Finite Group Databasebeta

← C7×D99⋊D13 #49114472

Subgroups — C7×D99⋊D13 #49114472

Order 36036.

120 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 40 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×C13×D99C211yesmaximal, characteristic, complemented
2C7×C11×D117C211yesmaximal, characteristic, complemented
3C7×C9×D143C211yesmaximal, characteristic, complemented
4C7×D33⋊D13—31nomaximal
5C7×C9×C11×C13C2211yescharacteristic, complemented, Hall
6C7×C13×D33—31no—
7C7×C11×D39—31no—
8C3×C7×D143D311yescharacteristic
9D99⋊D13C711yesmaximal, characteristic, direct product factor, Hall
10C7×D11×D13—91noHall
11C7×D9×D13—111nomaximal, Hall
12C3×C7×C11×C13C2×D311yescharacteristic
13C7×D9×D11—131nomaximal, Hall
14C13×D99C2×C711yescharacteristic, complemented
15C11×D117C2×C711yescharacteristic, complemented
16C9×D143C2×C711yescharacteristic, complemented
17C7×D143D911yescharacteristic, complemented
18C7×C13×D11—91no—
19C7×C11×D13—91no—
20D33⋊D13—31no—
21C7×D117D1111yescharacteristic, complemented
22C7×C13×D9—111no—
23C7×C9×D13—111no—
24C7×D99D1311yescharacteristic, complemented
25C7×C11×D9—131no—
26C7×C9×D11—131no—
27C9×C11×C13C22×C711yescharacteristic, complemented, Hall
28D3×C7×D13—331no—
29C7×C11×C13C2×D911yescharacteristic, complemented, Hall
30D3×C7×D11—391no—
31C13×D33—31no—
32C11×D39—31no—
33C3×D143D3×C711yescharacteristic
34C7×C9×C13C2×D1111yescharacteristic, complemented, Hall
35C7×C9×C11C2×D1311yescharacteristic, complemented, Hall
36D11×D13—91noHall
37C7×D39—31no—
38D3×C7×C13—331no—
39C3×C7×D13—111no—
40D9×D13—111noHall
41C7×D33—31no—
42D3×C7×C11—391no—
43C3×C7×D11—131no—
44C3×C11×C13C2×D3×C711yescharacteristic
45D9×D11—131noHall
46C2×C7×D13—991noHall
47C2×C7×D11—1171noHall
48D143C7×D911yescharacteristic, complemented
49C11×D13—91no—
50C13×D11—91no—
51C3×C7×C13D3×D1111yescharacteristic
52C2×C7×D9—1431noHall
53D117C7×D1111yescharacteristic, complemented
54C9×D13—111no—
55C13×D9—111no—
56C3×C7×C11D3×D1311yescharacteristic
57D99C7×D1311yescharacteristic, complemented
58C9×D11—131no—
59C11×D9—131no—
60C2×C7×C13—991no—
61C7×D13—91no—
62C7×D13—111no—
63D3×D13—331no—
64C2×C7×C11—1171no—
65C7×D11—91no—
66C7×D11—131no—
67C11×C13C2×C7×D911yescharacteristic, complemented, Hall
68D3×D11—391no—
69C2×C7×C9—1431no—
70C7×D9—111no—
71C7×D9—131no—
72C9×C13C2×C7×D1111yescharacteristic, complemented, Hall
73C9×C11C2×C7×D1311yescharacteristic, complemented, Hall
74C7×C13D9×D1111yescharacteristic, complemented, Hall
75C2×D3×C7—4291no—
76D39—31no—
77C3×D13—111no—
78D3×C13—331no—
79C7×C11D9×D1311yescharacteristic, complemented, Hall
80D33—31no—
81C3×D11—131no—
82D3×C11—391no—
83C7×C9D11×D1311yescharacteristic, complemented, Hall
84C2×D13—991noHall
85C2×D11—1171noHall
86C2×C3×C7—1431no—
87D3×C7—331no—
88D3×C7—391no—
89C3×C13D3×C7×D1111yescharacteristic
90C2×D9—1431noHall
91C3×C11D3×C7×D1311yescharacteristic
92C22×C7—12871noHall
93C2×C13—991no—
94D13—91no—
95D13—111no—
96C2×C11—1171no—
97D11—91no—
98D11—131no—
99C3×C7D33⋊D1311yescharacteristic
100C2×C9—1431no—
101D9—111no—
102D9—131no—
103C2×C7—991no—
104C2×C7—1171no—
105C2×C7—1431no—
106C13C7×D9×D1111yescharacteristic, complemented, Sylow
107C2×D3—4291no—
108C11C7×D9×D1311yescharacteristic, complemented, Sylow
109C9C7×D11×D1311yescharacteristic, complemented, Sylow
110C7D99⋊D1311yescharacteristic, direct product factor, Sylow
111C2×C3—1431no—
112D3—331no—
113D3—391no—
114C22—12871noSylow
115C3C7×D33⋊D1311yescharacteristic
116C2—991no—
117C2—1171no—
118C2—1431no—
subgroupG/H
center, hypercenterC7D99⋊D13
commutator, cosocle, hypocenterC9×C11×C13C22×C7
FrattiniC3C7×D33⋊D13
FittingC7×C9×C11×C13C22
socleC3×C7×C11×C13C2×D3
LCSG ▷ C9×C11×C13
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C7×C13×D99C2semidirect
2. C7×C11×D117C2semidirect
3. C7×C9×D143C2semidirect
5. C7×C9×C11×C13C22semidirect
9. D99⋊D13C7direct (N × H)
14. C13×D99C2×C7semidirect
15. C11×D117C2×C7semidirect
16. C9×D143C2×C7semidirect
17. C7×D143D9semidirect
21. C7×D117D11semidirect
24. C7×D99D13semidirect
27. C9×C11×C13C22×C7semidirect
29. C7×C11×C13C2×D9semidirect
34. C7×C9×C13C2×D11semidirect
35. C7×C9×C11C2×D13semidirect
48. D143C7×D9semidirect
53. D117C7×D11semidirect
57. D99C7×D13semidirect
67. C11×C13C2×C7×D9semidirect
72. C9×C13C2×C7×D11semidirect
73. C9×C11C2×C7×D13semidirect
74. C7×C13D9×D11semidirect
79. C7×C11D9×D13semidirect
83. C7×C9D11×D13semidirect
106. C13C7×D9×D11semidirect
108. C11C7×D9×D13semidirect
109. C9C7×D11×D13semidirect
110. C7D99⋊D13direct (N × H)

Maximal subgroups

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

subgroupindex
C7×C13×D992
C7×C11×D1172
C7×C9×D1432
C7×D33⋊D133
D99⋊D137
C7×D9×D1311
C7×D9×D1113