomaximal, Hall
7C11×D255—34no—
8C5×D561—34no—
9C3×C17×D55D314yescomplemented
10D55⋊D17—91noHall
11C3⋊D561D511yescharacteristic, complemented
12C11×C3⋊D51—51no—
13C32×C17×D11—51no—
14D5×C3⋊D51—111nomaximal, Hall
15C3×C5×C11×C17C2×D314yescomplemented
16D11×D51—154no—
17D55⋊(C3⋊D3)—171nomaximal, Hall
18C17×D55C3⋊D311yescharacteristic, complemented
19C11×D85—91no—
20C5×D187—91no—
21C32×C11×C17C2×D511yescharacteristic, complemented, Hall
22C3⋊D255D1111yescharacteristic, complemented
23C5×C3⋊D51—111no—
24C32×D5×C17—111no—
25D561—34no—
26C11×D51—154no—
27C3×C17×D11—54no—
28D5×D51—334no—
29C11×C3⋊D15—171no—
30C5×C3⋊D33—171no—
31C32×D55D1711yescharacteristic, complemented
32C5×C11×C17C2×C3⋊D311yescharacteristic, complemented, Hall
33C32×C5×C17C2×D1111yescharacteristic, complemented, Hall
34D11×D17—451noHall
35D15⋊D11—514no—
36C2×C3⋊D51—551noHall
37C3×C11×C17D3×D514yescomplemented
38D255—34no—
39C5×D51—334no—
40C3×D5×C17—114no—
41C32×C5×C11C2×D1711yescharacteristic, complemented, Hall
42C3⋊D3×D11—851noHall
43D187—91no—
44C11×D17—451no—
45C17×D11—51no—
46D5×D17—991noHall
47C11×D15—514no—
48C5×D33—514no—
49C3×D55D5114yescomplemented
50C2×C32×C17—551no—
51C3⋊D51—51no—
52C3⋊D51—111no—
53C3×C5×C17D3×D1114yescomplemented
54D5×D11—1531noHall
55C2×D51—1654no—
56C3⋊D33—171no—
57C11×C3⋊D3—851no—
58C32×D11—51no—
59C11×C17D5×C3⋊D311yescharacteristic, complemented, Hall
60D5×C3⋊D3—1871noHall
61D85—91no—
62C5×D17—991no—
63D5×C17—111no—
64C3×C5×C11C2×D5114yescomplemented
65C32×C17D5×D1111yescharacteristic, complemented, Hall
66D3×D11—2554no—
67D55C3⋊D5111yescharacteristic, complemented
68C5×D11—1531no—
69D5×C11—1531no—
70C2×C3×C17—554no—
71D51—154no—
72D51—334no—
73C32×C11D5×D1711yescharacteristic, complemented, Hall
74C3⋊D15—171no—
75C5×C3⋊D3—1871no—
76C32×D5—111no—
77C5×C17C3⋊D3×D1111yescharacteristic, complemented, Hall
78C2×D17—4951noHall
79D33—514no—
80C3×D11—54no—
81D3×C11—2554no—
82D3×D5—5614no—
83C5×C11C2×C3⋊D5111yescharacteristic, complemented, Hall
84C3×C17D15⋊D1114yescomplemented
85C32×C5D11×D1711yescharacteristic, complemented, Hall
86C2×D11—7651noHall
87C2×C3⋊D3—9351noHall
88C2×C17—551no—
89D17—451no—
90D17—991no—
91C3×C11D5×D5114yescomplemented
92D15—514no—
93C3×D5—114no—
94C5×D3—5614no—
95C2×C11—7651no—
96D11—51no—
97D11—1531no—
98C2×D5—16831noHall
99C2×C32—551no—
100C3⋊D3—851no—
101C3⋊D3—1871no—
102C17D55⋊(C3⋊D3)11yescharacteristic, complemented, Sylow
103C3×C5D11×D5114yescomplemented
104C2×D3—28054no—
105C11D5×C3⋊D5111yescharacteristic, complemented, Sylow
106C2×C5—16831no—
107D5—111no—
108D5—1531no—
109C32D55⋊D1711yescharacteristic, complemented, Sylow
110C2×C3—554no—
111D3—5614no—
112D3—2554no—
113C5D11×C3⋊D5111yescharacteristic, complemented, Sylow
114C22—84151noSylow
115C3D55⋊D5114yescomplemented
116C2—551no—
117C2—16831no—
118C2—7651no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C11×C17C22
LCSG ▷ C32×C5×C11×C17
UCSC1

Complements

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

NH ≅ G/Ntype
1. C32×C17×D55C2semidirect
2. C5×C3⋊D561C2semidirect
3. C11×C3⋊D255C2semidirect
5. C32×C5×C11×C17C22semidirect
9. C3×C17×D55D3semidirect
11. C3⋊D561D5semidirect
15. C3×C5×C11×C17C2×D3semidirect
18. C17×D55C3⋊D3semidirect
21. C32×C11×C17C2×D5semidirect
22. C3⋊D255D11semidirect
31. C32×D55D17semidirect
32. C5×C11×C17C2×C3⋊D3semidirect
33. C32×C5×C17C2×D11semidirect
37. C3×C11×C17D3×D5semidirect
41. C32×C5×C11C2×D17semidirect
49. C3×D55D51semidirect
53. C3×C5×C17D3×D11semidirect
59. C11×C17D5×C3⋊D3semidirect
64. C3×C5×C11C2×D51semidirect
65. C32×C17D5×D11semidirect
67. D55C3⋊D51semidirect
73. C32×C11D5×D17semidirect
77. C5×C17C3⋊D3×D11semidirect
83. C5×C11C2×C3⋊D51semidirect
84. C3×C17D15⋊D11semidirect
85. C32×C5D11×D17semidirect
91. C3×C11D5×D51semidirect
102. C17D55⋊(C3⋊D3)semidirect
103. C3×C5D11×D51semidirect
105. C11D5×C3⋊D51semidirect
109. C32D55⋊D17semidirect
113. C5D11×C3⋊D51semidirect
115. C3D55⋊D51semidirect

Maximal subgroups

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

subgroupindex
C32×C17×D552
C5×C3⋊D5612
C11×C3⋊D2552
D55⋊D513
D11×C3⋊D515
D5×C3⋊D5111
D55⋊(C3⋊D3)17