Finite Group Databasebeta

← D32×D4 #64310

Subgroups — D32×D4 #64310

Order 288.

499 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 499 conjugacy classes of subgroups — too many to draw. Only its 122 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×D32C212yesmaximal, complemented
2D4×C3⋊D3C211yesmaximal, characteristic, complemented
3C3×D3×D4C212yesmaximal, complemented
4#3811C212yesmaximal, complemented
5D3×#67C214yesmaximal, complemented
6#3802C211yesmaximal, characteristic, complemented
7D3×D12C212yesmaximal, complemented
8C4×D32C211yesmaximal, characteristic, complemented
9C2×D3×D4—32nomaximal
10C22×C3⋊D3C2212yescomplemented
11C22×C3×D3C2214yescomplemented
12C2×D32—28no—
13C2×D32C2211yescharacteristic
14C2×D32C2214yescomplemented
15C2×D32C2212yescomplemented
16C32×D4C2211yescharacteristic, complemented
17#638C2212yescomplemented
18C4⋊(C3⋊D3)C2211yescharacteristic, complemented
19C4×C3⋊D3C2211yescharacteristic, complemented
20C3×#67C2214yescomplemented
21C3×D12C2212yescomplemented
22C3×C4×D3C2212yescomplemented
23#626C2214yescomplemented
24#625C2212yescomplemented
25#624C2211yescharacteristic, complemented
26D3×Dic3C2212yescomplemented
27C23×D3—34no—
28C2×C3×D4—32no—
29C2×#67—34no—
30D3×D4—34no—
31D3×D4—32no—
32D3×D4—34no—
33D3×D4—32no—
34D3×D4—32no—
35D3×D4—61no—
36D3×D4D312yesdirect product factor
37C2×D12—32no—
38C2×C4×D3—32no—
39C22×C32C2312yescomplemented
40C2×C3⋊D3—24no—
41C2×C3⋊D3C2311yescharacteristic
42C2×C3⋊D3C2312yescomplemented
43C2×C3×D3—28no—
44C2×C3×D3C2312yes—
45C2×C3×D3C2314yescomplemented
46D32—24no—
47D32—28no—
48D32D414yesdirect product factor
49C32×C4C2311yescharacteristic, complemented
50C3⋊Dic3C2311yescharacteristic, complemented
51C3×Dic3C2312yescomplemented
52C22×D4—91noSylow
53C23×C3—34no—
54C22×D3—32no—
55C22×D3—34no—
56C22×D3—34no—
57C22×D3—34no—
58C22×D3—34no—
59C22×D3—62no—
60C22×D3—616no—
61C22×D3C2×D314yescomplemented
62C3×D4—21no—
63C3×D4—34no—
64C3×D4—32no—
65C3×D4C2×D312yescomplemented
66C2×C3×C4—32no—
67#67—34no—
68#67—34no—
69#67—34no—
70#67—62no—
71#67C2×D314yescomplemented
72C2×Dic3—32no—
73D12—34no—
74D12—32no—
75D12—61no—
76D12C2×D312yescomplemented
77C4×D3—32no—
78C4×D3—32no—
79C4×D3—32no—
80C4×D3—61no—
81C4×D3C2×D312yescomplemented
82C2×C32—22no—
83C2×C32C2411yescharacteristic
84C3⋊D3—22no—
85C3⋊D3C2×D412yescomplemented
86C3×D3—24no—
87C3×D3C2×D414yescomplemented
88C24—92no—
89C2×D4—32no—
90C2×D4—92no—
91C2×D4—92no—
92C2×D4—91no—
93C2×D4—94no—
94C2×D4—91no—
95C22×C4—91no—
96C22×C3—22no—
97C22×C3—32no—
98C22×C3—34no—
99C22×C3—68no—
100C22×C3C22×D314yescomplemented
101C2×D3—28no—
102C2×D3—32no—
103C2×D3—38no—
104C2×D3—34no—
105C2×D3—61no—
106C2×D3—62no—
107C2×D3—68no—
108C2×D3—68no—
109C2×D3—68no—
110C2×D3—68no—
111C2×D3—124no—
112C2×D3C22×D312yes—
113C2×D3C22×D314yescomplemented
114C3×C4—21no—
115C3×C4—32no—
116C3×C4C22×D312yescomplemented
117Dic3—32no—
118Dic3—61no—
119Dic3C22×D312yescomplemented
120C32C22×D411yescharacteristic, complemented, Sylow
121C23—34no—
122C23—91no—
123C23—94no—
124C23—92no—
125C23—92no—
126C23—188no—
127D4—34no—
128D4—32no—
129D4—94no—
130D4—92no—
131D4—92no—
132D4—91no—
133D4D3211yescharacteristic, direct product factor
134C2×C4—32no—
135C2×C4—91no—
136C2×C4—92no—
137C2×C4—91no—
138C2×C3—24no—
139C2×C3—21no—
140C2×C3—34no—
141C2×C3—42no—
142C2×C3—64no—
143C2×C3C23×D312yes—
144D3—24no—
145D3—34no—
146D3—62no—
147D3—64no—
148D3—122no—
149D3D3×D414yesdirect product factor
150C22—32no—
151C22—34no—
152C22—68no—
153C22—94no—
154C22—91no—
155C22—92no—
156C22—184no—
157C22—188no—
158C22—184no—
159C22C2×D3212yescomplemented
160C4—32no—
161C4—91no—
162C4C2×D3211yescharacteristic, complemented
163C3—21no—
164C3C2×D3×D412yescomplemented
165C2—22no—
166C2—34no—
167C2—64no—
168C2—92no—
169C2—182no—
170C2C22×D3211yescharacteristic
subgroupG/H
center, FrattiniC2C22×D32
commutator, socle, cosocleC2×C32C24
FittingC32×D4C22
hypercenterD4D32
hypocenterC32C22×D4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ D4

Complements

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

NH ≅ G/Ntype
1. C22×D32C2semidirect
2. D4×C3⋊D3C2semidirect
3. C3×D3×D4C2semidirect
4. #3811C2semidirect
5. D3×#67C2semidirect
6. #3802C2semidirect
7. D3×D12C2semidirect
8. C4×D32C2semidirect
10. C22×C3⋊D3C22semidirect
11. C22×C3×D3C22semidirect
14. C2×D32C22semidirect
15. C2×D32C22semidirect
16. C32×D4C22semidirect
17. #638C22semidirect
18. C4⋊(C3⋊D3)C22semidirect
19. C4×C3⋊D3C22semidirect
20. C3×#67C22semidirect
21. C3×D12C22semidirect
22. C3×C4×D3C22semidirect
23. #626C22semidirect
24. #625C22semidirect
25. #624C22semidirect
26. D3×Dic3C22semidirect
36. D3×D4D3direct (N × H)
39. C22×C32C23semidirect
42. C2×C3⋊D3C23semidirect
45. C2×C3×D3C23semidirect
48. D32D4direct (N × H)
49. C32×C4C23semidirect
50. C3⋊Dic3C23semidirect
51. C3×Dic3C23semidirect
61. C22×D3C2×D3semidirect
65. C3×D4C2×D3semidirect
71. #67C2×D3semidirect
76. D12C2×D3semidirect
81. C4×D3C2×D3semidirect
85. C3⋊D3C2×D4semidirect
87. C3×D3C2×D4semidirect
100. C22×C3C22×D3semidirect
113. C2×D3C22×D3semidirect
116. C3×C4C22×D3semidirect
119. Dic3C22×D3semidirect
120. C32C22×D4semidirect
133. D4D32direct (N × H)
149. D3D3×D4direct (N × H)
159. C22C2×D32semidirect
162. C4C2×D32semidirect
164. C3C2×D3×D4semidirect

Maximal subgroups

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

subgroupindex
C22×D322
D4×C3⋊D32
C3×D3×D42
#38112
D3×#672
#38022
D3×D122
C4×D322
C2×D3×D43