Finite Group Databasebeta

← C11×D63⋊D13 #49114484

Subgroups — C11×D63⋊D13 #49114484

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
1C11×C13×D63C211yesmaximal, characteristic, complemented
2C7×C11×D117C211yesmaximal, characteristic, complemented
3C9×C11×D91C211yesmaximal, characteristic, complemented
4C11×D21⋊D13—31nomaximal
5C7×C9×C11×C13C2211yescharacteristic, complemented, Hall
6C11×C13×D21—31no—
7C7×C11×D39—31no—
8C3×C11×D91D311yescharacteristic
9C11×D9×D13—71nomaximal, Hall
10C11×D7×D13—91noHall
11D63⋊D13C1111yesmaximal, characteristic, direct product factor, Hall
12C3×C7×C11×C13C2×D311yescharacteristic
13C11×D7×D9—131nomaximal, Hall
14C11×D117D711yescharacteristic, complemented
15C11×C13×D9—71no—
16C9×C11×D13—71no—
17C11×D91D911yescharacteristic, complemented
18C11×C13×D7—91no—
19C7×C11×D13—91no—
20D3×C11×D13—211no—
21C13×D63C2×C1111yescharacteristic, complemented
22C7×D117C2×C1111yescharacteristic, complemented
23C9×D91C2×C1111yescharacteristic, complemented
24C11×D63D1311yescharacteristic, complemented
25C7×C11×D9—131no—
26C9×C11×D7—131no—
27C9×C11×C13C2×D711yescharacteristic, complemented, Hall
28D21⋊D13—31no—
29C7×C11×C13C2×D911yescharacteristic, complemented, Hall
30D3×C11×D7—391no—
31C11×D39—31no—
32D3×C11×C13—211no—
33C3×C11×D13—71no—
34C7×C9×C13C22×C1111yescharacteristic, complemented, Hall
35C7×C9×C11C2×D1311yescharacteristic, complemented, Hall
36C2×C11×D13—631noHall
37C13×D21—31no—
38C7×D39—31no—
39C3×D91D3×C1111yescharacteristic
40D9×D13—71noHall
41C11×D21—31no—
42D3×C7×C11—391no—
43C3×C11×D7—131no—
44C3×C11×C13D3×D711yescharacteristic
45C2×C11×D9—911noHall
46D7×D13—91noHall
47C2×C11×D7—1171noHall
48C2×C11×C13—631no—
49C11×D13—71no—
50C11×D13—91no—
51C3×C7×C13C2×D3×C1111yescharacteristic
52D7×D9—131noHall
53D117C11×D711yescharacteristic, complemented
54C9×D13—71no—
55C13×D9—71no—
56C3×C7×C11D3×D1311yescharacteristic
57C2×C9×C11—911no—
58C11×D9—71no—
59C11×D9—131no—
60D91C11×D911yescharacteristic, complemented
61C7×D13—91no—
62C13×D7—91no—
63D3×D13—211no—
64C2×C7×C11—1171no—
65C11×D7—91no—
66C11×D7—131no—
67C11×C13D7×D911yescharacteristic, complemented, Hall
68C2×D3×C11—2731no—
69D63C11×D1311yescharacteristic, complemented
70C9×D7—131no—
71C7×D9—131no—
72C9×C13C2×C11×D711yescharacteristic, complemented, Hall
73C9×C11D7×D1311yescharacteristic, complemented, Hall
74C7×C13C2×C11×D911yescharacteristic, complemented, Hall
75D3×D7—391no—
76D39—31no—
77C3×D13—71no—
78D3×C13—211no—
79C7×C11D9×D1311yescharacteristic, complemented, Hall
80C2×C3×C11—911no—
81D3×C11—211no—
82D3×C11—391no—
83C7×C9C2×C11×D1311yescharacteristic, complemented, Hall
84C2×D13—631noHall
85C22×C11—8191noHall
86D21—31no—
87C3×D7—131no—
88D3×C7—391no—
89C3×C13D3×C11×D711yescharacteristic
90C2×D9—911noHall
91C3×C11D21⋊D1311yescharacteristic
92C2×D7—1171noHall
93C2×C13—631no—
94D13—71no—
95D13—91no—
96C2×C11—631no—
97C2×C11—911no—
98C2×C11—1171no—
99C3×C7D3×C11×D1311yescharacteristic
100C2×C9—911no—
101D9—71no—
102D9—131no—
103C2×C7—1171no—
104D7—91no—
105D7—131no—
106C13C11×D7×D911yescharacteristic, complemented, Sylow
107C2×D3—2731no—
108C11D63⋊D1311yescharacteristic, direct product factor, Sylow
109C9C11×D7×D1311yescharacteristic, complemented, Sylow
110C7C11×D9×D1311yescharacteristic, complemented, Sylow
111C2×C3—911no—
112D3—211no—
113D3—391no—
114C22—8191noSylow
115C3C11×D21⋊D1311yescharacteristic
116C2—631no—
117C2—911no—
118C2—1171no—
subgroupG/H
center, hypercenterC11D63⋊D13
commutator, cosocle, hypocenterC7×C9×C13C22×C11
FrattiniC3C11×D21⋊D13
FittingC7×C9×C11×C13C22
socleC3×C7×C11×C13C2×D3
LCSG ▷ C7×C9×C13
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C11×C13×D63C2semidirect
2. C7×C11×D117C2semidirect
3. C9×C11×D91C2semidirect
5. C7×C9×C11×C13C22semidirect
11. D63⋊D13C11direct (N × H)
14. C11×D117D7semidirect
17. C11×D91D9semidirect
21. C13×D63C2×C11semidirect
22. C7×D117C2×C11semidirect
23. C9×D91C2×C11semidirect
24. C11×D63D13semidirect
27. C9×C11×C13C2×D7semidirect
29. C7×C11×C13C2×D9semidirect
34. C7×C9×C13C22×C11semidirect
35. C7×C9×C11C2×D13semidirect
53. D117C11×D7semidirect
60. D91C11×D9semidirect
67. C11×C13D7×D9semidirect
69. D63C11×D13semidirect
72. C9×C13C2×C11×D7semidirect
73. C9×C11D7×D13semidirect
74. C7×C13C2×C11×D9semidirect
79. C7×C11D9×D13semidirect
83. C7×C9C2×C11×D13semidirect
106. C13C11×D7×D9semidirect
108. C11D63⋊D13direct (N × H)
109. C9C11×D7×D13semidirect
110. C7C11×D9×D13semidirect

Maximal subgroups

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

subgroupindex
C11×C13×D632
C7×C11×D1172
C9×C11×D912
C11×D21⋊D133
C11×D9×D137
D63⋊D1311
C11×D7×D913