Finite Group Databasebeta

← C2×#27159429 #38734929

Subgroups — C2×#27159429 #38734929

Order 24896.

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#27159429C2116yesmaximal, direct product factor
2C2×#20261966C212yesmaximal, complemented
3C2×#20261965C214yesmaximal, complemented
4C22×C22⋊D389C214yesmaximal, complemented
5C2×D4×D389C214yesmaximal, complemented
6C22×D4×C389C211yesmaximal, characteristic, complemented
7C23×D389C2214yescomplemented
8#20261966C22116yescomplemented
9#20261965C22132yescomplemented
10C2×Dic778C2212yescomplemented
11C2×D1556C2212yescomplemented
12C2×C22⋊D389C2218yescomplemented
13C2×C22⋊D389C2214yescomplemented
14C2×C22⋊D389C22132yescomplemented
15D4×D389C22132yescomplemented
16C22×Dic389C2214yescomplemented
17C2×C4×D389C2214yescomplemented
18C24×C389C2212yescomplemented
19C2×D4×C389C2214yescomplemented
20C2×D4×C389C2218yescomplemented
21C22×C4×C389C2211yescharacteristic, complemented
22C22×D389—48no—
23C22×D389C2314yes—
24C22×D389C23116yescomplemented
25Dic778C2318yescomplemented
26D1556C2318yescomplemented
27C22⋊D389C23132yescomplemented
28C22⋊D389C23116yescomplemented
29C2×Dic389C2314yes—
30C2×Dic389C23116yescomplemented
31C4×D389C23116yescomplemented
32C23×C389—44no—
33C23×C389C2311yescharacteristic
34C23×C389C2314yes—
35C23×C389C2318yescomplemented
36D4×C389C23116yescomplemented
37C2×C4×C389C2312yes—
38C2×C4×C389C2314yescomplemented
39C22×C389—28no—
40C22×C389—22no—
41C22×C389—48no—
42C22×C389C2412yes—
43C22×C389C2418yes—
44C22×C389C2411yescharacteristic
45C2×D389—28no—
46C2×D389—416no—
47C2×D389C2418yes—
48C4×C389C2414yes—
49Dic389C2418yes—
50C2×C389—28no—
51C2×C389—22no—
52C2×C389H(5,𝔽2)12yescomplemented
53C2×C389C2511yescharacteristic
54D389—28no—
55C389C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
56C2×H(5,𝔽2)—3891nomaximal, Sylow
57H(5,𝔽2)—38916no—
58C2×#41—3894no—
59C2×#41—3892no—
60C22×D4—3894no—
61C22×D4—3894no—
62C22×D4D38911yescharacteristic, complemented
63C24—3894no—
64C24C2×D38912yescomplemented
65#41—38932no—
66#41—38916no—
67C2×Q8—3892no—
68C2×D4—3898no—
69C2×D4—3894no—
70C2×D4—38932no—
71C2×D4—38932no—
72C2×D4—3892no—
73C2×D4C2×D38914yescomplemented
74C2×D4C2×D38918yescomplemented
75C22×C4—3894no—
76C22×C4—3894no—
77C22×C4C2×D38911yescharacteristic, complemented
78C23—44no—
79C23—15568no—
80C23—3894no—
81C23—38916no—
82C23C22×D38914yes—
83C23C22×D38911yescharacteristic
84C23C22×D38918yescomplemented
85Q8—3898no—
86D4—38932no—
87D4—38916no—
88D4—3898no—
89D4C22×D389116yescomplemented
90C2×C4—38916no—
91C2×C4—3894no—
92C2×C4—38916no—
93C2×C4C22×D38912yes—
94C2×C4C22×D38914yescomplemented
95C22—22no—
96C22—28no—
97C22—48no—
98C22—7788no—
99C22—155616no—
100C22—3898no—
101C22C23×D38918yes—
102C22C23×D38912yes—
103C22C23×D38911yescharacteristic
104C4—3898no—
105C4C23×D38914yes—
106C2—22no—
107C2—28no—
108C2—7788no—
109C2#2715942912yesdirect product factor
110C2C24×D38911yescharacteristic
subgroupG/H
centerC22C23×D389
commutator, cosocleC2×C389C25
FrattiniC2C24×D389
FittingC22×D4×C389C2
socleC22×C389C24
hypercenterC22×D4D389
hypocenterC389C2×H(5,𝔽2)
LCSG ▷ C2×C389 ▷ C389
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #27159429C2direct (N × H)
2. C2×#20261966C2semidirect
3. C2×#20261965C2semidirect
4. C22×C22⋊D389C2semidirect
5. C2×D4×D389C2semidirect
6. C22×D4×C389C2semidirect
7. C23×D389C22semidirect
8. #20261966C22semidirect
9. #20261965C22semidirect
10. C2×Dic778C22semidirect
11. C2×D1556C22semidirect
12. C2×C22⋊D389C22semidirect
13. C2×C22⋊D389C22semidirect
14. C2×C22⋊D389C22semidirect
15. D4×D389C22semidirect
16. C22×Dic389C22semidirect
17. C2×C4×D389C22semidirect
18. C24×C389C22semidirect
19. C2×D4×C389C22semidirect
20. C2×D4×C389C22semidirect
21. C22×C4×C389C22semidirect
24. C22×D389C23semidirect
25. Dic778C23semidirect
26. D1556C23semidirect
27. C22⋊D389C23semidirect
28. C22⋊D389C23semidirect
30. C2×Dic389C23semidirect
31. C4×D389C23semidirect
35. C23×C389C23semidirect
36. D4×C389C23semidirect
38. C2×C4×C389C23semidirect
52. C2×C389H(5,𝔽2)semidirect
55. C389C2×H(5,𝔽2)semidirect
62. C22×D4D389semidirect
64. C24C2×D389semidirect
73. C2×D4C2×D389semidirect
74. C2×D4C2×D389semidirect
77. C22×C4C2×D389semidirect
84. C23C22×D389semidirect
89. D4C22×D389semidirect
94. C2×C4C22×D389semidirect
109. C2#27159429direct (N × H)

Maximal subgroups

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

subgroupindex
#271594292
C2×#202619662
C2×#202619652
C22×C22⋊D3892
C2×D4×D3892
C22×D4×C3892
C2×H(5,𝔽2)389