Finite Group Databasebeta

← C11×D13×C3⋊D21 #49114977

Subgroups — C11×D13×C3⋊D21 #49114977

Order 36036.

240 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 80 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×C7×C11×D13C211yesmaximal, characteristic, complemented
2C11×C13×C3⋊D21C211yesmaximal, characteristic, complemented
3C11×C3⋊D273C211yesmaximal, characteristic, complemented
4C11×D13×D21—34nomaximal
5C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
6C11×D273—34no—
7C11×C13×D21—34no—
8C3×C7×C11×D13D314yescomplemented
9C11×C3⋊D3×D13—71nomaximal, Hall
10C11×D7×D13—91noHall
11D13×C3⋊D21C1111yesmaximal, characteristic, direct product factor, Hall
12C3×C7×C11×C13C2×D314yescomplemented
13C2×C11×C3⋊D21—131nomaximal, Hall
14C11×C3⋊D39—71no—
15C11×C13×C3⋊D3—71no—
16C32×C11×D13D711yescharacteristic, complemented
17C11×D91—91no—
18C11×C13×D7—91no—
19C7×C11×D13C3⋊D311yescharacteristic, complemented
20D3×C11×D13—214no—
21C3⋊D273C2×C1111yescharacteristic, complemented
22C13×C3⋊D21C2×C1111yescharacteristic, complemented
23C32×C7×D13C2×C1111yescharacteristic, complemented
24C2×C32×C7×C11—131no—
25C11×C3⋊D21—131no—
26C11×C3⋊D21D1311yescharacteristic, direct product factor
27C32×C11×C13C2×D711yescharacteristic, complemented, Hall
28D13×D21—34no—
29C7×C11×C13C2×C3⋊D311yescharacteristic, complemented, Hall
30C2×C11×D21—394no—
31C11×D39—214no—
32D3×C11×C13—214no—
33C3×C11×D13D2114yescomplemented
34C32×C7×C13C22×C1111yescharacteristic, complemented, Hall
35C32×C7×C11C2×D1311yescharacteristic, complemented, Hall
36C2×C11×D13—631noHall
37D273—34no—
38C13×D21—34no—
39C3×C7×D13D3×C1114yescomplemented
40C3⋊D3×D13—71noHall
41C2×C3×C7×C11—134no—
42C11×D21—34no—
43C11×D21—394no—
44C3×C11×C13C2×D2114yescomplemented
45C2×C11×C3⋊D3—911noHall
46D7×D13—91noHall
47C2×C11×D7—1171noHall
48C2×C11×C13—631no—
49C11×D13—631no—
50C11×D13C3⋊D2111yescharacteristic, direct product factor
51C3×C7×C13C2×D3×C1114yescomplemented
52C2×C3⋊D21—131noHall
53C3⋊D39—71no—
54C13×C3⋊D3—71no—
55C32×D13C11×D711yescharacteristic, complemented
56C3×C7×C11D3×D1314yescomplemented
57C2×C32×C11—131no—
58C11×C3⋊D3—71no—
59C11×C3⋊D3—911no—
60D91—91no—
61C7×D13C11×C3⋊D311yescharacteristic, complemented
62C13×D7—91no—
63D3×D13—214no—
64C2×C7×C11—131no—
65C11×D7—91no—
66C11×D7—1171no—
67C11×C13C2×C3⋊D2111yescharacteristic, complemented, Hall
68C2×D3×C11—2734no—
69C2×C32×C7—131no—
70C3⋊D21—131no—
71C3⋊D21C11×D1311yescharacteristic, direct product factor
72C32×C13C2×C11×D711yescharacteristic, complemented, Hall
73C32×C11D7×D1311yescharacteristic, complemented, Hall
74C7×C13C2×C11×C3⋊D311yescharacteristic, complemented, Hall
75C2×D21—394no—
76D39—214no—
77C3×D13C11×D2114yescomplemented
78D3×C13—214no—
79C7×C11C3⋊D3×D1311yescharacteristic, complemented, Hall
80C2×C3×C11—134no—
81D3×C11—2734no—
82D3×C11—214no—
83C32×C7C2×C11×D1311yescharacteristic, complemented, Hall
84C2×D13—631noHall
85C22×C11—8191noHall
86C2×C3×C7—134no—
87D21—34no—
88D21—394no—
89C3×C13C2×C11×D2114yescomplemented
90C2×C3⋊D3—911noHall
91C3×C11D13×D2114yescomplemented
92C2×D7—1171noHall
93C2×C13—631no—
94D13—631no—
95D13C11×C3⋊D2111yescharacteristic, direct product factor
96C2×C11—131no—
97C2×C11—8191no—
98C2×C11—631no—
99C3×C7D3×C11×D1314yescomplemented
100C2×C32—131no—
101C3⋊D3—71no—
102C3⋊D3—911no—
103C2×C7—131no—
104D7—91no—
105D7—1171no—
106C13C2×C11×C3⋊D2111yescharacteristic, complemented, Sylow
107C2×D3—2734no—
108C11D13×C3⋊D2111yescharacteristic, direct product factor, Sylow
109C32C11×D7×D1311yescharacteristic, complemented, Sylow
110C7C11×C3⋊D3×D1311yescharacteristic, complemented, Sylow
111C2×C3—134no—
112D3—2734no—
113D3—214no—
114C22—8191noSylow
115C3C11×D13×D2114yescomplemented
116C2—131no—
117C2—8191no—
118C2—631no—
subgroupG/H
center, hypercenterC11D13×C3⋊D21
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×C7×C11×D13C2semidirect
2. C11×C13×C3⋊D21C2semidirect
3. C11×C3⋊D273C2semidirect
5. C32×C7×C11×C13C22semidirect
8. C3×C7×C11×D13D3semidirect
11. D13×C3⋊D21C11direct (N × H)
12. C3×C7×C11×C13C2×D3semidirect
16. C32×C11×D13D7semidirect
19. C7×C11×D13C3⋊D3semidirect
21. C3⋊D273C2×C11semidirect
22. C13×C3⋊D21C2×C11semidirect
23. C32×C7×D13C2×C11semidirect
26. C11×C3⋊D21D13direct (N × H)
27. C32×C11×C13C2×D7semidirect
29. C7×C11×C13C2×C3⋊D3semidirect
33. C3×C11×D13D21semidirect
34. C32×C7×C13C22×C11semidirect
35. C32×C7×C11C2×D13semidirect
39. C3×C7×D13D3×C11semidirect
44. C3×C11×C13C2×D21semidirect
50. C11×D13C3⋊D21direct (N × H)
51. C3×C7×C13C2×D3×C11semidirect
55. C32×D13C11×D7semidirect
56. C3×C7×C11D3×D13semidirect
61. C7×D13C11×C3⋊D3semidirect
67. C11×C13C2×C3⋊D21semidirect
71. C3⋊D21C11×D13direct (N × H)
72. C32×C13C2×C11×D7semidirect
73. C32×C11D7×D13semidirect
74. C7×C13C2×C11×C3⋊D3semidirect
77. C3×D13C11×D21semidirect
79. C7×C11C3⋊D3×D13semidirect
83. C32×C7C2×C11×D13semidirect
89. C3×C13C2×C11×D21semidirect
91. C3×C11D13×D21semidirect
95. D13C11×C3⋊D21direct (N × H)
99. C3×C7D3×C11×D13semidirect
106. C13C2×C11×C3⋊D21semidirect
108. C11D13×C3⋊D21direct (N × H)
109. C32C11×D7×D13semidirect
110. C7C11×C3⋊D3×D13semidirect
115. C3C11×D13×D21semidirect

Maximal subgroups

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

subgroupindex
C32×C7×C11×D132
C11×C13×C3⋊D212
C11×C3⋊D2732
C11×D13×D213
C11×C3⋊D3×D137
D13×C3⋊D2111
C2×C11×C3⋊D2113