Finite Group Databasebeta

← C2×#13063370 #14583729

Subgroups — C2×#13063370 #14583729

Order 2752.

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#13063370C2116yesmaximal, direct product factor
2C2×#10621898C212yesmaximal, complemented
3C2×#10621900C214yesmaximal, complemented
4C22×C22⋊D43C214yesmaximal, complemented
5C2×D4×D43C214yesmaximal, complemented
6C22×D4×C43C211yesmaximal, characteristic, complemented
7C24×C43C2212yescomplemented
8C23×D43C2214yescomplemented
9C2×D4×C43C2214yescomplemented
10C2×D4×C43C2218yescomplemented
11C22×C4×C43C2211yescharacteristic, complemented
12C2×C22⋊D43C2218yescomplemented
13C2×C22⋊D43C2214yescomplemented
14C2×C22⋊D43C22132yescomplemented
15C22×Dic43C2214yescomplemented
16#10621900C22132yescomplemented
17D4×D43C22132yescomplemented
18#10621898C22116yescomplemented
19C2×D172C2212yescomplemented
20C2×C4×D43C2214yescomplemented
21C2×Dic86C2212yescomplemented
22C23×C43—44no—
23C23×C43C2314yes—
24C23×C43C2311yescharacteristic
25C23×C43C2318yescomplemented
26C22×D43—48no—
27C22×D43C2314yes—
28C22×D43C23116yescomplemented
29D4×C43C23116yescomplemented
30C2×C4×C43C2312yes—
31C2×C4×C43C2314yescomplemented
32C22⋊D43C23116yescomplemented
33C22⋊D43C23132yescomplemented
34C2×Dic43C2314yes—
35C2×Dic43C23116yescomplemented
36D172C2318yescomplemented
37C4×D43C23116yescomplemented
38Dic86C2318yescomplemented
39C22×C43—28no—
40C22×C43—22no—
41C22×C43—48no—
42C22×C43C2418yes—
43C22×C43C2412yes—
44C22×C43C2411yescharacteristic
45C2×D43—28no—
46C2×D43—416no—
47C2×D43C2418yes—
48C4×C43C2414yes—
49Dic43C2418yes—
50C2×C43—28no—
51C2×C43—22no—
52C2×C43H(5,𝔽2)12yescomplemented
53C2×C43C2511yescharacteristic
54D43—28no—
55C2×H(5,𝔽2)—431nomaximal, Sylow
56C43C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
57H(5,𝔽2)—4316no—
58C2×#41—434no—
59C2×#41—432no—
60C22×D4—434no—
61C22×D4—434no—
62C22×D4D4311yescharacteristic, complemented
63C24—434no—
64C24C2×D4312yescomplemented
65#41—4332no—
66#41—4316no—
67C2×Q8—432no—
68C2×D4—438no—
69C2×D4—434no—
70C2×D4—4332no—
71C2×D4—4332no—
72C2×D4—432no—
73C2×D4C2×D4314yescomplemented
74C2×D4C2×D4318yescomplemented
75C22×C4—434no—
76C22×C4—434no—
77C22×C4C2×D4311yescharacteristic, complemented
78C23—44no—
79C23—434no—
80C23—4316no—
81C23—1728no—
82C23C22×D4314yes—
83C23C22×D4311yescharacteristic
84C23C22×D4318yescomplemented
85Q8—438no—
86D4—4332no—
87D4—4316no—
88D4—438no—
89D4C22×D43116yescomplemented
90C2×C4—4316no—
91C2×C4—434no—
92C2×C4—4316no—
93C2×C4C22×D4312yes—
94C2×C4C22×D4314yescomplemented
95C22—22no—
96C22—28no—
97C22—48no—
98C22—438no—
99C22—868no—
100C22—17216no—
101C22C23×D4318yes—
102C22C23×D4312yes—
103C22C23×D4311yescharacteristic
104C4—438no—
105C4C23×D4314yes—
106C2—22no—
107C2—28no—
108C2—868no—
109C2#1306337012yesdirect product factor
110C2C24×D4311yescharacteristic
subgroupG/H
centerC22C23×D43
commutator, cosocleC2×C43C25
FrattiniC2C24×D43
FittingC22×D4×C43C2
socleC22×C43C24
hypercenterC22×D4D43
hypocenterC43C2×H(5,𝔽2)
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #13063370C2direct (N × H)
2. C2×#10621898C2semidirect
3. C2×#10621900C2semidirect
4. C22×C22⋊D43C2semidirect
5. C2×D4×D43C2semidirect
6. C22×D4×C43C2semidirect
7. C24×C43C22semidirect
8. C23×D43C22semidirect
9. C2×D4×C43C22semidirect
10. C2×D4×C43C22semidirect
11. C22×C4×C43C22semidirect
12. C2×C22⋊D43C22semidirect
13. C2×C22⋊D43C22semidirect
14. C2×C22⋊D43C22semidirect
15. C22×Dic43C22semidirect
16. #10621900C22semidirect
17. D4×D43C22semidirect
18. #10621898C22semidirect
19. C2×D172C22semidirect
20. C2×C4×D43C22semidirect
21. C2×Dic86C22semidirect
25. C23×C43C23semidirect
28. C22×D43C23semidirect
29. D4×C43C23semidirect
31. C2×C4×C43C23semidirect
32. C22⋊D43C23semidirect
33. C22⋊D43C23semidirect
35. C2×Dic43C23semidirect
36. D172C23semidirect
37. C4×D43C23semidirect
38. Dic86C23semidirect
52. C2×C43H(5,𝔽2)semidirect
56. C43C2×H(5,𝔽2)semidirect
62. C22×D4D43semidirect
64. C24C2×D43semidirect
73. C2×D4C2×D43semidirect
74. C2×D4C2×D43semidirect
77. C22×C4C2×D43semidirect
84. C23C22×D43semidirect
89. D4C22×D43semidirect
94. C2×C4C22×D43semidirect
109. C2#13063370direct (N × H)

Maximal subgroups

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

subgroupindex
#130633702
C2×#106218982
C2×#106219002
C22×C22⋊D432
C2×D4×D432
C22×D4×C432
C2×H(5,𝔽2)43