Finite Group Databasebeta

← C13×D11×C3⋊D21 #49114980

Subgroups — C13×D11×C3⋊D21 #49114980

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×C7×C13×D11C211yesmaximal, characteristic, complemented
2C11×C13×C3⋊D21C211yesmaximal, characteristic, complemented
3C13×C3⋊D231C211yesmaximal, characteristic, complemented
4C13×D11×D21—34nomaximal
5C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
6C13×D231—34no—
7C11×C13×D21—34no—
8C3×C7×C13×D11D314yescomplemented
9C13×C3⋊D3×D11—71nomaximal, Hall
10C13×D7×D11—91noHall
11C2×C13×C3⋊D21—111nomaximal, Hall
12C3×C7×C11×C13C2×D314yescomplemented
13D11×C3⋊D21C1311yesmaximal, characteristic, direct product factor, Hall
14C13×C3⋊D33—71no—
15C11×C13×C3⋊D3—71no—
16C32×C13×D11D711yescharacteristic, complemented
17C13×D77—91no—
18C11×C13×D7—91no—
19C7×C13×D11C3⋊D311yescharacteristic, complemented
20D3×C13×D11—214no—
21C2×C32×C7×C13—111no—
22C13×C3⋊D21—111no—
23C13×C3⋊D21D1111yescharacteristic, direct product factor
24C3⋊D231C2×C1311yescharacteristic, complemented
25C11×C3⋊D21C2×C1311yescharacteristic, complemented
26C32×C7×D11C2×C1311yescharacteristic, complemented
27C32×C11×C13C2×D711yescharacteristic, complemented, Hall
28C2×C13×D21—334no—
29C7×C11×C13C2×C3⋊D311yescharacteristic, complemented, Hall
30D11×D21—34no—
31C13×D33—214no—
32D3×C11×C13—214no—
33C3×C13×D11D2114yescomplemented
34C32×C7×C13C2×D1111yescharacteristic, complemented, Hall
35C32×C7×C11C22×C1311yescharacteristic, complemented, Hall
36C2×C13×D11—631noHall
37C2×C3×C7×C13—114no—
38C13×D21—34no—
39C13×D21—334no—
40C2×C13×C3⋊D3—771noHall
41D231—34no—
42C11×D21—34no—
43C3×C7×D11D3×C1314yescomplemented
44C3×C11×C13C2×D2114yescomplemented
45C3⋊D3×D11—71noHall
46C2×C13×D7—991noHall
47D7×D11—91noHall
48C2×C11×C13—631no—
49C13×D11—631no—
50C13×D11C3⋊D2111yescharacteristic, direct product factor
51C3×C7×C13D3×D1114yescomplemented
52C2×C3⋊D21—111noHall
53C2×C32×C13—111no—
54C13×C3⋊D3—71no—
55C13×C3⋊D3—771no—
56C3×C7×C11C2×D3×C1314yescomplemented
57C3⋊D33—71no—
58C11×C3⋊D3—71no—
59C32×D11C13×D711yescharacteristic, complemented
60C2×C7×C13—111no—
61C13×D7—91no—
62C13×D7—991no—
63C2×D3×C13—2314no—
64D77—91no—
65C7×D11C13×C3⋊D311yescharacteristic, complemented
66C11×D7—91no—
67C11×C13C2×C3⋊D2111yescharacteristic, complemented, Hall
68D3×D11—214no—
69C2×C32×C7—111no—
70C3⋊D21—111no—
71C3⋊D21C13×D1111yescharacteristic, direct product factor
72C32×C13D7×D1111yescharacteristic, complemented, Hall
73C32×C11C2×C13×D711yescharacteristic, complemented, Hall
74C7×C13C3⋊D3×D1111yescharacteristic, complemented, Hall
75C2×D21—334no—
76C2×C3×C13—114no—
77D3×C13—214no—
78D3×C13—2314no—
79C7×C11C2×C13×C3⋊D311yescharacteristic, complemented, Hall
80D33—214no—
81C3×D11C13×D2114yescomplemented
82D3×C11—214no—
83C32×C7C2×C13×D1111yescharacteristic, complemented, Hall
84C22×C13—6931noHall
85C2×D11—631noHall
86C2×C3×C7—114no—
87D21—34no—
88D21—334no—
89C3×C13D11×D2114yescomplemented
90C2×C3⋊D3—771noHall
91C3×C11C2×C13×D2114yescomplemented
92C2×D7—991noHall
93C2×C13—111no—
94C2×C13—631no—
95C2×C13—6931no—
96C2×C11—631no—
97D11—631no—
98D11C13×C3⋊D2111yescharacteristic, direct product factor
99C3×C7D3×C13×D1114yescomplemented
100C2×C32—111no—
101C3⋊D3—71no—
102C3⋊D3—771no—
103C2×C7—111no—
104D7—91no—
105D7—991no—
106C13D11×C3⋊D2111yescharacteristic, direct product factor, Sylow
107C2×D3—2314no—
108C11C2×C13×C3⋊D2111yescharacteristic, complemented, Sylow
109C32C13×D7×D1111yescharacteristic, complemented, Sylow
110C7C13×C3⋊D3×D1111yescharacteristic, complemented, Sylow
111C2×C3—114no—
112D3—214no—
113D3—2314no—
114C22—6931noSylow
115C3C13×D11×D2114yescomplemented
116C2—111no—
117C2—631no—
118C2—6931no—
subgroupG/H
center, hypercenterC13D11×C3⋊D21
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×C7×C13×D11C2semidirect
2. C11×C13×C3⋊D21C2semidirect
3. C13×C3⋊D231C2semidirect
5. C32×C7×C11×C13C22semidirect
8. C3×C7×C13×D11D3semidirect
12. C3×C7×C11×C13C2×D3semidirect
13. D11×C3⋊D21C13direct (N × H)
16. C32×C13×D11D7semidirect
19. C7×C13×D11C3⋊D3semidirect
23. C13×C3⋊D21D11direct (N × H)
24. C3⋊D231C2×C13semidirect
25. C11×C3⋊D21C2×C13semidirect
26. C32×C7×D11C2×C13semidirect
27. C32×C11×C13C2×D7semidirect
29. C7×C11×C13C2×C3⋊D3semidirect
33. C3×C13×D11D21semidirect
34. C32×C7×C13C2×D11semidirect
35. C32×C7×C11C22×C13semidirect
43. C3×C7×D11D3×C13semidirect
44. C3×C11×C13C2×D21semidirect
50. C13×D11C3⋊D21direct (N × H)
51. C3×C7×C13D3×D11semidirect
56. C3×C7×C11C2×D3×C13semidirect
59. C32×D11C13×D7semidirect
65. C7×D11C13×C3⋊D3semidirect
67. C11×C13C2×C3⋊D21semidirect
71. C3⋊D21C13×D11direct (N × H)
72. C32×C13D7×D11semidirect
73. C32×C11C2×C13×D7semidirect
74. C7×C13C3⋊D3×D11semidirect
79. C7×C11C2×C13×C3⋊D3semidirect
81. C3×D11C13×D21semidirect
83. C32×C7C2×C13×D11semidirect
89. C3×C13D11×D21semidirect
91. C3×C11C2×C13×D21semidirect
98. D11C13×C3⋊D21direct (N × H)
99. C3×C7D3×C13×D11semidirect
106. C13D11×C3⋊D21direct (N × H)
108. C11C2×C13×C3⋊D21semidirect
109. C32C13×D7×D11semidirect
110. C7C13×C3⋊D3×D11semidirect
115. C3C13×D11×D21semidirect

Maximal subgroups

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

subgroupindex
C32×C7×C13×D112
C11×C13×C3⋊D212
C13×C3⋊D2312
C13×D11×D213
C13×C3⋊D3×D117
C2×C13×C3⋊D2111
D11×C3⋊D2113