Finite Group Databasebeta

← C2×#41×D479 #44501220

Subgroups — C2×#41×D479 #44501220

Order 30656.

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×#21440163C211yesmaximal, characteristic, complemented
2C2×#21440162C213yesmaximal, complemented
3C2×#21440161C213yesmaximal, complemented
4#41×D479C2116yesmaximal, direct product factor
5C2×Q8×D479C211yesmaximal, characteristic, complemented
6C2×D4×D479C213yesmaximal, complemented
7C22×C4×D479C213yesmaximal, complemented
8C2×#41×C479C211yesmaximal, characteristic, complemented
9C23×D479C2213yes—
10#21440163C2218yescomplemented
11#21440162C22124yescomplemented
12#21440161C22124yescomplemented
13C2×Dic958C2213yescomplemented
14Q8×D479C2218yescomplemented
15C2×D1916C2213yescomplemented
16C2×C22⋊D479C2216yescomplemented
17D4×D479C22124yescomplemented
18C22×Dic479C2213yescomplemented
19C2×C4×D479C2211yescharacteristic
20C2×C4×D479C2213yes—
21C2×C4×D479C2213yescomplemented
22C2×C4×D479C2213yescomplemented
23C2×C4×D479C22124yescomplemented
24#41×C479C2218yescomplemented
25C2×Q8×C479C2211yescharacteristic, complemented
26C2×D4×C479C2213yescomplemented
27C22×C4×C479C2213yescomplemented
28C22×D479—212no—
29C22×D479C23112yes—
30C22×D479C2313yes—
31C22×D479C2311yescharacteristic
32Dic958C23112yescomplemented
33D1916C23112yescomplemented
34C22⋊D479C23124yescomplemented
35C2×Dic479C2311yescharacteristic
36C2×Dic479C2313yes—
37C2×Dic479C23112yescomplemented
38C4×D479C2314yes—
39C4×D479C23112yes—
40C4×D479C23112yescomplemented
41C4×D479C23112yescomplemented
42C23×C479C2313yes—
43Q8×C479C2314yescomplemented
44D4×C479C23112yescomplemented
45C2×C4×C479C2313yes—
46C2×C4×C479C2311yescharacteristic
47C2×C4×C479C23112yescomplemented
48C22×C479—26no—
49C22×C479C2416yes—
50C22×C479C2411yescharacteristic
51C2×D479—26no—
52C2×D479—224no—
53C2×D479#4114yesdirect product factor
54C2×D479C2416yes—
55C2×D479C2412yes—
56C4×C479C2412yes—
57C4×C479C2416yes—
58Dic479C2412yes—
59Dic479C2416yes—
60C2×C479—26no—
61C2×C479C2×#4112yescomplemented
62C2×C479C2511yescharacteristic
63D479—26no—
64D479C2×#4114yesdirect product factor
65C479C22×#4111yescharacteristic, complemented, Sylow
66C22×#41—4791nomaximal, Sylow
67C2×#41—47916no—
68C2×#41—4791no—
69C2×#41—4793no—
70C2×#41—4793no—
71C2×#41D47911yescharacteristic, direct product factor
72C22×Q8—4791no—
73C22×D4—4793no—
74C23×C4—4793no—
75C24—4793no—
76#41—4798no—
77#41—47924no—
78#41—47924no—
79#41C2×D47918yesdirect product factor
80C2×Q8—4798no—
81C2×Q8—4793no—
82C2×Q8C2×D47911yescharacteristic, complemented
83C2×D4—4796no—
84C2×D4—47924no—
85C2×D4—4793no—
86C2×D4C2×D47913yescomplemented
87C22×C4—4793no—
88C22×C4—4793no—
89C22×C4—4793no—
90C22×C4—4791no—
91C22×C4—4793no—
92C22×C4—47924no—
93C22×C4C2×D47913yescomplemented
94C23—95812no—
95C23—47912no—
96C23—4793no—
97C23—4791no—
98C23C22×D47913yes—
99Q8—47912no—
100Q8C22×D47914yescomplemented
101D4—47924no—
102D4—47912no—
103D4C22×D479112yescomplemented
104C2×C4—4791no—
105C2×C4—4793no—
106C2×C4—47912no—
107C2×C4—4794no—
108C2×C4—47912no—
109C2×C4—47912no—
110C2×C4—47912no—
111C2×C4C22×D47913yes—
112C2×C4C22×D47911yescharacteristic
113C2×C4C22×D479112yescomplemented
114C22—26no—
115C22—95824no—
116C22—9586no—
117C22—4796no—
118C22—4794no—
119C22—4792no—
120C22C23×D47916yes—
121C22C23×D47911yescharacteristic
122C4—4792no—
123C4—4796no—
124C4C23×D47912yes—
125C4C23×D47916yes—
126C2—26no—
127C2—9586no—
128C2—4794no—
129C2#41×D47912yesdirect product factor
130C2C24×D47911yescharacteristic
subgroupG/H
centerC2×C4C22×D479
commutator, cosocleC2×C479C25
FrattiniC2C24×D479
FittingC2×#41×C479C2
socleC22×C479C24
hypercenterC2×#41D479
hypocenterC479C22×#41
LCSG ▷ C2×C479 ▷ C479
UCSC1 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#21440163C2semidirect
2. C2×#21440162C2semidirect
3. C2×#21440161C2semidirect
4. #41×D479C2direct (N × H)
5. C2×Q8×D479C2semidirect
6. C2×D4×D479C2semidirect
7. C22×C4×D479C2semidirect
8. C2×#41×C479C2semidirect
10. #21440163C22semidirect
11. #21440162C22semidirect
12. #21440161C22semidirect
13. C2×Dic958C22semidirect
14. Q8×D479C22semidirect
15. C2×D1916C22semidirect
16. C2×C22⋊D479C22semidirect
17. D4×D479C22semidirect
18. C22×Dic479C22semidirect
21. C2×C4×D479C22semidirect
22. C2×C4×D479C22semidirect
23. C2×C4×D479C22semidirect
24. #41×C479C22semidirect
25. C2×Q8×C479C22semidirect
26. C2×D4×C479C22semidirect
27. C22×C4×C479C22semidirect
32. Dic958C23semidirect
33. D1916C23semidirect
34. C22⋊D479C23semidirect
37. C2×Dic479C23semidirect
40. C4×D479C23semidirect
41. C4×D479C23semidirect
43. Q8×C479C23semidirect
44. D4×C479C23semidirect
47. C2×C4×C479C23semidirect
53. C2×D479#41direct (N × H)
61. C2×C479C2×#41semidirect
64. D479C2×#41direct (N × H)
65. C479C22×#41semidirect
71. C2×#41D479direct (N × H)
79. #41C2×D479direct (N × H)
82. C2×Q8C2×D479semidirect
86. C2×D4C2×D479semidirect
93. C22×C4C2×D479semidirect
100. Q8C22×D479semidirect
103. D4C22×D479semidirect
113. C2×C4C22×D479semidirect
129. C2#41×D479direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#214401632
C2×#214401622
C2×#214401612
#41×D4792
C2×Q8×D4792
C2×D4×D4792
C22×C4×D4792
C2×#41×C4792
C22×#41479