Finite Group Databasebeta

← C24×M16×C89 #36440920

Subgroups — C24×M16×C89 #36440920

Order 22784.

13310 conjugacy classes of subgroups; only the 11166 normal subgroups are shown.

normal subgroups only

This group has 13310 conjugacy classes of subgroups — too many to draw. Only its 11166 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×C4×C89C211yesmaximal, characteristic
2C23×M16×C89C2160yesmaximal, direct product factor
3C24×C8×C89C212yesmaximal, complemented
4C26×C89C411yescharacteristic
5C24×C4×C89C411yescharacteristic
6C24×C4×C89C4130yes—
7C24×C4×C89C22130yes—
8C24×C4×C89C2211yescharacteristic
9C22×M16×C89C221560yesdirect product factor
10C23×C8×C89C22160yescomplemented
11C25×C89—216no—
12C25×C89C2×C4130yes—
13C25×C89C2×C411yescharacteristic
14C23×C4×C89C2×C41420yes—
15C23×C4×C89C2×C4130yes—
16C23×C4×C89C2×C4115yes—
17C23×C4×C89C23115yes—
18C23×C4×C89C231140yes—
19C2×M16×C89C231960yesdirect product factor
20C22×C8×C89C231280yescomplemented
21C24×C89—2240no—
22C24×C89M16116yesdirect product factor
23C24×C89C22×C41140yes—
24C24×C89C22×C4115yes—
25C22×C4×C89C22×C41840yes—
26C22×C4×C89C22×C41140yes—
27C22×C4×C89C22×C41105yes—
28C22×C4×C89C24135yes—
29C22×C4×C89C241120yes—
30M16×C89C241256yesdirect product factor
31C2×C8×C89C241240yescomplemented
32C23×C89—2560no—
33C23×C89C2×M161120yesdirect product factor
34C23×C89C23×C41120yes—
35C23×C89C23×C4135yes—
36C2×C4×C89C23×C41240yes—
37C2×C4×C89C23×C41105yes—
38C2×C4×C89C23×C41120yes—
39C2×C4×C89C25115yes—
40C2×C4×C89C25116yes—
41C8×C89C25132yescomplemented
42C22×C89—2240no—
43C22×C89C22×M161140yesdirect product factor
44C22×C89C24×C4116yes—
45C22×C89C24×C4115yes—
46C4×C89C24×C4115yes—
47C4×C89C24×C4116yes—
48C4×C89C2611yescharacteristic
49C24×M16C8911yesmaximal, characteristic, direct product factor, Sylow
50C2×C89—216no—
51C2×C89C23×M16130yesdirect product factor
52C2×C89C25×C411yescharacteristic
53C25×C4C2×C8911yescharacteristic
54C23×M16C2×C89160yesdirect product factor
55C24×C8C2×C8912yescomplemented
56C89C24×M1611yescharacteristic, direct product factor, Sylow
57C26C4×C8911yescharacteristic
58C24×C4C4×C89130yes—
59C24×C4C4×C8911yescharacteristic
60C24×C4C22×C89130yes—
61C24×C4C22×C8911yescharacteristic
62C22×M16C22×C891560yesdirect product factor
63C23×C8C22×C89160yescomplemented
64C25—216no—
65C25C2×C4×C89130yes—
66C25C2×C4×C8911yescharacteristic
67C23×C4C2×C4×C891420yes—
68C23×C4C2×C4×C89130yes—
69C23×C4C2×C4×C89115yes—
70C23×C4C23×C89115yes—
71C23×C4C23×C891140yes—
72C2×M16C23×C891960yesdirect product factor
73C22×C8C23×C891280yescomplemented
74C24—2240no—
75C24M16×C89116yesdirect product factor
76C24C22×C4×C891140yes—
77C24C22×C4×C89115yes—
78C22×C4C22×C4×C891840yes—
79C22×C4C22×C4×C891105yes—
80C22×C4C22×C4×C891140yes—
81C22×C4C24×C89135yes—
82C22×C4C24×C891120yes—
83M16C24×C891256yesdirect product factor
84C2×C8C24×C891240yescomplemented
85C23—2560no—
86C23C2×M16×C891120yesdirect product factor
87C23C23×C4×C891120yes—
88C23C23×C4×C89135yes—
89C2×C4C23×C4×C891240yes—
90C2×C4C23×C4×C891105yes—
91C2×C4C23×C4×C891120yes—
92C2×C4C25×C89115yes—
93C2×C4C25×C89116yes—
94C8C25×C89132yescomplemented
95C22—2240no—
96C22C22×M16×C891140yesdirect product factor
97C22C24×C4×C89116yes—
98C22C24×C4×C89115yes—
99C4C24×C4×C89115yes—
100C4C24×C4×C89116yes—
101C4C26×C8911yescharacteristic
102C2—216no—
103C2C23×M16×C89130yesdirect product factor
104C2C25×C4×C8911yescharacteristic
subgroupG/H
centerC24×C4×C89C22
commutatorC2C25×C4×C89
Frattini, cosocleC4C26×C89
socleC25×C89C2×C4
prime radicalC26×C89C4
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C24×C4×C89 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×M16×C89C2direct (N × H)
3. C24×C8×C89C2semidirect
9. C22×M16×C89C22direct (N × H)
10. C23×C8×C89C22semidirect
19. C2×M16×C89C23direct (N × H)
20. C22×C8×C89C23semidirect
22. C24×C89M16direct (N × H)
30. M16×C89C24direct (N × H)
31. C2×C8×C89C24semidirect
33. C23×C89C2×M16direct (N × H)
41. C8×C89C25semidirect
43. C22×C89C22×M16direct (N × H)
49. C24×M16C89direct (N × H)
51. C2×C89C23×M16direct (N × H)
54. C23×M16C2×C89direct (N × H)
55. C24×C8C2×C89semidirect
56. C89C24×M16direct (N × H)
62. C22×M16C22×C89direct (N × H)
63. C23×C8C22×C89semidirect
72. C2×M16C23×C89direct (N × H)
73. C22×C8C23×C89semidirect
75. C24M16×C89direct (N × H)
83. M16C24×C89direct (N × H)
84. C2×C8C24×C89semidirect
86. C23C2×M16×C89direct (N × H)
94. C8C25×C89semidirect
96. C22C22×M16×C89direct (N × H)
103. C2C23×M16×C89direct (N × H)

Maximal subgroups

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

subgroupindex
C25×C4×C892
C23×M16×C892
C24×C8×C892
C24×M1689