Finite Group Databasebeta

← C2×#19149725 #26012322

Subgroups — C2×#19149725 #26012322

Order 11072.

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#19149725C2116yesmaximal, direct product factor
2C2×#14583827C212yesmaximal, complemented
3C2×#14583826C213yesmaximal, complemented
4C22×D692C213yesmaximal, complemented
5C2×D4×D173C216yesmaximal, complemented
6C2×#41×C173C211yesmaximal, characteristic, complemented
7C23×D173C2216yescomplemented
8#14583827C22116yescomplemented
9#14583826C22124yescomplemented
10C2×Dic346C2211yescharacteristic, complemented
11C2×D692C2216yescomplemented
12C2×D692C2213yescomplemented
13C2×D692C22124yescomplemented
14C2×C22⋊D173C2216yescomplemented
15D4×D173C22148yescomplemented
16C2×C4×D173C2216yescomplemented
17#41×C173C2218yescomplemented
18C2×Q8×C173C2211yescharacteristic, complemented
19C2×D4×C173C2213yescomplemented
20C22×C4×C173C2213yescomplemented
21C22×D173—412no—
22C22×D173C2316yes—
23C22×D173C23124yescomplemented
24Dic346C2314yescomplemented
25D692C23124yescomplemented
26D692C23112yescomplemented
27C22⋊D173C23124yescomplemented
28C2×Dic173C2312yes—
29C4×D173C23124yescomplemented
30C23×C173C2313yes—
31Q8×C173C2314yescomplemented
32D4×C173C23112yescomplemented
33C2×C4×C173C2313yes—
34C2×C4×C173C2311yescharacteristic
35C2×C4×C173C23112yescomplemented
36C22×C173—26no—
37C22×C173C2416yes—
38C22×C173C2411yescharacteristic
39C2×D173—212no—
40C2×D173—424no—
41C2×D173C24112yes—
42C4×C173C2412yes—
43C4×C173C2416yes—
44Dic173C2414yes—
45C2×C173—26no—
46C2×C173H(5,𝔽2)12yescomplemented
47C2×C173C2511yescharacteristic
48D173—212no—
49C173C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
50C2×H(5,𝔽2)—1731nomaximal, Sylow
51H(5,𝔽2)—17316no—
52C2×#41—1732no—
53C2×#41—1733no—
54C2×#41D17311yescharacteristic, complemented
55C22×D4—1736no—
56C22×D4—1733no—
57C24—1736no—
58#41—17316no—
59#41—17324no—
60#41C2×D17318yescomplemented
61C2×Q8—1731no—
62C2×Q8C2×D17311yescharacteristic, complemented
63C2×D4—1736no—
64C2×D4—17348no—
65C2×D4—1736no—
66C2×D4—1733no—
67C2×D4—17324no—
68C2×D4C2×D17313yescomplemented
69C22×C4—1736no—
70C22×C4C2×D17313yescomplemented
71C23—1736no—
72C23—17324no—
73C23—69212no—
74C23C22×D17313yes—
75Q8—1734no—
76Q8C22×D17314yescomplemented
77D4—17324no—
78D4—17324no—
79D4—17312no—
80D4C22×D173112yescomplemented
81C2×C4—1732no—
82C2×C4—17324no—
83C2×C4C22×D17313yes—
84C2×C4C22×D17311yescharacteristic
85C2×C4C22×D173112yescomplemented
86C22—26no—
87C22—34612no—
88C22—17312no—
89C22—69224no—
90C22C23×D17316yes—
91C22C23×D17311yescharacteristic
92C4—1734no—
93C4C23×D17316yes—
94C4C23×D17312yes—
95C2—26no—
96C2—34612no—
97C2#1914972512yesdirect product factor
98C2C24×D17311yescharacteristic
subgroupG/H
centerC22C23×D173
commutator, cosocleC2×C173C25
FrattiniC2C24×D173
FittingC2×#41×C173C2
socleC22×C173C24
hypercenterC2×#41D173
hypocenterC173C2×H(5,𝔽2)
LCSG ▷ C2×C173 ▷ C173
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #19149725C2direct (N × H)
2. C2×#14583827C2semidirect
3. C2×#14583826C2semidirect
4. C22×D692C2semidirect
5. C2×D4×D173C2semidirect
6. C2×#41×C173C2semidirect
7. C23×D173C22semidirect
8. #14583827C22semidirect
9. #14583826C22semidirect
10. C2×Dic346C22semidirect
11. C2×D692C22semidirect
12. C2×D692C22semidirect
13. C2×D692C22semidirect
14. C2×C22⋊D173C22semidirect
15. D4×D173C22semidirect
16. C2×C4×D173C22semidirect
17. #41×C173C22semidirect
18. C2×Q8×C173C22semidirect
19. C2×D4×C173C22semidirect
20. C22×C4×C173C22semidirect
23. C22×D173C23semidirect
24. Dic346C23semidirect
25. D692C23semidirect
26. D692C23semidirect
27. C22⋊D173C23semidirect
29. C4×D173C23semidirect
31. Q8×C173C23semidirect
32. D4×C173C23semidirect
35. C2×C4×C173C23semidirect
46. C2×C173H(5,𝔽2)semidirect
49. C173C2×H(5,𝔽2)semidirect
54. C2×#41D173semidirect
60. #41C2×D173semidirect
62. C2×Q8C2×D173semidirect
68. C2×D4C2×D173semidirect
70. C22×C4C2×D173semidirect
76. Q8C22×D173semidirect
80. D4C22×D173semidirect
85. C2×C4C22×D173semidirect
97. C2#19149725direct (N × H)

Maximal subgroups

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

subgroupindex
#191497252
C2×#145838272
C2×#145838262
C22×D6922
C2×D4×D1732
C2×#41×C1732
C2×H(5,𝔽2)173