Finite Group Databasebeta

← C2×C32×C7×C13×D7 #37525670

Subgroups — C2×C32×C7×C13×D7 #37525670

Order 22932.

312 conjugacy classes of subgroups; only the 168 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 168 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
1C32×C7×C13×D7C212yesmaximal, direct product factor
2C2×C32×C72×C13C211yesmaximal, characteristic, complemented
3C2×C3×C7×C13×D7C314yesmaximal, direct product factor
4C32×C72×C13C2211yescharacteristic, complemented, Hall
5C3×C7×C13×D7C2×C318yesdirect product factor
6C2×C3×C72×C13C2×C314yescomplemented
7C2×C32×C13×D7C711yesmaximal, characteristic, direct product factor
8C22×C32×C7×C13—71nomaximal
9C2×C7×C13×D7C3211yescharacteristic, direct product factor, Hall
10C3×C72×C13C22×C314yescomplemented
11C2×C32×C7×D7C1311yesmaximal, characteristic, direct product factor, Hall
12C2×C32×C7×C13—23no—
13C2×C32×C7×C13—72no—
14C2×C32×C7×C13D711yescharacteristic, direct product factor
15C2×C32×C7×C13C2×C711yescharacteristic, complemented
16C32×C13×D7C2×C712yesdirect product factor
17C2×C72×C13C2×C3211yescharacteristic, complemented
18C7×C13×D7C2×C3212yesdirect product factor
19C22×C3×C7×C13—74no—
20C2×C3×C13×D7C3×C714yesdirect product factor
21C2×C32×C72C2×C1311yescharacteristic, complemented
22C32×C7×D7C2×C1312yesdirect product factor
23C32×C7×C13—23no—
24C32×C7×C13C2×D711yescharacteristic, direct product factor
25C32×C7×C13C22×C711yescharacteristic, complemented
26C72×C13C22×C3211yescharacteristic, complemented, Hall
27C2×C3×C7×D7C3×C1314yesdirect product factor
28C2×C3×C7×C13—212no—
29C2×C3×C7×C13—78no—
30C2×C3×C7×C13C3×D714yesdirect product factor
31C2×C3×C7×C13C2×C3×C714yescomplemented
32C3×C13×D7C2×C3×C718yesdirect product factor
33C22×C32×C13—71noHall
34C32×C72C22×C1311yescharacteristic, complemented, Hall
35C22×C7×C13—71no—
36C2×C13×D7C32×C711yescharacteristic, direct product factor
37C2×C3×C72C2×C3×C1314yescomplemented
38C3×C7×D7C2×C3×C1318yesdirect product factor
39C3×C7×C13—212no—
40C3×C7×C13C2×C3×D714yesdirect product factor
41C3×C7×C13C22×C3×C714yescomplemented
42C22×C32×C7—71no—
43C2×C32×D7C7×C1311yescharacteristic, direct product factor
44C2×C32×C13—72no—
45C2×C32×C13C7×D711yescharacteristic, direct product factor
46C2×C7×D7C32×C1311yescharacteristic, direct product factor, Hall
47C2×C7×C13—23no—
48C2×C7×C13—72no—
49C2×C7×C13C32×D711yescharacteristic, direct product factor
50C2×C7×C13C2×C32×C711yescharacteristic, complemented
51C13×D7C2×C32×C712yesdirect product factor
52C22×C3×C13—74no—
53C3×C72C22×C3×C1314yescomplemented
54C2×C32×C7—23no—
55C2×C32×C7—72no—
56C2×C32×C7C13×D711yescharacteristic, direct product factor
57C2×C32×C7C2×C7×C1311yescharacteristic, complemented
58C32×D7C2×C7×C1312yesdirect product factor
59C32×C13C2×C7×D711yescharacteristic, direct product factor, Hall
60C2×C72C2×C32×C1311yescharacteristic, complemented
61C7×D7C2×C32×C1312yesdirect product factor
62C7×C13—23no—
63C7×C13C2×C32×D711yescharacteristic, direct product factor
64C7×C13C22×C32×C711yescharacteristic, complemented
65C22×C3×C7—74no—
66C2×C3×D7C3×C7×C1314yesdirect product factor
67C2×C3×C13—78no—
68C2×C3×C13C3×C7×D714yesdirect product factor
69C32×C7—23no—
70C32×C7C2×C13×D711yescharacteristic, direct product factor
71C32×C7C22×C7×C1311yescharacteristic, complemented
72C22×C13—71noHall
73C72C22×C32×C1311yescharacteristic, complemented, Sylow
74C2×C3×C7—212no—
75C2×C3×C7—78no—
76C2×C3×C7C3×C13×D714yesdirect product factor
77C2×C3×C7C2×C3×C7×C1314yescomplemented
78C3×D7C2×C3×C7×C1318yesdirect product factor
79C3×C13C2×C3×C7×D714yesdirect product factor
80C22×C32—71noHall
81C22×C7—71no—
82C2×D7C32×C7×C1311yescharacteristic, direct product factor
83C2×C13—72no—
84C2×C13C32×C7×D711yescharacteristic, direct product factor
85C3×C7—212no—
86C3×C7C2×C3×C13×D714yesdirect product factor
87C3×C7C22×C3×C7×C1314yescomplemented
88C2×C32—72no—
89C2×C32C7×C13×D711yescharacteristic, direct product factor
90C2×C7—23no—
91C2×C7—72no—
92C2×C7C32×C13×D711yescharacteristic, direct product factor
93C2×C7C2×C32×C7×C1311yescharacteristic, complemented
94D7C2×C32×C7×C1312yesdirect product factor
95C13C2×C32×C7×D711yescharacteristic, direct product factor, Sylow
96C22×C3—74no—
97C32C2×C7×C13×D711yescharacteristic, direct product factor, Sylow
98C7—23no—
99C7C22×C32×C7×C1311yescharacteristic, complemented
100C7C2×C32×C13×D711yescharacteristic, direct product factor
101C2×C3—78no—
102C2×C3C3×C7×C13×D714yesdirect product factor
103C22—71noSylow
104C3C2×C3×C7×C13×D714yesdirect product factor
105C2—72no—
106C2C32×C7×C13×D711yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C32×C7×C13D7
commutator, cosocle, hypocenterC7C22×C32×C7×C13
FrattiniC1G
Fitting, socleC2×C32×C72×C13C2
LCSG ▷ C7
UCSC1 ◁ C2×C32×C7×C13

Complements

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

NH ≅ G/Ntype
1. C32×C7×C13×D7C2direct (N × H)
2. C2×C32×C72×C13C2semidirect
3. C2×C3×C7×C13×D7C3direct (N × H)
4. C32×C72×C13C22semidirect
5. C3×C7×C13×D7C2×C3direct (N × H)
6. C2×C3×C72×C13C2×C3semidirect
7. C2×C32×C13×D7C7direct (N × H)
9. C2×C7×C13×D7C32direct (N × H)
10. C3×C72×C13C22×C3semidirect
11. C2×C32×C7×D7C13direct (N × H)
14. C2×C32×C7×C13D7direct (N × H)
15. C2×C32×C7×C13C2×C7semidirect
16. C32×C13×D7C2×C7direct (N × H)
17. C2×C72×C13C2×C32semidirect
18. C7×C13×D7C2×C32direct (N × H)
20. C2×C3×C13×D7C3×C7direct (N × H)
21. C2×C32×C72C2×C13semidirect
22. C32×C7×D7C2×C13direct (N × H)
24. C32×C7×C13C2×D7direct (N × H)
25. C32×C7×C13C22×C7semidirect
26. C72×C13C22×C32semidirect
27. C2×C3×C7×D7C3×C13direct (N × H)
30. C2×C3×C7×C13C3×D7direct (N × H)
31. C2×C3×C7×C13C2×C3×C7semidirect
32. C3×C13×D7C2×C3×C7direct (N × H)
34. C32×C72C22×C13semidirect
36. C2×C13×D7C32×C7direct (N × H)
37. C2×C3×C72C2×C3×C13semidirect
38. C3×C7×D7C2×C3×C13direct (N × H)
40. C3×C7×C13C2×C3×D7direct (N × H)
41. C3×C7×C13C22×C3×C7semidirect
43. C2×C32×D7C7×C13direct (N × H)
45. C2×C32×C13C7×D7direct (N × H)
46. C2×C7×D7C32×C13direct (N × H)
49. C2×C7×C13C32×D7direct (N × H)
50. C2×C7×C13C2×C32×C7semidirect
51. C13×D7C2×C32×C7direct (N × H)
53. C3×C72C22×C3×C13semidirect
56. C2×C32×C7C13×D7direct (N × H)
57. C2×C32×C7C2×C7×C13semidirect
58. C32×D7C2×C7×C13direct (N × H)
59. C32×C13C2×C7×D7direct (N × H)
60. C2×C72C2×C32×C13semidirect
61. C7×D7C2×C32×C13direct (N × H)
63. C7×C13C2×C32×D7direct (N × H)
64. C7×C13C22×C32×C7semidirect
66. C2×C3×D7C3×C7×C13direct (N × H)
68. C2×C3×C13C3×C7×D7direct (N × H)
70. C32×C7C2×C13×D7direct (N × H)
71. C32×C7C22×C7×C13semidirect
73. C72C22×C32×C13semidirect
76. C2×C3×C7C3×C13×D7direct (N × H)
77. C2×C3×C7C2×C3×C7×C13semidirect
78. C3×D7C2×C3×C7×C13direct (N × H)
79. C3×C13C2×C3×C7×D7direct (N × H)
82. C2×D7C32×C7×C13direct (N × H)
84. C2×C13C32×C7×D7direct (N × H)
86. C3×C7C2×C3×C13×D7direct (N × H)
87. C3×C7C22×C3×C7×C13semidirect
89. C2×C32C7×C13×D7direct (N × H)
92. C2×C7C32×C13×D7direct (N × H)
93. C2×C7C2×C32×C7×C13semidirect
94. D7C2×C32×C7×C13direct (N × H)
95. C13C2×C32×C7×D7direct (N × H)
97. C32C2×C7×C13×D7direct (N × H)
99. C7C22×C32×C7×C13semidirect
100. C7C2×C32×C13×D7direct (N × H)
102. C2×C3C3×C7×C13×D7direct (N × H)
104. C3C2×C3×C7×C13×D7direct (N × H)
106. C2C32×C7×C13×D7direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C7×C13×D72
C2×C32×C72×C132
C2×C3×C7×C13×D73
C2×C32×C13×D77
C22×C32×C7×C137
C2×C32×C7×D713