Finite Group Databasebeta

← C11×C13×D7×C3⋊D3 #49114984

Subgroups — C11×C13×D7×C3⋊D3 #49114984

Order 36036.

240 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 88 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×C13×D7C211yesmaximal, characteristic, complemented
2C7×C11×C13×C3⋊D3C211yesmaximal, characteristic, complemented
3C11×C13×C3⋊D21C211yesmaximal, characteristic, complemented
4D3×C11×C13×D7—34nomaximal
5C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
6C11×C13×D21—34no—
7D3×C7×C11×C13—34no—
8C3×C11×C13×D7D314yescomplemented
9C2×C11×C13×C3⋊D3—71nomaximal, Hall
10C2×C11×C13×D7—91noHall
11C13×D7×C3⋊D3C1111yesmaximal, characteristic, direct product factor, Hall
12C3×C7×C11×C13C2×D314yescomplemented
13C11×D7×C3⋊D3C1311yesmaximal, characteristic, direct product factor, Hall
14C11×C13×C3⋊D3—71no—
15C11×C13×C3⋊D3D711yescharacteristic, direct product factor
16C2×C32×C11×C13—71no—
17C11×C13×D7—91no—
18C11×C13×D7C3⋊D311yescharacteristic, direct product factor
19C2×C7×C11×C13—91no—
20C2×D3×C11×C13—214no—
21C13×C3⋊D21C2×C1111yescharacteristic, complemented
22C7×C13×C3⋊D3C2×C1111yescharacteristic, complemented
23C32×C13×D7C2×C1111yescharacteristic, complemented
24C11×C3⋊D21C2×C1311yescharacteristic, complemented
25C7×C11×C3⋊D3C2×C1311yescharacteristic, complemented
26C32×C11×D7C2×C1311yescharacteristic, complemented
27C32×C11×C13C2×D711yescharacteristic, complemented, Hall
28D3×C13×D7—34no—
29C7×C11×C13C2×C3⋊D311yescharacteristic, complemented, Hall
30D3×C11×D7—34no—
31C2×C3×C11×C13—74no—
32D3×C11×C13—34no—
33D3×C11×C13—214no—
34C32×C7×C13C22×C1111yescharacteristic, complemented, Hall
35C32×C7×C11C22×C1311yescharacteristic, complemented, Hall
36C22×C11×C13—631noHall
37C13×D21—34no—
38D3×C7×C13—34no—
39C3×C13×D7D3×C1114yescomplemented
40C2×C13×C3⋊D3—71noHall
41C11×D21—34no—
42D3×C7×C11—34no—
43C3×C11×D7D3×C1314yescomplemented
44C3×C11×C13D3×D714yescomplemented
45C2×C11×C3⋊D3—71noHall
46C2×C13×D7—91noHall
47C2×C11×D7—91noHall
48C2×C11×C13—71no—
49C2×C11×C13—91no—
50C2×C11×C13—631no—
51C3×C7×C13C2×D3×C1114yescomplemented
52D7×C3⋊D3C11×C1311yescharacteristic, direct product factor, Hall
53C2×C32×C13—71no—
54C13×C3⋊D3—71no—
55C13×C3⋊D3C11×D711yescharacteristic, direct product factor
56C3×C7×C11C2×D3×C1314yescomplemented
57C2×C32×C11—71no—
58C11×C3⋊D3—71no—
59C11×C3⋊D3C13×D711yescharacteristic, direct product factor
60C2×C7×C13—91no—
61C13×D7—91no—
62C13×D7C11×C3⋊D311yescharacteristic, direct product factor
63C2×D3×C13—214no—
64C2×C7×C11—91no—
65C11×D7—91no—
66C11×D7C13×C3⋊D311yescharacteristic, direct product factor
67C11×C13D7×C3⋊D311yescharacteristic, direct product factor, Hall
68C2×D3×C11—214no—
69C3⋊D21C2×C11×C1311yescharacteristic, complemented
70C7×C3⋊D3C2×C11×C1311yescharacteristic, complemented
71C32×D7C2×C11×C1311yescharacteristic, complemented
72C32×C13C2×C11×D711yescharacteristic, complemented, Hall
73C32×C11C2×C13×D711yescharacteristic, complemented, Hall
74C7×C13C2×C11×C3⋊D311yescharacteristic, complemented, Hall
75D3×D7—34no—
76C2×C3×C13—74no—
77D3×C13—34no—
78D3×C13—214no—
79C7×C11C2×C13×C3⋊D311yescharacteristic, complemented, Hall
80C2×C3×C11—74no—
81D3×C11—34no—
82D3×C11—214no—
83C32×C7C22×C11×C1311yescharacteristic, complemented, Hall
84C22×C13—631noHall
85C22×C11—631noHall
86D21—34no—
87C3×D7D3×C11×C1314yescomplemented
88D3×C7—34no—
89C3×C13D3×C11×D714yescomplemented
90C2×C3⋊D3—71noHall
91C3×C11D3×C13×D714yescomplemented
92C2×D7—91noHall
93C2×C13—71no—
94C2×C13—91no—
95C2×C13—631no—
96C2×C11—71no—
97C2×C11—91no—
98C2×C11—631no—
99C3×C7C2×D3×C11×C1314yescomplemented
100C2×C32—71no—
101C3⋊D3—71no—
102C3⋊D3C11×C13×D711yescharacteristic, direct product factor
103C2×C7—91no—
104D7—91no—
105D7C11×C13×C3⋊D311yescharacteristic, direct product factor
106C13C11×D7×C3⋊D311yescharacteristic, direct product factor, Sylow
107C2×D3—214no—
108C11C13×D7×C3⋊D311yescharacteristic, direct product factor, Sylow
109C32C2×C11×C13×D711yescharacteristic, complemented, Sylow
110C7C2×C11×C13×C3⋊D311yescharacteristic, complemented, Sylow
111C2×C3—74no—
112D3—34no—
113D3—214no—
114C22—631noSylow
115C3D3×C11×C13×D714yescomplemented
116C2—71no—
117C2—91no—
118C2—631no—
subgroupG/H
center, hypercenterC11×C13D7×C3⋊D3
commutator, cosocle, hypocenterC32×C7C22×C11×C13
FrattiniC1G
Fitting, socleC32×C7×C11×C13C22
LCSG ▷ C32×C7
UCSC1 ◁ C11×C13

Complements

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

NH ≅ G/Ntype
1. C32×C11×C13×D7C2semidirect
2. C7×C11×C13×C3⋊D3C2semidirect
3. C11×C13×C3⋊D21C2semidirect
5. C32×C7×C11×C13C22semidirect
8. C3×C11×C13×D7D3semidirect
11. C13×D7×C3⋊D3C11direct (N × H)
12. C3×C7×C11×C13C2×D3semidirect
13. C11×D7×C3⋊D3C13direct (N × H)
15. C11×C13×C3⋊D3D7direct (N × H)
18. C11×C13×D7C3⋊D3direct (N × H)
21. C13×C3⋊D21C2×C11semidirect
22. C7×C13×C3⋊D3C2×C11semidirect
23. C32×C13×D7C2×C11semidirect
24. C11×C3⋊D21C2×C13semidirect
25. C7×C11×C3⋊D3C2×C13semidirect
26. C32×C11×D7C2×C13semidirect
27. C32×C11×C13C2×D7semidirect
29. C7×C11×C13C2×C3⋊D3semidirect
34. C32×C7×C13C22×C11semidirect
35. C32×C7×C11C22×C13semidirect
39. C3×C13×D7D3×C11semidirect
43. C3×C11×D7D3×C13semidirect
44. C3×C11×C13D3×D7semidirect
51. C3×C7×C13C2×D3×C11semidirect
52. D7×C3⋊D3C11×C13direct (N × H)
55. C13×C3⋊D3C11×D7direct (N × H)
56. C3×C7×C11C2×D3×C13semidirect
59. C11×C3⋊D3C13×D7direct (N × H)
62. C13×D7C11×C3⋊D3direct (N × H)
66. C11×D7C13×C3⋊D3direct (N × H)
67. C11×C13D7×C3⋊D3direct (N × H)
69. C3⋊D21C2×C11×C13semidirect
70. C7×C3⋊D3C2×C11×C13semidirect
71. C32×D7C2×C11×C13semidirect
72. C32×C13C2×C11×D7semidirect
73. C32×C11C2×C13×D7semidirect
74. C7×C13C2×C11×C3⋊D3semidirect
79. C7×C11C2×C13×C3⋊D3semidirect
83. C32×C7C22×C11×C13semidirect
87. C3×D7D3×C11×C13semidirect
89. C3×C13D3×C11×D7semidirect
91. C3×C11D3×C13×D7semidirect
99. C3×C7C2×D3×C11×C13semidirect
102. C3⋊D3C11×C13×D7direct (N × H)
105. D7C11×C13×C3⋊D3direct (N × H)
106. C13C11×D7×C3⋊D3direct (N × H)
108. C11C13×D7×C3⋊D3direct (N × H)
109. C32C2×C11×C13×D7semidirect
110. C7C2×C11×C13×C3⋊D3semidirect
115. C3D3×C11×C13×D7semidirect

Maximal subgroups

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

subgroupindex
C32×C11×C13×D72
C7×C11×C13×C3⋊D32
C11×C13×C3⋊D212
D3×C11×C13×D73
C2×C11×C13×C3⋊D37
C13×D7×C3⋊D311
C11×D7×C3⋊D313