Finite Group Databasebeta

← C17×D55⋊(C3⋊D3) #46778189

Subgroups — C17×D55⋊(C3⋊D3) #46778189

Order 33660.

240 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 70 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×C17×C3⋊D33C211yesmaximal, characteristic, complemented
3C11×C17×C3⋊D15C211yesmaximal, characteristic, complemented
4C17×D15⋊D11—34nomaximal
5C32×C5×C11×C17C2211yescharacteristic, complemented, Hall
6C17×C3⋊D3×D11—51nomaximal, Hall
7C11×C17×D15—34no—
8C5×C17×D33—34no—
9C3×C17×D55D314yescomplemented
10D5×C17×D11—91noHall
11C17×C3⋊D33D511yescharacteristic, complemented
12C11×C17×C3⋊D3—51no—
13C32×C17×D11—51no—
14D5×C17×C3⋊D3—111nomaximal, Hall
15C3×C5×C11×C17C2×D314yescomplemented
16D3×C17×D11—154no—
17D55⋊(C3⋊D3)C1711yesmaximal, characteristic, direct product factor, Hall
18C17×D55C3⋊D311yescharacteristic, complemented
19D5×C11×C17—91no—
20C5×C17×D11—91no—
21C32×C11×C17C2×D511yescharacteristic, complemented, Hall
22C17×C3⋊D15D1111yescharacteristic, complemented
23C5×C17×C3⋊D3—111no—
24C32×D5×C17—111no—
25C17×D33—34no—
26D3×C11×C17—154no—
27C3×C17×D11—54no—
28D3×D5×C17—334no—
29C11×C3⋊D15C2×C1711yescharacteristic, complemented
30C5×C3⋊D33C2×C1711yescharacteristic, complemented
31C32×D55C2×C1711yescharacteristic, complemented
32C5×C11×C17C2×C3⋊D311yescharacteristic, complemented, Hall
33C32×C5×C17C2×D1111yescharacteristic, complemented, Hall
34C2×C17×D11—451noHall
35D15⋊D11—34no—
36C2×C17×C3⋊D3—551noHall
37C3×C11×C17D3×D514yescomplemented
38C17×D15—34no—
39C5×D3×C17—334no—
40C3×D5×C17—114no—
41C32×C5×C11C22×C1711yescharacteristic, complemented, Hall
42C3⋊D3×D11—51noHall
43C2×C11×C17—451no—
44C17×D11—51no—
45C17×D11—91no—
46C2×D5×C17—991noHall
47C11×D15—34no—
48C5×D33—34no—
49C3×D55D3×C1714yescomplemented
50C2×C32×C17—551no—
51C17×C3⋊D3—51no—
52C17×C3⋊D3—111no—
53C3×C5×C17D3×D1114yescomplemented
54D5×D11—91noHall
55C2×D3×C17—1654no—
56C3⋊D33D5×C1711yescharacteristic, complemented
57C11×C3⋊D3—51no—
58C32×D11—51no—
59C11×C17D5×C3⋊D311yescharacteristic, complemented, Hall
60D5×C3⋊D3—111noHall
61C2×C5×C17—991no—
62D5×C17—91no—
63D5×C17—111no—
64C3×C5×C11C2×D3×C1714yescomplemented
65C32×C17D5×D1111yescharacteristic, complemented, Hall
66D3×D11—154no—
67D55C17×C3⋊D311yescharacteristic, complemented
68C5×D11—91no—
69D5×C11—91no—
70C2×C3×C17—554no—
71D3×C17—154no—
72D3×C17—334no—
73C32×C11C2×D5×C1711yescharacteristic, complemented, Hall
74C3⋊D15C17×D1111yescharacteristic, complemented
75C5×C3⋊D3—111no—
76C32×D5—111no—
77C5×C17C3⋊D3×D1111yescharacteristic, complemented, Hall
78C22×C17—4951noHall
79D33—34no—
80C3×D11—54no—
81D3×C11—154no—
82D3×D5—334no—
83C5×C11C2×C17×C3⋊D311yescharacteristic, complemented, Hall
84C3×C17D15⋊D1114yescomplemented
85C32×C5C2×C17×D1111yescharacteristic, complemented, Hall
86C2×D11—451noHall
87C2×C3⋊D3—551noHall
88C2×C17—451no—
89C2×C17—551no—
90C2×C17—991no—
91C3×C11D3×D5×C1714yescomplemented
92D15—34no—
93C3×D5—114no—
94C5×D3—334no—
95C2×C11—451no—
96D11—51no—
97D11—91no—
98C2×D5—991noHall
99C2×C32—551no—
100C3⋊D3—51no—
101C3⋊D3—111no—
102C17D55⋊(C3⋊D3)11yescharacteristic, direct product factor, Sylow
103C3×C5D3×C17×D1114yescomplemented
104C2×D3—1654no—
105C11D5×C17×C3⋊D311yescharacteristic, complemented, Sylow
106C2×C5—991no—
107D5—91no—
108D5—111no—
109C32D5×C17×D1111yescharacteristic, complemented, Sylow
110C2×C3—554no—
111D3—154no—
112D3—334no—
113C5C17×C3⋊D3×D1111yescharacteristic, complemented, Sylow
114C22—4951noSylow
115C3C17×D15⋊D1114yescomplemented
116C2—451no—
117C2—551no—
118C2—991no—
subgroupG/H
center, hypercenterC17D55⋊(C3⋊D3)
commutator, cosocle, hypocenterC32×C5×C11C22×C17
FrattiniC1G
Fitting, socleC32×C5×C11×C17C22
LCSG ▷ C32×C5×C11
UCSC1 ◁ C17

Complements

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

NH ≅ G/Ntype
1. C32×C17×D55C2semidirect
2. C5×C17×C3⋊D33C2semidirect
3. C11×C17×C3⋊D15C2semidirect
5. C32×C5×C11×C17C22semidirect
9. C3×C17×D55D3semidirect
11. C17×C3⋊D33D5semidirect
15. C3×C5×C11×C17C2×D3semidirect
17. D55⋊(C3⋊D3)C17direct (N × H)
18. C17×D55C3⋊D3semidirect
21. C32×C11×C17C2×D5semidirect
22. C17×C3⋊D15D11semidirect
29. C11×C3⋊D15C2×C17semidirect
30. C5×C3⋊D33C2×C17semidirect
31. C32×D55C2×C17semidirect
32. C5×C11×C17C2×C3⋊D3semidirect
33. C32×C5×C17C2×D11semidirect
37. C3×C11×C17D3×D5semidirect
41. C32×C5×C11C22×C17semidirect
49. C3×D55D3×C17semidirect
53. C3×C5×C17D3×D11semidirect
56. C3⋊D33D5×C17semidirect
59. C11×C17D5×C3⋊D3semidirect
64. C3×C5×C11C2×D3×C17semidirect
65. C32×C17D5×D11semidirect
67. D55C17×C3⋊D3semidirect
73. C32×C11C2×D5×C17semidirect
74. C3⋊D15C17×D11semidirect
77. C5×C17C3⋊D3×D11semidirect
83. C5×C11C2×C17×C3⋊D3semidirect
84. C3×C17D15⋊D11semidirect
85. C32×C5C2×C17×D11semidirect
91. C3×C11D3×D5×C17semidirect
102. C17D55⋊(C3⋊D3)direct (N × H)
103. C3×C5D3×C17×D11semidirect
105. C11D5×C17×C3⋊D3semidirect
109. C32D5×C17×D11semidirect
113. C5C17×C3⋊D3×D11semidirect
115. C3C17×D15⋊D11semidirect

Maximal subgroups

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

subgroupindex
C32×C17×D552
C5×C17×C3⋊D332
C11×C17×C3⋊D152
C17×D15⋊D113
C17×C3⋊D3×D115
D5×C17×C3⋊D311
D55⋊(C3⋊D3)17