Finite Group Databasebeta

← C24×C22⋊#595 #17981030

Subgroups — C24×C22⋊#595 #17981030

Order 4352.

43678 conjugacy classes of subgroups; only the 8408 normal subgroups are shown.

normal subgroups only

This group has 43678 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, complemented
2C23×C22⋊#595C2160yesmaximal, direct product factor
3C26×D17C211yesmaximal, characteristic
4C24×#595—232no—
5C24×#595C22160yescomplemented
6C22×C22⋊#595C221560yesdirect product factor
7C25×D17—232no—
8C25×D17C4130yescomplemented
9C25×D17C411yescharacteristic, complemented
10C25×D17C22130yes—
11C25×D17C2211yescharacteristic
12C26×C17C411yescharacteristic, complemented
13C25×C17—216no—
14C25×C17C2×C411yescharacteristic
15C25×C17C2×C4130yescomplemented
16C24×D17—216no—
17C24×D17—2480no—
18C24×D17—2480no—
19C24×D17C2×C4115yes—
20C24×D17C2×C41420yescomplemented
21C24×D17C2×C4130yescomplemented
22C24×D17D4132yes—
23C24×D17C231140yes—
24C24×D17C23115yes—
25C23×#595—2480no—
26C23×#595C231280yescomplemented
27C2×C22⋊#595C231960yesdirect product factor
28C24×C17—2240no—
29C24×C17C22⋊C4116yescomplemented
30C24×C17C22×C4115yes—
31C24×C17C22×C41140yescomplemented
32C23×D17—2240no—
33C23×D17—23360no—
34C23×D17—21120no—
35C23×D17C22⋊C41240yescomplemented
36C23×D17C22×C41105yes—
37C23×D17C22×C41840yescomplemented
38C23×D17C22×C41140yescomplemented
39C23×D17C2×D41240yes—
40C23×D17C241120yes—
41C23×D17C24135yes—
42C22×#595—21120no—
43C22×#595C241240yescomplemented
44C22⋊#595C241256yesdirect product factor
45C24×C22⋊C4—171nomaximal, Sylow
46C23×C17—2560no—
47C23×C17C2×C22⋊C41120yescomplemented
48C23×C17C23×C4135yes—
49C23×C17C23×C41120yescomplemented
50C22×D17—2560no—
51C22×D17—23360no—
52C22×D17—2480no—
53C22×D17C2×C22⋊C41840yescomplemented
54C22×D17C23×C41105yes—
55C22×D17C23×C41240yescomplemented
56C22×D17C23×C41120yescomplemented
57C22×D17C22×D41280yes—
58C22×D17C25116yes—
59C22×D17C25115yes—
60C2×#595—2480no—
61C2×#595C25132yescomplemented
62C27—171no—
63C25×C4—172no—
64C23×C22⋊C4—1760no—
65C22×C17—2240no—
66C22×C17C22×C22⋊C41140yescomplemented
67C22×C17C24×C4115yes—
68C22×C17C24×C4116yescomplemented
69C2×D17—2240no—
70C2×D17—232no—
71C2×D17—2480no—
72C2×D17C22×C22⋊C41420yescomplemented
73C2×D17C24×C4115yes—
74C2×D17C24×C4116yescomplemented
75C2×D17C23×D4160yes—
76C2×D17C2611yescharacteristic
77#595—232no—
78C26—171no—
79C26—171no—
80C26—1730no—
81C26—1730no—
82C26—3432no—
83C26#59511yescharacteristic, complemented
84C24×C4—1760no—
85C24×C4—3432no—
86C22×C22⋊C4—17560no—
87C2×C17—216no—
88C2×C17C23×C22⋊C4130yescomplemented
89C2×C17C25×C411yescharacteristic
90D17—216no—
91D17C23×C22⋊C4130yescomplemented
92D17C24×D412yes—
93C25—216no—
94C25—1732no—
95C25—1715no—
96C25—1715no—
97C25—1730no—
98C25—17140no—
99C25—17420no—
100C25—34480no—
101C25—34480no—
102C25—3416no—
103C25C2×#59511yescharacteristic
104C25C2×#595130yescomplemented
105C23×C4—17280no—
106C23×C4—34480no—
107C2×C22⋊C4—17960no—
108C17C24×C22⋊C411yescharacteristic, complemented, Sylow
109C24—2240no—
110C24—17240no—
111C24—17240no—
112C24—17105no—
113C24—1735no—
114C24—17140no—
115C24—17840no—
116C24—17120no—
117C24—341120no—
118C24—343360no—
119C24—34240no—
120C24C22⋊#595116yesdirect product factor
121C24C22×#595115yes—
122C24C22×#5951140yescomplemented
123C22×C4—17240no—
124C22×C4—341120no—
125C22⋊C4—17256no—
126C23—2560no—
127C23—17280no—
128C23—17840no—
129C23—1715no—
130C23—17105no—
131C23—17120no—
132C23—1716no—
133C23—17240no—
134C23—34480no—
135C23—343360no—
136C23—34560no—
137C23C2×C22⋊#5951120yesdirect product factor
138C23C23×#595135yes—
139C23C23×#5951120yescomplemented
140C2×C4—1732no—
141C2×C4—34480no—
142C22—2240no—
143C22—1760no—
144C22—17420no—
145C22—171no—
146C22—1715no—
147C22—1716no—
148C22—3432no—
149C22—34480no—
150C22—34240no—
151C22C22×C22⋊#5951140yesdirect product factor
152C22C24×#595115yes—
153C22C24×#595116yescomplemented
154C4—3432no—
155C2—216no—
156C2—172no—
157C2—1730no—
158C2—3416no—
159C2C23×C22⋊#595130yesdirect product factor
160C2C25×#59511yescharacteristic
subgroupG/H
centerC25C2×#595
commutatorC2×C17C25×C4
FrattiniC2C25×#595
FittingC26×C17C4
socleC25×C17C2×C4
prime radicalC26×D17C2
cosocleC2×D17C26
hypercenterC26#595
hypocenterC17C24×C22⋊C4
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C25 ◁ C26

Complements

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

NH ≅ G/Ntype
1. C25×#595C2semidirect
2. C23×C22⋊#595C2direct (N × H)
5. C24×#595C22semidirect
6. C22×C22⋊#595C22direct (N × H)
8. C25×D17C4semidirect
9. C25×D17C4semidirect
12. C26×C17C4semidirect
15. C25×C17C2×C4semidirect
20. C24×D17C2×C4semidirect
21. C24×D17C2×C4semidirect
26. C23×#595C23semidirect
27. C2×C22⋊#595C23direct (N × H)
29. C24×C17C22⋊C4semidirect
31. C24×C17C22×C4semidirect
35. C23×D17C22⋊C4semidirect
37. C23×D17C22×C4semidirect
38. C23×D17C22×C4semidirect
43. C22×#595C24semidirect
44. C22⋊#595C24direct (N × H)
47. C23×C17C2×C22⋊C4semidirect
49. C23×C17C23×C4semidirect
53. C22×D17C2×C22⋊C4semidirect
55. C22×D17C23×C4semidirect
56. C22×D17C23×C4semidirect
61. C2×#595C25semidirect
66. C22×C17C22×C22⋊C4semidirect
68. C22×C17C24×C4semidirect
72. C2×D17C22×C22⋊C4semidirect
74. C2×D17C24×C4semidirect
83. C26#595semidirect
88. C2×C17C23×C22⋊C4semidirect
91. D17C23×C22⋊C4semidirect
104. C25C2×#595semidirect
108. C17C24×C22⋊C4semidirect
120. C24C22⋊#595direct (N × H)
122. C24C22×#595semidirect
137. C23C2×C22⋊#595direct (N × H)
139. C23C23×#595semidirect
151. C22C22×C22⋊#595direct (N × H)
153. C22C24×#595semidirect
159. C2C23×C22⋊#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×C22⋊#5952
C26×D172
C24×C22⋊C417