Finite Group Databasebeta

← D55⋊(C3⋊(C7⋊D7)) #44568916

Subgroups — D55⋊(C3⋊(C7⋊D7)) #44568916

Order 32340.

400 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 105 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×C72×D55C211yesmaximal, characteristic, complemented
2C5×C3⋊(C7⋊D77)C211yesmaximal, characteristic, complemented
3C11×C3⋊(C5⋊(C7⋊D7))C211yesmaximal, characteristic, complemented
4D55⋊(C7⋊D7)—31nomaximal, Hall
5C3×C5×C72×C11C2211yescharacteristic, complemented, Hall
6D11×C3⋊(C7⋊D7)—51nomaximal, Hall
7C11×C5⋊(C7⋊D7)—31no—
8C72×D55D311yescharacteristic, complemented
9C5×C7⋊D77—31no—
10D55⋊D21—78nomaximal
11C3⋊(C7⋊D77)D511yescharacteristic, complemented
12C11×C3⋊(C7⋊D7)—51no—
13C3×C72×D11—51no—
14D5×C3⋊(C7⋊D7)—111nomaximal, Hall
15C5×C72×C11C2×D311yescharacteristic, complemented, Hall
16C11×D105—78no—
17C5×D231—78no—
18C3×C7×D55D718yescomplemented
19D11×C7⋊D7—151noHall
20C3×C72×C11C2×D511yescharacteristic, complemented, Hall
21D35⋊D11—218no—
22C3⋊(C5⋊(C7⋊D7))D1111yescharacteristic, complemented
23C5×C3⋊(C7⋊D7)—111no—
24C3×C72×D5—111no—
25C3×C5×C7×C11C2×D718yescomplemented
26C7⋊D77—31no—
27C11×C7⋊D7—151no—
28C72×D11—51no—
29D5×C7⋊D7—331noHall
30D11×D21—358no—
31C11×D35—218no—
32C7×D55D2118yescomplemented
33C5×D77—218no—
34C3×C5×C72C2×D1111yescharacteristic, complemented, Hall
35D15⋊D11—491noHall
36C2×C3⋊(C7⋊D7)—551noHall
37C72×C11D3×D511yescharacteristic, complemented, Hall
38C5⋊(C7⋊D7)—31no—
39C72×D5—111no—
40C5×C7⋊D7—331no—
41D231—78no—
42C11×D21—358no—
43C3×C7×D11—58no—
44D5×D21—778no—
45C5×C7×C11C2×D2118yescomplemented
46C11×D15—491no—
47C5×D33—491no—
48C3×D55C7⋊D711yescharacteristic, complemented
49D7×D11—1058no—
50C2×C3×C72—551no—
51C3⋊(C7⋊D7)—51no—
52C3⋊(C7⋊D7)—111no—
53C5×C72D3×D1111yescharacteristic, complemented, Hall
54C3×C7×C11D5×D718yescomplemented
55D5×D11—1471noHall
56D105—78no—
57C5×D21—778no—
58C3×C7×D5—118no—
59C2×C7⋊D7—1651noHall
60C3×C5×C11C2×C7⋊D711yescharacteristic, complemented, Hall
61D77—218no—
62C7×D11—58no—
63C11×D7—1058no—
64C3×C72D5×D1111yescharacteristic, complemented, Hall
65D5×D7—2318no—
66D3×D11—2451noHall
67D55C3⋊(C7⋊D7)11yescharacteristic, complemented
68C5×D11—1471no—
69D5×C11—1471no—
70C3×C5×C7D7×D1118yescomplemented
71C2×C72—551no—
72C7⋊D7—151no—
73C7⋊D7—331no—
74C2×D21—3858no—
75C7×C11D5×D2118yescomplemented
76D35—218no—
77C5×D7—2318no—
78C7×D5—118no—
79D33—491no—
80C3×D11—51no—
81D3×C11—2451no—
82D3×D5—5391noHall
83C5×C11C2×C3⋊(C7⋊D7)11yescharacteristic, complemented, Hall
84C72D15⋊D1111yescharacteristic, complemented, Sylow
85C2×D11—7351noHall
86C2×C3×C7—558no—
87D21—358no—
88D21—778no—
89C5×C7D11×D2118yescomplemented
90C3×C11D5×C7⋊D711yescharacteristic, complemented, Hall
91D15—491no—
92C3×D5—111no—
93C5×D3—5391no—
94C2×D7—11558no—
95C2×C11—7351no—
96D11—51no—
97D11—1471no—
98C3×C7D35⋊D1118yescomplemented
99C2×D5—16171noHall
100C3×C5D11×C7⋊D711yescharacteristic, complemented, Hall
101C2×C7—558no—
102D7—1058no—
103D7—2318no—
104C2×D3—26951noHall
105C11D5×C3⋊(C7⋊D7)11yescharacteristic, complemented, Sylow
106C2×C5—16171no—
107D5—111no—
108D5—1471no—
109C7D55⋊D2118yescomplemented
110C2×C3—551no—
111D3—5391no—
112D3—2451no—
113C5D11×C3⋊(C7⋊D7)11yescharacteristic, complemented, Sylow
114C22—80851noSylow
115C3D55⋊(C7⋊D7)11yescharacteristic, complemented, Sylow
116C2—551no—
117C2—16171no—
118C2—7351no—
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×C72×D55C2semidirect
2. C5×C3⋊(C7⋊D77)C2semidirect
3. C11×C3⋊(C5⋊(C7⋊D7))C2semidirect
5. C3×C5×C72×C11C22semidirect
8. C72×D55D3semidirect
11. C3⋊(C7⋊D77)D5semidirect
15. C5×C72×C11C2×D3semidirect
18. C3×C7×D55D7semidirect
20. C3×C72×C11C2×D5semidirect
22. C3⋊(C5⋊(C7⋊D7))D11semidirect
25. C3×C5×C7×C11C2×D7semidirect
32. C7×D55D21semidirect
34. C3×C5×C72C2×D11semidirect
37. C72×C11D3×D5semidirect
45. C5×C7×C11C2×D21semidirect
48. C3×D55C7⋊D7semidirect
53. C5×C72D3×D11semidirect
54. C3×C7×C11D5×D7semidirect
60. C3×C5×C11C2×C7⋊D7semidirect
64. C3×C72D5×D11semidirect
67. D55C3⋊(C7⋊D7)semidirect
70. C3×C5×C7D7×D11semidirect
75. C7×C11D5×D21semidirect
83. C5×C11C2×C3⋊(C7⋊D7)semidirect
84. C72D15⋊D11semidirect
89. C5×C7D11×D21semidirect
90. C3×C11D5×C7⋊D7semidirect
98. C3×C7D35⋊D11semidirect
100. C3×C5D11×C7⋊D7semidirect
105. C11D5×C3⋊(C7⋊D7)semidirect
109. C7D55⋊D21semidirect
113. C5D11×C3⋊(C7⋊D7)semidirect
115. C3D55⋊(C7⋊D7)semidirect

Maximal subgroups

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

subgroupindex
C3×C72×D552
C5×C3⋊(C7⋊D77)2
C11×C3⋊(C5⋊(C7⋊D7))2
D55⋊(C7⋊D7)3
D11×C3⋊(C7⋊D7)5
D55⋊D217
D5×C3⋊(C7⋊D7)11