Finite Group Databasebeta

← C2×#22582924 #31824293

Subgroups — C2×#22582924 #31824293

Order 17984.

898 conjugacy classes of subgroups; only the 447 normal subgroups are shown.

normal subgroups only

This group has 898 conjugacy classes of subgroups — too many to draw. Only its 447 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#22582924C2116yesmaximal, direct product factor
2C2×#17985138C212yesmaximal, complemented
3C2×#17985137C214yesmaximal, complemented
4C22×C22⋊D281C214yesmaximal, complemented
5C2×D4×D281C214yesmaximal, complemented
6C22×D4×C281C211yesmaximal, characteristic, complemented
7C23×D281C2214yescomplemented
8#17985138C22116yescomplemented
9#17985137C22132yescomplemented
10C2×Dic562C2212yescomplemented
11C2×D1124C2212yescomplemented
12C2×C22⋊D281C2218yescomplemented
13C2×C22⋊D281C2214yescomplemented
14C2×C22⋊D281C22132yescomplemented
15D4×D281C22132yescomplemented
16C22×Dic281C2214yescomplemented
17C2×C4×D281C2214yescomplemented
18C24×C281C2212yescomplemented
19C2×D4×C281C2214yescomplemented
20C2×D4×C281C2218yescomplemented
21C22×C4×C281C2211yescharacteristic, complemented
22C22×D281—48no—
23C22×D281C2314yes—
24C22×D281C23116yescomplemented
25Dic562C2318yescomplemented
26D1124C2318yescomplemented
27C22⋊D281C23132yescomplemented
28C22⋊D281C23116yescomplemented
29C2×Dic281C2314yes—
30C2×Dic281C23116yescomplemented
31C4×D281C23116yescomplemented
32C23×C281—44no—
33C23×C281C2311yescharacteristic
34C23×C281C2314yes—
35C23×C281C2318yescomplemented
36D4×C281C23116yescomplemented
37C2×C4×C281C2312yes—
38C2×C4×C281C2314yescomplemented
39C22×C281—22no—
40C22×C281—28no—
41C22×C281—48no—
42C22×C281C2412yes—
43C22×C281C2418yes—
44C22×C281C2411yescharacteristic
45C2×D281—28no—
46C2×D281—416no—
47C2×D281C2418yes—
48C4×C281C2414yes—
49Dic281C2418yes—
50C2×C281—28no—
51C2×C281—22no—
52C2×C281H(5,𝔽2)12yescomplemented
53C2×C281C2511yescharacteristic
54D281—28no—
55C281C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
56C2×H(5,𝔽2)—2811nomaximal, Sylow
57H(5,𝔽2)—28116no—
58C2×#41—2814no—
59C2×#41—2812no—
60C22×D4—2814no—
61C22×D4—2814no—
62C22×D4D28111yescharacteristic, complemented
63C24—2814no—
64C24C2×D28112yescomplemented
65#41—28132no—
66#41—28116no—
67C2×Q8—2812no—
68C2×D4—2818no—
69C2×D4—2814no—
70C2×D4—28132no—
71C2×D4—28132no—
72C2×D4—2812no—
73C2×D4C2×D28114yescomplemented
74C2×D4C2×D28118yescomplemented
75C22×C4—2814no—
76C22×C4—2814no—
77C22×C4C2×D28111yescharacteristic, complemented
78C23—44no—
79C23—2814no—
80C23—28116no—
81C23—11248no—
82C23C22×D28114yes—
83C23C22×D28111yescharacteristic
84C23C22×D28118yescomplemented
85Q8—2818no—
86D4—28132no—
87D4—28116no—
88D4—2818no—
89D4C22×D281116yescomplemented
90C2×C4—28116no—
91C2×C4—2814no—
92C2×C4—28116no—
93C2×C4C22×D28112yes—
94C2×C4C22×D28114yescomplemented
95C22—22no—
96C22—28no—
97C22—48no—
98C22—2818no—
99C22—5628no—
100C22—112416no—
101C22C23×D28118yes—
102C22C23×D28112yes—
103C22C23×D28111yescharacteristic
104C4—2818no—
105C4C23×D28114yes—
106C2—22no—
107C2—28no—
108C2—5628no—
109C2#2258292412yesdirect product factor
110C2C24×D28111yescharacteristic
subgroupG/H
centerC22C23×D281
commutator, cosocleC2×C281C25
FrattiniC2C24×D281
FittingC22×D4×C281C2
socleC22×C281C24
hypercenterC22×D4D281
hypocenterC281C2×H(5,𝔽2)
LCSG ▷ C2×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #22582924C2direct (N × H)
2. C2×#17985138C2semidirect
3. C2×#17985137C2semidirect
4. C22×C22⋊D281C2semidirect
5. C2×D4×D281C2semidirect
6. C22×D4×C281C2semidirect
7. C23×D281C22semidirect
8. #17985138C22semidirect
9. #17985137C22semidirect
10. C2×Dic562C22semidirect
11. C2×D1124C22semidirect
12. C2×C22⋊D281C22semidirect
13. C2×C22⋊D281C22semidirect
14. C2×C22⋊D281C22semidirect
15. D4×D281C22semidirect
16. C22×Dic281C22semidirect
17. C2×C4×D281C22semidirect
18. C24×C281C22semidirect
19. C2×D4×C281C22semidirect
20. C2×D4×C281C22semidirect
21. C22×C4×C281C22semidirect
24. C22×D281C23semidirect
25. Dic562C23semidirect
26. D1124C23semidirect
27. C22⋊D281C23semidirect
28. C22⋊D281C23semidirect
30. C2×Dic281C23semidirect
31. C4×D281C23semidirect
35. C23×C281C23semidirect
36. D4×C281C23semidirect
38. C2×C4×C281C23semidirect
52. C2×C281H(5,𝔽2)semidirect
55. C281C2×H(5,𝔽2)semidirect
62. C22×D4D281semidirect
64. C24C2×D281semidirect
73. C2×D4C2×D281semidirect
74. C2×D4C2×D281semidirect
77. C22×C4C2×D281semidirect
84. C23C22×D281semidirect
89. D4C22×D281semidirect
94. C2×C4C22×D281semidirect
109. C2#22582924direct (N × H)

Maximal subgroups

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

subgroupindex
#225829242
C2×#179851382
C2×#179851372
C22×C22⋊D2812
C2×D4×D2812
C22×D4×C2812
C2×H(5,𝔽2)281