Finite Group Databasebeta

← C11×C3⋊D3×D91 #49114986

Subgroups — C11×C3⋊D3×D91 #49114986

Order 36036.

240 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 72 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×C11×C13×C3⋊D3C211yesmaximal, characteristic, complemented
3C11×C3⋊D273C211yesmaximal, characteristic, complemented
4D3×C11×D91—34nomaximal
5C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
6C11×D273—34no—
7D3×C7×C11×C13—34no—
8C3×C11×D91D314yescomplemented
9C11×C3⋊D3×D13—71nomaximal, Hall
10C2×C11×D91—91noHall
11C3⋊D3×D91C1111yesmaximal, characteristic, direct product factor, Hall
12C3×C7×C11×C13C2×D314yescomplemented
13C11×D7×C3⋊D3—131nomaximal, Hall
14C11×C3⋊D39—71no—
15C11×C13×C3⋊D3D711yescharacteristic, complemented
16C32×C11×D13—71no—
17C11×D91—91no—
18C11×D91C3⋊D311yescharacteristic, direct product factor
19C2×C7×C11×C13—91no—
20D3×C11×D13—214no—
21C3⋊D273C2×C1111yescharacteristic, complemented
22C7×C13×C3⋊D3C2×C1111yescharacteristic, complemented
23C32×D91C2×C1111yescharacteristic, complemented
24C11×C3⋊D21—131no—
25C7×C11×C3⋊D3D1311yescharacteristic, complemented
26C32×C11×D7—131no—
27C32×C11×C13C2×D711yescharacteristic, complemented, Hall
28D3×D91—34no—
29C7×C11×C13C2×C3⋊D311yescharacteristic, complemented, Hall
30D3×C11×D7—394no—
31C11×D39—214no—
32D3×C11×C13—34no—
33C3×C11×D13—74no—
34C32×C7×C13C22×C1111yescharacteristic, complemented, Hall
35C32×C7×C11C2×D1311yescharacteristic, complemented, Hall
36C2×C11×D13—631noHall
37D273—34no—
38D3×C7×C13—34no—
39C3×D91D3×C1114yescomplemented
40C3⋊D3×D13—71noHall
41C11×D21—394no—
42D3×C7×C11—34no—
43C3×C11×D7—134no—
44C3×C11×C13D3×D714yescomplemented
45C2×C11×C3⋊D3—911noHall
46C2×D91—91noHall
47C2×C11×D7—1171noHall
48C2×C11×C13—91no—
49C11×D13—71no—
50C11×D13—631no—
51C3×C7×C13C2×D3×C1114yescomplemented
52D7×C3⋊D3—131noHall
53C3⋊D39—71no—
54C13×C3⋊D3C11×D711yescharacteristic, complemented
55C32×D13—71no—
56C3×C7×C11D3×D1314yescomplemented
57C2×C32×C11—911no—
58C11×C3⋊D3—911no—
59C11×C3⋊D3D9111yescharacteristic, direct product factor
60C2×C7×C13—91no—
61D91—91no—
62D91C11×C3⋊D311yescharacteristic, direct product factor
63D3×D13—214no—
64C2×C7×C11—91no—
65C11×D7—131no—
66C11×D7—1171no—
67C11×C13D7×C3⋊D311yescharacteristic, complemented, Hall
68C2×D3×C11—2734no—
69C3⋊D21—131no—
70C7×C3⋊D3C11×D1311yescharacteristic, complemented
71C32×D7—131no—
72C32×C13C2×C11×D711yescharacteristic, complemented, Hall
73C32×C11C2×D9111yescharacteristic, complemented, Hall
74C7×C13C2×C11×C3⋊D311yescharacteristic, complemented, Hall
75D3×D7—394no—
76D39—214no—
77C3×D13—74no—
78D3×C13—34no—
79C7×C11C3⋊D3×D1311yescharacteristic, complemented, Hall
80C2×C3×C11—914no—
81D3×C11—34no—
82D3×C11—2734no—
83C32×C7C2×C11×D1311yescharacteristic, complemented, Hall
84C2×D13—631noHall
85C22×C11—8191noHall
86D21—394no—
87C3×D7—134no—
88D3×C7—34no—
89C3×C13D3×C11×D714yescomplemented
90C2×C3⋊D3—911noHall
91C3×C11D3×D9114yescomplemented
92C2×D7—1171noHall
93C2×C13—91no—
94D13—71no—
95D13—631no—
96C2×C11—91no—
97C2×C11—8191no—
98C2×C11—911no—
99C3×C7D3×C11×D1314yescomplemented
100C2×C32—911no—
101C3⋊D3—911no—
102C3⋊D3C11×D9111yescharacteristic, direct product factor
103C2×C7—91no—
104D7—131no—
105D7—1171no—
106C13C11×D7×C3⋊D311yescharacteristic, complemented, Sylow
107C2×D3—2734no—
108C11C3⋊D3×D9111yescharacteristic, direct product factor, Sylow
109C32C2×C11×D9111yescharacteristic, complemented, Sylow
110C7C11×C3⋊D3×D1311yescharacteristic, complemented, Sylow
111C2×C3—914no—
112D3—34no—
113D3—2734no—
114C22—8191noSylow
115C3D3×C11×D9114yescomplemented
116C2—91no—
117C2—8191no—
118C2—911no—
subgroupG/H
center, hypercenterC11C3⋊D3×D91
commutator, cosocle, hypocenterC32×C7×C13C22×C11
FrattiniC1G
Fitting, socleC32×C7×C11×C13C22
LCSG ▷ C32×C7×C13
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C32×C11×D91C2semidirect
2. C7×C11×C13×C3⋊D3C2semidirect
3. C11×C3⋊D273C2semidirect
5. C32×C7×C11×C13C22semidirect
8. C3×C11×D91D3semidirect
11. C3⋊D3×D91C11direct (N × H)
12. C3×C7×C11×C13C2×D3semidirect
15. C11×C13×C3⋊D3D7semidirect
18. C11×D91C3⋊D3direct (N × H)
21. C3⋊D273C2×C11semidirect
22. C7×C13×C3⋊D3C2×C11semidirect
23. C32×D91C2×C11semidirect
25. C7×C11×C3⋊D3D13semidirect
27. C32×C11×C13C2×D7semidirect
29. C7×C11×C13C2×C3⋊D3semidirect
34. C32×C7×C13C22×C11semidirect
35. C32×C7×C11C2×D13semidirect
39. C3×D91D3×C11semidirect
44. C3×C11×C13D3×D7semidirect
51. C3×C7×C13C2×D3×C11semidirect
54. C13×C3⋊D3C11×D7semidirect
56. C3×C7×C11D3×D13semidirect
59. C11×C3⋊D3D91direct (N × H)
62. D91C11×C3⋊D3direct (N × H)
67. C11×C13D7×C3⋊D3semidirect
70. C7×C3⋊D3C11×D13semidirect
72. C32×C13C2×C11×D7semidirect
73. C32×C11C2×D91semidirect
74. C7×C13C2×C11×C3⋊D3semidirect
79. C7×C11C3⋊D3×D13semidirect
83. C32×C7C2×C11×D13semidirect
89. C3×C13D3×C11×D7semidirect
91. C3×C11D3×D91semidirect
99. C3×C7D3×C11×D13semidirect
102. C3⋊D3C11×D91direct (N × H)
106. C13C11×D7×C3⋊D3semidirect
108. C11C3⋊D3×D91direct (N × H)
109. C32C2×C11×D91semidirect
110. C7C11×C3⋊D3×D13semidirect
115. C3D3×C11×D91semidirect

Maximal subgroups

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

subgroupindex
C32×C11×D912
C7×C11×C13×C3⋊D32
C11×C3⋊D2732
D3×C11×D913
C11×C3⋊D3×D137
C3⋊D3×D9111
C11×D7×C3⋊D313