Finite Group Databasebeta

← C22×#20263295 #38755928

Subgroups — C22×#20263295 #38755928

Order 25216.

4544 conjugacy classes of subgroups; only the 805 normal subgroups are shown.

normal subgroups only

This group has 4544 conjugacy classes of subgroups — too many to draw. Only its 805 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
1C23×C22⋊D197C213yesmaximal, complemented
2C2×#20263295C2124yesmaximal, direct product factor
3C22×C22⋊Dic197C213yesmaximal, complemented
4C26×C197C211yesmaximal, characteristic, complemented
5C24×D197C2211yescharacteristic, complemented
6C22×C22⋊D197—224no—
7C22×C22⋊D197C22136yescomplemented
8C23×Dic197C2213yescomplemented
9#20263295C22164yesdirect product factor
10C2×C22⋊Dic197C22136yescomplemented
11C25×C197—224no—
12C25×C197C2213yes—
13C25×C197C22112yescomplemented
14C23×D197—212no—
15C23×D197C2316yescomplemented
16C2×C22⋊D197—2144no—
17C2×C22⋊D197C23148yescomplemented
18C22×Dic197—212no—
19C22×Dic197C23118yescomplemented
20C22⋊Dic197C23148yescomplemented
21C24×C197—2128no—
22C24×C197—224no—
23C24×C197—2144no—
24C24×C197D4124yescomplemented
25C24×C197C23118yes—
26C24×C197C2311yescharacteristic
27C24×C197C23116yescomplemented
28C22×D197—236no—
29C22×D197—416no—
30C22×D197C2414yescomplemented
31C22⋊D197—296no—
32C2×Dic197—236no—
33C2×Dic197C24112yescomplemented
34C23×C197—2384no—
35C23×C197—296no—
36C23×C197—272no—
37C23×C197—296no—
38C23×C197C2×D4112yes—
39C23×C197C2×D4172yescomplemented
40C23×C197C24112yes—
41C23×C197C2413yes—
42C22×C197—2128no—
43C22×C197—2144no—
44C22×C197—224no—
45C22×C197#120116yescomplemented
46C22×C197C22×D4118yes—
47C22×C197C22×D4124yescomplemented
48C22×C197C2511yescharacteristic
49C2×D197—212no—
50C2×D197—424no—
51Dic197—212no—
52C2×C197—224no—
53C2×C197C2×#120112yescomplemented
54C2×C197C23×D413yes—
55D197—44no—
56C197C22×#12011yescharacteristic, complemented, Sylow
57C22×#120—1971nomaximal, Sylow
58C26D19711yescharacteristic, complemented
59C23×D4—1973no—
60C2×#120—19724no—
61C22×C22⋊C4—1973no—
62C25—224no—
63C25—1971no—
64C25C2×D19713yes—
65C25C2×D197112yescomplemented
66C22×D4—39424no—
67C22×D4—19736no—
68C23×C4—1973no—
69#120—19764no—
70C2×C22⋊C4—19736no—
71C24—2128no—
72C24—224no—
73C24—2144no—
74C24—39412no—
75C24—1976no—
76C24C22⋊D197124yescomplemented
77C24C22×D197118yes—
78C24C22×D19711yescharacteristic
79C24C22×D197116yescomplemented
80C2×D4—394144no—
81C2×D4—19748no—
82C22×C4—39412no—
83C22×C4—19718no—
84C22⋊C4—19748no—
85C23—2384no—
86C23—296no—
87C23—272no—
88C23—296no—
89C23—78816no—
90C23—39436no—
91C23—1974no—
92C23C2×C22⋊D197112yes—
93C23C2×C22⋊D197172yescomplemented
94C23C23×D197112yes—
95C23C23×D19713yes—
96D4—39496no—
97C2×C4—39436no—
98C2×C4—19712no—
99C22—2128no—
100C22—224no—
101C22—2144no—
102C22—78824no—
103C22—39412no—
104C22#20263295116yesdirect product factor
105C22C22×C22⋊D197118yes—
106C22C22×C22⋊D197124yescomplemented
107C22C24×D19711yescharacteristic
108C4—39412no—
109C2—224no—
110C2—7884no—
111C2C2×#20263295112yesdirect product factor
112C2C23×C22⋊D19713yes—
subgroupG/H
centerC24C22×D197
commutator, cosocleC22×C197C25
FrattiniC22C24×D197
FittingC26×C197C2
socleC24×C197C23
hypercenterC26D197
hypocenterC197C22×#120
LCSG ▷ C22×C197 ▷ C197
UCSC1 ◁ C24 ◁ C26

Complements

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

NH ≅ G/Ntype
1. C23×C22⋊D197C2semidirect
2. C2×#20263295C2direct (N × H)
3. C22×C22⋊Dic197C2semidirect
4. C26×C197C2semidirect
5. C24×D197C22semidirect
7. C22×C22⋊D197C22semidirect
8. C23×Dic197C22semidirect
9. #20263295C22direct (N × H)
10. C2×C22⋊Dic197C22semidirect
13. C25×C197C22semidirect
15. C23×D197C23semidirect
17. C2×C22⋊D197C23semidirect
19. C22×Dic197C23semidirect
20. C22⋊Dic197C23semidirect
24. C24×C197D4semidirect
27. C24×C197C23semidirect
30. C22×D197C24semidirect
33. C2×Dic197C24semidirect
39. C23×C197C2×D4semidirect
45. C22×C197#120semidirect
47. C22×C197C22×D4semidirect
53. C2×C197C2×#120semidirect
56. C197C22×#120semidirect
58. C26D197semidirect
65. C25C2×D197semidirect
76. C24C22⋊D197semidirect
79. C24C22×D197semidirect
93. C23C2×C22⋊D197semidirect
104. C22#20263295direct (N × H)
106. C22C22×C22⋊D197semidirect
111. C2C2×#20263295direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C22⋊D1972
C2×#202632952
C22×C22⋊Dic1972
C26×C1972
C22×#120197