Finite Group Databasebeta

← C13×C3⋊D3×D77 #49114992

Subgroups — C13×C3⋊D3×D77 #49114992

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×C13×D77C211yesmaximal, characteristic, complemented
2C7×C11×C13×C3⋊D3C211yesmaximal, characteristic, complemented
3C13×C3⋊D231C211yesmaximal, characteristic, complemented
4D3×C13×D77—34nomaximal
5C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
6C13×D231—34no—
7D3×C7×C11×C13—34no—
8C3×C13×D77D314yescomplemented
9C13×C3⋊D3×D11—71nomaximal, Hall
10C2×C13×D77—91noHall
11C13×D7×C3⋊D3—111nomaximal, Hall
12C3×C7×C11×C13C2×D314yescomplemented
13C3⋊D3×D77C1311yesmaximal, characteristic, direct product factor, Hall
14C13×C3⋊D33—71no—
15C11×C13×C3⋊D3D711yescharacteristic, complemented
16C32×C13×D11—71no—
17C13×D77—91no—
18C13×D77C3⋊D311yescharacteristic, direct product factor
19C2×C7×C11×C13—91no—
20D3×C13×D11—214no—
21C13×C3⋊D21—111no—
22C7×C13×C3⋊D3D1111yescharacteristic, complemented
23C32×C13×D7—111no—
24C3⋊D231C2×C1311yescharacteristic, complemented
25C7×C11×C3⋊D3C2×C1311yescharacteristic, complemented
26C32×D77C2×C1311yescharacteristic, complemented
27C32×C11×C13C2×D711yescharacteristic, complemented, Hall
28D3×C13×D7—334no—
29C7×C11×C13C2×C3⋊D311yescharacteristic, complemented, Hall
30D3×D77—34no—
31C13×D33—214no—
32D3×C11×C13—34no—
33C3×C13×D11—74no—
34C32×C7×C13C2×D1111yescharacteristic, complemented, Hall
35C32×C7×C11C22×C1311yescharacteristic, complemented, Hall
36C2×C13×D11—631noHall
37C13×D21—334no—
38D3×C7×C13—34no—
39C3×C13×D7—114no—
40C2×C13×C3⋊D3—771noHall
41D231—34no—
42D3×C7×C11—34no—
43C3×D77D3×C1314yescomplemented
44C3×C11×C13D3×D714yescomplemented
45C3⋊D3×D11—71noHall
46C2×C13×D7—991noHall
47C2×D77—91noHall
48C2×C11×C13—91no—
49C13×D11—71no—
50C13×D11—631no—
51C3×C7×C13D3×D1114yescomplemented
52D7×C3⋊D3—111noHall
53C2×C32×C13—771no—
54C13×C3⋊D3—771no—
55C13×C3⋊D3D7711yescharacteristic, direct product factor
56C3×C7×C11C2×D3×C1314yescomplemented
57C3⋊D33—71no—
58C11×C3⋊D3C13×D711yescharacteristic, complemented
59C32×D11—71no—
60C2×C7×C13—91no—
61C13×D7—111no—
62C13×D7—991no—
63C2×D3×C13—2314no—
64C2×C7×C11—91no—
65D77—91no—
66D77C13×C3⋊D311yescharacteristic, direct product factor
67C11×C13D7×C3⋊D311yescharacteristic, complemented, Hall
68D3×D11—214no—
69C3⋊D21—111no—
70C7×C3⋊D3C13×D1111yescharacteristic, complemented
71C32×D7—111no—
72C32×C13C2×D7711yescharacteristic, complemented, Hall
73C32×C11C2×C13×D711yescharacteristic, complemented, Hall
74C7×C13C3⋊D3×D1111yescharacteristic, complemented, Hall
75D3×D7—334no—
76C2×C3×C13—774no—
77D3×C13—34no—
78D3×C13—2314no—
79C7×C11C2×C13×C3⋊D311yescharacteristic, complemented, Hall
80D33—214no—
81C3×D11—74no—
82D3×C11—34no—
83C32×C7C2×C13×D1111yescharacteristic, complemented, Hall
84C22×C13—6931noHall
85C2×D11—631noHall
86D21—334no—
87C3×D7—114no—
88D3×C7—34no—
89C3×C13D3×D7714yescomplemented
90C2×C3⋊D3—771noHall
91C3×C11D3×C13×D714yescomplemented
92C2×D7—991noHall
93C2×C13—91no—
94C2×C13—771no—
95C2×C13—6931no—
96C2×C11—91no—
97D11—71no—
98D11—631no—
99C3×C7D3×C13×D1114yescomplemented
100C2×C32—771no—
101C3⋊D3—771no—
102C3⋊D3C13×D7711yescharacteristic, direct product factor
103C2×C7—91no—
104D7—111no—
105D7—991no—
106C13C3⋊D3×D7711yescharacteristic, direct product factor, Sylow
107C2×D3—2314no—
108C11C13×D7×C3⋊D311yescharacteristic, complemented, Sylow
109C32C2×C13×D7711yescharacteristic, complemented, Sylow
110C7C13×C3⋊D3×D1111yescharacteristic, complemented, Sylow
111C2×C3—774no—
112D3—34no—
113D3—2314no—
114C22—6931noSylow
115C3D3×C13×D7714yescomplemented
116C2—91no—
117C2—771no—
118C2—6931no—
subgroupG/H
center, hypercenterC13C3⋊D3×D77
commutator, cosocle, hypocenterC32×C7×C11C22×C13
FrattiniC1G
Fitting, socleC32×C7×C11×C13C22
LCSG ▷ C32×C7×C11
UCSC1 ◁ C13

Complements

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

NH ≅ G/Ntype
1. C32×C13×D77C2semidirect
2. C7×C11×C13×C3⋊D3C2semidirect
3. C13×C3⋊D231C2semidirect
5. C32×C7×C11×C13C22semidirect
8. C3×C13×D77D3semidirect
12. C3×C7×C11×C13C2×D3semidirect
13. C3⋊D3×D77C13direct (N × H)
15. C11×C13×C3⋊D3D7semidirect
18. C13×D77C3⋊D3direct (N × H)
22. C7×C13×C3⋊D3D11semidirect
24. C3⋊D231C2×C13semidirect
25. C7×C11×C3⋊D3C2×C13semidirect
26. C32×D77C2×C13semidirect
27. C32×C11×C13C2×D7semidirect
29. C7×C11×C13C2×C3⋊D3semidirect
34. C32×C7×C13C2×D11semidirect
35. C32×C7×C11C22×C13semidirect
43. C3×D77D3×C13semidirect
44. C3×C11×C13D3×D7semidirect
51. C3×C7×C13D3×D11semidirect
55. C13×C3⋊D3D77direct (N × H)
56. C3×C7×C11C2×D3×C13semidirect
58. C11×C3⋊D3C13×D7semidirect
66. D77C13×C3⋊D3direct (N × H)
67. C11×C13D7×C3⋊D3semidirect
70. C7×C3⋊D3C13×D11semidirect
72. C32×C13C2×D77semidirect
73. C32×C11C2×C13×D7semidirect
74. C7×C13C3⋊D3×D11semidirect
79. C7×C11C2×C13×C3⋊D3semidirect
83. C32×C7C2×C13×D11semidirect
89. C3×C13D3×D77semidirect
91. C3×C11D3×C13×D7semidirect
99. C3×C7D3×C13×D11semidirect
102. C3⋊D3C13×D77direct (N × H)
106. C13C3⋊D3×D77direct (N × H)
108. C11C13×D7×C3⋊D3semidirect
109. C32C2×C13×D77semidirect
110. C7C13×C3⋊D3×D11semidirect
115. C3D3×C13×D77semidirect

Maximal subgroups

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

subgroupindex
C32×C13×D772
C7×C11×C13×C3⋊D32
C13×C3⋊D2312
D3×C13×D773
C13×C3⋊D3×D117
C13×D7×C3⋊D311
C3⋊D3×D7713