Finite Group Databasebeta

← #37560222

Subgroups — #37560222

Order 23872.

262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 107 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
1C2×#20238610C212yesmaximal, complemented
2#26045825C214yesmaximal, complemented
3#26045820C214yesmaximal, complemented
4#26045814C214yesmaximal, complemented
5C2×M16×C373C211yesmaximal, characteristic, complemented
6#20238610—22no—
7#20238610—22no—
8#20238610C2214yes—
9#20238610C2214yescomplemented
10C2×Dic746C2212yescomplemented
11C2×D1492C2212yescomplemented
12C2×C22⋊D373—22no—
13C2×C4×D373—22no—
14Dic1492C2214yescomplemented
15#20238599C2218yescomplemented
16D2984C2214yescomplemented
17C22×C4×C373C2211yescharacteristic
18M16×C373C2214yescomplemented
19C2×C8×C373C2212yescomplemented
20C22×D373—22no—
21Dic746—22no—
22Dic746C2314yes—
23D1492—22no—
24D1492C2314yes—
25C22⋊D373—24no—
26C22⋊D373—24no—
27C2×Dic373—22no—
28C4×D373—24no—
29C4×D373—24no—
30C23×C373D411yescharacteristic
31C2×C4×C373D412yes—
32C2×C4×C373D411yescharacteristic
33C2×C4×C373C2312yes—
34C2×C4×C373C2311yescharacteristic
35C8×C373C2314yes—
36C22×C373—41no—
37C22×C373C2×D412yes—
38C22×C373C2×D411yescharacteristic
39C2×D373—24no—
40C2×D373—44no—
41C4×C373C2×D412yes—
42C4×C373C2×D411yescharacteristic
43C4×C373C2411yescharacteristic
44Dic373—24no—
45C2×C373—22no—
46C2×C373—21no—
47C2×C373C22×D411yescharacteristic
48D373—44no—
49C373#57511yescharacteristic, complemented, Sylow
50#575—3731nomaximal, Sylow
51C2×#41—3732no—
52#137—3734no—
53AGL(1,ℤ/8)—3734no—
54#135—3734no—
55C2×M16D37311yescharacteristic, complemented
56#41—3734no—
57#41—3734no—
58#41—7462no—
59#41—7462no—
60C2×Q8—3732no—
61C2×D4—3732no—
62C2×D4—7462no—
63C22×C4—7462no—
64C22×C4C2×D37311yescharacteristic
65Q16—3734no—
66SD16—3738no—
67D8—3734no—
68M16C2×D37314yescomplemented
69C2×C8C2×D37312yescomplemented
70C23—7462no—
71C23D149211yescharacteristic
72Q8—3734no—
73Q8—7462no—
74D4—3734no—
75D4—7464no—
76D4—7464no—
77D4—7462no—
78C2×C4—7462no—
79C2×C4—7464no—
80C2×C4—7464no—
81C2×C4D149211yescharacteristic
82C2×C4D149212yes—
83C2×C4C22×D37312yes—
84C2×C4C22×D37311yescharacteristic
85C8C22×D37314yes—
86C22—41no—
87C22—14924no—
88C22—7464no—
89C22C2×D149212yes—
90C22C2×D149211yescharacteristic
91C4—7464no—
92C4C2×D149212yes—
93C4C2×D149211yescharacteristic
94C4C23×D37311yescharacteristic
95C2—22no—
96C2—21no—
97C2—14924no—
98C2C22×D149211yescharacteristic
subgroupG/H
centerC4C2×D1492
commutator, cosocleC4×C373C24
FrattiniC4C23×D373
FittingC2×M16×C373C2
socleC2×C373C22×D4
hypercenterC2×M16D373
hypocenterC373#575
LCSG ▷ C4×C373 ▷ C2×C373 ▷ C373
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×#20238610C2semidirect
2. #26045825C2semidirect
3. #26045820C2semidirect
4. #26045814C2semidirect
5. C2×M16×C373C2semidirect
9. #20238610C22semidirect
10. C2×Dic746C22semidirect
11. C2×D1492C22semidirect
14. Dic1492C22semidirect
15. #20238599C22semidirect
16. D2984C22semidirect
18. M16×C373C22semidirect
19. C2×C8×C373C22semidirect
49. C373#575semidirect
55. C2×M16D373semidirect
68. M16C2×D373semidirect
69. C2×C8C2×D373semidirect

Maximal subgroups

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

subgroupindex
C2×#202386102
#260458252
#260458202
#260458142
C2×M16×C3732
#575373