Finite Group Databasebeta

← C2×#41×D503 #44567106

Subgroups — C2×#41×D503 #44567106

Order 32192.

890 conjugacy classes of subgroups; only the 455 normal subgroups are shown.

normal subgroups only

This group has 890 conjugacy classes of subgroups — too many to draw. Only its 455 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×#22548884C211yesmaximal, characteristic, complemented
2C2×#22548883C213yesmaximal, complemented
3C2×#22548882C213yesmaximal, complemented
4#41×D503C2116yesmaximal, direct product factor
5C2×Q8×D503C211yesmaximal, characteristic, complemented
6C2×D4×D503C213yesmaximal, complemented
7C22×C4×D503C213yesmaximal, complemented
8C2×#41×C503C211yesmaximal, characteristic, complemented
9C23×D503C2213yes—
10#22548884C2218yescomplemented
11#22548883C22124yescomplemented
12#22548882C22124yescomplemented
13C2×Dic1006C2213yescomplemented
14Q8×D503C2218yescomplemented
15C2×D2012C2213yescomplemented
16C2×C22⋊D503C2216yescomplemented
17D4×D503C22124yescomplemented
18C22×Dic503C2213yescomplemented
19C2×C4×D503C2211yescharacteristic
20C2×C4×D503C2213yes—
21C2×C4×D503C2213yescomplemented
22C2×C4×D503C2213yescomplemented
23C2×C4×D503C22124yescomplemented
24#41×C503C2218yescomplemented
25C2×Q8×C503C2211yescharacteristic, complemented
26C2×D4×C503C2213yescomplemented
27C22×C4×C503C2213yescomplemented
28C22×D503—212no—
29C22×D503C23112yes—
30C22×D503C2313yes—
31C22×D503C2311yescharacteristic
32Dic1006C23112yescomplemented
33D2012C23112yescomplemented
34C22⋊D503C23124yescomplemented
35C2×Dic503C2311yescharacteristic
36C2×Dic503C2313yes—
37C2×Dic503C23112yescomplemented
38C4×D503C2314yes—
39C4×D503C23112yes—
40C4×D503C23112yescomplemented
41C4×D503C23112yescomplemented
42C23×C503C2313yes—
43Q8×C503C2314yescomplemented
44D4×C503C23112yescomplemented
45C2×C4×C503C2313yes—
46C2×C4×C503C2311yescharacteristic
47C2×C4×C503C23112yescomplemented
48C22×C503—26no—
49C22×C503C2416yes—
50C22×C503C2411yescharacteristic
51C2×D503—26no—
52C2×D503—224no—
53C2×D503#4114yesdirect product factor
54C2×D503C2416yes—
55C2×D503C2412yes—
56C4×C503C2412yes—
57C4×C503C2416yes—
58Dic503C2412yes—
59Dic503C2416yes—
60C2×C503—26no—
61C2×C503C2×#4112yescomplemented
62C2×C503C2511yescharacteristic
63D503—26no—
64D503C2×#4114yesdirect product factor
65C503C22×#4111yescharacteristic, complemented, Sylow
66C22×#41—5031nomaximal, Sylow
67C2×#41—50316no—
68C2×#41—5031no—
69C2×#41—5033no—
70C2×#41—5033no—
71C2×#41D50311yescharacteristic, direct product factor
72C22×Q8—5031no—
73C22×D4—5033no—
74C23×C4—5033no—
75C24—5033no—
76#41—5038no—
77#41—50324no—
78#41—50324no—
79#41C2×D50318yesdirect product factor
80C2×Q8—5038no—
81C2×Q8—5033no—
82C2×Q8C2×D50311yescharacteristic, complemented
83C2×D4—5036no—
84C2×D4—50324no—
85C2×D4—5033no—
86C2×D4C2×D50313yescomplemented
87C22×C4—5033no—
88C22×C4—5033no—
89C22×C4—5033no—
90C22×C4—5031no—
91C22×C4—5033no—
92C22×C4—50324no—
93C22×C4C2×D50313yescomplemented
94C23—100612no—
95C23—50312no—
96C23—5033no—
97C23—5031no—
98C23C22×D50313yes—
99Q8—50312no—
100Q8C22×D50314yescomplemented
101D4—50324no—
102D4—50312no—
103D4C22×D503112yescomplemented
104C2×C4—5031no—
105C2×C4—5033no—
106C2×C4—50312no—
107C2×C4—5034no—
108C2×C4—50312no—
109C2×C4—50312no—
110C2×C4—50312no—
111C2×C4C22×D50313yes—
112C2×C4C22×D50311yescharacteristic
113C2×C4C22×D503112yescomplemented
114C22—26no—
115C22—100624no—
116C22—10066no—
117C22—5036no—
118C22—5034no—
119C22—5032no—
120C22C23×D50316yes—
121C22C23×D50311yescharacteristic
122C4—5032no—
123C4—5036no—
124C4C23×D50312yes—
125C4C23×D50316yes—
126C2—26no—
127C2—10066no—
128C2—5034no—
129C2#41×D50312yesdirect product factor
130C2C24×D50311yescharacteristic
subgroupG/H
centerC2×C4C22×D503
commutator, cosocleC2×C503C25
FrattiniC2C24×D503
FittingC2×#41×C503C2
socleC22×C503C24
hypercenterC2×#41D503
hypocenterC503C22×#41
LCSG ▷ C2×C503 ▷ C503
UCSC1 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#22548884C2semidirect
2. C2×#22548883C2semidirect
3. C2×#22548882C2semidirect
4. #41×D503C2direct (N × H)
5. C2×Q8×D503C2semidirect
6. C2×D4×D503C2semidirect
7. C22×C4×D503C2semidirect
8. C2×#41×C503C2semidirect
10. #22548884C22semidirect
11. #22548883C22semidirect
12. #22548882C22semidirect
13. C2×Dic1006C22semidirect
14. Q8×D503C22semidirect
15. C2×D2012C22semidirect
16. C2×C22⋊D503C22semidirect
17. D4×D503C22semidirect
18. C22×Dic503C22semidirect
21. C2×C4×D503C22semidirect
22. C2×C4×D503C22semidirect
23. C2×C4×D503C22semidirect
24. #41×C503C22semidirect
25. C2×Q8×C503C22semidirect
26. C2×D4×C503C22semidirect
27. C22×C4×C503C22semidirect
32. Dic1006C23semidirect
33. D2012C23semidirect
34. C22⋊D503C23semidirect
37. C2×Dic503C23semidirect
40. C4×D503C23semidirect
41. C4×D503C23semidirect
43. Q8×C503C23semidirect
44. D4×C503C23semidirect
47. C2×C4×C503C23semidirect
53. C2×D503#41direct (N × H)
61. C2×C503C2×#41semidirect
64. D503C2×#41direct (N × H)
65. C503C22×#41semidirect
71. C2×#41D503direct (N × H)
79. #41C2×D503direct (N × H)
82. C2×Q8C2×D503semidirect
86. C2×D4C2×D503semidirect
93. C22×C4C2×D503semidirect
100. Q8C22×D503semidirect
103. D4C22×D503semidirect
113. C2×C4C22×D503semidirect
129. C2#41×D503direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#225488842
C2×#225488832
C2×#225488822
#41×D5032
C2×Q8×D5032
C2×D4×D5032
C22×C4×D5032
C2×#41×C5032
C22×#41503