Finite Group Databasebeta

← D57⋊(C3⋊(C7⋊D7)) #45692721

Subgroups — D57⋊(C3⋊(C7⋊D7)) #45692721

Order 33516.

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

normal subgroups only

This group has 440 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×D57C211yesmaximal, characteristic, complemented
2C3×C3⋊(C7⋊D133)C211yesmaximal, characteristic, complemented
3C19×C3⋊(C3⋊(C7⋊D7))C211yesmaximal, characteristic, complemented
4D57⋊(C7⋊D7)—31nomaximal
5D19×C3⋊(C7⋊D7)—31nomaximal
6C32×C72×C19C2211yescharacteristic, complemented, Hall
7C3⋊(C7⋊D133)D311yescharacteristic, complemented
8C19×C3⋊(C7⋊D7)—31no—
9C19×C3⋊(C7⋊D7)—31no—
10C19×C3⋊(C7⋊D7)—61no—
11C72×D57D311yescharacteristic, complemented
12C3×C7⋊D133—31no—
13C3×C72×D19—31no—
14D57⋊D21—78nomaximal
15D19×C7⋊D7—91noHall
16C3×C72×C19—21no—
17C3×C72×C19C2×D311yescharacteristic, complemented
18C3×C72×C19C2×D311yescharacteristic, complemented
19C19×C3⋊D21—78no—
20C3×D399—78no—
21C3×C7×D57D718yescomplemented
22C7⋊D133—31no—
23C19×C7⋊D7—91no—
24C72×D19—31no—
25D3×C3⋊(C7⋊D7)—191nomaximal, Hall
26D21⋊D19—218no—
27D19×D21—218no—
28C32×C7×C19C2×D718yescomplemented
29C72×C19D3211yescharacteristic, complemented, Hall
30C3⋊(C3⋊(C7⋊D7))D1911yescharacteristic, complemented
31C3×C3⋊(C7⋊D7)—191no—
32C3×D3×C72—191no—
33D399—78no—
34C19×D21—218no—
35C19×D21—218no—
36C19×D21—428no—
37C7×D57D2118yescomplemented
38C3×D133—218no—
39C3×C7×D19—38no—
40(C3⋊D3)⋊D19—491noHall
41C2×C3⋊(C7⋊D7)—571no—
42D3×C7⋊D7—571no—
43D7×D19—638no—
44C32×C72C2×D1911yescharacteristic, complemented, Hall
45C3×C7×C19—28no—
46C3×C7×C19D3×D718yescomplemented
47C3×C7×C19C2×D2118yescomplemented
48C3⋊D3×C19—491no—
49C3×D57—491no—
50C3×D57C7⋊D711yescharacteristic, complemented
51C2×C3×C72—571no—
52C3⋊(C7⋊D7)—31no—
53C3⋊(C7⋊D7)—31no—
54C3⋊(C7⋊D7)—61no—
55C3⋊(C7⋊D7)—191no—
56D3×C72—191no—
57C3×C7⋊D7—571no—
58D133—218no—
59C7×D19—38no—
60D7×C19—638no—
61D3×D21—1338no—
62D3×D19—1471no—
63D3×D19—1471no—
64C2×C7⋊D7—1711noHall
65C32×C19C2×C7⋊D711yescharacteristic, complemented, Hall
66C3×C72—21no—
67C3×C72D3×D1911yescharacteristic, complemented
68C3×C72D3×D1911yescharacteristic, complemented
69C7×C19D3×D2118yescomplemented
70C3⋊D21—78no—
71C3×D21—1338no—
72C3×D3×C7—198no—
73D57—491no—
74D57C3⋊(C7⋊D7)11yescharacteristic, complemented
75C3×D19—31no—
76C3×D19—1471no—
77D3×C19—2941no—
78D3×C19—1471no—
79D3×C19—1471no—
80C2×C72—571no—
81C7⋊D7—91no—
82C7⋊D7—571no—
83C2×D21—3998no—
84D3×D7—3998no—
85C2×D19—4411noHall
86C32×C7D7×D1918yescomplemented
87C3×C19—21no—
88C3×C19D3×C7⋊D711yescharacteristic, complemented
89C3×C19C2×C3⋊(C7⋊D7)11yescharacteristic, complemented
90C72(C3⋊D3)⋊D1911yescharacteristic, complemented, Sylow
91C2×C3×C7—578no—
92D21—218no—
93D21—218no—
94D21—428no—
95D21—1338no—
96C3×D7—3998no—
97D3×C7—198no—
98C2×C19—4411no—
99D19—31no—
100D19—1471no—
101D32—9311noHall
102C2×D7—11978no—
103C3×C7—28no—
104C3×C7D19×D2118yescomplemented
105C3×C7D21⋊D1918yescomplemented
106C19D3×C3⋊(C7⋊D7)11yescharacteristic, complemented, Sylow
107C3⋊D3—491no—
108C3×D3—191no—
109C3×D3—9311no—
110C2×C7—578no—
111D7—638no—
112D7—3998no—
113C2×D3—27931no—
114C2×D3—27931no—
115C32D19×C7⋊D711yescharacteristic, complemented, Sylow
116C7D57⋊D2118yescomplemented
117C2×C3—571no—
118C2×C3—27931no—
119D3—191no—
120D3—2941no—
121D3—1471no—
122D3—1471no—
123D3—9311no—
124C22—83791noSylow
125C3—21no—
126C3D19×C3⋊(C7⋊D7)11yescharacteristic, complemented
127C3D57⋊(C7⋊D7)11yescharacteristic, complemented
128C2—571no—
129C2—4411no—
130C2—27931no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C72×C19C22
LCSG ▷ C32×C72×C19
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C72×D57C2semidirect
2. C3×C3⋊(C7⋊D133)C2semidirect
3. C19×C3⋊(C3⋊(C7⋊D7))C2semidirect
6. C32×C72×C19C22semidirect
7. C3⋊(C7⋊D133)D3semidirect
11. C72×D57D3semidirect
17. C3×C72×C19C2×D3semidirect
18. C3×C72×C19C2×D3semidirect
21. C3×C7×D57D7semidirect
28. C32×C7×C19C2×D7semidirect
29. C72×C19D32semidirect
30. C3⋊(C3⋊(C7⋊D7))D19semidirect
37. C7×D57D21semidirect
44. C32×C72C2×D19semidirect
46. C3×C7×C19D3×D7semidirect
47. C3×C7×C19C2×D21semidirect
50. C3×D57C7⋊D7semidirect
65. C32×C19C2×C7⋊D7semidirect
67. C3×C72D3×D19semidirect
68. C3×C72D3×D19semidirect
69. C7×C19D3×D21semidirect
74. D57C3⋊(C7⋊D7)semidirect
86. C32×C7D7×D19semidirect
88. C3×C19D3×C7⋊D7semidirect
89. C3×C19C2×C3⋊(C7⋊D7)semidirect
90. C72(C3⋊D3)⋊D19semidirect
104. C3×C7D19×D21semidirect
105. C3×C7D21⋊D19semidirect
106. C19D3×C3⋊(C7⋊D7)semidirect
115. C32D19×C7⋊D7semidirect
116. C7D57⋊D21semidirect
126. C3D19×C3⋊(C7⋊D7)semidirect
127. C3D57⋊(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×D572
C3×C3⋊(C7⋊D133)2
C19×C3⋊(C3⋊(C7⋊D7))2
D57⋊(C7⋊D7)3
D19×C3⋊(C7⋊D7)3
D57⋊D217
D3×C3⋊(C7⋊D7)19