Finite Group Databasebeta

← C2×D3×C13⋊C3×C49 #37524253

Subgroups — C2×D3×C13⋊C3×C49 #37524253

Order 22932.

132 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 63 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
1C2×C3×C13⋊C3×C49C211yesmaximal, characteristic, complemented
2D3×C13⋊C3×C49C212yesmaximal, direct product factor
3C2×D3×C13×C49C311yesmaximal, characteristic, complemented
4C22×C13⋊C3×C49—31nomaximal
5C3×C13⋊C3×C49C2211yescharacteristic, complemented, Hall
6D3×C13×C49C2×C312yescomplemented
7C2×C13⋊C3×C49—21no—
8C2×C13⋊C3×C49—32no—
9C2×C13⋊C3×C49D311yescharacteristic, direct product factor
10C2×C3×C13×C49C2×C311yescharacteristic, complemented
11C2×D3×C7×C13⋊C3C711yesmaximal, characteristic
12C22×C13×C49—31noHall
13C3×C13×C49C22×C311yescharacteristic, complemented
14C13⋊C3×C49—21no—
15C13⋊C3×C49C2×D311yescharacteristic, direct product factor
16C2×C3×D3×C49—131nomaximal, Hall
17C2×C3×C7×C13⋊C3C2×C711yescharacteristic
18D3×C7×C13⋊C3C2×C712yes—
19C2×C13×C49—32no—
20C2×C13×C49C3×D311yescharacteristic, complemented
21C2×D3×C7×C13C3×C711yescharacteristic
22C22×C7×C13⋊C3—31no—
23C2×C32×C49—131no—
24C3×D3×C49—132no—
25C3×C7×C13⋊C3C22×C711yescharacteristic
26C13×C49C2×C3×D311yescharacteristic, complemented, Hall
27C22×C3×C49—391no—
28C2×D3×C49C13⋊C311yescharacteristic, direct product factor
29C2×C3×C7×C13C2×C3×C711yescharacteristic
30D3×C7×C13C2×C3×C712yes—
31C2×C7×C13⋊C3—21no—
32C2×C7×C13⋊C3—32no—
33C2×C7×C13⋊C3D3×C711yescharacteristic
34C2×D3×C13⋊C3C4911yescharacteristic, direct product factor, Hall
35C32×C49—131noHall
36C22×C7×C13—31no—
37C2×C3×C49—131no—
38C2×C3×C49—261no—
39C2×C3×C49—392no—
40C2×C3×C49C2×C13⋊C311yescharacteristic, complemented
41D3×C49C2×C13⋊C312yesdirect product factor
42C3×C7×C13C22×C3×C711yescharacteristic
43C7×C13⋊C3—21no—
44C7×C13⋊C3C2×D3×C711yescharacteristic
45C2×C3×D3×C7—131no—
46C2×C3×C13⋊C3C2×C4911yescharacteristic, complemented
47D3×C13⋊C3C2×C4912yesdirect product factor
48C22×C49—31noHall
49C2×C7×C13—32no—
50C2×C7×C13C3×D3×C711yescharacteristic
51C2×D3×C13C3×C4911yescharacteristic, complemented
52C22×C13⋊C3—31no—
53C3×C49—131no—
54C3×C49—261no—
55C3×C49C22×C13⋊C311yescharacteristic, complemented
56C2×C32×C7—131no—
57C3×D3×C7—132no—
58C3×C13⋊C3C22×C4911yescharacteristic, complemented, Hall
59C2×C49—32no—
60C2×C49D3×C13⋊C311yescharacteristic, direct product factor
61C7×C13C2×C3×D3×C711yescharacteristic
62C22×C3×C7—391no—
63C2×D3×C7C7×C13⋊C311yescharacteristic
64C2×C3×C13C2×C3×C4911yescharacteristic, complemented
65D3×C13C2×C3×C4912yescomplemented
66C2×C13⋊C3—21no—
67C2×C13⋊C3—32no—
68C2×C13⋊C3D3×C4911yescharacteristic, direct product factor
69C32×C7—131no—
70C22×C13—31noHall
71C49C2×D3×C13⋊C311yescharacteristic, direct product factor, Sylow
72C2×C3×C7—131no—
73C2×C3×C7—261no—
74C2×C3×C7—392no—
75C2×C3×C7C2×C7×C13⋊C311yescharacteristic
76D3×C7C2×C7×C13⋊C312yes—
77C3×C13C22×C3×C4911yescharacteristic, complemented
78C13⋊C3—21no—
79C13⋊C3C2×D3×C4911yescharacteristic, direct product factor
80C2×C3×D3—131noHall
81C22×C7—31no—
82C2×C13—32no—
83C2×C13C3×D3×C4911yescharacteristic, complemented
84C3×C7—131no—
85C3×C7—261no—
86C3×C7C22×C7×C13⋊C311yescharacteristic
87C2×C32—131no—
88C3×D3—132no—
89C2×C7—32no—
90C2×C7D3×C7×C13⋊C311yescharacteristic
91C13C2×C3×D3×C4911yescharacteristic, complemented, Sylow
92C22×C3—391no—
93C2×D3C13⋊C3×C4911yescharacteristic, direct product factor
94C32—131noSylow
95C7C2×D3×C7×C13⋊C311yescharacteristic
96C2×C3—131no—
97C2×C3—261no—
98C2×C3—392no—
99C2×C3C2×C13⋊C3×C4911yescharacteristic, complemented
100D3C2×C13⋊C3×C4912yesdirect product factor
101C22—31noSylow
102C3—131no—
103C3—261no—
104C3C22×C13⋊C3×C4911yescharacteristic, complemented
105C2—32no—
106C2D3×C13⋊C3×C4911yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C49D3×C13⋊C3
commutator, hypocenterC3×C13C22×C3×C49
FrattiniC7C2×D3×C7×C13⋊C3
FittingC2×C3×C13×C49C2×C3
socleC2×C3×C7×C13C2×C3×C7
prime radicalC2×D3×C7×C13⋊C3C7
cosocleC3×C7×C13C22×C3×C7
LCSG ▷ C3×C13
UCSC1 ◁ C2×C49

Complements

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

NH ≅ G/Ntype
1. C2×C3×C13⋊C3×C49C2semidirect
2. D3×C13⋊C3×C49C2direct (N × H)
3. C2×D3×C13×C49C3semidirect
5. C3×C13⋊C3×C49C22semidirect
6. D3×C13×C49C2×C3semidirect
9. C2×C13⋊C3×C49D3direct (N × H)
10. C2×C3×C13×C49C2×C3semidirect
13. C3×C13×C49C22×C3semidirect
15. C13⋊C3×C49C2×D3direct (N × H)
20. C2×C13×C49C3×D3semidirect
26. C13×C49C2×C3×D3semidirect
28. C2×D3×C49C13⋊C3direct (N × H)
34. C2×D3×C13⋊C3C49direct (N × H)
40. C2×C3×C49C2×C13⋊C3semidirect
41. D3×C49C2×C13⋊C3direct (N × H)
46. C2×C3×C13⋊C3C2×C49semidirect
47. D3×C13⋊C3C2×C49direct (N × H)
51. C2×D3×C13C3×C49semidirect
55. C3×C49C22×C13⋊C3semidirect
58. C3×C13⋊C3C22×C49semidirect
60. C2×C49D3×C13⋊C3direct (N × H)
64. C2×C3×C13C2×C3×C49semidirect
65. D3×C13C2×C3×C49semidirect
68. C2×C13⋊C3D3×C49direct (N × H)
71. C49C2×D3×C13⋊C3direct (N × H)
77. C3×C13C22×C3×C49semidirect
79. C13⋊C3C2×D3×C49direct (N × H)
83. C2×C13C3×D3×C49semidirect
91. C13C2×C3×D3×C49semidirect
93. C2×D3C13⋊C3×C49direct (N × H)
99. C2×C3C2×C13⋊C3×C49semidirect
100. D3C2×C13⋊C3×C49direct (N × H)
104. C3C22×C13⋊C3×C49semidirect
106. C2D3×C13⋊C3×C49direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C13⋊C3×C492
D3×C13⋊C3×C492
C2×D3×C13×C493
C22×C13⋊C3×C493
C2×D3×C7×C13⋊C37
C2×C3×D3×C4913