Finite Group Databasebeta

← C2×#41×D397 #38763347

Subgroups — C2×#41×D397 #38763347

Order 25408.

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×#20263732C211yesmaximal, characteristic, complemented
2C2×#20263731C213yesmaximal, complemented
3C2×#20263730C213yesmaximal, complemented
4#41×D397C2116yesmaximal, direct product factor
5C2×Q8×D397C211yesmaximal, characteristic, complemented
6C2×D4×D397C213yesmaximal, complemented
7C22×C4×D397C213yesmaximal, complemented
8C2×#41×C397C211yesmaximal, characteristic, complemented
9C23×D397C2213yes—
10#20263732C2218yescomplemented
11#20263731C22124yescomplemented
12#20263730C22124yescomplemented
13C2×Dic794C2213yescomplemented
14Q8×D397C2218yescomplemented
15C2×D1588C2213yescomplemented
16C2×C22⋊D397C2216yescomplemented
17D4×D397C22124yescomplemented
18C22×Dic397C2213yescomplemented
19C2×C4×D397C2211yescharacteristic
20C2×C4×D397C2213yes—
21C2×C4×D397C2213yescomplemented
22C2×C4×D397C2213yescomplemented
23C2×C4×D397C22124yescomplemented
24#41×C397C2218yescomplemented
25C2×Q8×C397C2211yescharacteristic, complemented
26C2×D4×C397C2213yescomplemented
27C22×C4×C397C2213yescomplemented
28C22×D397—212no—
29C22×D397C23112yes—
30C22×D397C2313yes—
31C22×D397C2311yescharacteristic
32Dic794C23112yescomplemented
33D1588C23112yescomplemented
34C22⋊D397C23124yescomplemented
35C2×Dic397C2311yescharacteristic
36C2×Dic397C2313yes—
37C2×Dic397C23112yescomplemented
38C4×D397C2314yes—
39C4×D397C23112yes—
40C4×D397C23112yescomplemented
41C4×D397C23112yescomplemented
42C23×C397C2313yes—
43Q8×C397C2314yescomplemented
44D4×C397C23112yescomplemented
45C2×C4×C397C2313yes—
46C2×C4×C397C2311yescharacteristic
47C2×C4×C397C23112yescomplemented
48C22×C397—26no—
49C22×C397C2416yes—
50C22×C397C2411yescharacteristic
51C2×D397—26no—
52C2×D397—224no—
53C2×D397#4114yesdirect product factor
54C2×D397C2416yes—
55C2×D397C2412yes—
56C4×C397C2412yes—
57C4×C397C2416yes—
58Dic397C2412yes—
59Dic397C2416yes—
60C2×C397—26no—
61C2×C397C2×#4112yescomplemented
62C2×C397C2511yescharacteristic
63D397—26no—
64D397C2×#4114yesdirect product factor
65C397C22×#4111yescharacteristic, complemented, Sylow
66C22×#41—3971nomaximal, Sylow
67C2×#41—39716no—
68C2×#41—3971no—
69C2×#41—3973no—
70C2×#41—3973no—
71C2×#41D39711yescharacteristic, direct product factor
72C22×Q8—3971no—
73C22×D4—3973no—
74C23×C4—3973no—
75C24—3973no—
76#41—3978no—
77#41—39724no—
78#41—39724no—
79#41C2×D39718yesdirect product factor
80C2×Q8—3978no—
81C2×Q8—3973no—
82C2×Q8C2×D39711yescharacteristic, complemented
83C2×D4—3976no—
84C2×D4—39724no—
85C2×D4—3973no—
86C2×D4C2×D39713yescomplemented
87C22×C4—3973no—
88C22×C4—3973no—
89C22×C4—3973no—
90C22×C4—3971no—
91C22×C4—3973no—
92C22×C4—39724no—
93C22×C4C2×D39713yescomplemented
94C23—79412no—
95C23—39712no—
96C23—3973no—
97C23—3971no—
98C23C22×D39713yes—
99Q8—39712no—
100Q8C22×D39714yescomplemented
101D4—39724no—
102D4—39712no—
103D4C22×D397112yescomplemented
104C2×C4—3971no—
105C2×C4—3973no—
106C2×C4—39712no—
107C2×C4—3974no—
108C2×C4—39712no—
109C2×C4—39712no—
110C2×C4—39712no—
111C2×C4C22×D39713yes—
112C2×C4C22×D39711yescharacteristic
113C2×C4C22×D397112yescomplemented
114C22—26no—
115C22—79424no—
116C22—7946no—
117C22—3976no—
118C22—3974no—
119C22—3972no—
120C22C23×D39716yes—
121C22C23×D39711yescharacteristic
122C4—3972no—
123C4—3976no—
124C4C23×D39712yes—
125C4C23×D39716yes—
126C2—26no—
127C2—7946no—
128C2—3974no—
129C2#41×D39712yesdirect product factor
130C2C24×D39711yescharacteristic
subgroupG/H
centerC2×C4C22×D397
commutator, cosocleC2×C397C25
FrattiniC2C24×D397
FittingC2×#41×C397C2
socleC22×C397C24
hypercenterC2×#41D397
hypocenterC397C22×#41
LCSG ▷ C2×C397 ▷ C397
UCSC1 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#20263732C2semidirect
2. C2×#20263731C2semidirect
3. C2×#20263730C2semidirect
4. #41×D397C2direct (N × H)
5. C2×Q8×D397C2semidirect
6. C2×D4×D397C2semidirect
7. C22×C4×D397C2semidirect
8. C2×#41×C397C2semidirect
10. #20263732C22semidirect
11. #20263731C22semidirect
12. #20263730C22semidirect
13. C2×Dic794C22semidirect
14. Q8×D397C22semidirect
15. C2×D1588C22semidirect
16. C2×C22⋊D397C22semidirect
17. D4×D397C22semidirect
18. C22×Dic397C22semidirect
21. C2×C4×D397C22semidirect
22. C2×C4×D397C22semidirect
23. C2×C4×D397C22semidirect
24. #41×C397C22semidirect
25. C2×Q8×C397C22semidirect
26. C2×D4×C397C22semidirect
27. C22×C4×C397C22semidirect
32. Dic794C23semidirect
33. D1588C23semidirect
34. C22⋊D397C23semidirect
37. C2×Dic397C23semidirect
40. C4×D397C23semidirect
41. C4×D397C23semidirect
43. Q8×C397C23semidirect
44. D4×C397C23semidirect
47. C2×C4×C397C23semidirect
53. C2×D397#41direct (N × H)
61. C2×C397C2×#41semidirect
64. D397C2×#41direct (N × H)
65. C397C22×#41semidirect
71. C2×#41D397direct (N × H)
79. #41C2×D397direct (N × H)
82. C2×Q8C2×D397semidirect
86. C2×D4C2×D397semidirect
93. C22×C4C2×D397semidirect
100. Q8C22×D397semidirect
103. D4C22×D397semidirect
113. C2×C4C22×D397semidirect
129. C2#41×D397direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#202637322
C2×#202637312
C2×#202637302
#41×D3972
C2×Q8×D3972
C2×D4×D3972
C22×C4×D3972
C2×#41×C3972
C22×#41397