Finite Group Databasebeta

← C2×#41×D521 #45688257

Subgroups — C2×#41×D521 #45688257

Order 33344.

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×#22552365C211yesmaximal, characteristic, complemented
2C2×#22552364C213yesmaximal, complemented
3C2×#22552363C213yesmaximal, complemented
4#41×D521C2116yesmaximal, direct product factor
5C2×Q8×D521C211yesmaximal, characteristic, complemented
6C2×D4×D521C213yesmaximal, complemented
7C22×C4×D521C213yesmaximal, complemented
8C2×#41×C521C211yesmaximal, characteristic, complemented
9C23×D521C2213yes—
10#22552365C2218yescomplemented
11#22552364C22124yescomplemented
12#22552363C22124yescomplemented
13C2×Dic1042C2213yescomplemented
14Q8×D521C2218yescomplemented
15C2×D2084C2213yescomplemented
16C2×C22⋊D521C2216yescomplemented
17D4×D521C22124yescomplemented
18C22×Dic521C2213yescomplemented
19C2×C4×D521C2211yescharacteristic
20C2×C4×D521C2213yes—
21C2×C4×D521C2213yescomplemented
22C2×C4×D521C2213yescomplemented
23C2×C4×D521C22124yescomplemented
24#41×C521C2218yescomplemented
25C2×Q8×C521C2211yescharacteristic, complemented
26C2×D4×C521C2213yescomplemented
27C22×C4×C521C2213yescomplemented
28C22×D521—212no—
29C22×D521C23112yes—
30C22×D521C2313yes—
31C22×D521C2311yescharacteristic
32Dic1042C23112yescomplemented
33D2084C23112yescomplemented
34C22⋊D521C23124yescomplemented
35C2×Dic521C2311yescharacteristic
36C2×Dic521C2313yes—
37C2×Dic521C23112yescomplemented
38C4×D521C2314yes—
39C4×D521C23112yes—
40C4×D521C23112yescomplemented
41C4×D521C23112yescomplemented
42C23×C521C2313yes—
43Q8×C521C2314yescomplemented
44D4×C521C23112yescomplemented
45C2×C4×C521C2313yes—
46C2×C4×C521C2311yescharacteristic
47C2×C4×C521C23112yescomplemented
48C22×C521—26no—
49C22×C521C2416yes—
50C22×C521C2411yescharacteristic
51C2×D521—26no—
52C2×D521—224no—
53C2×D521#4114yesdirect product factor
54C2×D521C2416yes—
55C2×D521C2412yes—
56C4×C521C2412yes—
57C4×C521C2416yes—
58Dic521C2412yes—
59Dic521C2416yes—
60C2×C521—26no—
61C2×C521C2×#4112yescomplemented
62C2×C521C2511yescharacteristic
63D521—26no—
64D521C2×#4114yesdirect product factor
65C521C22×#4111yescharacteristic, complemented, Sylow
66C22×#41—5211nomaximal, Sylow
67C2×#41—52116no—
68C2×#41—5211no—
69C2×#41—5213no—
70C2×#41—5213no—
71C2×#41D52111yescharacteristic, direct product factor
72C22×Q8—5211no—
73C22×D4—5213no—
74C23×C4—5213no—
75C24—5213no—
76#41—5218no—
77#41—52124no—
78#41—52124no—
79#41C2×D52118yesdirect product factor
80C2×Q8—5218no—
81C2×Q8—5213no—
82C2×Q8C2×D52111yescharacteristic, complemented
83C2×D4—5216no—
84C2×D4—52124no—
85C2×D4—5213no—
86C2×D4C2×D52113yescomplemented
87C22×C4—5213no—
88C22×C4—5213no—
89C22×C4—5213no—
90C22×C4—5211no—
91C22×C4—5213no—
92C22×C4—52124no—
93C22×C4C2×D52113yescomplemented
94C23—5211no—
95C23—52112no—
96C23—5213no—
97C23—104212no—
98C23C22×D52113yes—
99Q8—52112no—
100Q8C22×D52114yescomplemented
101D4—52124no—
102D4—52112no—
103D4C22×D521112yescomplemented
104C2×C4—5211no—
105C2×C4—5213no—
106C2×C4—52112no—
107C2×C4—5214no—
108C2×C4—52112no—
109C2×C4—52112no—
110C2×C4—52112no—
111C2×C4C22×D52113yes—
112C2×C4C22×D52111yescharacteristic
113C2×C4C22×D521112yescomplemented
114C22—26no—
115C22—5214no—
116C22—5212no—
117C22—5216no—
118C22—104224no—
119C22—10426no—
120C22C23×D52116yes—
121C22C23×D52111yescharacteristic
122C4—5212no—
123C4—5216no—
124C4C23×D52112yes—
125C4C23×D52116yes—
126C2—26no—
127C2—5214no—
128C2—10426no—
129C2#41×D52112yesdirect product factor
130C2C24×D52111yescharacteristic
subgroupG/H
centerC2×C4C22×D521
commutator, cosocleC2×C521C25
FrattiniC2C24×D521
FittingC2×#41×C521C2
socleC22×C521C24
hypercenterC2×#41D521
hypocenterC521C22×#41
LCSG ▷ C2×C521 ▷ C521
UCSC1 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#22552365C2semidirect
2. C2×#22552364C2semidirect
3. C2×#22552363C2semidirect
4. #41×D521C2direct (N × H)
5. C2×Q8×D521C2semidirect
6. C2×D4×D521C2semidirect
7. C22×C4×D521C2semidirect
8. C2×#41×C521C2semidirect
10. #22552365C22semidirect
11. #22552364C22semidirect
12. #22552363C22semidirect
13. C2×Dic1042C22semidirect
14. Q8×D521C22semidirect
15. C2×D2084C22semidirect
16. C2×C22⋊D521C22semidirect
17. D4×D521C22semidirect
18. C22×Dic521C22semidirect
21. C2×C4×D521C22semidirect
22. C2×C4×D521C22semidirect
23. C2×C4×D521C22semidirect
24. #41×C521C22semidirect
25. C2×Q8×C521C22semidirect
26. C2×D4×C521C22semidirect
27. C22×C4×C521C22semidirect
32. Dic1042C23semidirect
33. D2084C23semidirect
34. C22⋊D521C23semidirect
37. C2×Dic521C23semidirect
40. C4×D521C23semidirect
41. C4×D521C23semidirect
43. Q8×C521C23semidirect
44. D4×C521C23semidirect
47. C2×C4×C521C23semidirect
53. C2×D521#41direct (N × H)
61. C2×C521C2×#41semidirect
64. D521C2×#41direct (N × H)
65. C521C22×#41semidirect
71. C2×#41D521direct (N × H)
79. #41C2×D521direct (N × H)
82. C2×Q8C2×D521semidirect
86. C2×D4C2×D521semidirect
93. C22×C4C2×D521semidirect
100. Q8C22×D521semidirect
103. D4C22×D521semidirect
113. C2×C4C22×D521semidirect
129. C2#41×D521direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#225523652
C2×#225523642
C2×#225523632
#41×D5212
C2×Q8×D5212
C2×D4×D5212
C22×C4×D5212
C2×#41×C5212
C22×#41521