Finite Group Databasebeta

← C2×C3×D3×C13×C49 #37524319

Subgroups — C2×C3×D3×C13×C49 #37524319

Order 22932.

132 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 84 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×D3×C13×C49C212yesmaximal, direct product factor
2C2×C32×C13×C49C211yesmaximal, characteristic, complemented
3C2×D3×C13×C49C311yesmaximal, characteristic, direct product factor
4C22×C3×C13×C49—31nomaximal
5C32×C13×C49C2211yescharacteristic, complemented, Hall
6D3×C13×C49C2×C312yesdirect product factor
7C2×C3×C13×C49—21no—
8C2×C3×C13×C49—32no—
9C2×C3×C13×C49D311yescharacteristic, direct product factor
10C2×C3×C13×C49C2×C311yescharacteristic, complemented
11C2×C3×D3×C7×C13C711yesmaximal, characteristic
12C22×C13×C49—31noHall
13C3×C13×C49—21no—
14C3×C13×C49C2×D311yescharacteristic, direct product factor
15C3×C13×C49C22×C311yescharacteristic, complemented
16C2×C3×D3×C49C1311yesmaximal, characteristic, direct product factor, Hall
17C2×C32×C7×C13C2×C711yescharacteristic
18C3×D3×C7×C13C2×C712yes—
19C2×C13×C49—32no—
20C2×C13×C49C3×D311yescharacteristic, direct product factor
21C22×C3×C7×C13—31no—
22C2×D3×C7×C13C3×C711yescharacteristic
23C2×C32×C49C2×C1311yescharacteristic, complemented
24C3×D3×C49C2×C1312yesdirect product factor
25C32×C7×C13C22×C711yescharacteristic
26C13×C49C2×C3×D311yescharacteristic, direct product factor, Hall
27C22×C3×C49—31no—
28C2×D3×C49C3×C1311yescharacteristic, direct product factor
29C2×C3×C7×C13—21no—
30C2×C3×C7×C13—32no—
31C2×C3×C7×C13D3×C711yescharacteristic
32C2×C3×C7×C13C2×C3×C711yescharacteristic
33D3×C7×C13C2×C3×C712yes—
34C2×C3×D3×C13C4911yescharacteristic, direct product factor, Hall
35C32×C49C22×C1311yescharacteristic, complemented, Hall
36C22×C7×C13—31no—
37C2×C3×C49—21no—
38C2×C3×C49—32no—
39C2×C3×C49D3×C1311yescharacteristic, direct product factor
40C2×C3×C49C2×C3×C1311yescharacteristic, complemented
41D3×C49C2×C3×C1312yesdirect product factor
42C3×C7×C13—21no—
43C3×C7×C13C2×D3×C711yescharacteristic
44C3×C7×C13C22×C3×C711yescharacteristic
45C2×C3×D3×C7C7×C1311yescharacteristic
46C2×C32×C13C2×C4911yescharacteristic, complemented
47C3×D3×C13C2×C4912yesdirect product factor
48C22×C49—31noHall
49C2×C7×C13—32no—
50C2×C7×C13C3×D3×C711yescharacteristic
51C22×C3×C13—31no—
52C2×D3×C13C3×C4911yescharacteristic, direct product factor
53C3×C49—21no—
54C3×C49C2×D3×C1311yescharacteristic, direct product factor
55C3×C49C22×C3×C1311yescharacteristic, complemented
56C2×C32×C7C2×C7×C1311yescharacteristic
57C3×D3×C7C2×C7×C1312yes—
58C32×C13C22×C4911yescharacteristic, complemented, Hall
59C2×C49—32no—
60C2×C49C3×D3×C1311yescharacteristic, direct product factor
61C7×C13C2×C3×D3×C711yescharacteristic
62C22×C3×C7—31no—
63C2×D3×C7C3×C7×C1311yescharacteristic
64C2×C3×C13—21no—
65C2×C3×C13—32no—
66C2×C3×C13D3×C4911yescharacteristic, direct product factor
67C2×C3×C13C2×C3×C4911yescharacteristic, complemented
68D3×C13C2×C3×C4912yesdirect product factor
69C32×C7C22×C7×C1311yescharacteristic
70C22×C13—31noHall
71C49C2×C3×D3×C1311yescharacteristic, direct product factor, Sylow
72C2×C3×C7—21no—
73C2×C3×C7—32no—
74C2×C3×C7D3×C7×C1311yescharacteristic
75C2×C3×C7C2×C3×C7×C1311yescharacteristic
76D3×C7C2×C3×C7×C1312yes—
77C3×C13—21no—
78C3×C13C2×D3×C4911yescharacteristic, direct product factor
79C3×C13C22×C3×C4911yescharacteristic, complemented
80C2×C3×D3C13×C4911yescharacteristic, direct product factor, Hall
81C22×C7—31no—
82C2×C13—32no—
83C2×C13C3×D3×C4911yescharacteristic, direct product factor
84C3×C7—21no—
85C3×C7C2×D3×C7×C1311yescharacteristic
86C3×C7C22×C3×C7×C1311yescharacteristic
87C2×C32C2×C13×C4911yescharacteristic, complemented
88C3×D3C2×C13×C4912yesdirect product factor
89C2×C7—32no—
90C2×C7C3×D3×C7×C1311yescharacteristic
91C13C2×C3×D3×C4911yescharacteristic, direct product factor, Sylow
92C22×C3—31no—
93C2×D3C3×C13×C4911yescharacteristic, direct product factor
94C32C22×C13×C4911yescharacteristic, complemented, Sylow
95C7C2×C3×D3×C7×C1311yescharacteristic
96C2×C3—21no—
97C2×C3—32no—
98C2×C3C2×C3×C13×C4911yescharacteristic, complemented
99C2×C3D3×C13×C4911yescharacteristic, direct product factor
100D3C2×C3×C13×C4912yesdirect product factor
101C22—31noSylow
102C3—21no—
103C3C22×C3×C13×C4911yescharacteristic, complemented
104C3C2×D3×C13×C4911yescharacteristic, direct product factor
105C2—32no—
106C2C3×D3×C13×C4911yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C13×C49D3
commutator, hypocenterC3C22×C3×C13×C49
FrattiniC7C2×C3×D3×C7×C13
FittingC2×C32×C13×C49C2
socleC2×C32×C7×C13C2×C7
prime radicalC2×C3×D3×C7×C13C7
cosocleC3×C7C22×C3×C7×C13
LCSG ▷ C3
UCSC1 ◁ C2×C3×C13×C49

Complements

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

NH ≅ G/Ntype
1. C3×D3×C13×C49C2direct (N × H)
2. C2×C32×C13×C49C2semidirect
3. C2×D3×C13×C49C3direct (N × H)
5. C32×C13×C49C22semidirect
6. D3×C13×C49C2×C3direct (N × H)
9. C2×C3×C13×C49D3direct (N × H)
10. C2×C3×C13×C49C2×C3semidirect
14. C3×C13×C49C2×D3direct (N × H)
15. C3×C13×C49C22×C3semidirect
16. C2×C3×D3×C49C13direct (N × H)
20. C2×C13×C49C3×D3direct (N × H)
23. C2×C32×C49C2×C13semidirect
24. C3×D3×C49C2×C13direct (N × H)
26. C13×C49C2×C3×D3direct (N × H)
28. C2×D3×C49C3×C13direct (N × H)
34. C2×C3×D3×C13C49direct (N × H)
35. C32×C49C22×C13semidirect
39. C2×C3×C49D3×C13direct (N × H)
40. C2×C3×C49C2×C3×C13semidirect
41. D3×C49C2×C3×C13direct (N × H)
46. C2×C32×C13C2×C49semidirect
47. C3×D3×C13C2×C49direct (N × H)
52. C2×D3×C13C3×C49direct (N × H)
54. C3×C49C2×D3×C13direct (N × H)
55. C3×C49C22×C3×C13semidirect
58. C32×C13C22×C49semidirect
60. C2×C49C3×D3×C13direct (N × H)
66. C2×C3×C13D3×C49direct (N × H)
67. C2×C3×C13C2×C3×C49semidirect
68. D3×C13C2×C3×C49direct (N × H)
71. C49C2×C3×D3×C13direct (N × H)
78. C3×C13C2×D3×C49direct (N × H)
79. C3×C13C22×C3×C49semidirect
80. C2×C3×D3C13×C49direct (N × H)
83. C2×C13C3×D3×C49direct (N × H)
87. C2×C32C2×C13×C49semidirect
88. C3×D3C2×C13×C49direct (N × H)
91. C13C2×C3×D3×C49direct (N × H)
93. C2×D3C3×C13×C49direct (N × H)
94. C32C22×C13×C49semidirect
98. C2×C3C2×C3×C13×C49semidirect
99. C2×C3D3×C13×C49direct (N × H)
100. D3C2×C3×C13×C49direct (N × H)
103. C3C22×C3×C13×C49semidirect
104. C3C2×D3×C13×C49direct (N × H)
106. C2C3×D3×C13×C49direct (N × H)

Maximal subgroups

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

subgroupindex
C3×D3×C13×C492
C2×C32×C13×C492
C2×D3×C13×C493
C22×C3×C13×C493
C2×C3×D3×C7×C137
C2×C3×D3×C4913