Finite Group Databasebeta

← C7×(C3⋊D3)⋊D145 #49141622

Subgroups — C7×(C3⋊D3)⋊D145 #49141622

Order 36540.

176 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 50 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
1C3×C7×D435C212yesmaximal, complemented
2C5×C7×C3⋊D3×C29C211yesmaximal, characteristic, complemented
3D3×C7×D145—32nomaximal
4C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
5C7×(C3⋊D3)⋊D29—51nomaximal, Hall
6C7×D435D312yescomplemented
7C5×D3×C7×C29—32no—
8C5×D3×C7×C29—61no—
9C3×C7×D145—32no—
10(C3⋊D3)⋊D145C711yesmaximal, characteristic, direct product factor, Hall
11C2×C7×D145—91noHall
12C7×C3⋊D3×C29D511yescharacteristic, complemented
13C3×C7×D87—52no—
14C3×C5×C7×C29—21no—
15C3×C5×C7×C29C2×D312yescomplemented
16C5×C3⋊D3×C29C2×C711yescharacteristic, complemented
17C3×D435C2×C712yescomplemented
18D3×C7×D29—152no—
19C7×D145—32no—
20C2×C5×C7×C29—91no—
21C32×C7×C29C2×D511yescharacteristic, complemented, Hall
22D3×D145—32no—
23C32×C5×C29C22×C711yescharacteristic, complemented, Hall
24C7×(C3⋊D3)⋊D5—291nomaximal, Hall
25C7×D87—52no—
26D3×C7×C29—32no—
27D3×C7×C29—61no—
28C3×C7×D29—152no—
29(C3⋊D3)⋊D29—51noHall
30C5×C7×C29D3211yescharacteristic, complemented, Hall
31D435D3×C712yescomplemented
32C5×D3×C29—32no—
33C5×D3×C29—61no—
34C3×D145—32no—
35C2×C7×D29—451noHall
36C5×C7×C3⋊D3D2911yescharacteristic, complemented
37C3×C7×D15—292no—
38C3×C7×C29—21no—
39C3×C7×C29D3×D512yescomplemented
40C2×D145—91noHall
41C3⋊D3×C29C7×D511yescharacteristic, complemented
42C3×D87—52no—
43C3×C5×C29—21no—
44C3×C5×C29C2×D3×C712yescomplemented
45D3×C7×D5—872no—
46C2×C7×C29—91no—
47C7×D29—152no—
48D3×D29—152no—
49C32×C5×C7C2×D2911yescharacteristic, complemented, Hall
50C2×C5×C29—91no—
51D145—32no—
52C32×C29C2×C7×D511yescharacteristic, complemented, Hall
53D32×C7—1451noHall
54C7×D15—292no—
55C5×D3×C7—32no—
56C5×D3×C7—61no—
57C3×C7×D5—872no—
58C7×C29(C3⋊D3)⋊D511yescharacteristic, complemented, Hall
59(C3⋊D3)⋊D5—291noHall
60D87—52no—
61C3×D29—152no—
62D3×C29—32no—
63D3×C29—61no—
64C5×C29D32×C711yescharacteristic, complemented, Hall
65C2×C7×D5—2611noHall
66C7×C3⋊D3D14511yescharacteristic, complemented
67C3×D3×C7—1452no—
68C2×D29—451noHall
69C3×C5×C7—21no—
70C3×C5×C7D3×D2912yescomplemented
71C5×C3⋊D3C7×D2911yescharacteristic, complemented
72C3×D15—292no—
73C3×C29—21no—
74C3×C29D3×C7×D512yescomplemented
75C2×D3×C7—4352no—
76C2×C5×C7—91no—
77C7×D5—872no—
78C32×C7C2×D14511yescharacteristic, complemented, Hall
79D3×D5—872no—
80C2×C29—91no—
81D29—152no—
82C32×C5C2×C7×D2911yescharacteristic, complemented, Hall
83C2×C3×C7—4352no—
84D3×C7—32no—
85D3×C7—61no—
86D3×C7—1452no—
87D32—1451noHall
88C5×C7(C3⋊D3)⋊D2911yescharacteristic, complemented, Hall
89D15—292no—
90C3×D5—872no—
91C5×D3—32no—
92C5×D3—61no—
93C29C7×(C3⋊D3)⋊D511yescharacteristic, complemented, Sylow
94C22×C7—13051noHall
95C3×C7—21no—
96C3×C7D3×D14512yescomplemented
97C2×D5—2611noHall
98C3⋊D3C7×D14511yescharacteristic, complemented
99C3×D3—1452no—
100C3×C5—21no—
101C3×C5D3×C7×D2912yescomplemented
102C2×C7—91no—
103C2×C7—4352no—
104C2×D3—4352no—
105C2×C5—91no—
106D5—872no—
107C32C2×C7×D14511yescharacteristic, complemented, Sylow
108C7(C3⋊D3)⋊D14511yescharacteristic, direct product factor, Sylow
109C2×C3—4352no—
110D3—32no—
111D3—61no—
112D3—1452no—
113C5C7×(C3⋊D3)⋊D2911yescharacteristic, complemented, Sylow
114C22—13051noSylow
115C3—21no—
116C3D3×C7×D14512yescomplemented
117C2—91no—
118C2—4352no—
subgroupG/H
center, hypercenterC7(C3⋊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. C3×C7×D435C2semidirect
2. C5×C7×C3⋊D3×C29C2semidirect
4. C32×C5×C7×C29C22semidirect
6. C7×D435D3semidirect
10. (C3⋊D3)⋊D145C7direct (N × H)
12. C7×C3⋊D3×C29D5semidirect
15. C3×C5×C7×C29C2×D3semidirect
16. C5×C3⋊D3×C29C2×C7semidirect
17. C3×D435C2×C7semidirect
21. C32×C7×C29C2×D5semidirect
23. C32×C5×C29C22×C7semidirect
30. C5×C7×C29D32semidirect
31. D435D3×C7semidirect
36. C5×C7×C3⋊D3D29semidirect
39. C3×C7×C29D3×D5semidirect
41. C3⋊D3×C29C7×D5semidirect
44. C3×C5×C29C2×D3×C7semidirect
49. C32×C5×C7C2×D29semidirect
52. C32×C29C2×C7×D5semidirect
58. C7×C29(C3⋊D3)⋊D5semidirect
64. C5×C29D32×C7semidirect
66. C7×C3⋊D3D145semidirect
70. C3×C5×C7D3×D29semidirect
71. C5×C3⋊D3C7×D29semidirect
74. C3×C29D3×C7×D5semidirect
78. C32×C7C2×D145semidirect
82. C32×C5C2×C7×D29semidirect
88. C5×C7(C3⋊D3)⋊D29semidirect
93. C29C7×(C3⋊D3)⋊D5semidirect
96. C3×C7D3×D145semidirect
98. C3⋊D3C7×D145semidirect
101. C3×C5D3×C7×D29semidirect
107. C32C2×C7×D145semidirect
108. C7(C3⋊D3)⋊D145direct (N × H)
113. C5C7×(C3⋊D3)⋊D29semidirect
116. C3D3×C7×D145semidirect

Maximal subgroups

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

subgroupindex
C3×C7×D4352
C5×C7×C3⋊D3×C292
D3×C7×D1453
C7×(C3⋊D3)⋊D295
(C3⋊D3)⋊D1457
C7×(C3⋊D3)⋊D529