Finite Group Databasebeta

← C2×C7×C3⋊D357 #44473023

Subgroups — C2×C7×C3⋊D357 #44473023

Order 29988.

312 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 102 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×C3⋊D357C212yesmaximal, direct product factor
2C2×C32×C72×C17C211yesmaximal, characteristic, complemented
3C2×C7×D357—34nomaximal
4C32×C72×C17C2211yescharacteristic, complemented, Hall
5C7×D357—38no—
6C2×C3×C72×C17D314yescomplemented
7C2×C7×C3⋊D51—71nomaximal
8C2×C3⋊D357C711yesmaximal, characteristic, direct product factor
9C2×C7×D119—91noHall
10C3×C72×C17C2×D314yescomplemented
11C3⋊D357C2×C712yesdirect product factor
12C7×C3⋊D51—72no—
13C2×C32×C7×C17—23no—
14C2×C32×C7×C17D711yescharacteristic, complemented
15C2×C32×C7×C17C2×C711yescharacteristic, complemented
16C2×C7×C3⋊D21—171nomaximal, Hall
17C2×C72×C17C3⋊D311yescharacteristic, complemented
18C7×D119—92no—
19C2×D357—34no—
20C2×C7×D51—214no—
21C32×C7×C17—23no—
22C32×C7×C17C2×D711yescharacteristic, complemented
23C32×C7×C17C22×C711yescharacteristic, complemented
24C2×C32×C72D1711yescharacteristic, complemented
25C7×C3⋊D21—172no—
26C72×C17C2×C3⋊D311yescharacteristic, complemented, Hall
27C2×C3×C7×C17—212no—
28C2×C3×C7×C17D3×C714yescomplemented
29C2×C3×C7×C17D2114yescomplemented
30D357—38no—
31C7×D51—218no—
32C2×C3⋊D51—71noHall
33C2×C7×D21—514no—
34C2×D119—91no—
35C2×C7×D17—631no—
36C32×C72C2×D1711yescharacteristic, complemented, Hall
37C3×C7×C17—212no—
38C3×C7×C17C2×D3×C714yescomplemented
39C3×C7×C17C2×D2114yescomplemented
40C2×C32×C17C7×D711yescharacteristic, complemented
41C3⋊D51—72no—
42C2×C3×C72D5114yescomplemented
43C7×D21—518no—
44C2×C3⋊D21—171no—
45C2×C7×C3⋊D3—1191no—
46C2×C7×C17—23no—
47C2×C7×C17C7×C3⋊D311yescharacteristic, complemented
48C2×C7×C17C3⋊D2111yescharacteristic, complemented
49D119—92no—
50C7×D17—632no—
51C2×D51—214no—
52C2×C7×D7—1531noHall
53C32×C17C2×C7×D711yescharacteristic, complemented, Hall
54C3×C72C2×D5114yescomplemented
55C2×C32×C7—23no—
56C2×C32×C7C7×D1711yescharacteristic, complemented
57C2×C32×C7D11911yescharacteristic, complemented
58C3⋊D21—172no—
59C7×C3⋊D3—1192no—
60C7×C17—23no—
61C7×C17C2×C7×C3⋊D311yescharacteristic, complemented
62C7×C17C2×C3⋊D2111yescharacteristic, complemented
63C2×C3×C17C7×D2114yescomplemented
64D51—218no—
65C2×C72C3⋊D5111yescharacteristic, complemented
66C7×D7—1532no—
67C2×D21—514no—
68C2×D3×C7—3574no—
69C2×D17—631noHall
70C32×C7—23no—
71C32×C7C2×C7×D1711yescharacteristic, complemented
72C32×C7C2×D11911yescharacteristic, complemented
73C3×C17C2×C7×D2114yescomplemented
74C72C2×C3⋊D5111yescharacteristic, complemented, Sylow
75C2×C3×C7—212no—
76C2×C3×C7C7×D5114yescomplemented
77C2×C3×C7D35714yescomplemented
78D21—518no—
79D3×C7—3578no—
80C2×C3⋊D3—1191noHall
81C2×C17C7×C3⋊D2111yescharacteristic, complemented
82D17—632no—
83C22×C7—10711no—
84C2×D7—1531no—
85C3×C7—212no—
86C3×C7C2×C7×D5114yescomplemented
87C3×C7C2×D35714yescomplemented
88C2×C32C7×D11911yescharacteristic, complemented
89C3⋊D3—1192no—
90C17C2×C7×C3⋊D2111yescharacteristic, complemented, Sylow
91C2×C7—23no—
92C2×C7—10712no—
93C2×C7C7×C3⋊D5111yescharacteristic, complemented
94C2×C7C3⋊D35711yescharacteristic, direct product factor
95D7—1532no—
96C2×D3—3574no—
97C32C2×C7×D11911yescharacteristic, complemented, Sylow
98C7—23no—
99C7C2×C3⋊D35711yescharacteristic, direct product factor
100C7C2×C7×C3⋊D5111yescharacteristic, complemented
101C2×C3C7×D35714yescomplemented
102D3—3578no—
103C22—10711noSylow
104C3C2×C7×D35714yescomplemented
105C2—10712no—
106C2C7×C3⋊D35711yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C7C3⋊D357
commutator, cosocle, hypocenterC32×C7×C17C22×C7
FrattiniC1G
Fitting, socleC2×C32×C72×C17C2
LCSG ▷ C32×C7×C17
UCSC1 ◁ C2×C7

Complements

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

NH ≅ G/Ntype
1. C7×C3⋊D357C2direct (N × H)
2. C2×C32×C72×C17C2semidirect
4. C32×C72×C17C22semidirect
6. C2×C3×C72×C17D3semidirect
8. C2×C3⋊D357C7direct (N × H)
10. C3×C72×C17C2×D3semidirect
11. C3⋊D357C2×C7direct (N × H)
14. C2×C32×C7×C17D7semidirect
15. C2×C32×C7×C17C2×C7semidirect
17. C2×C72×C17C3⋊D3semidirect
22. C32×C7×C17C2×D7semidirect
23. C32×C7×C17C22×C7semidirect
24. C2×C32×C72D17semidirect
26. C72×C17C2×C3⋊D3semidirect
28. C2×C3×C7×C17D3×C7semidirect
29. C2×C3×C7×C17D21semidirect
36. C32×C72C2×D17semidirect
38. C3×C7×C17C2×D3×C7semidirect
39. C3×C7×C17C2×D21semidirect
40. C2×C32×C17C7×D7semidirect
42. C2×C3×C72D51semidirect
47. C2×C7×C17C7×C3⋊D3semidirect
48. C2×C7×C17C3⋊D21semidirect
53. C32×C17C2×C7×D7semidirect
54. C3×C72C2×D51semidirect
56. C2×C32×C7C7×D17semidirect
57. C2×C32×C7D119semidirect
61. C7×C17C2×C7×C3⋊D3semidirect
62. C7×C17C2×C3⋊D21semidirect
63. C2×C3×C17C7×D21semidirect
65. C2×C72C3⋊D51semidirect
71. C32×C7C2×C7×D17semidirect
72. C32×C7C2×D119semidirect
73. C3×C17C2×C7×D21semidirect
74. C72C2×C3⋊D51semidirect
76. C2×C3×C7C7×D51semidirect
77. C2×C3×C7D357semidirect
81. C2×C17C7×C3⋊D21semidirect
86. C3×C7C2×C7×D51semidirect
87. C3×C7C2×D357semidirect
88. C2×C32C7×D119semidirect
90. C17C2×C7×C3⋊D21semidirect
93. C2×C7C7×C3⋊D51semidirect
94. C2×C7C3⋊D357direct (N × H)
97. C32C2×C7×D119semidirect
99. C7C2×C3⋊D357direct (N × H)
100. C7C2×C7×C3⋊D51semidirect
101. C2×C3C7×D357semidirect
104. C3C2×C7×D357semidirect
106. C2C7×C3⋊D357direct (N × H)

Maximal subgroups

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

subgroupindex
C7×C3⋊D3572
C2×C32×C72×C172
C2×C7×D3573
C2×C7×C3⋊D517
C2×C3⋊D3577
C2×C7×C3⋊D2117