Finite Group Databasebeta

← D4×D1124 #31824099

Subgroups — D4×D1124 #31824099

Order 17984.

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×D1124C212yesmaximal, complemented
2C2×D4×D281C212yesmaximal, complemented
3#22582876C211yesmaximal, characteristic, complemented
4#22582854C212yesmaximal, complemented
5#22582853C212yesmaximal, complemented
6#22582849C214yesmaximal, complemented
7C4×D1124C211yesmaximal, characteristic, complemented
8C4×D4×C281C211yesmaximal, characteristic, complemented
9C23×D281C2214yescomplemented
10C2×D1124—28no—
11C2×D1124C2211yescharacteristic
12C2×D1124C2214yescomplemented
13C2×D1124C2212yescomplemented
14C2×D1124C2212yescomplemented
15C2×D1124C2212yescomplemented
16C2×C22⋊D281C2214yescomplemented
17D4×D281—28no—
18C2×C4×D281C2212yescomplemented
19C4⋊Dic281C2211yescharacteristic, complemented
20#17985115C2212yescomplemented
21#17985115C2214yescomplemented
22C2×D4×C281C2211yescharacteristic
23C22×C4×C281C2212yescomplemented
24C4⋊C4×C281C2211yescharacteristic, complemented
25C22⋊C4×C281C2212yescomplemented
26C42×C281C2211yescharacteristic, complemented
27C22×D281—28no—
28C22×D281—28no—
29C22×D281—44no—
30C22×D281C2314yes—
31C22×D281C2312yes—
32D1124—28no—
33D1124—24no—
34D1124—24no—
35D1124—42no—
36D1124D414yesdirect product factor
37C22⋊D281—28no—
38C2×Dic281C2312yes—
39C4×D281—24no—
40C23×C281C2312yes—
41D4×C281D414yescomplemented
42C2×C4×C281—24no—
43C2×C4×C281C2311yescharacteristic
44C2×C4×C281C2312yes—
45C2×C4×C281C2311yescharacteristic
46C2×C4×C281C2311yescharacteristic
47C22×C281—22no—
48C22×C281—22no—
49C22×C281C2×D414yescomplemented
50C22×C281C2411yescharacteristic
51C2×D281—22no—
52C2×D281—22no—
53C2×D281—24no—
54C2×D281—24no—
55C2×D281—24no—
56C2×D281—416no—
57C2×D281C2×D414yescomplemented
58C4×C281—22no—
59C4×C281—21no—
60C4×C281C2×D412yescomplemented
61C4×C281C2×D412yescomplemented
62Dic281—22no—
63C2×C281—24no—
64C2×C281C22×D411yescharacteristic
65C2×C281C22×D411yescharacteristic
66C2×C281H(5,𝔽2)11yescharacteristic
67D281—24no—
68D281—44no—
69C281D4211yescharacteristic, complemented, Sylow
70D42—2811nomaximal, Sylow
71C22×D4—2812no—
72C22×D4—2812no—
73#127—2811no—
74#121—2812no—
75#121—2812no—
76#120—2814no—
77C4×D4—2811no—
78C4×D4D28111yescharacteristic, complemented
79C24—2814no—
80C2×D4—2814no—
81C2×D4—2811no—
82C2×D4—2814no—
83C2×D4—2812no—
84C2×D4—2812no—
85C2×D4—2812no—
86C2×D4—5628no—
87C2×D4—5628no—
88C2×D4C2×D28111yescharacteristic
89C22×C4—2812no—
90C22×C4C2×D28112yescomplemented
91C4⋊C4—2811no—
92C4⋊C4C2×D28111yescharacteristic, complemented
93C22⋊C4—2812no—
94C22⋊C4—2814no—
95C22⋊C4C2×D28112yescomplemented
96C42C2×D28111yescharacteristic, complemented
97C23—2812no—
98C23—2814no—
99C23—5628no—
100C23—5628no—
101C23—11244no—
102C23C22×D28112yes—
103D4—2814no—
104D4—5628no—
105D4—5628no—
106D4—5624no—
107D4—5624no—
108D4—11242no—
109D4D112414yesdirect product factor
110C2×C4—24no—
111C2×C4—2812no—
112C2×C4—5624no—
113C2×C4C22×D28111yescharacteristic
114C2×C4C22×D28112yes—
115C2×C4C22×D28111yescharacteristic
116C2×C4C22×D28111yescharacteristic
117C22—22no—
118C22—22no—
119C22—2814no—
120C22—5622no—
121C22—5622no—
122C22—5624no—
123C22—5624no—
124C22—5624no—
125C22—112416no—
126C22C2×D112414yescomplemented
127C22C23×D28111yescharacteristic
128C4—22no—
129C4—21no—
130C4—5622no—
131C4D4×D28112yescomplemented
132C4C2×D112412yescomplemented
133C2—24no—
134C2—5624no—
135C2—11244no—
136C2C2×D4×D28111yescharacteristic
137C2C22×D112411yescharacteristic
138C2#2258292511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D281
commutator, socle, cosocleC22×C281C24
FittingC4×D4×C281C2
hypercenterC4×D4D281
hypocenterC281D42
LCSG ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×D1124C2semidirect
2. C2×D4×D281C2semidirect
3. #22582876C2semidirect
4. #22582854C2semidirect
5. #22582853C2semidirect
6. #22582849C2semidirect
7. C4×D1124C2semidirect
8. C4×D4×C281C2semidirect
9. C23×D281C22semidirect
12. C2×D1124C22semidirect
13. C2×D1124C22semidirect
14. C2×D1124C22semidirect
15. C2×D1124C22semidirect
16. C2×C22⋊D281C22semidirect
18. C2×C4×D281C22semidirect
19. C4⋊Dic281C22semidirect
20. #17985115C22semidirect
21. #17985115C22semidirect
23. C22×C4×C281C22semidirect
24. C4⋊C4×C281C22semidirect
25. C22⋊C4×C281C22semidirect
26. C42×C281C22semidirect
36. D1124D4direct (N × H)
41. D4×C281D4semidirect
49. C22×C281C2×D4semidirect
57. C2×D281C2×D4semidirect
60. C4×C281C2×D4semidirect
61. C4×C281C2×D4semidirect
69. C281D42semidirect
78. C4×D4D281semidirect
90. C22×C4C2×D281semidirect
92. C4⋊C4C2×D281semidirect
95. C22⋊C4C2×D281semidirect
96. C42C2×D281semidirect
109. D4D1124direct (N × H)
126. C22C2×D1124semidirect
131. C4D4×D281semidirect
132. C4C2×D1124semidirect

Maximal subgroups

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

subgroupindex
C22×D11242
C2×D4×D2812
#225828762
#225828542
#225828532
#225828492
C4×D11242
C4×D4×C2812
D42281