Finite Group Databasebeta

← C2×#41×D541 #46831000

Subgroups — C2×#41×D541 #46831000

Order 34624.

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×#22575837C211yesmaximal, characteristic, complemented
2C2×#22575836C213yesmaximal, complemented
3C2×#22575835C213yesmaximal, complemented
4#41×D541C2116yesmaximal, direct product factor
5C2×Q8×D541C211yesmaximal, characteristic, complemented
6C2×D4×D541C213yesmaximal, complemented
7C22×C4×D541C213yesmaximal, complemented
8C2×#41×C541C211yesmaximal, characteristic, complemented
9C23×D541C2213yes—
10#22575837C2218yescomplemented
11#22575836C22124yescomplemented
12#22575835C22124yescomplemented
13C2×Dic1082C2213yescomplemented
14Q8×D541C2218yescomplemented
15C2×D2164C2213yescomplemented
16C2×C22⋊D541C2216yescomplemented
17D4×D541C22124yescomplemented
18C22×Dic541C2213yescomplemented
19C2×C4×D541C2211yescharacteristic
20C2×C4×D541C2213yes—
21C2×C4×D541C22124yescomplemented
22C2×C4×D541C2213yescomplemented
23C2×C4×D541C2213yescomplemented
24#41×C541C2218yescomplemented
25C2×Q8×C541C2211yescharacteristic, complemented
26C2×D4×C541C2213yescomplemented
27C22×C4×C541C2213yescomplemented
28C22×D541—212no—
29C22×D541C23112yes—
30C22×D541C2313yes—
31C22×D541C2311yescharacteristic
32Dic1082C23112yescomplemented
33D2164C23112yescomplemented
34C22⋊D541C23124yescomplemented
35C2×Dic541C2311yescharacteristic
36C2×Dic541C2313yes—
37C2×Dic541C23112yescomplemented
38C4×D541C2314yes—
39C4×D541C23112yes—
40C4×D541C23112yescomplemented
41C4×D541C23112yescomplemented
42C23×C541C2313yes—
43Q8×C541C2314yescomplemented
44D4×C541C23112yescomplemented
45C2×C4×C541C2313yes—
46C2×C4×C541C2311yescharacteristic
47C2×C4×C541C23112yescomplemented
48C22×C541—26no—
49C22×C541C2416yes—
50C22×C541C2411yescharacteristic
51C2×D541—26no—
52C2×D541—224no—
53C2×D541#4114yesdirect product factor
54C2×D541C2416yes—
55C2×D541C2412yes—
56C4×C541C2412yes—
57C4×C541C2416yes—
58Dic541C2412yes—
59Dic541C2416yes—
60C2×C541—26no—
61C2×C541C2×#4112yescomplemented
62C2×C541C2511yescharacteristic
63D541—26no—
64D541C2×#4114yesdirect product factor
65C541C22×#4111yescharacteristic, complemented, Sylow
66C22×#41—5411nomaximal, Sylow
67C2×#41—54116no—
68C2×#41—5411no—
69C2×#41—5413no—
70C2×#41—5413no—
71C2×#41D54111yescharacteristic, direct product factor
72C22×Q8—5411no—
73C22×D4—5413no—
74C23×C4—5413no—
75C24—5413no—
76#41—5418no—
77#41—54124no—
78#41—54124no—
79#41C2×D54118yesdirect product factor
80C2×Q8—5418no—
81C2×Q8—5413no—
82C2×Q8C2×D54111yescharacteristic, complemented
83C2×D4—5416no—
84C2×D4—54124no—
85C2×D4—5413no—
86C2×D4C2×D54113yescomplemented
87C22×C4—5413no—
88C22×C4—5413no—
89C22×C4—5413no—
90C22×C4—5411no—
91C22×C4—5413no—
92C22×C4—54124no—
93C22×C4C2×D54113yescomplemented
94C23—5411no—
95C23—54112no—
96C23—5413no—
97C23—108212no—
98C23C22×D54113yes—
99Q8—54112no—
100Q8C22×D54114yescomplemented
101D4—54124no—
102D4—54112no—
103D4C22×D541112yescomplemented
104C2×C4—5411no—
105C2×C4—5413no—
106C2×C4—54112no—
107C2×C4—5414no—
108C2×C4—54112no—
109C2×C4—54112no—
110C2×C4—54112no—
111C2×C4C22×D54113yes—
112C2×C4C22×D54111yescharacteristic
113C2×C4C22×D541112yescomplemented
114C22—26no—
115C22—5412no—
116C22—5414no—
117C22—5416no—
118C22—108224no—
119C22—10826no—
120C22C23×D54116yes—
121C22C23×D54111yescharacteristic
122C4—5412no—
123C4—5416no—
124C4C23×D54112yes—
125C4C23×D54116yes—
126C2—26no—
127C2—5414no—
128C2—10826no—
129C2#41×D54112yesdirect product factor
130C2C24×D54111yescharacteristic
subgroupG/H
centerC2×C4C22×D541
commutator, cosocleC2×C541C25
FrattiniC2C24×D541
FittingC2×#41×C541C2
socleC22×C541C24
hypercenterC2×#41D541
hypocenterC541C22×#41
LCSG ▷ C2×C541 ▷ C541
UCSC1 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#22575837C2semidirect
2. C2×#22575836C2semidirect
3. C2×#22575835C2semidirect
4. #41×D541C2direct (N × H)
5. C2×Q8×D541C2semidirect
6. C2×D4×D541C2semidirect
7. C22×C4×D541C2semidirect
8. C2×#41×C541C2semidirect
10. #22575837C22semidirect
11. #22575836C22semidirect
12. #22575835C22semidirect
13. C2×Dic1082C22semidirect
14. Q8×D541C22semidirect
15. C2×D2164C22semidirect
16. C2×C22⋊D541C22semidirect
17. D4×D541C22semidirect
18. C22×Dic541C22semidirect
21. C2×C4×D541C22semidirect
22. C2×C4×D541C22semidirect
23. C2×C4×D541C22semidirect
24. #41×C541C22semidirect
25. C2×Q8×C541C22semidirect
26. C2×D4×C541C22semidirect
27. C22×C4×C541C22semidirect
32. Dic1082C23semidirect
33. D2164C23semidirect
34. C22⋊D541C23semidirect
37. C2×Dic541C23semidirect
40. C4×D541C23semidirect
41. C4×D541C23semidirect
43. Q8×C541C23semidirect
44. D4×C541C23semidirect
47. C2×C4×C541C23semidirect
53. C2×D541#41direct (N × H)
61. C2×C541C2×#41semidirect
64. D541C2×#41direct (N × H)
65. C541C22×#41semidirect
71. C2×#41D541direct (N × H)
79. #41C2×D541direct (N × H)
82. C2×Q8C2×D541semidirect
86. C2×D4C2×D541semidirect
93. C22×C4C2×D541semidirect
100. Q8C22×D541semidirect
103. D4C22×D541semidirect
113. C2×C4C22×D541semidirect
129. C2#41×D541direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#225758372
C2×#225758362
C2×#225758352
#41×D5412
C2×Q8×D5412
C2×D4×D5412
C22×C4×D5412
C2×#41×C5412
C22×#41541