Finite Group Databasebeta

← C3×S4×C11⋊C5 #72247313

Subgroups — C3×S4×C11⋊C5 #72247313

Order 3960.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×A4×C11⋊C5C211yesmaximal, characteristic, complemented
2S4×C11⋊C5C311yesmaximal, characteristic, direct product factor
3C3×D4×C11⋊C5—31nomaximal
4C3×D3×C11⋊C5—41nomaximal
5C3×C11×S4C511yesmaximal, characteristic, complemented, Hall
6C22×C3×C11⋊C5—31no—
7C22×C3×C11⋊C5D311yescharacteristic, complemented
8A4×C11⋊C5—21no—
9A4×C11⋊C5C2×C311yescharacteristic, complemented
10C3×C4×C11⋊C5—31no—
11C32×C11⋊C5—41noHall
12D4×C11⋊C5—31noHall
13C3×C11×A4C2×C511yescharacteristic, complemented
14C3×C5×S4—111nomaximal, Hall
15C2×C3×C11⋊C5—31no—
16C2×C3×C11⋊C5—61no—
17D3×C11⋊C5—41no—
18C11×S4C3×C511yescharacteristic, complemented
19C3×D4×C11—31no—
20C22×C11⋊C5—31no—
21C22×C11⋊C5C3×D311yescharacteristic, complemented
22C4×C11⋊C5—31no—
23C3×D3×C11—41no—
24C3×C5×A4—111no—
25C3×C11⋊C5—41no—
26C3×C11⋊C5—81no—
27C3×C11⋊C5S411yescharacteristic, direct product factor
28C22×C3×C11—31no—
29C22×C3×C11C5×D311yescharacteristic, complemented
30C11×A4—21no—
31C11×A4C2×C3×C511yescharacteristic, complemented
32C3×C4×C11—31no—
33C5×S4—111no—
34C3×C5×D4—331no—
35C2×C11⋊C5—31no—
36C2×C11⋊C5—61no—
37C32×C11—41noHall
38C3×C5×D3—441no—
39D4×C11—31noHall
40C3×S4C11⋊C511yescharacteristic, direct product factor, Hall
41C2×C3×C11—31no—
42C2×C3×C11—61no—
43D3×C11—41no—
44C22×C3×C5—111no—
45C22×C3×C5—331no—
46C5×A4—111no—
47C5×A4—221no—
48C3×C4×C5—331no—
49C11⋊C5C3×S411yescharacteristic, direct product factor, Hall
50C32×C5—441noHall
51C22×C11—31no—
52C22×C11C3×C5×D311yescharacteristic, complemented
53C4×C11—31no—
54C5×D4—331noHall
55C3×A4C2×C11⋊C511yescharacteristic, complemented
56C3×C11—41no—
57C3×C11—81no—
58C3×C11C5×S411yescharacteristic, complemented
59C2×C3×C5—331no—
60C2×C3×C5—661no—
61C5×D3—441no—
62S4C3×C11⋊C511yescharacteristic, direct product factor
63C3×D4—31no—
64C2×C11—31no—
65C2×C11—61no—
66C22×C5—111no—
67C22×C5—331no—
68C4×C5—331no—
69C3×D3—41no—
70C3×C5—111no—
71C3×C5—441no—
72C3×C5—881no—
73C22×C3—31no—
74C22×C3D3×C11⋊C511yescharacteristic, complemented
75A4—21no—
76A4C2×C3×C11⋊C511yescharacteristic, complemented
77C3×C4—31no—
78C11C3×C5×S411yescharacteristic, complemented, Sylow
79C2×C5—331no—
80C2×C5—661no—
81C32—41noSylow
82D4—31noSylow
83C2×C3—31no—
84C2×C3—61no—
85D3—41no—
86C5—111noSylow
87C22—31no—
88C22C3×D3×C11⋊C511yescharacteristic, complemented
89C4—31no—
90C3—41no—
91C3—81no—
92C3S4×C11⋊C511yescharacteristic, direct product factor
93C2—31no—
94C2—61no—
subgroupG/H
center, hypercenterC3S4×C11⋊C5
commutator, cosocle, hypocenterC11×A4C2×C3×C5
FrattiniC1G
Fitting, socleC22×C3×C11C5×D3
LCSG ▷ C11×A4
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×A4×C11⋊C5C2semidirect
2. S4×C11⋊C5C3direct (N × H)
5. C3×C11×S4C5semidirect
7. C22×C3×C11⋊C5D3semidirect
9. A4×C11⋊C5C2×C3semidirect
13. C3×C11×A4C2×C5semidirect
18. C11×S4C3×C5semidirect
21. C22×C11⋊C5C3×D3semidirect
27. C3×C11⋊C5S4direct (N × H)
29. C22×C3×C11C5×D3semidirect
31. C11×A4C2×C3×C5semidirect
40. C3×S4C11⋊C5direct (N × H)
49. C11⋊C5C3×S4direct (N × H)
52. C22×C11C3×C5×D3semidirect
55. C3×A4C2×C11⋊C5semidirect
58. C3×C11C5×S4semidirect
62. S4C3×C11⋊C5direct (N × H)
74. C22×C3D3×C11⋊C5semidirect
76. A4C2×C3×C11⋊C5semidirect
78. C11C3×C5×S4semidirect
88. C22C3×D3×C11⋊C5semidirect
92. C3S4×C11⋊C5direct (N × H)

Maximal subgroups

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

subgroupindex
C3×A4×C11⋊C52
S4×C11⋊C53
C3×D4×C11⋊C53
C3×D3×C11⋊C54
C3×C11×S45
C3×C5×S411