Finite Group Databasebeta

← C23×#16864403 #46825684

Subgroups — C23×#16864403 #46825684

Order 34432.

6520 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#16864403C2156yesmaximal, direct product factor
2C23×D1076C213yesmaximal, complemented
3C23×C4×D269C213yesmaximal, complemented
4C23×Q8×C269C211yesmaximal, characteristic, complemented
5C24×D269C2213yes—
6C2×#16864403C221448yesdirect product factor
7C22×D1076C22184yescomplemented
8C23×Dic269C2211yescharacteristic
9C22×C4×D269C22184yescomplemented
10C22×Q8×C269C22128yescomplemented
11C23×C4×C269C2213yes—
12C23×D269—224no—
13C23×D269C23142yes—
14#16864403C231512yesdirect product factor
15C2×D1076C231336yescomplemented
16C22×Dic269C23114yes—
17C2×C4×D269C231336yescomplemented
18C24×C269C2311yescharacteristic
19C2×Q8×C269C231112yescomplemented
20C22×C4×C269C23142yes—
21C22×D269—2168no—
22C22×D269C24184yes—
23D1076C241192yescomplemented
24C2×Dic269C24128yes—
25C4×D269C241192yescomplemented
26C23×C269#4118yescomplemented
27C23×C269C2417yes—
28Q8×C269C24164yescomplemented
29C2×C4×C269C24184yes—
30C22×C269C2×#41128yescomplemented
31C22×C269C2517yes—
32C2×D269—2168no—
33C2×D269C25124yes—
34C4×C269C25124yes—
35Dic269C2518yes—
36C2×C269C22×#41114yescomplemented
37C2×C269C2611yescharacteristic
38D269—224no—
39C269C23×#4111yescharacteristic, complemented, Sylow
40C23×#41—2691nomaximal, Sylow
41C22×#41—26956no—
42C23×Q8D26911yescharacteristic, complemented
43C23×D4—2693no—
44C24×C4—2693no—
45C25—2693no—
46C2×#41—269448no—
47C22×Q8C2×D269128yescomplemented
48C22×D4—26984no—
49C23×C4—2691no—
50C23×C4—26984no—
51C23×C4C2×D26913yes—
52C24—26942no—
53C24—53824no—
54C24C22×D26911yescharacteristic
55#41—269512no—
56C2×Q8C22×D2691112yescomplemented
57C2×D4—269336no—
58C22×C4—26914no—
59C22×C4—269336no—
60C22×C4C22×D269142yes—
61C23—26984no—
62C23—538168no—
63C23#1686440318yesdirect product factor
64C23C23×D26917yes—
65Q8C23×D269164yescomplemented
66D4—269192no—
67C2×C4—26928no—
68C2×C4—269192no—
69C2×C4C23×D269184yes—
70C22—26924no—
71C22—538168no—
72C22C2×#16864403128yesdirect product factor
73C22C24×D26917yes—
74C4—2698no—
75C4C24×D269124yes—
76C2—53824no—
77C2C22×#16864403114yesdirect product factor
78C2C25×D26911yescharacteristic
subgroupG/H
centerC24C22×D269
commutator, cosocleC2×C269C26
FrattiniC2C25×D269
FittingC23×Q8×C269C2
socleC24×C269C23
hypercenterC23×Q8D269
hypocenterC269C23×#41
LCSG ▷ C2×C269 ▷ C269
UCSC1 ◁ C24 ◁ C23×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#16864403C2direct (N × H)
2. C23×D1076C2semidirect
3. C23×C4×D269C2semidirect
4. C23×Q8×C269C2semidirect
6. C2×#16864403C22direct (N × H)
7. C22×D1076C22semidirect
9. C22×C4×D269C22semidirect
10. C22×Q8×C269C22semidirect
14. #16864403C23direct (N × H)
15. C2×D1076C23semidirect
17. C2×C4×D269C23semidirect
19. C2×Q8×C269C23semidirect
23. D1076C24semidirect
25. C4×D269C24semidirect
26. C23×C269#41semidirect
28. Q8×C269C24semidirect
30. C22×C269C2×#41semidirect
36. C2×C269C22×#41semidirect
39. C269C23×#41semidirect
42. C23×Q8D269semidirect
47. C22×Q8C2×D269semidirect
56. C2×Q8C22×D269semidirect
63. C23#16864403direct (N × H)
65. Q8C23×D269semidirect
72. C22C2×#16864403direct (N × H)
77. C2C22×#16864403direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#168644032
C23×D10762
C23×C4×D2692
C23×Q8×C2692
C23×#41269