Finite Group Databasebeta

← D3×C72×D13⋊C3 #37525154

Subgroups — D3×C72×D13⋊C3 #37525154

Order 22932.

440 conjugacy classes of subgroups; only the 170 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 170 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
1D3×C72×C13⋊C3C211yesmaximal, characteristic, complemented
2C72×C3⋊(D13⋊C3)C211yesmaximal, characteristic, complemented
3C3×C72×D13⋊C3C211yesmaximal, characteristic, complemented
4D3×C72×D13C311yesmaximal, characteristic, complemented
5C2×C72×D13⋊C3—31nomaximal
6C3×C72×C13⋊C3C2211yescharacteristic, complemented, Hall
7C72×D39C2×C311yescharacteristic, complemented
8D3×C72×C13C2×C311yescharacteristic, complemented
9C3×C72×D13C2×C311yescharacteristic, complemented
10C2×C72×C13⋊C3—31no—
11C72×D13⋊C3—21no—
12C72×D13⋊C3—31no—
13C72×D13⋊C3D311yescharacteristic, direct product factor
14D3×C7×D13⋊C3C718yesmaximal, direct product factor
15C2×C72×D13—31noHall
16C3×C72×C13C22×C311yescharacteristic, complemented
17C72×C13⋊C3—21no—
18C72×C13⋊C3C2×D311yescharacteristic, complemented
19C2×C3×D3×C72—131nomaximal, Hall
20C7×C3⋊(D13⋊C3)C2×C718yescomplemented
21D3×C7×C13⋊C3C2×C718yescomplemented
22C3×C7×D13⋊C3C2×C718yescomplemented
23C2×C72×C13—31no—
24C72×D13—31no—
25C72×D13C3×D311yescharacteristic, complemented
26D3×C7×D13C3×C718yescomplemented
27C2×C7×D13⋊C3—38no—
28C2×C32×C72—131no—
29C3×D3×C72—131no—
30C3×D3×C72—131no—
31C3×C7×C13⋊C3C22×C718yescomplemented
32C72×C13C2×C3×D311yescharacteristic, complemented, Hall
33C22×C3×C72—391no—
34C2×D3×C72—131no—
35C7×D39C2×C3×C718yescomplemented
36D3×C7×C13C2×C3×C718yescomplemented
37C3×C7×D13C2×C3×C718yescomplemented
38C2×C7×C13⋊C3—38no—
39C7×D13⋊C3—28no—
40C7×D13⋊C3—38no—
41C7×D13⋊C3D3×C718yesdirect product factor
42D3×D13⋊C3C7211yescharacteristic, direct product factor, Hall
43C32×C72—131noHall
44C2×C7×D13—38no—
45C2×C3×C72—131no—
46C2×C3×C72—131no—
47C2×C3×C72—261no—
48C2×C3×C72—391no—
49C2×C3×C72—391no—
50D3×C72—131no—
51D3×C72D13⋊C311yescharacteristic, direct product factor
52C3×C7×C13C22×C3×C718yescomplemented
53C7×C13⋊C3—28no—
54C7×C13⋊C3C2×D3×C718yescomplemented
55C2×C3×D3×C7—138no—
56C3⋊(D13⋊C3)C2×C7211yescharacteristic, complemented
57D3×C13⋊C3C2×C7211yescharacteristic, complemented
58C3×D13⋊C3C2×C7211yescharacteristic, complemented
59C22×C72—391noHall
60C2×C7×C13—38no—
61C7×D13—38no—
62C7×D13C3×D3×C718yescomplemented
63D3×D13C3×C7211yescharacteristic, complemented
64C2×D13⋊C3—31no—
65C3×C72—131no—
66C3×C72—261no—
67C3×C72C2×D13⋊C311yescharacteristic, complemented
68C2×C32×C7—138no—
69C3×D3×C7—138no—
70C3×D3×C7—138no—
71C3×C13⋊C3C22×C7211yescharacteristic, complemented, Hall
72C2×C72—31no—
73C2×C72—131no—
74C2×C72—391no—
75C7×C13C2×C3×D3×C718yescomplemented
76C22×C3×C7—398no—
77C2×D3×C7—138no—
78D39C2×C3×C7211yescharacteristic, complemented
79C3×D13C2×C3×C7211yescharacteristic, complemented
80D3×C13C2×C3×C7211yescharacteristic, complemented
81C2×C13⋊C3—31no—
82D13⋊C3—21no—
83D13⋊C3—31no—
84D13⋊C3D3×C7211yescharacteristic, direct product factor
85C32×C7—138no—
86C2×D13—31noHall
87C72D3×D13⋊C311yescharacteristic, direct product factor, Sylow
88C2×C3×C7—138no—
89C2×C3×C7—138no—
90C2×C3×C7—268no—
91C2×C3×C7—398no—
92C2×C3×C7—398no—
93D3×C7—138no—
94D3×C7C7×D13⋊C318yesdirect product factor
95C3×C13C22×C3×C7211yescharacteristic, complemented
96C13⋊C3—21no—
97C13⋊C3C2×D3×C7211yescharacteristic, complemented
98C2×C3×D3—131noHall
99C22×C7—398no—
100C2×C13—31no—
101D13—31no—
102D13C3×D3×C7211yescharacteristic, complemented
103C3×C7—138no—
104C3×C7—268no—
105C3×C7C2×C7×D13⋊C318yescomplemented
106C2×C32—131no—
107C3×D3—131no—
108C3×D3—131no—
109C2×C7—38no—
110C2×C7—138no—
111C2×C7—398no—
112C13C2×C3×D3×C7211yescharacteristic, complemented, Sylow
113C22×C3—391no—
114C2×D3—131no—
115C32—131noSylow
116C7D3×C7×D13⋊C318yesdirect product factor
117C2×C3—131no—
118C2×C3—131no—
119C2×C3—261no—
120C2×C3—391no—
121C2×C3—391no—
122D3—131no—
123D3C72×D13⋊C311yescharacteristic, direct product factor
124C22—391noSylow
125C3—131no—
126C3—261no—
127C3C2×C72×D13⋊C311yescharacteristic, complemented
128C2—31no—
129C2—131no—
130C2—391no—
subgroupG/H
center, hypercenterC72D3×D13⋊C3
commutator, cosocle, hypocenterC3×C13C22×C3×C72
FrattiniC1G
Fitting, socleC3×C72×C13C22×C3
LCSG ▷ C3×C13
UCSC1 ◁ C72

Complements

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

NH ≅ G/Ntype
1. D3×C72×C13⋊C3C2semidirect
2. C72×C3⋊(D13⋊C3)C2semidirect
3. C3×C72×D13⋊C3C2semidirect
4. D3×C72×D13C3semidirect
6. C3×C72×C13⋊C3C22semidirect
7. C72×D39C2×C3semidirect
8. D3×C72×C13C2×C3semidirect
9. C3×C72×D13C2×C3semidirect
13. C72×D13⋊C3D3direct (N × H)
14. D3×C7×D13⋊C3C7direct (N × H)
16. C3×C72×C13C22×C3semidirect
18. C72×C13⋊C3C2×D3semidirect
20. C7×C3⋊(D13⋊C3)C2×C7semidirect
21. D3×C7×C13⋊C3C2×C7semidirect
22. C3×C7×D13⋊C3C2×C7semidirect
25. C72×D13C3×D3semidirect
26. D3×C7×D13C3×C7semidirect
31. C3×C7×C13⋊C3C22×C7semidirect
32. C72×C13C2×C3×D3semidirect
35. C7×D39C2×C3×C7semidirect
36. D3×C7×C13C2×C3×C7semidirect
37. C3×C7×D13C2×C3×C7semidirect
41. C7×D13⋊C3D3×C7direct (N × H)
42. D3×D13⋊C3C72direct (N × H)
51. D3×C72D13⋊C3direct (N × H)
52. C3×C7×C13C22×C3×C7semidirect
54. C7×C13⋊C3C2×D3×C7semidirect
56. C3⋊(D13⋊C3)C2×C72semidirect
57. D3×C13⋊C3C2×C72semidirect
58. C3×D13⋊C3C2×C72semidirect
62. C7×D13C3×D3×C7semidirect
63. D3×D13C3×C72semidirect
67. C3×C72C2×D13⋊C3semidirect
71. C3×C13⋊C3C22×C72semidirect
75. C7×C13C2×C3×D3×C7semidirect
78. D39C2×C3×C72semidirect
79. C3×D13C2×C3×C72semidirect
80. D3×C13C2×C3×C72semidirect
84. D13⋊C3D3×C72direct (N × H)
87. C72D3×D13⋊C3direct (N × H)
94. D3×C7C7×D13⋊C3direct (N × H)
95. C3×C13C22×C3×C72semidirect
97. C13⋊C3C2×D3×C72semidirect
102. D13C3×D3×C72semidirect
105. C3×C7C2×C7×D13⋊C3semidirect
112. C13C2×C3×D3×C72semidirect
116. C7D3×C7×D13⋊C3direct (N × H)
123. D3C72×D13⋊C3direct (N × H)
127. C3C2×C72×D13⋊C3semidirect

Maximal subgroups

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

subgroupindex
D3×C72×C13⋊C32
C72×C3⋊(D13⋊C3)2
C3×C72×D13⋊C32
D3×C72×D133
C2×C72×D13⋊C33
D3×C7×D13⋊C37
C2×C3×D3×C7213