Finite Group Databasebeta

← C2×#13063371 #14583730

Subgroups — C2×#13063371 #14583730

Order 2752.

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#13063371C2116yesmaximal, direct product factor
2C2×#10621902C212yesmaximal, complemented
3C2×#10621898C213yesmaximal, complemented
4C22×D172C213yesmaximal, complemented
5C2×D4×D43C216yesmaximal, complemented
6C2×#41×C43C211yesmaximal, characteristic, complemented
7C23×D43C2216yescomplemented
8#41×C43C2218yescomplemented
9C2×Q8×C43C2211yescharacteristic, complemented
10C2×D4×C43C2213yescomplemented
11C22×C4×C43C2213yescomplemented
12C2×C22⋊D43C2216yescomplemented
13#10621902C22116yescomplemented
14D4×D43C22148yescomplemented
15#10621898C22124yescomplemented
16C2×D172C2216yescomplemented
17C2×D172C2213yescomplemented
18C2×D172C22124yescomplemented
19C2×C4×D43C2216yescomplemented
20C2×Dic86C2211yescharacteristic, complemented
21C23×C43C2313yes—
22C22×D43—412no—
23C22×D43C2316yes—
24C22×D43C23124yescomplemented
25Q8×C43C2314yescomplemented
26D4×C43C23112yescomplemented
27C2×C4×C43C2311yescharacteristic
28C2×C4×C43C2313yes—
29C2×C4×C43C23112yescomplemented
30C22⋊D43C23124yescomplemented
31C2×Dic43C2312yes—
32D172C23112yescomplemented
33D172C23124yescomplemented
34C4×D43C23124yescomplemented
35Dic86C2314yescomplemented
36C22×C43—26no—
37C22×C43C2416yes—
38C22×C43C2411yescharacteristic
39C2×D43—212no—
40C2×D43—424no—
41C2×D43C24112yes—
42C4×C43C2412yes—
43C4×C43C2416yes—
44Dic43C2414yes—
45C2×C43—26no—
46C2×C43H(5,𝔽2)12yescomplemented
47C2×C43C2511yescharacteristic
48D43—212no—
49C2×H(5,𝔽2)—431nomaximal, Sylow
50C43C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
51H(5,𝔽2)—4316no—
52C2×#41—432no—
53C2×#41—433no—
54C2×#41D4311yescharacteristic, complemented
55C22×D4—436no—
56C22×D4—433no—
57C24—436no—
58#41—4316no—
59#41—4324no—
60#41C2×D4318yescomplemented
61C2×Q8—431no—
62C2×Q8C2×D4311yescharacteristic, complemented
63C2×D4—436no—
64C2×D4—4348no—
65C2×D4—436no—
66C2×D4—433no—
67C2×D4—4324no—
68C2×D4C2×D4313yescomplemented
69C22×C4—436no—
70C22×C4C2×D4313yescomplemented
71C23—436no—
72C23—4324no—
73C23—17212no—
74C23C22×D4313yes—
75Q8—434no—
76Q8C22×D4314yescomplemented
77D4—4324no—
78D4—4324no—
79D4—4312no—
80D4C22×D43112yescomplemented
81C2×C4—432no—
82C2×C4—4324no—
83C2×C4C22×D4313yes—
84C2×C4C22×D4311yescharacteristic
85C2×C4C22×D43112yescomplemented
86C22—26no—
87C22—4312no—
88C22—8612no—
89C22—17224no—
90C22C23×D4316yes—
91C22C23×D4311yescharacteristic
92C4—434no—
93C4C23×D4316yes—
94C4C23×D4312yes—
95C2—26no—
96C2—8612no—
97C2#1306337112yesdirect product factor
98C2C24×D4311yescharacteristic
subgroupG/H
centerC22C23×D43
commutator, cosocleC2×C43C25
FrattiniC2C24×D43
FittingC2×#41×C43C2
socleC22×C43C24
hypercenterC2×#41D43
hypocenterC43C2×H(5,𝔽2)
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #13063371C2direct (N × H)
2. C2×#10621902C2semidirect
3. C2×#10621898C2semidirect
4. C22×D172C2semidirect
5. C2×D4×D43C2semidirect
6. C2×#41×C43C2semidirect
7. C23×D43C22semidirect
8. #41×C43C22semidirect
9. C2×Q8×C43C22semidirect
10. C2×D4×C43C22semidirect
11. C22×C4×C43C22semidirect
12. C2×C22⋊D43C22semidirect
13. #10621902C22semidirect
14. D4×D43C22semidirect
15. #10621898C22semidirect
16. C2×D172C22semidirect
17. C2×D172C22semidirect
18. C2×D172C22semidirect
19. C2×C4×D43C22semidirect
20. C2×Dic86C22semidirect
24. C22×D43C23semidirect
25. Q8×C43C23semidirect
26. D4×C43C23semidirect
29. C2×C4×C43C23semidirect
30. C22⋊D43C23semidirect
32. D172C23semidirect
33. D172C23semidirect
34. C4×D43C23semidirect
35. Dic86C23semidirect
46. C2×C43H(5,𝔽2)semidirect
50. C43C2×H(5,𝔽2)semidirect
54. C2×#41D43semidirect
60. #41C2×D43semidirect
62. C2×Q8C2×D43semidirect
68. C2×D4C2×D43semidirect
70. C22×C4C2×D43semidirect
76. Q8C22×D43semidirect
80. D4C22×D43semidirect
85. C2×C4C22×D43semidirect
97. C2#13063371direct (N × H)

Maximal subgroups

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

subgroupindex
#130633712
C2×#106219022
C2×#106218982
C22×D1722
C2×D4×D432
C2×#41×C432
C2×H(5,𝔽2)43