Finite Group Databasebeta

← C11⋊C5×#568 #72269497

Subgroups — C11⋊C5×#568 #72269497

Order 3520.

516 conjugacy classes of subgroups; only the 357 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 357 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×#41×C11⋊C5C211yesmaximal, characteristic
2#131×C11⋊C5C218yesmaximal, complemented
3C2×M16×C11⋊C5C216yesmaximal, complemented
4#41×C11⋊C5C414yes—
5#41×C11⋊C5C2214yes—
6C2×Q8×C11⋊C5C411yescharacteristic
7C2×D4×C11⋊C5C413yes—
8C22×C4×C11⋊C5C2213yes—
9M16×C11⋊C5C2214yes—
10M16×C11⋊C5C22112yescomplemented
11C2×C8×C11⋊C5C22112yescomplemented
12C11×#568C511yesmaximal, characteristic, complemented, Hall
13C23×C11⋊C5C2×C413yes—
14Q8×C11⋊C5C2×C414yes—
15D4×C11⋊C5C2×C4112yes—
16C2×C4×C11⋊C5C2×C413yes—
17C2×C4×C11⋊C5C2×C416yes—
18C2×C4×C11⋊C5C2316yes—
19C2×C4×C11⋊C5C2311yescharacteristic
20C8×C11⋊C5C2318yes—
21C2×C11×#41C2×C511yescharacteristic
22C11×#131C2×C518yescomplemented
23C2×C11×M16C2×C516yescomplemented
24C5×#568—111nomaximal, Hall
25C22×C11⋊C5—43no—
26C22×C11⋊C5C22×C411yescharacteristic
27C22×C11⋊C5C22×C416yes—
28C4×C11⋊C5C22×C411yescharacteristic
29C4×C11⋊C5C22×C416yes—
30C4×C11⋊C5C2411yescharacteristic
31C11×#41C4×C514yes—
32C11×#41C22×C514yes—
33C2×Q8×C11C4×C511yescharacteristic
34C2×D4×C11C4×C513yes—
35C22×C4×C11C22×C513yes—
36C11×M16C22×C514yes—
37C11×M16C22×C5112yescomplemented
38C2×C8×C11C22×C5112yescomplemented
39C2×C5×#41—111no—
40C5×#131—118no—
41C2×C5×M16—116no—
42C2×C11⋊C5—21no—
43C2×C11⋊C5—26no—
44C2×C11⋊C5C23×C411yescharacteristic
45C23×C11C2×C4×C513yes—
46Q8×C11C2×C4×C514yes—
47D4×C11C2×C4×C5112yes—
48C2×C4×C11C2×C4×C513yes—
49C2×C4×C11C2×C4×C516yes—
50C2×C4×C11C23×C516yes—
51C2×C4×C11C23×C511yescharacteristic
52C8×C11C23×C518yes—
53C5×#41—114no—
54C5×#41—114no—
55C2×C5×Q8—111no—
56C2×C5×D4—113no—
57C22×C4×C5—113no—
58C5×M16—114no—
59C5×M16—1112no—
60C2×C5×C8—1112no—
61#568C11⋊C511yescharacteristic, direct product factor, Sylow
62C11⋊C5#56811yescharacteristic, direct product factor, Hall
63C22×C11—43no—
64C22×C11C22×C4×C511yescharacteristic
65C22×C11C22×C4×C516yes—
66C4×C11C22×C4×C511yescharacteristic
67C4×C11C22×C4×C516yes—
68C4×C11C24×C511yescharacteristic
69C23×C5—113no—
70C5×Q8—114no—
71C5×D4—1112no—
72C2×C4×C5—113no—
73C2×C4×C5—116no—
74C2×C4×C5—116no—
75C2×C4×C5—111no—
76C5×C8—118no—
77C2×#41C2×C11⋊C511yescharacteristic
78#131C2×C11⋊C518yescomplemented
79C2×M16C2×C11⋊C516yescomplemented
80C2×C11—21no—
81C2×C11—26no—
82C2×C11C23×C4×C511yescharacteristic
83C22×C5—111no—
84C22×C5—116no—
85C22×C5—443no—
86C4×C5—111no—
87C4×C5—116no—
88C4×C5—111no—
89#41C4×C11⋊C514yes—
90#41C22×C11⋊C514yes—
91C2×Q8C4×C11⋊C511yescharacteristic
92C2×D4C4×C11⋊C513yes—
93C22×C4C22×C11⋊C513yes—
94M16C22×C11⋊C514yes—
95M16C22×C11⋊C5112yescomplemented
96C2×C8C22×C11⋊C5112yescomplemented
97C11C5×#56811yescharacteristic, complemented, Sylow
98C2×C5—111no—
99C2×C5—221no—
100C2×C5—226no—
101C23C2×C4×C11⋊C513yes—
102Q8C2×C4×C11⋊C514yes—
103D4C2×C4×C11⋊C5112yes—
104C2×C4C2×C4×C11⋊C513yes—
105C2×C4C2×C4×C11⋊C516yes—
106C2×C4C23×C11⋊C516yes—
107C2×C4C23×C11⋊C511yescharacteristic
108C8C23×C11⋊C518yes—
109C5—111noSylow
110C22—43no—
111C22C22×C4×C11⋊C511yescharacteristic
112C22C22×C4×C11⋊C516yes—
113C4C22×C4×C11⋊C511yescharacteristic
114C4C22×C4×C11⋊C516yes—
115C4C24×C11⋊C511yescharacteristic
116C2—21no—
117C2—26no—
118C2C23×C4×C11⋊C511yescharacteristic
subgroupG/H
center, FrattiniC4C24×C11⋊C5
commutator, socleC2×C11C23×C4×C5
FittingC11×#568C5
prime radicalC2×#41×C11⋊C5C2
cosocleC4×C11C24×C5
hypercenter#568C11⋊C5
hypocenterC11C5×#568
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ #568

Complements

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

NH ≅ G/Ntype
2. #131×C11⋊C5C2semidirect
3. C2×M16×C11⋊C5C2semidirect
10. M16×C11⋊C5C22semidirect
11. C2×C8×C11⋊C5C22semidirect
12. C11×#568C5semidirect
22. C11×#131C2×C5semidirect
23. C2×C11×M16C2×C5semidirect
37. C11×M16C22×C5semidirect
38. C2×C8×C11C22×C5semidirect
61. #568C11⋊C5direct (N × H)
62. C11⋊C5#568direct (N × H)
78. #131C2×C11⋊C5semidirect
79. C2×M16C2×C11⋊C5semidirect
95. M16C22×C11⋊C5semidirect
96. C2×C8C22×C11⋊C5semidirect
97. C11C5×#568semidirect

Maximal subgroups

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

subgroupindex
C2×#41×C11⋊C52
#131×C11⋊C52
C2×M16×C11⋊C52
C11×#5685
C5×#56811