Finite Group Databasebeta

← C2×C7×C17×C3⋊D21 #44473022

Subgroups — C2×C7×C17×C3⋊D21 #44473022

Order 29988.

312 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 108 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
1C7×C17×C3⋊D21C212yesmaximal, direct product factor
2C2×C32×C72×C17C211yesmaximal, characteristic, complemented
3C2×C7×C17×D21—34nomaximal
4C32×C72×C17C2211yescharacteristic, complemented, Hall
5C7×C17×D21—38no—
6C2×C3×C72×C17D314yescomplemented
7C2×C7×C17×C3⋊D3—71nomaximal
8C2×C17×C3⋊D21C711yesmaximal, characteristic, direct product factor
9C2×C7×D7×C17—91noHall
10C3×C72×C17C2×D314yescomplemented
11C17×C3⋊D21C2×C712yesdirect product factor
12C7×C17×C3⋊D3—72no—
13C2×C32×C7×C17—23no—
14C2×C32×C7×C17D711yescharacteristic, complemented
15C2×C32×C7×C17C2×C711yescharacteristic, complemented
16C2×C7×C3⋊D21C1711yesmaximal, characteristic, direct product factor, Hall
17C2×C72×C17C3⋊D311yescharacteristic, complemented
18C7×D7×C17—92no—
19C2×C17×D21—34no—
20C2×D3×C7×C17—214no—
21C32×C7×C17—23no—
22C32×C7×C17C2×D711yescharacteristic, complemented
23C32×C7×C17C22×C711yescharacteristic, complemented
24C2×C32×C72C2×C1711yescharacteristic, complemented
25C7×C3⋊D21C2×C1712yesdirect product factor
26C72×C17C2×C3⋊D311yescharacteristic, complemented, Hall
27C2×C3×C7×C17—212no—
28C2×C3×C7×C17D3×C714yescomplemented
29C2×C3×C7×C17D2114yescomplemented
30C17×D21—38no—
31D3×C7×C17—218no—
32C2×C17×C3⋊D3—71noHall
33C2×C7×D21—34no—
34C22×C7×C17—631no—
35C2×D7×C17—91no—
36C32×C72C22×C1711yescharacteristic, complemented, Hall
37C3×C7×C17—212no—
38C3×C7×C17C2×D3×C714yescomplemented
39C3×C7×C17C2×D2114yescomplemented
40C2×C32×C17C7×D711yescharacteristic, complemented
41C17×C3⋊D3—72no—
42C2×C3×C72D3×C1714yescomplemented
43C7×D21—38no—
44C2×C3⋊D21C7×C1711yescharacteristic, direct product factor
45C2×C7×C3⋊D3—71no—
46C2×C7×C17—23no—
47C2×C7×C17—632no—
48C2×C7×C17C7×C3⋊D311yescharacteristic, complemented
49C2×C7×C17C3⋊D2111yescharacteristic, direct product factor
50D7×C17—92no—
51C2×D3×C17—214no—
52C2×C7×D7—91noHall
53C32×C17C2×C7×D711yescharacteristic, complemented, Hall
54C3×C72C2×D3×C1714yescomplemented
55C2×C32×C7—23no—
56C2×C32×C7D7×C1711yescharacteristic, complemented
57C2×C32×C7C2×C7×C1711yescharacteristic, complemented
58C3⋊D21C2×C7×C1712yesdirect product factor
59C7×C3⋊D3—72no—
60C7×C17—23no—
61C7×C17C2×C7×C3⋊D311yescharacteristic, complemented
62C7×C17C2×C3⋊D2111yescharacteristic, direct product factor
63C2×C3×C17C7×D2114yescomplemented
64D3×C17—218no—
65C2×C72C17×C3⋊D311yescharacteristic, complemented
66C7×D7—92no—
67C2×D21—34no—
68C2×D3×C7—214no—
69C22×C17—631noHall
70C32×C7—23no—
71C32×C7C2×D7×C1711yescharacteristic, complemented
72C32×C7C22×C7×C1711yescharacteristic, complemented
73C3×C17C2×C7×D2114yescomplemented
74C72C2×C17×C3⋊D311yescharacteristic, complemented, Sylow
75C2×C3×C7—212no—
76C2×C3×C7D3×C7×C1714yescomplemented
77C2×C3×C7C17×D2114yescomplemented
78D21—38no—
79D3×C7—218no—
80C2×C3⋊D3—71noHall
81C2×C17—632no—
82C2×C17C7×C3⋊D2111yescharacteristic, direct product factor
83C22×C7—631no—
84C2×D7—91no—
85C3×C7—212no—
86C3×C7C2×D3×C7×C1714yescomplemented
87C3×C7C2×C17×D2114yescomplemented
88C2×C32C7×D7×C1711yescharacteristic, complemented
89C3⋊D3—72no—
90C17C2×C7×C3⋊D2111yescharacteristic, direct product factor, Sylow
91C2×C7—23no—
92C2×C7—632no—
93C2×C7C7×C17×C3⋊D311yescharacteristic, complemented
94C2×C7C17×C3⋊D2111yescharacteristic, direct product factor
95D7—92no—
96C2×D3—214no—
97C32C2×C7×D7×C1711yescharacteristic, complemented, Sylow
98C7—23no—
99C7C2×C17×C3⋊D2111yescharacteristic, direct product factor
100C7C2×C7×C17×C3⋊D311yescharacteristic, complemented
101C2×C3C7×C17×D2114yescomplemented
102D3—218no—
103C22—631noSylow
104C3C2×C7×C17×D2114yescomplemented
105C2—632no—
106C2C7×C17×C3⋊D2111yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C7×C17C3⋊D21
commutator, cosocle, hypocenterC32×C7C22×C7×C17
FrattiniC1G
Fitting, socleC2×C32×C72×C17C2
LCSG ▷ C32×C7
UCSC1 ◁ C2×C7×C17

Complements

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

NH ≅ G/Ntype
1. C7×C17×C3⋊D21C2direct (N × H)
2. C2×C32×C72×C17C2semidirect
4. C32×C72×C17C22semidirect
6. C2×C3×C72×C17D3semidirect
8. C2×C17×C3⋊D21C7direct (N × H)
10. C3×C72×C17C2×D3semidirect
11. C17×C3⋊D21C2×C7direct (N × H)
14. C2×C32×C7×C17D7semidirect
15. C2×C32×C7×C17C2×C7semidirect
16. C2×C7×C3⋊D21C17direct (N × H)
17. C2×C72×C17C3⋊D3semidirect
22. C32×C7×C17C2×D7semidirect
23. C32×C7×C17C22×C7semidirect
24. C2×C32×C72C2×C17semidirect
25. C7×C3⋊D21C2×C17direct (N × H)
26. C72×C17C2×C3⋊D3semidirect
28. C2×C3×C7×C17D3×C7semidirect
29. C2×C3×C7×C17D21semidirect
36. C32×C72C22×C17semidirect
38. C3×C7×C17C2×D3×C7semidirect
39. C3×C7×C17C2×D21semidirect
40. C2×C32×C17C7×D7semidirect
42. C2×C3×C72D3×C17semidirect
44. C2×C3⋊D21C7×C17direct (N × H)
48. C2×C7×C17C7×C3⋊D3semidirect
49. C2×C7×C17C3⋊D21direct (N × H)
53. C32×C17C2×C7×D7semidirect
54. C3×C72C2×D3×C17semidirect
56. C2×C32×C7D7×C17semidirect
57. C2×C32×C7C2×C7×C17semidirect
58. C3⋊D21C2×C7×C17direct (N × H)
61. C7×C17C2×C7×C3⋊D3semidirect
62. C7×C17C2×C3⋊D21direct (N × H)
63. C2×C3×C17C7×D21semidirect
65. C2×C72C17×C3⋊D3semidirect
71. C32×C7C2×D7×C17semidirect
72. C32×C7C22×C7×C17semidirect
73. C3×C17C2×C7×D21semidirect
74. C72C2×C17×C3⋊D3semidirect
76. C2×C3×C7D3×C7×C17semidirect
77. C2×C3×C7C17×D21semidirect
82. C2×C17C7×C3⋊D21direct (N × H)
86. C3×C7C2×D3×C7×C17semidirect
87. C3×C7C2×C17×D21semidirect
88. C2×C32C7×D7×C17semidirect
90. C17C2×C7×C3⋊D21direct (N × H)
93. C2×C7C7×C17×C3⋊D3semidirect
94. C2×C7C17×C3⋊D21direct (N × H)
97. C32C2×C7×D7×C17semidirect
99. C7C2×C17×C3⋊D21direct (N × H)
100. C7C2×C7×C17×C3⋊D3semidirect
101. C2×C3C7×C17×D21semidirect
104. C3C2×C7×C17×D21semidirect
106. C2C7×C17×C3⋊D21direct (N × H)

Maximal subgroups

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

subgroupindex
C7×C17×C3⋊D212
C2×C32×C72×C172
C2×C7×C17×D213
C2×C7×C17×C3⋊D37
C2×C17×C3⋊D217
C2×C7×C3⋊D2117