Finite Group Databasebeta

← C22×D4×D359 #37527263

Subgroups — C22×D4×D359 #37527263

Order 22976.

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×D359C212yesmaximal, complemented
2C22×D1436C211yesmaximal, characteristic, complemented
3C22×C22⋊D359C212yesmaximal, complemented
4C2×D4×D359C2124yesmaximal, direct product factor
5C22×C4×D359C211yesmaximal, characteristic, complemented
6C22×D4×C359C211yesmaximal, characteristic, complemented
7C23×D359—216no—
8C23×D359C2211yescharacteristic
9C23×D359C2212yescomplemented
10C23×D359C22124yescomplemented
11C2×D1436C22112yescomplemented
12C2×C22⋊D359C22124yescomplemented
13D4×D359C22164yesdirect product factor
14C22×Dic359C2211yescharacteristic, complemented
15C2×C4×D359C22112yescomplemented
16C24×C359C2212yescomplemented
17C2×D4×C359C22112yescomplemented
18C22×C4×C359C2211yescharacteristic, complemented
19C22×D359—28no—
20C22×D359—296no—
21C22×D359D418yesdirect product factor
22C22×D359C2316yes—
23C22×D359C23132yescomplemented
24C22×D359C23112yescomplemented
25D1436C23116yescomplemented
26C22⋊D359C23132yescomplemented
27C2×Dic359C2316yescomplemented
28C4×D359C23116yescomplemented
29C23×C359—28no—
30C23×C359C2311yescharacteristic
31C23×C359C23112yescomplemented
32D4×C359C23116yescomplemented
33C2×C4×C359C2316yescomplemented
34C22×C359—224no—
35C22×C359C2×D414yescomplemented
36C22×C359C2413yes—
37C22×C359C2418yescomplemented
38C2×D359—224no—
39C2×D359—264no—
40C2×D359C2×D4124yesdirect product factor
41C2×D359C2414yes—
42C2×D359C2418yescomplemented
43C4×C359C2414yescomplemented
44Dic359C2414yescomplemented
45C2×C359—28no—
46C2×C359C22×D416yescomplemented
47C2×C359C2511yescharacteristic
48D359—28no—
49D359C22×D418yesdirect product factor
50C359C23×D411yescharacteristic, complemented, Sylow
51C23×D4—3591nomaximal, Sylow
52C25—3592no—
53C22×D4—3592no—
54C22×D4—35924no—
55C22×D4—3591no—
56C22×D4D35911yescharacteristic, direct product factor
57C23×C4—3591no—
58C24—3591no—
59C24—3592no—
60C24—35924no—
61C24—71816no—
62C24C2×D35912yescomplemented
63C2×D4—35924no—
64C2×D4—35964no—
65C2×D4—35912no—
66C2×D4C2×D359112yesdirect product factor
67C22×C4—3591no—
68C22×C4—35912no—
69C22×C4C2×D35911yescharacteristic, complemented
70C23—28no—
71C23—3598no—
72C23—3596no—
73C23—35912no—
74C23—35932no—
75C23—71896no—
76C23—7188no—
77C23C22×D35911yescharacteristic
78C23C22×D359112yescomplemented
79D4—35932no—
80D4—35916no—
81D4C22×D359116yesdirect product factor
82C2×C4—3596no—
83C2×C4—35916no—
84C2×C4C22×D35916yescomplemented
85C22—224no—
86C22—3594no—
87C22—35924no—
88C22—3598no—
89C22—71864no—
90C22—71824no—
91C22D4×D35914yesdirect product factor
92C22C23×D35913yes—
93C22C23×D35918yescomplemented
94C4—3594no—
95C4C23×D35914yescomplemented
96C2—28no—
97C2—3598no—
98C2—7188no—
99C2C2×D4×D35916yesdirect product factor
100C2C24×D35911yescharacteristic
subgroupG/H
centerC23C22×D359
commutator, cosocleC2×C359C25
FrattiniC2C24×D359
FittingC22×D4×C359C2
socleC23×C359C23
hypercenterC22×D4D359
hypocenterC359C23×D4
LCSG ▷ C2×C359 ▷ C359
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C24×D359C2semidirect
2. C22×D1436C2semidirect
3. C22×C22⋊D359C2semidirect
4. C2×D4×D359C2direct (N × H)
5. C22×C4×D359C2semidirect
6. C22×D4×C359C2semidirect
9. C23×D359C22semidirect
10. C23×D359C22semidirect
11. C2×D1436C22semidirect
12. C2×C22⋊D359C22semidirect
13. D4×D359C22direct (N × H)
14. C22×Dic359C22semidirect
15. C2×C4×D359C22semidirect
16. C24×C359C22semidirect
17. C2×D4×C359C22semidirect
18. C22×C4×C359C22semidirect
21. C22×D359D4direct (N × H)
23. C22×D359C23semidirect
24. C22×D359C23semidirect
25. D1436C23semidirect
26. C22⋊D359C23semidirect
27. C2×Dic359C23semidirect
28. C4×D359C23semidirect
31. C23×C359C23semidirect
32. D4×C359C23semidirect
33. C2×C4×C359C23semidirect
35. C22×C359C2×D4semidirect
37. C22×C359C24semidirect
40. C2×D359C2×D4direct (N × H)
42. C2×D359C24semidirect
43. C4×C359C24semidirect
44. Dic359C24semidirect
46. C2×C359C22×D4semidirect
49. D359C22×D4direct (N × H)
50. C359C23×D4semidirect
56. C22×D4D359direct (N × H)
62. C24C2×D359semidirect
66. C2×D4C2×D359direct (N × H)
69. C22×C4C2×D359semidirect
78. C23C22×D359semidirect
81. D4C22×D359direct (N × H)
84. C2×C4C22×D359semidirect
91. C22D4×D359direct (N × H)
93. C22C23×D359semidirect
95. C4C23×D359semidirect
99. C2C2×D4×D359direct (N × H)

Maximal subgroups

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

subgroupindex
C24×D3592
C22×D14362
C22×C22⋊D3592
C2×D4×D3592
C22×C4×D3592
C22×D4×C3592
C23×D4359