Finite Group Databasebeta

← D4×D1132 #31827101

Subgroups — D4×D1132 #31827101

Order 18112.

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×D1132C212yesmaximal, complemented
2C2×D4×D283C212yesmaximal, complemented
3#22583607C211yesmaximal, characteristic, complemented
4#22583585C212yesmaximal, complemented
5#22583584C212yesmaximal, complemented
6#22583580C214yesmaximal, complemented
7C4×D1132C211yesmaximal, characteristic, complemented
8C4×D4×C283C211yesmaximal, characteristic, complemented
9C23×D283C2214yescomplemented
10C2×D1132—28no—
11C2×D1132C2211yescharacteristic
12C2×D1132C2214yescomplemented
13C2×D1132C2212yescomplemented
14C2×D1132C2212yescomplemented
15C2×D1132C2212yescomplemented
16C2×C22⋊D283C2214yescomplemented
17D4×D283—28no—
18C2×C4×D283C2212yescomplemented
19C4⋊Dic283C2211yescharacteristic, complemented
20(C2×D283)⋊C4C2212yescomplemented
21(C2×D283)⋊C4C2214yescomplemented
22C2×D4×C283C2211yescharacteristic
23C22×C4×C283C2212yescomplemented
24C4⋊C4×C283C2211yescharacteristic, complemented
25C22⋊C4×C283C2212yescomplemented
26C42×C283C2211yescharacteristic, complemented
27C22×D283—28no—
28C22×D283—28no—
29C22×D283—44no—
30C22×D283C2314yes—
31C22×D283C2312yes—
32D1132—28no—
33D1132—24no—
34D1132—24no—
35D1132—42no—
36D1132D414yesdirect product factor
37C22⋊D283—28no—
38C2×Dic283C2312yes—
39C4×D283—24no—
40C23×C283C2312yes—
41D4×C283D414yescomplemented
42C2×C4×C283—24no—
43C2×C4×C283C2311yescharacteristic
44C2×C4×C283C2312yes—
45C2×C4×C283C2311yescharacteristic
46C2×C4×C283C2311yescharacteristic
47C22×C283—22no—
48C22×C283—22no—
49C22×C283C2×D414yescomplemented
50C22×C283C2411yescharacteristic
51C2×D283—22no—
52C2×D283—22no—
53C2×D283—24no—
54C2×D283—24no—
55C2×D283—24no—
56C2×D283—416no—
57C2×D283C2×D414yescomplemented
58C4×C283—22no—
59C4×C283—21no—
60C4×C283C2×D412yescomplemented
61C4×C283C2×D412yescomplemented
62Dic283—22no—
63C2×C283—24no—
64C2×C283C22×D411yescharacteristic
65C2×C283C22×D411yescharacteristic
66C2×C283H(5,𝔽2)11yescharacteristic
67D283—24no—
68D283—44no—
69C283D4211yescharacteristic, complemented, Sylow
70D42—2831nomaximal, Sylow
71C22×D4—2832no—
72C22×D4—2832no—
73#127—2831no—
74#121—2832no—
75#121—2832no—
76#120—2834no—
77C4×D4—2831no—
78C4×D4D28311yescharacteristic, complemented
79C24—2834no—
80C2×D4—2834no—
81C2×D4—2831no—
82C2×D4—2834no—
83C2×D4—2832no—
84C2×D4—2832no—
85C2×D4—2832no—
86C2×D4—5668no—
87C2×D4—5668no—
88C2×D4C2×D28311yescharacteristic
89C22×C4—2832no—
90C22×C4C2×D28312yescomplemented
91C4⋊C4—2831no—
92C4⋊C4C2×D28311yescharacteristic, complemented
93C22⋊C4—2832no—
94C22⋊C4—2834no—
95C22⋊C4C2×D28312yescomplemented
96C42C2×D28311yescharacteristic, complemented
97C23—2832no—
98C23—2834no—
99C23—5668no—
100C23—5668no—
101C23—11324no—
102C23C22×D28312yes—
103D4—2834no—
104D4—5668no—
105D4—5668no—
106D4—5664no—
107D4—5664no—
108D4—11322no—
109D4D113214yesdirect product factor
110C2×C4—24no—
111C2×C4—2832no—
112C2×C4—5664no—
113C2×C4C22×D28311yescharacteristic
114C2×C4C22×D28312yes—
115C2×C4C22×D28311yescharacteristic
116C2×C4C22×D28311yescharacteristic
117C22—22no—
118C22—22no—
119C22—2834no—
120C22—5662no—
121C22—5662no—
122C22—5664no—
123C22—5664no—
124C22—5664no—
125C22—113216no—
126C22C2×D113214yescomplemented
127C22C23×D28311yescharacteristic
128C4—22no—
129C4—21no—
130C4—5662no—
131C4D4×D28312yescomplemented
132C4C2×D113212yescomplemented
133C2—24no—
134C2—5664no—
135C2—11324no—
136C2C2×D4×D28311yescharacteristic
137C2C22×D113211yescharacteristic
138C2#2258365611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D283
commutator, socle, cosocleC22×C283C24
FittingC4×D4×C283C2
hypercenterC4×D4D283
hypocenterC283D42
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×D1132C2semidirect
2. C2×D4×D283C2semidirect
3. #22583607C2semidirect
4. #22583585C2semidirect
5. #22583584C2semidirect
6. #22583580C2semidirect
7. C4×D1132C2semidirect
8. C4×D4×C283C2semidirect
9. C23×D283C22semidirect
12. C2×D1132C22semidirect
13. C2×D1132C22semidirect
14. C2×D1132C22semidirect
15. C2×D1132C22semidirect
16. C2×C22⋊D283C22semidirect
18. C2×C4×D283C22semidirect
19. C4⋊Dic283C22semidirect
20. (C2×D283)⋊C4C22semidirect
21. (C2×D283)⋊C4C22semidirect
23. C22×C4×C283C22semidirect
24. C4⋊C4×C283C22semidirect
25. C22⋊C4×C283C22semidirect
26. C42×C283C22semidirect
36. D1132D4direct (N × H)
41. D4×C283D4semidirect
49. C22×C283C2×D4semidirect
57. C2×D283C2×D4semidirect
60. C4×C283C2×D4semidirect
61. C4×C283C2×D4semidirect
69. C283D42semidirect
78. C4×D4D283semidirect
90. C22×C4C2×D283semidirect
92. C4⋊C4C2×D283semidirect
95. C22⋊C4C2×D283semidirect
96. C42C2×D283semidirect
109. D4D1132direct (N × H)
126. C22C2×D1132semidirect
131. C4D4×D283semidirect
132. C4C2×D1132semidirect

Maximal subgroups

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

subgroupindex
C22×D11322
C2×D4×D2832
#225836072
#225835852
#225835842
#225835802
C4×D11322
C4×D4×C2832
D42283