Finite Group Databasebeta

← C22×D4×D233 #28417255

Subgroups — C22×D4×D233 #28417255

Order 14912.

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×D233C212yesmaximal, complemented
2C22×D932C211yesmaximal, characteristic, complemented
3C22×C22⋊D233C212yesmaximal, complemented
4C2×D4×D233C2124yesmaximal, direct product factor
5C22×C4×D233C211yesmaximal, characteristic, complemented
6C22×D4×C233C211yesmaximal, characteristic, complemented
7C23×D233—216no—
8C23×D233C2211yescharacteristic
9C23×D233C2212yescomplemented
10C23×D233C22124yescomplemented
11C2×D932C22112yescomplemented
12C2×C22⋊D233C22124yescomplemented
13D4×D233C22164yesdirect product factor
14C22×Dic233C2211yescharacteristic, complemented
15C2×C4×D233C22112yescomplemented
16C24×C233C2212yescomplemented
17C2×D4×C233C22112yescomplemented
18C22×C4×C233C2211yescharacteristic, complemented
19C22×D233—28no—
20C22×D233—296no—
21C22×D233D418yesdirect product factor
22C22×D233C2316yes—
23C22×D233C23132yescomplemented
24C22×D233C23112yescomplemented
25D932C23116yescomplemented
26C22⋊D233C23132yescomplemented
27C2×Dic233C2316yescomplemented
28C4×D233C23116yescomplemented
29C23×C233—28no—
30C23×C233C2311yescharacteristic
31C23×C233C23112yescomplemented
32D4×C233C23116yescomplemented
33C2×C4×C233C2316yescomplemented
34C22×C233—224no—
35C22×C233C2×D414yescomplemented
36C22×C233C2413yes—
37C22×C233C2418yescomplemented
38C2×D233—224no—
39C2×D233—264no—
40C2×D233C2×D4124yesdirect product factor
41C2×D233C2414yes—
42C2×D233C2418yescomplemented
43C4×C233C2414yescomplemented
44Dic233C2414yescomplemented
45C2×C233—28no—
46C2×C233C22×D416yescomplemented
47C2×C233C2511yescharacteristic
48D233—28no—
49D233C22×D418yesdirect product factor
50C233C23×D411yescharacteristic, complemented, Sylow
51C23×D4—2331nomaximal, Sylow
52C25—2332no—
53C22×D4—2332no—
54C22×D4—23324no—
55C22×D4—2331no—
56C22×D4D23311yescharacteristic, direct product factor
57C23×C4—2331no—
58C24—46616no—
59C24—2332no—
60C24—23324no—
61C24—2331no—
62C24C2×D23312yescomplemented
63C2×D4—23324no—
64C2×D4—23364no—
65C2×D4—23312no—
66C2×D4C2×D233112yesdirect product factor
67C22×C4—2331no—
68C22×C4—23312no—
69C22×C4C2×D23311yescharacteristic, complemented
70C23—28no—
71C23—46696no—
72C23—4668no—
73C23—23312no—
74C23—23332no—
75C23—2338no—
76C23—2336no—
77C23C22×D23311yescharacteristic
78C23C22×D233112yescomplemented
79D4—23332no—
80D4—23316no—
81D4C22×D233116yesdirect product factor
82C2×C4—2336no—
83C2×C4—23316no—
84C2×C4C22×D23316yescomplemented
85C22—224no—
86C22—46664no—
87C22—46624no—
88C22—2338no—
89C22—23324no—
90C22—2334no—
91C22D4×D23314yesdirect product factor
92C22C23×D23313yes—
93C22C23×D23318yescomplemented
94C4—2334no—
95C4C23×D23314yescomplemented
96C2—28no—
97C2—4668no—
98C2—2338no—
99C2C2×D4×D23316yesdirect product factor
100C2C24×D23311yescharacteristic
subgroupG/H
centerC23C22×D233
commutator, cosocleC2×C233C25
FrattiniC2C24×D233
FittingC22×D4×C233C2
socleC23×C233C23
hypercenterC22×D4D233
hypocenterC233C23×D4
LCSG ▷ C2×C233 ▷ C233
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C24×D233C2semidirect
2. C22×D932C2semidirect
3. C22×C22⋊D233C2semidirect
4. C2×D4×D233C2direct (N × H)
5. C22×C4×D233C2semidirect
6. C22×D4×C233C2semidirect
9. C23×D233C22semidirect
10. C23×D233C22semidirect
11. C2×D932C22semidirect
12. C2×C22⋊D233C22semidirect
13. D4×D233C22direct (N × H)
14. C22×Dic233C22semidirect
15. C2×C4×D233C22semidirect
16. C24×C233C22semidirect
17. C2×D4×C233C22semidirect
18. C22×C4×C233C22semidirect
21. C22×D233D4direct (N × H)
23. C22×D233C23semidirect
24. C22×D233C23semidirect
25. D932C23semidirect
26. C22⋊D233C23semidirect
27. C2×Dic233C23semidirect
28. C4×D233C23semidirect
31. C23×C233C23semidirect
32. D4×C233C23semidirect
33. C2×C4×C233C23semidirect
35. C22×C233C2×D4semidirect
37. C22×C233C24semidirect
40. C2×D233C2×D4direct (N × H)
42. C2×D233C24semidirect
43. C4×C233C24semidirect
44. Dic233C24semidirect
46. C2×C233C22×D4semidirect
49. D233C22×D4direct (N × H)
50. C233C23×D4semidirect
56. C22×D4D233direct (N × H)
62. C24C2×D233semidirect
66. C2×D4C2×D233direct (N × H)
69. C22×C4C2×D233semidirect
78. C23C22×D233semidirect
81. D4C22×D233direct (N × H)
84. C2×C4C22×D233semidirect
91. C22D4×D233direct (N × H)
93. C22C23×D233semidirect
95. C4C23×D233semidirect
99. C2C2×D4×D233direct (N × H)

Maximal subgroups

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

subgroupindex
C24×D2332
C22×D9322
C22×C22⋊D2332
C2×D4×D2332
C22×C4×D2332
C22×D4×C2332
C23×D4233