Finite Group Databasebeta

← C7×C3⋊D3×D145 #49141656

Subgroups — C7×C3⋊D3×D145 #49141656

Order 36540.

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

normal subgroups only

This group has 240 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
1C32×C7×D145C211yesmaximal, characteristic, complemented
2C5×C7×C3⋊D3×C29C211yesmaximal, characteristic, complemented
3C7×C3⋊D435C211yesmaximal, characteristic, complemented
4D3×C7×D145—34nomaximal
5C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
6C7×C3⋊D3×D29—51nomaximal, Hall
7C7×D435—34no—
8C5×D3×C7×C29—34no—
9C3×C7×D145D314yescomplemented
10C3⋊D3×D145C711yesmaximal, characteristic, direct product factor, Hall
11C2×C7×D145—91noHall
12C7×C3⋊D87—51no—
13C7×C3⋊D3×C29D511yescharacteristic, complemented
14C32×C7×D29—51no—
15C3×C5×C7×C29C2×D314yescomplemented
16C3⋊D435C2×C711yescharacteristic, complemented
17C5×C3⋊D3×C29C2×C711yescharacteristic, complemented
18C32×D145C2×C711yescharacteristic, complemented
19D3×C7×D29—154no—
20C7×D145—91no—
21C7×D145C3⋊D311yescharacteristic, direct product factor
22C2×C5×C7×C29—91no—
23C32×C7×C29C2×D511yescharacteristic, complemented, Hall
24D3×D145—34no—
25C32×C5×C29C22×C711yescharacteristic, complemented, Hall
26C7×D5×C3⋊D3—291nomaximal, Hall
27C7×D87—154no—
28D3×C7×C29—34no—
29C3×C7×D29—54no—
30C3⋊D3×D29—51noHall
31C5×C7×C29C2×C3⋊D311yescharacteristic, complemented, Hall
32D435—34no—
33C5×D3×C29—34no—
34C3×D145D3×C714yescomplemented
35C2×C7×D29—451noHall
36C7×C3⋊D15—291no—
37C5×C7×C3⋊D3D2911yescharacteristic, complemented
38C32×C7×D5—291no—
39C3×C7×C29D3×D514yescomplemented
40C2×D145—91noHall
41C3⋊D87—51no—
42C3⋊D3×C29C7×D511yescharacteristic, complemented
43C32×D29—51no—
44C3×C5×C29C2×D3×C714yescomplemented
45D3×C7×D5—874no—
46C2×C7×C29—91no—
47C7×D29—51no—
48C7×D29—451no—
49D3×D29—154no—
50C32×C5×C7C2×D2911yescharacteristic, complemented, Hall
51C2×C5×C29—91no—
52D145—91no—
53D145C7×C3⋊D311yescharacteristic, direct product factor
54C32×C29C2×C7×D511yescharacteristic, complemented, Hall
55C2×C7×C3⋊D3—1451noHall
56C7×D15—874no—
57C5×D3×C7—34no—
58C3×C7×D5—294no—
59C7×C29D5×C3⋊D311yescharacteristic, complemented, Hall
60D5×C3⋊D3—291noHall
61D87—154no—
62C3×D29—54no—
63D3×C29—34no—
64C5×C29C2×C7×C3⋊D311yescharacteristic, complemented, Hall
65C2×C7×D5—2611noHall
66C2×C32×C7—1451no—
67C7×C3⋊D3—1451no—
68C7×C3⋊D3D14511yescharacteristic, direct product factor
69C2×D29—451noHall
70C3×C5×C7D3×D2914yescomplemented
71C3⋊D15—291no—
72C5×C3⋊D3C7×D2911yescharacteristic, complemented
73C32×D5—291no—
74C3×C29D3×C7×D514yescomplemented
75C2×D3×C7—4354no—
76C2×C5×C7—91no—
77C7×D5—2611no—
78C7×D5—291no—
79C32×C7C2×D14511yescharacteristic, complemented, Hall
80D3×D5—874no—
81C2×C29—91no—
82D29—51no—
83D29—451no—
84C32×C5C2×C7×D2911yescharacteristic, complemented, Hall
85C2×C3×C7—1454no—
86D3×C7—34no—
87D3×C7—4354no—
88C2×C3⋊D3—1451noHall
89C5×C7C3⋊D3×D2911yescharacteristic, complemented, Hall
90D15—874no—
91C3×D5—294no—
92C5×D3—34no—
93C29C7×D5×C3⋊D311yescharacteristic, complemented, Sylow
94C22×C7—13051noHall
95C3×C7D3×D14514yescomplemented
96C2×D5—2611noHall
97C2×C32—1451no—
98C3⋊D3—1451no—
99C3⋊D3C7×D14511yescharacteristic, direct product factor
100C3×C5D3×C7×D2914yescomplemented
101C2×C7—91no—
102C2×C7—13051no—
103C2×C7—1451no—
104C2×D3—4354no—
105C2×C5—91no—
106D5—2611no—
107D5—291no—
108C32C2×C7×D14511yescharacteristic, complemented, Sylow
109C7C3⋊D3×D14511yescharacteristic, direct product factor, Sylow
110C2×C3—1454no—
111D3—34no—
112D3—4354no—
113C5C7×C3⋊D3×D2911yescharacteristic, complemented, Sylow
114C22—13051noSylow
115C3D3×C7×D14514yescomplemented
116C2—91no—
117C2—13051no—
118C2—1451no—
subgroupG/H
center, hypercenterC7C3⋊D3×D145
commutator, cosocle, hypocenterC32×C5×C29C22×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C29C22
LCSG ▷ C32×C5×C29
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C32×C7×D145C2semidirect
2. C5×C7×C3⋊D3×C29C2semidirect
3. C7×C3⋊D435C2semidirect
5. C32×C5×C7×C29C22semidirect
9. C3×C7×D145D3semidirect
10. C3⋊D3×D145C7direct (N × H)
13. C7×C3⋊D3×C29D5semidirect
15. C3×C5×C7×C29C2×D3semidirect
16. C3⋊D435C2×C7semidirect
17. C5×C3⋊D3×C29C2×C7semidirect
18. C32×D145C2×C7semidirect
21. C7×D145C3⋊D3direct (N × H)
23. C32×C7×C29C2×D5semidirect
25. C32×C5×C29C22×C7semidirect
31. C5×C7×C29C2×C3⋊D3semidirect
34. C3×D145D3×C7semidirect
37. C5×C7×C3⋊D3D29semidirect
39. C3×C7×C29D3×D5semidirect
42. C3⋊D3×C29C7×D5semidirect
44. C3×C5×C29C2×D3×C7semidirect
50. C32×C5×C7C2×D29semidirect
53. D145C7×C3⋊D3direct (N × H)
54. C32×C29C2×C7×D5semidirect
59. C7×C29D5×C3⋊D3semidirect
64. C5×C29C2×C7×C3⋊D3semidirect
68. C7×C3⋊D3D145direct (N × H)
70. C3×C5×C7D3×D29semidirect
72. C5×C3⋊D3C7×D29semidirect
74. C3×C29D3×C7×D5semidirect
79. C32×C7C2×D145semidirect
84. C32×C5C2×C7×D29semidirect
89. C5×C7C3⋊D3×D29semidirect
93. C29C7×D5×C3⋊D3semidirect
95. C3×C7D3×D145semidirect
99. C3⋊D3C7×D145direct (N × H)
100. C3×C5D3×C7×D29semidirect
108. C32C2×C7×D145semidirect
109. C7C3⋊D3×D145direct (N × H)
113. C5C7×C3⋊D3×D29semidirect
115. C3D3×C7×D145semidirect

Maximal subgroups

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

subgroupindex
C32×C7×D1452
C5×C7×C3⋊D3×C292
C7×C3⋊D4352
D3×C7×D1453
C7×C3⋊D3×D295
C3⋊D3×D1457
C7×D5×C3⋊D329