Finite Group Databasebeta

← C2×C7×C3⋊D231 #34085075

Subgroups — C2×C7×C3⋊D231 #34085075

Order 19404.

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⋊D231C212yesmaximal, direct product factor
2C2×C32×C72×C11C211yesmaximal, characteristic, complemented
3C2×C7×D231—34nomaximal
4C32×C72×C11C2211yescharacteristic, complemented, Hall
5C7×D231—38no—
6C2×C3×C72×C11D314yescomplemented
7C2×C7×C3⋊D33—71nomaximal
8C2×C3⋊D231C711yesmaximal, characteristic, direct product factor
9C2×C7×D77—91noHall
10C2×C7×C3⋊D21—111nomaximal, Hall
11C3×C72×C11C2×D314yescomplemented
12C2×C32×C7×C11—23no—
13C2×C32×C7×C11D711yescharacteristic, complemented
14C2×C32×C7×C11C2×C711yescharacteristic, complemented
15C3⋊D231C2×C712yesdirect product factor
16C7×C3⋊D33—72no—
17C2×C72×C11C3⋊D311yescharacteristic, complemented
18C7×D77—92no—
19C2×D231—34no—
20C2×C7×D33—214no—
21C2×C32×C72D1111yescharacteristic, complemented
22C7×C3⋊D21—112no—
23C32×C7×C11—23no—
24C32×C7×C11C2×D711yescharacteristic, complemented
25C32×C7×C11C22×C711yescharacteristic, complemented
26C2×C7×D21—334no—
27C72×C11C2×C3⋊D311yescharacteristic, complemented, Hall
28C2×C3×C7×C11—212no—
29C2×C3×C7×C11D3×C714yescomplemented
30C2×C3×C7×C11D2114yescomplemented
31D231—38no—
32C7×D33—218no—
33C32×C72C2×D1111yescharacteristic, complemented, Hall
34C2×C3⋊D33—71noHall
35C2×D77—91no—
36C2×C7×D11—631no—
37C2×C3×C72D3314yescomplemented
38C7×D21—338no—
39C2×C3⋊D21—111no—
40C2×C7×C3⋊D3—771no—
41C3×C7×C11—212no—
42C3×C7×C11C2×D3×C714yescomplemented
43C3×C7×C11C2×D2114yescomplemented
44C2×C32×C11C7×D711yescharacteristic, complemented
45C3⋊D33—72no—
46C2×C7×D7—991noHall
47C2×C7×C11—23no—
48C2×C7×C11C7×C3⋊D311yescharacteristic, complemented
49C2×C7×C11C3⋊D2111yescharacteristic, complemented
50D77—92no—
51C7×D11—632no—
52C3×C72C2×D3314yescomplemented
53C2×D33—214no—
54C2×C32×C7—23no—
55C2×C32×C7C7×D1111yescharacteristic, complemented
56C2×C32×C7D7711yescharacteristic, complemented
57C3⋊D21—112no—
58C7×C3⋊D3—772no—
59C32×C11C2×C7×D711yescharacteristic, complemented, Hall
60C2×C72C3⋊D3311yescharacteristic, complemented
61C7×D7—992no—
62C2×D21—334no—
63C2×D3×C7—2314no—
64C7×C11—23no—
65C7×C11C2×C7×C3⋊D311yescharacteristic, complemented
66C7×C11C2×C3⋊D2111yescharacteristic, complemented
67C2×C3×C11C7×D2114yescomplemented
68D33—218no—
69C32×C7—23no—
70C32×C7C2×C7×D1111yescharacteristic, complemented
71C32×C7C2×D7711yescharacteristic, complemented
72C72C2×C3⋊D3311yescharacteristic, complemented, Sylow
73C2×D11—631noHall
74C2×C3×C7—212no—
75C2×C3×C7C7×D3314yescomplemented
76C2×C3×C7D23114yescomplemented
77D21—338no—
78D3×C7—2318no—
79C2×C3⋊D3—771noHall
80C3×C11C2×C7×D2114yescomplemented
81C22×C7—6931no—
82C2×D7—991no—
83C2×C11C7×C3⋊D2111yescharacteristic, complemented
84D11—632no—
85C3×C7—212no—
86C3×C7C2×C7×D3314yescomplemented
87C3×C7C2×D23114yescomplemented
88C2×C32C7×D7711yescharacteristic, complemented
89C3⋊D3—772no—
90C2×C7—23no—
91C2×C7—6932no—
92C2×C7C7×C3⋊D3311yescharacteristic, complemented
93C2×C7C3⋊D23111yescharacteristic, direct product factor
94D7—992no—
95C2×D3—2314no—
96C11C2×C7×C3⋊D2111yescharacteristic, complemented, Sylow
97C32C2×C7×D7711yescharacteristic, complemented, Sylow
98C7—23no—
99C7C2×C3⋊D23111yescharacteristic, direct product factor
100C7C2×C7×C3⋊D3311yescharacteristic, complemented
101C2×C3C7×D23114yescomplemented
102D3—2318no—
103C22—6931noSylow
104C3C2×C7×D23114yescomplemented
105C2—6932no—
106C2C7×C3⋊D23111yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C7C3⋊D231
commutator, cosocle, hypocenterC32×C7×C11C22×C7
FrattiniC1G
Fitting, socleC2×C32×C72×C11C2
LCSG ▷ C32×C7×C11
UCSC1 ◁ C2×C7

Complements

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

NH ≅ G/Ntype
1. C7×C3⋊D231C2direct (N × H)
2. C2×C32×C72×C11C2semidirect
4. C32×C72×C11C22semidirect
6. C2×C3×C72×C11D3semidirect
8. C2×C3⋊D231C7direct (N × H)
11. C3×C72×C11C2×D3semidirect
13. C2×C32×C7×C11D7semidirect
14. C2×C32×C7×C11C2×C7semidirect
15. C3⋊D231C2×C7direct (N × H)
17. C2×C72×C11C3⋊D3semidirect
21. C2×C32×C72D11semidirect
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×C72C2×D11semidirect
37. C2×C3×C72D33semidirect
42. C3×C7×C11C2×D3×C7semidirect
43. C3×C7×C11C2×D21semidirect
44. C2×C32×C11C7×D7semidirect
48. C2×C7×C11C7×C3⋊D3semidirect
49. C2×C7×C11C3⋊D21semidirect
52. C3×C72C2×D33semidirect
55. C2×C32×C7C7×D11semidirect
56. C2×C32×C7D77semidirect
59. C32×C11C2×C7×D7semidirect
60. C2×C72C3⋊D33semidirect
65. C7×C11C2×C7×C3⋊D3semidirect
66. C7×C11C2×C3⋊D21semidirect
67. C2×C3×C11C7×D21semidirect
70. C32×C7C2×C7×D11semidirect
71. C32×C7C2×D77semidirect
72. C72C2×C3⋊D33semidirect
75. C2×C3×C7C7×D33semidirect
76. C2×C3×C7D231semidirect
80. C3×C11C2×C7×D21semidirect
83. C2×C11C7×C3⋊D21semidirect
86. C3×C7C2×C7×D33semidirect
87. C3×C7C2×D231semidirect
88. C2×C32C7×D77semidirect
92. C2×C7C7×C3⋊D33semidirect
93. C2×C7C3⋊D231direct (N × H)
96. C11C2×C7×C3⋊D21semidirect
97. C32C2×C7×D77semidirect
99. C7C2×C3⋊D231direct (N × H)
100. C7C2×C7×C3⋊D33semidirect
101. C2×C3C7×D231semidirect
104. C3C2×C7×D231semidirect
106. C2C7×C3⋊D231direct (N × H)

Maximal subgroups

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

subgroupindex
C7×C3⋊D2312
C2×C32×C72×C112
C2×C7×D2313
C2×C7×C3⋊D337
C2×C3⋊D2317
C2×C7×C3⋊D2111