Finite Group Databasebeta

← C2×C4×D32 #64302

Subgroups — C2×C4×D32 #64302

Order 288.

499 conjugacy classes of subgroups; only the 180 normal subgroups are shown.

normal subgroups only

This group has 499 conjugacy classes of subgroups — too many to draw. Only its 180 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×D32C211yesmaximal, characteristic
2C2×C4×C3⋊D3C211yesmaximal, characteristic, complemented
3C2×C3×C4×D3C212yesmaximal, complemented
4C2×#624C211yesmaximal, characteristic, complemented
5C2×D3×Dic3C212yesmaximal, complemented
6C4×D32C218yesmaximal, direct product factor
7C22×C4×D3—32nomaximal
8C22×C3⋊D3C2211yescharacteristic
9C22×C3×D3C2212yes—
10C2×D32C418yesdirect product factor
11C2×D32C2214yes—
12C2×C32×C4C2211yescharacteristic, complemented
13C2×C3⋊Dic3C2211yescharacteristic, complemented
14C4×C3⋊D3C2214yescomplemented
15C2×C3×Dic3C2212yescomplemented
16C3×C4×D3C2218yescomplemented
17#624C2214yescomplemented
18D3×Dic3C2218yescomplemented
19C23×D3—32no—
20C22×C3×C4—32no—
21C22×Dic3—32no—
22C2×C4×D3—32no—
23C2×C4×D3—32no—
24C2×C4×D3—32no—
25C2×C4×D3—316no—
26C2×C4×D3—61no—
27C2×C4×D3D312yesdirect product factor
28C22×C32C2311yescharacteristic
29C2×C3⋊D3C2×C414yescomplemented
30C2×C3⋊D3C2312yes—
31C2×C3×D3C2×C418yescomplemented
32C2×C3×D3C2314yes—
33D32C2×C4116yesdirect product factor
34C32×C4C2312yescomplemented
35C3⋊Dic3C2312yescomplemented
36C3×Dic3C2314yescomplemented
37C23×C4—91noSylow
38C23×C3—32no—
39C22×D3—32no—
40C22×D3—316no—
41C22×D3—38no—
42C22×D3—61no—
43C22×D3C2×D312yes—
44C2×C3×C4—21no—
45C2×C3×C4—32no—
46C2×C3×C4—38no—
47C2×C3×C4C2×D312yescomplemented
48C2×Dic3—32no—
49C2×Dic3—38no—
50C2×Dic3—61no—
51C2×Dic3C2×D312yescomplemented
52C4×D3—38no—
53C4×D3—38no—
54C4×D3—38no—
55C4×D3—64no—
56C4×D3C2×D318yesdirect product factor
57C2×C32C22×C412yescomplemented
58C2×C32C2411yescharacteristic
59C3⋊D3C22×C414yescomplemented
60C3×D3C22×C418yescomplemented
61C24—91no—
62C22×C4—32no—
63C22×C4—91no—
64C22×C4—98no—
65C22×C4—92no—
66C22×C4—91no—
67C22×C3—21no—
68C22×C3—38no—
69C22×C3—34no—
70C22×C3C22×D312yes—
71C2×D3—38no—
72C2×D3—34no—
73C2×D3—332no—
74C2×D3—62no—
75C2×D3—64no—
76C2×D3C4×D318yesdirect product factor
77C2×D3C22×D314yes—
78C3×C4—22no—
79C3×C4—34no—
80C3×C4C22×D314yescomplemented
81Dic3—34no—
82Dic3—62no—
83Dic3C22×D314yescomplemented
84C32C23×C411yescharacteristic, complemented, Sylow
85C23—32no—
86C23—94no—
87C23—98no—
88C23—91no—
89C2×C4—32no—
90C2×C4—38no—
91C2×C4—94no—
92C2×C4—98no—
93C2×C4—91no—
94C2×C4—94no—
95C2×C4D3211yescharacteristic, direct product factor
96C2×C3—21no—
97C2×C3—22no—
98C2×C3—38no—
99C2×C3C2×C4×D314yescomplemented
100C2×C3C23×D312yes—
101D3—38no—
102D3—64no—
103D3C2×C4×D318yesdirect product factor
104C22—34no—
105C22—38no—
106C22—916no—
107C22—92no—
108C22—94no—
109C22C2×D3211yescharacteristic
110C4—34no—
111C4—92no—
112C4C2×D3212yesdirect product factor
113C3—21no—
114C3C22×C4×D312yescomplemented
115C2—38no—
116C2—94no—
117C2C4×D3212yesdirect product factor
118C2C22×D3211yescharacteristic
subgroupG/H
center, hypercenterC2×C4D32
commutator, hypocenterC32C23×C4
FrattiniC2C22×D32
FittingC2×C32×C4C22
socleC22×C32C23
prime radicalC22×D32C2
cosocleC2×C32C24
LCSG ▷ C32
UCSC1 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C3⋊D3C2semidirect
3. C2×C3×C4×D3C2semidirect
4. C2×#624C2semidirect
5. C2×D3×Dic3C2semidirect
6. C4×D32C2direct (N × H)
10. C2×D32C4direct (N × H)
12. C2×C32×C4C22semidirect
13. C2×C3⋊Dic3C22semidirect
14. C4×C3⋊D3C22semidirect
15. C2×C3×Dic3C22semidirect
16. C3×C4×D3C22semidirect
17. #624C22semidirect
18. D3×Dic3C22semidirect
27. C2×C4×D3D3direct (N × H)
29. C2×C3⋊D3C2×C4semidirect
31. C2×C3×D3C2×C4semidirect
33. D32C2×C4direct (N × H)
34. C32×C4C23semidirect
35. C3⋊Dic3C23semidirect
36. C3×Dic3C23semidirect
47. C2×C3×C4C2×D3semidirect
51. C2×Dic3C2×D3semidirect
56. C4×D3C2×D3direct (N × H)
57. C2×C32C22×C4semidirect
59. C3⋊D3C22×C4semidirect
60. C3×D3C22×C4semidirect
76. C2×D3C4×D3direct (N × H)
80. C3×C4C22×D3semidirect
83. Dic3C22×D3semidirect
84. C32C23×C4semidirect
95. C2×C4D32direct (N × H)
99. C2×C3C2×C4×D3semidirect
103. D3C2×C4×D3direct (N × H)
112. C4C2×D32direct (N × H)
114. C3C22×C4×D3semidirect
117. C2C4×D32direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D322
C2×C4×C3⋊D32
C2×C3×C4×D32
C2×#6242
C2×D3×Dic32
C4×D322
C22×C4×D33