Finite Group Databasebeta

← C3×D57⋊(C7⋊D7) #45692701

Subgroups — C3×D57⋊(C7⋊D7) #45692701

Order 33516.

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

normal subgroups only

This group has 440 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
1C32×C7⋊D133C211yesmaximal, characteristic, complemented
2C3×C72×D57C211yesmaximal, characteristic, complemented
3C3×C19×C3⋊(C7⋊D7)C211yesmaximal, characteristic, complemented
4D57⋊(C7⋊D7)C311yesmaximal, characteristic, direct product factor
5C3×D19×C7⋊D7—31nomaximal
6C32×C72×C19C2211yescharacteristic, complemented, Hall
7C19×C3⋊(C7⋊D7)C2×C311yescharacteristic, complemented
8C72×D57C2×C311yescharacteristic, complemented
9C3×C7⋊D133—21no—
10C3×C7⋊D133D311yescharacteristic, complemented
11C3×C7⋊D133C2×C311yescharacteristic, complemented
12C3×C19×C7⋊D7—31no—
13C3×C72×D19—31no—
14C3×D21⋊D19—78nomaximal
15D19×C7⋊D7—31noHall
16C3×C72×C19—21no—
17C3×C72×C19C2×D311yescharacteristic, complemented
18C3×C72×C19C22×C311yescharacteristic, complemented
19C3×C19×D21—78no—
20C3×C7×D57D718yescomplemented
21C32×D133—78no—
22C7⋊D133C3×D311yescharacteristic, complemented
23C19×C7⋊D7—31no—
24C72×D19—31no—
25C3×D3×C7⋊D7—191nomaximal, Hall
26D21⋊D19—78no—
27C3×D7×D19—218no—
28C32×C7×C19C2×D718yescomplemented
29C72×C19C2×C3×D311yescharacteristic, complemented, Hall
30C3×C3⋊(C7⋊D7)D1911yescharacteristic, complemented
31C3×D3×C72—191no—
32C32×C7⋊D7—191no—
33C19×D21—78no—
34C7×D57C3×D718yescomplemented
35C3×D133—78no—
36C3×D133—78no—
37C3×D133—148no—
38C3×D7×C19—218no—
39C3×C7×D19—38no—
40C3×D3×D19—491noHall
41C2×C3×C7⋊D7—571no—
42D3×C7⋊D7—191no—
43D7×D19—218no—
44C32×C72C2×D1911yescharacteristic, complemented, Hall
45C3×C7×C19—28no—
46C3×C7×C19D3×D718yescomplemented
47C3×C7×C19C2×C3×D718yescomplemented
48C3×D57C7⋊D711yescharacteristic, complemented
49C3×D3×C19—491no—
50C32×D19—491no—
51C2×C3×C72—571no—
52C3⋊(C7⋊D7)C3×D1911yescharacteristic, complemented
53D3×C72—191no—
54C3×C7⋊D7—31no—
55C3×C7⋊D7—191no—
56C3×C7⋊D7—191no—
57C3×C7⋊D7—381no—
58D133—78no—
59C7×D19—38no—
60D7×C19—218no—
61C3×D3×D7—1338no—
62C2×C3×D19—1471no—
63D3×D19—491no—
64C2×C7⋊D7—571noHall
65C32×C19C2×C7⋊D711yescharacteristic, complemented, Hall
66C3×C72—21no—
67C3×C72D3×D1911yescharacteristic, complemented
68C3×C72C2×C3×D1911yescharacteristic, complemented
69C7×C19C3×D3×D718yescomplemented
70C3×D21—78no—
71C3×D3×C7—198no—
72C32×D7—1338no—
73C2×C3×C19—1471no—
74D57C3×C7⋊D711yescharacteristic, complemented
75C3×D19—31no—
76C3×D19—491no—
77C3×D19—491no—
78C3×D19—981no—
79D3×C19—491no—
80C2×C72—571no—
81C7⋊D7—31no—
82C7⋊D7—191no—
83C2×C3×D7—3998no—
84D3×D7—1338no—
85C2×D19—1471noHall
86C32×C7D7×D1918yescomplemented
87C3×C19—21no—
88C3×C19D3×C7⋊D711yescharacteristic, complemented
89C3×C19C2×C3×C7⋊D711yescharacteristic, complemented
90C72C3×D3×D1911yescharacteristic, complemented, Sylow
91C2×C3×C7—578no—
92D21—78no—
93C3×D7—2668no—
94C3×D7—218no—
95C3×D7—1338no—
96C3×D7—1338no—
97D3×C7—198no—
98C2×C19—1471no—
99D19—31no—
100D19—491no—
101C2×C3×D3—9311noHall
102C2×D7—3998no—
103C3×C7—28no—
104C3×C7C3×D7×D1918yescomplemented
105C3×C7D21⋊D1918yescomplemented
106C19C3×D3×C7⋊D711yescharacteristic, complemented, Sylow
107C2×C32—9311no—
108C3×D3—191no—
109C3×D3—491no—
110C2×C7—578no—
111D7—218no—
112D7—1338no—
113C22×C3—27931no—
114C2×D3—9311no—
115C32D19×C7⋊D711yescharacteristic, complemented, Sylow
116C7C3×D21⋊D1918yescomplemented
117C2×C3—571no—
118C2×C3—18621no—
119C2×C3—1471no—
120C2×C3—9311no—
121C2×C3—9311no—
122D3—191no—
123D3—491no—
124C22—27931noSylow
125C3—21no—
126C3C3×D19×C7⋊D711yescharacteristic, complemented
127C3D57⋊(C7⋊D7)11yescharacteristic, direct product factor
128C2—571no—
129C2—1471no—
130C2—9311no—
subgroupG/H
center, hypercenterC3D57⋊(C7⋊D7)
commutator, cosocle, hypocenterC3×C72×C19C22×C3
FrattiniC1G
Fitting, socleC32×C72×C19C22
LCSG ▷ C3×C72×C19
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C32×C7⋊D133C2semidirect
2. C3×C72×D57C2semidirect
3. C3×C19×C3⋊(C7⋊D7)C2semidirect
4. D57⋊(C7⋊D7)C3direct (N × H)
6. C32×C72×C19C22semidirect
7. C19×C3⋊(C7⋊D7)C2×C3semidirect
8. C72×D57C2×C3semidirect
10. C3×C7⋊D133D3semidirect
11. C3×C7⋊D133C2×C3semidirect
17. C3×C72×C19C2×D3semidirect
18. C3×C72×C19C22×C3semidirect
20. C3×C7×D57D7semidirect
22. C7⋊D133C3×D3semidirect
28. C32×C7×C19C2×D7semidirect
29. C72×C19C2×C3×D3semidirect
30. C3×C3⋊(C7⋊D7)D19semidirect
34. C7×D57C3×D7semidirect
44. C32×C72C2×D19semidirect
46. C3×C7×C19D3×D7semidirect
47. C3×C7×C19C2×C3×D7semidirect
48. C3×D57C7⋊D7semidirect
52. C3⋊(C7⋊D7)C3×D19semidirect
65. C32×C19C2×C7⋊D7semidirect
67. C3×C72D3×D19semidirect
68. C3×C72C2×C3×D19semidirect
69. C7×C19C3×D3×D7semidirect
74. D57C3×C7⋊D7semidirect
86. C32×C7D7×D19semidirect
88. C3×C19D3×C7⋊D7semidirect
89. C3×C19C2×C3×C7⋊D7semidirect
90. C72C3×D3×D19semidirect
104. C3×C7C3×D7×D19semidirect
105. C3×C7D21⋊D19semidirect
106. C19C3×D3×C7⋊D7semidirect
115. C32D19×C7⋊D7semidirect
116. C7C3×D21⋊D19semidirect
126. C3C3×D19×C7⋊D7semidirect
127. C3D57⋊(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
C32×C7⋊D1332
C3×C72×D572
C3×C19×C3⋊(C7⋊D7)2
D57⋊(C7⋊D7)3
C3×D19×C7⋊D73
C3×D21⋊D197
C3×D3×C7⋊D719