Finite Group Databasebeta

← D4×SD16 #3281

Subgroups — D4×SD16 #3281

Order 128.

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

normal subgroups only

This group has 273 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×SD16C212yesmaximal, complemented
2D4×Q8C211yesmaximal, characteristic, complemented
3D42C211yesmaximal, characteristic
4#492C211yesmaximal, characteristic, complemented
5#465C212yesmaximal, complemented
6#461C211yesmaximal, characteristic, complemented
7#460C211yesmaximal, characteristic, complemented
8#450C212yesmaximal, complemented
9#448C212yesmaximal, complemented
10C4×SD16C211yesmaximal, characteristic, complemented
11C8×D4C211yesmaximal, characteristic, complemented
12C22×Q8C2212yescomplemented
13C22×D4—21no—
14C22×D4C2212yes—
15C2×SD16—28no—
16C2×SD16C2212yes—
17C2×SD16C2211yescharacteristic
18C2×SD16C2212yescomplemented
19C2×SD16C2212yescomplemented
20C2×SD16C2212yescomplemented
21C22×C8C2212yescomplemented
22C4⋊Q8—21no—
23C4⋊Q8C2211yescharacteristic, complemented
24#127C2211yescharacteristic
25C22⋊Q8—22no—
26C22⋊Q8C2212yescomplemented
27#121—21no—
28#121C2212yes—
29#120—22no—
30C4×Q8C2211yescharacteristic, complemented
31C4×D4—21no—
32C4×D4C2211yescharacteristic
33C4×D4C2211yescharacteristic
34#106C2211yescharacteristic, complemented
35C4⋊C8C2211yescharacteristic, complemented
36#103C2211yescharacteristic, complemented
37#103C2212yescomplemented
38#102C2211yescharacteristic
39#102C2212yescomplemented
40C22⋊C8C2212yescomplemented
41C4×C8C2211yescharacteristic, complemented
42C24—22no—
43C2×Q8—22no—
44C2×Q8—24no—
45C2×Q8—42no—
46C2×Q8C2312yes—
47C2×Q8C2311yescharacteristic
48C2×D4—24no—
49C2×D4—22no—
50C2×D4—22no—
51C2×D4—21no—
52C2×D4—21no—
53C2×D4—42no—
54C2×D4—44no—
55C2×D4D411yescharacteristic
56C2×D4C2312yes—
57C2×D4C2311yescharacteristic
58C22×C4—22no—
59C22×C4—21no—
60C22×C4C2312yes—
61SD16—24no—
62SD16—24no—
63SD16—24no—
64SD16—42no—
65SD16D414yesdirect product factor
66C2×C8—24no—
67C2×C8C2311yescharacteristic
68C2×C8C2312yes—
69C2×C8C2311yescharacteristic
70C4⋊C4—21no—
71C4⋊C4—21no—
72C4⋊C4—21no—
73C4⋊C4—22no—
74C4⋊C4D411yescharacteristic
75C4⋊C4C2311yescharacteristic
76C4⋊C4C2311yescharacteristic
77C22⋊C4—22no—
78C22⋊C4—21no—
79C22⋊C4—22no—
80C22⋊C4D412yes—
81C42—21no—
82C42C2311yescharacteristic
83C23—21no—
84C23—22no—
85C23—44no—
86C23—44no—
87C23—82no—
88C23C2×D412yes—
89Q8—21no—
90Q8—22no—
91Q8—22no—
92Q8—44no—
93Q8C2×D412yescomplemented
94D4—22no—
95D4—21no—
96D4—22no—
97D4—44no—
98D4—44no—
99D4—42no—
100D4—81no—
101D4SD1614yesdirect product factor
102D4C2×D412yes—
103C2×C4—21no—
104C2×C4—22no—
105C2×C4—22no—
106C2×C4—21no—
107C2×C4—21no—
108C2×C4—22no—
109C2×C4—44no—
110C2×C4—42no—
111C2×C4C2×D411yescharacteristic
112C2×C4C2×D412yes—
113C2×C4C2×D411yescharacteristic
114C2×C4C2411yescharacteristic
115C8—22no—
116C8—21no—
117C8C2×D412yescomplemented
118C22—22no—
119C22—22no—
120C22—22no—
121C22—41no—
122C22—41no—
123C22—42no—
124C22—42no—
125C22—42no—
126C22—88no—
127C22C2×SD1614yescomplemented
128C22C22×D411yescharacteristic
129C4—22no—
130C4—22no—
131C4—21no—
132C4—42no—
133C4—41no—
134C4—41no—
135C4C2×SD1612yescomplemented
136C4C22×D411yescharacteristic
137C4H(5,𝔽2)11yescharacteristic
138C2—24no—
139C2—42no—
140C2—82no—
141C2D4211yescharacteristic
142C2C22×SD1611yescharacteristic
143C2#57711yescharacteristic
subgroupG/H
center, socleC22C22×D4
commutator, Frattini, cosocleC2×C4C24
prime radicalD42C2
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×SD16C2semidirect
2. D4×Q8C2semidirect
4. #492C2semidirect
5. #465C2semidirect
6. #461C2semidirect
7. #460C2semidirect
8. #450C2semidirect
9. #448C2semidirect
10. C4×SD16C2semidirect
11. C8×D4C2semidirect
12. C22×Q8C22semidirect
18. C2×SD16C22semidirect
19. C2×SD16C22semidirect
20. C2×SD16C22semidirect
21. C22×C8C22semidirect
23. C4⋊Q8C22semidirect
26. C22⋊Q8C22semidirect
30. C4×Q8C22semidirect
34. #106C22semidirect
35. C4⋊C8C22semidirect
36. #103C22semidirect
37. #103C22semidirect
39. #102C22semidirect
40. C22⋊C8C22semidirect
41. C4×C8C22semidirect
65. SD16D4direct (N × H)
93. Q8C2×D4semidirect
101. D4SD16direct (N × H)
117. C8C2×D4semidirect
127. C22C2×SD16semidirect
135. C4C2×SD16semidirect

Maximal subgroups

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

subgroupindex
C22×SD162
D4×Q82
D422
#4922
#4652
#4612
#4602
#4502
#4482
C4×SD162
C8×D42