Finite Group Databasebeta

← D4×D8 #3279

Subgroups — D4×D8 #3279

Order 128.

310 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 104 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×D8C212yesmaximal, complemented
2D42C212yesmaximal, complemented
3#493C211yesmaximal, characteristic, complemented
4#466C212yesmaximal, complemented
5#459C212yesmaximal, complemented
6#447C214yesmaximal, complemented
7C4×D8C211yesmaximal, characteristic, complemented
8C8×D4C211yesmaximal, characteristic, complemented
9C22×D4—22no—
10C22×D4C2214yescomplemented
11C2×D8—28no—
12C2×D8C2211yescharacteristic
13C2×D8C2214yescomplemented
14C2×D8C2212yescomplemented
15C2×D8C2212yescomplemented
16C22×C8C2212yescomplemented
17#127C2212yescomplemented
18#121—22no—
19#121C2214yescomplemented
20#120—24no—
21C4×D4C2211yescharacteristic
22C4×D4C2212yescomplemented
23#107C2211yescharacteristic, complemented
24C4⋊C8C2211yescharacteristic, complemented
25#102C2212yescomplemented
26#102C2214yescomplemented
27C22⋊C8C2212yescomplemented
28C4×C8C2211yescharacteristic, complemented
29C24—24no—
30C2×D4—28no—
31C2×D4—24no—
32C2×D4—24no—
33C2×D4—22no—
34C2×D4—22no—
35C2×D4—44no—
36C2×D4—48no—
37C2×D4D411yescharacteristic
38C2×D4C2314yes—
39C2×D4C2312yes—
40C22×C4—22no—
41C22×C4C2312yes—
42D8—28no—
43D8—24no—
44D8—42no—
45D8D414yesdirect product factor
46C2×C8—24no—
47C2×C8C2311yescharacteristic
48C2×C8C2312yes—
49C2×C8C2311yescharacteristic
50C4⋊C4D411yescharacteristic
51C4⋊C4C2312yes—
52C22⋊C4—22no—
53C22⋊C4—24no—
54C22⋊C4D412yes—
55C42C2311yescharacteristic
56C23—22no—
57C23—24no—
58C23—48no—
59C23—48no—
60C23—84no—
61C23C2×D412yes—
62D4—24no—
63D4—22no—
64D4—24no—
65D4—48no—
66D4—48no—
67D4—44no—
68D4—82no—
69D4D814yesdirect product factor
70D4C2×D414yescomplemented
71C2×C4—22no—
72C2×C4—22no—
73C2×C4—22no—
74C2×C4—44no—
75C2×C4C2×D411yescharacteristic
76C2×C4C2×D412yes—
77C2×C4C2×D411yescharacteristic
78C2×C4C2411yescharacteristic
79C8—22no—
80C8—21no—
81C8C2×D412yescomplemented
82C22—22no—
83C22—22no—
84C22—24no—
85C22—42no—
86C22—42no—
87C22—44no—
88C22—44no—
89C22—44no—
90C22—816no—
91C22C2×D814yescomplemented
92C22C22×D411yescharacteristic
93C4—22no—
94C4—21no—
95C4—42no—
96C4C2×D812yescomplemented
97C4C22×D411yescharacteristic
98C4H(5,𝔽2)11yescharacteristic
99C2—24no—
100C2—44no—
101C2—84no—
102C2D4211yescharacteristic
103C2C22×D811yescharacteristic
104C2#57611yescharacteristic
subgroupG/H
center, socleC22C22×D4
commutator, Frattini, cosocleC2×C4C24
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C4×D4 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×D8C2semidirect
2. D42C2semidirect
3. #493C2semidirect
4. #466C2semidirect
5. #459C2semidirect
6. #447C2semidirect
7. C4×D8C2semidirect
8. C8×D4C2semidirect
10. C22×D4C22semidirect
13. C2×D8C22semidirect
14. C2×D8C22semidirect
15. C2×D8C22semidirect
16. C22×C8C22semidirect
17. #127C22semidirect
19. #121C22semidirect
22. C4×D4C22semidirect
23. #107C22semidirect
24. C4⋊C8C22semidirect
25. #102C22semidirect
26. #102C22semidirect
27. C22⋊C8C22semidirect
28. C4×C8C22semidirect
45. D8D4direct (N × H)
69. D4D8direct (N × H)
70. D4C2×D4semidirect
81. C8C2×D4semidirect
91. C22C2×D8semidirect
96. C4C2×D8semidirect

Maximal subgroups

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

subgroupindex
C22×D82
D422
#4932
#4662
#4592
#4472
C4×D82
C8×D42