Finite Group Databasebeta

← C2×C3×C49×D39 #37524318

Subgroups — C2×C3×C49×D39 #37524318

Order 22932.

132 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 66 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×C49×D39C212yesmaximal, direct product factor
2C2×C32×C13×C49C211yesmaximal, characteristic, complemented
3C2×C49×D39C311yesmaximal, characteristic, direct product factor
4C2×C3×D13×C49—31nomaximal
5C32×C13×C49C2211yescharacteristic, complemented, Hall
6C49×D39C2×C312yesdirect product factor
7C3×D13×C49—32no—
8C2×C3×C13×C49—21no—
9C2×C3×C13×C49D311yescharacteristic, complemented
10C2×C3×C13×C49C2×C311yescharacteristic, complemented
11C2×C3×C7×D39C711yesmaximal, characteristic
12C2×D13×C49—31noHall
13C3×C13×C49—21no—
14C3×C13×C49C2×D311yescharacteristic, complemented
15C3×C13×C49C22×C311yescharacteristic, complemented
16C2×C3×D3×C49—131nomaximal, Hall
17C2×C32×C7×C13C2×C711yescharacteristic
18C3×C7×D39C2×C712yes—
19C2×C13×C49C3×D311yescharacteristic, complemented
20D13×C49—32no—
21C2×C7×D39C3×C711yescharacteristic
22C2×C3×C7×D13—31no—
23C2×C32×C49D1311yescharacteristic, complemented
24C3×D3×C49—132no—
25C32×C7×C13C22×C711yescharacteristic
26C13×C49C2×C3×D311yescharacteristic, complemented, Hall
27C22×C3×C49—391no—
28C2×D3×C49—131no—
29C2×C3×C7×C13—21no—
30C2×C3×C7×C13D3×C711yescharacteristic
31C2×C3×C7×C13C2×C3×C711yescharacteristic
32C7×D39C2×C3×C712yes—
33C3×C7×D13—32no—
34C2×C3×D39C4911yescharacteristic, direct product factor, Hall
35C32×C49C2×D1311yescharacteristic, complemented, Hall
36C2×C7×D13—31no—
37C2×C3×C49—21no—
38C2×C3×C49—392no—
39C2×C3×C49C3×D1311yescharacteristic, complemented
40C2×C3×C49D3911yescharacteristic, direct product factor
41D3×C49—132no—
42C3×C7×C13—21no—
43C3×C7×C13C2×D3×C711yescharacteristic
44C3×C7×C13C22×C3×C711yescharacteristic
45C2×C3×D3×C7—131no—
46C2×C32×C13C2×C4911yescharacteristic, complemented
47C3×D39C2×C4912yesdirect product factor
48C22×C49—391noHall
49C2×C7×C13C3×D3×C711yescharacteristic
50C7×D13—32no—
51C2×D39C3×C4911yescharacteristic, direct product factor
52C2×C3×D13—31no—
53C3×C49—21no—
54C3×C49C2×C3×D1311yescharacteristic, complemented
55C3×C49C2×D3911yescharacteristic, direct product factor
56C2×C32×C7C7×D1311yescharacteristic
57C3×D3×C7—132no—
58C32×C13C22×C4911yescharacteristic, complemented, Hall
59C2×C49—392no—
60C2×C49C3×D3911yescharacteristic, direct product factor
61C7×C13C2×C3×D3×C711yescharacteristic
62C22×C3×C7—391no—
63C2×D3×C7—131no—
64C2×C3×C13—21no—
65C2×C3×C13D3×C4911yescharacteristic, complemented
66C2×C3×C13C2×C3×C4911yescharacteristic, complemented
67D39C2×C3×C4912yesdirect product factor
68C3×D13—32no—
69C32×C7C2×C7×D1311yescharacteristic
70C2×D13—31noHall
71C49C2×C3×D3911yescharacteristic, direct product factor, Sylow
72C2×C3×C7—21no—
73C2×C3×C7—392no—
74C2×C3×C7C3×C7×D1311yescharacteristic
75C2×C3×C7C7×D3911yescharacteristic
76D3×C7—132no—
77C3×C13—21no—
78C3×C13C2×D3×C4911yescharacteristic, complemented
79C3×C13C22×C3×C4911yescharacteristic, complemented
80C2×C3×D3—131noHall
81C22×C7—391no—
82C2×C13C3×D3×C4911yescharacteristic, complemented
83D13—32no—
84C3×C7—21no—
85C3×C7C2×C3×C7×D1311yescharacteristic
86C3×C7C2×C7×D3911yescharacteristic
87C2×C32D13×C4911yescharacteristic, complemented
88C3×D3—132no—
89C2×C7—392no—
90C2×C7C3×C7×D3911yescharacteristic
91C13C2×C3×D3×C4911yescharacteristic, complemented, Sylow
92C22×C3—391no—
93C2×D3—131no—
94C32C2×D13×C4911yescharacteristic, complemented, Sylow
95C7C2×C3×C7×D3911yescharacteristic
96C2×C3—21no—
97C2×C3—392no—
98C2×C3C3×D13×C4911yescharacteristic, complemented
99C2×C3C49×D3911yescharacteristic, direct product factor
100D3—132no—
101C22—391noSylow
102C3—21no—
103C3C2×C3×D13×C4911yescharacteristic, complemented
104C3C2×C49×D3911yescharacteristic, direct product factor
105C2—392no—
106C2C3×C49×D3911yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C49D39
commutator, hypocenterC3×C13C22×C3×C49
FrattiniC7C2×C3×C7×D39
FittingC2×C32×C13×C49C2
socleC2×C32×C7×C13C2×C7
prime radicalC2×C3×C7×D39C7
cosocleC3×C7×C13C22×C3×C7
LCSG ▷ C3×C13
UCSC1 ◁ C2×C3×C49

Complements

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

NH ≅ G/Ntype
1. C3×C49×D39C2direct (N × H)
2. C2×C32×C13×C49C2semidirect
3. C2×C49×D39C3direct (N × H)
5. C32×C13×C49C22semidirect
6. C49×D39C2×C3direct (N × H)
9. C2×C3×C13×C49D3semidirect
10. C2×C3×C13×C49C2×C3semidirect
14. C3×C13×C49C2×D3semidirect
15. C3×C13×C49C22×C3semidirect
19. C2×C13×C49C3×D3semidirect
23. C2×C32×C49D13semidirect
26. C13×C49C2×C3×D3semidirect
34. C2×C3×D39C49direct (N × H)
35. C32×C49C2×D13semidirect
39. C2×C3×C49C3×D13semidirect
40. C2×C3×C49D39direct (N × H)
46. C2×C32×C13C2×C49semidirect
47. C3×D39C2×C49direct (N × H)
51. C2×D39C3×C49direct (N × H)
54. C3×C49C2×C3×D13semidirect
55. C3×C49C2×D39direct (N × H)
58. C32×C13C22×C49semidirect
60. C2×C49C3×D39direct (N × H)
65. C2×C3×C13D3×C49semidirect
66. C2×C3×C13C2×C3×C49semidirect
67. D39C2×C3×C49direct (N × H)
71. C49C2×C3×D39direct (N × H)
78. C3×C13C2×D3×C49semidirect
79. C3×C13C22×C3×C49semidirect
82. C2×C13C3×D3×C49semidirect
87. C2×C32D13×C49semidirect
91. C13C2×C3×D3×C49semidirect
94. C32C2×D13×C49semidirect
98. C2×C3C3×D13×C49semidirect
99. C2×C3C49×D39direct (N × H)
103. C3C2×C3×D13×C49semidirect
104. C3C2×C49×D39direct (N × H)
106. C2C3×C49×D39direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C49×D392
C2×C32×C13×C492
C2×C49×D393
C2×C3×D13×C493
C2×C3×C7×D397
C2×C3×D3×C4913