Finite Group Databasebeta

← C3⋊D3×D1001 #49114994

Subgroups — C3⋊D3×D1001 #49114994

Order 36036.

240 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 64 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×D1001C211yesmaximal, characteristic, complemented
2C7×C11×C13×C3⋊D3C211yesmaximal, characteristic, complemented
3C3⋊D3003C211yesmaximal, characteristic, complemented
4D3×D1001—34nomaximal
5C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
6D3003—34no—
7D3×C7×C11×C13—34no—
8C3×D1001D314yescomplemented
9C3⋊D3×D143—71nomaximal, Hall
10C2×D1001—91noHall
11C3⋊D3×D91—111nomaximal, Hall
12C3×C7×C11×C13C2×D314yescomplemented
13C3⋊D3×D77—131nomaximal, Hall
14C3⋊D429—71no—
15C11×C13×C3⋊D3D711yescharacteristic, complemented
16C32×D143—71no—
17D1001—91no—
18D1001C3⋊D311yescharacteristic, direct product factor
19C2×C7×C11×C13—91no—
20D3×D143—214no—
21C3⋊D273—111no—
22C7×C13×C3⋊D3D1111yescharacteristic, complemented
23C32×D91—111no—
24C3⋊D231—131no—
25C7×C11×C3⋊D3D1311yescharacteristic, complemented
26C32×D77—131no—
27C32×C11×C13C2×D711yescharacteristic, complemented, Hall
28D3×D91—334no—
29C7×C11×C13C2×C3⋊D311yescharacteristic, complemented, Hall
30D3×D77—394no—
31D429—214no—
32D3×C11×C13—34no—
33C3×D143—74no—
34C32×C7×C13C2×D1111yescharacteristic, complemented, Hall
35C32×C7×C11C2×D1311yescharacteristic, complemented, Hall
36C2×D143—631noHall
37D273—334no—
38D3×C7×C13—34no—
39C3×D91—114no—
40C3⋊D3×D13—771noHall
41D231—394no—
42D3×C7×C11—34no—
43C3×D77—134no—
44C3×C11×C13D3×D714yescomplemented
45C3⋊D3×D11—911noHall
46C2×D91—991noHall
47C2×D77—1171noHall
48C2×C11×C13—91no—
49D143—71no—
50D143—631no—
51C3×C7×C13D3×D1114yescomplemented
52D7×C3⋊D3—1431noHall
53C3⋊D39—771no—
54C13×C3⋊D3D7711yescharacteristic, complemented
55C32×D13—771no—
56C3×C7×C11D3×D1314yescomplemented
57C3⋊D33—911no—
58C11×C3⋊D3D9111yescharacteristic, complemented
59C32×D11—911no—
60C2×C7×C13—91no—
61D91—111no—
62D91—991no—
63D3×D13—2314no—
64C2×C7×C11—91no—
65D77—131no—
66D77—1171no—
67C11×C13D7×C3⋊D311yescharacteristic, complemented, Hall
68D3×D11—2734no—
69C3⋊D21—1431no—
70C7×C3⋊D3D14311yescharacteristic, complemented
71C32×D7—1431no—
72C32×C13C2×D7711yescharacteristic, complemented, Hall
73C32×C11C2×D9111yescharacteristic, complemented, Hall
74C7×C13C3⋊D3×D1111yescharacteristic, complemented, Hall
75D3×D7—4294no—
76D39—2314no—
77C3×D13—774no—
78D3×C13—34no—
79C7×C11C3⋊D3×D1311yescharacteristic, complemented, Hall
80D33—2734no—
81C3×D11—914no—
82D3×C11—34no—
83C32×C7C2×D14311yescharacteristic, complemented, Hall
84C2×D13—6931noHall
85C2×D11—8191noHall
86D21—4294no—
87C3×D7—1434no—
88D3×C7—34no—
89C3×C13D3×D7714yescomplemented
90C2×C3⋊D3—10011noHall
91C3×C11D3×D9114yescomplemented
92C2×D7—12871noHall
93C2×C13—91no—
94D13—771no—
95D13—6931no—
96C2×C11—91no—
97D11—8191no—
98D11—911no—
99C3×C7D3×D14314yescomplemented
100C2×C32—10011no—
101C3⋊D3—10011no—
102C3⋊D3D100111yescharacteristic, direct product factor
103C2×C7—91no—
104D7—12871no—
105D7—1431no—
106C13C3⋊D3×D7711yescharacteristic, complemented, Sylow
107C2×D3—30034no—
108C11C3⋊D3×D9111yescharacteristic, complemented, Sylow
109C32C2×D100111yescharacteristic, complemented, Sylow
110C7C3⋊D3×D14311yescharacteristic, complemented, Sylow
111C2×C3—10014no—
112D3—34no—
113D3—30034no—
114C22—90091noSylow
115C3D3×D100114yescomplemented
116C2—91no—
117C2—90091no—
118C2—10011no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C7×C11×C13C22
LCSG ▷ C32×C7×C11×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C32×D1001C2semidirect
2. C7×C11×C13×C3⋊D3C2semidirect
3. C3⋊D3003C2semidirect
5. C32×C7×C11×C13C22semidirect
8. C3×D1001D3semidirect
12. C3×C7×C11×C13C2×D3semidirect
15. C11×C13×C3⋊D3D7semidirect
18. D1001C3⋊D3direct (N × H)
22. C7×C13×C3⋊D3D11semidirect
25. C7×C11×C3⋊D3D13semidirect
27. C32×C11×C13C2×D7semidirect
29. C7×C11×C13C2×C3⋊D3semidirect
34. C32×C7×C13C2×D11semidirect
35. C32×C7×C11C2×D13semidirect
44. C3×C11×C13D3×D7semidirect
51. C3×C7×C13D3×D11semidirect
54. C13×C3⋊D3D77semidirect
56. C3×C7×C11D3×D13semidirect
58. C11×C3⋊D3D91semidirect
67. C11×C13D7×C3⋊D3semidirect
70. C7×C3⋊D3D143semidirect
72. C32×C13C2×D77semidirect
73. C32×C11C2×D91semidirect
74. C7×C13C3⋊D3×D11semidirect
79. C7×C11C3⋊D3×D13semidirect
83. C32×C7C2×D143semidirect
89. C3×C13D3×D77semidirect
91. C3×C11D3×D91semidirect
99. C3×C7D3×D143semidirect
102. C3⋊D3D1001direct (N × H)
106. C13C3⋊D3×D77semidirect
108. C11C3⋊D3×D91semidirect
109. C32C2×D1001semidirect
110. C7C3⋊D3×D143semidirect
115. C3D3×D1001semidirect

Maximal subgroups

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

subgroupindex
C32×D10012
C7×C11×C13×C3⋊D32
C3⋊D30032
D3×D10013
C3⋊D3×D1437
C3⋊D3×D9111
C3⋊D3×D7713