Finite Group Databasebeta

← D13×C3⋊D231 #49114979

Subgroups — D13×C3⋊D231 #49114979

Order 36036.

240 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 76 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×C11×D13C211yesmaximal, characteristic, complemented
2C13×C3⋊D231C211yesmaximal, characteristic, complemented
3C3⋊D3003C211yesmaximal, characteristic, complemented
4D13×D231—34nomaximal
5C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
6D3003—34no—
7C13×D231—34no—
8C3×C7×C11×D13D314yescomplemented
9D13×C3⋊D33—71nomaximal, Hall
10D13×D77—91noHall
11D13×C3⋊D21—111nomaximal, Hall
12C3×C7×C11×C13C2×D314yescomplemented
13C2×C3⋊D231—131nomaximal, Hall
14C3⋊D429—71no—
15C13×C3⋊D33—71no—
16C32×C11×D13D711yescharacteristic, complemented
17D1001—91no—
18C13×D77—91no—
19C7×C11×D13C3⋊D311yescharacteristic, complemented
20D13×D33—214no—
21C3⋊D273—111no—
22C13×C3⋊D21—111no—
23C32×C7×D13D1111yescharacteristic, complemented
24C2×C32×C7×C11—131no—
25C3⋊D231—131no—
26C3⋊D231D1311yescharacteristic, direct product factor
27C32×C11×C13C2×D711yescharacteristic, complemented, Hall
28D13×D21—334no—
29C7×C11×C13C2×C3⋊D311yescharacteristic, complemented, Hall
30C2×D231—394no—
31D429—214no—
32C13×D33—214no—
33C3×C11×D13D2114yescomplemented
34C32×C7×C13C2×D1111yescharacteristic, complemented, Hall
35C32×C7×C11C2×D1311yescharacteristic, complemented, Hall
36D11×D13—631noHall
37D273—334no—
38C13×D21—334no—
39C3×C7×D13D3314yescomplemented
40C3⋊D3×D13—771noHall
41C2×C3×C7×C11—134no—
42D231—34no—
43D231—394no—
44C3×C11×C13C2×D2114yescomplemented
45C2×C3⋊D33—911noHall
46D7×D13—991noHall
47C2×D77—1171noHall
48D143—631no—
49C11×D13C3⋊D2111yescharacteristic, complemented
50C13×D11—631no—
51C3×C7×C13C2×D3314yescomplemented
52C2×C3⋊D21—1431noHall
53C3⋊D39—771no—
54C13×C3⋊D3—771no—
55C32×D13D7711yescharacteristic, complemented
56C3×C7×C11D3×D1314yescomplemented
57C2×C32×C11—131no—
58C3⋊D33—71no—
59C3⋊D33—911no—
60D91—991no—
61C7×D13C3⋊D3311yescharacteristic, complemented
62C13×D7—991no—
63D3×D13—2314no—
64C2×C7×C11—131no—
65D77—91no—
66D77—1171no—
67C11×C13C2×C3⋊D2111yescharacteristic, complemented, Hall
68C2×D33—2734no—
69C2×C32×C7—131no—
70C3⋊D21—111no—
71C3⋊D21—1431no—
72C32×C13C2×D7711yescharacteristic, complemented, Hall
73C32×C11D7×D1311yescharacteristic, complemented, Hall
74C7×C13C2×C3⋊D3311yescharacteristic, complemented, Hall
75C2×D21—4294no—
76D39—2314no—
77C3×D13D23114yescomplemented
78D3×C13—2314no—
79C7×C11C3⋊D3×D1311yescharacteristic, complemented, Hall
80C2×C3×C11—134no—
81D33—2734no—
82D33—214no—
83C32×C7D11×D1311yescharacteristic, complemented, Hall
84C2×D13—6931noHall
85C2×D11—8191noHall
86C2×C3×C7—134no—
87D21—334no—
88D21—4294no—
89C3×C13C2×D23114yescomplemented
90C2×C3⋊D3—10011noHall
91C3×C11D13×D2114yescomplemented
92C2×D7—12871noHall
93C2×C13—6931no—
94D13—6931no—
95D13C3⋊D23111yescharacteristic, direct product factor
96C2×C11—131no—
97D11—8191no—
98D11—631no—
99C3×C7D13×D3314yescomplemented
100C2×C32—131no—
101C3⋊D3—771no—
102C3⋊D3—10011no—
103C2×C7—131no—
104D7—12871no—
105D7—991no—
106C13C2×C3⋊D23111yescharacteristic, complemented, Sylow
107C2×D3—30034no—
108C11D13×C3⋊D2111yescharacteristic, complemented, Sylow
109C32D13×D7711yescharacteristic, complemented, Sylow
110C7D13×C3⋊D3311yescharacteristic, complemented, Sylow
111C2×C3—134no—
112D3—30034no—
113D3—2314no—
114C22—90091noSylow
115C3D13×D23114yescomplemented
116C2—131no—
117C2—90091no—
118C2—6931no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C7×C11×C13C22
LCSG ▷ C32×C7×C11×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C32×C7×C11×D13C2semidirect
2. C13×C3⋊D231C2semidirect
3. C3⋊D3003C2semidirect
5. C32×C7×C11×C13C22semidirect
8. C3×C7×C11×D13D3semidirect
12. C3×C7×C11×C13C2×D3semidirect
16. C32×C11×D13D7semidirect
19. C7×C11×D13C3⋊D3semidirect
23. C32×C7×D13D11semidirect
26. C3⋊D231D13direct (N × H)
27. C32×C11×C13C2×D7semidirect
29. C7×C11×C13C2×C3⋊D3semidirect
33. C3×C11×D13D21semidirect
34. C32×C7×C13C2×D11semidirect
35. C32×C7×C11C2×D13semidirect
39. C3×C7×D13D33semidirect
44. C3×C11×C13C2×D21semidirect
49. C11×D13C3⋊D21semidirect
51. C3×C7×C13C2×D33semidirect
55. C32×D13D77semidirect
56. C3×C7×C11D3×D13semidirect
61. C7×D13C3⋊D33semidirect
67. C11×C13C2×C3⋊D21semidirect
72. C32×C13C2×D77semidirect
73. C32×C11D7×D13semidirect
74. C7×C13C2×C3⋊D33semidirect
77. C3×D13D231semidirect
79. C7×C11C3⋊D3×D13semidirect
83. C32×C7D11×D13semidirect
89. C3×C13C2×D231semidirect
91. C3×C11D13×D21semidirect
95. D13C3⋊D231direct (N × H)
99. C3×C7D13×D33semidirect
106. C13C2×C3⋊D231semidirect
108. C11D13×C3⋊D21semidirect
109. C32D13×D77semidirect
110. C7D13×C3⋊D33semidirect
115. C3D13×D231semidirect

Maximal subgroups

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

subgroupindex
C32×C7×C11×D132
C13×C3⋊D2312
C3⋊D30032
D13×D2313
D13×C3⋊D337
D13×C3⋊D2111
C2×C3⋊D23113