Finite Group Databasebeta

← C13×D77⋊(C3⋊D3) #49114996

Subgroups — C13×D77⋊(C3⋊D3) #49114996

Order 36036.

240 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 70 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×C13×C3⋊D33C211yesmaximal, characteristic, complemented
3C11×C13×C3⋊D21C211yesmaximal, characteristic, complemented
4C13×D21⋊D11—34nomaximal
5C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
6C11×C13×D21—34no—
7C7×C13×D33—34no—
8C3×C13×D77D314yescomplemented
9C13×C3⋊D3×D11—71nomaximal, Hall
10C13×D7×D11—91noHall
11C13×D7×C3⋊D3—111nomaximal, Hall
12C3×C7×C11×C13C2×D314yescomplemented
13D77⋊(C3⋊D3)C1311yesmaximal, characteristic, direct product factor, Hall
14C13×C3⋊D33D711yescharacteristic, complemented
15C11×C13×C3⋊D3—71no—
16C32×C13×D11—71no—
17C13×D77C3⋊D311yescharacteristic, complemented
18C11×C13×D7—91no—
19C7×C13×D11—91no—
20D3×C13×D11—214no—
21C13×C3⋊D21D1111yescharacteristic, complemented
22C7×C13×C3⋊D3—111no—
23C32×C13×D7—111no—
24C11×C3⋊D21C2×C1311yescharacteristic, complemented
25C7×C3⋊D33C2×C1311yescharacteristic, complemented
26C32×D77C2×C1311yescharacteristic, complemented
27C32×C11×C13C2×D711yescharacteristic, complemented, Hall
28D3×C13×D7—334no—
29C7×C11×C13C2×C3⋊D311yescharacteristic, complemented, Hall
30D21⋊D11—34no—
31C13×D33—34no—
32D3×C11×C13—214no—
33C3×C13×D11—74no—
34C32×C7×C13C2×D1111yescharacteristic, complemented, Hall
35C32×C7×C11C22×C1311yescharacteristic, complemented, Hall
36C2×C13×D11—631noHall
37C13×D21—34no—
38D3×C7×C13—334no—
39C3×C13×D7—114no—
40C2×C13×C3⋊D3—771noHall
41C11×D21—34no—
42C7×D33—34no—
43C3×D77D3×C1314yescomplemented
44C3×C11×C13D3×D714yescomplemented
45C3⋊D3×D11—71noHall
46C2×C13×D7—991noHall
47D7×D11—91noHall
48C2×C11×C13—631no—
49C13×D11—71no—
50C13×D11—91no—
51C3×C7×C13D3×D1114yescomplemented
52D7×C3⋊D3—111noHall
53C2×C32×C13—771no—
54C13×C3⋊D3—71no—
55C13×C3⋊D3—111no—
56C3×C7×C11C2×D3×C1314yescomplemented
57C3⋊D33C13×D711yescharacteristic, complemented
58C11×C3⋊D3—71no—
59C32×D11—71no—
60C2×C7×C13—991no—
61C13×D7—91no—
62C13×D7—111no—
63C2×D3×C13—2314no—
64D77C13×C3⋊D311yescharacteristic, complemented
65C7×D11—91no—
66C11×D7—91no—
67C11×C13D7×C3⋊D311yescharacteristic, complemented, Hall
68D3×D11—214no—
69C3⋊D21C13×D1111yescharacteristic, complemented
70C7×C3⋊D3—111no—
71C32×D7—111no—
72C32×C13D7×D1111yescharacteristic, complemented, Hall
73C32×C11C2×C13×D711yescharacteristic, complemented, Hall
74C7×C13C3⋊D3×D1111yescharacteristic, complemented, Hall
75D3×D7—334no—
76C2×C3×C13—774no—
77D3×C13—214no—
78D3×C13—334no—
79C7×C11C2×C13×C3⋊D311yescharacteristic, complemented, Hall
80D33—34no—
81C3×D11—74no—
82D3×C11—214no—
83C32×C7C2×C13×D1111yescharacteristic, complemented, Hall
84C22×C13—6931noHall
85C2×D11—631noHall
86D21—34no—
87C3×D7—114no—
88D3×C7—334no—
89C3×C13D21⋊D1114yescomplemented
90C2×C3⋊D3—771noHall
91C3×C11D3×C13×D714yescomplemented
92C2×D7—991noHall
93C2×C13—631no—
94C2×C13—771no—
95C2×C13—991no—
96C2×C11—631no—
97D11—71no—
98D11—91no—
99C3×C7D3×C13×D1114yescomplemented
100C2×C32—771no—
101C3⋊D3—71no—
102C3⋊D3—111no—
103C2×C7—991no—
104D7—91no—
105D7—111no—
106C13D77⋊(C3⋊D3)11yescharacteristic, direct product factor, Sylow
107C2×D3—2314no—
108C11C13×D7×C3⋊D311yescharacteristic, complemented, Sylow
109C32C13×D7×D1111yescharacteristic, complemented, Sylow
110C7C13×C3⋊D3×D1111yescharacteristic, complemented, Sylow
111C2×C3—774no—
112D3—214no—
113D3—334no—
114C22—6931noSylow
115C3C13×D21⋊D1114yescomplemented
116C2—631no—
117C2—771no—
118C2—991no—
subgroupG/H
center, hypercenterC13D77⋊(C3⋊D3)
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×C13×C3⋊D33C2semidirect
3. C11×C13×C3⋊D21C2semidirect
5. C32×C7×C11×C13C22semidirect
8. C3×C13×D77D3semidirect
12. C3×C7×C11×C13C2×D3semidirect
13. D77⋊(C3⋊D3)C13direct (N × H)
14. C13×C3⋊D33D7semidirect
17. C13×D77C3⋊D3semidirect
21. C13×C3⋊D21D11semidirect
24. C11×C3⋊D21C2×C13semidirect
25. C7×C3⋊D33C2×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
56. C3×C7×C11C2×D3×C13semidirect
57. C3⋊D33C13×D7semidirect
64. D77C13×C3⋊D3semidirect
67. C11×C13D7×C3⋊D3semidirect
69. C3⋊D21C13×D11semidirect
72. C32×C13D7×D11semidirect
73. C32×C11C2×C13×D7semidirect
74. C7×C13C3⋊D3×D11semidirect
79. C7×C11C2×C13×C3⋊D3semidirect
83. C32×C7C2×C13×D11semidirect
89. C3×C13D21⋊D11semidirect
91. C3×C11D3×C13×D7semidirect
99. C3×C7D3×C13×D11semidirect
106. C13D77⋊(C3⋊D3)direct (N × H)
108. C11C13×D7×C3⋊D3semidirect
109. C32C13×D7×D11semidirect
110. C7C13×C3⋊D3×D11semidirect
115. C3C13×D21⋊D11semidirect

Maximal subgroups

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

subgroupindex
C32×C13×D772
C7×C13×C3⋊D332
C11×C13×C3⋊D212
C13×D21⋊D113
C13×C3⋊D3×D117
C13×D7×C3⋊D311
D77⋊(C3⋊D3)13