Finite Group Databasebeta

← C2×#30632910 #44567112

Subgroups — C2×#30632910 #44567112

Order 32192.

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#30632910C2116yesmaximal, direct product factor
2C2×#22548884C212yesmaximal, complemented
3C2×#22548883C213yesmaximal, complemented
4C22×D2012C213yesmaximal, complemented
5C2×D4×D503C216yesmaximal, complemented
6C2×#41×C503C211yesmaximal, characteristic, complemented
7C23×D503C2216yescomplemented
8#22548884C22116yescomplemented
9#22548883C22124yescomplemented
10C2×Dic1006C2211yescharacteristic, complemented
11C2×D2012C2216yescomplemented
12C2×D2012C2213yescomplemented
13C2×D2012C22124yescomplemented
14C2×C22⋊D503C2216yescomplemented
15D4×D503C22148yescomplemented
16C2×C4×D503C2216yescomplemented
17#41×C503C2218yescomplemented
18C2×Q8×C503C2211yescharacteristic, complemented
19C2×D4×C503C2213yescomplemented
20C22×C4×C503C2213yescomplemented
21C22×D503—412no—
22C22×D503C2316yes—
23C22×D503C23124yescomplemented
24Dic1006C2314yescomplemented
25D2012C23124yescomplemented
26D2012C23112yescomplemented
27C22⋊D503C23124yescomplemented
28C2×Dic503C2312yes—
29C4×D503C23124yescomplemented
30C23×C503C2313yes—
31Q8×C503C2314yescomplemented
32D4×C503C23112yescomplemented
33C2×C4×C503C2311yescharacteristic
34C2×C4×C503C2313yes—
35C2×C4×C503C23112yescomplemented
36C22×C503—26no—
37C22×C503C2416yes—
38C22×C503C2411yescharacteristic
39C2×D503—212no—
40C2×D503—424no—
41C2×D503C24112yes—
42C4×C503C2412yes—
43C4×C503C2416yes—
44Dic503C2414yes—
45C2×C503—26no—
46C2×C503H(5,𝔽2)12yescomplemented
47C2×C503C2511yescharacteristic
48D503—212no—
49C503C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
50C2×H(5,𝔽2)—5031nomaximal, Sylow
51H(5,𝔽2)—50316no—
52C2×#41—5032no—
53C2×#41—5033no—
54C2×#41D50311yescharacteristic, complemented
55C22×D4—5036no—
56C22×D4—5033no—
57C24—5036no—
58#41—50316no—
59#41—50324no—
60#41C2×D50318yescomplemented
61C2×Q8—5031no—
62C2×Q8C2×D50311yescharacteristic, complemented
63C2×D4—5036no—
64C2×D4—50348no—
65C2×D4—5036no—
66C2×D4—5033no—
67C2×D4—50324no—
68C2×D4C2×D50313yescomplemented
69C22×C4—5036no—
70C22×C4C2×D50313yescomplemented
71C23—201212no—
72C23—50324no—
73C23—5036no—
74C23C22×D50313yes—
75Q8—5034no—
76Q8C22×D50314yescomplemented
77D4—50324no—
78D4—50324no—
79D4—50312no—
80D4C22×D503112yescomplemented
81C2×C4—5032no—
82C2×C4—50324no—
83C2×C4C22×D50313yes—
84C2×C4C22×D50311yescharacteristic
85C2×C4C22×D503112yescomplemented
86C22—26no—
87C22—201224no—
88C22—100612no—
89C22—50312no—
90C22C23×D50316yes—
91C22C23×D50311yescharacteristic
92C4—5034no—
93C4C23×D50316yes—
94C4C23×D50312yes—
95C2—26no—
96C2—100612no—
97C2#3063291012yesdirect product factor
98C2C24×D50311yescharacteristic
subgroupG/H
centerC22C23×D503
commutator, cosocleC2×C503C25
FrattiniC2C24×D503
FittingC2×#41×C503C2
socleC22×C503C24
hypercenterC2×#41D503
hypocenterC503C2×H(5,𝔽2)
LCSG ▷ C2×C503 ▷ C503
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #30632910C2direct (N × H)
2. C2×#22548884C2semidirect
3. C2×#22548883C2semidirect
4. C22×D2012C2semidirect
5. C2×D4×D503C2semidirect
6. C2×#41×C503C2semidirect
7. C23×D503C22semidirect
8. #22548884C22semidirect
9. #22548883C22semidirect
10. C2×Dic1006C22semidirect
11. C2×D2012C22semidirect
12. C2×D2012C22semidirect
13. C2×D2012C22semidirect
14. C2×C22⋊D503C22semidirect
15. D4×D503C22semidirect
16. C2×C4×D503C22semidirect
17. #41×C503C22semidirect
18. C2×Q8×C503C22semidirect
19. C2×D4×C503C22semidirect
20. C22×C4×C503C22semidirect
23. C22×D503C23semidirect
24. Dic1006C23semidirect
25. D2012C23semidirect
26. D2012C23semidirect
27. C22⋊D503C23semidirect
29. C4×D503C23semidirect
31. Q8×C503C23semidirect
32. D4×C503C23semidirect
35. C2×C4×C503C23semidirect
46. C2×C503H(5,𝔽2)semidirect
49. C503C2×H(5,𝔽2)semidirect
54. C2×#41D503semidirect
60. #41C2×D503semidirect
62. C2×Q8C2×D503semidirect
68. C2×D4C2×D503semidirect
70. C22×C4C2×D503semidirect
76. Q8C22×D503semidirect
80. D4C22×D503semidirect
85. C2×C4C22×D503semidirect
97. C2#30632910direct (N × H)

Maximal subgroups

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

subgroupindex
#306329102
C2×#225488842
C2×#225488832
C22×D20122
C2×D4×D5032
C2×#41×C5032
C2×H(5,𝔽2)503