Finite Group Databasebeta

← C2×C3×C11×(C13⋊C3)⋊D7 #49114841

Subgroups — C2×C3×C11×(C13⋊C3)⋊D7 #49114841

Order 36036.

240 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 100 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
1C2×C3×C7×C11×C13⋊C3C211yesmaximal, characteristic, complemented
2C3×C11×(C13⋊C3)⋊D7C212yesmaximal, direct product factor
3C2×C3×C11×D91C311yesmaximal, characteristic, complemented
4C2×C11×(C13⋊C3)⋊D7C313yesmaximal, direct product factor
5C3×C7×C11×C13⋊C3C2211yescharacteristic, complemented, Hall
6C11×(C13⋊C3)⋊D7C2×C316yesdirect product factor
7C3×C11×D91C2×C312yescomplemented
8C2×C7×C11×C13⋊C3C2×C313yescomplemented
9C2×C3×C7×C11×C13C2×C311yescharacteristic, complemented
10C2×C3×C11×D13⋊C3—71nomaximal, Hall
11C2×C11×D91C3211yescharacteristic, complemented, Hall
12C2×C3×(C13⋊C3)⋊D7C1111yesmaximal, characteristic, direct product factor, Hall
13C7×C11×C13⋊C3C22×C313yescomplemented
14C3×C7×C11×C13C22×C311yescharacteristic, complemented
15C2×C32×C11×D7—131nomaximal, Hall
16C2×C3×C11×C13⋊C3D711yescharacteristic, complemented
17C3×C11×D13⋊C3—72no—
18C11×D91C2×C3212yescomplemented
19C2×C7×C11×C13C2×C3211yescharacteristic, complemented
20C2×C3×C11×D13—71no—
21C2×C11×D13⋊C3—73no—
22C2×C3×C7×C13⋊C3C2×C1111yescharacteristic, complemented
23C3×(C13⋊C3)⋊D7C2×C1112yesdirect product factor
24C2×C32×C7×C11—131no—
25C32×C11×D7—132no—
26C3×C11×C13⋊C3C2×D711yescharacteristic, complemented, Hall
27C2×C3×D91C3×C1111yescharacteristic, complemented
28C2×(C13⋊C3)⋊D7C3×C1113yesdirect product factor
29C7×C11×C13C22×C3211yescharacteristic, complemented, Hall
30C2×C3×C11×D7—133no—
31C2×C3×C11×D7—131no—
32C2×C3×C11×C13C3×D711yescharacteristic, complemented
33C3×C11×D13—72no—
34C2×C11×C13⋊C3C3×D713yescomplemented
35C11×D13⋊C3—76no—
36C3×C7×C13⋊C3C22×C1111yescharacteristic, complemented, Hall
37C32×C7×C11—131noHall
38C2×C11×D13—71noHall
39C2×C3×C7×C13C2×C3×C1111yescharacteristic, complemented
40C3×D91C2×C3×C1112yescomplemented
41C2×C7×C13⋊C3C2×C3×C1113yescomplemented
42(C13⋊C3)⋊D7C2×C3×C1116yesdirect product factor
43C2×C3×D13⋊C3—71noHall
44C2×C3×C7×C11—133no—
45C2×C3×C7×C11D13⋊C311yescharacteristic, complemented
46C3×C11×D7—136no—
47C3×C11×D7—132no—
48C3×C11×C13C2×C3×D711yescharacteristic, complemented
49C11×C13⋊C3C2×C3×D713yescomplemented
50C22×C32×C11—911noHall
51C2×D91C32×C1111yescharacteristic, complemented, Hall
52C2×C11×D7—131noHall
53C2×C11×C13C32×D711yescharacteristic, complemented
54C11×D13—72no—
55C3×C7×C13C22×C3×C1111yescharacteristic, complemented
56C7×C13⋊C3C22×C3×C1113yescomplemented
57C2×C32×D7—131noHall
58C2×C3×C13⋊C3C11×D711yescharacteristic, complemented
59C3×D13⋊C3—72no—
60C3×C7×C11—133no—
61C3×C7×C11C2×D13⋊C311yescharacteristic, complemented
62C2×C32×C11—131no—
63C2×C32×C11—912no—
64C2×C7×C13C2×C32×C1111yescharacteristic, complemented
65D91C2×C32×C1112yescomplemented
66C2×C3×D13—71no—
67C2×D13⋊C3—73no—
68C2×C7×C11C3×D13⋊C311yescharacteristic, complemented
69C11×D7—132no—
70C11×C13C2×C32×D711yescharacteristic, complemented, Hall
71C22×C3×C11—913no—
72C22×C3×C11—911no—
73C2×C32×C7—131no—
74C32×D7—132no—
75C3×C13⋊C3C2×C11×D711yescharacteristic, complemented, Hall
76C32×C11—131noHall
77C7×C13C22×C32×C1111yescharacteristic, complemented, Hall
78C2×C3×D7—133no—
79C2×C3×D7—131no—
80C2×C3×C13C3×C11×D711yescharacteristic, complemented
81C3×D13—72no—
82C2×C13⋊C3C3×C11×D713yescomplemented
83D13⋊C3—76no—
84C7×C11C2×C3×D13⋊C311yescharacteristic, complemented, Hall
85C2×C3×C11—133no—
86C2×C3×C11—916no—
87C2×C3×C11—912no—
88C2×C3×C11(C13⋊C3)⋊D711yescharacteristic, direct product factor
89C32×C7—131noHall
90C2×D13—71noHall
91C22×C11—911noHall
92C2×C3×C7—133no—
93C2×C3×C7C11×D13⋊C311yescharacteristic, complemented
94C3×D7—136no—
95C3×D7—132no—
96C3×C13C2×C3×C11×D711yescharacteristic, complemented
97C13⋊C3C2×C3×C11×D713yescomplemented
98C22×C32—911noHall
99C3×C11—133no—
100C3×C11C2×(C13⋊C3)⋊D711yescharacteristic, direct product factor
101C2×D7—131noHall
102C2×C13C32×C11×D711yescharacteristic, complemented
103D13—72no—
104C2×C11—912no—
105C2×C11C3×(C13⋊C3)⋊D711yescharacteristic, direct product factor
106C3×C7—133no—
107C3×C7C2×C11×D13⋊C311yescharacteristic, complemented
108C2×C32—131no—
109C2×C32—912no—
110C2×C7C3×C11×D13⋊C311yescharacteristic, complemented
111D7—132no—
112C13C2×C32×C11×D711yescharacteristic, complemented, Sylow
113C22×C3—913no—
114C22×C3—911no—
115C11C2×C3×(C13⋊C3)⋊D711yescharacteristic, direct product factor, Sylow
116C32—131noSylow
117C7C2×C3×C11×D13⋊C311yescharacteristic, complemented, Sylow
118C2×C3—133no—
119C2×C3—916no—
120C2×C3—912no—
121C2×C3C11×(C13⋊C3)⋊D711yescharacteristic, direct product factor
122C22—911noSylow
123C3—133no—
124C3C2×C11×(C13⋊C3)⋊D711yescharacteristic, direct product factor
125C2—912no—
126C2C3×C11×(C13⋊C3)⋊D711yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C11(C13⋊C3)⋊D7
commutator, cosocle, hypocenterC7×C13C22×C32×C11
FrattiniC1G
Fitting, socleC2×C3×C7×C11×C13C2×C3
LCSG ▷ C7×C13
UCSC1 ◁ C2×C3×C11

Complements

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

NH ≅ G/Ntype
1. C2×C3×C7×C11×C13⋊C3C2semidirect
2. C3×C11×(C13⋊C3)⋊D7C2direct (N × H)
3. C2×C3×C11×D91C3semidirect
4. C2×C11×(C13⋊C3)⋊D7C3direct (N × H)
5. C3×C7×C11×C13⋊C3C22semidirect
6. C11×(C13⋊C3)⋊D7C2×C3direct (N × H)
7. C3×C11×D91C2×C3semidirect
8. C2×C7×C11×C13⋊C3C2×C3semidirect
9. C2×C3×C7×C11×C13C2×C3semidirect
11. C2×C11×D91C32semidirect
12. C2×C3×(C13⋊C3)⋊D7C11direct (N × H)
13. C7×C11×C13⋊C3C22×C3semidirect
14. C3×C7×C11×C13C22×C3semidirect
16. C2×C3×C11×C13⋊C3D7semidirect
18. C11×D91C2×C32semidirect
19. C2×C7×C11×C13C2×C32semidirect
22. C2×C3×C7×C13⋊C3C2×C11semidirect
23. C3×(C13⋊C3)⋊D7C2×C11direct (N × H)
26. C3×C11×C13⋊C3C2×D7semidirect
27. C2×C3×D91C3×C11semidirect
28. C2×(C13⋊C3)⋊D7C3×C11direct (N × H)
29. C7×C11×C13C22×C32semidirect
32. C2×C3×C11×C13C3×D7semidirect
34. C2×C11×C13⋊C3C3×D7semidirect
36. C3×C7×C13⋊C3C22×C11semidirect
39. C2×C3×C7×C13C2×C3×C11semidirect
40. C3×D91C2×C3×C11semidirect
41. C2×C7×C13⋊C3C2×C3×C11semidirect
42. (C13⋊C3)⋊D7C2×C3×C11direct (N × H)
45. C2×C3×C7×C11D13⋊C3semidirect
48. C3×C11×C13C2×C3×D7semidirect
49. C11×C13⋊C3C2×C3×D7semidirect
51. C2×D91C32×C11semidirect
53. C2×C11×C13C32×D7semidirect
55. C3×C7×C13C22×C3×C11semidirect
56. C7×C13⋊C3C22×C3×C11semidirect
58. C2×C3×C13⋊C3C11×D7semidirect
61. C3×C7×C11C2×D13⋊C3semidirect
64. C2×C7×C13C2×C32×C11semidirect
65. D91C2×C32×C11semidirect
68. C2×C7×C11C3×D13⋊C3semidirect
70. C11×C13C2×C32×D7semidirect
75. C3×C13⋊C3C2×C11×D7semidirect
77. C7×C13C22×C32×C11semidirect
80. C2×C3×C13C3×C11×D7semidirect
82. C2×C13⋊C3C3×C11×D7semidirect
84. C7×C11C2×C3×D13⋊C3semidirect
88. C2×C3×C11(C13⋊C3)⋊D7direct (N × H)
93. C2×C3×C7C11×D13⋊C3semidirect
96. C3×C13C2×C3×C11×D7semidirect
97. C13⋊C3C2×C3×C11×D7semidirect
100. C3×C11C2×(C13⋊C3)⋊D7direct (N × H)
102. C2×C13C32×C11×D7semidirect
105. C2×C11C3×(C13⋊C3)⋊D7direct (N × H)
107. C3×C7C2×C11×D13⋊C3semidirect
110. C2×C7C3×C11×D13⋊C3semidirect
112. C13C2×C32×C11×D7semidirect
115. C11C2×C3×(C13⋊C3)⋊D7direct (N × H)
117. C7C2×C3×C11×D13⋊C3semidirect
121. C2×C3C11×(C13⋊C3)⋊D7direct (N × H)
124. C3C2×C11×(C13⋊C3)⋊D7direct (N × H)
126. C2C3×C11×(C13⋊C3)⋊D7direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C7×C11×C13⋊C32
C3×C11×(C13⋊C3)⋊D72
C2×C3×C11×D913
C2×C11×(C13⋊C3)⋊D73
C2×C3×C11×D13⋊C37
C2×C3×(C13⋊C3)⋊D711
C2×C32×C11×D713