Finite Group Databasebeta

← C23×C42×D17 #17940872

Subgroups — C23×C42×D17 #17940872

Order 4352.

24030 conjugacy classes of subgroups; only the 13515 normal subgroups are shown.

normal subgroups only

This group has 24030 conjugacy classes of subgroups — too many to draw. Only its 13515 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×C4×D17C213yesmaximal
2C23×C4×Dic17C213yesmaximal, complemented
3C22×C42×D17C2156yesmaximal, direct product factor
4C23×C42×C17C211yesmaximal, characteristic, complemented
5C25×D17C2211yescharacteristic
6C24×Dic17C2213yes—
7C23×C4×D17C4196yesdirect product factor
8C23×C4×D17C22184yes—
9C22×C4×Dic17C22184yescomplemented
10C2×C42×D17C221448yesdirect product factor
11C24×C4×C17C2213yes—
12C22×C42×C17C22128yescomplemented
13C25×C17C2311yescharacteristic
14C24×D17C2×C4148yes—
15C24×D17C23114yes—
16C23×C4×C17C2×C4148yescomplemented
17C23×C4×C17C23142yes—
18C23×Dic17C2×C4148yescomplemented
19C23×Dic17C23142yes—
20C22×C4×D17C2×C411344yesdirect product factor
21C22×C4×D17C231336yes—
22C2×C42×C17C231112yescomplemented
23C2×C4×Dic17C231336yescomplemented
24C42×D17C231512yesdirect product factor
25C24×C17C22×C4124yes—
26C24×C17C2417yes—
27C23×D17C421256yesdirect product factor
28C23×D17C22×C41336yes—
29C23×D17C24128yes—
30C22×C4×C17C22×C41336yescomplemented
31C22×C4×C17C24184yes—
32C22×Dic17C22×C41336yescomplemented
33C22×Dic17C24184yes—
34C2×C4×D17C22×C412688yesdirect product factor
35C2×C4×D17C241192yes—
36C42×C17C24164yescomplemented
37C4×Dic17C241192yescomplemented
38C24×C42—171nomaximal, Sylow
39C23×C17C2×C42164yescomplemented
40C23×C17C23×C4184yes—
41C23×C17C2517yes—
42C22×D17C2×C421896yesdirect product factor
43C22×D17C23×C41336yes—
44C22×D17C2518yes—
45C2×C4×C17C23×C41336yescomplemented
46C2×C4×C17C25124yes—
47C2×Dic17C23×C41336yescomplemented
48C2×Dic17C25124yes—
49C4×D17C23×C41768yesdirect product factor
50C25×C4—173no—
51C23×C42—1756no—
52C23×C42—173no—
53C23×C42D1711yescharacteristic, direct product factor
54C22×C17C22×C421112yescomplemented
55C22×C17C24×C4142yes—
56C22×C17C2611yescharacteristic
57C2×D17C22×C421448yesdirect product factor
58C2×D17C24×C4148yes—
59C4×C17C24×C4148yescomplemented
60Dic17C24×C4148yescomplemented
61C26—171no—
62C24×C4—173no—
63C24×C4—1796no—
64C24×C4—1784no—
65C24×C4C2×D1713yes—
66C22×C42—1784no—
67C22×C42—17448no—
68C22×C42C2×D17128yesdirect product factor
69C2×C17C23×C42128yescomplemented
70C2×C17C25×C413yes—
71D17C23×C42132yesdirect product factor
72C25—1748no—
73C25—1714no—
74C25C22×D1711yescharacteristic
75C23×C4—1748no—
76C23×C4—1742no—
77C23×C4—171344no—
78C23×C4—17336no—
79C23×C4C4×D17148yesdirect product factor
80C23×C4C22×D17142yes—
81C2×C42—17336no—
82C2×C42—17512no—
83C2×C42C22×D171112yesdirect product factor
84C17C24×C4211yescharacteristic, complemented, Sylow
85C24—17336no—
86C24—1728no—
87C24—17256no—
88C24C2×C4×D17124yes—
89C24C23×D1717yes—
90C22×C4—17336no—
91C22×C4—1784no—
92C22×C4—172688no—
93C22×C4—17192no—
94C22×C4C2×C4×D171336yesdirect product factor
95C22×C4C23×D17184yes—
96C42—17192no—
97C42C23×D17164yesdirect product factor
98C23—17896no—
99C23—17336no—
100C23—178no—
101C23C42×D17164yesdirect product factor
102C23C22×C4×D17184yes—
103C23C24×D1717yes—
104C2×C4—17336no—
105C2×C4—1724no—
106C2×C4—17768no—
107C2×C4C22×C4×D171336yesdirect product factor
108C2×C4C24×D17124yes—
109C22—17448no—
110C22—1748no—
111C22C2×C42×D171112yesdirect product factor
112C22C23×C4×D17142yes—
113C22C25×D1711yescharacteristic
114C4—1748no—
115C4C23×C4×D17148yesdirect product factor
116C2—1732no—
117C2C22×C42×D17128yesdirect product factor
118C2C24×C4×D1713yes—
subgroupG/H
center, hypercenterC23×C42D17
commutator, hypocenterC17C24×C42
FrattiniC22C25×D17
FittingC23×C42×C17C2
socleC25×C17C23
prime radicalC25×D17C22
cosocleC22×C17C26
LCSG ▷ C17
UCSC1 ◁ C23×C42

Complements

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

NH ≅ G/Ntype
2. C23×C4×Dic17C2semidirect
3. C22×C42×D17C2direct (N × H)
4. C23×C42×C17C2semidirect
7. C23×C4×D17C4direct (N × H)
9. C22×C4×Dic17C22semidirect
10. C2×C42×D17C22direct (N × H)
12. C22×C42×C17C22semidirect
16. C23×C4×C17C2×C4semidirect
18. C23×Dic17C2×C4semidirect
20. C22×C4×D17C2×C4direct (N × H)
22. C2×C42×C17C23semidirect
23. C2×C4×Dic17C23semidirect
24. C42×D17C23direct (N × H)
27. C23×D17C42direct (N × H)
30. C22×C4×C17C22×C4semidirect
32. C22×Dic17C22×C4semidirect
34. C2×C4×D17C22×C4direct (N × H)
36. C42×C17C24semidirect
37. C4×Dic17C24semidirect
39. C23×C17C2×C42semidirect
42. C22×D17C2×C42direct (N × H)
45. C2×C4×C17C23×C4semidirect
47. C2×Dic17C23×C4semidirect
49. C4×D17C23×C4direct (N × H)
53. C23×C42D17direct (N × H)
54. C22×C17C22×C42semidirect
57. C2×D17C22×C42direct (N × H)
59. C4×C17C24×C4semidirect
60. Dic17C24×C4semidirect
68. C22×C42C2×D17direct (N × H)
69. C2×C17C23×C42semidirect
71. D17C23×C42direct (N × H)
79. C23×C4C4×D17direct (N × H)
83. C2×C42C22×D17direct (N × H)
84. C17C24×C42semidirect
94. C22×C4C2×C4×D17direct (N × H)
97. C42C23×D17direct (N × H)
101. C23C42×D17direct (N × H)
107. C2×C4C22×C4×D17direct (N × H)
111. C22C2×C42×D17direct (N × H)
115. C4C23×C4×D17direct (N × H)
117. C2C22×C42×D17direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C4×D172
C23×C4×Dic172
C22×C42×D172
C23×C42×C172
C24×C4217