Finite Group Databasebeta

← C2×#3415 #62632

Subgroups — C2×#3415 #62632

Order 256.

1063 conjugacy classes of subgroups; only the 479 normal subgroups are shown.

normal subgroups only

This group has 1063 conjugacy classes of subgroups — too many to draw. Only its 479 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×#576C212yesmaximal, complemented
2#3415C2116yesmaximal, direct product factor
3C2×#509C216yesmaximal, complemented
4C2×#508C213yesmaximal, complemented
5C22×D16C213yesmaximal, complemented
6C2×#504C211yesmaximal, characteristic, complemented
7C2×H(5,𝔽2)—22no—
8#576—28no—
9#576C22116yescomplemented
10C2×AGL(1,ℤ/8)—26no—
11C2×#135C2216yescomplemented
12C22×D8C2216yescomplemented
13C2×#131C2211yescharacteristic
14#509C22148yescomplemented
15#508C22124yescomplemented
16C2×Q32C2211yescharacteristic, complemented
17C2×SD32C2216yescomplemented
18C2×D16C2213yescomplemented
19C2×D16C2216yescomplemented
20C2×D16C22124yescomplemented
21#504C2218yescomplemented
22C2×M32C2213yescomplemented
23C22×C16C2213yescomplemented
24H(5,𝔽2)—216no—
25H(5,𝔽2)—48no—
26C2×#41—26no—
27C2×#41—42no—
28C2×#41D411yescharacteristic
29C22×D4—26no—
30C22×D4—46no—
31AGL(1,ℤ/8)—248no—
32#135—212no—
33#135C23124yescomplemented
34C2×Q16C2312yes—
35C2×SD16—26no—
36C2×D8—26no—
37C2×D8—212no—
38C2×D8C2316yes—
39C2×D8C23124yescomplemented
40#131D414yes—
41#131C2314yes—
42C2×M16D413yes—
43C22×C8C2313yes—
44Q32C2314yescomplemented
45SD32C23124yescomplemented
46D16C23112yescomplemented
47D16C23124yescomplemented
48M32C23112yescomplemented
49C2×C16C2311yescharacteristic
50C2×C16C2313yes—
51C2×C16C23112yescomplemented
52C24—46no—
53#41—224no—
54#41—416no—
55#41—412no—
56#41D814yes—
57#41C2×D414yes—
58C2×Q8—22no—
59C2×Q8D811yescharacteristic
60C2×D4—26no—
61C2×D4—224no—
62C2×D4—46no—
63C2×D4—448no—
64C2×D4—46no—
65C2×D4—412no—
66C2×D4D813yes—
67C22×C4—46no—
68C22×C4C2×D413yes—
69Q16—22no—
70Q16C2414yes—
71SD16—224no—
72D8—26no—
73D8—224no—
74D8C24112yes—
75M16C2×D4112yes—
76C2×C8C2×D413yes—
77C2×C8C2×D416yes—
78C2×C8C2411yescharacteristic
79C2×C8C2416yes—
80C16C2412yes—
81C16C2416yes—
82C23—46no—
83C23—424no—
84C23—1612no—
85C23C2×D813yes—
86Q8—24no—
87Q8—42no—
88Q8C2×D814yes—
89D4—212no—
90D4—424no—
91D4—424no—
92D4—46no—
93D4C2×D8112yes—
94C2×C4—42no—
95C2×C4—424no—
96C2×C4C2×D816yes—
97C2×C4C2×D813yes—
98C2×C4C22×D416yes—
99C2×C4C22×D411yescharacteristic
100C8C22×D411yescharacteristic
101C8C22×D416yes—
102C8C2511yescharacteristic
103C22—26no—
104C22—412no—
105C22—812no—
106C22—1624no—
107C22C22×D816yes—
108C22C22×D811yescharacteristic
109C4—44no—
110C4C22×D816yes—
111C4C22×D811yescharacteristic
112C4C23×D411yescharacteristic
113C2—26no—
114C2—812no—
115C2#341512yesdirect product factor
116C2C23×D811yescharacteristic
subgroupG/H
center, socleC22C22×D8
commutator, Frattini, cosocleC8C25
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131 ◁ G
LECSG ▷ C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#576C2semidirect
2. #3415C2direct (N × H)
3. C2×#509C2semidirect
4. C2×#508C2semidirect
5. C22×D16C2semidirect
6. C2×#504C2semidirect
9. #576C22semidirect
11. C2×#135C22semidirect
12. C22×D8C22semidirect
14. #509C22semidirect
15. #508C22semidirect
16. C2×Q32C22semidirect
17. C2×SD32C22semidirect
18. C2×D16C22semidirect
19. C2×D16C22semidirect
20. C2×D16C22semidirect
21. #504C22semidirect
22. C2×M32C22semidirect
23. C22×C16C22semidirect
33. #135C23semidirect
39. C2×D8C23semidirect
44. Q32C23semidirect
45. SD32C23semidirect
46. D16C23semidirect
47. D16C23semidirect
48. M32C23semidirect
51. C2×C16C23semidirect
115. C2#3415direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#5762
#34152
C2×#5092
C2×#5082
C22×D162
C2×#5042