Finite Group Databasebeta

← #49114999

Subgroups — #49114999

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×C3⋊D429C211yesmaximal, characteristic, complemented
3C11×C13×C3⋊D21C211yesmaximal, characteristic, complemented
4D21⋊D143—34nomaximal
5C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
6C11×C13×D21—34no—
7C7×D429—34no—
8C3×D1001D314yescomplemented
9C3⋊D3×D143—71nomaximal, Hall
10D7×D143—91noHall
11D91⋊(C3⋊D3)—111nomaximal, Hall
12C3×C7×C11×C13C2×D314yescomplemented
13D77⋊(C3⋊D3)—131nomaximal, Hall
14C3⋊D429D711yescharacteristic, complemented
15C11×C13×C3⋊D3—71no—
16C32×D143—71no—
17D1001C3⋊D311yescharacteristic, complemented
18C11×C13×D7—91no—
19C7×D143—91no—
20D3×D143—214no—
21C13×C3⋊D21D1111yescharacteristic, complemented
22C7×C3⋊D39—111no—
23C32×D91—111no—
24C11×C3⋊D21D1311yescharacteristic, complemented
25C7×C3⋊D33—131no—
26C32×D77—131no—
27C32×C11×C13C2×D711yescharacteristic, complemented, Hall
28D21⋊D13—334no—
29C7×C11×C13C2×C3⋊D311yescharacteristic, complemented, Hall
30D21⋊D11—394no—
31D429—34no—
32D3×C11×C13—214no—
33C3×D143—74no—
34C32×C7×C13C2×D1111yescharacteristic, complemented, Hall
35C32×C7×C11C2×D1311yescharacteristic, complemented, Hall
36C2×D143—631noHall
37C13×D21—34no—
38C7×D39—334no—
39C3×D91—114no—
40C3⋊D3×D13—771noHall
41C11×D21—34no—
42C7×D33—394no—
43C3×D77—134no—
44C3×C11×C13D3×D714yescomplemented
45C3⋊D3×D11—911noHall
46D7×D13—991noHall
47D7×D11—1171noHall
48C2×C11×C13—631no—
49D143—71no—
50D143—91no—
51C3×C7×C13D3×D1114yescomplemented
52D7×C3⋊D3—1431noHall
53C3⋊D39—111no—
54C13×C3⋊D3—71no—
55C32×D13—771no—
56C3×C7×C11D3×D1314yescomplemented
57C3⋊D33—131no—
58C11×C3⋊D3—71no—
59C32×D11—911no—
60D91—111no—
61C7×D13—991no—
62C13×D7—91no—
63D3×D13—2314no—
64D77—131no—
65C7×D11—1171no—
66C11×D7—91no—
67C11×C13D7×C3⋊D311yescharacteristic, complemented, Hall
68D3×D11—2734no—
69C3⋊D21D14311yescharacteristic, complemented
70C7×C3⋊D3—1431no—
71C32×D7—1431no—
72C32×C13D7×D1111yescharacteristic, complemented, Hall
73C32×C11D7×D1311yescharacteristic, complemented, Hall
74C7×C13C3⋊D3×D1111yescharacteristic, complemented, Hall
75D3×D7—4294no—
76D39—334no—
77C3×D13—774no—
78D3×C13—214no—
79C7×C11C3⋊D3×D1311yescharacteristic, complemented, Hall
80D33—394no—
81C3×D11—914no—
82D3×C11—214no—
83C32×C7C2×D14311yescharacteristic, complemented, Hall
84C2×D13—6931noHall
85C2×D11—8191noHall
86D21—34no—
87C3×D7—1434no—
88D3×C7—4294no—
89C3×C13D21⋊D1114yescomplemented
90C2×C3⋊D3—10011noHall
91C3×C11D21⋊D1314yescomplemented
92C2×D7—12871noHall
93C2×C13—631no—
94D13—771no—
95D13—991no—
96C2×C11—631no—
97D11—911no—
98D11—1171no—
99C3×C7D3×D14314yescomplemented
100C2×C32—10011no—
101C3⋊D3—71no—
102C3⋊D3—1431no—
103C2×C7—12871no—
104D7—91no—
105D7—1431no—
106C13D77⋊(C3⋊D3)11yescharacteristic, complemented, Sylow
107C2×D3—30034no—
108C11D91⋊(C3⋊D3)11yescharacteristic, complemented, Sylow
109C32D7×D14311yescharacteristic, complemented, Sylow
110C7C3⋊D3×D14311yescharacteristic, complemented, Sylow
111C2×C3—10014no—
112D3—214no—
113D3—4294no—
114C22—90091noSylow
115C3D21⋊D14314yescomplemented
116C2—12871no—
117C2—631no—
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×C3⋊D429C2semidirect
3. C11×C13×C3⋊D21C2semidirect
5. C32×C7×C11×C13C22semidirect
8. C3×D1001D3semidirect
12. C3×C7×C11×C13C2×D3semidirect
14. C3⋊D429D7semidirect
17. D1001C3⋊D3semidirect
21. C13×C3⋊D21D11semidirect
24. C11×C3⋊D21D13semidirect
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
56. C3×C7×C11D3×D13semidirect
67. C11×C13D7×C3⋊D3semidirect
69. C3⋊D21D143semidirect
72. C32×C13D7×D11semidirect
73. C32×C11D7×D13semidirect
74. C7×C13C3⋊D3×D11semidirect
79. C7×C11C3⋊D3×D13semidirect
83. C32×C7C2×D143semidirect
89. C3×C13D21⋊D11semidirect
91. C3×C11D21⋊D13semidirect
99. C3×C7D3×D143semidirect
106. C13D77⋊(C3⋊D3)semidirect
108. C11D91⋊(C3⋊D3)semidirect
109. C32D7×D143semidirect
110. C7C3⋊D3×D143semidirect
115. C3D21⋊D143semidirect

Maximal subgroups

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

subgroupindex
C32×D10012
C7×C3⋊D4292
C11×C13×C3⋊D212
D21⋊D1433
C3⋊D3×D1437
D91⋊(C3⋊D3)11
D77⋊(C3⋊D3)13