Finite Group Databasebeta

← C24×SD16×C89 #36440926

Subgroups — C24×SD16×C89 #36440926

Order 22784.

13310 conjugacy classes of subgroups; only the 6878 normal subgroups are shown.

normal subgroups only

This group has 13310 conjugacy classes of subgroups — too many to draw. Only its 6878 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
1C24×Q8×C89C211yesmaximal, characteristic, complemented
2C24×D4×C89C211yesmaximal, characteristic
3C23×SD16×C89C2160yesmaximal, direct product factor
4C24×C8×C89C211yesmaximal, characteristic, complemented
5C26×C89—21no—
6C23×Q8×C89—215no—
7C23×Q8×C89C22130yescomplemented
8C23×D4×C89—215no—
9C23×D4×C89C22130yes—
10C24×C4×C89—21no—
11C24×C4×C89C2211yescharacteristic
12C22×SD16×C89C221560yesdirect product factor
13C23×C8×C89C22130yescomplemented
14C25×C89—230no—
15C25×C89—416no—
16C25×C89D411yescharacteristic
17C22×Q8×C89—2210no—
18C22×Q8×C89C231140yescomplemented
19C22×D4×C89—2210no—
20C22×D4×C89C231140yes—
21C23×C4×C89—230no—
22C23×C4×C89D4115yes—
23C23×C4×C89C23115yes—
24C2×SD16×C89C231960yesdirect product factor
25C22×C8×C89C231140yescomplemented
26C24×C89—2140no—
27C24×C89—4240no—
28C24×C89SD16116yesdirect product factor
29C24×C89C2×D4115yes—
30C2×Q8×C89—2420no—
31C2×Q8×C89C241120yescomplemented
32C2×D4×C89—2420no—
33C2×D4×C89C241120yes—
34C22×C4×C89—2140no—
35C22×C4×C89C2×D41105yes—
36C22×C4×C89C24135yes—
37SD16×C89C241256yesdirect product factor
38C2×C8×C89C241120yescomplemented
39C23×C89—2120no—
40C23×C89—4560no—
41C23×C89C2×SD161120yesdirect product factor
42C23×C89C22×D4135yes—
43Q8×C89—2120no—
44Q8×C89C25116yescomplemented
45D4×C89—2120no—
46D4×C89C25116yes—
47C2×C4×C89—2120no—
48C2×C4×C89C22×D41105yes—
49C2×C4×C89C25115yes—
50C8×C89C25116yescomplemented
51C22×C89—216no—
52C22×C89—4240no—
53C22×C89C22×SD161140yesdirect product factor
54C22×C89C23×D4115yes—
55C4×C89—216no—
56C4×C89C23×D4115yes—
57C4×C89C2611yescharacteristic
58C24×SD16C8911yesmaximal, characteristic, direct product factor, Sylow
59C2×C89—416no—
60C2×C89C23×SD16130yesdirect product factor
61C2×C89C24×D411yescharacteristic
62C24×Q8C2×C8911yescharacteristic, complemented
63C24×D4C2×C8911yescharacteristic
64C23×SD16C2×C89160yesdirect product factor
65C24×C8C2×C8911yescharacteristic, complemented
66C89C24×SD1611yescharacteristic, direct product factor, Sylow
67C26—21no—
68C23×Q8—215no—
69C23×Q8C22×C89130yescomplemented
70C23×D4—215no—
71C23×D4C22×C89130yes—
72C24×C4—21no—
73C24×C4C22×C8911yescharacteristic
74C22×SD16C22×C891560yesdirect product factor
75C23×C8C22×C89130yescomplemented
76C25—230no—
77C25—416no—
78C25D4×C8911yescharacteristic
79C22×Q8—2210no—
80C22×Q8C23×C891140yescomplemented
81C22×D4—2210no—
82C22×D4C23×C891140yes—
83C23×C4—230no—
84C23×C4D4×C89115yes—
85C23×C4C23×C89115yes—
86C2×SD16C23×C891960yesdirect product factor
87C22×C8C23×C891140yescomplemented
88C24—2140no—
89C24—4240no—
90C24SD16×C89116yesdirect product factor
91C24C2×D4×C89115yes—
92C2×Q8—2420no—
93C2×Q8C24×C891120yescomplemented
94C2×D4—2420no—
95C2×D4C24×C891120yes—
96C22×C4—2140no—
97C22×C4C2×D4×C891105yes—
98C22×C4C24×C89135yes—
99SD16C24×C891256yesdirect product factor
100C2×C8C24×C891120yescomplemented
101C23—2120no—
102C23—4560no—
103C23C2×SD16×C891120yesdirect product factor
104C23C22×D4×C89135yes—
105Q8—2120no—
106Q8C25×C89116yescomplemented
107D4—2120no—
108D4C25×C89116yes—
109C2×C4—2120no—
110C2×C4C22×D4×C891105yes—
111C2×C4C25×C89115yes—
112C8C25×C89116yescomplemented
113C22—216no—
114C22—4240no—
115C22C22×SD16×C891140yesdirect product factor
116C22C23×D4×C89115yes—
117C4—216no—
118C4C23×D4×C89115yes—
119C4C26×C8911yescharacteristic
120C2—416no—
121C2C23×SD16×C89130yesdirect product factor
122C2C24×D4×C8911yescharacteristic
subgroupG/H
center, socleC25×C89D4
commutator, Frattini, cosocleC4C26×C89
prime radicalC24×D4×C89C2
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C25×C89 ◁ C24×C4×C89 ◁ G

Complements

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

NH ≅ G/Ntype
1. C24×Q8×C89C2semidirect
3. C23×SD16×C89C2direct (N × H)
4. C24×C8×C89C2semidirect
7. C23×Q8×C89C22semidirect
12. C22×SD16×C89C22direct (N × H)
13. C23×C8×C89C22semidirect
18. C22×Q8×C89C23semidirect
24. C2×SD16×C89C23direct (N × H)
25. C22×C8×C89C23semidirect
28. C24×C89SD16direct (N × H)
31. C2×Q8×C89C24semidirect
37. SD16×C89C24direct (N × H)
38. C2×C8×C89C24semidirect
41. C23×C89C2×SD16direct (N × H)
44. Q8×C89C25semidirect
50. C8×C89C25semidirect
53. C22×C89C22×SD16direct (N × H)
58. C24×SD16C89direct (N × H)
60. C2×C89C23×SD16direct (N × H)
62. C24×Q8C2×C89semidirect
64. C23×SD16C2×C89direct (N × H)
65. C24×C8C2×C89semidirect
66. C89C24×SD16direct (N × H)
69. C23×Q8C22×C89semidirect
74. C22×SD16C22×C89direct (N × H)
75. C23×C8C22×C89semidirect
80. C22×Q8C23×C89semidirect
86. C2×SD16C23×C89direct (N × H)
87. C22×C8C23×C89semidirect
90. C24SD16×C89direct (N × H)
93. C2×Q8C24×C89semidirect
99. SD16C24×C89direct (N × H)
100. C2×C8C24×C89semidirect
103. C23C2×SD16×C89direct (N × H)
106. Q8C25×C89semidirect
112. C8C25×C89semidirect
115. C22C22×SD16×C89direct (N × H)
121. C2C23×SD16×C89direct (N × H)

Maximal subgroups

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

subgroupindex
C24×Q8×C892
C24×D4×C892
C23×SD16×C892
C24×C8×C892
C24×SD1689