Finite Group Databasebeta

← C2×#29506428 #44501226

Subgroups — C2×#29506428 #44501226

Order 30656.

898 conjugacy classes of subgroups; only the 447 normal subgroups are shown.

normal subgroups only

This group has 898 conjugacy classes of subgroups — too many to draw. Only its 447 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
1#29506428C2116yesmaximal, direct product factor
2C2×#21440163C212yesmaximal, complemented
3C2×#21440162C213yesmaximal, complemented
4C22×D1916C213yesmaximal, complemented
5C2×D4×D479C216yesmaximal, complemented
6C2×#41×C479C211yesmaximal, characteristic, complemented
7C23×D479C2216yescomplemented
8#21440163C22116yescomplemented
9#21440162C22124yescomplemented
10C2×Dic958C2211yescharacteristic, complemented
11C2×D1916C2216yescomplemented
12C2×D1916C2213yescomplemented
13C2×D1916C22124yescomplemented
14C2×C22⋊D479C2216yescomplemented
15D4×D479C22148yescomplemented
16C2×C4×D479C2216yescomplemented
17#41×C479C2218yescomplemented
18C2×Q8×C479C2211yescharacteristic, complemented
19C2×D4×C479C2213yescomplemented
20C22×C4×C479C2213yescomplemented
21C22×D479—412no—
22C22×D479C2316yes—
23C22×D479C23124yescomplemented
24Dic958C2314yescomplemented
25D1916C23124yescomplemented
26D1916C23112yescomplemented
27C22⋊D479C23124yescomplemented
28C2×Dic479C2312yes—
29C4×D479C23124yescomplemented
30C23×C479C2313yes—
31Q8×C479C2314yescomplemented
32D4×C479C23112yescomplemented
33C2×C4×C479C2311yescharacteristic
34C2×C4×C479C2313yes—
35C2×C4×C479C23112yescomplemented
36C22×C479—26no—
37C22×C479C2416yes—
38C22×C479C2411yescharacteristic
39C2×D479—212no—
40C2×D479—424no—
41C2×D479C24112yes—
42C4×C479C2412yes—
43C4×C479C2416yes—
44Dic479C2414yes—
45C2×C479—26no—
46C2×C479H(5,𝔽2)12yescomplemented
47C2×C479C2511yescharacteristic
48D479—212no—
49C479C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
50C2×H(5,𝔽2)—4791nomaximal, Sylow
51H(5,𝔽2)—47916no—
52C2×#41—4792no—
53C2×#41—4793no—
54C2×#41D47911yescharacteristic, complemented
55C22×D4—4796no—
56C22×D4—4793no—
57C24—4796no—
58#41—47916no—
59#41—47924no—
60#41C2×D47918yescomplemented
61C2×Q8—4791no—
62C2×Q8C2×D47911yescharacteristic, complemented
63C2×D4—4796no—
64C2×D4—47948no—
65C2×D4—4796no—
66C2×D4—4793no—
67C2×D4—47924no—
68C2×D4C2×D47913yescomplemented
69C22×C4—4796no—
70C22×C4C2×D47913yescomplemented
71C23—191612no—
72C23—47924no—
73C23—4796no—
74C23C22×D47913yes—
75Q8—4794no—
76Q8C22×D47914yescomplemented
77D4—47924no—
78D4—47924no—
79D4—47912no—
80D4C22×D479112yescomplemented
81C2×C4—4792no—
82C2×C4—47924no—
83C2×C4C22×D47913yes—
84C2×C4C22×D47911yescharacteristic
85C2×C4C22×D479112yescomplemented
86C22—26no—
87C22—191624no—
88C22—95812no—
89C22—47912no—
90C22C23×D47916yes—
91C22C23×D47911yescharacteristic
92C4—4794no—
93C4C23×D47916yes—
94C4C23×D47912yes—
95C2—26no—
96C2—95812no—
97C2#2950642812yesdirect product factor
98C2C24×D47911yescharacteristic
subgroupG/H
centerC22C23×D479
commutator, cosocleC2×C479C25
FrattiniC2C24×D479
FittingC2×#41×C479C2
socleC22×C479C24
hypercenterC2×#41D479
hypocenterC479C2×H(5,𝔽2)
LCSG ▷ C2×C479 ▷ C479
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #29506428C2direct (N × H)
2. C2×#21440163C2semidirect
3. C2×#21440162C2semidirect
4. C22×D1916C2semidirect
5. C2×D4×D479C2semidirect
6. C2×#41×C479C2semidirect
7. C23×D479C22semidirect
8. #21440163C22semidirect
9. #21440162C22semidirect
10. C2×Dic958C22semidirect
11. C2×D1916C22semidirect
12. C2×D1916C22semidirect
13. C2×D1916C22semidirect
14. C2×C22⋊D479C22semidirect
15. D4×D479C22semidirect
16. C2×C4×D479C22semidirect
17. #41×C479C22semidirect
18. C2×Q8×C479C22semidirect
19. C2×D4×C479C22semidirect
20. C22×C4×C479C22semidirect
23. C22×D479C23semidirect
24. Dic958C23semidirect
25. D1916C23semidirect
26. D1916C23semidirect
27. C22⋊D479C23semidirect
29. C4×D479C23semidirect
31. Q8×C479C23semidirect
32. D4×C479C23semidirect
35. C2×C4×C479C23semidirect
46. C2×C479H(5,𝔽2)semidirect
49. C479C2×H(5,𝔽2)semidirect
54. C2×#41D479semidirect
60. #41C2×D479semidirect
62. C2×Q8C2×D479semidirect
68. C2×D4C2×D479semidirect
70. C22×C4C2×D479semidirect
76. Q8C22×D479semidirect
80. D4C22×D479semidirect
85. C2×C4C22×D479semidirect
97. C2#29506428direct (N × H)

Maximal subgroups

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

subgroupindex
#295064282
C2×#214401632
C2×#214401622
C22×D19162
C2×D4×D4792
C2×#41×C4792
C2×H(5,𝔽2)479