Finite Group Databasebeta

← C2×C3×C72×D39 #37525675

Subgroups — C2×C3×C72×D39 #37525675

Order 22932.

440 conjugacy classes of subgroups; only the 220 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 220 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
1C3×C72×D39C212yesmaximal, direct product factor
2C2×C32×C72×C13C211yesmaximal, characteristic, complemented
3C2×C3×C72×D13—31nomaximal
4C2×C72×D39C311yesmaximal, characteristic, direct product factor
5C32×C72×C13C2211yescharacteristic, complemented, Hall
6C72×D39C2×C312yesdirect product factor
7C3×C72×D13—32no—
8C2×C3×C72×C13—21no—
9C2×C3×C72×C13D311yescharacteristic, complemented
10C2×C3×C72×C13C2×C311yescharacteristic, complemented
11C2×C3×C7×D39C718yesmaximal, direct product factor
12C2×C72×D13—31noHall
13C3×C72×C13—21no—
14C3×C72×C13C2×D311yescharacteristic, complemented
15C3×C72×C13C22×C311yescharacteristic, complemented
16C2×C3×D3×C72—131nomaximal, Hall
17C2×C32×C7×C13C2×C718yescomplemented
18C3×C7×D39C2×C7116yesdirect product factor
19C2×C72×C13C3×D311yescharacteristic, complemented
20C72×D13—32no—
21C2×C7×D39C3×C718yesdirect product factor
22C2×C3×C7×D13—38no—
23C2×C32×C72D1311yescharacteristic, complemented
24C3×D3×C72—132no—
25C32×C7×C13C22×C718yescomplemented
26C72×C13C2×C3×D311yescharacteristic, complemented, Hall
27C22×C3×C72—391no—
28C2×D3×C72—131no—
29C2×C3×C7×C13—28no—
30C2×C3×C7×C13D3×C718yescomplemented
31C2×C3×C7×C13C2×C3×C718yescomplemented
32C7×D39C2×C3×C7116yesdirect product factor
33C3×C7×D13—316no—
34C2×C3×D39C7211yescharacteristic, direct product factor, Hall
35C32×C72C2×D1311yescharacteristic, complemented, Hall
36C2×C7×D13—38no—
37C2×C3×C72—21no—
38C2×C3×C72—392no—
39C2×C3×C72C3×D1311yescharacteristic, complemented
40C2×C3×C72D3911yescharacteristic, direct product factor
41D3×C72—132no—
42C3×C7×C13—28no—
43C3×C7×C13C2×D3×C718yescomplemented
44C3×C7×C13C22×C3×C718yescomplemented
45C2×C3×D3×C7—138no—
46C2×C32×C13C2×C7211yescharacteristic, complemented
47C3×D39C2×C7212yesdirect product factor
48C22×C72—391noHall
49C2×C7×C13C3×D3×C718yescomplemented
50C7×D13—316no—
51C2×D39C3×C7211yescharacteristic, direct product factor
52C2×C3×D13—31no—
53C3×C72—21no—
54C3×C72C2×C3×D1311yescharacteristic, complemented
55C3×C72C2×D3911yescharacteristic, direct product factor
56C2×C32×C7C7×D1318yescomplemented
57C3×D3×C7—1316no—
58C32×C13C22×C7211yescharacteristic, complemented, Hall
59C2×C72—392no—
60C2×C72C3×D3911yescharacteristic, direct product factor
61C7×C13C2×C3×D3×C718yescomplemented
62C22×C3×C7—398no—
63C2×D3×C7—138no—
64C2×C3×C13—21no—
65C2×C3×C13D3×C7211yescharacteristic, complemented
66C2×C3×C13C2×C3×C7211yescharacteristic, complemented
67D39C2×C3×C7212yesdirect product factor
68C3×D13—32no—
69C32×C7C2×C7×D1318yescomplemented
70C2×D13—31noHall
71C72C2×C3×D3911yescharacteristic, direct product factor, Sylow
72C2×C3×C7—28no—
73C2×C3×C7—3916no—
74C2×C3×C7C3×C7×D1318yescomplemented
75C2×C3×C7C7×D3918yesdirect product factor
76D3×C7—1316no—
77C3×C13—21no—
78C3×C13C2×D3×C7211yescharacteristic, complemented
79C3×C13C22×C3×C7211yescharacteristic, complemented
80C2×C3×D3—131noHall
81C22×C7—398no—
82C2×C13C3×D3×C7211yescharacteristic, complemented
83D13—32no—
84C3×C7—28no—
85C3×C7C2×C3×C7×D1318yescomplemented
86C3×C7C2×C7×D3918yesdirect product factor
87C2×C32C72×D1311yescharacteristic, complemented
88C3×D3—132no—
89C2×C7—3916no—
90C2×C7C3×C7×D3918yesdirect product factor
91C13C2×C3×D3×C7211yescharacteristic, complemented, Sylow
92C22×C3—391no—
93C2×D3—131no—
94C32C2×C72×D1311yescharacteristic, complemented, Sylow
95C7C2×C3×C7×D3918yesdirect product factor
96C2×C3—21no—
97C2×C3—392no—
98C2×C3C3×C72×D1311yescharacteristic, complemented
99C2×C3C72×D3911yescharacteristic, direct product factor
100D3—132no—
101C22—391noSylow
102C3—21no—
103C3C2×C72×D3911yescharacteristic, direct product factor
104C3C2×C3×C72×D1311yescharacteristic, complemented
105C2—392no—
106C2C3×C72×D3911yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C72D39
commutator, cosocle, hypocenterC3×C13C22×C3×C72
FrattiniC1G
Fitting, socleC2×C32×C72×C13C2
LCSG ▷ C3×C13
UCSC1 ◁ C2×C3×C72

Complements

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

NH ≅ G/Ntype
1. C3×C72×D39C2direct (N × H)
2. C2×C32×C72×C13C2semidirect
4. C2×C72×D39C3direct (N × H)
5. C32×C72×C13C22semidirect
6. C72×D39C2×C3direct (N × H)
9. C2×C3×C72×C13D3semidirect
10. C2×C3×C72×C13C2×C3semidirect
11. C2×C3×C7×D39C7direct (N × H)
14. C3×C72×C13C2×D3semidirect
15. C3×C72×C13C22×C3semidirect
17. C2×C32×C7×C13C2×C7semidirect
18. C3×C7×D39C2×C7direct (N × H)
19. C2×C72×C13C3×D3semidirect
21. C2×C7×D39C3×C7direct (N × H)
23. C2×C32×C72D13semidirect
25. C32×C7×C13C22×C7semidirect
26. C72×C13C2×C3×D3semidirect
30. C2×C3×C7×C13D3×C7semidirect
31. C2×C3×C7×C13C2×C3×C7semidirect
32. C7×D39C2×C3×C7direct (N × H)
34. C2×C3×D39C72direct (N × H)
35. C32×C72C2×D13semidirect
39. C2×C3×C72C3×D13semidirect
40. C2×C3×C72D39direct (N × H)
43. C3×C7×C13C2×D3×C7semidirect
44. C3×C7×C13C22×C3×C7semidirect
46. C2×C32×C13C2×C72semidirect
47. C3×D39C2×C72direct (N × H)
49. C2×C7×C13C3×D3×C7semidirect
51. C2×D39C3×C72direct (N × H)
54. C3×C72C2×C3×D13semidirect
55. C3×C72C2×D39direct (N × H)
56. C2×C32×C7C7×D13semidirect
58. C32×C13C22×C72semidirect
60. C2×C72C3×D39direct (N × H)
61. C7×C13C2×C3×D3×C7semidirect
65. C2×C3×C13D3×C72semidirect
66. C2×C3×C13C2×C3×C72semidirect
67. D39C2×C3×C72direct (N × H)
69. C32×C7C2×C7×D13semidirect
71. C72C2×C3×D39direct (N × H)
74. C2×C3×C7C3×C7×D13semidirect
75. C2×C3×C7C7×D39direct (N × H)
78. C3×C13C2×D3×C72semidirect
79. C3×C13C22×C3×C72semidirect
82. C2×C13C3×D3×C72semidirect
85. C3×C7C2×C3×C7×D13semidirect
86. C3×C7C2×C7×D39direct (N × H)
87. C2×C32C72×D13semidirect
90. C2×C7C3×C7×D39direct (N × H)
91. C13C2×C3×D3×C72semidirect
94. C32C2×C72×D13semidirect
95. C7C2×C3×C7×D39direct (N × H)
98. C2×C3C3×C72×D13semidirect
99. C2×C3C72×D39direct (N × H)
103. C3C2×C72×D39direct (N × H)
104. C3C2×C3×C72×D13semidirect
106. C2C3×C72×D39direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C72×D392
C2×C32×C72×C132
C2×C3×C72×D133
C2×C72×D393
C2×C3×C7×D397
C2×C3×D3×C7213