Finite Group Databasebeta

← C24×C4⋊C4×C89 #36440488

Subgroups — C24×C4⋊C4×C89 #36440488

Order 22784.

19742 conjugacy classes of subgroups; only the 15454 normal subgroups are shown.

normal subgroups only

This group has 19742 conjugacy classes of subgroups — too many to draw. Only its 15454 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×C89C212yesmaximal
2C25×C4×C89C211yesmaximal, characteristic
3C23×C4⋊C4×C89C2160yesmaximal, direct product factor
4C26×C89C2211yescharacteristic
5C24×C4×C89—232no—
6C24×C4×C89C4132yescomplemented
7C24×C4×C89C22160yes—
8C24×C4×C89C22130yes—
9C22×C4⋊C4×C89C221560yesdirect product factor
10C25×C89C2×C4116yes—
11C25×C89D4116yes—
12C25×C89Q8116yes—
13C25×C89C23115yes—
14C23×C4×C89—2480no—
15C23×C4×C89C2×C41480yescomplemented
16C23×C4×C89C231280yes—
17C23×C4×C89C231140yes—
18C2×C4⋊C4×C89C231960yesdirect product factor
19C24×C89C4⋊C41256yesdirect product factor
20C24×C89C22×C41120yes—
21C24×C89C2×D41120yes—
22C24×C89C2×Q81120yes—
23C24×C89C24135yes—
24C22×C4×C89—21120no—
25C22×C4×C89C22×C411120yescomplemented
26C22×C4×C89C241240yes—
27C22×C4×C89C241120yes—
28C4⋊C4×C89C241256yesdirect product factor
29C23×C89C2×C4⋊C41960yesdirect product factor
30C23×C89C23×C41140yes—
31C23×C89C22×D41140yes—
32C23×C89C22×Q81140yes—
33C23×C89C25115yes—
34C2×C4×C89—2480no—
35C2×C4×C89C23×C41480yescomplemented
36C2×C4×C89C25132yes—
37C2×C4×C89C25116yes—
38C22×C89C22×C4⋊C41560yesdirect product factor
39C22×C89C24×C4130yes—
40C22×C89C23×D4130yes—
41C22×C89C23×Q8130yes—
42C22×C89C2611yescharacteristic
43C4×C89—232no—
44C4×C89C24×C4132yescomplemented
45C24×C4⋊C4C8911yesmaximal, characteristic, direct product factor, Sylow
46C2×C89C23×C4⋊C4160yesdirect product factor
47C2×C89C25×C411yescharacteristic
48C2×C89C24×D411yescharacteristic
49C2×C89C24×Q811yescharacteristic
50C25×C4C2×C8912yes—
51C25×C4C2×C8911yescharacteristic
52C23×C4⋊C4C2×C89160yesdirect product factor
53C89C24×C4⋊C411yescharacteristic, direct product factor, Sylow
54C26C22×C8911yescharacteristic
55C24×C4—232no—
56C24×C4C4×C89132yescomplemented
57C24×C4C22×C89160yes—
58C24×C4C22×C89130yes—
59C22×C4⋊C4C22×C891560yesdirect product factor
60C25C2×C4×C89116yes—
61C25D4×C89116yes—
62C25Q8×C89116yes—
63C25C23×C89115yes—
64C23×C4—2480no—
65C23×C4C2×C4×C891480yescomplemented
66C23×C4C23×C891280yes—
67C23×C4C23×C891140yes—
68C2×C4⋊C4C23×C891960yesdirect product factor
69C24C4⋊C4×C891256yesdirect product factor
70C24C22×C4×C891120yes—
71C24C2×D4×C891120yes—
72C24C2×Q8×C891120yes—
73C24C24×C89135yes—
74C22×C4—21120no—
75C22×C4C22×C4×C8911120yescomplemented
76C22×C4C24×C891240yes—
77C22×C4C24×C891120yes—
78C4⋊C4C24×C891256yesdirect product factor
79C23C2×C4⋊C4×C891960yesdirect product factor
80C23C23×C4×C891140yes—
81C23C22×D4×C891140yes—
82C23C22×Q8×C891140yes—
83C23C25×C89115yes—
84C2×C4—2480no—
85C2×C4C23×C4×C891480yescomplemented
86C2×C4C25×C89132yes—
87C2×C4C25×C89116yes—
88C22C22×C4⋊C4×C891560yesdirect product factor
89C22C24×C4×C89130yes—
90C22C23×D4×C89130yes—
91C22C23×Q8×C89130yes—
92C22C26×C8911yescharacteristic
93C4—232no—
94C4C24×C4×C89132yescomplemented
95C2C23×C4⋊C4×C89160yesdirect product factor
96C2C25×C4×C8911yescharacteristic
97C2C24×D4×C8911yescharacteristic
98C2C24×Q8×C8911yescharacteristic
subgroupG/H
center, socle, prime radicalC26×C89C22
commutatorC2C25×C4×C89
Frattini, cosocleC22C26×C89
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C26×C89 ◁ G

Complements

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

NH ≅ G/Ntype
3. C23×C4⋊C4×C89C2direct (N × H)
6. C24×C4×C89C4semidirect
9. C22×C4⋊C4×C89C22direct (N × H)
15. C23×C4×C89C2×C4semidirect
18. C2×C4⋊C4×C89C23direct (N × H)
19. C24×C89C4⋊C4direct (N × H)
25. C22×C4×C89C22×C4semidirect
28. C4⋊C4×C89C24direct (N × H)
29. C23×C89C2×C4⋊C4direct (N × H)
35. C2×C4×C89C23×C4semidirect
38. C22×C89C22×C4⋊C4direct (N × H)
44. C4×C89C24×C4semidirect
45. C24×C4⋊C4C89direct (N × H)
46. C2×C89C23×C4⋊C4direct (N × H)
52. C23×C4⋊C4C2×C89direct (N × H)
53. C89C24×C4⋊C4direct (N × H)
56. C24×C4C4×C89semidirect
59. C22×C4⋊C4C22×C89direct (N × H)
65. C23×C4C2×C4×C89semidirect
68. C2×C4⋊C4C23×C89direct (N × H)
69. C24C4⋊C4×C89direct (N × H)
75. C22×C4C22×C4×C89semidirect
78. C4⋊C4C24×C89direct (N × H)
79. C23C2×C4⋊C4×C89direct (N × H)
85. C2×C4C23×C4×C89semidirect
88. C22C22×C4⋊C4×C89direct (N × H)
94. C4C24×C4×C89semidirect
95. C2C23×C4⋊C4×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×C4⋊C4×C892
C24×C4⋊C489