Finite Group Databasebeta

← C22×#15691358 #27161906

Subgroups — C22×#15691358 #27161906

Order 12608.

890 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15691358C2124yesmaximal, direct product factor
2C22×Dic394C211yesmaximal, characteristic, complemented
3C22×D788C211yesmaximal, characteristic, complemented
4C22×C22⋊D197C212yesmaximal, complemented
5C22×C4×D197C212yesmaximal, complemented
6C23×C4×C197C211yesmaximal, characteristic, complemented
7C23×D197C2212yes—
8#15691358C22164yesdirect product factor
9C2×Dic394C22112yescomplemented
10C2×D788C22112yescomplemented
11C2×C22⋊D197C22124yescomplemented
12C22×Dic197C2212yes—
13C2×C4×D197C22124yescomplemented
14C24×C197C2211yescharacteristic
15C22×C4×C197C2211yescharacteristic
16C22×C4×C197C2211yescharacteristic
17C22×C4×C197C22112yescomplemented
18C22×D197—28no—
19C22×D197C23112yes—
20Dic394C23116yescomplemented
21D788C23116yescomplemented
22C22⋊D197C23132yescomplemented
23C2×Dic197C23112yes—
24C4×D197C23132yescomplemented
25C23×C197—24no—
26C23×C197C2316yes—
27C23×C197C2311yescharacteristic
28C2×C4×C197C2316yes—
29C2×C4×C197C2316yes—
30C2×C4×C197C23116yescomplemented
31C22×C197—212no—
32C22×C197#4114yescomplemented
33C22×C197C2414yes—
34C22×C197C2413yes—
35C2×D197—224no—
36C2×D197C2418yes—
37C4×C197C2414yes—
38C4×C197C2414yes—
39Dic197C2418yes—
40C2×C197—24no—
41C2×C197C2×#4116yescomplemented
42C2×C197C2511yescharacteristic
43D197—28no—
44C197C22×#4111yescharacteristic, complemented, Sylow
45C22×#41—1971nomaximal, Sylow
46C2×#41—19724no—
47C22×Q8—1971no—
48C22×D4—1972no—
49C22×D4—1971no—
50C23×C4—1972no—
51C23×C4D19711yescharacteristic, complemented
52C24—1972no—
53C24C2×D19711yescharacteristic
54#41—19764no—
55C2×Q8—19712no—
56C2×D4—19724no—
57C2×D4—19712no—
58C22×C4—1972no—
59C22×C4—19724no—
60C22×C4C2×D19711yescharacteristic
61C22×C4C2×D19711yescharacteristic
62C22×C4C2×D197112yescomplemented
63C23—24no—
64C23—3948no—
65C23—19712no—
66C23C22×D19716yes—
67C23C22×D19711yescharacteristic
68Q8—19716no—
69D4—19732no—
70D4—19716no—
71C2×C4—19712no—
72C2×C4—19732no—
73C2×C4C22×D19716yes—
74C2×C4C22×D19716yes—
75C2×C4C22×D197116yescomplemented
76C22—212no—
77C22—39424no—
78C22—1978no—
79C22#1569135814yesdirect product factor
80C22C23×D19714yes—
81C22C23×D19713yes—
82C4—1978no—
83C4C23×D19714yes—
84C4C23×D19714yes—
85C2—24no—
86C2—3948no—
87C2C2×#1569135816yesdirect product factor
88C2C24×D19711yescharacteristic
subgroupG/H
centerC22×C4C2×D197
commutator, cosocleC2×C197C25
FrattiniC2C24×D197
FittingC23×C4×C197C2
socleC23×C197C23
hypercenterC23×C4D197
hypocenterC197C22×#41
LCSG ▷ C2×C197 ▷ C197
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×#15691358C2direct (N × H)
2. C22×Dic394C2semidirect
3. C22×D788C2semidirect
4. C22×C22⋊D197C2semidirect
5. C22×C4×D197C2semidirect
6. C23×C4×C197C2semidirect
8. #15691358C22direct (N × H)
9. C2×Dic394C22semidirect
10. C2×D788C22semidirect
11. C2×C22⋊D197C22semidirect
13. C2×C4×D197C22semidirect
17. C22×C4×C197C22semidirect
20. Dic394C23semidirect
21. D788C23semidirect
22. C22⋊D197C23semidirect
24. C4×D197C23semidirect
30. C2×C4×C197C23semidirect
32. C22×C197#41semidirect
41. C2×C197C2×#41semidirect
44. C197C22×#41semidirect
51. C23×C4D197semidirect
62. C22×C4C2×D197semidirect
75. C2×C4C22×D197semidirect
79. C22#15691358direct (N × H)
87. C2C2×#15691358direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156913582
C22×Dic3942
C22×D7882
C22×C22⋊D1972
C22×C4×D1972
C23×C4×C1972
C22×#41197