Finite Group Databasebeta

← D7×C3⋊D429 #49114989

Subgroups — D7×C3⋊D429 #49114989

Order 36036.

240 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 76 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
1C32×C11×C13×D7C211yesmaximal, characteristic, complemented
2C7×C3⋊D429C211yesmaximal, characteristic, complemented
3C3⋊D3003C211yesmaximal, characteristic, complemented
4D7×D429—34nomaximal
5C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
6D3003—34no—
7C7×D429—34no—
8C3×C11×C13×D7D314yescomplemented
9C2×C3⋊D429—71nomaximal, Hall
10D7×D143—91noHall
11D7×C3⋊D39—111nomaximal, Hall
12C3×C7×C11×C13C2×D314yescomplemented
13D7×C3⋊D33—131nomaximal, Hall
14C3⋊D429—71no—
15C3⋊D429D711yescharacteristic, direct product factor
16C2×C32×C11×C13—71no—
17D1001—91no—
18C11×C13×D7C3⋊D311yescharacteristic, complemented
19C7×D143—91no—
20C2×D429—214no—
21C3⋊D273—111no—
22C7×C3⋊D39—111no—
23C32×C13×D7D1111yescharacteristic, complemented
24C3⋊D231—131no—
25C7×C3⋊D33—131no—
26C32×C11×D7D1311yescharacteristic, complemented
27C32×C11×C13C2×D711yescharacteristic, complemented, Hall
28D7×D39—334no—
29C7×C11×C13C2×C3⋊D311yescharacteristic, complemented, Hall
30D7×D33—394no—
31C2×C3×C11×C13—74no—
32D429—34no—
33D429—214no—
34C32×C7×C13C2×D1111yescharacteristic, complemented, Hall
35C32×C7×C11C2×D1311yescharacteristic, complemented, Hall
36C2×D143—631noHall
37D273—334no—
38C7×D39—334no—
39C3×C13×D7D3314yescomplemented
40C2×C3⋊D39—771noHall
41D231—394no—
42C7×D33—394no—
43C3×C11×D7D3914yescomplemented
44C3×C11×C13D3×D714yescomplemented
45C2×C3⋊D33—911noHall
46D7×D13—991noHall
47D7×D11—1171noHall
48C2×C11×C13—71no—
49D143—91no—
50D143—631no—
51C3×C7×C13C2×D3314yescomplemented
52D7×C3⋊D3—1431noHall
53C2×C32×C13—71no—
54C3⋊D39—111no—
55C3⋊D39—771no—
56C3×C7×C11C2×D3914yescomplemented
57C2×C32×C11—71no—
58C3⋊D33—131no—
59C3⋊D33—911no—
60D91—991no—
61C7×D13—991no—
62C13×D7C3⋊D3311yescharacteristic, complemented
63C2×D39—2314no—
64D77—1171no—
65C7×D11—1171no—
66C11×D7C3⋊D3911yescharacteristic, complemented
67C11×C13D7×C3⋊D311yescharacteristic, complemented, Hall
68C2×D33—2734no—
69C3⋊D21—1431no—
70C7×C3⋊D3—1431no—
71C32×D7D14311yescharacteristic, complemented
72C32×C13D7×D1111yescharacteristic, complemented, Hall
73C32×C11D7×D1311yescharacteristic, complemented, Hall
74C7×C13C2×C3⋊D3311yescharacteristic, complemented, Hall
75D3×D7—4294no—
76C2×C3×C13—74no—
77D39—334no—
78D39—2314no—
79C7×C11C2×C3⋊D3911yescharacteristic, complemented, Hall
80C2×C3×C11—74no—
81D33—2734no—
82D33—394no—
83C32×C7C2×D14311yescharacteristic, complemented, Hall
84C2×D13—6931noHall
85C2×D11—8191noHall
86D21—4294no—
87C3×D7D42914yescomplemented
88D3×C7—4294no—
89C3×C13D7×D3314yescomplemented
90C2×C3⋊D3—10011noHall
91C3×C11D7×D3914yescomplemented
92C2×D7—12871noHall
93C2×C13—71no—
94D13—991no—
95D13—6931no—
96C2×C11—71no—
97D11—8191no—
98D11—1171no—
99C3×C7C2×D42914yescomplemented
100C2×C32—71no—
101C3⋊D3—1431no—
102C3⋊D3—10011no—
103C2×C7—12871no—
104D7—12871no—
105D7C3⋊D42911yescharacteristic, direct product factor
106C13D7×C3⋊D3311yescharacteristic, complemented, Sylow
107C2×D3—30034no—
108C11D7×C3⋊D3911yescharacteristic, complemented, Sylow
109C32D7×D14311yescharacteristic, complemented, Sylow
110C7C2×C3⋊D42911yescharacteristic, complemented, Sylow
111C2×C3—74no—
112D3—4294no—
113D3—30034no—
114C22—90091noSylow
115C3D7×D42914yescomplemented
116C2—71no—
117C2—12871no—
118C2—90091no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C7×C11×C13C22
LCSG ▷ C32×C7×C11×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C32×C11×C13×D7C2semidirect
2. C7×C3⋊D429C2semidirect
3. C3⋊D3003C2semidirect
5. C32×C7×C11×C13C22semidirect
8. C3×C11×C13×D7D3semidirect
12. C3×C7×C11×C13C2×D3semidirect
15. C3⋊D429D7direct (N × H)
18. C11×C13×D7C3⋊D3semidirect
23. C32×C13×D7D11semidirect
26. C32×C11×D7D13semidirect
27. C32×C11×C13C2×D7semidirect
29. C7×C11×C13C2×C3⋊D3semidirect
34. C32×C7×C13C2×D11semidirect
35. C32×C7×C11C2×D13semidirect
39. C3×C13×D7D33semidirect
43. C3×C11×D7D39semidirect
44. C3×C11×C13D3×D7semidirect
51. C3×C7×C13C2×D33semidirect
56. C3×C7×C11C2×D39semidirect
62. C13×D7C3⋊D33semidirect
66. C11×D7C3⋊D39semidirect
67. C11×C13D7×C3⋊D3semidirect
71. C32×D7D143semidirect
72. C32×C13D7×D11semidirect
73. C32×C11D7×D13semidirect
74. C7×C13C2×C3⋊D33semidirect
79. C7×C11C2×C3⋊D39semidirect
83. C32×C7C2×D143semidirect
87. C3×D7D429semidirect
89. C3×C13D7×D33semidirect
91. C3×C11D7×D39semidirect
99. C3×C7C2×D429semidirect
105. D7C3⋊D429direct (N × H)
106. C13D7×C3⋊D33semidirect
108. C11D7×C3⋊D39semidirect
109. C32D7×D143semidirect
110. C7C2×C3⋊D429semidirect
115. C3D7×D429semidirect

Maximal subgroups

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

subgroupindex
C32×C11×C13×D72
C7×C3⋊D4292
C3⋊D30032
D7×D4293
C2×C3⋊D4297
D7×C3⋊D3911
D7×C3⋊D3313