Finite Group Databasebeta

← C2×#41×D401 #38786939

Subgroups — C2×#41×D401 #38786939

Order 25664.

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×#20264367C211yesmaximal, characteristic, complemented
2C2×#20264366C213yesmaximal, complemented
3C2×#20264365C213yesmaximal, complemented
4#41×D401C2116yesmaximal, direct product factor
5C2×Q8×D401C211yesmaximal, characteristic, complemented
6C2×D4×D401C213yesmaximal, complemented
7C22×C4×D401C213yesmaximal, complemented
8C2×#41×C401C211yesmaximal, characteristic, complemented
9C23×D401C2213yes—
10#20264367C2218yescomplemented
11#20264366C22124yescomplemented
12#20264365C22124yescomplemented
13C2×Dic802C2213yescomplemented
14Q8×D401C2218yescomplemented
15C2×D1604C2213yescomplemented
16C2×C22⋊D401C2216yescomplemented
17D4×D401C22124yescomplemented
18C22×Dic401C2213yescomplemented
19C2×C4×D401C2211yescharacteristic
20C2×C4×D401C2213yes—
21C2×C4×D401C2213yescomplemented
22C2×C4×D401C2213yescomplemented
23C2×C4×D401C22124yescomplemented
24#41×C401C2218yescomplemented
25C2×Q8×C401C2211yescharacteristic, complemented
26C2×D4×C401C2213yescomplemented
27C22×C4×C401C2213yescomplemented
28C22×D401—212no—
29C22×D401C23112yes—
30C22×D401C2313yes—
31C22×D401C2311yescharacteristic
32Dic802C23112yescomplemented
33D1604C23112yescomplemented
34C22⋊D401C23124yescomplemented
35C2×Dic401C2311yescharacteristic
36C2×Dic401C2313yes—
37C2×Dic401C23112yescomplemented
38C4×D401C2314yes—
39C4×D401C23112yes—
40C4×D401C23112yescomplemented
41C4×D401C23112yescomplemented
42C23×C401C2313yes—
43Q8×C401C2314yescomplemented
44D4×C401C23112yescomplemented
45C2×C4×C401C2313yes—
46C2×C4×C401C2311yescharacteristic
47C2×C4×C401C23112yescomplemented
48C22×C401—26no—
49C22×C401C2416yes—
50C22×C401C2411yescharacteristic
51C2×D401—26no—
52C2×D401—224no—
53C2×D401#4114yesdirect product factor
54C2×D401C2416yes—
55C2×D401C2412yes—
56C4×C401C2412yes—
57C4×C401C2416yes—
58Dic401C2412yes—
59Dic401C2416yes—
60C2×C401—26no—
61C2×C401C2×#4112yescomplemented
62C2×C401C2511yescharacteristic
63D401—26no—
64D401C2×#4114yesdirect product factor
65C401C22×#4111yescharacteristic, complemented, Sylow
66C22×#41—4011nomaximal, Sylow
67C2×#41—40116no—
68C2×#41—4011no—
69C2×#41—4013no—
70C2×#41—4013no—
71C2×#41D40111yescharacteristic, direct product factor
72C22×Q8—4011no—
73C22×D4—4013no—
74C23×C4—4013no—
75C24—4013no—
76#41—4018no—
77#41—40124no—
78#41—40124no—
79#41C2×D40118yesdirect product factor
80C2×Q8—4018no—
81C2×Q8—4013no—
82C2×Q8C2×D40111yescharacteristic, complemented
83C2×D4—4016no—
84C2×D4—40124no—
85C2×D4—4013no—
86C2×D4C2×D40113yescomplemented
87C22×C4—4013no—
88C22×C4—4013no—
89C22×C4—4013no—
90C22×C4—4011no—
91C22×C4—4013no—
92C22×C4—40124no—
93C22×C4C2×D40113yescomplemented
94C23—80212no—
95C23—40112no—
96C23—4013no—
97C23—4011no—
98C23C22×D40113yes—
99Q8—40112no—
100Q8C22×D40114yescomplemented
101D4—40124no—
102D4—40112no—
103D4C22×D401112yescomplemented
104C2×C4—4011no—
105C2×C4—4013no—
106C2×C4—40112no—
107C2×C4—4014no—
108C2×C4—40112no—
109C2×C4—40112no—
110C2×C4—40112no—
111C2×C4C22×D40113yes—
112C2×C4C22×D40111yescharacteristic
113C2×C4C22×D401112yescomplemented
114C22—26no—
115C22—80224no—
116C22—8026no—
117C22—4016no—
118C22—4014no—
119C22—4012no—
120C22C23×D40116yes—
121C22C23×D40111yescharacteristic
122C4—4012no—
123C4—4016no—
124C4C23×D40112yes—
125C4C23×D40116yes—
126C2—26no—
127C2—8026no—
128C2—4014no—
129C2#41×D40112yesdirect product factor
130C2C24×D40111yescharacteristic
subgroupG/H
centerC2×C4C22×D401
commutator, cosocleC2×C401C25
FrattiniC2C24×D401
FittingC2×#41×C401C2
socleC22×C401C24
hypercenterC2×#41D401
hypocenterC401C22×#41
LCSG ▷ C2×C401 ▷ C401
UCSC1 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#20264367C2semidirect
2. C2×#20264366C2semidirect
3. C2×#20264365C2semidirect
4. #41×D401C2direct (N × H)
5. C2×Q8×D401C2semidirect
6. C2×D4×D401C2semidirect
7. C22×C4×D401C2semidirect
8. C2×#41×C401C2semidirect
10. #20264367C22semidirect
11. #20264366C22semidirect
12. #20264365C22semidirect
13. C2×Dic802C22semidirect
14. Q8×D401C22semidirect
15. C2×D1604C22semidirect
16. C2×C22⋊D401C22semidirect
17. D4×D401C22semidirect
18. C22×Dic401C22semidirect
21. C2×C4×D401C22semidirect
22. C2×C4×D401C22semidirect
23. C2×C4×D401C22semidirect
24. #41×C401C22semidirect
25. C2×Q8×C401C22semidirect
26. C2×D4×C401C22semidirect
27. C22×C4×C401C22semidirect
32. Dic802C23semidirect
33. D1604C23semidirect
34. C22⋊D401C23semidirect
37. C2×Dic401C23semidirect
40. C4×D401C23semidirect
41. C4×D401C23semidirect
43. Q8×C401C23semidirect
44. D4×C401C23semidirect
47. C2×C4×C401C23semidirect
53. C2×D401#41direct (N × H)
61. C2×C401C2×#41semidirect
64. D401C2×#41direct (N × H)
65. C401C22×#41semidirect
71. C2×#41D401direct (N × H)
79. #41C2×D401direct (N × H)
82. C2×Q8C2×D401semidirect
86. C2×D4C2×D401semidirect
93. C22×C4C2×D401semidirect
100. Q8C22×D401semidirect
103. D4C22×D401semidirect
113. C2×C4C22×D401semidirect
129. C2#41×D401direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#202643672
C2×#202643662
C2×#202643652
#41×D4012
C2×Q8×D4012
C2×D4×D4012
C22×C4×D4012
C2×#41×C4012
C22×#41401