Finite Group Databasebeta

← #49141669

Subgroups — #49141669

Order 36540.

240 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 61 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×D1015C211yesmaximal, characteristic, complemented
2C5×C3⋊D609C211yesmaximal, characteristic, complemented
3C7×C29×C3⋊D15C211yesmaximal, characteristic, complemented
4D15⋊D203—34nomaximal
5C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
6C3⋊D3×D203—51nomaximal, Hall
7C7×C29×D15—34no—
8C5×D609—34no—
9C3×D1015D314yescomplemented
10D145⋊(C3⋊D3)—71nomaximal, Hall
11D5×D203—91noHall
12C3⋊D609D511yescharacteristic, complemented
13C7×C3⋊D3×C29—51no—
14C32×D203—51no—
15C3×C5×C7×C29C2×D314yescomplemented
16C29×C3⋊D15D711yescharacteristic, complemented
17C5×C3⋊D87—71no—
18C32×D145—71no—
19D3×D203—154no—
20D1015C3⋊D311yescharacteristic, complemented
21C7×D5×C29—91no—
22C5×D203—91no—
23C32×C7×C29C2×D511yescharacteristic, complemented, Hall
24D15⋊D29—214no—
25C32×C5×C29C2×D711yescharacteristic, complemented, Hall
26D35⋊(C3⋊D3)—291nomaximal, Hall
27D609—34no—
28D3×C7×C29—154no—
29C3×D203—54no—
30C3⋊D3×D29—351noHall
31C5×C7×C29C2×C3⋊D311yescharacteristic, complemented, Hall
32C29×D15—34no—
33C5×D87—214no—
34C3×D145—74no—
35C2×D203—451noHall
36C7×C3⋊D15D2911yescharacteristic, complemented
37C5×C3⋊D21—291no—
38C32×D35—291no—
39C3×C7×C29D3×D514yescomplemented
40D5×D29—631noHall
41C3⋊D87—71no—
42C3⋊D3×C29—51no—
43C32×D29—351no—
44C3×C5×C29D3×D714yescomplemented
45D15⋊D7—874no—
46C2×C7×C29—451no—
47D203—51no—
48D203—91no—
49D3×D29—1054no—
50C32×C5×C7C2×D2911yescharacteristic, complemented, Hall
51D145—71no—
52C5×D29—631no—
53D5×C29—91no—
54C32×C29D5×D711yescharacteristic, complemented, Hall
55D7×C3⋊D3—1451noHall
56C7×D15—34no—
57C5×D21—874no—
58C3×D35—294no—
59C7×C29D5×C3⋊D311yescharacteristic, complemented, Hall
60D5×C3⋊D3—2031noHall
61D87—214no—
62C3×D29—354no—
63D3×C29—154no—
64C5×C29D7×C3⋊D311yescharacteristic, complemented, Hall
65D5×D7—2611noHall
66C3⋊D21—291no—
67C7×C3⋊D3—51no—
68C32×D7—1451no—
69C2×D29—3151noHall
70C3×C5×C7D3×D2914yescomplemented
71C3⋊D15D20311yescharacteristic, complemented
72C5×C3⋊D3—2031no—
73C32×D5—2031no—
74C3×C29D15⋊D714yescomplemented
75D3×D7—4354no—
76D35—291no—
77C5×D7—2611no—
78C7×D5—91no—
79C32×C7D5×D2911yescharacteristic, complemented, Hall
80D3×D5—6094no—
81C2×C29—451no—
82D29—351no—
83D29—631no—
84C32×C5C2×D20311yescharacteristic, complemented, Hall
85D21—874no—
86C3×D7—1454no—
87D3×C7—154no—
88C2×C3⋊D3—10151noHall
89C5×C7C3⋊D3×D2911yescharacteristic, complemented, Hall
90D15—34no—
91C3×D5—2034no—
92C5×D3—6094no—
93C29D35⋊(C3⋊D3)11yescharacteristic, complemented, Sylow
94C2×D7—13051noHall
95C3×C7D15⋊D2914yescomplemented
96C2×D5—18271noHall
97C2×C32—10151no—
98C3⋊D3—51no—
99C3⋊D3—2031no—
100C3×C5D3×D20314yescomplemented
101C2×C7—451no—
102D7—2611no—
103D7—1451no—
104C2×D3—30454no—
105C2×C5—18271no—
106D5—91no—
107D5—2031no—
108C32D5×D20311yescharacteristic, complemented, Sylow
109C7D145⋊(C3⋊D3)11yescharacteristic, complemented, Sylow
110C2×C3—10154no—
111D3—154no—
112D3—6094no—
113C5C3⋊D3×D20311yescharacteristic, complemented, Sylow
114C22—91351noSylow
115C3D15⋊D20314yescomplemented
116C2—18271no—
117C2—451no—
118C2—10151no—
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. C32×D1015C2semidirect
2. C5×C3⋊D609C2semidirect
3. C7×C29×C3⋊D15C2semidirect
5. C32×C5×C7×C29C22semidirect
9. C3×D1015D3semidirect
12. C3⋊D609D5semidirect
15. C3×C5×C7×C29C2×D3semidirect
16. C29×C3⋊D15D7semidirect
20. D1015C3⋊D3semidirect
23. C32×C7×C29C2×D5semidirect
25. C32×C5×C29C2×D7semidirect
31. C5×C7×C29C2×C3⋊D3semidirect
36. C7×C3⋊D15D29semidirect
39. C3×C7×C29D3×D5semidirect
44. C3×C5×C29D3×D7semidirect
50. C32×C5×C7C2×D29semidirect
54. C32×C29D5×D7semidirect
59. C7×C29D5×C3⋊D3semidirect
64. C5×C29D7×C3⋊D3semidirect
70. C3×C5×C7D3×D29semidirect
71. C3⋊D15D203semidirect
74. C3×C29D15⋊D7semidirect
79. C32×C7D5×D29semidirect
84. C32×C5C2×D203semidirect
89. C5×C7C3⋊D3×D29semidirect
93. C29D35⋊(C3⋊D3)semidirect
95. C3×C7D15⋊D29semidirect
100. C3×C5D3×D203semidirect
108. C32D5×D203semidirect
109. C7D145⋊(C3⋊D3)semidirect
113. C5C3⋊D3×D203semidirect
115. C3D15⋊D203semidirect

Maximal subgroups

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

subgroupindex
C32×D10152
C5×C3⋊D6092
C7×C29×C3⋊D152
D15⋊D2033
C3⋊D3×D2035
D145⋊(C3⋊D3)7
D35⋊(C3⋊D3)29