Finite Group Databasebeta

← D51⋊(C3⋊(C7⋊D7)) #44472973

Subgroups — D51⋊(C3⋊(C7⋊D7)) #44472973

Order 29988.

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×D51C211yesmaximal, characteristic, complemented
2C3×C3⋊(C7⋊D119)C211yesmaximal, characteristic, complemented
3C17×C3⋊(C3⋊(C7⋊D7))C211yesmaximal, characteristic, complemented
4D51⋊(C7⋊D7)—31nomaximal
5D17×C3⋊(C7⋊D7)—31nomaximal
6C32×C72×C17C2211yescharacteristic, complemented, Hall
7C3⋊(C7⋊D119)D311yescharacteristic, complemented
8C17×C3⋊(C7⋊D7)—31no—
9C17×C3⋊(C7⋊D7)—31no—
10C17×C3⋊(C7⋊D7)—61no—
11C72×D51D311yescharacteristic, complemented
12C3×C7⋊D119—31no—
13C3×C72×D17—31no—
14D51⋊D21—78nomaximal
15D17×C7⋊D7—91noHall
16C3×C72×C17—21no—
17C3×C72×C17C2×D311yescharacteristic, complemented
18C3×C72×C17C2×D311yescharacteristic, complemented
19C17×C3⋊D21—78no—
20C3×D357—78no—
21C3×C7×D51D718yescomplemented
22D3×C3⋊(C7⋊D7)—171nomaximal, Hall
23C7⋊D119—31no—
24C17×C7⋊D7—91no—
25C72×D17—31no—
26D21⋊D17—218no—
27D17×D21—218no—
28C32×C7×C17C2×D718yescomplemented
29C3⋊(C3⋊(C7⋊D7))D1711yescharacteristic, complemented
30C3×C3⋊(C7⋊D7)—171no—
31C3×D3×C72—171no—
32C72×C17D3211yescharacteristic, complemented, Hall
33D357—78no—
34C17×D21—218no—
35C17×D21—218no—
36C17×D21—428no—
37C7×D51D2118yescomplemented
38C3×D119—218no—
39C3×C7×D17—38no—
40(C3⋊D3)⋊D17—491noHall
41C2×C3⋊(C7⋊D7)—511no—
42D3×C7⋊D7—511no—
43D7×D17—638no—
44C32×C72C2×D1711yescharacteristic, complemented, Hall
45C3×C7×C17—28no—
46C3×C7×C17D3×D718yescomplemented
47C3×C7×C17C2×D2118yescomplemented
48C17×C3⋊D3—491no—
49C3×D51—491no—
50C3×D51C7⋊D711yescharacteristic, complemented
51C2×C3×C72—511no—
52C3⋊(C7⋊D7)—31no—
53C3⋊(C7⋊D7)—31no—
54C3⋊(C7⋊D7)—61no—
55C3⋊(C7⋊D7)—171no—
56D3×C72—171no—
57C3×C7⋊D7—511no—
58D3×D21—1198no—
59D119—218no—
60C7×D17—38no—
61D7×C17—638no—
62D3×D17—1471no—
63D3×D17—1471no—
64C2×C7⋊D7—1531noHall
65C32×C17C2×C7⋊D711yescharacteristic, complemented, Hall
66C3×C72—21no—
67C3×C72D3×D1711yescharacteristic, complemented
68C3×C72D3×D1711yescharacteristic, complemented
69C3⋊D21—78no—
70C3×D21—1198no—
71C3×D3×C7—178no—
72C7×C17D3×D2118yescomplemented
73D51—491no—
74D51C3⋊(C7⋊D7)11yescharacteristic, complemented
75C3×D17—31no—
76C3×D17—1471no—
77D3×C17—2941no—
78D3×C17—1471no—
79D3×C17—1471no—
80C2×C72—511no—
81C7⋊D7—91no—
82C7⋊D7—511no—
83C2×D21—3578no—
84D3×D7—3578no—
85C2×D17—4411noHall
86C32×C7D7×D1718yescomplemented
87C3×C17—21no—
88C3×C17D3×C7⋊D711yescharacteristic, complemented
89C3×C17C2×C3⋊(C7⋊D7)11yescharacteristic, complemented
90C72(C3⋊D3)⋊D1711yescharacteristic, complemented, Sylow
91C2×C3×C7—518no—
92D21—218no—
93D21—218no—
94D21—428no—
95D21—1198no—
96C3×D7—3578no—
97D3×C7—178no—
98D32—8331noHall
99C2×C17—4411no—
100D17—31no—
101D17—1471no—
102C2×D7—10718no—
103C3×C7—28no—
104C3×C7D17×D2118yescomplemented
105C3×C7D21⋊D1718yescomplemented
106C3⋊D3—491no—
107C3×D3—171no—
108C3×D3—8331no—
109C17D3×C3⋊(C7⋊D7)11yescharacteristic, complemented, Sylow
110C2×C7—518no—
111D7—638no—
112D7—3578no—
113C2×D3—24991no—
114C2×D3—24991no—
115C32D17×C7⋊D711yescharacteristic, complemented, Sylow
116C7D51⋊D2118yescomplemented
117C2×C3—511no—
118C2×C3—24991no—
119D3—171no—
120D3—2941no—
121D3—8331no—
122D3—1471no—
123D3—1471no—
124C22—74971noSylow
125C3—21no—
126C3D17×C3⋊(C7⋊D7)11yescharacteristic, complemented
127C3D51⋊(C7⋊D7)11yescharacteristic, complemented
128C2—511no—
129C2—4411no—
130C2—24991no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C72×C17C22
LCSG ▷ C32×C72×C17
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C72×D51C2semidirect
2. C3×C3⋊(C7⋊D119)C2semidirect
3. C17×C3⋊(C3⋊(C7⋊D7))C2semidirect
6. C32×C72×C17C22semidirect
7. C3⋊(C7⋊D119)D3semidirect
11. C72×D51D3semidirect
17. C3×C72×C17C2×D3semidirect
18. C3×C72×C17C2×D3semidirect
21. C3×C7×D51D7semidirect
28. C32×C7×C17C2×D7semidirect
29. C3⋊(C3⋊(C7⋊D7))D17semidirect
32. C72×C17D32semidirect
37. C7×D51D21semidirect
44. C32×C72C2×D17semidirect
46. C3×C7×C17D3×D7semidirect
47. C3×C7×C17C2×D21semidirect
50. C3×D51C7⋊D7semidirect
65. C32×C17C2×C7⋊D7semidirect
67. C3×C72D3×D17semidirect
68. C3×C72D3×D17semidirect
72. C7×C17D3×D21semidirect
74. D51C3⋊(C7⋊D7)semidirect
86. C32×C7D7×D17semidirect
88. C3×C17D3×C7⋊D7semidirect
89. C3×C17C2×C3⋊(C7⋊D7)semidirect
90. C72(C3⋊D3)⋊D17semidirect
104. C3×C7D17×D21semidirect
105. C3×C7D21⋊D17semidirect
109. C17D3×C3⋊(C7⋊D7)semidirect
115. C32D17×C7⋊D7semidirect
116. C7D51⋊D21semidirect
126. C3D17×C3⋊(C7⋊D7)semidirect
127. C3D51⋊(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×D512
C3×C3⋊(C7⋊D119)2
C17×C3⋊(C3⋊(C7⋊D7))2
D51⋊(C7⋊D7)3
D17×C3⋊(C7⋊D7)3
D51⋊D217
D3×C3⋊(C7⋊D7)17