Finite Group Databasebeta

← C2×#30659753 #45688262

Subgroups — C2×#30659753 #45688262

Order 33344.

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#30659753C2116yesmaximal, direct product factor
2C2×#22552364C212yesmaximal, complemented
3C2×#22552363C214yesmaximal, complemented
4C22×C22⋊D521C214yesmaximal, complemented
5C2×D4×D521C214yesmaximal, complemented
6C22×D4×C521C211yesmaximal, characteristic, complemented
7C23×D521C2214yescomplemented
8#22552364C22116yescomplemented
9#22552363C22132yescomplemented
10C2×Dic1042C2212yescomplemented
11C2×D2084C2212yescomplemented
12C2×C22⋊D521C2218yescomplemented
13C2×C22⋊D521C2214yescomplemented
14C2×C22⋊D521C22132yescomplemented
15D4×D521C22132yescomplemented
16C22×Dic521C2214yescomplemented
17C2×C4×D521C2214yescomplemented
18C24×C521C2212yescomplemented
19C2×D4×C521C2214yescomplemented
20C2×D4×C521C2218yescomplemented
21C22×C4×C521C2211yescharacteristic, complemented
22C22×D521—48no—
23C22×D521C2314yes—
24C22×D521C23116yescomplemented
25Dic1042C2318yescomplemented
26D2084C2318yescomplemented
27C22⋊D521C23132yescomplemented
28C22⋊D521C23116yescomplemented
29C2×Dic521C2314yes—
30C2×Dic521C23116yescomplemented
31C4×D521C23116yescomplemented
32C23×C521—44no—
33C23×C521C2311yescharacteristic
34C23×C521C2314yes—
35C23×C521C2318yescomplemented
36D4×C521C23116yescomplemented
37C2×C4×C521C2312yes—
38C2×C4×C521C2314yescomplemented
39C22×C521—22no—
40C22×C521—28no—
41C22×C521—48no—
42C22×C521C2412yes—
43C22×C521C2418yes—
44C22×C521C2411yescharacteristic
45C2×D521—28no—
46C2×D521—416no—
47C2×D521C2418yes—
48C4×C521C2414yes—
49Dic521C2418yes—
50C2×C521—28no—
51C2×C521—22no—
52C2×C521H(5,𝔽2)12yescomplemented
53C2×C521C2511yescharacteristic
54D521—28no—
55C521C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
56C2×H(5,𝔽2)—5211nomaximal, Sylow
57H(5,𝔽2)—52116no—
58C2×#41—5214no—
59C2×#41—5212no—
60C22×D4—5214no—
61C22×D4—5214no—
62C22×D4D52111yescharacteristic, complemented
63C24—5214no—
64C24C2×D52112yescomplemented
65#41—52132no—
66#41—52116no—
67C2×Q8—5212no—
68C2×D4—5218no—
69C2×D4—5214no—
70C2×D4—52132no—
71C2×D4—52132no—
72C2×D4—5212no—
73C2×D4C2×D52114yescomplemented
74C2×D4C2×D52118yescomplemented
75C22×C4—5214no—
76C22×C4—5214no—
77C22×C4C2×D52111yescharacteristic, complemented
78C23—44no—
79C23—5214no—
80C23—52116no—
81C23—20848no—
82C23C22×D52114yes—
83C23C22×D52111yescharacteristic
84C23C22×D52118yescomplemented
85Q8—5218no—
86D4—52132no—
87D4—52116no—
88D4—5218no—
89D4C22×D521116yescomplemented
90C2×C4—52116no—
91C2×C4—5214no—
92C2×C4—52116no—
93C2×C4C22×D52112yes—
94C2×C4C22×D52114yescomplemented
95C22—22no—
96C22—28no—
97C22—48no—
98C22—5218no—
99C22—10428no—
100C22—208416no—
101C22C23×D52118yes—
102C22C23×D52112yes—
103C22C23×D52111yescharacteristic
104C4—5218no—
105C4C23×D52114yes—
106C2—22no—
107C2—28no—
108C2—10428no—
109C2#3065975312yesdirect product factor
110C2C24×D52111yescharacteristic
subgroupG/H
centerC22C23×D521
commutator, cosocleC2×C521C25
FrattiniC2C24×D521
FittingC22×D4×C521C2
socleC22×C521C24
hypercenterC22×D4D521
hypocenterC521C2×H(5,𝔽2)
LCSG ▷ C2×C521 ▷ C521
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #30659753C2direct (N × H)
2. C2×#22552364C2semidirect
3. C2×#22552363C2semidirect
4. C22×C22⋊D521C2semidirect
5. C2×D4×D521C2semidirect
6. C22×D4×C521C2semidirect
7. C23×D521C22semidirect
8. #22552364C22semidirect
9. #22552363C22semidirect
10. C2×Dic1042C22semidirect
11. C2×D2084C22semidirect
12. C2×C22⋊D521C22semidirect
13. C2×C22⋊D521C22semidirect
14. C2×C22⋊D521C22semidirect
15. D4×D521C22semidirect
16. C22×Dic521C22semidirect
17. C2×C4×D521C22semidirect
18. C24×C521C22semidirect
19. C2×D4×C521C22semidirect
20. C2×D4×C521C22semidirect
21. C22×C4×C521C22semidirect
24. C22×D521C23semidirect
25. Dic1042C23semidirect
26. D2084C23semidirect
27. C22⋊D521C23semidirect
28. C22⋊D521C23semidirect
30. C2×Dic521C23semidirect
31. C4×D521C23semidirect
35. C23×C521C23semidirect
36. D4×C521C23semidirect
38. C2×C4×C521C23semidirect
52. C2×C521H(5,𝔽2)semidirect
55. C521C2×H(5,𝔽2)semidirect
62. C22×D4D521semidirect
64. C24C2×D521semidirect
73. C2×D4C2×D521semidirect
74. C2×D4C2×D521semidirect
77. C22×C4C2×D521semidirect
84. C23C22×D521semidirect
89. D4C22×D521semidirect
94. C2×C4C22×D521semidirect
109. C2#30659753direct (N × H)

Maximal subgroups

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

subgroupindex
#306597532
C2×#225523642
C2×#225523632
C22×C22⋊D5212
C2×D4×D5212
C22×D4×C5212
C2×H(5,𝔽2)521