Finite Group Databasebeta

← C2×#1009 #5962

Subgroups — C2×#1009 #5962

Order 192.

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
1C2×C3×#41C211yesmaximal, characteristic, complemented
2#1009C2116yesmaximal, direct product factor
3C2×#239C212yesmaximal, complemented
4C2×D3×D4C216yesmaximal, complemented
5C2×#235C213yesmaximal, complemented
6C22×D12C213yesmaximal, complemented
7C2×H(5,𝔽2)—31nomaximal, Sylow
8C23×D3C2216yescomplemented
9C3×#41C2218yescomplemented
10C2×C3×Q8C2211yescharacteristic, complemented
11C2×C3×D4C2213yescomplemented
12C22×C3×C4C2213yescomplemented
13C2×#67C2216yescomplemented
14#239C22116yescomplemented
15D3×D4C22148yescomplemented
16#235C22124yescomplemented
17C2×D12C2213yescomplemented
18C2×D12C2216yescomplemented
19C2×D12C22124yescomplemented
20C2×C4×D3C2216yescomplemented
21C2×Dic6C2211yescharacteristic, complemented
22H(5,𝔽2)—316no—
23C2×#41—32no—
24C2×#41—33no—
25C2×#41D311yescharacteristic, complemented
26C22×D4—36no—
27C22×D4—33no—
28C23×C3C2313yes—
29C22×D3—412no—
30C22×D3C2316yes—
31C22×D3C23124yescomplemented
32C3×Q8C2314yescomplemented
33C3×D4C23112yescomplemented
34C2×C3×C4C2311yescharacteristic
35C2×C3×C4C2313yes—
36C2×C3×C4C23112yescomplemented
37#67C23124yescomplemented
38C2×Dic3C2312yes—
39D12C23112yescomplemented
40D12C23124yescomplemented
41C4×D3C23124yescomplemented
42Dic6C2314yescomplemented
43C24—36no—
44#41—316no—
45#41—324no—
46#41C2×D318yescomplemented
47C2×Q8—31no—
48C2×Q8C2×D311yescharacteristic, complemented
49C2×D4—36no—
50C2×D4—348no—
51C2×D4—36no—
52C2×D4—33no—
53C2×D4—324no—
54C2×D4C2×D313yescomplemented
55C22×C4—36no—
56C22×C4C2×D313yescomplemented
57C22×C3—26no—
58C22×C3C2416yes—
59C22×C3C2411yescharacteristic
60C2×D3—212no—
61C2×D3—424no—
62C2×D3C24112yes—
63C3×C4C2412yes—
64C3×C4C2416yes—
65Dic3C2414yes—
66C23—36no—
67C23—324no—
68C23—1212no—
69C23C22×D313yes—
70Q8—34no—
71Q8C22×D314yescomplemented
72D4—324no—
73D4—324no—
74D4—312no—
75D4C22×D3112yescomplemented
76C2×C4—32no—
77C2×C4—324no—
78C2×C4C22×D313yes—
79C2×C4C22×D311yescharacteristic
80C2×C4C22×D3112yescomplemented
81C2×C3—26no—
82C2×C3H(5,𝔽2)12yescomplemented
83C2×C3C2511yescharacteristic
84D3—212no—
85C22—26no—
86C22—312no—
87C22—612no—
88C22—1224no—
89C22C23×D316yes—
90C22C23×D311yescharacteristic
91C4—34no—
92C4C23×D316yes—
93C4C23×D312yes—
94C3C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
95C2—26no—
96C2—612no—
97C2#100912yesdirect product factor
98C2C24×D311yescharacteristic
subgroupG/H
centerC22C23×D3
commutator, cosocleC2×C3C25
FrattiniC2C24×D3
FittingC2×C3×#41C2
socleC22×C3C24
hypercenterC2×#41D3
hypocenterC3C2×H(5,𝔽2)
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C3×#41C2semidirect
2. #1009C2direct (N × H)
3. C2×#239C2semidirect
4. C2×D3×D4C2semidirect
5. C2×#235C2semidirect
6. C22×D12C2semidirect
8. C23×D3C22semidirect
9. C3×#41C22semidirect
10. C2×C3×Q8C22semidirect
11. C2×C3×D4C22semidirect
12. C22×C3×C4C22semidirect
13. C2×#67C22semidirect
14. #239C22semidirect
15. D3×D4C22semidirect
16. #235C22semidirect
17. C2×D12C22semidirect
18. C2×D12C22semidirect
19. C2×D12C22semidirect
20. C2×C4×D3C22semidirect
21. C2×Dic6C22semidirect
25. C2×#41D3semidirect
31. C22×D3C23semidirect
32. C3×Q8C23semidirect
33. C3×D4C23semidirect
36. C2×C3×C4C23semidirect
37. #67C23semidirect
39. D12C23semidirect
40. D12C23semidirect
41. C4×D3C23semidirect
42. Dic6C23semidirect
46. #41C2×D3semidirect
48. C2×Q8C2×D3semidirect
54. C2×D4C2×D3semidirect
56. C22×C4C2×D3semidirect
71. Q8C22×D3semidirect
75. D4C22×D3semidirect
80. C2×C4C22×D3semidirect
82. C2×C3H(5,𝔽2)semidirect
94. C3C2×H(5,𝔽2)semidirect
97. C2#1009direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#412
#10092
C2×#2392
C2×D3×D42
C2×#2352
C22×D122
C2×H(5,𝔽2)3