Finite Group Databasebeta

← D3×C17×C3⋊(C7⋊D7) #44472971

Subgroups — D3×C17×C3⋊(C7⋊D7) #44472971

Order 29988.

440 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 128 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×D3×C72×C17C211yesmaximal, characteristic, complemented
2C3×C17×C3⋊(C7⋊D7)C211yesmaximal, characteristic, complemented
3C17×C3⋊(C3⋊(C7⋊D7))C211yesmaximal, characteristic, complemented
4C2×C17×C3⋊(C7⋊D7)—31nomaximal
5D3×C17×C7⋊D7—31nomaximal
6C32×C72×C17C2211yescharacteristic, complemented, Hall
7C17×C3⋊(C7⋊D7)—31no—
8C17×C3⋊(C7⋊D7)—31no—
9C17×C3⋊(C7⋊D7)—61no—
10C17×C3⋊(C7⋊D7)D311yescharacteristic, direct product factor
11D3×C72×C17D311yescharacteristic, complemented
12C3×C17×C7⋊D7—31no—
13C2×C3×C72×C17—31no—
14D3×C17×D21—78nomaximal
15C2×C17×C7⋊D7—91noHall
16C3×C72×C17—21no—
17C3×C72×C17C2×D311yescharacteristic, complemented
18C3×C72×C17C2×D311yescharacteristic, complemented
19C17×C3⋊D21—78no—
20C3×C17×D21—78no—
21C3×D3×C7×C17D718yescomplemented
22D3×C3⋊(C7⋊D7)C1711yesmaximal, characteristic, direct product factor, Hall
23C2×C72×C17—31no—
24C17×C7⋊D7—31no—
25C17×C7⋊D7—91no—
26C2×C17×D21—218no—
27D3×D7×C17—218no—
28C32×C7×C17C2×D718yescomplemented
29C3⋊(C3⋊(C7⋊D7))C2×C1711yescharacteristic, complemented
30C3×C3⋊(C7⋊D7)C2×C1711yescharacteristic, complemented
31C3×D3×C72C2×C1711yescharacteristic, complemented
32C72×C17D3211yescharacteristic, complemented, Hall
33C2×C3×C7×C17—38no—
34C17×D21—78no—
35C17×D21—218no—
36C17×D21—218no—
37C17×D21—428no—
38D3×C7×C17D2118yescomplemented
39C3×D7×C17—218no—
40D32×C17—491noHall
41C2×C3⋊(C7⋊D7)—31no—
42D3×C7⋊D7—31no—
43C2×D7×C17—638no—
44C32×C72C22×C1711yescharacteristic, complemented, Hall
45C3×C7×C17—28no—
46C3×C7×C17D3×D718yescomplemented
47C3×C7×C17C2×D2118yescomplemented
48C17×C3⋊D3—491no—
49C3×D3×C17—491no—
50C3×D3×C17C7⋊D711yescharacteristic, complemented
51C2×C3×C72—31no—
52C3⋊(C7⋊D7)—31no—
53C3⋊(C7⋊D7)—31no—
54C3⋊(C7⋊D7)—61no—
55C3⋊(C7⋊D7)D3×C1711yescharacteristic, direct product factor
56D3×C72D3×C1711yescharacteristic, complemented
57C3×C7⋊D7—31no—
58D3×D21—78no—
59C2×C7×C17—38no—
60D7×C17—218no—
61D7×C17—638no—
62C2×D3×C17—1471no—
63C2×D3×C17—1471no—
64C2×C7⋊D7—91noHall
65C32×C17C2×C7⋊D711yescharacteristic, complemented, Hall
66C3×C72—21no—
67C3×C72C2×D3×C1711yescharacteristic, complemented
68C3×C72C2×D3×C1711yescharacteristic, complemented
69C3⋊D21—78no—
70C3×D21—78no—
71C3×D3×C7D7×C1718yescomplemented
72C7×C17D3×D2118yescomplemented
73C2×C3×C17—31no—
74C2×C3×C17—1471no—
75D3×C17—2941no—
76D3×C17—491no—
77D3×C17—1471no—
78D3×C17—1471no—
79D3×C17C3⋊(C7⋊D7)11yescharacteristic, direct product factor
80C2×C72—31no—
81C7⋊D7—31no—
82C7⋊D7—91no—
83C2×D21—218no—
84D3×D7—218no—
85C22×C17—4411noHall
86C32×C7C2×D7×C1718yescomplemented
87C3×C17—21no—
88C3×C17D3×C7⋊D711yescharacteristic, complemented
89C3×C17C2×C3⋊(C7⋊D7)11yescharacteristic, complemented
90C72D32×C1711yescharacteristic, complemented, Sylow
91C2×C3×C7—38no—
92D21—78no—
93D21—218no—
94D21—218no—
95D21—428no—
96C3×D7—218no—
97D3×C7C17×D2118yescomplemented
98D32—491noHall
99C2×C17—31no—
100C2×C17—1471no—
101C2×C17—4411no—
102C2×D7—638no—
103C3×C7—28no—
104C3×C7D3×D7×C1718yescomplemented
105C3×C7C2×C17×D2118yescomplemented
106C3⋊D3—491no—
107C3×D3—491no—
108C3×D3C17×C7⋊D711yescharacteristic, complemented
109C17D3×C3⋊(C7⋊D7)11yescharacteristic, direct product factor, Sylow
110C2×C7—38no—
111D7—218no—
112D7—638no—
113C2×D3—1471no—
114C2×D3—1471no—
115C32C2×C17×C7⋊D711yescharacteristic, complemented, Sylow
116C7D3×C17×D2118yescomplemented
117C2×C3—31no—
118C2×C3—1471no—
119D3—2941no—
120D3—491no—
121D3—1471no—
122D3—1471no—
123D3C17×C3⋊(C7⋊D7)11yescharacteristic, direct product factor
124C22—4411noSylow
125C3—21no—
126C3D3×C17×C7⋊D711yescharacteristic, complemented
127C3C2×C17×C3⋊(C7⋊D7)11yescharacteristic, complemented
128C2—31no—
129C2—1471no—
130C2—4411no—
subgroupG/H
center, hypercenterC17D3×C3⋊(C7⋊D7)
commutator, cosocle, hypocenterC32×C72C22×C17
FrattiniC1G
Fitting, socleC32×C72×C17C22
LCSG ▷ C32×C72
UCSC1 ◁ C17

Complements

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

NH ≅ G/Ntype
1. C3×D3×C72×C17C2semidirect
2. C3×C17×C3⋊(C7⋊D7)C2semidirect
3. C17×C3⋊(C3⋊(C7⋊D7))C2semidirect
6. C32×C72×C17C22semidirect
10. C17×C3⋊(C7⋊D7)D3direct (N × H)
11. D3×C72×C17D3semidirect
17. C3×C72×C17C2×D3semidirect
18. C3×C72×C17C2×D3semidirect
21. C3×D3×C7×C17D7semidirect
22. D3×C3⋊(C7⋊D7)C17direct (N × H)
28. C32×C7×C17C2×D7semidirect
29. C3⋊(C3⋊(C7⋊D7))C2×C17semidirect
30. C3×C3⋊(C7⋊D7)C2×C17semidirect
31. C3×D3×C72C2×C17semidirect
32. C72×C17D32semidirect
38. D3×C7×C17D21semidirect
44. C32×C72C22×C17semidirect
46. C3×C7×C17D3×D7semidirect
47. C3×C7×C17C2×D21semidirect
50. C3×D3×C17C7⋊D7semidirect
55. C3⋊(C7⋊D7)D3×C17direct (N × H)
56. D3×C72D3×C17semidirect
65. C32×C17C2×C7⋊D7semidirect
67. C3×C72C2×D3×C17semidirect
68. C3×C72C2×D3×C17semidirect
71. C3×D3×C7D7×C17semidirect
72. C7×C17D3×D21semidirect
79. D3×C17C3⋊(C7⋊D7)direct (N × H)
86. C32×C7C2×D7×C17semidirect
88. C3×C17D3×C7⋊D7semidirect
89. C3×C17C2×C3⋊(C7⋊D7)semidirect
90. C72D32×C17semidirect
97. D3×C7C17×D21semidirect
104. C3×C7D3×D7×C17semidirect
105. C3×C7C2×C17×D21semidirect
108. C3×D3C17×C7⋊D7semidirect
109. C17D3×C3⋊(C7⋊D7)direct (N × H)
115. C32C2×C17×C7⋊D7semidirect
116. C7D3×C17×D21semidirect
123. D3C17×C3⋊(C7⋊D7)direct (N × H)
126. C3D3×C17×C7⋊D7semidirect
127. C3C2×C17×C3⋊(C7⋊D7)semidirect

Maximal subgroups

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

subgroupindex
C3×D3×C72×C172
C3×C17×C3⋊(C7⋊D7)2
C17×C3⋊(C3⋊(C7⋊D7))2
C2×C17×C3⋊(C7⋊D7)3
D3×C17×C7⋊D73
D3×C17×D217
D3×C3⋊(C7⋊D7)17