Finite Group Databasebeta

← C2×#41×D263 #30682763

Subgroups — C2×#41×D263 #30682763

Order 16832.

890 conjugacy classes of subgroups; only the 455 normal subgroups are shown.

normal subgroups only

This group has 890 conjugacy classes of subgroups — too many to draw. Only its 455 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
1C2×#16862377C211yesmaximal, characteristic, complemented
2C2×#16862376C213yesmaximal, complemented
3C2×#16862375C213yesmaximal, complemented
4#41×D263C2116yesmaximal, direct product factor
5C2×Q8×D263C211yesmaximal, characteristic, complemented
6C2×D4×D263C213yesmaximal, complemented
7C22×C4×D263C213yesmaximal, complemented
8C2×#41×C263C211yesmaximal, characteristic, complemented
9C23×D263C2213yes—
10#16862377C2218yescomplemented
11#16862376C22124yescomplemented
12#16862375C22124yescomplemented
13C2×Dic526C2213yescomplemented
14Q8×D263C2218yescomplemented
15C2×D1052C2213yescomplemented
16C2×C22⋊D263C2216yescomplemented
17D4×D263C22124yescomplemented
18C22×Dic263C2213yescomplemented
19C2×C4×D263C2211yescharacteristic
20C2×C4×D263C2213yes—
21C2×C4×D263C2213yescomplemented
22C2×C4×D263C2213yescomplemented
23C2×C4×D263C22124yescomplemented
24#41×C263C2218yescomplemented
25C2×Q8×C263C2211yescharacteristic, complemented
26C2×D4×C263C2213yescomplemented
27C22×C4×C263C2213yescomplemented
28C22×D263—212no—
29C22×D263C23112yes—
30C22×D263C2313yes—
31C22×D263C2311yescharacteristic
32Dic526C23112yescomplemented
33D1052C23112yescomplemented
34C22⋊D263C23124yescomplemented
35C2×Dic263C2311yescharacteristic
36C2×Dic263C2313yes—
37C2×Dic263C23112yescomplemented
38C4×D263C2314yes—
39C4×D263C23112yes—
40C4×D263C23112yescomplemented
41C4×D263C23112yescomplemented
42C23×C263C2313yes—
43Q8×C263C2314yescomplemented
44D4×C263C23112yescomplemented
45C2×C4×C263C2313yes—
46C2×C4×C263C2311yescharacteristic
47C2×C4×C263C23112yescomplemented
48C22×C263—26no—
49C22×C263C2416yes—
50C22×C263C2411yescharacteristic
51C2×D263—26no—
52C2×D263—224no—
53C2×D263#4114yesdirect product factor
54C2×D263C2416yes—
55C2×D263C2412yes—
56C4×C263C2412yes—
57C4×C263C2416yes—
58Dic263C2412yes—
59Dic263C2416yes—
60C2×C263—26no—
61C2×C263C2×#4112yescomplemented
62C2×C263C2511yescharacteristic
63D263—26no—
64D263C2×#4114yesdirect product factor
65C263C22×#4111yescharacteristic, complemented, Sylow
66C22×#41—2631nomaximal, Sylow
67C2×#41—26316no—
68C2×#41—2631no—
69C2×#41—2633no—
70C2×#41—2633no—
71C2×#41D26311yescharacteristic, direct product factor
72C22×Q8—2631no—
73C22×D4—2633no—
74C23×C4—2633no—
75C24—2633no—
76#41—2638no—
77#41—26324no—
78#41—26324no—
79#41C2×D26318yesdirect product factor
80C2×Q8—2638no—
81C2×Q8—2633no—
82C2×Q8C2×D26311yescharacteristic, complemented
83C2×D4—2636no—
84C2×D4—26324no—
85C2×D4—2633no—
86C2×D4C2×D26313yescomplemented
87C22×C4—2633no—
88C22×C4—2633no—
89C22×C4—2633no—
90C22×C4—2631no—
91C22×C4—2633no—
92C22×C4—26324no—
93C22×C4C2×D26313yescomplemented
94C23—2631no—
95C23—26312no—
96C23—2633no—
97C23—52612no—
98C23C22×D26313yes—
99Q8—26312no—
100Q8C22×D26314yescomplemented
101D4—26324no—
102D4—26312no—
103D4C22×D263112yescomplemented
104C2×C4—2631no—
105C2×C4—2633no—
106C2×C4—26312no—
107C2×C4—2634no—
108C2×C4—26312no—
109C2×C4—26312no—
110C2×C4—26312no—
111C2×C4C22×D26313yes—
112C2×C4C22×D26311yescharacteristic
113C2×C4C22×D263112yescomplemented
114C22—26no—
115C22—2634no—
116C22—2632no—
117C22—2636no—
118C22—52624no—
119C22—5266no—
120C22C23×D26316yes—
121C22C23×D26311yescharacteristic
122C4—2632no—
123C4—2636no—
124C4C23×D26312yes—
125C4C23×D26316yes—
126C2—26no—
127C2—2634no—
128C2—5266no—
129C2#41×D26312yesdirect product factor
130C2C24×D26311yescharacteristic
subgroupG/H
centerC2×C4C22×D263
commutator, cosocleC2×C263C25
FrattiniC2C24×D263
FittingC2×#41×C263C2
socleC22×C263C24
hypercenterC2×#41D263
hypocenterC263C22×#41
LCSG ▷ C2×C263 ▷ C263
UCSC1 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#16862377C2semidirect
2. C2×#16862376C2semidirect
3. C2×#16862375C2semidirect
4. #41×D263C2direct (N × H)
5. C2×Q8×D263C2semidirect
6. C2×D4×D263C2semidirect
7. C22×C4×D263C2semidirect
8. C2×#41×C263C2semidirect
10. #16862377C22semidirect
11. #16862376C22semidirect
12. #16862375C22semidirect
13. C2×Dic526C22semidirect
14. Q8×D263C22semidirect
15. C2×D1052C22semidirect
16. C2×C22⋊D263C22semidirect
17. D4×D263C22semidirect
18. C22×Dic263C22semidirect
21. C2×C4×D263C22semidirect
22. C2×C4×D263C22semidirect
23. C2×C4×D263C22semidirect
24. #41×C263C22semidirect
25. C2×Q8×C263C22semidirect
26. C2×D4×C263C22semidirect
27. C22×C4×C263C22semidirect
32. Dic526C23semidirect
33. D1052C23semidirect
34. C22⋊D263C23semidirect
37. C2×Dic263C23semidirect
40. C4×D263C23semidirect
41. C4×D263C23semidirect
43. Q8×C263C23semidirect
44. D4×C263C23semidirect
47. C2×C4×C263C23semidirect
53. C2×D263#41direct (N × H)
61. C2×C263C2×#41semidirect
64. D263C2×#41direct (N × H)
65. C263C22×#41semidirect
71. C2×#41D263direct (N × H)
79. #41C2×D263direct (N × H)
82. C2×Q8C2×D263semidirect
86. C2×D4C2×D263semidirect
93. C22×C4C2×D263semidirect
100. Q8C22×D263semidirect
103. D4C22×D263semidirect
113. C2×C4C22×D263semidirect
129. C2#41×D263direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168623772
C2×#168623762
C2×#168623752
#41×D2632
C2×Q8×D2632
C2×D4×D2632
C22×C4×D2632
C2×#41×C2632
C22×#41263