Finite Group Databasebeta

← D91⋊(C3⋊D33) #49114991

Subgroups — D91⋊(C3⋊D33) #49114991

Order 36036.

240 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 65 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×C11×D91C211yesmaximal, characteristic, complemented
2C7×C3⋊D429C211yesmaximal, characteristic, complemented
3C13×C3⋊D231C211yesmaximal, characteristic, complemented
4D91⋊D33—34nomaximal
5C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
6C13×D231—34no—
7C7×D429—34no—
8C3×C11×D91D314yescomplemented
9D13×C3⋊D33—71nomaximal, Hall
10D77⋊D13—91noHall
11D91⋊(C3⋊D3)—111nomaximal, Hall
12C3×C7×C11×C13C2×D314yescomplemented
13D7×C3⋊D33—131nomaximal, Hall
14C3⋊D429D711yescharacteristic, complemented
15C13×C3⋊D33—71no—
16C32×C11×D13—71no—
17C13×D77—91no—
18C11×D91C3⋊D311yescharacteristic, complemented
19C7×D143—91no—
20D13×D33—214no—
21C13×C3⋊D21—111no—
22C7×C3⋊D39—111no—
23C32×D91D1111yescharacteristic, complemented
24C3⋊D231D1311yescharacteristic, complemented
25C7×C3⋊D33—131no—
26C32×C11×D7—131no—
27C32×C11×C13C2×D711yescharacteristic, complemented, Hall
28D21⋊D13—334no—
29C7×C11×C13C2×C3⋊D311yescharacteristic, complemented, Hall
30D7×D33—394no—
31D429—34no—
32C13×D33—214no—
33C3×C11×D13—74no—
34C32×C7×C13C2×D1111yescharacteristic, complemented, Hall
35C32×C7×C11C2×D1311yescharacteristic, complemented, Hall
36D11×D13—631noHall
37C13×D21—334no—
38C7×D39—334no—
39C3×D91D3314yescomplemented
40C3⋊D3×D13—771noHall
41D231—34no—
42C7×D33—394no—
43C3×C11×D7—134no—
44C3×C11×C13D3×D714yescomplemented
45C2×C3⋊D33—911noHall
46D7×D13—991noHall
47D7×D11—1171noHall
48D143—91no—
49C11×D13—71no—
50C13×D11—631no—
51C3×C7×C13C2×D3314yescomplemented
52D7×C3⋊D3—1431noHall
53C3⋊D39—111no—
54C13×C3⋊D3—771no—
55C32×D13—71no—
56C3×C7×C11D3×D1314yescomplemented
57C2×C32×C11—911no—
58C3⋊D33—71no—
59C3⋊D33—131no—
60D91C3⋊D3311yescharacteristic, complemented
61C7×D13—991no—
62C13×D7—991no—
63D3×D13—2314no—
64D77—91no—
65C7×D11—1171no—
66C11×D7—131no—
67C11×C13D7×C3⋊D311yescharacteristic, complemented, Hall
68C2×D33—2734no—
69C3⋊D21—111no—
70C7×C3⋊D3—1431no—
71C32×D7—131no—
72C32×C13D7×D1111yescharacteristic, complemented, Hall
73C32×C11D7×D1311yescharacteristic, complemented, Hall
74C7×C13C2×C3⋊D3311yescharacteristic, complemented, Hall
75D3×D7—4294no—
76D39—334no—
77C3×D13—74no—
78D3×C13—2314no—
79C7×C11C3⋊D3×D1311yescharacteristic, complemented, Hall
80C2×C3×C11—914no—
81D33—214no—
82D33—394no—
83C32×C7D11×D1311yescharacteristic, complemented, Hall
84C2×D13—6931noHall
85C2×D11—8191noHall
86D21—334no—
87C3×D7—134no—
88D3×C7—4294no—
89C3×C13D7×D3314yescomplemented
90C2×C3⋊D3—10011noHall
91C3×C11D21⋊D1314yescomplemented
92C2×D7—12871noHall
93C2×C13—6931no—
94D13—71no—
95D13—991no—
96C2×C11—911no—
97D11—631no—
98D11—1171no—
99C3×C7D13×D3314yescomplemented
100C2×C32—911no—
101C3⋊D3—771no—
102C3⋊D3—1431no—
103C2×C7—12871no—
104D7—131no—
105D7—991no—
106C13D7×C3⋊D3311yescharacteristic, complemented, Sylow
107C2×D3—30034no—
108C11D91⋊(C3⋊D3)11yescharacteristic, complemented, Sylow
109C32D77⋊D1311yescharacteristic, complemented, Sylow
110C7D13×C3⋊D3311yescharacteristic, complemented, Sylow
111C2×C3—914no—
112D3—4294no—
113D3—2314no—
114C22—90091noSylow
115C3D91⋊D3314yescomplemented
116C2—12871no—
117C2—911no—
118C2—6931no—
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×C11×D91C2semidirect
2. C7×C3⋊D429C2semidirect
3. C13×C3⋊D231C2semidirect
5. C32×C7×C11×C13C22semidirect
8. C3×C11×D91D3semidirect
12. C3×C7×C11×C13C2×D3semidirect
14. C3⋊D429D7semidirect
18. C11×D91C3⋊D3semidirect
23. C32×D91D11semidirect
24. C3⋊D231D13semidirect
27. C32×C11×C13C2×D7semidirect
29. C7×C11×C13C2×C3⋊D3semidirect
34. C32×C7×C13C2×D11semidirect
35. C32×C7×C11C2×D13semidirect
39. C3×D91D33semidirect
44. C3×C11×C13D3×D7semidirect
51. C3×C7×C13C2×D33semidirect
56. C3×C7×C11D3×D13semidirect
60. D91C3⋊D33semidirect
67. C11×C13D7×C3⋊D3semidirect
72. C32×C13D7×D11semidirect
73. C32×C11D7×D13semidirect
74. C7×C13C2×C3⋊D33semidirect
79. C7×C11C3⋊D3×D13semidirect
83. C32×C7D11×D13semidirect
89. C3×C13D7×D33semidirect
91. C3×C11D21⋊D13semidirect
99. C3×C7D13×D33semidirect
106. C13D7×C3⋊D33semidirect
108. C11D91⋊(C3⋊D3)semidirect
109. C32D77⋊D13semidirect
110. C7D13×C3⋊D33semidirect
115. C3D91⋊D33semidirect

Maximal subgroups

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

subgroupindex
C32×C11×D912
C7×C3⋊D4292
C13×C3⋊D2312
D91⋊D333
D13×C3⋊D337
D91⋊(C3⋊D3)11
D7×C3⋊D3313