Finite Group Databasebeta

← C22×D4×D541 #46830995

Subgroups — C22×D4×D541 #46830995

Order 34624.

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×D541C212yesmaximal, complemented
2C22×D2164C211yesmaximal, characteristic, complemented
3C22×C22⋊D541C212yesmaximal, complemented
4C2×D4×D541C2124yesmaximal, direct product factor
5C22×C4×D541C211yesmaximal, characteristic, complemented
6C22×D4×C541C211yesmaximal, characteristic, complemented
7C23×D541—216no—
8C23×D541C2211yescharacteristic
9C23×D541C2212yescomplemented
10C23×D541C22124yescomplemented
11C2×D2164C22112yescomplemented
12C2×C22⋊D541C22124yescomplemented
13D4×D541C22164yesdirect product factor
14C22×Dic541C2211yescharacteristic, complemented
15C2×C4×D541C22112yescomplemented
16C24×C541C2212yescomplemented
17C2×D4×C541C22112yescomplemented
18C22×C4×C541C2211yescharacteristic, complemented
19C22×D541—28no—
20C22×D541—296no—
21C22×D541D418yesdirect product factor
22C22×D541C2316yes—
23C22×D541C23132yescomplemented
24C22×D541C23112yescomplemented
25D2164C23116yescomplemented
26C22⋊D541C23132yescomplemented
27C2×Dic541C2316yescomplemented
28C4×D541C23116yescomplemented
29C23×C541—28no—
30C23×C541C2311yescharacteristic
31C23×C541C23112yescomplemented
32D4×C541C23116yescomplemented
33C2×C4×C541C2316yescomplemented
34C22×C541—224no—
35C22×C541C2×D414yescomplemented
36C22×C541C2413yes—
37C22×C541C2418yescomplemented
38C2×D541—224no—
39C2×D541—264no—
40C2×D541C2×D4124yesdirect product factor
41C2×D541C2414yes—
42C2×D541C2418yescomplemented
43C4×C541C2414yescomplemented
44Dic541C2414yescomplemented
45C2×C541—28no—
46C2×C541C22×D416yescomplemented
47C2×C541C2511yescharacteristic
48D541—28no—
49D541C22×D418yesdirect product factor
50C541C23×D411yescharacteristic, complemented, Sylow
51C23×D4—5411nomaximal, Sylow
52C25—5412no—
53C22×D4—5412no—
54C22×D4—54124no—
55C22×D4—5411no—
56C22×D4D54111yescharacteristic, direct product factor
57C23×C4—5411no—
58C24—5411no—
59C24—5412no—
60C24—54124no—
61C24—108216no—
62C24C2×D54112yescomplemented
63C2×D4—54124no—
64C2×D4—54164no—
65C2×D4—54112no—
66C2×D4C2×D541112yesdirect product factor
67C22×C4—5411no—
68C22×C4—54112no—
69C22×C4C2×D54111yescharacteristic, complemented
70C23—28no—
71C23—5418no—
72C23—5416no—
73C23—54112no—
74C23—54132no—
75C23—108296no—
76C23—10828no—
77C23C22×D54111yescharacteristic
78C23C22×D541112yescomplemented
79D4—54132no—
80D4—54116no—
81D4C22×D541116yesdirect product factor
82C2×C4—5416no—
83C2×C4—54116no—
84C2×C4C22×D54116yescomplemented
85C22—224no—
86C22—5414no—
87C22—54124no—
88C22—5418no—
89C22—108264no—
90C22—108224no—
91C22D4×D54114yesdirect product factor
92C22C23×D54113yes—
93C22C23×D54118yescomplemented
94C4—5414no—
95C4C23×D54114yescomplemented
96C2—28no—
97C2—5418no—
98C2—10828no—
99C2C2×D4×D54116yesdirect product factor
100C2C24×D54111yescharacteristic
subgroupG/H
centerC23C22×D541
commutator, cosocleC2×C541C25
FrattiniC2C24×D541
FittingC22×D4×C541C2
socleC23×C541C23
hypercenterC22×D4D541
hypocenterC541C23×D4
LCSG ▷ C2×C541 ▷ C541
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C24×D541C2semidirect
2. C22×D2164C2semidirect
3. C22×C22⋊D541C2semidirect
4. C2×D4×D541C2direct (N × H)
5. C22×C4×D541C2semidirect
6. C22×D4×C541C2semidirect
9. C23×D541C22semidirect
10. C23×D541C22semidirect
11. C2×D2164C22semidirect
12. C2×C22⋊D541C22semidirect
13. D4×D541C22direct (N × H)
14. C22×Dic541C22semidirect
15. C2×C4×D541C22semidirect
16. C24×C541C22semidirect
17. C2×D4×C541C22semidirect
18. C22×C4×C541C22semidirect
21. C22×D541D4direct (N × H)
23. C22×D541C23semidirect
24. C22×D541C23semidirect
25. D2164C23semidirect
26. C22⋊D541C23semidirect
27. C2×Dic541C23semidirect
28. C4×D541C23semidirect
31. C23×C541C23semidirect
32. D4×C541C23semidirect
33. C2×C4×C541C23semidirect
35. C22×C541C2×D4semidirect
37. C22×C541C24semidirect
40. C2×D541C2×D4direct (N × H)
42. C2×D541C24semidirect
43. C4×C541C24semidirect
44. Dic541C24semidirect
46. C2×C541C22×D4semidirect
49. D541C22×D4direct (N × H)
50. C541C23×D4semidirect
56. C22×D4D541direct (N × H)
62. C24C2×D541semidirect
66. C2×D4C2×D541direct (N × H)
69. C22×C4C2×D541semidirect
78. C23C22×D541semidirect
81. D4C22×D541direct (N × H)
84. C2×C4C22×D541semidirect
91. C22D4×D541direct (N × H)
93. C22C23×D541semidirect
95. C4C23×D541semidirect
99. C2C2×D4×D541direct (N × H)

Maximal subgroups

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

subgroupindex
C24×D5412
C22×D21642
C22×C22⋊D5412
C2×D4×D5412
C22×C4×D5412
C22×D4×C5412
C23×D4541