Finite Group Databasebeta

← C2×#30659754 #45688263

Subgroups — C2×#30659754 #45688263

Order 33344.

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#30659754C2116yesmaximal, direct product factor
2C2×#22552365C212yesmaximal, complemented
3C2×#22552364C213yesmaximal, complemented
4C22×D2084C213yesmaximal, complemented
5C2×D4×D521C216yesmaximal, complemented
6C2×#41×C521C211yesmaximal, characteristic, complemented
7C23×D521C2216yescomplemented
8#22552365C22116yescomplemented
9#22552364C22124yescomplemented
10C2×Dic1042C2211yescharacteristic, complemented
11C2×D2084C2216yescomplemented
12C2×D2084C2213yescomplemented
13C2×D2084C22124yescomplemented
14C2×C22⋊D521C2216yescomplemented
15D4×D521C22148yescomplemented
16C2×C4×D521C2216yescomplemented
17#41×C521C2218yescomplemented
18C2×Q8×C521C2211yescharacteristic, complemented
19C2×D4×C521C2213yescomplemented
20C22×C4×C521C2213yescomplemented
21C22×D521—412no—
22C22×D521C2316yes—
23C22×D521C23124yescomplemented
24Dic1042C2314yescomplemented
25D2084C23124yescomplemented
26D2084C23112yescomplemented
27C22⋊D521C23124yescomplemented
28C2×Dic521C2312yes—
29C4×D521C23124yescomplemented
30C23×C521C2313yes—
31Q8×C521C2314yescomplemented
32D4×C521C23112yescomplemented
33C2×C4×C521C2311yescharacteristic
34C2×C4×C521C2313yes—
35C2×C4×C521C23112yescomplemented
36C22×C521—26no—
37C22×C521C2416yes—
38C22×C521C2411yescharacteristic
39C2×D521—212no—
40C2×D521—424no—
41C2×D521C24112yes—
42C4×C521C2412yes—
43C4×C521C2416yes—
44Dic521C2414yes—
45C2×C521—26no—
46C2×C521H(5,𝔽2)12yescomplemented
47C2×C521C2511yescharacteristic
48D521—212no—
49C521C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
50C2×H(5,𝔽2)—5211nomaximal, Sylow
51H(5,𝔽2)—52116no—
52C2×#41—5212no—
53C2×#41—5213no—
54C2×#41D52111yescharacteristic, complemented
55C22×D4—5216no—
56C22×D4—5213no—
57C24—5216no—
58#41—52116no—
59#41—52124no—
60#41C2×D52118yescomplemented
61C2×Q8—5211no—
62C2×Q8C2×D52111yescharacteristic, complemented
63C2×D4—5216no—
64C2×D4—52148no—
65C2×D4—5216no—
66C2×D4—5213no—
67C2×D4—52124no—
68C2×D4C2×D52113yescomplemented
69C22×C4—5216no—
70C22×C4C2×D52113yescomplemented
71C23—5216no—
72C23—52124no—
73C23—208412no—
74C23C22×D52113yes—
75Q8—5214no—
76Q8C22×D52114yescomplemented
77D4—52124no—
78D4—52124no—
79D4—52112no—
80D4C22×D521112yescomplemented
81C2×C4—5212no—
82C2×C4—52124no—
83C2×C4C22×D52113yes—
84C2×C4C22×D52111yescharacteristic
85C2×C4C22×D521112yescomplemented
86C22—26no—
87C22—52112no—
88C22—104212no—
89C22—208424no—
90C22C23×D52116yes—
91C22C23×D52111yescharacteristic
92C4—5214no—
93C4C23×D52116yes—
94C4C23×D52112yes—
95C2—26no—
96C2—104212no—
97C2#3065975412yesdirect product factor
98C2C24×D52111yescharacteristic
subgroupG/H
centerC22C23×D521
commutator, cosocleC2×C521C25
FrattiniC2C24×D521
FittingC2×#41×C521C2
socleC22×C521C24
hypercenterC2×#41D521
hypocenterC521C2×H(5,𝔽2)
LCSG ▷ C2×C521 ▷ C521
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #30659754C2direct (N × H)
2. C2×#22552365C2semidirect
3. C2×#22552364C2semidirect
4. C22×D2084C2semidirect
5. C2×D4×D521C2semidirect
6. C2×#41×C521C2semidirect
7. C23×D521C22semidirect
8. #22552365C22semidirect
9. #22552364C22semidirect
10. C2×Dic1042C22semidirect
11. C2×D2084C22semidirect
12. C2×D2084C22semidirect
13. C2×D2084C22semidirect
14. C2×C22⋊D521C22semidirect
15. D4×D521C22semidirect
16. C2×C4×D521C22semidirect
17. #41×C521C22semidirect
18. C2×Q8×C521C22semidirect
19. C2×D4×C521C22semidirect
20. C22×C4×C521C22semidirect
23. C22×D521C23semidirect
24. Dic1042C23semidirect
25. D2084C23semidirect
26. D2084C23semidirect
27. C22⋊D521C23semidirect
29. C4×D521C23semidirect
31. Q8×C521C23semidirect
32. D4×C521C23semidirect
35. C2×C4×C521C23semidirect
46. C2×C521H(5,𝔽2)semidirect
49. C521C2×H(5,𝔽2)semidirect
54. C2×#41D521semidirect
60. #41C2×D521semidirect
62. C2×Q8C2×D521semidirect
68. C2×D4C2×D521semidirect
70. C22×C4C2×D521semidirect
76. Q8C22×D521semidirect
80. D4C22×D521semidirect
85. C2×C4C22×D521semidirect
97. C2#30659754direct (N × H)

Maximal subgroups

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

subgroupindex
#306597542
C2×#225523652
C2×#225523642
C22×D20842
C2×D4×D5212
C2×#41×C5212
C2×H(5,𝔽2)521