Finite Group Databasebeta

← D11×C3⋊D273 #49114981

Subgroups — D11×C3⋊D273 #49114981

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×C13×D11C211yesmaximal, characteristic, complemented
2C11×C3⋊D273C211yesmaximal, characteristic, complemented
3C3⋊D3003C211yesmaximal, characteristic, complemented
4D11×D273—34nomaximal
5C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
6D3003—34no—
7C11×D273—34no—
8C3×C7×C13×D11D314yescomplemented
9D11×C3⋊D39—71nomaximal, Hall
10D11×D91—91noHall
11C2×C3⋊D273—111nomaximal, Hall
12C3×C7×C11×C13C2×D314yescomplemented
13D11×C3⋊D21—131nomaximal, Hall
14C3⋊D429—71no—
15C11×C3⋊D39—71no—
16C32×C13×D11D711yescharacteristic, complemented
17D1001—91no—
18C11×D91—91no—
19C7×C13×D11C3⋊D311yescharacteristic, complemented
20D11×D39—214no—
21C2×C32×C7×C13—111no—
22C3⋊D273—111no—
23C3⋊D273D1111yescharacteristic, direct product factor
24C3⋊D231—131no—
25C11×C3⋊D21—131no—
26C32×C7×D11D1311yescharacteristic, complemented
27C32×C11×C13C2×D711yescharacteristic, complemented, Hall
28C2×D273—334no—
29C7×C11×C13C2×C3⋊D311yescharacteristic, complemented, Hall
30D11×D21—394no—
31D429—214no—
32C11×D39—214no—
33C3×C13×D11D2114yescomplemented
34C32×C7×C13C2×D1111yescharacteristic, complemented, Hall
35C32×C7×C11C2×D1311yescharacteristic, complemented, Hall
36D11×D13—631noHall
37C2×C3×C7×C13—114no—
38D273—34no—
39D273—334no—
40C2×C3⋊D39—771noHall
41D231—394no—
42C11×D21—394no—
43C3×C7×D11D3914yescomplemented
44C3×C11×C13C2×D2114yescomplemented
45C3⋊D3×D11—911noHall
46C2×D91—991noHall
47D7×D11—1171noHall
48D143—631no—
49C11×D13—631no—
50C13×D11C3⋊D2111yescharacteristic, complemented
51C3×C7×C13D3×D1114yescomplemented
52C2×C3⋊D21—1431noHall
53C2×C32×C13—111no—
54C3⋊D39—71no—
55C3⋊D39—771no—
56C3×C7×C11C2×D3914yescomplemented
57C3⋊D33—911no—
58C11×C3⋊D3—911no—
59C32×D11D9111yescharacteristic, complemented
60C2×C7×C13—111no—
61D91—91no—
62D91—991no—
63C2×D39—2314no—
64D77—1171no—
65C7×D11C3⋊D3911yescharacteristic, complemented
66C11×D7—1171no—
67C11×C13C2×C3⋊D2111yescharacteristic, complemented, Hall
68D3×D11—2734no—
69C2×C32×C7—111no—
70C3⋊D21—131no—
71C3⋊D21—1431no—
72C32×C13D7×D1111yescharacteristic, complemented, Hall
73C32×C11C2×D9111yescharacteristic, complemented, Hall
74C7×C13C3⋊D3×D1111yescharacteristic, complemented, Hall
75C2×D21—4294no—
76C2×C3×C13—114no—
77D39—214no—
78D39—2314no—
79C7×C11C2×C3⋊D3911yescharacteristic, complemented, Hall
80D33—2734no—
81C3×D11D27314yescomplemented
82D3×C11—2734no—
83C32×C7D11×D1311yescharacteristic, complemented, Hall
84C2×D13—6931noHall
85C2×D11—8191noHall
86C2×C3×C7—114no—
87D21—394no—
88D21—4294no—
89C3×C13D11×D2114yescomplemented
90C2×C3⋊D3—10011noHall
91C3×C11C2×D27314yescomplemented
92C2×D7—12871noHall
93C2×C13—111no—
94D13—631no—
95D13—6931no—
96C2×C11—8191no—
97D11—8191no—
98D11C3⋊D27311yescharacteristic, direct product factor
99C3×C7D11×D3914yescomplemented
100C2×C32—111no—
101C3⋊D3—911no—
102C3⋊D3—10011no—
103C2×C7—111no—
104D7—12871no—
105D7—1171no—
106C13D11×C3⋊D2111yescharacteristic, complemented, Sylow
107C2×D3—30034no—
108C11C2×C3⋊D27311yescharacteristic, complemented, Sylow
109C32D11×D9111yescharacteristic, complemented, Sylow
110C7D11×C3⋊D3911yescharacteristic, complemented, Sylow
111C2×C3—114no—
112D3—2734no—
113D3—30034no—
114C22—90091noSylow
115C3D11×D27314yescomplemented
116C2—111no—
117C2—90091no—
118C2—8191no—
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×C13×D11C2semidirect
2. C11×C3⋊D273C2semidirect
3. C3⋊D3003C2semidirect
5. C32×C7×C11×C13C22semidirect
8. C3×C7×C13×D11D3semidirect
12. C3×C7×C11×C13C2×D3semidirect
16. C32×C13×D11D7semidirect
19. C7×C13×D11C3⋊D3semidirect
23. C3⋊D273D11direct (N × H)
26. C32×C7×D11D13semidirect
27. C32×C11×C13C2×D7semidirect
29. C7×C11×C13C2×C3⋊D3semidirect
33. C3×C13×D11D21semidirect
34. C32×C7×C13C2×D11semidirect
35. C32×C7×C11C2×D13semidirect
43. C3×C7×D11D39semidirect
44. C3×C11×C13C2×D21semidirect
50. C13×D11C3⋊D21semidirect
51. C3×C7×C13D3×D11semidirect
56. C3×C7×C11C2×D39semidirect
59. C32×D11D91semidirect
65. C7×D11C3⋊D39semidirect
67. C11×C13C2×C3⋊D21semidirect
72. C32×C13D7×D11semidirect
73. C32×C11C2×D91semidirect
74. C7×C13C3⋊D3×D11semidirect
79. C7×C11C2×C3⋊D39semidirect
81. C3×D11D273semidirect
83. C32×C7D11×D13semidirect
89. C3×C13D11×D21semidirect
91. C3×C11C2×D273semidirect
98. D11C3⋊D273direct (N × H)
99. C3×C7D11×D39semidirect
106. C13D11×C3⋊D21semidirect
108. C11C2×C3⋊D273semidirect
109. C32D11×D91semidirect
110. C7D11×C3⋊D39semidirect
115. C3D11×D273semidirect

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×C3⋊D2732
C3⋊D30032
D11×D2733
D11×C3⋊D397
C2×C3⋊D27311
D11×C3⋊D2113