Finite Group Databasebeta

← #44568923

Subgroups — #44568923

Order 32340.

400 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 97 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×C5⋊(C7⋊D77)C211yesmaximal, characteristic, complemented
2C5×C11×C3⋊(C7⋊D7)C211yesmaximal, characteristic, complemented
3C72×D165C211yesmaximal, characteristic, complemented
4C7⋊D7×D55—31nomaximal, Hall
5C3×C5×C72×C11C2211yescharacteristic, complemented, Hall
6D33⋊(C7⋊D7)—51nomaximal, Hall
7C5⋊(C7⋊D77)D311yescharacteristic, complemented
8C72×D55—31no—
9C5×C11×C7⋊D7—31no—
10D21⋊D55—78nomaximal
11C11×C3⋊(C7⋊D7)D511yescharacteristic, complemented
12C72×D33—51no—
13C3×C7⋊D77—51no—
14D15⋊(C7⋊D7)—111nomaximal, Hall
15C5×C72×C11C2×D311yescharacteristic, complemented, Hall
16C7×D165D718yescomplemented
17C5×C11×D21—78no—
18C3×D385—78no—
19D11×C7⋊D7—151noHall
20C3×C72×C11C2×D511yescharacteristic, complemented, Hall
21D7×D55—218no—
22C72×D15—111no—
23C5×C3⋊(C7⋊D7)D1111yescharacteristic, complemented
24C3×C5⋊(C7⋊D7)—111no—
25C3×C5×C7×C11C2×D718yescomplemented
26C7⋊D77—51no—
27C11×C7⋊D7—31no—
28C72×D11—151no—
29D5×C7⋊D7—331noHall
30D21⋊D11—358no—
31D385—78no—
32C7×D55—38no—
33C5×C11×D7—218no—
34C3×C5×C72C2×D1111yescharacteristic, complemented, Hall
35D3×D55—491noHall
36D3×C7⋊D7—551noHall
37C72×C11D3×D511yescharacteristic, complemented, Hall
38C5⋊(C7⋊D7)—111no—
39C72×D5—331no—
40C5×C7⋊D7—31no—
41C11×D21—78no—
42C7×D33—58no—
43C3×D77—358no—
44D15⋊D7—778no—
45C5×C7×C11D3×D718yescomplemented
46D165C7⋊D711yescharacteristic, complemented
47C5×D3×C11—491no—
48C3×D55—491no—
49D7×D11—1058no—
50C3⋊(C7⋊D7)D5511yescharacteristic, complemented
51D3×C72—551no—
52C3×C7⋊D7—551no—
53C5×C72D3×D1111yescharacteristic, complemented, Hall
54C3×C7×C11D5×D718yescomplemented
55C2×D55—1471noHall
56C7×D15—118no—
57C5×D21—78no—
58C3×D35—778no—
59C2×C7⋊D7—1651noHall
60C3×C5×C11C2×C7⋊D711yescharacteristic, complemented, Hall
61D77—358no—
62C7×D11—158no—
63C11×D7—218no—
64C3×C72C2×D5511yescharacteristic, complemented, Hall
65D5×D7—2318no—
66D3×D11—2451noHall
67C2×C5×C11—1471no—
68D55—31no—
69D55—491no—
70C3×C5×C7D7×D1118yescomplemented
71C2×C72—1651no—
72C7⋊D7—31no—
73C7⋊D7—551no—
74D3×D7—3858no—
75C7×C11D15⋊D718yescomplemented
76D35—778no—
77C5×D7—218no—
78C7×D5—338no—
79D33—51no—
80C3×D11—2451no—
81D3×C11—491no—
82D3×D5—5391noHall
83C5×C11D3×C7⋊D711yescharacteristic, complemented, Hall
84C72D3×D5511yescharacteristic, complemented, Sylow
85C2×D11—7351noHall
86D21—78no—
87C3×D7—3858no—
88D3×C7—558no—
89C5×C7D21⋊D1118yescomplemented
90C3×C11D5×C7⋊D711yescharacteristic, complemented, Hall
91D15—111no—
92C3×D5—5391no—
93C5×D3—491no—
94C2×D7—11558no—
95C2×C11—1471no—
96D11—151no—
97D11—2451no—
98C3×C7D7×D5518yescomplemented
99C2×D5—16171noHall
100C3×C5D11×C7⋊D711yescharacteristic, complemented, Hall
101C2×C7—1658no—
102D7—218no—
103D7—3858no—
104C2×D3—26951noHall
105C11D15⋊(C7⋊D7)11yescharacteristic, complemented, Sylow
106C2×C5—1471no—
107D5—5391no—
108D5—331no—
109C7D21⋊D5518yescomplemented
110C2×C3—26951no—
111D3—491no—
112D3—551no—
113C5D33⋊(C7⋊D7)11yescharacteristic, complemented, Sylow
114C22—80851noSylow
115C3C7⋊D7×D5511yescharacteristic, complemented, Sylow
116C2—26951no—
117C2—1471no—
118C2—1651no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C72×C11C22
LCSG ▷ C3×C5×C72×C11
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C5⋊(C7⋊D77)C2semidirect
2. C5×C11×C3⋊(C7⋊D7)C2semidirect
3. C72×D165C2semidirect
5. C3×C5×C72×C11C22semidirect
7. C5⋊(C7⋊D77)D3semidirect
11. C11×C3⋊(C7⋊D7)D5semidirect
15. C5×C72×C11C2×D3semidirect
16. C7×D165D7semidirect
20. C3×C72×C11C2×D5semidirect
23. C5×C3⋊(C7⋊D7)D11semidirect
25. C3×C5×C7×C11C2×D7semidirect
34. C3×C5×C72C2×D11semidirect
37. C72×C11D3×D5semidirect
45. C5×C7×C11D3×D7semidirect
46. D165C7⋊D7semidirect
50. C3⋊(C7⋊D7)D55semidirect
53. C5×C72D3×D11semidirect
54. C3×C7×C11D5×D7semidirect
60. C3×C5×C11C2×C7⋊D7semidirect
64. C3×C72C2×D55semidirect
70. C3×C5×C7D7×D11semidirect
75. C7×C11D15⋊D7semidirect
83. C5×C11D3×C7⋊D7semidirect
84. C72D3×D55semidirect
89. C5×C7D21⋊D11semidirect
90. C3×C11D5×C7⋊D7semidirect
98. C3×C7D7×D55semidirect
100. C3×C5D11×C7⋊D7semidirect
105. C11D15⋊(C7⋊D7)semidirect
109. C7D21⋊D55semidirect
113. C5D33⋊(C7⋊D7)semidirect
115. C3C7⋊D7×D55semidirect

Maximal subgroups

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

subgroupindex
C3×C5⋊(C7⋊D77)2
C5×C11×C3⋊(C7⋊D7)2
C72×D1652
C7⋊D7×D553
D33⋊(C7⋊D7)5
D21⋊D557
D15⋊(C7⋊D7)11