Finite Group Databasebeta

← C3×D55⋊(C7⋊D7) #44568836

Subgroups — C3×D55⋊(C7⋊D7) #44568836

Order 32340.

400 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 110 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⋊D77C211yesmaximal, characteristic, complemented
2C3×C72×D55C211yesmaximal, characteristic, complemented
3C3×C11×C5⋊(C7⋊D7)C211yesmaximal, characteristic, complemented
4D55⋊(C7⋊D7)C311yesmaximal, characteristic, direct product factor, Hall
5C3×C5×C72×C11C2211yescharacteristic, complemented, Hall
6C3×D11×C7⋊D7—51nomaximal, Hall
7C11×C5⋊(C7⋊D7)C2×C311yescharacteristic, complemented
8C72×D55C2×C311yescharacteristic, complemented
9C5×C7⋊D77C2×C311yescharacteristic, complemented
10C3×D35⋊D11—78nomaximal
11C3×C7⋊D77D511yescharacteristic, complemented
12C3×C11×C7⋊D7—51no—
13C3×C72×D11—51no—
14C3×D5×C7⋊D7—111nomaximal, Hall
15C5×C72×C11C22×C311yescharacteristic, complemented, Hall
16C3×C11×D35—78no—
17C3×C7×D55D718yescomplemented
18C3×C5×D77—78no—
19D11×C7⋊D7—51noHall
20C3×C72×C11C2×D511yescharacteristic, complemented, Hall
21D35⋊D11—78no—
22C3×C5⋊(C7⋊D7)D1111yescharacteristic, complemented
23C3×C72×D5—111no—
24C3×C5×C7⋊D7—111no—
25C3×C5×C7×C11C2×D718yescomplemented
26C7⋊D77C3×D511yescharacteristic, complemented
27C11×C7⋊D7—51no—
28C72×D11—51no—
29D5×C7⋊D7—111noHall
30C3×D7×D11—358no—
31C11×D35—78no—
32C7×D55C3×D718yescomplemented
33C5×D77—78no—
34C3×C5×C72C2×D1111yescharacteristic, complemented, Hall
35C3×D5×D11—491noHall
36C2×C3×C7⋊D7—551noHall
37C72×C11C2×C3×D511yescharacteristic, complemented, Hall
38C5⋊(C7⋊D7)C3×D1111yescharacteristic, complemented
39C72×D5—111no—
40C5×C7⋊D7—111no—
41C3×D77—78no—
42C3×C11×D7—358no—
43C3×C7×D11—58no—
44C3×D5×D7—778no—
45C5×C7×C11C2×C3×D718yescomplemented
46C3×D55C7⋊D711yescharacteristic, complemented
47C3×D5×C11—491no—
48C3×C5×D11—491no—
49D7×D11—358no—
50C2×C3×C72—551no—
51C3×C7⋊D7—51no—
52C3×C7⋊D7—111no—
53C5×C72C2×C3×D1111yescharacteristic, complemented, Hall
54C3×C7×C11D5×D718yescomplemented
55D5×D11—491noHall
56C3×D35—78no—
57C3×C7×D5—118no—
58C3×C5×D7—778no—
59C2×C7⋊D7—551noHall
60C3×C5×C11C2×C7⋊D711yescharacteristic, complemented, Hall
61D77—78no—
62C7×D11—58no—
63C11×D7—358no—
64C3×C72D5×D1111yescharacteristic, complemented, Hall
65D5×D7—778no—
66C2×C3×D11—2451noHall
67D55C3×C7⋊D711yescharacteristic, complemented
68C5×D11—491no—
69D5×C11—491no—
70C3×C5×C7D7×D1118yescomplemented
71C2×C72—551no—
72C7⋊D7—51no—
73C7⋊D7—111no—
74C2×C3×D7—3858no—
75C7×C11C3×D5×D718yescomplemented
76D35—78no—
77C5×D7—778no—
78C7×D5—118no—
79C2×C3×C11—2451no—
80C3×D11—51no—
81C3×D11—491no—
82C2×C3×D5—5391noHall
83C5×C11C2×C3×C7⋊D711yescharacteristic, complemented, Hall
84C72C3×D5×D1111yescharacteristic, complemented, Sylow
85C2×D11—2451noHall
86C2×C3×C7—558no—
87C3×D7—358no—
88C3×D7—778no—
89C5×C7C3×D7×D1118yescomplemented
90C3×C11D5×C7⋊D711yescharacteristic, complemented, Hall
91C2×C3×C5—5391no—
92C3×D5—111no—
93C3×D5—491no—
94C2×D7—3858no—
95C2×C11—2451no—
96D11—51no—
97D11—491no—
98C3×C7D35⋊D1118yescomplemented
99C2×D5—5391noHall
100C3×C5D11×C7⋊D711yescharacteristic, complemented, Hall
101C2×C7—558no—
102D7—358no—
103D7—778no—
104C22×C3—26951noHall
105C11C3×D5×C7⋊D711yescharacteristic, complemented, Sylow
106C2×C5—5391no—
107D5—111no—
108D5—491no—
109C7C3×D35⋊D1118yescomplemented
110C2×C3—5391no—
111C2×C3—551no—
112C2×C3—2451no—
113C5C3×D11×C7⋊D711yescharacteristic, complemented, Sylow
114C22—26951noSylow
115C3D55⋊(C7⋊D7)11yescharacteristic, direct product factor, Sylow
116C2—5391no—
117C2—551no—
118C2—2451no—
subgroupG/H
center, hypercenterC3D55⋊(C7⋊D7)
commutator, cosocle, hypocenterC5×C72×C11C22×C3
FrattiniC1G
Fitting, socleC3×C5×C72×C11C22
LCSG ▷ C5×C72×C11
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×C5×C7⋊D77C2semidirect
2. C3×C72×D55C2semidirect
3. C3×C11×C5⋊(C7⋊D7)C2semidirect
4. D55⋊(C7⋊D7)C3direct (N × H)
5. C3×C5×C72×C11C22semidirect
7. C11×C5⋊(C7⋊D7)C2×C3semidirect
8. C72×D55C2×C3semidirect
9. C5×C7⋊D77C2×C3semidirect
11. C3×C7⋊D77D5semidirect
15. C5×C72×C11C22×C3semidirect
17. C3×C7×D55D7semidirect
20. C3×C72×C11C2×D5semidirect
22. C3×C5⋊(C7⋊D7)D11semidirect
25. C3×C5×C7×C11C2×D7semidirect
26. C7⋊D77C3×D5semidirect
32. C7×D55C3×D7semidirect
34. C3×C5×C72C2×D11semidirect
37. C72×C11C2×C3×D5semidirect
38. C5⋊(C7⋊D7)C3×D11semidirect
45. C5×C7×C11C2×C3×D7semidirect
46. C3×D55C7⋊D7semidirect
53. C5×C72C2×C3×D11semidirect
54. C3×C7×C11D5×D7semidirect
60. C3×C5×C11C2×C7⋊D7semidirect
64. C3×C72D5×D11semidirect
67. D55C3×C7⋊D7semidirect
70. C3×C5×C7D7×D11semidirect
75. C7×C11C3×D5×D7semidirect
83. C5×C11C2×C3×C7⋊D7semidirect
84. C72C3×D5×D11semidirect
89. C5×C7C3×D7×D11semidirect
90. C3×C11D5×C7⋊D7semidirect
98. C3×C7D35⋊D11semidirect
100. C3×C5D11×C7⋊D7semidirect
105. C11C3×D5×C7⋊D7semidirect
109. C7C3×D35⋊D11semidirect
113. C5C3×D11×C7⋊D7semidirect
115. C3D55⋊(C7⋊D7)direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×C7⋊D772
C3×C72×D552
C3×C11×C5⋊(C7⋊D7)2
D55⋊(C7⋊D7)3
C3×D11×C7⋊D75
C3×D35⋊D117
C3×D5×C7⋊D711