Finite Group Databasebeta

← C2×#21418581 #28417266

Subgroups — C2×#21418581 #28417266

Order 14912.

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#21418581C2116yesmaximal, direct product factor
2C2×#16836595C212yesmaximal, complemented
3C2×#16836594C213yesmaximal, complemented
4C22×D932C213yesmaximal, complemented
5C2×D4×D233C216yesmaximal, complemented
6C2×#41×C233C211yesmaximal, characteristic, complemented
7C23×D233C2216yescomplemented
8#16836595C22116yescomplemented
9#16836594C22124yescomplemented
10C2×Dic466C2211yescharacteristic, complemented
11C2×D932C2216yescomplemented
12C2×D932C2213yescomplemented
13C2×D932C22124yescomplemented
14C2×C22⋊D233C2216yescomplemented
15D4×D233C22148yescomplemented
16C2×C4×D233C2216yescomplemented
17#41×C233C2218yescomplemented
18C2×Q8×C233C2211yescharacteristic, complemented
19C2×D4×C233C2213yescomplemented
20C22×C4×C233C2213yescomplemented
21C22×D233—412no—
22C22×D233C2316yes—
23C22×D233C23124yescomplemented
24Dic466C2314yescomplemented
25D932C23124yescomplemented
26D932C23112yescomplemented
27C22⋊D233C23124yescomplemented
28C2×Dic233C2312yes—
29C4×D233C23124yescomplemented
30C23×C233C2313yes—
31Q8×C233C2314yescomplemented
32D4×C233C23112yescomplemented
33C2×C4×C233C2311yescharacteristic
34C2×C4×C233C2313yes—
35C2×C4×C233C23112yescomplemented
36C22×C233—26no—
37C22×C233C2416yes—
38C22×C233C2411yescharacteristic
39C2×D233—212no—
40C2×D233—424no—
41C2×D233C24112yes—
42C4×C233C2412yes—
43C4×C233C2416yes—
44Dic233C2414yes—
45C2×C233—26no—
46C2×C233H(5,𝔽2)12yescomplemented
47C2×C233C2511yescharacteristic
48D233—212no—
49C233C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
50C2×H(5,𝔽2)—2331nomaximal, Sylow
51H(5,𝔽2)—23316no—
52C2×#41—2332no—
53C2×#41—2333no—
54C2×#41D23311yescharacteristic, complemented
55C22×D4—2336no—
56C22×D4—2333no—
57C24—2336no—
58#41—23316no—
59#41—23324no—
60#41C2×D23318yescomplemented
61C2×Q8—2331no—
62C2×Q8C2×D23311yescharacteristic, complemented
63C2×D4—2336no—
64C2×D4—23348no—
65C2×D4—2336no—
66C2×D4—2333no—
67C2×D4—23324no—
68C2×D4C2×D23313yescomplemented
69C22×C4—2336no—
70C22×C4C2×D23313yescomplemented
71C23—93212no—
72C23—23324no—
73C23—2336no—
74C23C22×D23313yes—
75Q8—2334no—
76Q8C22×D23314yescomplemented
77D4—23324no—
78D4—23324no—
79D4—23312no—
80D4C22×D233112yescomplemented
81C2×C4—2332no—
82C2×C4—23324no—
83C2×C4C22×D23313yes—
84C2×C4C22×D23311yescharacteristic
85C2×C4C22×D233112yescomplemented
86C22—26no—
87C22—93224no—
88C22—46612no—
89C22—23312no—
90C22C23×D23316yes—
91C22C23×D23311yescharacteristic
92C4—2334no—
93C4C23×D23316yes—
94C4C23×D23312yes—
95C2—26no—
96C2—46612no—
97C2#2141858112yesdirect product factor
98C2C24×D23311yescharacteristic
subgroupG/H
centerC22C23×D233
commutator, cosocleC2×C233C25
FrattiniC2C24×D233
FittingC2×#41×C233C2
socleC22×C233C24
hypercenterC2×#41D233
hypocenterC233C2×H(5,𝔽2)
LCSG ▷ C2×C233 ▷ C233
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #21418581C2direct (N × H)
2. C2×#16836595C2semidirect
3. C2×#16836594C2semidirect
4. C22×D932C2semidirect
5. C2×D4×D233C2semidirect
6. C2×#41×C233C2semidirect
7. C23×D233C22semidirect
8. #16836595C22semidirect
9. #16836594C22semidirect
10. C2×Dic466C22semidirect
11. C2×D932C22semidirect
12. C2×D932C22semidirect
13. C2×D932C22semidirect
14. C2×C22⋊D233C22semidirect
15. D4×D233C22semidirect
16. C2×C4×D233C22semidirect
17. #41×C233C22semidirect
18. C2×Q8×C233C22semidirect
19. C2×D4×C233C22semidirect
20. C22×C4×C233C22semidirect
23. C22×D233C23semidirect
24. Dic466C23semidirect
25. D932C23semidirect
26. D932C23semidirect
27. C22⋊D233C23semidirect
29. C4×D233C23semidirect
31. Q8×C233C23semidirect
32. D4×C233C23semidirect
35. C2×C4×C233C23semidirect
46. C2×C233H(5,𝔽2)semidirect
49. C233C2×H(5,𝔽2)semidirect
54. C2×#41D233semidirect
60. #41C2×D233semidirect
62. C2×Q8C2×D233semidirect
68. C2×D4C2×D233semidirect
70. C22×C4C2×D233semidirect
76. Q8C22×D233semidirect
80. D4C22×D233semidirect
85. C2×C4C22×D233semidirect
97. C2#21418581direct (N × H)

Maximal subgroups

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

subgroupindex
#214185812
C2×#168365952
C2×#168365942
C22×D9322
C2×D4×D2332
C2×#41×C2332
C2×H(5,𝔽2)233