Finite Group Databasebeta

← (C3⋊D3)⋊D1015 #49141629

Subgroups — (C3⋊D3)⋊D1015 #49141629

Order 36540.

176 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 45 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×D3045C212yesmaximal, complemented
2C5×C7×C3⋊D3×C29C211yesmaximal, characteristic, complemented
3D3×D1015—32nomaximal
4C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
5(C3⋊D3)⋊D203—51nomaximal, Hall
6D3045D312yescomplemented
7C5×D3×C7×C29—32no—
8C5×D3×C7×C29—61no—
9C3×D1015—32no—
10(C3⋊D3)⋊D145—71nomaximal, Hall
11C2×D1015—91noHall
12C7×C3⋊D3×C29D511yescharacteristic, complemented
13C3×D609—52no—
14C3×C5×C7×C29—21no—
15C3×C5×C7×C29C2×D312yescomplemented
16C5×C3⋊D3×C29D711yescharacteristic, complemented
17C3×D435—72no—
18D3×D203—152no—
19D1015—32no—
20C2×C5×C7×C29—91no—
21C32×C7×C29C2×D511yescharacteristic, complemented, Hall
22D3×D145—212no—
23C32×C5×C29C2×D711yescharacteristic, complemented, Hall
24(C3⋊D3)⋊D35—291nomaximal, Hall
25D609—52no—
26D3×C7×C29—32no—
27D3×C7×C29—61no—
28C3×D203—152no—
29(C3⋊D3)⋊D29—351noHall
30C5×C7×C29D3211yescharacteristic, complemented, Hall
31D435—72no—
32C5×D3×C29—32no—
33C5×D3×C29—61no—
34C3×D145—212no—
35C2×D203—451noHall
36C5×C7×C3⋊D3D2911yescharacteristic, complemented
37C3×D105—292no—
38C3×C7×C29—21no—
39C3×C7×C29D3×D512yescomplemented
40C2×D145—631noHall
41C3⋊D3×C29D3511yescharacteristic, complemented
42C3×D87—352no—
43C3×C5×C29—21no—
44C3×C5×C29D3×D712yescomplemented
45D3×D35—872no—
46C2×C7×C29—91no—
47D203—152no—
48D3×D29—1052no—
49C32×C5×C7C2×D2911yescharacteristic, complemented, Hall
50C2×C5×C29—91no—
51D145—212no—
52C32×C29C2×D3511yescharacteristic, complemented, Hall
53(C3⋊D3)⋊D7—1451noHall
54D105—292no—
55C5×D3×C7—32no—
56C5×D3×C7—61no—
57C3×D35—872no—
58C7×C29(C3⋊D3)⋊D511yescharacteristic, complemented, Hall
59(C3⋊D3)⋊D5—2031noHall
60D87—352no—
61C3×D29—1052no—
62D3×C29—32no—
63D3×C29—61no—
64C5×C29(C3⋊D3)⋊D711yescharacteristic, complemented, Hall
65C2×D35—2611noHall
66C7×C3⋊D3D14511yescharacteristic, complemented
67C3×D21—1452no—
68C2×D29—3151noHall
69C3×C5×C7—21no—
70C3×C5×C7D3×D2912yescomplemented
71C5×C3⋊D3D20311yescharacteristic, complemented
72C3×D15—2032no—
73C3×C29—21no—
74C3×C29D3×D3512yescomplemented
75D3×D7—4352no—
76C2×C5×C7—91no—
77D35—872no—
78C32×C7C2×D14511yescharacteristic, complemented, Hall
79D3×D5—6092no—
80C2×C29—91no—
81D29—1052no—
82C32×C5C2×D20311yescharacteristic, complemented, Hall
83D21—1452no—
84C3×D7—4352no—
85D3×C7—32no—
86D3×C7—61no—
87D32—10151noHall
88C5×C7(C3⋊D3)⋊D2911yescharacteristic, complemented, Hall
89D15—2032no—
90C3×D5—6092no—
91C5×D3—32no—
92C5×D3—61no—
93C29(C3⋊D3)⋊D3511yescharacteristic, complemented, Sylow
94C2×D7—13051noHall
95C3×C7—21no—
96C3×C7D3×D14512yescomplemented
97C2×D5—18271noHall
98C3⋊D3D101511yescharacteristic, complemented
99C3×D3—10152no—
100C3×C5—21no—
101C3×C5D3×D20312yescomplemented
102C2×C7—91no—
103D7—4352no—
104C2×D3—30452no—
105C2×C5—91no—
106D5—6092no—
107C32C2×D101511yescharacteristic, complemented, Sylow
108C7(C3⋊D3)⋊D14511yescharacteristic, complemented, Sylow
109C2×C3—30452no—
110D3—32no—
111D3—61no—
112D3—10152no—
113C5(C3⋊D3)⋊D20311yescharacteristic, complemented, Sylow
114C22—91351noSylow
115C3—21no—
116C3D3×D101512yescomplemented
117C2—91no—
118C2—30452no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C7×C29C22
LCSG ▷ C32×C5×C7×C29
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×D3045C2semidirect
2. C5×C7×C3⋊D3×C29C2semidirect
4. C32×C5×C7×C29C22semidirect
6. D3045D3semidirect
12. C7×C3⋊D3×C29D5semidirect
15. C3×C5×C7×C29C2×D3semidirect
16. C5×C3⋊D3×C29D7semidirect
21. C32×C7×C29C2×D5semidirect
23. C32×C5×C29C2×D7semidirect
30. C5×C7×C29D32semidirect
36. C5×C7×C3⋊D3D29semidirect
39. C3×C7×C29D3×D5semidirect
41. C3⋊D3×C29D35semidirect
44. C3×C5×C29D3×D7semidirect
49. C32×C5×C7C2×D29semidirect
52. C32×C29C2×D35semidirect
58. C7×C29(C3⋊D3)⋊D5semidirect
64. C5×C29(C3⋊D3)⋊D7semidirect
66. C7×C3⋊D3D145semidirect
70. C3×C5×C7D3×D29semidirect
71. C5×C3⋊D3D203semidirect
74. C3×C29D3×D35semidirect
78. C32×C7C2×D145semidirect
82. C32×C5C2×D203semidirect
88. C5×C7(C3⋊D3)⋊D29semidirect
93. C29(C3⋊D3)⋊D35semidirect
96. C3×C7D3×D145semidirect
98. C3⋊D3D1015semidirect
101. C3×C5D3×D203semidirect
107. C32C2×D1015semidirect
108. C7(C3⋊D3)⋊D145semidirect
113. C5(C3⋊D3)⋊D203semidirect
116. C3D3×D1015semidirect

Maximal subgroups

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

subgroupindex
C3×D30452
C5×C7×C3⋊D3×C292
D3×D10153
(C3⋊D3)⋊D2035
(C3⋊D3)⋊D1457
(C3⋊D3)⋊D3529