Finite Group Databasebeta

← D4×D148 #14558169

Subgroups — D4×D148 #14558169

Order 2368.

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×D148C212yesmaximal, complemented
2C2×D4×D37C212yesmaximal, complemented
3#11924533C211yesmaximal, characteristic, complemented
4#11924511C212yesmaximal, complemented
5#11924510C212yesmaximal, complemented
6#11924506C214yesmaximal, complemented
7C4×D148C211yesmaximal, characteristic, complemented
8C4×D4×C37C211yesmaximal, characteristic, complemented
9C23×D37C2214yescomplemented
10C2×D4×C37C2211yescharacteristic
11C22×C4×C37C2212yescomplemented
12C2×C22⋊D37C2214yescomplemented
13D4×D37—28no—
14C2×D148—28no—
15C2×D148C2211yescharacteristic
16C2×D148C2214yescomplemented
17C2×D148C2212yescomplemented
18C2×D148C2212yescomplemented
19C2×D148C2212yescomplemented
20C2×C4×D37C2212yescomplemented
21C4⋊C4×C37C2211yescharacteristic, complemented
22C22⋊C4×C37C2212yescomplemented
23C42×C37C2211yescharacteristic, complemented
24#10596938C2212yescomplemented
25#10596938C2214yescomplemented
26C4⋊Dic37C2211yescharacteristic, complemented
27C23×C37C2312yes—
28C22×D37—28no—
29C22×D37—28no—
30C22×D37—44no—
31C22×D37C2314yes—
32C22×D37C2312yes—
33D4×C37D414yescomplemented
34C2×C4×C37—24no—
35C2×C4×C37C2311yescharacteristic
36C2×C4×C37C2312yes—
37C2×C4×C37C2311yescharacteristic
38C2×C4×C37C2311yescharacteristic
39C22⋊D37—28no—
40C2×Dic37C2312yes—
41D148—28no—
42D148—24no—
43D148—24no—
44D148—42no—
45D148D414yesdirect product factor
46C4×D37—24no—
47C22×C37—22no—
48C22×C37—22no—
49C22×C37C2×D414yescomplemented
50C22×C37C2411yescharacteristic
51C2×D37—22no—
52C2×D37—22no—
53C2×D37—24no—
54C2×D37—24no—
55C2×D37—24no—
56C2×D37—416no—
57C2×D37C2×D414yescomplemented
58C4×C37—22no—
59C4×C37—21no—
60C4×C37C2×D412yescomplemented
61C4×C37C2×D412yescomplemented
62Dic37—22no—
63C2×C37—24no—
64C2×C37C22×D411yescharacteristic
65C2×C37C22×D411yescharacteristic
66C2×C37H(5,𝔽2)11yescharacteristic
67D37—24no—
68D37—44no—
69D42—371nomaximal, Sylow
70C37D4211yescharacteristic, complemented, Sylow
71C22×D4—372no—
72C22×D4—372no—
73#127—371no—
74#121—372no—
75#121—372no—
76#120—374no—
77C4×D4—371no—
78C4×D4D3711yescharacteristic, complemented
79C24—374no—
80C2×D4—374no—
81C2×D4—371no—
82C2×D4—374no—
83C2×D4—372no—
84C2×D4—372no—
85C2×D4—372no—
86C2×D4—748no—
87C2×D4—748no—
88C2×D4C2×D3711yescharacteristic
89C22×C4—372no—
90C22×C4C2×D3712yescomplemented
91C4⋊C4—371no—
92C4⋊C4C2×D3711yescharacteristic, complemented
93C22⋊C4—372no—
94C22⋊C4—374no—
95C22⋊C4C2×D3712yescomplemented
96C42C2×D3711yescharacteristic, complemented
97C23—372no—
98C23—374no—
99C23—748no—
100C23—748no—
101C23—1484no—
102C23C22×D3712yes—
103D4—374no—
104D4—748no—
105D4—748no—
106D4—744no—
107D4—744no—
108D4—1482no—
109D4D14814yesdirect product factor
110C2×C4—24no—
111C2×C4—372no—
112C2×C4—744no—
113C2×C4C22×D3711yescharacteristic
114C2×C4C22×D3712yes—
115C2×C4C22×D3711yescharacteristic
116C2×C4C22×D3711yescharacteristic
117C22—22no—
118C22—22no—
119C22—374no—
120C22—742no—
121C22—742no—
122C22—744no—
123C22—744no—
124C22—744no—
125C22—14816no—
126C22C2×D14814yescomplemented
127C22C23×D3711yescharacteristic
128C4—22no—
129C4—21no—
130C4—742no—
131C4C2×D14812yescomplemented
132C4D4×D3712yescomplemented
133C2—24no—
134C2—744no—
135C2—1484no—
136C2C2×D4×D3711yescharacteristic
137C2C22×D14811yescharacteristic
138C2#1192458211yescharacteristic
subgroupG/H
center, FrattiniC22C23×D37
commutator, socle, cosocleC22×C37C24
FittingC4×D4×C37C2
hypercenterC4×D4D37
hypocenterC37D42
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×D148C2semidirect
2. C2×D4×D37C2semidirect
3. #11924533C2semidirect
4. #11924511C2semidirect
5. #11924510C2semidirect
6. #11924506C2semidirect
7. C4×D148C2semidirect
8. C4×D4×C37C2semidirect
9. C23×D37C22semidirect
11. C22×C4×C37C22semidirect
12. C2×C22⋊D37C22semidirect
16. C2×D148C22semidirect
17. C2×D148C22semidirect
18. C2×D148C22semidirect
19. C2×D148C22semidirect
20. C2×C4×D37C22semidirect
21. C4⋊C4×C37C22semidirect
22. C22⋊C4×C37C22semidirect
23. C42×C37C22semidirect
24. #10596938C22semidirect
25. #10596938C22semidirect
26. C4⋊Dic37C22semidirect
33. D4×C37D4semidirect
45. D148D4direct (N × H)
49. C22×C37C2×D4semidirect
57. C2×D37C2×D4semidirect
60. C4×C37C2×D4semidirect
61. C4×C37C2×D4semidirect
70. C37D42semidirect
78. C4×D4D37semidirect
90. C22×C4C2×D37semidirect
92. C4⋊C4C2×D37semidirect
95. C22⋊C4C2×D37semidirect
96. C42C2×D37semidirect
109. D4D148direct (N × H)
126. C22C2×D148semidirect
131. C4C2×D148semidirect
132. C4D4×D37semidirect

Maximal subgroups

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

subgroupindex
C22×D1482
C2×D4×D372
#119245332
#119245112
#119245102
#119245062
C4×D1482
C4×D4×C372
D4237