Finite Group Databasebeta

← C11×D91⋊(C3⋊D3) #49114987

Subgroups — C11×D91⋊(C3⋊D3) #49114987

Order 36036.

240 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 70 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×C3⋊D39C211yesmaximal, characteristic, complemented
3C11×C13×C3⋊D21C211yesmaximal, characteristic, complemented
4C11×D21⋊D13—34nomaximal
5C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
6C11×C13×D21—34no—
7C7×C11×D39—34no—
8C3×C11×D91D314yescomplemented
9C11×C3⋊D3×D13—71nomaximal, Hall
10C11×D7×D13—91noHall
11D91⋊(C3⋊D3)C1111yesmaximal, characteristic, direct product factor, Hall
12C3×C7×C11×C13C2×D314yescomplemented
13C11×D7×C3⋊D3—131nomaximal, Hall
14C11×C3⋊D39D711yescharacteristic, complemented
15C11×C13×C3⋊D3—71no—
16C32×C11×D13—71no—
17C11×D91C3⋊D311yescharacteristic, complemented
18C11×C13×D7—91no—
19C7×C11×D13—91no—
20D3×C11×D13—214no—
21C13×C3⋊D21C2×C1111yescharacteristic, complemented
22C7×C3⋊D39C2×C1111yescharacteristic, complemented
23C32×D91C2×C1111yescharacteristic, complemented
24C11×C3⋊D21D1311yescharacteristic, complemented
25C7×C11×C3⋊D3—131no—
26C32×C11×D7—131no—
27C32×C11×C13C2×D711yescharacteristic, complemented, Hall
28D21⋊D13—34no—
29C7×C11×C13C2×C3⋊D311yescharacteristic, complemented, Hall
30D3×C11×D7—394no—
31C11×D39—34no—
32D3×C11×C13—214no—
33C3×C11×D13—74no—
34C32×C7×C13C22×C1111yescharacteristic, complemented, Hall
35C32×C7×C11C2×D1311yescharacteristic, complemented, Hall
36C2×C11×D13—631noHall
37C13×D21—34no—
38C7×D39—34no—
39C3×D91D3×C1114yescomplemented
40C3⋊D3×D13—71noHall
41C11×D21—34no—
42D3×C7×C11—394no—
43C3×C11×D7—134no—
44C3×C11×C13D3×D714yescomplemented
45C2×C11×C3⋊D3—911noHall
46D7×D13—91noHall
47C2×C11×D7—1171noHall
48C2×C11×C13—631no—
49C11×D13—71no—
50C11×D13—91no—
51C3×C7×C13C2×D3×C1114yescomplemented
52D7×C3⋊D3—131noHall
53C3⋊D39C11×D711yescharacteristic, complemented
54C13×C3⋊D3—71no—
55C32×D13—71no—
56C3×C7×C11D3×D1314yescomplemented
57C2×C32×C11—911no—
58C11×C3⋊D3—71no—
59C11×C3⋊D3—131no—
60D91C11×C3⋊D311yescharacteristic, complemented
61C7×D13—91no—
62C13×D7—91no—
63D3×D13—214no—
64C2×C7×C11—1171no—
65C11×D7—91no—
66C11×D7—131no—
67C11×C13D7×C3⋊D311yescharacteristic, complemented, Hall
68C2×D3×C11—2734no—
69C3⋊D21C11×D1311yescharacteristic, complemented
70C7×C3⋊D3—131no—
71C32×D7—131no—
72C32×C13C2×C11×D711yescharacteristic, complemented, Hall
73C32×C11D7×D1311yescharacteristic, complemented, Hall
74C7×C13C2×C11×C3⋊D311yescharacteristic, complemented, Hall
75D3×D7—394no—
76D39—34no—
77C3×D13—74no—
78D3×C13—214no—
79C7×C11C3⋊D3×D1311yescharacteristic, complemented, Hall
80C2×C3×C11—914no—
81D3×C11—214no—
82D3×C11—394no—
83C32×C7C2×C11×D1311yescharacteristic, complemented, Hall
84C2×D13—631noHall
85C22×C11—8191noHall
86D21—34no—
87C3×D7—134no—
88D3×C7—394no—
89C3×C13D3×C11×D714yescomplemented
90C2×C3⋊D3—911noHall
91C3×C11D21⋊D1314yescomplemented
92C2×D7—1171noHall
93C2×C13—631no—
94D13—71no—
95D13—91no—
96C2×C11—631no—
97C2×C11—911no—
98C2×C11—1171no—
99C3×C7D3×C11×D1314yescomplemented
100C2×C32—911no—
101C3⋊D3—71no—
102C3⋊D3—131no—
103C2×C7—1171no—
104D7—91no—
105D7—131no—
106C13C11×D7×C3⋊D311yescharacteristic, complemented, Sylow
107C2×D3—2734no—
108C11D91⋊(C3⋊D3)11yescharacteristic, direct product factor, Sylow
109C32C11×D7×D1311yescharacteristic, complemented, Sylow
110C7C11×C3⋊D3×D1311yescharacteristic, complemented, Sylow
111C2×C3—914no—
112D3—214no—
113D3—394no—
114C22—8191noSylow
115C3C11×D21⋊D1314yescomplemented
116C2—631no—
117C2—911no—
118C2—1171no—
subgroupG/H
center, hypercenterC11D91⋊(C3⋊D3)
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×C3⋊D39C2semidirect
3. C11×C13×C3⋊D21C2semidirect
5. C32×C7×C11×C13C22semidirect
8. C3×C11×D91D3semidirect
11. D91⋊(C3⋊D3)C11direct (N × H)
12. C3×C7×C11×C13C2×D3semidirect
14. C11×C3⋊D39D7semidirect
17. C11×D91C3⋊D3semidirect
21. C13×C3⋊D21C2×C11semidirect
22. C7×C3⋊D39C2×C11semidirect
23. C32×D91C2×C11semidirect
24. C11×C3⋊D21D13semidirect
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
53. C3⋊D39C11×D7semidirect
56. C3×C7×C11D3×D13semidirect
60. D91C11×C3⋊D3semidirect
67. C11×C13D7×C3⋊D3semidirect
69. C3⋊D21C11×D13semidirect
72. C32×C13C2×C11×D7semidirect
73. C32×C11D7×D13semidirect
74. C7×C13C2×C11×C3⋊D3semidirect
79. C7×C11C3⋊D3×D13semidirect
83. C32×C7C2×C11×D13semidirect
89. C3×C13D3×C11×D7semidirect
91. C3×C11D21⋊D13semidirect
99. C3×C7D3×C11×D13semidirect
106. C13C11×D7×C3⋊D3semidirect
108. C11D91⋊(C3⋊D3)direct (N × H)
109. C32C11×D7×D13semidirect
110. C7C11×C3⋊D3×D13semidirect
115. C3C11×D21⋊D13semidirect

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×C3⋊D392
C11×C13×C3⋊D212
C11×D21⋊D133
C11×C3⋊D3×D137
D91⋊(C3⋊D3)11
C11×D7×C3⋊D313