Finite Group Databasebeta

← D4×D1916 #44501031

Subgroups — D4×D1916 #44501031

Order 30656.

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×D1916C212yesmaximal, complemented
2C2×D4×D479C212yesmaximal, complemented
3#29506379C211yesmaximal, characteristic, complemented
4#29506357C212yesmaximal, complemented
5#29506356C212yesmaximal, complemented
6#29506352C214yesmaximal, complemented
7C4×D1916C211yesmaximal, characteristic, complemented
8C4×D4×C479C211yesmaximal, characteristic, complemented
9C23×D479C2214yescomplemented
10C2×D1916—28no—
11C2×D1916C2211yescharacteristic
12C2×D1916C2214yescomplemented
13C2×D1916C2212yescomplemented
14C2×D1916C2212yescomplemented
15C2×D1916C2212yescomplemented
16C2×C22⋊D479C2214yescomplemented
17D4×D479—28no—
18C2×C4×D479C2212yescomplemented
19C4⋊Dic479C2211yescharacteristic, complemented
20(C2×D479)⋊C4C2212yescomplemented
21(C2×D479)⋊C4C2214yescomplemented
22C2×D4×C479C2211yescharacteristic
23C22×C4×C479C2212yescomplemented
24C4⋊C4×C479C2211yescharacteristic, complemented
25C22⋊C4×C479C2212yescomplemented
26C42×C479C2211yescharacteristic, complemented
27C22×D479—28no—
28C22×D479—28no—
29C22×D479—44no—
30C22×D479C2314yes—
31C22×D479C2312yes—
32D1916—28no—
33D1916—24no—
34D1916—24no—
35D1916—42no—
36D1916D414yesdirect product factor
37C22⋊D479—28no—
38C2×Dic479C2312yes—
39C4×D479—24no—
40C23×C479C2312yes—
41D4×C479D414yescomplemented
42C2×C4×C479—24no—
43C2×C4×C479C2311yescharacteristic
44C2×C4×C479C2312yes—
45C2×C4×C479C2311yescharacteristic
46C2×C4×C479C2311yescharacteristic
47C22×C479—22no—
48C22×C479—22no—
49C22×C479C2×D414yescomplemented
50C22×C479C2411yescharacteristic
51C2×D479—22no—
52C2×D479—22no—
53C2×D479—24no—
54C2×D479—24no—
55C2×D479—24no—
56C2×D479—416no—
57C2×D479C2×D414yescomplemented
58C4×C479—22no—
59C4×C479—21no—
60C4×C479C2×D412yescomplemented
61C4×C479C2×D412yescomplemented
62Dic479—22no—
63C2×C479—24no—
64C2×C479C22×D411yescharacteristic
65C2×C479C22×D411yescharacteristic
66C2×C479H(5,𝔽2)11yescharacteristic
67D479—24no—
68D479—44no—
69C479D4211yescharacteristic, complemented, Sylow
70D42—4791nomaximal, Sylow
71C22×D4—4792no—
72C22×D4—4792no—
73#127—4791no—
74#121—4792no—
75#121—4792no—
76#120—4794no—
77C4×D4—4791no—
78C4×D4D47911yescharacteristic, complemented
79C24—4794no—
80C2×D4—9588no—
81C2×D4—9588no—
82C2×D4—4794no—
83C2×D4—4792no—
84C2×D4—4794no—
85C2×D4—4792no—
86C2×D4—4792no—
87C2×D4—4791no—
88C2×D4C2×D47911yescharacteristic
89C22×C4—4792no—
90C22×C4C2×D47912yescomplemented
91C4⋊C4—4791no—
92C4⋊C4C2×D47911yescharacteristic, complemented
93C22⋊C4—4792no—
94C22⋊C4—4794no—
95C22⋊C4C2×D47912yescomplemented
96C42C2×D47911yescharacteristic, complemented
97C23—19164no—
98C23—9588no—
99C23—9588no—
100C23—4794no—
101C23—4792no—
102C23C22×D47912yes—
103D4—19162no—
104D4—9588no—
105D4—9588no—
106D4—9584no—
107D4—9584no—
108D4—4794no—
109D4D191614yesdirect product factor
110C2×C4—24no—
111C2×C4—9584no—
112C2×C4—4792no—
113C2×C4C22×D47911yescharacteristic
114C2×C4C22×D47912yes—
115C2×C4C22×D47911yescharacteristic
116C2×C4C22×D47911yescharacteristic
117C22—22no—
118C22—22no—
119C22—191616no—
120C22—9584no—
121C22—9584no—
122C22—9584no—
123C22—9582no—
124C22—9582no—
125C22—4794no—
126C22C2×D191614yescomplemented
127C22C23×D47911yescharacteristic
128C4—22no—
129C4—21no—
130C4—9582no—
131C4D4×D47912yescomplemented
132C4C2×D191612yescomplemented
133C2—24no—
134C2—19164no—
135C2—9584no—
136C2C2×D4×D47911yescharacteristic
137C2C22×D191611yescharacteristic
138C2#2950642811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D479
commutator, socle, cosocleC22×C479C24
FittingC4×D4×C479C2
hypercenterC4×D4D479
hypocenterC479D42
LCSG ▷ C22×C479 ▷ C479
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×D1916C2semidirect
2. C2×D4×D479C2semidirect
3. #29506379C2semidirect
4. #29506357C2semidirect
5. #29506356C2semidirect
6. #29506352C2semidirect
7. C4×D1916C2semidirect
8. C4×D4×C479C2semidirect
9. C23×D479C22semidirect
12. C2×D1916C22semidirect
13. C2×D1916C22semidirect
14. C2×D1916C22semidirect
15. C2×D1916C22semidirect
16. C2×C22⋊D479C22semidirect
18. C2×C4×D479C22semidirect
19. C4⋊Dic479C22semidirect
20. (C2×D479)⋊C4C22semidirect
21. (C2×D479)⋊C4C22semidirect
23. C22×C4×C479C22semidirect
24. C4⋊C4×C479C22semidirect
25. C22⋊C4×C479C22semidirect
26. C42×C479C22semidirect
36. D1916D4direct (N × H)
41. D4×C479D4semidirect
49. C22×C479C2×D4semidirect
57. C2×D479C2×D4semidirect
60. C4×C479C2×D4semidirect
61. C4×C479C2×D4semidirect
69. C479D42semidirect
78. C4×D4D479semidirect
90. C22×C4C2×D479semidirect
92. C4⋊C4C2×D479semidirect
95. C22⋊C4C2×D479semidirect
96. C42C2×D479semidirect
109. D4D1916direct (N × H)
126. C22C2×D1916semidirect
131. C4D4×D479semidirect
132. C4C2×D1916semidirect

Maximal subgroups

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

subgroupindex
C22×D19162
C2×D4×D4792
#295063792
#295063572
#295063562
#295063522
C4×D19162
C4×D4×C4792
D42479