Finite Group Databasebeta

← C2×C7×C11×C3⋊D21 #34085076

Subgroups — C2×C7×C11×C3⋊D21 #34085076

Order 19404.

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×C11×C3⋊D21C212yesmaximal, direct product factor
2C2×C32×C72×C11C211yesmaximal, characteristic, complemented
3C2×C7×C11×D21—34nomaximal
4C32×C72×C11C2211yescharacteristic, complemented, Hall
5C7×C11×D21—38no—
6C2×C3×C72×C11D314yescomplemented
7C2×C7×C11×C3⋊D3—71nomaximal
8C2×C11×C3⋊D21C711yesmaximal, characteristic, direct product factor
9C2×C7×C11×D7—91noHall
10C2×C7×C3⋊D21C1111yesmaximal, characteristic, direct product factor, Hall
11C3×C72×C11C2×D314yescomplemented
12C2×C32×C7×C11—23no—
13C2×C32×C7×C11D711yescharacteristic, complemented
14C2×C32×C7×C11C2×C711yescharacteristic, complemented
15C11×C3⋊D21C2×C712yesdirect product factor
16C7×C11×C3⋊D3—72no—
17C2×C72×C11C3⋊D311yescharacteristic, complemented
18C7×C11×D7—92no—
19C2×C11×D21—34no—
20C2×D3×C7×C11—214no—
21C2×C32×C72C2×C1111yescharacteristic, complemented
22C7×C3⋊D21C2×C1112yesdirect product factor
23C32×C7×C11—23no—
24C32×C7×C11C2×D711yescharacteristic, complemented
25C32×C7×C11C22×C711yescharacteristic, complemented
26C2×C7×D21—34no—
27C72×C11C2×C3⋊D311yescharacteristic, complemented, Hall
28C2×C3×C7×C11—212no—
29C2×C3×C7×C11D3×C714yescomplemented
30C2×C3×C7×C11D2114yescomplemented
31C11×D21—38no—
32D3×C7×C11—218no—
33C32×C72C22×C1111yescharacteristic, complemented, Hall
34C2×C11×C3⋊D3—71noHall
35C22×C7×C11—631no—
36C2×C11×D7—91no—
37C2×C3×C72D3×C1114yescomplemented
38C7×D21—38no—
39C2×C3⋊D21C7×C1111yescharacteristic, direct product factor
40C2×C7×C3⋊D3—71no—
41C3×C7×C11—212no—
42C3×C7×C11C2×D3×C714yescomplemented
43C3×C7×C11C2×D2114yescomplemented
44C2×C32×C11C7×D711yescharacteristic, complemented
45C11×C3⋊D3—72no—
46C2×C7×D7—91noHall
47C2×C7×C11—23no—
48C2×C7×C11—632no—
49C2×C7×C11C7×C3⋊D311yescharacteristic, complemented
50C2×C7×C11C3⋊D2111yescharacteristic, direct product factor
51C11×D7—92no—
52C3×C72C2×D3×C1114yescomplemented
53C2×D3×C11—214no—
54C2×C32×C7—23no—
55C2×C32×C7C11×D711yescharacteristic, complemented
56C2×C32×C7C2×C7×C1111yescharacteristic, complemented
57C3⋊D21C2×C7×C1112yesdirect product factor
58C7×C3⋊D3—72no—
59C32×C11C2×C7×D711yescharacteristic, complemented, Hall
60C2×C72C11×C3⋊D311yescharacteristic, complemented
61C7×D7—92no—
62C2×D21—34no—
63C2×D3×C7—214no—
64C7×C11—23no—
65C7×C11C2×C7×C3⋊D311yescharacteristic, complemented
66C7×C11C2×C3⋊D2111yescharacteristic, direct product factor
67C2×C3×C11C7×D2114yescomplemented
68D3×C11—218no—
69C32×C7—23no—
70C32×C7C2×C11×D711yescharacteristic, complemented
71C32×C7C22×C7×C1111yescharacteristic, complemented
72C72C2×C11×C3⋊D311yescharacteristic, complemented, Sylow
73C22×C11—631noHall
74C2×C3×C7—212no—
75C2×C3×C7D3×C7×C1114yescomplemented
76C2×C3×C7C11×D2114yescomplemented
77D21—38no—
78D3×C7—218no—
79C2×C3⋊D3—71noHall
80C3×C11C2×C7×D2114yescomplemented
81C22×C7—631no—
82C2×D7—91no—
83C2×C11—632no—
84C2×C11C7×C3⋊D2111yescharacteristic, direct product factor
85C3×C7—212no—
86C3×C7C2×D3×C7×C1114yescomplemented
87C3×C7C2×C11×D2114yescomplemented
88C2×C32C7×C11×D711yescharacteristic, complemented
89C3⋊D3—72no—
90C2×C7—23no—
91C2×C7—632no—
92C2×C7C7×C11×C3⋊D311yescharacteristic, complemented
93C2×C7C11×C3⋊D2111yescharacteristic, direct product factor
94D7—92no—
95C2×D3—214no—
96C11C2×C7×C3⋊D2111yescharacteristic, direct product factor, Sylow
97C32C2×C7×C11×D711yescharacteristic, complemented, Sylow
98C7—23no—
99C7C2×C11×C3⋊D2111yescharacteristic, direct product factor
100C7C2×C7×C11×C3⋊D311yescharacteristic, complemented
101C2×C3C7×C11×D2114yescomplemented
102D3—218no—
103C22—631noSylow
104C3C2×C7×C11×D2114yescomplemented
105C2—632no—
106C2C7×C11×C3⋊D2111yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C7×C11C3⋊D21
commutator, cosocle, hypocenterC32×C7C22×C7×C11
FrattiniC1G
Fitting, socleC2×C32×C72×C11C2
LCSG ▷ C32×C7
UCSC1 ◁ C2×C7×C11

Complements

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

NH ≅ G/Ntype
1. C7×C11×C3⋊D21C2direct (N × H)
2. C2×C32×C72×C11C2semidirect
4. C32×C72×C11C22semidirect
6. C2×C3×C72×C11D3semidirect
8. C2×C11×C3⋊D21C7direct (N × H)
10. C2×C7×C3⋊D21C11direct (N × H)
11. C3×C72×C11C2×D3semidirect
13. C2×C32×C7×C11D7semidirect
14. C2×C32×C7×C11C2×C7semidirect
15. C11×C3⋊D21C2×C7direct (N × H)
17. C2×C72×C11C3⋊D3semidirect
21. C2×C32×C72C2×C11semidirect
22. C7×C3⋊D21C2×C11direct (N × H)
24. C32×C7×C11C2×D7semidirect
25. C32×C7×C11C22×C7semidirect
27. C72×C11C2×C3⋊D3semidirect
29. C2×C3×C7×C11D3×C7semidirect
30. C2×C3×C7×C11D21semidirect
33. C32×C72C22×C11semidirect
37. C2×C3×C72D3×C11semidirect
39. C2×C3⋊D21C7×C11direct (N × H)
42. C3×C7×C11C2×D3×C7semidirect
43. C3×C7×C11C2×D21semidirect
44. C2×C32×C11C7×D7semidirect
49. C2×C7×C11C7×C3⋊D3semidirect
50. C2×C7×C11C3⋊D21direct (N × H)
52. C3×C72C2×D3×C11semidirect
55. C2×C32×C7C11×D7semidirect
56. C2×C32×C7C2×C7×C11semidirect
57. C3⋊D21C2×C7×C11direct (N × H)
59. C32×C11C2×C7×D7semidirect
60. C2×C72C11×C3⋊D3semidirect
65. C7×C11C2×C7×C3⋊D3semidirect
66. C7×C11C2×C3⋊D21direct (N × H)
67. C2×C3×C11C7×D21semidirect
70. C32×C7C2×C11×D7semidirect
71. C32×C7C22×C7×C11semidirect
72. C72C2×C11×C3⋊D3semidirect
75. C2×C3×C7D3×C7×C11semidirect
76. C2×C3×C7C11×D21semidirect
80. C3×C11C2×C7×D21semidirect
84. C2×C11C7×C3⋊D21direct (N × H)
86. C3×C7C2×D3×C7×C11semidirect
87. C3×C7C2×C11×D21semidirect
88. C2×C32C7×C11×D7semidirect
92. C2×C7C7×C11×C3⋊D3semidirect
93. C2×C7C11×C3⋊D21direct (N × H)
96. C11C2×C7×C3⋊D21direct (N × H)
97. C32C2×C7×C11×D7semidirect
99. C7C2×C11×C3⋊D21direct (N × H)
100. C7C2×C7×C11×C3⋊D3semidirect
101. C2×C3C7×C11×D21semidirect
104. C3C2×C7×C11×D21semidirect
106. C2C7×C11×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×C11×C3⋊D212
C2×C32×C72×C112
C2×C7×C11×D213
C2×C7×C11×C3⋊D37
C2×C11×C3⋊D217
C2×C7×C3⋊D2111