Finite Group Databasebeta

← D4×D172 #14583535

Subgroups — D4×D172 #14583535

Order 2752.

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×D172C212yesmaximal, complemented
2C2×D4×D43C212yesmaximal, complemented
3#13063322C211yesmaximal, characteristic, complemented
4#13063300C212yesmaximal, complemented
5#13063299C212yesmaximal, complemented
6#13063295C214yesmaximal, complemented
7C4×D172C211yesmaximal, characteristic, complemented
8C4×D4×C43C211yesmaximal, characteristic, complemented
9C23×D43C2214yescomplemented
10C2×D4×C43C2211yescharacteristic
11C22×C4×C43C2212yescomplemented
12C2×C22⋊D43C2214yescomplemented
13D4×D43—28no—
14C2×D172—28no—
15C2×D172C2211yescharacteristic
16C2×D172C2214yescomplemented
17C2×D172C2212yescomplemented
18C2×D172C2212yescomplemented
19C2×D172C2212yescomplemented
20C2×C4×D43C2212yescomplemented
21C4⋊C4×C43C2211yescharacteristic, complemented
22C22⋊C4×C43C2212yescomplemented
23C42×C43C2211yescharacteristic, complemented
24(C2×D43)⋊C4C2212yescomplemented
25(C2×D43)⋊C4C2214yescomplemented
26C4⋊Dic43C2211yescharacteristic, complemented
27C23×C43C2312yes—
28C22×D43—28no—
29C22×D43—28no—
30C22×D43—44no—
31C22×D43C2314yes—
32C22×D43C2312yes—
33D4×C43D414yescomplemented
34C2×C4×C43—24no—
35C2×C4×C43C2311yescharacteristic
36C2×C4×C43C2312yes—
37C2×C4×C43C2311yescharacteristic
38C2×C4×C43C2311yescharacteristic
39C22⋊D43—28no—
40C2×Dic43C2312yes—
41D172—28no—
42D172—24no—
43D172—24no—
44D172—42no—
45D172D414yesdirect product factor
46C4×D43—24no—
47C22×C43—22no—
48C22×C43—22no—
49C22×C43C2×D414yescomplemented
50C22×C43C2411yescharacteristic
51C2×D43—22no—
52C2×D43—22no—
53C2×D43—24no—
54C2×D43—24no—
55C2×D43—24no—
56C2×D43—416no—
57C2×D43C2×D414yescomplemented
58C4×C43—22no—
59C4×C43—21no—
60C4×C43C2×D412yescomplemented
61C4×C43C2×D412yescomplemented
62Dic43—22no—
63C2×C43—24no—
64C2×C43C22×D411yescharacteristic
65C2×C43C22×D411yescharacteristic
66C2×C43H(5,𝔽2)11yescharacteristic
67D43—24no—
68D43—44no—
69D42—431nomaximal, Sylow
70C43D4211yescharacteristic, complemented, Sylow
71C22×D4—432no—
72C22×D4—432no—
73#127—431no—
74#121—432no—
75#121—432no—
76#120—434no—
77C4×D4—431no—
78C4×D4D4311yescharacteristic, complemented
79C24—434no—
80C2×D4—434no—
81C2×D4—431no—
82C2×D4—434no—
83C2×D4—432no—
84C2×D4—432no—
85C2×D4—432no—
86C2×D4—868no—
87C2×D4—868no—
88C2×D4C2×D4311yescharacteristic
89C22×C4—432no—
90C22×C4C2×D4312yescomplemented
91C4⋊C4—431no—
92C4⋊C4C2×D4311yescharacteristic, complemented
93C22⋊C4—432no—
94C22⋊C4—434no—
95C22⋊C4C2×D4312yescomplemented
96C42C2×D4311yescharacteristic, complemented
97C23—432no—
98C23—434no—
99C23—868no—
100C23—868no—
101C23—1724no—
102C23C22×D4312yes—
103D4—434no—
104D4—868no—
105D4—868no—
106D4—864no—
107D4—864no—
108D4—1722no—
109D4D17214yesdirect product factor
110C2×C4—24no—
111C2×C4—432no—
112C2×C4—864no—
113C2×C4C22×D4311yescharacteristic
114C2×C4C22×D4312yes—
115C2×C4C22×D4311yescharacteristic
116C2×C4C22×D4311yescharacteristic
117C22—22no—
118C22—22no—
119C22—434no—
120C22—862no—
121C22—862no—
122C22—864no—
123C22—864no—
124C22—864no—
125C22—17216no—
126C22C2×D17214yescomplemented
127C22C23×D4311yescharacteristic
128C4—22no—
129C4—21no—
130C4—862no—
131C4C2×D17212yescomplemented
132C4D4×D4312yescomplemented
133C2—24no—
134C2—864no—
135C2—1724no—
136C2C2×D4×D4311yescharacteristic
137C2C22×D17211yescharacteristic
138C2#1306337111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D43
commutator, socle, cosocleC22×C43C24
FittingC4×D4×C43C2
hypercenterC4×D4D43
hypocenterC43D42
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×D172C2semidirect
2. C2×D4×D43C2semidirect
3. #13063322C2semidirect
4. #13063300C2semidirect
5. #13063299C2semidirect
6. #13063295C2semidirect
7. C4×D172C2semidirect
8. C4×D4×C43C2semidirect
9. C23×D43C22semidirect
11. C22×C4×C43C22semidirect
12. C2×C22⋊D43C22semidirect
16. C2×D172C22semidirect
17. C2×D172C22semidirect
18. C2×D172C22semidirect
19. C2×D172C22semidirect
20. C2×C4×D43C22semidirect
21. C4⋊C4×C43C22semidirect
22. C22⋊C4×C43C22semidirect
23. C42×C43C22semidirect
24. (C2×D43)⋊C4C22semidirect
25. (C2×D43)⋊C4C22semidirect
26. C4⋊Dic43C22semidirect
33. D4×C43D4semidirect
45. D172D4direct (N × H)
49. C22×C43C2×D4semidirect
57. C2×D43C2×D4semidirect
60. C4×C43C2×D4semidirect
61. C4×C43C2×D4semidirect
70. C43D42semidirect
78. C4×D4D43semidirect
90. C22×C4C2×D43semidirect
92. C4⋊C4C2×D43semidirect
95. C22⋊C4C2×D43semidirect
96. C42C2×D43semidirect
109. D4D172direct (N × H)
126. C22C2×D172semidirect
131. C4C2×D172semidirect
132. C4D4×D43semidirect

Maximal subgroups

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

subgroupindex
C22×D1722
C2×D4×D432
#130633222
#130633002
#130632992
#130632952
C4×D1722
C4×D4×C432
D4243