Finite Group Databasebeta

← C2×#31772674 #46831006

Subgroups — C2×#31772674 #46831006

Order 34624.

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#31772674C2116yesmaximal, direct product factor
2C2×#22575837C212yesmaximal, complemented
3C2×#22575836C213yesmaximal, complemented
4C22×D2164C213yesmaximal, complemented
5C2×D4×D541C216yesmaximal, complemented
6C2×#41×C541C211yesmaximal, characteristic, complemented
7C23×D541C2216yescomplemented
8#22575837C22116yescomplemented
9#22575836C22124yescomplemented
10C2×Dic1082C2211yescharacteristic, complemented
11C2×D2164C2216yescomplemented
12C2×D2164C2213yescomplemented
13C2×D2164C22124yescomplemented
14C2×C22⋊D541C2216yescomplemented
15D4×D541C22148yescomplemented
16C2×C4×D541C2216yescomplemented
17#41×C541C2218yescomplemented
18C2×Q8×C541C2211yescharacteristic, complemented
19C2×D4×C541C2213yescomplemented
20C22×C4×C541C2213yescomplemented
21C22×D541—412no—
22C22×D541C2316yes—
23C22×D541C23124yescomplemented
24Dic1082C2314yescomplemented
25D2164C23124yescomplemented
26D2164C23112yescomplemented
27C22⋊D541C23124yescomplemented
28C2×Dic541C2312yes—
29C4×D541C23124yescomplemented
30C23×C541C2313yes—
31Q8×C541C2314yescomplemented
32D4×C541C23112yescomplemented
33C2×C4×C541C2311yescharacteristic
34C2×C4×C541C2313yes—
35C2×C4×C541C23112yescomplemented
36C22×C541—26no—
37C22×C541C2416yes—
38C22×C541C2411yescharacteristic
39C2×D541—212no—
40C2×D541—424no—
41C2×D541C24112yes—
42C4×C541C2416yes—
43C4×C541C2412yes—
44Dic541C2414yes—
45C2×C541—26no—
46C2×C541H(5,𝔽2)12yescomplemented
47C2×C541C2511yescharacteristic
48D541—212no—
49C541C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
50C2×H(5,𝔽2)—5411nomaximal, Sylow
51H(5,𝔽2)—54116no—
52C2×#41—5412no—
53C2×#41—5413no—
54C2×#41D54111yescharacteristic, complemented
55C22×D4—5416no—
56C22×D4—5413no—
57C24—5416no—
58#41—54116no—
59#41—54124no—
60#41C2×D54118yescomplemented
61C2×Q8—5411no—
62C2×Q8C2×D54111yescharacteristic, complemented
63C2×D4—5416no—
64C2×D4—54148no—
65C2×D4—5416no—
66C2×D4—5413no—
67C2×D4—54124no—
68C2×D4C2×D54113yescomplemented
69C22×C4—5416no—
70C22×C4C2×D54113yescomplemented
71C23—5416no—
72C23—54124no—
73C23—216412no—
74C23C22×D54113yes—
75Q8—5414no—
76Q8C22×D54114yescomplemented
77D4—54124no—
78D4—54124no—
79D4—54112no—
80D4C22×D541112yescomplemented
81C2×C4—5412no—
82C2×C4—54124no—
83C2×C4C22×D54113yes—
84C2×C4C22×D54111yescharacteristic
85C2×C4C22×D541112yescomplemented
86C22—26no—
87C22—54112no—
88C22—108212no—
89C22—216424no—
90C22C23×D54116yes—
91C22C23×D54111yescharacteristic
92C4—5414no—
93C4C23×D54116yes—
94C4C23×D54112yes—
95C2—26no—
96C2—108212no—
97C2#3177267412yesdirect product factor
98C2C24×D54111yescharacteristic
subgroupG/H
centerC22C23×D541
commutator, cosocleC2×C541C25
FrattiniC2C24×D541
FittingC2×#41×C541C2
socleC22×C541C24
hypercenterC2×#41D541
hypocenterC541C2×H(5,𝔽2)
LCSG ▷ C2×C541 ▷ C541
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #31772674C2direct (N × H)
2. C2×#22575837C2semidirect
3. C2×#22575836C2semidirect
4. C22×D2164C2semidirect
5. C2×D4×D541C2semidirect
6. C2×#41×C541C2semidirect
7. C23×D541C22semidirect
8. #22575837C22semidirect
9. #22575836C22semidirect
10. C2×Dic1082C22semidirect
11. C2×D2164C22semidirect
12. C2×D2164C22semidirect
13. C2×D2164C22semidirect
14. C2×C22⋊D541C22semidirect
15. D4×D541C22semidirect
16. C2×C4×D541C22semidirect
17. #41×C541C22semidirect
18. C2×Q8×C541C22semidirect
19. C2×D4×C541C22semidirect
20. C22×C4×C541C22semidirect
23. C22×D541C23semidirect
24. Dic1082C23semidirect
25. D2164C23semidirect
26. D2164C23semidirect
27. C22⋊D541C23semidirect
29. C4×D541C23semidirect
31. Q8×C541C23semidirect
32. D4×C541C23semidirect
35. C2×C4×C541C23semidirect
46. C2×C541H(5,𝔽2)semidirect
49. C541C2×H(5,𝔽2)semidirect
54. C2×#41D541semidirect
60. #41C2×D541semidirect
62. C2×Q8C2×D541semidirect
68. C2×D4C2×D541semidirect
70. C22×C4C2×D541semidirect
76. Q8C22×D541semidirect
80. D4C22×D541semidirect
85. C2×C4C22×D541semidirect
97. C2#31772674direct (N × H)

Maximal subgroups

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

subgroupindex
#317726742
C2×#225758372
C2×#225758362
C22×D21642
C2×D4×D5412
C2×#41×C5412
C2×H(5,𝔽2)541