Finite Group Databasebeta

← D4×D956 #29505408

Subgroups — D4×D956 #29505408

Order 15296.

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×D956C212yesmaximal, complemented
2C2×D4×D239C212yesmaximal, complemented
3#21439957C211yesmaximal, characteristic, complemented
4#21439935C212yesmaximal, complemented
5#21439934C212yesmaximal, complemented
6#21439930C214yesmaximal, complemented
7C4×D956C211yesmaximal, characteristic, complemented
8C4×D4×C239C211yesmaximal, characteristic, complemented
9C23×D239C2214yescomplemented
10C2×D956—28no—
11C2×D956C2211yescharacteristic
12C2×D956C2214yescomplemented
13C2×D956C2212yescomplemented
14C2×D956C2212yescomplemented
15C2×D956C2212yescomplemented
16C2×C22⋊D239C2214yescomplemented
17D4×D239—28no—
18C2×C4×D239C2212yescomplemented
19C4⋊Dic239C2211yescharacteristic, complemented
20(C2×D239)⋊C4C2212yescomplemented
21(C2×D239)⋊C4C2214yescomplemented
22C2×D4×C239C2211yescharacteristic
23C22×C4×C239C2212yescomplemented
24C4⋊C4×C239C2211yescharacteristic, complemented
25C22⋊C4×C239C2212yescomplemented
26C42×C239C2211yescharacteristic, complemented
27C22×D239—28no—
28C22×D239—28no—
29C22×D239—44no—
30C22×D239C2314yes—
31C22×D239C2312yes—
32D956—28no—
33D956—24no—
34D956—24no—
35D956—42no—
36D956D414yesdirect product factor
37C22⋊D239—28no—
38C2×Dic239C2312yes—
39C4×D239—24no—
40C23×C239C2312yes—
41D4×C239D414yescomplemented
42C2×C4×C239—24no—
43C2×C4×C239C2311yescharacteristic
44C2×C4×C239C2312yes—
45C2×C4×C239C2311yescharacteristic
46C2×C4×C239C2311yescharacteristic
47C22×C239—22no—
48C22×C239—22no—
49C22×C239C2×D414yescomplemented
50C22×C239C2411yescharacteristic
51C2×D239—22no—
52C2×D239—22no—
53C2×D239—24no—
54C2×D239—24no—
55C2×D239—24no—
56C2×D239—416no—
57C2×D239C2×D414yescomplemented
58C4×C239—22no—
59C4×C239—21no—
60C4×C239C2×D412yescomplemented
61C4×C239C2×D412yescomplemented
62Dic239—22no—
63C2×C239—24no—
64C2×C239C22×D411yescharacteristic
65C2×C239C22×D411yescharacteristic
66C2×C239H(5,𝔽2)11yescharacteristic
67D239—24no—
68D239—44no—
69C239D4211yescharacteristic, complemented, Sylow
70D42—2391nomaximal, Sylow
71C22×D4—2392no—
72C22×D4—2392no—
73#127—2391no—
74#121—2392no—
75#121—2392no—
76#120—2394no—
77C4×D4—2391no—
78C4×D4D23911yescharacteristic, complemented
79C24—2394no—
80C2×D4—4788no—
81C2×D4—4788no—
82C2×D4—2394no—
83C2×D4—2392no—
84C2×D4—2394no—
85C2×D4—2392no—
86C2×D4—2392no—
87C2×D4—2391no—
88C2×D4C2×D23911yescharacteristic
89C22×C4—2392no—
90C22×C4C2×D23912yescomplemented
91C4⋊C4—2391no—
92C4⋊C4C2×D23911yescharacteristic, complemented
93C22⋊C4—2392no—
94C22⋊C4—2394no—
95C22⋊C4C2×D23912yescomplemented
96C42C2×D23911yescharacteristic, complemented
97C23—9564no—
98C23—4788no—
99C23—4788no—
100C23—2394no—
101C23—2392no—
102C23C22×D23912yes—
103D4—9562no—
104D4—4788no—
105D4—4788no—
106D4—4784no—
107D4—4784no—
108D4—2394no—
109D4D95614yesdirect product factor
110C2×C4—24no—
111C2×C4—4784no—
112C2×C4—2392no—
113C2×C4C22×D23911yescharacteristic
114C2×C4C22×D23912yes—
115C2×C4C22×D23911yescharacteristic
116C2×C4C22×D23911yescharacteristic
117C22—22no—
118C22—22no—
119C22—95616no—
120C22—4784no—
121C22—4784no—
122C22—4784no—
123C22—4782no—
124C22—4782no—
125C22—2394no—
126C22C2×D95614yescomplemented
127C22C23×D23911yescharacteristic
128C4—21no—
129C4—22no—
130C4—4782no—
131C4D4×D23912yescomplemented
132C4C2×D95612yescomplemented
133C2—24no—
134C2—9564no—
135C2—4784no—
136C2C2×D4×D23911yescharacteristic
137C2C22×D95611yescharacteristic
138C2#2144000611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D239
commutator, socle, cosocleC22×C239C24
FittingC4×D4×C239C2
hypercenterC4×D4D239
hypocenterC239D42
LCSG ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×D956C2semidirect
2. C2×D4×D239C2semidirect
3. #21439957C2semidirect
4. #21439935C2semidirect
5. #21439934C2semidirect
6. #21439930C2semidirect
7. C4×D956C2semidirect
8. C4×D4×C239C2semidirect
9. C23×D239C22semidirect
12. C2×D956C22semidirect
13. C2×D956C22semidirect
14. C2×D956C22semidirect
15. C2×D956C22semidirect
16. C2×C22⋊D239C22semidirect
18. C2×C4×D239C22semidirect
19. C4⋊Dic239C22semidirect
20. (C2×D239)⋊C4C22semidirect
21. (C2×D239)⋊C4C22semidirect
23. C22×C4×C239C22semidirect
24. C4⋊C4×C239C22semidirect
25. C22⋊C4×C239C22semidirect
26. C42×C239C22semidirect
36. D956D4direct (N × H)
41. D4×C239D4semidirect
49. C22×C239C2×D4semidirect
57. C2×D239C2×D4semidirect
60. C4×C239C2×D4semidirect
61. C4×C239C2×D4semidirect
69. C239D42semidirect
78. C4×D4D239semidirect
90. C22×C4C2×D239semidirect
92. C4⋊C4C2×D239semidirect
95. C22⋊C4C2×D239semidirect
96. C42C2×D239semidirect
109. D4D956direct (N × H)
126. C22C2×D956semidirect
131. C4D4×D239semidirect
132. C4C2×D956semidirect

Maximal subgroups

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

subgroupindex
C22×D9562
C2×D4×D2392
#214399572
#214399352
#214399342
#214399302
C4×D9562
C4×D4×C2392
D42239