Finite Group Databasebeta

← #46778192

Subgroups — #46778192

Order 33660.

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

normal subgroups only

This group has 240 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×D935C211yesmaximal, characteristic, complemented
2C5×C3⋊D561C211yesmaximal, characteristic, complemented
3C11×C17×C3⋊D15C211yesmaximal, characteristic, complemented
4D15⋊D187—34nomaximal
5C32×C5×C11×C17C2211yescharacteristic, complemented, Hall
6C3⋊D3×D187—51nomaximal, Hall
7C11×C17×D15—34no—
8C5×D561—34no—
9C3×D935D314yescomplemented
10D5×D187—91noHall
11C3⋊D561D511yescharacteristic, complemented
12C11×C17×C3⋊D3—51no—
13C32×D187—51no—
14D85⋊(C3⋊D3)—111nomaximal, Hall
15C3×C5×C11×C17C2×D314yescomplemented
16D3×D187—154no—
17D55⋊(C3⋊D3)—171nomaximal, Hall
18D935C3⋊D311yescharacteristic, complemented
19D5×C11×C17—91no—
20C5×D187—91no—
21C32×C11×C17C2×D511yescharacteristic, complemented, Hall
22C17×C3⋊D15D1111yescharacteristic, complemented
23C5×C3⋊D51—111no—
24C32×D85—111no—
25D561—34no—
26D3×C11×C17—154no—
27C3×D187—54no—
28D15⋊D17—334no—
29C11×C3⋊D15D1711yescharacteristic, complemented
30C5×C3⋊D33—171no—
31C32×D55—171no—
32C5×C11×C17C2×C3⋊D311yescharacteristic, complemented, Hall
33C32×C5×C17C2×D1111yescharacteristic, complemented, Hall
34C2×D187—451noHall
35D15⋊D11—514no—
36C3⋊D3×D17—551noHall
37C3×C11×C17D3×D514yescomplemented
38C17×D15—34no—
39C5×D51—334no—
40C3×D85—114no—
41C32×C5×C11C2×D1711yescharacteristic, complemented, Hall
42C3⋊D3×D11—851noHall
43C2×C11×C17—451no—
44D187—51no—
45D187—91no—
46D5×D17—991noHall
47C11×D15—34no—
48C5×D33—514no—
49C3×D55—174no—
50C3⋊D51—111no—
51C17×C3⋊D3—51no—
52C32×D17—551no—
53C3×C5×C17D3×D1114yescomplemented
54D5×D11—1531noHall
55D3×D17—1654no—
56C3⋊D33—171no—
57C11×C3⋊D3—51no—
58C32×D11—851no—
59C11×C17D5×C3⋊D311yescharacteristic, complemented, Hall
60D5×C3⋊D3—1871noHall
61D85—111no—
62C5×D17—991no—
63D5×C17—91no—
64C3×C5×C11D3×D1714yescomplemented
65C32×C17D5×D1111yescharacteristic, complemented, Hall
66D3×D11—2554no—
67D55—171no—
68C5×D11—1531no—
69D5×C11—91no—
70D51—334no—
71C3×D17—554no—
72D3×C17—154no—
73C32×C11D5×D1711yescharacteristic, complemented, Hall
74C3⋊D15D18711yescharacteristic, complemented
75C5×C3⋊D3—1871no—
76C32×D5—1871no—
77C5×C17C3⋊D3×D1111yescharacteristic, complemented, Hall
78C2×D17—4951noHall
79D33—514no—
80C3×D11—854no—
81D3×C11—154no—
82D3×D5—5614no—
83C5×C11C3⋊D3×D1711yescharacteristic, complemented, Hall
84C3×C17D15⋊D1114yescomplemented
85C32×C5C2×D18711yescharacteristic, complemented, Hall
86C2×D11—7651noHall
87C2×C3⋊D3—9351noHall
88C2×C17—451no—
89D17—551no—
90D17—991no—
91C3×C11D15⋊D1714yescomplemented
92D15—34no—
93C3×D5—1874no—
94C5×D3—5614no—
95C2×C11—451no—
96D11—851no—
97D11—1531no—
98C2×D5—16831noHall
99C2×C32—9351no—
100C3⋊D3—51no—
101C3⋊D3—1871no—
102C17D55⋊(C3⋊D3)11yescharacteristic, complemented, Sylow
103C3×C5D3×D18714yescomplemented
104C2×D3—28054no—
105C11D85⋊(C3⋊D3)11yescharacteristic, complemented, Sylow
106C2×C5—16831no—
107D5—91no—
108D5—1871no—
109C32D5×D18711yescharacteristic, complemented, Sylow
110C2×C3—9354no—
111D3—154no—
112D3—5614no—
113C5C3⋊D3×D18711yescharacteristic, complemented, Sylow
114C22—84151noSylow
115C3D15⋊D18714yescomplemented
116C2—451no—
117C2—16831no—
118C2—9351no—
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×D935C2semidirect
2. C5×C3⋊D561C2semidirect
3. C11×C17×C3⋊D15C2semidirect
5. C32×C5×C11×C17C22semidirect
9. C3×D935D3semidirect
11. C3⋊D561D5semidirect
15. C3×C5×C11×C17C2×D3semidirect
18. D935C3⋊D3semidirect
21. C32×C11×C17C2×D5semidirect
22. C17×C3⋊D15D11semidirect
29. C11×C3⋊D15D17semidirect
32. C5×C11×C17C2×C3⋊D3semidirect
33. C32×C5×C17C2×D11semidirect
37. C3×C11×C17D3×D5semidirect
41. C32×C5×C11C2×D17semidirect
53. C3×C5×C17D3×D11semidirect
59. C11×C17D5×C3⋊D3semidirect
64. C3×C5×C11D3×D17semidirect
65. C32×C17D5×D11semidirect
73. C32×C11D5×D17semidirect
74. C3⋊D15D187semidirect
77. C5×C17C3⋊D3×D11semidirect
83. C5×C11C3⋊D3×D17semidirect
84. C3×C17D15⋊D11semidirect
85. C32×C5C2×D187semidirect
91. C3×C11D15⋊D17semidirect
102. C17D55⋊(C3⋊D3)semidirect
103. C3×C5D3×D187semidirect
105. C11D85⋊(C3⋊D3)semidirect
109. C32D5×D187semidirect
113. C5C3⋊D3×D187semidirect
115. C3D15⋊D187semidirect

Maximal subgroups

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

subgroupindex
C32×D9352
C5×C3⋊D5612
C11×C17×C3⋊D152
D15⋊D1873
C3⋊D3×D1875
D85⋊(C3⋊D3)11
D55⋊(C3⋊D3)17