Finite Group Databasebeta

← D4×D188 #15689759

Subgroups — D4×D188 #15689759

Order 3008.

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×D188C212yesmaximal, complemented
2C2×D4×D47C212yesmaximal, complemented
3#13094021C211yesmaximal, characteristic, complemented
4#13093999C212yesmaximal, complemented
5#13093998C212yesmaximal, complemented
6#13093994C214yesmaximal, complemented
7C4×D188C211yesmaximal, characteristic, complemented
8C4×D4×C47C211yesmaximal, characteristic, complemented
9C23×D47C2214yescomplemented
10C2×D4×C47C2211yescharacteristic
11C22×C4×C47C2212yescomplemented
12C2×C22⋊D47C2214yescomplemented
13D4×D47—28no—
14C2×D188—28no—
15C2×D188C2211yescharacteristic
16C2×D188C2214yescomplemented
17C2×D188C2212yescomplemented
18C2×D188C2212yescomplemented
19C2×D188C2212yescomplemented
20C2×C4×D47C2212yescomplemented
21C4⋊C4×C47C2211yescharacteristic, complemented
22C22⋊C4×C47C2212yescomplemented
23C42×C47C2211yescharacteristic, complemented
24(C2×D47)⋊C4C2212yescomplemented
25(C2×D47)⋊C4C2214yescomplemented
26C4⋊Dic47C2211yescharacteristic, complemented
27C23×C47C2312yes—
28C22×D47—28no—
29C22×D47—28no—
30C22×D47—44no—
31C22×D47C2314yes—
32C22×D47C2312yes—
33D4×C47D414yescomplemented
34C2×C4×C47—24no—
35C2×C4×C47C2311yescharacteristic
36C2×C4×C47C2312yes—
37C2×C4×C47C2311yescharacteristic
38C2×C4×C47C2311yescharacteristic
39C22⋊D47—28no—
40C2×Dic47C2312yes—
41D188—28no—
42D188—24no—
43D188—24no—
44D188—42no—
45D188D414yesdirect product factor
46C4×D47—24no—
47C22×C47—22no—
48C22×C47—22no—
49C22×C47C2×D414yescomplemented
50C22×C47C2411yescharacteristic
51C2×D47—22no—
52C2×D47—22no—
53C2×D47—24no—
54C2×D47—24no—
55C2×D47—24no—
56C2×D47—416no—
57C2×D47C2×D414yescomplemented
58C4×C47—22no—
59C4×C47—21no—
60C4×C47C2×D412yescomplemented
61C4×C47C2×D412yescomplemented
62Dic47—22no—
63C2×C47—24no—
64C2×C47C22×D411yescharacteristic
65C2×C47C22×D411yescharacteristic
66C2×C47H(5,𝔽2)11yescharacteristic
67D47—24no—
68D47—44no—
69D42—471nomaximal, Sylow
70C47D4211yescharacteristic, complemented, Sylow
71C22×D4—472no—
72C22×D4—472no—
73#127—471no—
74#121—472no—
75#121—472no—
76#120—474no—
77C4×D4—471no—
78C4×D4D4711yescharacteristic, complemented
79C24—474no—
80C2×D4—474no—
81C2×D4—471no—
82C2×D4—474no—
83C2×D4—472no—
84C2×D4—472no—
85C2×D4—472no—
86C2×D4—948no—
87C2×D4—948no—
88C2×D4C2×D4711yescharacteristic
89C22×C4—472no—
90C22×C4C2×D4712yescomplemented
91C4⋊C4—471no—
92C4⋊C4C2×D4711yescharacteristic, complemented
93C22⋊C4—472no—
94C22⋊C4—474no—
95C22⋊C4C2×D4712yescomplemented
96C42C2×D4711yescharacteristic, complemented
97C23—472no—
98C23—474no—
99C23—948no—
100C23—948no—
101C23—1884no—
102C23C22×D4712yes—
103D4—474no—
104D4—948no—
105D4—948no—
106D4—944no—
107D4—944no—
108D4—1882no—
109D4D18814yesdirect product factor
110C2×C4—24no—
111C2×C4—472no—
112C2×C4—944no—
113C2×C4C22×D4711yescharacteristic
114C2×C4C22×D4712yes—
115C2×C4C22×D4711yescharacteristic
116C2×C4C22×D4711yescharacteristic
117C22—22no—
118C22—22no—
119C22—474no—
120C22—942no—
121C22—942no—
122C22—944no—
123C22—944no—
124C22—944no—
125C22—18816no—
126C22C2×D18814yescomplemented
127C22C23×D4711yescharacteristic
128C4—22no—
129C4—21no—
130C4—942no—
131C4C2×D18812yescomplemented
132C4D4×D4712yescomplemented
133C2—24no—
134C2—944no—
135C2—1884no—
136C2C2×D4×D4711yescharacteristic
137C2C22×D18811yescharacteristic
138C2#1309407011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D47
commutator, socle, cosocleC22×C47C24
FittingC4×D4×C47C2
hypercenterC4×D4D47
hypocenterC47D42
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×D188C2semidirect
2. C2×D4×D47C2semidirect
3. #13094021C2semidirect
4. #13093999C2semidirect
5. #13093998C2semidirect
6. #13093994C2semidirect
7. C4×D188C2semidirect
8. C4×D4×C47C2semidirect
9. C23×D47C22semidirect
11. C22×C4×C47C22semidirect
12. C2×C22⋊D47C22semidirect
16. C2×D188C22semidirect
17. C2×D188C22semidirect
18. C2×D188C22semidirect
19. C2×D188C22semidirect
20. C2×C4×D47C22semidirect
21. C4⋊C4×C47C22semidirect
22. C22⋊C4×C47C22semidirect
23. C42×C47C22semidirect
24. (C2×D47)⋊C4C22semidirect
25. (C2×D47)⋊C4C22semidirect
26. C4⋊Dic47C22semidirect
33. D4×C47D4semidirect
45. D188D4direct (N × H)
49. C22×C47C2×D4semidirect
57. C2×D47C2×D4semidirect
60. C4×C47C2×D4semidirect
61. C4×C47C2×D4semidirect
70. C47D42semidirect
78. C4×D4D47semidirect
90. C22×C4C2×D47semidirect
92. C4⋊C4C2×D47semidirect
95. C22⋊C4C2×D47semidirect
96. C42C2×D47semidirect
109. D4D188direct (N × H)
126. C22C2×D188semidirect
131. C4C2×D188semidirect
132. C4D4×D47semidirect

Maximal subgroups

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

subgroupindex
C22×D1882
C2×D4×D472
#130940212
#130939992
#130939982
#130939942
C4×D1882
C4×D4×C472
D4247