Finite Group Databasebeta

← C17×D45⋊D11 #46777933

Subgroups — C17×D45⋊D11 #46777933

Order 33660.

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

normal subgroups only

This group has 120 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×C17×D45C211yesmaximal, characteristic, complemented
2C5×C17×D99C211yesmaximal, characteristic, complemented
3C9×C17×D55C211yesmaximal, characteristic, complemented
4C17×D15⋊D11—31nomaximal
5C5×C9×C11×C17C2211yescharacteristic, complemented, Hall
6C17×D9×D11—51nomaximal, Hall
7C11×C17×D15—31no—
8C5×C17×D33—31no—
9C3×C17×D55D311yescharacteristic
10D5×C17×D11—91noHall
11C17×D99D511yescharacteristic, complemented
12C11×C17×D9—51no—
13C9×C17×D11—51no—
14D5×C17×D9—111nomaximal, Hall
15C3×C5×C11×C17C2×D311yescharacteristic
16D3×C17×D11—151no—
17D45⋊D11C1711yesmaximal, characteristic, direct product factor, Hall
18C17×D55D911yescharacteristic, complemented
19D5×C11×C17—91no—
20C5×C17×D11—91no—
21C9×C11×C17C2×D511yescharacteristic, complemented, Hall
22C17×D45D1111yescharacteristic, complemented
23C5×C17×D9—111no—
24C9×D5×C17—111no—
25C17×D33—31no—
26D3×C11×C17—151no—
27C3×C17×D11—51no—
28D3×D5×C17—331no—
29C11×D45C2×C1711yescharacteristic, complemented
30C5×D99C2×C1711yescharacteristic, complemented
31C9×D55C2×C1711yescharacteristic, complemented
32C5×C11×C17C2×D911yescharacteristic, complemented, Hall
33C5×C9×C17C2×D1111yescharacteristic, complemented, Hall
34C2×C17×D11—451noHall
35D15⋊D11—31no—
36C2×C17×D9—551noHall
37C3×C11×C17D3×D511yescharacteristic
38C17×D15—31no—
39C5×D3×C17—331no—
40C3×D5×C17—111no—
41C5×C9×C11C22×C1711yescharacteristic, complemented, Hall
42D9×D11—51noHall
43C2×C11×C17—451no—
44C17×D11—51no—
45C17×D11—91no—
46C2×D5×C17—991noHall
47C11×D15—31no—
48C5×D33—31no—
49C3×D55D3×C1711yescharacteristic
50C2×C9×C17—551no—
51C17×D9—51no—
52C17×D9—111no—
53C3×C5×C17D3×D1111yescharacteristic
54D5×D11—91noHall
55C2×D3×C17—1651no—
56D99D5×C1711yescharacteristic, complemented
57C9×D11—51no—
58C11×D9—51no—
59C11×C17D5×D911yescharacteristic, complemented, Hall
60D5×D9—111noHall
61C2×C5×C17—991no—
62D5×C17—91no—
63D5×C17—111no—
64C3×C5×C11C2×D3×C1711yescharacteristic
65C9×C17D5×D1111yescharacteristic, complemented, Hall
66D3×D11—151no—
67D55C17×D911yescharacteristic, complemented
68C5×D11—91no—
69D5×C11—91no—
70C2×C3×C17—551no—
71D3×C17—151no—
72D3×C17—331no—
73C9×C11C2×D5×C1711yescharacteristic, complemented, Hall
74D45C17×D1111yescharacteristic, complemented
75C9×D5—111no—
76C5×D9—111no—
77C5×C17D9×D1111yescharacteristic, complemented, Hall
78C22×C17—4951noHall
79D33—31no—
80C3×D11—51no—
81D3×C11—151no—
82D3×D5—331no—
83C5×C11C2×C17×D911yescharacteristic, complemented, Hall
84C3×C17D15⋊D1111yescharacteristic
85C5×C9C2×C17×D1111yescharacteristic, complemented, Hall
86C2×D11—451noHall
87C2×D9—551noHall
88C2×C17—451no—
89C2×C17—551no—
90C2×C17—991no—
91C3×C11D3×D5×C1711yescharacteristic
92D15—31no—
93C3×D5—111no—
94C5×D3—331no—
95C2×C11—451no—
96D11—51no—
97D11—91no—
98C2×D5—991noHall
99C2×C9—551no—
100D9—51no—
101D9—111no—
102C17D45⋊D1111yescharacteristic, direct product factor, Sylow
103C3×C5D3×C17×D1111yescharacteristic
104C2×D3—1651no—
105C11D5×C17×D911yescharacteristic, complemented, Sylow
106C2×C5—991no—
107D5—91no—
108D5—111no—
109C9D5×C17×D1111yescharacteristic, complemented, Sylow
110C2×C3—551no—
111D3—151no—
112D3—331no—
113C5C17×D9×D1111yescharacteristic, complemented, Sylow
114C22—4951noSylow
115C3C17×D15⋊D1111yescharacteristic
116C2—451no—
117C2—551no—
118C2—991no—
subgroupG/H
center, hypercenterC17D45⋊D11
commutator, cosocle, hypocenterC5×C9×C11C22×C17
FrattiniC3C17×D15⋊D11
FittingC5×C9×C11×C17C22
socleC3×C5×C11×C17C2×D3
LCSG ▷ C5×C9×C11
UCSC1 ◁ C17

Complements

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

NH ≅ G/Ntype
1. C11×C17×D45C2semidirect
2. C5×C17×D99C2semidirect
3. C9×C17×D55C2semidirect
5. C5×C9×C11×C17C22semidirect
11. C17×D99D5semidirect
17. D45⋊D11C17direct (N × H)
18. C17×D55D9semidirect
21. C9×C11×C17C2×D5semidirect
22. C17×D45D11semidirect
29. C11×D45C2×C17semidirect
30. C5×D99C2×C17semidirect
31. C9×D55C2×C17semidirect
32. C5×C11×C17C2×D9semidirect
33. C5×C9×C17C2×D11semidirect
41. C5×C9×C11C22×C17semidirect
56. D99D5×C17semidirect
59. C11×C17D5×D9semidirect
65. C9×C17D5×D11semidirect
67. D55C17×D9semidirect
73. C9×C11C2×D5×C17semidirect
74. D45C17×D11semidirect
77. C5×C17D9×D11semidirect
83. C5×C11C2×C17×D9semidirect
85. C5×C9C2×C17×D11semidirect
102. C17D45⋊D11direct (N × H)
105. C11D5×C17×D9semidirect
109. C9D5×C17×D11semidirect
113. C5C17×D9×D11semidirect

Maximal subgroups

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

subgroupindex
C11×C17×D452
C5×C17×D992
C9×C17×D552
C17×D15⋊D113
C17×D9×D115
D5×C17×D911
D45⋊D1117