Finite Group Databasebeta

← C2×S4×C11⋊C5 #72222544

Subgroups — C2×S4×C11⋊C5 #72222544

Order 2640.

132 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 27 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×A4×C11⋊C5C211yesmaximal, characteristic, complemented
2S4×C11⋊C5C212yesmaximal, direct product factor
3C2×D4×C11⋊C5—31nomaximal, Hall
4C2×D3×C11⋊C5—41nomaximal
5A4×C11⋊C5C2211yescharacteristic, complemented
6C2×C11×S4C511yesmaximal, characteristic, complemented, Hall
7C23×C11⋊C5—31no—
8C23×C11⋊C5D311yescharacteristic, complemented
9D4×C11⋊C5—32no—
10D4×C11⋊C5—32no—
11C2×C4×C11⋊C5—31no—
12C2×C3×C11⋊C5—41no—
13D3×C11⋊C5—42no—
14C2×C11×A4C2×C511yescharacteristic, complemented
15C11×S4C2×C512yescomplemented
16C2×C5×S4—111nomaximal, Hall
17C22×C11⋊C5—31no—
18C22×C11⋊C5—31no—
19C22×C11⋊C5—32no—
20C22×C11⋊C5—61no—
21C22×C11⋊C5—61no—
22C22×C11⋊C5C2×D311yescharacteristic, complemented
23C4×C11⋊C5—32no—
24C2×D4×C11—31noHall
25C3×C11⋊C5—41noHall
26C2×D3×C11—41no—
27C11×A4C22×C511yescharacteristic, complemented
28C2×C5×A4—111no—
29C5×S4—112no—
30C2×C11⋊C5—31no—
31C2×C11⋊C5—31no—
32C2×C11⋊C5—62no—
33C2×C11⋊C5S411yescharacteristic, direct product factor
34C23×C11—31no—
35C23×C11C5×D311yescharacteristic, complemented
36D4×C11—32no—
37D4×C11—32no—
38C2×C4×C11—31no—
39C2×C5×D4—331noHall
40C2×C3×C11—41no—
41D3×C11—42no—
42C2×C5×D3—441no—
43C5×A4—111no—
44C11⋊C5C2×S411yescharacteristic, direct product factor, Hall
45C2×S4C11⋊C511yescharacteristic, direct product factor, Hall
46C22×C11—31no—
47C22×C11—31no—
48C22×C11—32no—
49C22×C11—61no—
50C22×C11—61no—
51C22×C11C2×C5×D311yescharacteristic, complemented
52C4×C11—32no—
53C23×C5—111no—
54C23×C5—331no—
55C5×D4—332no—
56C5×D4—332no—
57C2×C4×C5—331no—
58C3×C11—41noHall
59C2×C3×C5—441no—
60C5×D3—442no—
61C2×A4C2×C11⋊C511yescharacteristic, complemented
62S4C2×C11⋊C512yesdirect product factor
63C2×C11—31no—
64C2×C11—31no—
65C2×C11—62no—
66C2×C11C5×S411yescharacteristic, complemented
67C22×C5—111no—
68C22×C5—331no—
69C22×C5—331no—
70C22×C5—332no—
71C22×C5—661no—
72C22×C5—661no—
73C4×C5—332no—
74C2×D4—31noSylow
75C3×C5—441noHall
76C2×D3—41no—
77A4C22×C11⋊C511yescharacteristic, complemented
78C11C2×C5×S411yescharacteristic, complemented, Sylow
79C2×C5—111no—
80C2×C5—331no—
81C2×C5—331no—
82C2×C5—662no—
83C23—31no—
84C23D3×C11⋊C511yescharacteristic, complemented
85D4—32no—
86D4—32no—
87C2×C4—31no—
88C2×C3—41no—
89D3—42no—
90C5—111noSylow
91C22—31no—
92C22—31no—
93C22—32no—
94C22—61no—
95C22—61no—
96C22C2×D3×C11⋊C511yescharacteristic, complemented
97C4—32no—
98C3—41noSylow
99C2—31no—
100C2—31no—
101C2—62no—
102C2S4×C11⋊C511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2S4×C11⋊C5
commutator, cosocle, hypocenterC11×A4C22×C5
FrattiniC1G
Fitting, socleC23×C11C5×D3
LCSG ▷ C11×A4
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×A4×C11⋊C5C2semidirect
2. S4×C11⋊C5C2direct (N × H)
5. A4×C11⋊C5C22semidirect
6. C2×C11×S4C5semidirect
8. C23×C11⋊C5D3semidirect
14. C2×C11×A4C2×C5semidirect
15. C11×S4C2×C5semidirect
22. C22×C11⋊C5C2×D3semidirect
27. C11×A4C22×C5semidirect
33. C2×C11⋊C5S4direct (N × H)
35. C23×C11C5×D3semidirect
44. C11⋊C5C2×S4direct (N × H)
45. C2×S4C11⋊C5direct (N × H)
51. C22×C11C2×C5×D3semidirect
61. C2×A4C2×C11⋊C5semidirect
62. S4C2×C11⋊C5direct (N × H)
66. C2×C11C5×S4semidirect
77. A4C22×C11⋊C5semidirect
78. C11C2×C5×S4semidirect
84. C23D3×C11⋊C5semidirect
96. C22C2×D3×C11⋊C5semidirect
102. C2S4×C11⋊C5direct (N × H)

Maximal subgroups

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

subgroupindex
C2×A4×C11⋊C52
S4×C11⋊C52
C2×D4×C11⋊C53
C2×D3×C11⋊C54
C2×C11×S45
C2×C5×S411