Finite Group Databasebeta

← C22×C22⋊C4×C11⋊C5 #72248834

Subgroups — C22×C22⋊C4×C11⋊C5 #72248834

Order 3520.

1348 conjugacy classes of subgroups; only the 507 normal subgroups are shown.

normal subgroups only

This group has 1348 conjugacy classes of subgroups — too many to draw. Only its 507 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
1C25×C11⋊C5C211yesmaximal, characteristic
2C23×C4×C11⋊C5C212yesmaximal, complemented
3C2×C22⋊C4×C11⋊C5C2112yesmaximal, direct product factor
4C24×C11⋊C5—28no—
5C24×C11⋊C5C418yescomplemented
6C24×C11⋊C5C2216yes—
7C24×C11⋊C5C2211yescharacteristic
8C22×C4×C11⋊C5—28no—
9C22×C4×C11⋊C5C22112yescomplemented
10C22⋊C4×C11⋊C5C22116yesdirect product factor
11C22×C11×C22⋊C4C511yesmaximal, characteristic, complemented, Hall
12C23×C11⋊C5—232no—
13C23×C11⋊C5—224no—
14C23×C11⋊C5C2×C414yes—
15C23×C11⋊C5C2×C4124yescomplemented
16C23×C11⋊C5D418yes—
17C23×C11⋊C5C2314yes—
18C23×C11⋊C5C2313yes—
19C2×C4×C11⋊C5—224no—
20C2×C4×C11⋊C5C2318yescomplemented
21C25×C11C2×C511yescharacteristic
22C23×C4×C11C2×C512yescomplemented
23C2×C11×C22⋊C4C2×C5112yescomplemented
24C22×C5×C22⋊C4—111nomaximal, Hall
25C22×C11⋊C5—248no—
26C22×C11⋊C5—28no—
27C22×C11⋊C5C22⋊C4116yesdirect product factor
28C22×C11⋊C5C22×C416yes—
29C22×C11⋊C5C22×C418yescomplemented
30C22×C11⋊C5C2×D4112yes—
31C22×C11⋊C5C2411yescharacteristic
32C4×C11⋊C5—28no—
33C24×C11—28no—
34C24×C11C4×C518yescomplemented
35C24×C11C22×C516yes—
36C24×C11C22×C511yescharacteristic
37C22×C4×C11—28no—
38C22×C4×C11C22×C5112yescomplemented
39C11×C22⋊C4C22×C5116yescomplemented
40C25×C5—111no—
41C23×C4×C5—112no—
42C2×C5×C22⋊C4—1112no—
43C2×C11⋊C5—28no—
44C2×C11⋊C5C2×C22⋊C4112yesdirect product factor
45C2×C11⋊C5C23×C411yescharacteristic
46C2×C11⋊C5C22×D412yes—
47C23×C11—232no—
48C23×C11—224no—
49C23×C11C2×C4×C514yes—
50C23×C11C2×C4×C5124yescomplemented
51C23×C11C5×D418yes—
52C23×C11C23×C514yes—
53C23×C11C23×C513yes—
54C2×C4×C11—224no—
55C2×C4×C11C23×C518yescomplemented
56C24×C5—118no—
57C24×C5—116no—
58C24×C5—111no—
59C24×C5—228no—
60C22×C4×C5—1112no—
61C22×C4×C5—228no—
62C5×C22⋊C4—1116no—
63C22×C22⋊C4C11⋊C511yescharacteristic, direct product factor, Sylow
64C11⋊C5C22×C22⋊C411yescharacteristic, direct product factor, Hall
65C22×C11—248no—
66C22×C11—28no—
67C22×C11C5×C22⋊C4116yescomplemented
68C22×C11C22×C4×C516yes—
69C22×C11C22×C4×C518yescomplemented
70C22×C11C2×C5×D4112yes—
71C22×C11C24×C511yescharacteristic
72C4×C11—28no—
73C23×C5—114no—
74C23×C5—1124no—
75C23×C5—118no—
76C23×C5—113no—
77C23×C5—114no—
78C23×C5—2232no—
79C23×C5—2224no—
80C2×C4×C5—118no—
81C2×C4×C5—2224no—
82C25C2×C11⋊C511yescharacteristic
83C23×C4C2×C11⋊C512yescomplemented
84C2×C22⋊C4C2×C11⋊C5112yesdirect product factor
85C2×C11—28no—
86C2×C11C2×C5×C22⋊C4112yescomplemented
87C2×C11C23×C4×C511yescharacteristic
88C2×C11C22×C5×D412yes—
89C22×C5—1116no—
90C22×C5—116no—
91C22×C5—118no—
92C22×C5—1112no—
93C22×C5—111no—
94C22×C5—228no—
95C22×C5—2248no—
96C4×C5—228no—
97C24—28no—
98C24C4×C11⋊C518yescomplemented
99C24C22×C11⋊C516yes—
100C24C22×C11⋊C511yescharacteristic
101C22×C4—28no—
102C22×C4C22×C11⋊C5112yescomplemented
103C22⋊C4C22×C11⋊C5116yesdirect product factor
104C11C22×C5×C22⋊C411yescharacteristic, complemented, Sylow
105C2×C5—111no—
106C2×C5—112no—
107C2×C5—1112no—
108C2×C5—228no—
109C23—232no—
110C23—224no—
111C23C2×C4×C11⋊C514yes—
112C23C2×C4×C11⋊C5124yescomplemented
113C23D4×C11⋊C518yes—
114C23C23×C11⋊C514yes—
115C23C23×C11⋊C513yes—
116C2×C4—224no—
117C2×C4C23×C11⋊C518yescomplemented
118C5—111noSylow
119C22—28no—
120C22—248no—
121C22C22⋊C4×C11⋊C5116yesdirect product factor
122C22C22×C4×C11⋊C516yes—
123C22C22×C4×C11⋊C518yescomplemented
124C22C2×D4×C11⋊C5112yes—
125C22C24×C11⋊C511yescharacteristic
126C4—28no—
127C2—28no—
128C2C2×C22⋊C4×C11⋊C5112yesdirect product factor
129C2C23×C4×C11⋊C511yescharacteristic
130C2C22×D4×C11⋊C512yes—
subgroupG/H
centerC24C22×C11⋊C5
commutatorC2×C11C23×C4×C5
FrattiniC22C24×C11⋊C5
FittingC22×C11×C22⋊C4C5
socleC24×C11C22×C5
prime radicalC25×C11⋊C5C2
cosocleC22×C11C24×C5
hypercenterC22×C22⋊C4C11⋊C5
hypocenterC11C22×C5×C22⋊C4
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C23×C4×C11⋊C5C2semidirect
3. C2×C22⋊C4×C11⋊C5C2direct (N × H)
5. C24×C11⋊C5C4semidirect
9. C22×C4×C11⋊C5C22semidirect
10. C22⋊C4×C11⋊C5C22direct (N × H)
11. C22×C11×C22⋊C4C5semidirect
15. C23×C11⋊C5C2×C4semidirect
20. C2×C4×C11⋊C5C23semidirect
22. C23×C4×C11C2×C5semidirect
23. C2×C11×C22⋊C4C2×C5semidirect
27. C22×C11⋊C5C22⋊C4direct (N × H)
29. C22×C11⋊C5C22×C4semidirect
34. C24×C11C4×C5semidirect
38. C22×C4×C11C22×C5semidirect
39. C11×C22⋊C4C22×C5semidirect
44. C2×C11⋊C5C2×C22⋊C4direct (N × H)
50. C23×C11C2×C4×C5semidirect
55. C2×C4×C11C23×C5semidirect
63. C22×C22⋊C4C11⋊C5direct (N × H)
64. C11⋊C5C22×C22⋊C4direct (N × H)
67. C22×C11C5×C22⋊C4semidirect
69. C22×C11C22×C4×C5semidirect
83. C23×C4C2×C11⋊C5semidirect
84. C2×C22⋊C4C2×C11⋊C5direct (N × H)
86. C2×C11C2×C5×C22⋊C4semidirect
98. C24C4×C11⋊C5semidirect
102. C22×C4C22×C11⋊C5semidirect
103. C22⋊C4C22×C11⋊C5direct (N × H)
104. C11C22×C5×C22⋊C4semidirect
112. C23C2×C4×C11⋊C5semidirect
117. C2×C4C23×C11⋊C5semidirect
121. C22C22⋊C4×C11⋊C5direct (N × H)
123. C22C22×C4×C11⋊C5semidirect
128. C2C2×C22⋊C4×C11⋊C5direct (N × H)

Maximal subgroups

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

subgroupindex
C25×C11⋊C52
C23×C4×C11⋊C52
C2×C22⋊C4×C11⋊C52
C22×C11×C22⋊C45
C22×C5×C22⋊C411