Finite Group Databasebeta

← C24×C4×#595 #17981029

Subgroups — C24×C4×#595 #17981029

Order 4352.

24030 conjugacy classes of subgroups; only the 12696 normal subgroups are shown.

normal subgroups only

This group has 24030 conjugacy classes of subgroups — too many to draw. Only its 12696 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
1C25×#595C212yesmaximal
2C23×C4×#595C2160yesmaximal, direct product factor
3C24×C4×D17C211yesmaximal, characteristic
4C24×#595C4164yesdirect product factor
5C24×#595C22160yes—
6C22×C4×#595C221560yesdirect product factor
7C25×D17C2211yescharacteristic
8C24×Dic17C411yescharacteristic, complemented
9C23×C4×D17C4130yescomplemented
10C23×C4×D17C22130yes—
11C24×C4×C17C411yescharacteristic, complemented
12C25×C17C2×C411yescharacteristic
13C24×D17C2×C4115yes—
14C24×D17C2×C4132yes—
15C24×D17C23115yes—
16C23×#595C2×C41960yesdirect product factor
17C23×#595C231280yes—
18C23×C4×C17C2×C4130yescomplemented
19C23×Dic17C2×C4130yescomplemented
20C22×C4×D17C2×C41420yescomplemented
21C22×C4×D17C231140yes—
22C2×C4×#595C231960yesdirect product factor
23C24×C17C42116yescomplemented
24C24×C17C22×C4115yes—
25C23×D17C421240yescomplemented
26C23×D17C22×C41105yes—
27C23×D17C22×C41240yes—
28C23×D17C24135yes—
29C22×#595C22×C412240yesdirect product factor
30C22×#595C241240yes—
31C22×C4×C17C22×C41140yescomplemented
32C22×Dic17C22×C41140yescomplemented
33C2×C4×D17C22×C41840yescomplemented
34C2×C4×D17C241120yes—
35C4×#595C241256yesdirect product factor
36C24×C42—171nomaximal, Sylow
37C23×C17C2×C421120yescomplemented
38C23×C17C23×C4135yes—
39C22×D17C2×C421840yescomplemented
40C22×D17C23×C41280yes—
41C22×D17C23×C41105yes—
42C22×D17C25115yes—
43C2×#595C23×C41960yesdirect product factor
44C2×#595C25132yes—
45C2×C4×C17C23×C41120yescomplemented
46C2×Dic17C23×C41120yescomplemented
47C4×D17C23×C41240yescomplemented
48C4×D17C25116yes—
49C25×C4—172no—
50C25×C4—171no—
51C23×C42—1760no—
52C22×C17C22×C421140yescomplemented
53C22×C17C24×C4115yes—
54C2×D17C22×C421420yescomplemented
55C2×D17C24×C4160yes—
56C2×D17C24×C4115yes—
57C2×D17C2611yescharacteristic
58#595C24×C4164yesdirect product factor
59C4×C17C24×C4116yescomplemented
60Dic17C24×C4116yescomplemented
61C26—171no—
62C24×C4—1760no—
63C24×C4—1764no—
64C24×C4—171no—
65C24×C4—1730no—
66C24×C4—1730no—
67C24×C4#59511yescharacteristic, direct product factor
68C22×C42—17560no—
69C2×C17C23×C42130yescomplemented
70C2×C17C25×C411yescharacteristic
71D17C23×C42130yescomplemented
72D17C25×C412yes—
73C25—1732no—
74C25—1715no—
75C25—1715no—
76C25C2×#59511yescharacteristic
77C23×C4—17960no—
78C23×C4—17280no—
79C23×C4—1730no—
80C23×C4—17420no—
81C23×C4—17140no—
82C23×C4C2×#595130yesdirect product factor
83C2×C42—17960no—
84C17C24×C4211yescharacteristic, complemented, Sylow
85C24—17240no—
86C24—17240no—
87C24—17105no—
88C24—1735no—
89C24C4×#595116yesdirect product factor
90C24C22×#595115yes—
91C22×C4—172240no—
92C22×C4—17240no—
93C22×C4—17140no—
94C22×C4—17840no—
95C22×C4—17120no—
96C22×C4C22×#5951140yesdirect product factor
97C42—17256no—
98C23—17280no—
99C23—17840no—
100C23—1715no—
101C23—17105no—
102C23C2×C4×#5951120yesdirect product factor
103C23C23×#595135yes—
104C2×C4—1732no—
105C2×C4—17960no—
106C2×C4—17120no—
107C2×C4—1716no—
108C2×C4—17240no—
109C2×C4C23×#5951120yesdirect product factor
110C22—1760no—
111C22—17420no—
112C22—171no—
113C22—1715no—
114C22C22×C4×#5951140yesdirect product factor
115C22C24×#595115yes—
116C4—1764no—
117C4—1716no—
118C4C24×#595116yesdirect product factor
119C2—172no—
120C2—1730no—
121C2C23×C4×#595130yesdirect product factor
122C2C25×#59511yescharacteristic
subgroupG/H
center, hypercenterC24×C4#595
commutator, hypocenterC17C24×C42
FrattiniC2C25×#595
FittingC24×C4×C17C4
socleC25×C17C2×C4
prime radicalC25×D17C22
cosocleC2×D17C26
LCSG ▷ C17
UCSC1 ◁ C24×C4

Complements

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

NH ≅ G/Ntype
2. C23×C4×#595C2direct (N × H)
4. C24×#595C4direct (N × H)
6. C22×C4×#595C22direct (N × H)
8. C24×Dic17C4semidirect
9. C23×C4×D17C4semidirect
11. C24×C4×C17C4semidirect
16. C23×#595C2×C4direct (N × H)
18. C23×C4×C17C2×C4semidirect
19. C23×Dic17C2×C4semidirect
20. C22×C4×D17C2×C4semidirect
22. C2×C4×#595C23direct (N × H)
23. C24×C17C42semidirect
25. C23×D17C42semidirect
29. C22×#595C22×C4direct (N × H)
31. C22×C4×C17C22×C4semidirect
32. C22×Dic17C22×C4semidirect
33. C2×C4×D17C22×C4semidirect
35. C4×#595C24direct (N × H)
37. C23×C17C2×C42semidirect
39. C22×D17C2×C42semidirect
43. C2×#595C23×C4direct (N × H)
45. C2×C4×C17C23×C4semidirect
46. C2×Dic17C23×C4semidirect
47. C4×D17C23×C4semidirect
52. C22×C17C22×C42semidirect
54. C2×D17C22×C42semidirect
58. #595C24×C4direct (N × H)
59. C4×C17C24×C4semidirect
60. Dic17C24×C4semidirect
67. C24×C4#595direct (N × H)
69. C2×C17C23×C42semidirect
71. D17C23×C42semidirect
82. C23×C4C2×#595direct (N × H)
84. C17C24×C42semidirect
89. C24C4×#595direct (N × H)
96. C22×C4C22×#595direct (N × H)
102. C23C2×C4×#595direct (N × H)
109. C2×C4C23×#595direct (N × H)
114. C22C22×C4×#595direct (N × H)
118. C4C24×#595direct (N × H)
121. C2C23×C4×#595direct (N × H)

Maximal subgroups

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

subgroupindex
C25×#5952
C23×C4×#5952
C24×C4×D172
C24×C4217