Finite Group Databasebeta

← D3×#120 #5588

Subgroups — D3×#120 #5588

Order 192.

662 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 131 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
1C24×D3C211yesmaximal, characteristic, complemented
2C2×D3×D4C213yesmaximal, complemented
3C3×#120C211yesmaximal, characteristic, complemented
4#953C211yesmaximal, characteristic, complemented
5#937C213yesmaximal, complemented
6#882C213yesmaximal, complemented
7D3×C22⋊C4C213yesmaximal, complemented
8C2×#120—31nomaximal, Sylow
9C24×C3C2211yescharacteristic, complemented
10C23×D3—212no—
11C23×D3C2213yes—
12C23×D3C2213yescomplemented
13C23×D3C2211yescharacteristic, complemented
14C2×C3×D4C2213yescomplemented
15C2×#67C2213yescomplemented
16C2×#67C2213yescomplemented
17D3×D4—212no—
18C2×D12C2213yescomplemented
19C2×C4×D3C2213yescomplemented
20C3×C22⋊C4C2213yescomplemented
21#217C2213yescomplemented
22(C2×D3)⋊C4C2216yescomplemented
23C25—31no—
24C22×D4—33no—
25#120—31no—
26#120—33no—
27#120—33no—
28#120D311yescharacteristic, direct product factor
29C2×C22⋊C4—33no—
30C23×C3—26no—
31C23×C3C2313yes—
32C23×C3C2311yescharacteristic, complemented
33C22×D3—232no—
34C22×D3—26no—
35C22×D3—212no—
36C22×D3—212no—
37C22×D3—26no—
38C22×D3D4112yescomplemented
39C22×D3C2313yes—
40C22×D3C2311yescharacteristic
41C22×D3C2311yescharacteristic, complemented
42C3×D4—26no—
43C2×C3×C4C2313yescomplemented
44#67—26no—
45#67—26no—
46C2×Dic3C2313yescomplemented
47D12—26no—
48C4×D3—26no—
49C24—33no—
50C24—33no—
51C24—31no—
52C24—612no—
53C24C2×D311yescharacteristic, complemented
54C2×D4—33no—
55C2×D4—33no—
56C2×D4—33no—
57C2×D4—612no—
58C2×D4C2×D313yescomplemented
59C22×C4—33no—
60C22⋊C4—33no—
61C22⋊C4—36no—
62C22⋊C4C2×D313yescomplemented
63C22×C3—28no—
64C22×C3—26no—
65C22×C3—23no—
66C22×C3C2×D416yescomplemented
67C22×C3C2411yescharacteristic
68C2×D3—224no—
69C2×D3—26no—
70C2×D3—224no—
71C2×D3—23no—
72C2×D3—44no—
73C2×D3C2×D416yes—
74C2×D3C2×D416yescomplemented
75C3×C4—23no—
76Dic3—23no—
77C23—26no—
78C23—31no—
79C23—312no—
80C23—33no—
81C23—31no—
82C23—612no—
83C23—612no—
84C23—66no—
85C23—632no—
86C23—66no—
87C23C22×D313yes—
88C23C22×D311yescharacteristic, complemented
89D4—26no—
90D4—66no—
91D4—66no—
92D4—66no—
93C2×C4—33no—
94C2×C4—66no—
95C2×C4C22×D313yescomplemented
96C2×C3—26no—
97C2×C3—41no—
98C2×C3C22×D413yes—
99D3—26no—
100D3—41no—
101D3#12014yesdirect product factor
102C22—28no—
103C22—26no—
104C22—23no—
105C22—36no—
106C22—36no—
107C22—624no—
108C22—624no—
109C22—66no—
110C22—63no—
111C22—124no—
112C22D3×D416yescomplemented
113C22C23×D311yescharacteristic
114C4—23no—
115C4—63no—
116C3C2×#12011yescharacteristic, complemented, Sylow
117C2—26no—
118C2—34no—
119C2—41no—
120C2—66no—
121C2—121no—
122C2C2×D3×D413yes—
subgroupG/H
center, FrattiniC22C23×D3
commutator, socle, cosocleC22×C3C24
FittingC3×#120C2
hypercenter#120D3
hypocenterC3C2×#120
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C24×D3C2semidirect
2. C2×D3×D4C2semidirect
3. C3×#120C2semidirect
4. #953C2semidirect
5. #937C2semidirect
6. #882C2semidirect
7. D3×C22⋊C4C2semidirect
9. C24×C3C22semidirect
12. C23×D3C22semidirect
13. C23×D3C22semidirect
14. C2×C3×D4C22semidirect
15. C2×#67C22semidirect
16. C2×#67C22semidirect
18. C2×D12C22semidirect
19. C2×C4×D3C22semidirect
20. C3×C22⋊C4C22semidirect
21. #217C22semidirect
22. (C2×D3)⋊C4C22semidirect
28. #120D3direct (N × H)
32. C23×C3C23semidirect
38. C22×D3D4semidirect
41. C22×D3C23semidirect
43. C2×C3×C4C23semidirect
46. C2×Dic3C23semidirect
53. C24C2×D3semidirect
58. C2×D4C2×D3semidirect
62. C22⋊C4C2×D3semidirect
66. C22×C3C2×D4semidirect
74. C2×D3C2×D4semidirect
88. C23C22×D3semidirect
95. C2×C4C22×D3semidirect
101. D3#120direct (N × H)
112. C22D3×D4semidirect
116. C3C2×#120semidirect

Maximal subgroups

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

subgroupindex
C24×D32
C2×D3×D42
C3×#1202
#9532
#9372
#8822
D3×C22⋊C42
C2×#1203