Finite Group Databasebeta

← C11×C13⋊C3×Dic21 #49114587

Subgroups — C11×C13⋊C3×Dic21 #49114587

Order 36036.

112 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 54 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
1C2×C3×C7×C11×C13⋊C3C211yesmaximal, characteristic
2C11×Dic7×C13⋊C3—31nomaximal
3C11×C13×Dic21C311yesmaximal, characteristic, complemented
4C3×C7×C11×C13⋊C3C411yescharacteristic, complemented, Hall
5C2×C7×C11×C13⋊C3—21no—
6C2×C7×C11×C13⋊C3D311yescharacteristic
7C2×C3×C7×C11×C13C2×C311yescharacteristic
8C11×Dic3×C13⋊C3—71nomaximal, Hall
9C11×C13×Dic7—31noHall
10C13⋊C3×Dic21C1111yesmaximal, characteristic, direct product factor, Hall
11C7×C11×C13⋊C3—21no—
12C7×C11×C13⋊C3Dic311yescharacteristic, complemented
13C3×C7×C11×C13C3×C411yescharacteristic, complemented
14C3×C11×Dic21—131nomaximal, Hall
15C2×C3×C11×C13⋊C3D711yescharacteristic
16C2×C7×C11×C13C3×D311yescharacteristic
17C11×Dic3×C13—71no—
18C4×C11×C13⋊C3—211no—
19C2×C3×C7×C13⋊C3C2×C1111yescharacteristic
20C2×C32×C7×C11—131no—
21C3×C11×C13⋊C3Dic711yescharacteristic, complemented, Hall
22C13×Dic21C3×C1111yescharacteristic, complemented
23Dic7×C13⋊C3—31no—
24C7×C11×C13C3×Dic311yescharacteristic, complemented, Hall
25C11×Dic21C13⋊C311yescharacteristic, direct product factor
26C3×C11×Dic7—391no—
27C2×C3×C11×C13C3×D711yescharacteristic
28C2×C11×C13⋊C3—21no—
29C2×C11×C13⋊C3D2111yescharacteristic
30C3×C7×C13⋊C3C4×C1111yescharacteristic, complemented, Hall
31C32×C7×C11—131noHall
32C4×C11×C13—211noHall
33C2×C3×C7×C13C2×C3×C1111yescharacteristic
34C2×C7×C13⋊C3—21no—
35C2×C7×C13⋊C3D3×C1111yescharacteristic
36Dic3×C13⋊C3—71noHall
37C2×C3×C7×C11—131no—
38C2×C3×C7×C11—261no—
39C2×C3×C7×C11C2×C13⋊C311yescharacteristic
40C3×C11×C13C3×Dic711yescharacteristic, complemented
41C11×C13⋊C3—21no—
42C11×C13⋊C3Dic2111yescharacteristic, direct product factor
43C3×C11×Dic3—911noHall
44C13×Dic7—31noHall
45C11×Dic7—31noHall
46C2×C11×C13C3×D2111yescharacteristic
47C3×C7×C13C3×C4×C1111yescharacteristic, complemented
48C7×C13⋊C3—21no—
49C7×C13⋊C3C11×Dic311yescharacteristic, complemented
50C3×Dic21—131noHall
51C2×C3×C13⋊C3C11×D711yescharacteristic
52C3×C7×C11—131no—
53C3×C7×C11—261no—
54C3×C7×C11C4×C13⋊C311yescharacteristic, complemented
55C2×C32×C11—131no—
56C2×C7×C13C3×D3×C1111yescharacteristic
57Dic3×C13—71no—
58C4×C13⋊C3—211no—
59C2×C7×C11D3×C13⋊C311yescharacteristic
60C11×C13C3×Dic2111yescharacteristic, complemented, Hall
61C3×C4×C11—2731no—
62C11×Dic3—71no—
63C2×C32×C7—131no—
64C3×C13⋊C3C11×Dic711yescharacteristic, complemented, Hall
65C32×C11—131noHall
66C7×C13C3×C11×Dic311yescharacteristic, complemented, Hall
67Dic21C11×C13⋊C311yescharacteristic, direct product factor
68C3×Dic7—391no—
69C2×C3×C13C3×C11×D711yescharacteristic
70C2×C13⋊C3—21no—
71C2×C13⋊C3C11×D2111yescharacteristic
72C7×C11Dic3×C13⋊C311yescharacteristic, complemented, Hall
73C2×C3×C11—131no—
74C2×C3×C11—261no—
75C2×C3×C11D7×C13⋊C311yescharacteristic
76C32×C7—131noHall
77C4×C13—211noHall
78C4×C11—211noHall
79C2×C3×C7—131no—
80C2×C3×C7—261no—
81C2×C3×C7C2×C11×C13⋊C311yescharacteristic
82C3×C13C3×C11×Dic711yescharacteristic, complemented
83C13⋊C3—21no—
84C13⋊C3C11×Dic2111yescharacteristic, direct product factor
85C3×Dic3—911noHall
86C3×C11—131no—
87C3×C11—261no—
88C3×C11Dic7×C13⋊C311yescharacteristic, complemented
89Dic7—31noHall
90C2×C13C3×C11×D2111yescharacteristic
91C2×C11C13⋊C3×D2111yescharacteristic
92C3×C7—131no—
93C3×C7—261no—
94C3×C7C4×C11×C13⋊C311yescharacteristic, complemented
95C2×C32—131no—
96C2×C7D3×C11×C13⋊C311yescharacteristic
97C13C3×C11×Dic2111yescharacteristic, complemented, Sylow
98C3×C4—2731no—
99Dic3—71no—
100C11C13⋊C3×Dic2111yescharacteristic, direct product factor, Sylow
101C32—131noSylow
102C7C11×Dic3×C13⋊C311yescharacteristic, complemented, Sylow
103C2×C3—131no—
104C2×C3—261no—
105C2×C3C11×D7×C13⋊C311yescharacteristic
106C4—211noSylow
107C3—131no—
108C3—261no—
109C3C11×Dic7×C13⋊C311yescharacteristic, complemented
110C2C11×C13⋊C3×D2111yescharacteristic
subgroupG/H
center, hypercenterC2×C11C13⋊C3×D21
commutator, hypocenterC3×C7×C13C3×C4×C11
FrattiniC2C11×C13⋊C3×D21
Fitting, socleC2×C3×C7×C11×C13C2×C3
prime radicalC2×C3×C7×C11×C13⋊C3C2
cosocleC2×C3×C7×C13C2×C3×C11
LCSG ▷ C3×C7×C13
UCSC1 ◁ C2×C11

Complements

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

NH ≅ G/Ntype
3. C11×C13×Dic21C3semidirect
4. C3×C7×C11×C13⋊C3C4semidirect
10. C13⋊C3×Dic21C11direct (N × H)
12. C7×C11×C13⋊C3Dic3semidirect
13. C3×C7×C11×C13C3×C4semidirect
21. C3×C11×C13⋊C3Dic7semidirect
22. C13×Dic21C3×C11semidirect
24. C7×C11×C13C3×Dic3semidirect
25. C11×Dic21C13⋊C3direct (N × H)
30. C3×C7×C13⋊C3C4×C11semidirect
40. C3×C11×C13C3×Dic7semidirect
42. C11×C13⋊C3Dic21direct (N × H)
47. C3×C7×C13C3×C4×C11semidirect
49. C7×C13⋊C3C11×Dic3semidirect
54. C3×C7×C11C4×C13⋊C3semidirect
60. C11×C13C3×Dic21semidirect
64. C3×C13⋊C3C11×Dic7semidirect
66. C7×C13C3×C11×Dic3semidirect
67. Dic21C11×C13⋊C3direct (N × H)
72. C7×C11Dic3×C13⋊C3semidirect
82. C3×C13C3×C11×Dic7semidirect
84. C13⋊C3C11×Dic21direct (N × H)
88. C3×C11Dic7×C13⋊C3semidirect
94. C3×C7C4×C11×C13⋊C3semidirect
97. C13C3×C11×Dic21semidirect
100. C11C13⋊C3×Dic21direct (N × H)
102. C7C11×Dic3×C13⋊C3semidirect
109. C3C11×Dic7×C13⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C7×C11×C13⋊C32
C11×Dic7×C13⋊C33
C11×C13×Dic213
C11×Dic3×C13⋊C37
C13⋊C3×Dic2111
C3×C11×Dic2113