Finite Group Databasebeta

← C2×D3×D16 #82016

Subgroups — C2×D3×D16 #82016

Order 384.

440 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C2×D3×D8C212yesmaximal, complemented
2C2×C3×D16C211yesmaximal, characteristic, complemented
3C2×#826C212yesmaximal, complemented
4D3×D16C218yesmaximal, direct product factor
5C2×D48C211yesmaximal, characteristic, complemented
6C2×D3×C16C211yesmaximal, characteristic, complemented
7C22×D16—31nomaximal, Sylow
8C2×D3×D4—22no—
9C2×C3×D8C2212yescomplemented
10C2×#213—22no—
11D3×D8—24no—
12D3×D8C2218yescomplemented
13C2×D24C2212yescomplemented
14C2×D3×C8C2211yescharacteristic
15C3×D16C2214yescomplemented
16C2×C3×C16C2211yescharacteristic, complemented
17#826C2218yescomplemented
18C2×C3⋊C16C2211yescharacteristic, complemented
19D48C2214yescomplemented
20D3×C16C2214yescomplemented
21C22×D8—32no—
22C2×D16—32no—
23C2×D16—38no—
24C2×D16—31no—
25C2×D16D311yescharacteristic, direct product factor
26C22×C16—31no—
27C23×D3—42no—
28C2×C3×D4—22no—
29C2×#67—42no—
30D3×D4—28no—
31D3×D4—44no—
32C2×D12—22no—
33C2×C4×D3D411yescharacteristic
34C3×D8—22no—
35C3×D8C2314yescomplemented
36C2×C3×C8C2311yescharacteristic
37#213—28no—
38C2×C3⋊C8D411yescharacteristic
39D24—22no—
40D24C2314yescomplemented
41D3×C8D412yes—
42D3×C8C2312yes—
43C3×C16C2312yescomplemented
44C3⋊C16C2312yescomplemented
45C22×D4—62no—
46C2×D8—38no—
47C2×D8—32no—
48C2×D8—64no—
49C2×D8—62no—
50C2×D8C2×D312yescomplemented
51C22×C8—31no—
52D16—38no—
53D16—34no—
54D16C2×D314yesdirect product factor
55C2×C16—31no—
56C2×C16—34no—
57C2×C16C2×D311yescharacteristic, complemented
58C23×C3—42no—
59C22×D3—42no—
60C22×D3—48no—
61C22×D3—88no—
62C22×D3D811yescharacteristic
63C3×D4—24no—
64C3×D4—42no—
65C2×C3×C4C2×D411yescharacteristic
66#67—48no—
67C2×Dic3D811yescharacteristic
68D12—24no—
69D12—42no—
70C4×D3D812yes—
71C4×D3C2×D412yes—
72C3×C8C2×D411yescharacteristic
73C3×C8C2411yescharacteristic
74C3⋊C8C2×D412yes—
75C24—122no—
76C2×D4—22no—
77C2×D4—68no—
78C2×D4—62no—
79C2×D4—124no—
80C2×D4—122no—
81C22×C4—31no—
82D8—22no—
83D8—34no—
84D8—68no—
85D8—62no—
86D8C22×D314yescomplemented
87C2×C8—31no—
88C2×C8—32no—
89C2×C8—32no—
90C2×C8C22×D311yescharacteristic
91C16—32no—
92C16C22×D312yescomplemented
93C22×C3—44no—
94C22×C3—84no—
95C22×C3C2×D811yescharacteristic
96C2×D3—44no—
97C2×D3—84no—
98C2×D3—816no—
99C2×D3D1614yesdirect product factor
100C2×D3C2×D812yes—
101C3×C4C2×D811yescharacteristic
102C3×C4C22×D411yescharacteristic
103Dic3C2×D812yes—
104C23—31no—
105C23—42no—
106C23—128no—
107C23—122no—
108C23—248no—
109D4—24no—
110D4—42no—
111D4—64no—
112D4—128no—
113D4—122no—
114C2×C4—31no—
115C2×C4—32no—
116C2×C4—32no—
117C2×C4D3×D411yescharacteristic
118C8—32no—
119C8D3×D411yescharacteristic
120C8C23×D311yescharacteristic
121C2×C3—84no—
122C2×C3C2×D1612yescomplemented
123C2×C3C22×D811yescharacteristic
124D3—84no—
125D3C2×D1614yesdirect product factor
126C22—34no—
127C22—32no—
128C22—44no—
129C22—84no—
130C22—124no—
131C22—2416no—
132C22—244no—
133C22D3×D811yescharacteristic
134C4—32no—
135C4D3×D811yescharacteristic
136C4C2×D3×D411yescharacteristic
137C3C22×D1611yescharacteristic, complemented, Sylow
138C2—34no—
139C2—84no—
140C2—244no—
141C2D3×D1612yesdirect product factor
142C2C2×D3×D811yescharacteristic
subgroupG/H
centerC22D3×D8
commutator, cosocleC3×C8C24
FrattiniC8C23×D3
FittingC2×C3×D16C2
socleC22×C3C2×D8
hypercenterC2×D16D3
hypocenterC3C22×D16
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

Complements

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

NH ≅ G/Ntype
1. C2×D3×D8C2semidirect
2. C2×C3×D16C2semidirect
3. C2×#826C2semidirect
4. D3×D16C2direct (N × H)
5. C2×D48C2semidirect
6. C2×D3×C16C2semidirect
9. C2×C3×D8C22semidirect
12. D3×D8C22semidirect
13. C2×D24C22semidirect
15. C3×D16C22semidirect
16. C2×C3×C16C22semidirect
17. #826C22semidirect
18. C2×C3⋊C16C22semidirect
19. D48C22semidirect
20. D3×C16C22semidirect
25. C2×D16D3direct (N × H)
35. C3×D8C23semidirect
40. D24C23semidirect
43. C3×C16C23semidirect
44. C3⋊C16C23semidirect
50. C2×D8C2×D3semidirect
54. D16C2×D3direct (N × H)
57. C2×C16C2×D3semidirect
86. D8C22×D3semidirect
92. C16C22×D3semidirect
99. C2×D3D16direct (N × H)
122. C2×C3C2×D16semidirect
125. D3C2×D16direct (N × H)
137. C3C22×D16semidirect
141. C2D3×D16direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D3×D82
C2×C3×D162
C2×#8262
D3×D162
C2×D482
C2×D3×C162
C22×D163