Finite Group Databasebeta

← C13×D7×C3⋊D33 #49114988

Subgroups — C13×D7×C3⋊D33 #49114988

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×C11×C13×D7C211yesmaximal, characteristic, complemented
2C7×C13×C3⋊D33C211yesmaximal, characteristic, complemented
3C13×C3⋊D231C211yesmaximal, characteristic, complemented
4C13×D7×D33—34nomaximal
5C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
6C13×D231—34no—
7C7×C13×D33—34no—
8C3×C11×C13×D7D314yescomplemented
9C2×C13×C3⋊D33—71nomaximal, Hall
10C13×D7×D11—91noHall
11C13×D7×C3⋊D3—111nomaximal, Hall
12C3×C7×C11×C13C2×D314yescomplemented
13D7×C3⋊D33C1311yesmaximal, characteristic, direct product factor, Hall
14C13×C3⋊D33—71no—
15C13×C3⋊D33D711yescharacteristic, direct product factor
16C2×C32×C11×C13—71no—
17C13×D77—91no—
18C11×C13×D7C3⋊D311yescharacteristic, complemented
19C7×C13×D11—91no—
20C2×C13×D33—214no—
21C13×C3⋊D21—111no—
22C7×C13×C3⋊D3—111no—
23C32×C13×D7D1111yescharacteristic, complemented
24C3⋊D231C2×C1311yescharacteristic, complemented
25C7×C3⋊D33C2×C1311yescharacteristic, complemented
26C32×C11×D7C2×C1311yescharacteristic, complemented
27C32×C11×C13C2×D711yescharacteristic, complemented, Hall
28D3×C13×D7—334no—
29C7×C11×C13C2×C3⋊D311yescharacteristic, complemented, Hall
30D7×D33—34no—
31C2×C3×C11×C13—74no—
32C13×D33—34no—
33C13×D33—214no—
34C32×C7×C13C2×D1111yescharacteristic, complemented, Hall
35C32×C7×C11C22×C1311yescharacteristic, complemented, Hall
36C2×C13×D11—631noHall
37C13×D21—334no—
38D3×C7×C13—334no—
39C3×C13×D7D3314yescomplemented
40C2×C13×C3⋊D3—771noHall
41D231—34no—
42C7×D33—34no—
43C3×C11×D7D3×C1314yescomplemented
44C3×C11×C13D3×D714yescomplemented
45C2×C3⋊D33—71noHall
46C2×C13×D7—991noHall
47D7×D11—91noHall
48C2×C11×C13—71no—
49C13×D11—91no—
50C13×D11—631no—
51C3×C7×C13C2×D3314yescomplemented
52D7×C3⋊D3—111noHall
53C2×C32×C13—71no—
54C13×C3⋊D3—111no—
55C13×C3⋊D3—771no—
56C3×C7×C11C2×D3×C1314yescomplemented
57C2×C32×C11—71no—
58C3⋊D33—71no—
59C3⋊D33C13×D711yescharacteristic, direct product factor
60C2×C7×C13—991no—
61C13×D7—991no—
62C13×D7C3⋊D3311yescharacteristic, direct product factor
63C2×D3×C13—2314no—
64D77—91no—
65C7×D11—91no—
66C11×D7C13×C3⋊D311yescharacteristic, complemented
67C11×C13D7×C3⋊D311yescharacteristic, complemented, Hall
68C2×D33—214no—
69C3⋊D21—111no—
70C7×C3⋊D3—111no—
71C32×D7C13×D1111yescharacteristic, complemented
72C32×C13D7×D1111yescharacteristic, complemented, Hall
73C32×C11C2×C13×D711yescharacteristic, complemented, Hall
74C7×C13C2×C3⋊D3311yescharacteristic, complemented, Hall
75D3×D7—334no—
76C2×C3×C13—74no—
77D3×C13—334no—
78D3×C13—2314no—
79C7×C11C2×C13×C3⋊D311yescharacteristic, complemented, Hall
80C2×C3×C11—74no—
81D33—34no—
82D33—214no—
83C32×C7C2×C13×D1111yescharacteristic, complemented, Hall
84C22×C13—6931noHall
85C2×D11—631noHall
86D21—334no—
87C3×D7C13×D3314yescomplemented
88D3×C7—334no—
89C3×C13D7×D3314yescomplemented
90C2×C3⋊D3—771noHall
91C3×C11D3×C13×D714yescomplemented
92C2×D7—991noHall
93C2×C13—71no—
94C2×C13—991no—
95C2×C13—6931no—
96C2×C11—71no—
97D11—91no—
98D11—631no—
99C3×C7C2×C13×D3314yescomplemented
100C2×C32—71no—
101C3⋊D3—111no—
102C3⋊D3—771no—
103C2×C7—991no—
104D7—991no—
105D7C13×C3⋊D3311yescharacteristic, direct product factor
106C13D7×C3⋊D3311yescharacteristic, direct product factor, Sylow
107C2×D3—2314no—
108C11C13×D7×C3⋊D311yescharacteristic, complemented, Sylow
109C32C13×D7×D1111yescharacteristic, complemented, Sylow
110C7C2×C13×C3⋊D3311yescharacteristic, complemented, Sylow
111C2×C3—74no—
112D3—334no—
113D3—2314no—
114C22—6931noSylow
115C3C13×D7×D3314yescomplemented
116C2—71no—
117C2—991no—
118C2—6931no—
subgroupG/H
center, hypercenterC13D7×C3⋊D33
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×C11×C13×D7C2semidirect
2. C7×C13×C3⋊D33C2semidirect
3. C13×C3⋊D231C2semidirect
5. C32×C7×C11×C13C22semidirect
8. C3×C11×C13×D7D3semidirect
12. C3×C7×C11×C13C2×D3semidirect
13. D7×C3⋊D33C13direct (N × H)
15. C13×C3⋊D33D7direct (N × H)
18. C11×C13×D7C3⋊D3semidirect
23. C32×C13×D7D11semidirect
24. C3⋊D231C2×C13semidirect
25. C7×C3⋊D33C2×C13semidirect
26. C32×C11×D7C2×C13semidirect
27. C32×C11×C13C2×D7semidirect
29. C7×C11×C13C2×C3⋊D3semidirect
34. C32×C7×C13C2×D11semidirect
35. C32×C7×C11C22×C13semidirect
39. C3×C13×D7D33semidirect
43. C3×C11×D7D3×C13semidirect
44. C3×C11×C13D3×D7semidirect
51. C3×C7×C13C2×D33semidirect
56. C3×C7×C11C2×D3×C13semidirect
59. C3⋊D33C13×D7direct (N × H)
62. C13×D7C3⋊D33direct (N × H)
66. C11×D7C13×C3⋊D3semidirect
67. C11×C13D7×C3⋊D3semidirect
71. C32×D7C13×D11semidirect
72. C32×C13D7×D11semidirect
73. C32×C11C2×C13×D7semidirect
74. C7×C13C2×C3⋊D33semidirect
79. C7×C11C2×C13×C3⋊D3semidirect
83. C32×C7C2×C13×D11semidirect
87. C3×D7C13×D33semidirect
89. C3×C13D7×D33semidirect
91. C3×C11D3×C13×D7semidirect
99. C3×C7C2×C13×D33semidirect
105. D7C13×C3⋊D33direct (N × H)
106. C13D7×C3⋊D33direct (N × H)
108. C11C13×D7×C3⋊D3semidirect
109. C32C13×D7×D11semidirect
110. C7C2×C13×C3⋊D33semidirect
115. C3C13×D7×D33semidirect

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×C13×C3⋊D332
C13×C3⋊D2312
C13×D7×D333
C2×C13×C3⋊D337
C13×D7×C3⋊D311
D7×C3⋊D3313