Finite Group Databasebeta

← C3×C7×C13×Dic33 #49114607

Subgroups — C3×C7×C13×Dic33 #49114607

Order 36036.

112 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 72 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×C32×C7×C11×C13C211yesmaximal, characteristic
2C7×C13×Dic33C311yesmaximal, characteristic, direct product factor
3C3×C7×C13×Dic11—31nomaximal
4C32×C7×C11×C13C411yescharacteristic, complemented, Hall
5C2×C3×C7×C11×C13—21no—
6C2×C3×C7×C11×C13D311yescharacteristic
7C2×C3×C7×C11×C13C2×C311yescharacteristic
8C3×C13×Dic33C711yesmaximal, characteristic, direct product factor, Hall
9C7×C13×Dic11—31noHall
10C3×C7×Dic3×C13—111nomaximal, Hall
11C3×C7×C11×C13—21no—
12C3×C7×C11×C13Dic311yescharacteristic, complemented
13C3×C7×C11×C13C3×C411yescharacteristic, complemented
14C3×C7×Dic33C1311yesmaximal, characteristic, direct product factor, Hall
15C2×C32×C11×C13C2×C711yescharacteristic
16C2×C7×C11×C13C3×D311yescharacteristic
17C13×Dic33C3×C711yescharacteristic, direct product factor
18C3×C13×Dic11—31no—
19C2×C32×C7×C13D1111yescharacteristic
20C2×C32×C7×C11C2×C1311yescharacteristic
21C32×C11×C13C4×C711yescharacteristic, complemented, Hall
22C3×C4×C7×C13—331no—
23C7×Dic3×C13—111no—
24C7×C11×C13C3×Dic311yescharacteristic, complemented, Hall
25C7×Dic33C3×C1311yescharacteristic, direct product factor
26C3×C7×Dic11—31no—
27C2×C3×C11×C13—21no—
28C2×C3×C11×C13D3×C711yescharacteristic
29C2×C3×C11×C13C2×C3×C711yescharacteristic
30C32×C7×C13Dic1111yescharacteristic, complemented, Hall
31C32×C7×C11C4×C1311yescharacteristic, complemented, Hall
32C13×Dic11—31noHall
33C2×C3×C7×C13—21no—
34C2×C3×C7×C13C3×D1111yescharacteristic
35C2×C3×C7×C13D3311yescharacteristic
36C3×Dic3×C13—111noHall
37C2×C3×C7×C11—21no—
38C2×C3×C7×C11D3×C1311yescharacteristic
39C2×C3×C7×C11C2×C3×C1311yescharacteristic
40C3×C11×C13—21no—
41C3×C11×C13C7×Dic311yescharacteristic, complemented
42C3×C11×C13C3×C4×C711yescharacteristic, complemented
43C3×Dic33C7×C1311yescharacteristic, direct product factor, Hall
44C4×C7×C13—331noHall
45C7×Dic11—31noHall
46C2×C11×C13C3×D3×C711yescharacteristic
47C3×C7×C13—21no—
48C3×C7×C13C3×Dic1111yescharacteristic, complemented
49C3×C7×C13Dic3311yescharacteristic, direct product factor
50C3×C7×Dic3—111noHall
51C2×C32×C13C7×D1111yescharacteristic
52C3×C7×C11—21no—
53C3×C7×C11Dic3×C1311yescharacteristic, complemented
54C3×C7×C11C3×C4×C1311yescharacteristic, complemented
55C2×C32×C11C2×C7×C1311yescharacteristic
56C2×C7×C13C3×D3311yescharacteristic
57C3×C4×C13—331no—
58Dic3×C13—111no—
59C2×C7×C11C3×D3×C1311yescharacteristic
60C11×C13C3×C7×Dic311yescharacteristic, complemented, Hall
61Dic33C3×C7×C1311yescharacteristic, direct product factor
62C3×Dic11—31no—
63C2×C32×C7C13×D1111yescharacteristic
64C32×C13C7×Dic1111yescharacteristic, complemented, Hall
65C32×C11C4×C7×C1311yescharacteristic, complemented, Hall
66C7×C13C3×Dic3311yescharacteristic, direct product factor, Hall
67C3×C4×C7—331no—
68C7×Dic3—111no—
69C2×C3×C13—21no—
70C2×C3×C13C3×C7×D1111yescharacteristic
71C2×C3×C13C7×D3311yescharacteristic
72C7×C11C3×Dic3×C1311yescharacteristic, complemented, Hall
73C2×C3×C11—21no—
74C2×C3×C11D3×C7×C1311yescharacteristic
75C2×C3×C11C2×C3×C7×C1311yescharacteristic
76C32×C7C13×Dic1111yescharacteristic, complemented, Hall
77C4×C13—331noHall
78Dic11—31noHall
79C2×C3×C7—21no—
80C2×C3×C7C3×C13×D1111yescharacteristic
81C2×C3×C7C13×D3311yescharacteristic
82C3×C13—21no—
83C3×C13C3×C7×Dic1111yescharacteristic, complemented
84C3×C13C7×Dic3311yescharacteristic, direct product factor
85C3×Dic3—111noHall
86C3×C11—21no—
87C3×C11C7×Dic3×C1311yescharacteristic, complemented
88C3×C11C3×C4×C7×C1311yescharacteristic, complemented
89C4×C7—331noHall
90C2×C13C3×C7×D3311yescharacteristic
91C2×C11C3×D3×C7×C1311yescharacteristic
92C3×C7—21no—
93C3×C7C3×C13×Dic1111yescharacteristic, complemented
94C3×C7C13×Dic3311yescharacteristic, direct product factor
95C2×C32C7×C13×D1111yescharacteristic
96C2×C7C3×C13×D3311yescharacteristic
97C13C3×C7×Dic3311yescharacteristic, direct product factor, Sylow
98C3×C4—331no—
99Dic3—111no—
100C11C3×C7×Dic3×C1311yescharacteristic, complemented, Sylow
101C32C7×C13×Dic1111yescharacteristic, complemented, Sylow
102C7C3×C13×Dic3311yescharacteristic, direct product factor, Sylow
103C2×C3—21no—
104C2×C3C3×C7×C13×D1111yescharacteristic
105C2×C3C7×C13×D3311yescharacteristic
106C4—331noSylow
107C3—21no—
108C3C3×C7×C13×Dic1111yescharacteristic, complemented
109C3C7×C13×Dic3311yescharacteristic, direct product factor
110C2C3×C7×C13×D3311yescharacteristic
subgroupG/H
center, hypercenterC2×C3×C7×C13D33
commutator, hypocenterC3×C11C3×C4×C7×C13
FrattiniC2C3×C7×C13×D33
Fitting, socle, prime radicalC2×C32×C7×C11×C13C2
cosocleC2×C3×C11C2×C3×C7×C13
LCSG ▷ C3×C11
UCSC1 ◁ C2×C3×C7×C13

Complements

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

NH ≅ G/Ntype
2. C7×C13×Dic33C3direct (N × H)
4. C32×C7×C11×C13C4semidirect
8. C3×C13×Dic33C7direct (N × H)
12. C3×C7×C11×C13Dic3semidirect
13. C3×C7×C11×C13C3×C4semidirect
14. C3×C7×Dic33C13direct (N × H)
17. C13×Dic33C3×C7direct (N × H)
21. C32×C11×C13C4×C7semidirect
24. C7×C11×C13C3×Dic3semidirect
25. C7×Dic33C3×C13direct (N × H)
30. C32×C7×C13Dic11semidirect
31. C32×C7×C11C4×C13semidirect
41. C3×C11×C13C7×Dic3semidirect
42. C3×C11×C13C3×C4×C7semidirect
43. C3×Dic33C7×C13direct (N × H)
48. C3×C7×C13C3×Dic11semidirect
49. C3×C7×C13Dic33direct (N × H)
53. C3×C7×C11Dic3×C13semidirect
54. C3×C7×C11C3×C4×C13semidirect
60. C11×C13C3×C7×Dic3semidirect
61. Dic33C3×C7×C13direct (N × H)
64. C32×C13C7×Dic11semidirect
65. C32×C11C4×C7×C13semidirect
66. C7×C13C3×Dic33direct (N × H)
72. C7×C11C3×Dic3×C13semidirect
76. C32×C7C13×Dic11semidirect
83. C3×C13C3×C7×Dic11semidirect
84. C3×C13C7×Dic33direct (N × H)
87. C3×C11C7×Dic3×C13semidirect
88. C3×C11C3×C4×C7×C13semidirect
93. C3×C7C3×C13×Dic11semidirect
94. C3×C7C13×Dic33direct (N × H)
97. C13C3×C7×Dic33direct (N × H)
100. C11C3×C7×Dic3×C13semidirect
101. C32C7×C13×Dic11semidirect
102. C7C3×C13×Dic33direct (N × H)
108. C3C3×C7×C13×Dic11semidirect
109. C3C7×C13×Dic33direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C7×C11×C132
C7×C13×Dic333
C3×C7×C13×Dic113
C3×C13×Dic337
C3×C7×Dic3×C1311
C3×C7×Dic3313