Finite Group Databasebeta

← #49114995

Subgroups — #49114995

Order 36036.

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×D1001C211yesmaximal, characteristic, complemented
2C7×C11×C3⋊D39C211yesmaximal, characteristic, complemented
3C13×C3⋊D231C211yesmaximal, characteristic, complemented
4D39⋊D77—34nomaximal
5C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
6C13×D231—34no—
7C7×C11×D39—34no—
8C3×D1001D314yescomplemented
9D143⋊(C3⋊D3)—71nomaximal, Hall
10D13×D77—91noHall
11D91⋊(C3⋊D3)—111nomaximal, Hall
12C3×C7×C11×C13C2×D314yescomplemented
13C3⋊D3×D77—131nomaximal, Hall
14C13×C3⋊D33—71no—
15C11×C3⋊D39D711yescharacteristic, complemented
16C32×D143—71no—
17D1001C3⋊D311yescharacteristic, complemented
18C13×D77—91no—
19C7×C11×D13—91no—
20D33⋊D13—214no—
21C13×C3⋊D21—111no—
22C7×C3⋊D39D1111yescharacteristic, complemented
23C32×D91—111no—
24C3⋊D231D1311yescharacteristic, complemented
25C7×C11×C3⋊D3—131no—
26C32×D77—131no—
27C32×C11×C13C2×D711yescharacteristic, complemented, Hall
28D21⋊D13—334no—
29C7×C11×C13C2×C3⋊D311yescharacteristic, complemented, Hall
30D3×D77—394no—
31C13×D33—214no—
32C11×D39—34no—
33C3×D143—74no—
34C32×C7×C13C2×D1111yescharacteristic, complemented, Hall
35C32×C7×C11C2×D1311yescharacteristic, complemented, Hall
36D11×D13—631noHall
37C13×D21—334no—
38C7×D39—34no—
39C3×D91—114no—
40C3⋊D3×D13—771noHall
41D231—34no—
42D3×C7×C11—394no—
43C3×D77—134no—
44C3×C11×C13D3×D714yescomplemented
45C3⋊D3×D11—911noHall
46D7×D13—991noHall
47C2×D77—1171noHall
48D143—71no—
49C11×D13—91no—
50C13×D11—631no—
51C3×C7×C13D3×D1114yescomplemented
52D7×C3⋊D3—1431noHall
53C3⋊D39D7711yescharacteristic, complemented
54C13×C3⋊D3—771no—
55C32×D13—771no—
56C3×C7×C11D3×D1314yescomplemented
57C3⋊D33—71no—
58C11×C3⋊D3—131no—
59C32×D11—911no—
60D91—111no—
61C7×D13—91no—
62C13×D7—991no—
63D3×D13—2314no—
64C2×C7×C11—1171no—
65D77—91no—
66D77—131no—
67C11×C13D7×C3⋊D311yescharacteristic, complemented, Hall
68D3×D11—2734no—
69C3⋊D21—111no—
70C7×C3⋊D3—131no—
71C32×D7—1431no—
72C32×C13C2×D7711yescharacteristic, complemented, Hall
73C32×C11D7×D1311yescharacteristic, complemented, Hall
74C7×C13C3⋊D3×D1111yescharacteristic, complemented, Hall
75D3×D7—4294no—
76D39—34no—
77C3×D13—774no—
78D3×C13—2314no—
79C7×C11C3⋊D3×D1311yescharacteristic, complemented, Hall
80D33—214no—
81C3×D11—914no—
82D3×C11—394no—
83C32×C7D11×D1311yescharacteristic, complemented, Hall
84C2×D13—6931noHall
85C2×D11—8191noHall
86D21—334no—
87C3×D7—1434no—
88D3×C7—394no—
89C3×C13D3×D7714yescomplemented
90C2×C3⋊D3—10011noHall
91C3×C11D21⋊D1314yescomplemented
92C2×D7—12871noHall
93C2×C13—6931no—
94D13—91no—
95D13—771no—
96C2×C11—1171no—
97D11—631no—
98D11—911no—
99C3×C7D33⋊D1314yescomplemented
100C2×C32—10011no—
101C3⋊D3—131no—
102C3⋊D3—771no—
103C2×C7—1171no—
104D7—991no—
105D7—1431no—
106C13C3⋊D3×D7711yescharacteristic, complemented, Sylow
107C2×D3—30034no—
108C11D91⋊(C3⋊D3)11yescharacteristic, complemented, Sylow
109C32D13×D7711yescharacteristic, complemented, Sylow
110C7D143⋊(C3⋊D3)11yescharacteristic, complemented, Sylow
111C2×C3—10014no—
112D3—394no—
113D3—2314no—
114C22—90091noSylow
115C3D39⋊D7714yescomplemented
116C2—1171no—
117C2—6931no—
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×C3⋊D39C2semidirect
3. C13×C3⋊D231C2semidirect
5. C32×C7×C11×C13C22semidirect
8. C3×D1001D3semidirect
12. C3×C7×C11×C13C2×D3semidirect
15. C11×C3⋊D39D7semidirect
17. D1001C3⋊D3semidirect
22. C7×C3⋊D39D11semidirect
24. C3⋊D231D13semidirect
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
53. C3⋊D39D77semidirect
56. C3×C7×C11D3×D13semidirect
67. C11×C13D7×C3⋊D3semidirect
72. C32×C13C2×D77semidirect
73. C32×C11D7×D13semidirect
74. C7×C13C3⋊D3×D11semidirect
79. C7×C11C3⋊D3×D13semidirect
83. C32×C7D11×D13semidirect
89. C3×C13D3×D77semidirect
91. C3×C11D21⋊D13semidirect
99. C3×C7D33⋊D13semidirect
106. C13C3⋊D3×D77semidirect
108. C11D91⋊(C3⋊D3)semidirect
109. C32D13×D77semidirect
110. C7D143⋊(C3⋊D3)semidirect
115. C3D39⋊D77semidirect

Maximal subgroups

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

subgroupindex
C32×D10012
C7×C11×C3⋊D392
C13×C3⋊D2312
D39⋊D773
D143⋊(C3⋊D3)7
D91⋊(C3⋊D3)11
C3⋊D3×D7713