Finite Group Databasebeta

← C24×C4⋊#595 #17981031

Subgroups — C24×C4⋊#595 #17981031

Order 4352.

19742 conjugacy classes of subgroups; only the 8408 normal subgroups are shown.

normal subgroups only

This group has 19742 conjugacy classes of subgroups — too many to draw. Only its 8408 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×#595—232no—
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×D17D4116yes—
15C24×D17Q8116yes—
16C24×D17C23115yes—
17C23×#595—2480no—
18C23×#595C231280yes—
19C23×C4×C17C2×C4130yescomplemented
20C23×Dic17C2×C4130yescomplemented
21C22×C4×D17C2×C41420yescomplemented
22C22×C4×D17C231140yes—
23C2×C4⋊#595C231960yesdirect product factor
24C24×C17C4⋊C4116yescomplemented
25C24×C17C22×C4115yes—
26C23×D17C4⋊C41240yescomplemented
27C23×D17C22×C41105yes—
28C23×D17C2×D41120yes—
29C23×D17C2×Q81120yes—
30C23×D17C24135yes—
31C22×#595—21120no—
32C22×#595C241240yes—
33C22×C4×C17C22×C41140yescomplemented
34C22×Dic17C22×C41140yescomplemented
35C2×C4×D17C22×C41840yescomplemented
36C2×C4×D17C241120yes—
37C4⋊#595C241256yesdirect product factor
38C24×C4⋊C4—171nomaximal, Sylow
39C23×C17C2×C4⋊C41120yescomplemented
40C23×C17C23×C4135yes—
41C22×D17C2×C4⋊C41840yescomplemented
42C22×D17C23×C41105yes—
43C22×D17C22×D41140yes—
44C22×D17C22×Q81140yes—
45C22×D17C25115yes—
46C2×#595—2480no—
47C2×#595C25132yes—
48C2×C4×C17C23×C41120yescomplemented
49C2×Dic17C23×C41120yescomplemented
50C4×D17C23×C41240yescomplemented
51C4×D17C25116yes—
52C25×C4—171no—
53C25×C4—172no—
54C23×C4⋊C4—1760no—
55C22×C17C22×C4⋊C41140yescomplemented
56C22×C17C24×C4115yes—
57C2×D17C22×C4⋊C41420yescomplemented
58C2×D17C24×C4115yes—
59C2×D17C23×D4130yes—
60C2×D17C23×Q8130yes—
61C2×D17C2611yescharacteristic
62#595—232no—
63C4×C17C24×C4116yescomplemented
64Dic17C24×C4116yescomplemented
65C26—171no—
66C24×C4—171no—
67C24×C4—1730no—
68C24×C4—1730no—
69C24×C4—1760no—
70C24×C4—3432no—
71C24×C4#59511yescharacteristic, complemented
72C22×C4⋊C4—17560no—
73C2×C17C23×C4⋊C4130yescomplemented
74C2×C17C25×C411yescharacteristic
75D17C23×C4⋊C4130yescomplemented
76D17C24×D411yescharacteristic
77D17C24×Q811yescharacteristic
78C25—1716no—
79C25—1716no—
80C25—1715no—
81C25—1715no—
82C25C2×#59511yescharacteristic
83C23×C4—1730no—
84C23×C4—17140no—
85C23×C4—17420no—
86C23×C4—17280no—
87C23×C4—34480no—
88C23×C4C2×#595130yescomplemented
89C2×C4⋊C4—17960no—
90C17C24×C4⋊C411yescharacteristic, complemented, Sylow
91C24—17240no—
92C24—17120no—
93C24—17120no—
94C24—17105no—
95C24—1735no—
96C24C4⋊#595116yesdirect product factor
97C24C22×#595115yes—
98C22×C4—17140no—
99C22×C4—17840no—
100C22×C4—17120no—
101C22×C4—17240no—
102C22×C4—341120no—
103C22×C4C22×#5951140yescomplemented
104C4⋊C4—17256no—
105C23—17140no—
106C23—17840no—
107C23—17140no—
108C23—1715no—
109C23—17105no—
110C23C2×C4⋊#5951120yesdirect product factor
111C23C23×#595135yes—
112C2×C4—17120no—
113C2×C4—1716no—
114C2×C4—17240no—
115C2×C4—1732no—
116C2×C4—34480no—
117C2×C4C23×#5951120yescomplemented
118C22—1730no—
119C22—17420no—
120C22—1730no—
121C22—171no—
122C22—1715no—
123C22C22×C4⋊#5951140yesdirect product factor
124C22C24×#595115yes—
125C4—1716no—
126C4—3432no—
127C4C24×#595116yescomplemented
128C2—171no—
129C2—171no—
130C2—1730no—
131C2C23×C4⋊#595130yesdirect product factor
132C2C25×#59511yescharacteristic
subgroupG/H
centerC25C2×#595
commutatorC2×C17C25×C4
FrattiniC2C25×#595
FittingC24×C4×C17C4
socleC25×C17C2×C4
prime radicalC25×D17C22
cosocleC2×D17C26
hypercenterC24×C4#595
hypocenterC17C24×C4⋊C4
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C25 ◁ C24×C4

Complements

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

NH ≅ G/Ntype
2. C23×C4⋊#595C2direct (N × H)
6. C22×C4⋊#595C22direct (N × H)
8. C24×Dic17C4semidirect
9. C23×C4×D17C4semidirect
11. C24×C4×C17C4semidirect
19. C23×C4×C17C2×C4semidirect
20. C23×Dic17C2×C4semidirect
21. C22×C4×D17C2×C4semidirect
23. C2×C4⋊#595C23direct (N × H)
24. C24×C17C4⋊C4semidirect
26. C23×D17C4⋊C4semidirect
33. C22×C4×C17C22×C4semidirect
34. C22×Dic17C22×C4semidirect
35. C2×C4×D17C22×C4semidirect
37. C4⋊#595C24direct (N × H)
39. C23×C17C2×C4⋊C4semidirect
41. C22×D17C2×C4⋊C4semidirect
48. C2×C4×C17C23×C4semidirect
49. C2×Dic17C23×C4semidirect
50. C4×D17C23×C4semidirect
55. C22×C17C22×C4⋊C4semidirect
57. C2×D17C22×C4⋊C4semidirect
63. C4×C17C24×C4semidirect
64. Dic17C24×C4semidirect
71. C24×C4#595semidirect
73. C2×C17C23×C4⋊C4semidirect
75. D17C23×C4⋊C4semidirect
88. C23×C4C2×#595semidirect
90. C17C24×C4⋊C4semidirect
96. C24C4⋊#595direct (N × H)
103. C22×C4C22×#595semidirect
110. C23C2×C4⋊#595direct (N × H)
117. C2×C4C23×#595semidirect
123. C22C22×C4⋊#595direct (N × H)
127. C4C24×#595semidirect
131. 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×C4⋊C417