Finite Group Databasebeta

← #37560224

Subgroups — #37560224

Order 23872.

268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 99 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
1#26045838C212yesmaximal, complemented
2#26045819C214yesmaximal, complemented
3#26045817C212yesmaximal, complemented
4#26045815C212yesmaximal, complemented
5C2×D2984C211yesmaximal, characteristic, complemented
6D8×D373C212yesmaximal, complemented
7#26045798C211yesmaximal, characteristic, complemented
8#135×C373C211yesmaximal, characteristic, complemented
9#20238611C2214yescomplemented
10#20238610—22no—
11#20238610C2211yescharacteristic
12C2×D1492—22no—
13C2×D1492C2212yescomplemented
14D4×D373—24no—
15D4×D373C2214yescomplemented
16#20238597C2214yescomplemented
17D2984C2212yescomplemented
18D2984C2212yescomplemented
19#20238595C2214yescomplemented
20#20238594C2211yescharacteristic, complemented
21#20238593C2212yescomplemented
22C8×D373C2212yescomplemented
23#41×C373C2212yescomplemented
24Q16×C373C2211yescharacteristic, complemented
25SD16×C373C2212yescomplemented
26D8×C373C2211yescharacteristic, complemented
27C2×C8×C373C2211yescharacteristic, complemented
28C22×D373—22no—
29C22×D373—24no—
30Dic746D411yescharacteristic
31D1492—24no—
32D1492—22no—
33D1492D411yescharacteristic
34D1492C2314yes—
35C22⋊D373—24no—
36C22⋊D373D412yes—
37C4×D373—24no—
38C4×D373C2312yes—
39#15688412C2312yes—
40Q8×C373C2312yes—
41D4×C373—22no—
42D4×C373C2312yes—
43C2×C4×C373—22no—
44C2×C4×C373C2311yescharacteristic
45C8×C373C2311yescharacteristic
46C8×C373C2311yescharacteristic
47C22×C373—22no—
48C22×C373C2×D411yescharacteristic
49C2×D373—24no—
50C2×D373—84no—
51C2×D373—82no—
52C2×D373C2×D412yes—
53C4×C373—22no—
54C4×C373C2×D411yescharacteristic
55C4×C373C2411yescharacteristic
56Dic373C2×D412yes—
57C2×C373—21no—
58C2×C373—42no—
59C2×C373C22×D411yescharacteristic
60D373—22no—
61D373—44no—
62C373#57611yescharacteristic, complemented, Sylow
63#576—3731nomaximal, Sylow
64H(5,𝔽2)—3732no—
65AGL(1,ℤ/8)—3732no—
66AGL(1,ℤ/8)—3734no—
67#135—3732no—
68#135D37311yescharacteristic, complemented
69C2×D8—3732no—
70C2×D8—3731no—
71#131—3731no—
72#41—3731no—
73#41—3734no—
74#41—7462no—
75#41C2×D37312yescomplemented
76C2×D4—3734no—
77C2×D4—3732no—
78C2×D4—7462no—
79C2×D4—7464no—
80Q16C2×D37311yescharacteristic, complemented
81SD16—3734no—
82SD16C2×D37312yescomplemented
83D8—3734no—
84D8—3732no—
85D8—3732no—
86D8C2×D37311yescharacteristic, complemented
87M16—3731no—
88M16—3732no—
89C2×C8—3732no—
90C2×C8C2×D37311yescharacteristic, complemented
91C23—7464no—
92C23—7462no—
93Q8—3731no—
94Q8C22×D37312yes—
95D4—22no—
96D4—3732no—
97D4—3731no—
98D4—3734no—
99D4—7464no—
100D4—7464no—
101D4—7462no—
102D4C22×D37312yes—
103C2×C4—22no—
104C2×C4—3732no—
105C2×C4—7464no—
106C2×C4C22×D37311yescharacteristic
107C8—3732no—
108C8C22×D37311yescharacteristic
109C8C22×D37311yescharacteristic
110C22—22no—
111C22—3732no—
112C22—29842no—
113C22—29844no—
114C22—7464no—
115C22D4×D37311yescharacteristic
116C4—22no—
117C4—3732no—
118C4D4×D37311yescharacteristic
119C4C23×D37311yescharacteristic
120C2—21no—
121C2—42no—
122C2—14924no—
123C2—7462no—
124C2C2×D4×D37311yescharacteristic
subgroupG/H
centerC2C2×D4×D373
commutator, cosocleC4×C373C24
FrattiniC4C23×D373
Fitting#135×C373C2
socleC2×C373C22×D4
hypercenter#135D373
hypocenterC373#576
LCSG ▷ C4×C373 ▷ C2×C373 ▷ C373
UCSC1 ◁ C2 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #26045838C2semidirect
2. #26045819C2semidirect
3. #26045817C2semidirect
4. #26045815C2semidirect
5. C2×D2984C2semidirect
6. D8×D373C2semidirect
7. #26045798C2semidirect
8. #135×C373C2semidirect
9. #20238611C22semidirect
13. C2×D1492C22semidirect
15. D4×D373C22semidirect
16. #20238597C22semidirect
17. D2984C22semidirect
18. D2984C22semidirect
19. #20238595C22semidirect
20. #20238594C22semidirect
21. #20238593C22semidirect
22. C8×D373C22semidirect
23. #41×C373C22semidirect
24. Q16×C373C22semidirect
25. SD16×C373C22semidirect
26. D8×C373C22semidirect
27. C2×C8×C373C22semidirect
62. C373#576semidirect
68. #135D373semidirect
75. #41C2×D373semidirect
80. Q16C2×D373semidirect
82. SD16C2×D373semidirect
86. D8C2×D373semidirect
90. C2×C8C2×D373semidirect

Maximal subgroups

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

subgroupindex
#260458382
#260458192
#260458172
#260458152
C2×D29842
D8×D3732
#260457982
#135×C3732
#576373