Finite Group Databasebeta

← C2×C32×C7×D91 #37525671

Subgroups — C2×C32×C7×D91 #37525671

Order 22932.

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

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 132 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×D91C212yesmaximal, direct product factor
2C2×C32×C72×C13C211yesmaximal, characteristic, complemented
3C2×C3×C7×D91C314yesmaximal, direct product factor
4C32×C72×C13C2211yescharacteristic, complemented, Hall
5C3×C7×D91C2×C318yesdirect product factor
6C2×C3×C72×C13C2×C314yescomplemented
7C2×C32×C7×D13—71nomaximal
8C2×C32×D91C711yesmaximal, characteristic, direct product factor
9C2×C7×D91C3211yescharacteristic, direct product factor, Hall
10C3×C72×C13C22×C314yescomplemented
11C2×C32×C7×D7—131nomaximal, Hall
12C2×C32×C7×C13—23no—
13C2×C32×C7×C13D711yescharacteristic, complemented
14C2×C32×C7×C13C2×C711yescharacteristic, complemented
15C32×D91C2×C712yesdirect product factor
16C32×C7×D13—72no—
17C2×C72×C13C2×C3211yescharacteristic, complemented
18C7×D91C2×C3212yesdirect product factor
19C2×C3×D91C3×C714yesdirect product factor
20C2×C3×C7×D13—74no—
21C2×C32×C72D1311yescharacteristic, complemented
22C32×C7×D7—132no—
23C32×C7×C13—23no—
24C32×C7×C13C2×D711yescharacteristic, complemented
25C32×C7×C13C22×C711yescharacteristic, complemented
26C72×C13C22×C3211yescharacteristic, complemented, Hall
27C2×C3×C7×D7—134no—
28C2×C3×C7×C13—212no—
29C2×C3×C7×C13C3×D714yescomplemented
30C2×C3×C7×C13C2×C3×C714yescomplemented
31C3×D91C2×C3×C718yesdirect product factor
32C3×C7×D13—78no—
33C2×C32×D13—71noHall
34C32×C72C2×D1311yescharacteristic, complemented, Hall
35C2×D91C32×C711yescharacteristic, direct product factor
36C2×C7×D13—71no—
37C2×C3×C72C3×D1314yescomplemented
38C3×C7×D7—138no—
39C3×C7×C13—212no—
40C3×C7×C13C2×C3×D714yescomplemented
41C3×C7×C13C22×C3×C714yescomplemented
42C22×C32×C7—911no—
43C2×C32×D7—131no—
44C2×C32×C13C7×D711yescharacteristic, complemented
45C32×D13—72no—
46C2×C7×D7—131noHall
47C2×C7×C13—23no—
48C2×C7×C13C32×D711yescharacteristic, complemented
49C2×C7×C13C2×C32×C711yescharacteristic, complemented
50D91C2×C32×C712yesdirect product factor
51C7×D13—72no—
52C2×C3×D13—74no—
53C3×C72C2×C3×D1314yescomplemented
54C2×C32×C7—23no—
55C2×C32×C7—912no—
56C2×C32×C7C7×D1311yescharacteristic, complemented
57C2×C32×C7D9111yescharacteristic, direct product factor
58C32×D7—132no—
59C32×C13C2×C7×D711yescharacteristic, complemented, Hall
60C2×C72C32×D1311yescharacteristic, complemented
61C7×D7—132no—
62C7×C13—23no—
63C7×C13C2×C32×D711yescharacteristic, complemented
64C7×C13C22×C32×C711yescharacteristic, complemented
65C22×C3×C7—914no—
66C2×C3×D7—134no—
67C2×C3×C13C3×C7×D714yescomplemented
68C3×D13—78no—
69C32×C7—23no—
70C32×C7C2×C7×D1311yescharacteristic, complemented
71C32×C7C2×D9111yescharacteristic, direct product factor
72C2×D13—71noHall
73C72C2×C32×D1311yescharacteristic, complemented, Sylow
74C2×C3×C7—212no—
75C2×C3×C7—918no—
76C2×C3×C7C3×C7×D1314yescomplemented
77C2×C3×C7C3×D9114yesdirect product factor
78C3×D7—138no—
79C3×C13C2×C3×C7×D714yescomplemented
80C22×C32—911noHall
81C22×C7—911no—
82C2×D7—131no—
83C2×C13C32×C7×D711yescharacteristic, complemented
84D13—72no—
85C3×C7—212no—
86C3×C7C2×C3×C7×D1314yescomplemented
87C3×C7C2×C3×D9114yesdirect product factor
88C2×C32—912no—
89C2×C32C7×D9111yescharacteristic, direct product factor
90C2×C7—23no—
91C2×C7—912no—
92C2×C7C32×C7×D1311yescharacteristic, complemented
93C2×C7C32×D9111yescharacteristic, direct product factor
94D7—132no—
95C13C2×C32×C7×D711yescharacteristic, complemented, Sylow
96C22×C3—914no—
97C32C2×C7×D9111yescharacteristic, direct product factor, Sylow
98C7—23no—
99C7C2×C32×D9111yescharacteristic, direct product factor
100C7C2×C32×C7×D1311yescharacteristic, complemented
101C2×C3—918no—
102C2×C3C3×C7×D9114yesdirect product factor
103C22—911noSylow
104C3C2×C3×C7×D9114yesdirect product factor
105C2—912no—
106C2C32×C7×D9111yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C32×C7D91
commutator, cosocle, hypocenterC7×C13C22×C32×C7
FrattiniC1G
Fitting, socleC2×C32×C72×C13C2
LCSG ▷ C7×C13
UCSC1 ◁ C2×C32×C7

Complements

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

NH ≅ G/Ntype
1. C32×C7×D91C2direct (N × H)
2. C2×C32×C72×C13C2semidirect
3. C2×C3×C7×D91C3direct (N × H)
4. C32×C72×C13C22semidirect
5. C3×C7×D91C2×C3direct (N × H)
6. C2×C3×C72×C13C2×C3semidirect
8. C2×C32×D91C7direct (N × H)
9. C2×C7×D91C32direct (N × H)
10. C3×C72×C13C22×C3semidirect
13. C2×C32×C7×C13D7semidirect
14. C2×C32×C7×C13C2×C7semidirect
15. C32×D91C2×C7direct (N × H)
17. C2×C72×C13C2×C32semidirect
18. C7×D91C2×C32direct (N × H)
19. C2×C3×D91C3×C7direct (N × H)
21. C2×C32×C72D13semidirect
24. C32×C7×C13C2×D7semidirect
25. C32×C7×C13C22×C7semidirect
26. C72×C13C22×C32semidirect
29. C2×C3×C7×C13C3×D7semidirect
30. C2×C3×C7×C13C2×C3×C7semidirect
31. C3×D91C2×C3×C7direct (N × H)
34. C32×C72C2×D13semidirect
35. C2×D91C32×C7direct (N × H)
37. C2×C3×C72C3×D13semidirect
40. C3×C7×C13C2×C3×D7semidirect
41. C3×C7×C13C22×C3×C7semidirect
44. C2×C32×C13C7×D7semidirect
48. C2×C7×C13C32×D7semidirect
49. C2×C7×C13C2×C32×C7semidirect
50. D91C2×C32×C7direct (N × H)
53. C3×C72C2×C3×D13semidirect
56. C2×C32×C7C7×D13semidirect
57. C2×C32×C7D91direct (N × H)
59. C32×C13C2×C7×D7semidirect
60. C2×C72C32×D13semidirect
63. C7×C13C2×C32×D7semidirect
64. C7×C13C22×C32×C7semidirect
67. C2×C3×C13C3×C7×D7semidirect
70. C32×C7C2×C7×D13semidirect
71. C32×C7C2×D91direct (N × H)
73. C72C2×C32×D13semidirect
76. C2×C3×C7C3×C7×D13semidirect
77. C2×C3×C7C3×D91direct (N × H)
79. C3×C13C2×C3×C7×D7semidirect
83. C2×C13C32×C7×D7semidirect
86. C3×C7C2×C3×C7×D13semidirect
87. C3×C7C2×C3×D91direct (N × H)
89. C2×C32C7×D91direct (N × H)
92. C2×C7C32×C7×D13semidirect
93. C2×C7C32×D91direct (N × H)
95. C13C2×C32×C7×D7semidirect
97. C32C2×C7×D91direct (N × H)
99. C7C2×C32×D91direct (N × H)
100. C7C2×C32×C7×D13semidirect
102. C2×C3C3×C7×D91direct (N × H)
104. C3C2×C3×C7×D91direct (N × H)
106. C2C32×C7×D91direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C7×D912
C2×C32×C72×C132
C2×C3×C7×D913
C2×C32×C7×D137
C2×C32×D917
C2×C32×C7×D713