Finite Group Databasebeta

← #36345344

Subgroups — #36345344

Order 21780.

296 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 43 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×C11×D165C212yesmaximal, complemented
2C5×C3⋊(C3⋊(C11⋊D11))C211yesmaximal, characteristic, complemented
3D55⋊D33—32nomaximal
4C32×C5×C112C2211yescharacteristic, complemented, Hall
5D332—51nomaximal, Hall
6C11×D165D312yescomplemented
7C5×C3⋊(C11⋊D11)—32no—
8C5×C3⋊(C11⋊D11)—61no—
9C3×C11×D55—32no—
10D55⋊D11—91noHall
11C3⋊(C3⋊(C11⋊D11))D511yescharacteristic, complemented
12C3×C11×D33—52no—
13D15⋊D33—112nomaximal
14C3×C5×C112—21no—
15C3×C5×C112C2×D312yescomplemented
16D11×D33—152no—
17C11×D55—32no—
18C5×C11⋊D11—91no—
19C32×C112C2×D511yescharacteristic, complemented, Hall
20C5×C3⋊D33—112no—
21C5×C3⋊D33—225no—
22C3×D165D1112yescomplemented
23C3×C11×D15—112no—
24C3⋊(C11⋊D11)—32no—
25C3⋊(C11⋊D11)—61no—
26C11×D33—52no—
27C3×C11×D11—152no—
28D15⋊D11—332no—
29D5×D33—332no—
30C5×C112D3211yescharacteristic, complemented, Hall
31C32×C5×C11—25no—
32C32×C5×C11C2×D1112yescomplemented
33D112—451noHall
34D3×D33—552no—
35C3×C112—21no—
36C3×C112D3×D512yescomplemented
37D165D3312yescomplemented
38C11×D15—112no—
39C5×D33—332no—
40C5×D33—332no—
41C5×D33—6610no—
42C5×D33—662no—
43C5×D33—6610no—
44C3×D55—32no—
45C3×D5×C11—332no—
46C11⋊D11—91no—
47C11×D11—152no—
48D5×D11—992no—
49C3⋊D33—112no—
50C3⋊D33—225no—
51C3×D33—52no—
52C3×D3×C11—552no—
53(C3⋊D3)⋊D5—1211noHall
54C3×C5×C11—210no—
55C3×C5×C11—210no—
56C3×C5×C11—22no—
57C3×C5×C11D3×D1112yescomplemented
58C3×C5×C11C2×D3312yescomplemented
59C2×D33—1652no—
60D3×D11—1652no—
61C112(C3⋊D3)⋊D511yescharacteristic, complemented, Sylow
62D55—32no—
63C5×D11—992no—
64C5×D11—1985no—
65D5×C11—332no—
66C32×C11—25no—
67C32×C11D5×D1112yescomplemented
68C5×C3⋊D3—1211no—
69C3×D15—112no—
70C2×C3×C11—1652no—
71D33—52no—
72D33—332no—
73D33—332no—
74D33—6610no—
75D33—662no—
76D33—6610no—
77C3×D11—152no—
78D3×C11—552no—
79D3×D5—3632no—
80C5×C11—25no—
81C5×C11D3×D3312yescomplemented
82C32×C5D11211yescharacteristic, complemented, Hall
83C2×D11—4952no—
84D32—6051noHall
85C3×C11—210no—
86C3×C11—22no—
87C3×C11—210no—
88C3×C11D5×D3312yescomplemented
89C3×C11D15⋊D1112yescomplemented
90D15—112no—
91C3×D5—332no—
92C5×D3—3632no—
93C5×D3—7261no—
94C2×C11—1652no—
95D11—152no—
96D11—992no—
97D11—1985no—
98C2×D5—10891noHall
99C3⋊D3—1211no—
100C3×D3—552no—
101C3×C5—21no—
102C3×C5D11×D3312yescomplemented
103C2×D3—18152no—
104C11—25no—
105C11D15⋊D3312yescomplemented
106C2×C5—10891no—
107D5—332no—
108C32D55⋊D1111yescharacteristic, complemented, Sylow
109C2×C3—1652no—
110D3—552no—
111D3—3632no—
112D3—7261no—
113C5D33211yescharacteristic, complemented, Sylow
114C22—54451noSylow
115C3—21no—
116C3D55⋊D3312yescomplemented
117C2—10891no—
118C2—1652no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C112C22
LCSG ▷ C32×C5×C112
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C11×D165C2semidirect
2. C5×C3⋊(C3⋊(C11⋊D11))C2semidirect
4. C32×C5×C112C22semidirect
6. C11×D165D3semidirect
11. C3⋊(C3⋊(C11⋊D11))D5semidirect
15. C3×C5×C112C2×D3semidirect
19. C32×C112C2×D5semidirect
22. C3×D165D11semidirect
30. C5×C112D32semidirect
32. C32×C5×C11C2×D11semidirect
36. C3×C112D3×D5semidirect
37. D165D33semidirect
57. C3×C5×C11D3×D11semidirect
58. C3×C5×C11C2×D33semidirect
61. C112(C3⋊D3)⋊D5semidirect
67. C32×C11D5×D11semidirect
81. C5×C11D3×D33semidirect
82. C32×C5D112semidirect
88. C3×C11D5×D33semidirect
89. C3×C11D15⋊D11semidirect
102. C3×C5D11×D33semidirect
105. C11D15⋊D33semidirect
108. C32D55⋊D11semidirect
113. C5D332semidirect
116. C3D55⋊D33semidirect

Maximal subgroups

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

subgroupindex
C3×C11×D1652
C5×C3⋊(C3⋊(C11⋊D11))2
D55⋊D333
D3325
D15⋊D3311