Finite Group Databasebeta

← D4×D1556 #38734735

Subgroups — D4×D1556 #38734735

Order 24896.

428 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 123 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
1C22×D1556C212yesmaximal, complemented
2C2×D4×D389C212yesmaximal, complemented
3#27159381C211yesmaximal, characteristic, complemented
4#27159359C212yesmaximal, complemented
5#27159358C212yesmaximal, complemented
6#27159354C214yesmaximal, complemented
7C4×D1556C211yesmaximal, characteristic, complemented
8C4×D4×C389C211yesmaximal, characteristic, complemented
9C23×D389C2214yescomplemented
10C2×D1556—28no—
11C2×D1556C2211yescharacteristic
12C2×D1556C2214yescomplemented
13C2×D1556C2212yescomplemented
14C2×D1556C2212yescomplemented
15C2×D1556C2212yescomplemented
16C2×C22⋊D389C2214yescomplemented
17D4×D389—28no—
18C2×C4×D389C2212yescomplemented
19C4⋊Dic389C2211yescharacteristic, complemented
20#20261943C2212yescomplemented
21#20261943C2214yescomplemented
22C2×D4×C389C2211yescharacteristic
23C22×C4×C389C2212yescomplemented
24C4⋊C4×C389C2211yescharacteristic, complemented
25C22⋊C4×C389C2212yescomplemented
26C42×C389C2211yescharacteristic, complemented
27C22×D389—28no—
28C22×D389—28no—
29C22×D389—44no—
30C22×D389C2314yes—
31C22×D389C2312yes—
32D1556—28no—
33D1556—24no—
34D1556—24no—
35D1556—42no—
36D1556D414yesdirect product factor
37C22⋊D389—28no—
38C2×Dic389C2312yes—
39C4×D389—24no—
40C23×C389C2312yes—
41D4×C389D414yescomplemented
42C2×C4×C389—24no—
43C2×C4×C389C2311yescharacteristic
44C2×C4×C389C2312yes—
45C2×C4×C389C2311yescharacteristic
46C2×C4×C389C2311yescharacteristic
47C22×C389—22no—
48C22×C389—22no—
49C22×C389C2×D414yescomplemented
50C22×C389C2411yescharacteristic
51C2×D389—22no—
52C2×D389—22no—
53C2×D389—24no—
54C2×D389—24no—
55C2×D389—24no—
56C2×D389—416no—
57C2×D389C2×D414yescomplemented
58C4×C389—22no—
59C4×C389—21no—
60C4×C389C2×D412yescomplemented
61C4×C389C2×D412yescomplemented
62Dic389—22no—
63C2×C389—24no—
64C2×C389C22×D411yescharacteristic
65C2×C389C22×D411yescharacteristic
66C2×C389H(5,𝔽2)11yescharacteristic
67D389—24no—
68D389—44no—
69C389D4211yescharacteristic, complemented, Sylow
70D42—3891nomaximal, Sylow
71C22×D4—3892no—
72C22×D4—3892no—
73#127—3891no—
74#121—3892no—
75#121—3892no—
76#120—3894no—
77C4×D4—3891no—
78C4×D4D38911yescharacteristic, complemented
79C24—3894no—
80C2×D4—7788no—
81C2×D4—7788no—
82C2×D4—3894no—
83C2×D4—3894no—
84C2×D4—3892no—
85C2×D4—3892no—
86C2×D4—3892no—
87C2×D4—3891no—
88C2×D4C2×D38911yescharacteristic
89C22×C4—3892no—
90C22×C4C2×D38912yescomplemented
91C4⋊C4—3891no—
92C4⋊C4C2×D38911yescharacteristic, complemented
93C22⋊C4—3892no—
94C22⋊C4—3894no—
95C22⋊C4C2×D38912yescomplemented
96C42C2×D38911yescharacteristic, complemented
97C23—7788no—
98C23—7788no—
99C23—15564no—
100C23—3894no—
101C23—3892no—
102C23C22×D38912yes—
103D4—7788no—
104D4—7788no—
105D4—7784no—
106D4—7784no—
107D4—15562no—
108D4—3894no—
109D4D155614yesdirect product factor
110C2×C4—24no—
111C2×C4—7784no—
112C2×C4—3892no—
113C2×C4C22×D38911yescharacteristic
114C2×C4C22×D38912yes—
115C2×C4C22×D38911yescharacteristic
116C2×C4C22×D38911yescharacteristic
117C22—22no—
118C22—22no—
119C22—7782no—
120C22—7782no—
121C22—7784no—
122C22—7784no—
123C22—7784no—
124C22—155616no—
125C22—3894no—
126C22C2×D155614yescomplemented
127C22C23×D38911yescharacteristic
128C4—22no—
129C4—21no—
130C4—7782no—
131C4D4×D38912yescomplemented
132C4C2×D155612yescomplemented
133C2—24no—
134C2—7784no—
135C2—15564no—
136C2C2×D4×D38911yescharacteristic
137C2C22×D155611yescharacteristic
138C2#2715943011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D389
commutator, socle, cosocleC22×C389C24
FittingC4×D4×C389C2
hypercenterC4×D4D389
hypocenterC389D42
LCSG ▷ C22×C389 ▷ C389
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×D1556C2semidirect
2. C2×D4×D389C2semidirect
3. #27159381C2semidirect
4. #27159359C2semidirect
5. #27159358C2semidirect
6. #27159354C2semidirect
7. C4×D1556C2semidirect
8. C4×D4×C389C2semidirect
9. C23×D389C22semidirect
12. C2×D1556C22semidirect
13. C2×D1556C22semidirect
14. C2×D1556C22semidirect
15. C2×D1556C22semidirect
16. C2×C22⋊D389C22semidirect
18. C2×C4×D389C22semidirect
19. C4⋊Dic389C22semidirect
20. #20261943C22semidirect
21. #20261943C22semidirect
23. C22×C4×C389C22semidirect
24. C4⋊C4×C389C22semidirect
25. C22⋊C4×C389C22semidirect
26. C42×C389C22semidirect
36. D1556D4direct (N × H)
41. D4×C389D4semidirect
49. C22×C389C2×D4semidirect
57. C2×D389C2×D4semidirect
60. C4×C389C2×D4semidirect
61. C4×C389C2×D4semidirect
69. C389D42semidirect
78. C4×D4D389semidirect
90. C22×C4C2×D389semidirect
92. C4⋊C4C2×D389semidirect
95. C22⋊C4C2×D389semidirect
96. C42C2×D389semidirect
109. D4D1556direct (N × H)
126. C22C2×D1556semidirect
131. C4D4×D389semidirect
132. C4C2×D1556semidirect

Maximal subgroups

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

subgroupindex
C22×D15562
C2×D4×D3892
#271593812
#271593592
#271593582
#271593542
C4×D15562
C4×D4×C3892
D42389