Finite Group Databasebeta

← D4×D1516 #37565880

Subgroups — D4×D1516 #37565880

Order 24256.

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×D1516C212yesmaximal, complemented
2C2×D4×D379C212yesmaximal, complemented
3#27131328C211yesmaximal, characteristic, complemented
4#27131306C212yesmaximal, complemented
5#27131305C212yesmaximal, complemented
6#27131301C214yesmaximal, complemented
7C4×D1516C211yesmaximal, characteristic, complemented
8C4×D4×C379C211yesmaximal, characteristic, complemented
9C23×D379C2214yescomplemented
10C2×D1516—28no—
11C2×D1516C2211yescharacteristic
12C2×D1516C2214yescomplemented
13C2×D1516C2212yescomplemented
14C2×D1516C2212yescomplemented
15C2×D1516C2212yescomplemented
16C2×C22⋊D379C2214yescomplemented
17D4×D379—28no—
18C2×C4×D379C2212yescomplemented
19C4⋊Dic379C2211yescharacteristic, complemented
20(C2×D379)⋊C4C2212yescomplemented
21(C2×D379)⋊C4C2214yescomplemented
22C2×D4×C379C2211yescharacteristic
23C22×C4×C379C2212yescomplemented
24C4⋊C4×C379C2211yescharacteristic, complemented
25C22⋊C4×C379C2212yescomplemented
26C42×C379C2211yescharacteristic, complemented
27C22×D379—28no—
28C22×D379—28no—
29C22×D379—44no—
30C22×D379C2314yes—
31C22×D379C2312yes—
32D1516—28no—
33D1516—24no—
34D1516—24no—
35D1516—42no—
36D1516D414yesdirect product factor
37C22⋊D379—28no—
38C2×Dic379C2312yes—
39C4×D379—24no—
40C23×C379C2312yes—
41D4×C379D414yescomplemented
42C2×C4×C379—24no—
43C2×C4×C379C2311yescharacteristic
44C2×C4×C379C2312yes—
45C2×C4×C379C2311yescharacteristic
46C2×C4×C379C2311yescharacteristic
47C22×C379—22no—
48C22×C379—22no—
49C22×C379C2×D414yescomplemented
50C22×C379C2411yescharacteristic
51C2×D379—22no—
52C2×D379—22no—
53C2×D379—24no—
54C2×D379—24no—
55C2×D379—24no—
56C2×D379—416no—
57C2×D379C2×D414yescomplemented
58C4×C379—22no—
59C4×C379—21no—
60C4×C379C2×D412yescomplemented
61C4×C379C2×D412yescomplemented
62Dic379—22no—
63C2×C379—24no—
64C2×C379C22×D411yescharacteristic
65C2×C379C22×D411yescharacteristic
66C2×C379H(5,𝔽2)11yescharacteristic
67D379—24no—
68D379—44no—
69C379D4211yescharacteristic, complemented, Sylow
70D42—3791nomaximal, Sylow
71C22×D4—3792no—
72C22×D4—3792no—
73#127—3791no—
74#121—3792no—
75#121—3792no—
76#120—3794no—
77C4×D4—3791no—
78C4×D4D37911yescharacteristic, complemented
79C24—3794no—
80C2×D4—3794no—
81C2×D4—3791no—
82C2×D4—3792no—
83C2×D4—3794no—
84C2×D4—3792no—
85C2×D4—3792no—
86C2×D4—7588no—
87C2×D4—7588no—
88C2×D4C2×D37911yescharacteristic
89C22×C4—3792no—
90C22×C4C2×D37912yescomplemented
91C4⋊C4—3791no—
92C4⋊C4C2×D37911yescharacteristic, complemented
93C22⋊C4—3792no—
94C22⋊C4—3794no—
95C22⋊C4C2×D37912yescomplemented
96C42C2×D37911yescharacteristic, complemented
97C23—3792no—
98C23—3794no—
99C23—15164no—
100C23—7588no—
101C23—7588no—
102C23C22×D37912yes—
103D4—3794no—
104D4—15162no—
105D4—7588no—
106D4—7588no—
107D4—7584no—
108D4—7584no—
109D4D151614yesdirect product factor
110C2×C4—24no—
111C2×C4—3792no—
112C2×C4—7584no—
113C2×C4C22×D37911yescharacteristic
114C2×C4C22×D37912yes—
115C2×C4C22×D37911yescharacteristic
116C2×C4C22×D37911yescharacteristic
117C22—22no—
118C22—22no—
119C22—3794no—
120C22—151616no—
121C22—7584no—
122C22—7584no—
123C22—7584no—
124C22—7582no—
125C22—7582no—
126C22C2×D151614yescomplemented
127C22C23×D37911yescharacteristic
128C4—22no—
129C4—21no—
130C4—7582no—
131C4D4×D37912yescomplemented
132C4C2×D151612yescomplemented
133C2—24no—
134C2—15164no—
135C2—7584no—
136C2C2×D4×D37911yescharacteristic
137C2C22×D151611yescharacteristic
138C2#2713137711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D379
commutator, socle, cosocleC22×C379C24
FittingC4×D4×C379C2
hypercenterC4×D4D379
hypocenterC379D42
LCSG ▷ C22×C379 ▷ C379
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×D1516C2semidirect
2. C2×D4×D379C2semidirect
3. #27131328C2semidirect
4. #27131306C2semidirect
5. #27131305C2semidirect
6. #27131301C2semidirect
7. C4×D1516C2semidirect
8. C4×D4×C379C2semidirect
9. C23×D379C22semidirect
12. C2×D1516C22semidirect
13. C2×D1516C22semidirect
14. C2×D1516C22semidirect
15. C2×D1516C22semidirect
16. C2×C22⋊D379C22semidirect
18. C2×C4×D379C22semidirect
19. C4⋊Dic379C22semidirect
20. (C2×D379)⋊C4C22semidirect
21. (C2×D379)⋊C4C22semidirect
23. C22×C4×C379C22semidirect
24. C4⋊C4×C379C22semidirect
25. C22⋊C4×C379C22semidirect
26. C42×C379C22semidirect
36. D1516D4direct (N × H)
41. D4×C379D4semidirect
49. C22×C379C2×D4semidirect
57. C2×D379C2×D4semidirect
60. C4×C379C2×D4semidirect
61. C4×C379C2×D4semidirect
69. C379D42semidirect
78. C4×D4D379semidirect
90. C22×C4C2×D379semidirect
92. C4⋊C4C2×D379semidirect
95. C22⋊C4C2×D379semidirect
96. C42C2×D379semidirect
109. D4D1516direct (N × H)
126. C22C2×D1516semidirect
131. C4D4×D379semidirect
132. C4C2×D1516semidirect

Maximal subgroups

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

subgroupindex
C22×D15162
C2×D4×D3792
#271313282
#271313062
#271313052
#271313012
C4×D15162
C4×D4×C3792
D42379