Finite Group Databasebeta

← C22×D4×D397 #38763342

Subgroups — C22×D4×D397 #38763342

Order 25408.

1362 conjugacy classes of subgroups; only the 503 normal subgroups are shown.

normal subgroups only

This group has 1362 conjugacy classes of subgroups — too many to draw. Only its 503 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
1C24×D397C212yesmaximal, complemented
2C22×D1588C211yesmaximal, characteristic, complemented
3C22×C22⋊D397C212yesmaximal, complemented
4C2×D4×D397C2124yesmaximal, direct product factor
5C22×C4×D397C211yesmaximal, characteristic, complemented
6C22×D4×C397C211yesmaximal, characteristic, complemented
7C23×D397—216no—
8C23×D397C2211yescharacteristic
9C23×D397C2212yescomplemented
10C23×D397C22124yescomplemented
11C2×D1588C22112yescomplemented
12C2×C22⋊D397C22124yescomplemented
13D4×D397C22164yesdirect product factor
14C22×Dic397C2211yescharacteristic, complemented
15C2×C4×D397C22112yescomplemented
16C24×C397C2212yescomplemented
17C2×D4×C397C22112yescomplemented
18C22×C4×C397C2211yescharacteristic, complemented
19C22×D397—28no—
20C22×D397—296no—
21C22×D397D418yesdirect product factor
22C22×D397C2316yes—
23C22×D397C23132yescomplemented
24C22×D397C23112yescomplemented
25D1588C23116yescomplemented
26C22⋊D397C23132yescomplemented
27C2×Dic397C2316yescomplemented
28C4×D397C23116yescomplemented
29C23×C397—28no—
30C23×C397C2311yescharacteristic
31C23×C397C23112yescomplemented
32D4×C397C23116yescomplemented
33C2×C4×C397C2316yescomplemented
34C22×C397—224no—
35C22×C397C2×D414yescomplemented
36C22×C397C2413yes—
37C22×C397C2418yescomplemented
38C2×D397—224no—
39C2×D397—264no—
40C2×D397C2×D4124yesdirect product factor
41C2×D397C2414yes—
42C2×D397C2418yescomplemented
43C4×C397C2414yescomplemented
44Dic397C2414yescomplemented
45C2×C397—28no—
46C2×C397C22×D416yescomplemented
47C2×C397C2511yescharacteristic
48D397—28no—
49D397C22×D418yesdirect product factor
50C397C23×D411yescharacteristic, complemented, Sylow
51C23×D4—3971nomaximal, Sylow
52C25—3972no—
53C22×D4—3972no—
54C22×D4—39724no—
55C22×D4—3971no—
56C22×D4D39711yescharacteristic, direct product factor
57C23×C4—3971no—
58C24—79416no—
59C24—3972no—
60C24—39724no—
61C24—3971no—
62C24C2×D39712yescomplemented
63C2×D4—39724no—
64C2×D4—39764no—
65C2×D4—39712no—
66C2×D4C2×D397112yesdirect product factor
67C22×C4—3971no—
68C22×C4—39712no—
69C22×C4C2×D39711yescharacteristic, complemented
70C23—28no—
71C23—79496no—
72C23—7948no—
73C23—39712no—
74C23—39732no—
75C23—3978no—
76C23—3976no—
77C23C22×D39711yescharacteristic
78C23C22×D397112yescomplemented
79D4—39732no—
80D4—39716no—
81D4C22×D397116yesdirect product factor
82C2×C4—3976no—
83C2×C4—39716no—
84C2×C4C22×D39716yescomplemented
85C22—224no—
86C22—79464no—
87C22—79424no—
88C22—3978no—
89C22—3974no—
90C22—39724no—
91C22D4×D39714yesdirect product factor
92C22C23×D39713yes—
93C22C23×D39718yescomplemented
94C4—3974no—
95C4C23×D39714yescomplemented
96C2—28no—
97C2—7948no—
98C2—3978no—
99C2C2×D4×D39716yesdirect product factor
100C2C24×D39711yescharacteristic
subgroupG/H
centerC23C22×D397
commutator, cosocleC2×C397C25
FrattiniC2C24×D397
FittingC22×D4×C397C2
socleC23×C397C23
hypercenterC22×D4D397
hypocenterC397C23×D4
LCSG ▷ C2×C397 ▷ C397
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C24×D397C2semidirect
2. C22×D1588C2semidirect
3. C22×C22⋊D397C2semidirect
4. C2×D4×D397C2direct (N × H)
5. C22×C4×D397C2semidirect
6. C22×D4×C397C2semidirect
9. C23×D397C22semidirect
10. C23×D397C22semidirect
11. C2×D1588C22semidirect
12. C2×C22⋊D397C22semidirect
13. D4×D397C22direct (N × H)
14. C22×Dic397C22semidirect
15. C2×C4×D397C22semidirect
16. C24×C397C22semidirect
17. C2×D4×C397C22semidirect
18. C22×C4×C397C22semidirect
21. C22×D397D4direct (N × H)
23. C22×D397C23semidirect
24. C22×D397C23semidirect
25. D1588C23semidirect
26. C22⋊D397C23semidirect
27. C2×Dic397C23semidirect
28. C4×D397C23semidirect
31. C23×C397C23semidirect
32. D4×C397C23semidirect
33. C2×C4×C397C23semidirect
35. C22×C397C2×D4semidirect
37. C22×C397C24semidirect
40. C2×D397C2×D4direct (N × H)
42. C2×D397C24semidirect
43. C4×C397C24semidirect
44. Dic397C24semidirect
46. C2×C397C22×D4semidirect
49. D397C22×D4direct (N × H)
50. C397C23×D4semidirect
56. C22×D4D397direct (N × H)
62. C24C2×D397semidirect
66. C2×D4C2×D397direct (N × H)
69. C22×C4C2×D397semidirect
78. C23C22×D397semidirect
81. D4C22×D397direct (N × H)
84. C2×C4C22×D397semidirect
91. C22D4×D397direct (N × H)
93. C22C23×D397semidirect
95. C4C23×D397semidirect
99. C2C2×D4×D397direct (N × H)

Maximal subgroups

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

subgroupindex
C24×D3972
C22×D15882
C22×C22⋊D3972
C2×D4×D3972
C22×C4×D3972
C22×D4×C3972
C23×D4397