Finite Group Databasebeta

← #37528719

Subgroups — #37528719

Order 23100.

320 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 79 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×C5⋊D35C211yesmaximal, characteristic, complemented
2C52×D231C211yesmaximal, characteristic, complemented
3C7×C3⋊(C5⋊D55)C211yesmaximal, characteristic, complemented
4D77⋊(C5⋊D5)—31nomaximal, Hall
5C3×C52×C7×C11C2211yescharacteristic, complemented, Hall
6D35⋊D33—56nomaximal
7C11×C5⋊D35D311yescharacteristic, complemented
8C7×C5⋊D55—31no—
9C52×D77—31no—
10C5⋊D5×D33—71nomaximal, Hall
11C7×D165—56no—
12C5×D231D516yescomplemented
13C3×C11×D35—56no—
14D21⋊(C5⋊D5)—111nomaximal, Hall
15C52×C7×C11C2×D311yescharacteristic, complemented, Hall
16C3⋊(C5⋊D55)D711yescharacteristic, complemented
17C52×D33—71no—
18C3×C11×C5⋊D5—71no—
19D35⋊D11—156no—
20C3×C5×C7×C11C2×D516yescomplemented
21D11×C5⋊D5—211noHall
22C7×C3⋊(C5⋊D5)—111no—
23C52×D21—111no—
24C3×C5⋊D35D1111yescharacteristic, complemented
25D7×D33—251noHall
26C3×C52×C11C2×D711yescharacteristic, complemented, Hall
27C11×D35—56no—
28C7×D55—156no—
29C5×D77—36no—
30D7×C5⋊D5—331noHall
31D5×D33—356no—
32C5⋊D55—31no—
33C11×C5⋊D5—71no—
34C52×D11—211no—
35C3×C52×C7C2×D1111yescharacteristic, complemented, Hall
36D231C5⋊D511yescharacteristic, complemented
37C7×D33—251no—
38C3×C11×D7—251no—
39D15⋊D7—556no—
40C5×C7×C11D3×D516yescomplemented
41C5⋊D35D3311yescharacteristic, complemented
42C7×C5⋊D5—331no—
43C52×D7—331no—
44D165—56no—
45C5×D33—76no—
46C3×D5×C11—356no—
47D7×D11—751noHall
48D3×C5⋊D5—771noHall
49C52×C11D3×D711yescharacteristic, complemented, Hall
50C3×C7×C11C2×C5⋊D511yescharacteristic, complemented, Hall
51D5×D11—1056no—
52C7×D15—556no—
53C5×D21—116no—
54C3×D35—56no—
55C52×C7C2×D3311yescharacteristic, complemented, Hall
56C3×C5×C11D5×D716yescomplemented
57D77—31no—
58C7×D11—751no—
59C11×D7—251no—
60C3⋊(C5⋊D5)—111no—
61C52×D3—771no—
62C3×C5⋊D5—71no—
63D5×D7—1656no—
64C2×D33—1751noHall
65D55—156no—
66C5×D11—216no—
67D5×C11—356no—
68C3×C5×C7D5×D1116yescomplemented
69C2×C5⋊D5—2311noHall
70D3×D7—2751noHall
71C7×C11D3×C5⋊D511yescharacteristic, complemented, Hall
72C3×C52D7×D1111yescharacteristic, complemented, Hall
73D35—56no—
74C5×D7—336no—
75C7×D5—1656no—
76C2×C3×C11—1751no—
77D33—71no—
78D33—251no—
79D3×D5—3856no—
80C5×C11D15⋊D716yescomplemented
81C2×C52—2311no—
82C5⋊D5—71no—
83C5⋊D5—331no—
84C2×D11—5251noHall
85D21—111no—
86C3×D7—251no—
87D3×C7—2751no—
88C5×C7D5×D3316yescomplemented
89C3×C11D7×C5⋊D511yescharacteristic, complemented, Hall
90D15—556no—
91C3×D5—356no—
92C5×D3—776no—
93C2×D7—8251noHall
94C52D7×D3311yescharacteristic, complemented, Sylow
95C2×C11—1751no—
96D11—211no—
97D11—751no—
98C3×C7D11×C5⋊D511yescharacteristic, complemented, Hall
99C2×D5—11556no—
100C3×C5D35⋊D1116yescomplemented
101C2×C7—8251no—
102D7—251no—
103D7—331no—
104C2×D3—19251noHall
105C11D21⋊(C5⋊D5)11yescharacteristic, complemented, Sylow
106C2×C5—2316no—
107D5—356no—
108D5—1656no—
109C7C5⋊D5×D3311yescharacteristic, complemented, Sylow
110C2×C3—1751no—
111D3—2751no—
112D3—771no—
113C5D35⋊D3316yescomplemented
114C22—57751noSylow
115C3D77⋊(C5⋊D5)11yescharacteristic, complemented, Sylow
116C2—8251no—
117C2—1751no—
118C2—2311no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C52×C7×C11C22
LCSG ▷ C3×C52×C7×C11
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C11×C5⋊D35C2semidirect
2. C52×D231C2semidirect
3. C7×C3⋊(C5⋊D55)C2semidirect
5. C3×C52×C7×C11C22semidirect
7. C11×C5⋊D35D3semidirect
12. C5×D231D5semidirect
15. C52×C7×C11C2×D3semidirect
16. C3⋊(C5⋊D55)D7semidirect
20. C3×C5×C7×C11C2×D5semidirect
24. C3×C5⋊D35D11semidirect
26. C3×C52×C11C2×D7semidirect
35. C3×C52×C7C2×D11semidirect
36. D231C5⋊D5semidirect
40. C5×C7×C11D3×D5semidirect
41. C5⋊D35D33semidirect
49. C52×C11D3×D7semidirect
50. C3×C7×C11C2×C5⋊D5semidirect
55. C52×C7C2×D33semidirect
56. C3×C5×C11D5×D7semidirect
68. C3×C5×C7D5×D11semidirect
71. C7×C11D3×C5⋊D5semidirect
72. C3×C52D7×D11semidirect
80. C5×C11D15⋊D7semidirect
88. C5×C7D5×D33semidirect
89. C3×C11D7×C5⋊D5semidirect
94. C52D7×D33semidirect
98. C3×C7D11×C5⋊D5semidirect
100. C3×C5D35⋊D11semidirect
105. C11D21⋊(C5⋊D5)semidirect
109. C7C5⋊D5×D33semidirect
113. C5D35⋊D33semidirect
115. C3D77⋊(C5⋊D5)semidirect

Maximal subgroups

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

subgroupindex
C3×C11×C5⋊D352
C52×D2312
C7×C3⋊(C5⋊D55)2
D77⋊(C5⋊D5)3
D35⋊D335
C5⋊D5×D337
D21⋊(C5⋊D5)11