Finite Group Databasebeta

← C3×D3×SD16 #64036

Subgroups — C3×D3×SD16 #64036

Order 288.

146 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 58 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
1C3×D3×Q8C211yesmaximal, characteristic, complemented
2C3×D3×D4C211yesmaximal, characteristic
3C32×SD16C211yesmaximal, characteristic, complemented
4C3×#215C211yesmaximal, characteristic, complemented
5C3×#214C211yesmaximal, characteristic, complemented
6C3×#204C211yesmaximal, characteristic, complemented
7C3×D3×C8C211yesmaximal, characteristic, complemented
8C2×C3×SD16—31nomaximal
9D3×SD16C311yesmaximal, characteristic, direct product factor
10C22×C3×D3—21no—
11C32×Q8C2211yescharacteristic, complemented
12C32×D4C2211yescharacteristic
13C3×#67—21no—
14C3×D12C2211yescharacteristic
15C3×C4×D3—21no—
16C3×C4×D3C2211yescharacteristic
17C3×Dic6—21no—
18C3×Dic6C2211yescharacteristic, complemented
19C32×C8C2211yescharacteristic, complemented
20C3×C3⋊C8C2211yescharacteristic, complemented
21C2×C3×Q8—31no—
22C2×C3×D4—31no—
23D3×Q8C2×C311yescharacteristic, complemented
24D3×D4C2×C311yescharacteristic
25C3×SD16—21no—
26C3×SD16—31no—
27C3×SD16—31no—
28C3×SD16—31no—
29C3×SD16D311yescharacteristic, direct product factor
30C3×SD16C2×C311yescharacteristic, complemented
31C2×C3×C8—31no—
32#215C2×C311yescharacteristic, complemented
33#214C2×C311yescharacteristic, complemented
34#204C2×C311yescharacteristic, complemented
35D3×C8C2×C311yescharacteristic, complemented
36C22×C32—21no—
37C2×C3×D3—21no—
38C2×C3×D3—42no—
39C2×C3×D3D411yescharacteristic
40C32×C4—21no—
41C32×C4C2311yescharacteristic
42C3×Dic3—21no—
43C3×Dic3D411yescharacteristic
44C2×SD16—31noSylow
45C23×C3—61no—
46C22×D3—21no—
47C3×Q8—21no—
48C3×Q8—31no—
49C3×Q8—61no—
50C3×Q8C2×D311yescharacteristic, complemented
51C3×Q8C22×C311yescharacteristic, complemented
52C3×D4—21no—
53C3×D4—31no—
54C3×D4—61no—
55C3×D4C2×D311yescharacteristic
56C3×D4C22×C311yescharacteristic
57C2×C3×C4—31no—
58C2×C3×C4—61no—
59#67—21no—
60D12C22×C311yescharacteristic
61C4×D3—21no—
62C4×D3C22×C311yescharacteristic
63Dic6—21no—
64Dic6C22×C311yescharacteristic, complemented
65C3×C8—21no—
66C3×C8—31no—
67C3×C8C2×D311yescharacteristic, complemented
68C3×C8C22×C311yescharacteristic, complemented
69C3⋊C8C22×C311yescharacteristic, complemented
70C2×C32—41no—
71C2×C32C2×D411yescharacteristic
72C3×D3—41no—
73C3×D3SD1612yesdirect product factor
74C2×Q8—31no—
75C2×D4—31no—
76SD16—31no—
77SD16—31no—
78SD16—31no—
79SD16C3×D311yescharacteristic, direct product factor
80C2×C8—31no—
81C22×C3—21no—
82C22×C3—21no—
83C22×C3—31no—
84C22×C3—41no—
85C22×C3—61no—
86C22×C3—122no—
87C2×D3—21no—
88C2×D3—42no—
89C2×D3C3×D411yescharacteristic
90C3×C4—21no—
91C3×C4—21no—
92C3×C4—21no—
93C3×C4—31no—
94C3×C4—41no—
95C3×C4—61no—
96C3×C4C22×D311yescharacteristic
97C3×C4C23×C311yescharacteristic
98Dic3—21no—
99Dic3C3×D411yescharacteristic
100C32C2×SD1611yescharacteristic, complemented, Sylow
101C23—61no—
102Q8—31no—
103Q8—61no—
104Q8C2×C3×D311yescharacteristic, complemented
105D4—31no—
106D4—61no—
107D4C2×C3×D311yescharacteristic
108C2×C4—31no—
109C2×C4—61no—
110C8—31no—
111C8C2×C3×D311yescharacteristic, complemented
112C2×C3—21no—
113C2×C3—32no—
114C2×C3—41no—
115C2×C3—41no—
116C2×C3—81no—
117C2×C3—121no—
118C2×C3D3×D411yescharacteristic
119C2×C3C2×C3×D411yescharacteristic
120D3—41no—
121D3C3×SD1612yesdirect product factor
122C22—21no—
123C22—31no—
124C22—61no—
125C22—122no—
126C4—21no—
127C4—31no—
128C4—61no—
129C4C22×C3×D311yescharacteristic
130C3—21no—
131C3D3×SD1611yescharacteristic, direct product factor
132C3C2×C3×SD1611yescharacteristic, complemented
133C2—32no—
134C2—41no—
135C2—121no—
136C2C3×D3×D411yescharacteristic
subgroupG/H
centerC2×C3D3×D4
commutator, cosocleC3×C4C23×C3
FrattiniC4C22×C3×D3
FittingC32×SD16C2
socleC2×C32C2×D4
prime radicalC3×D3×D4C2
hypercenterC3×SD16D3
hypocenterC3C2×C3×SD16
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×SD16

Complements

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

NH ≅ G/Ntype
1. C3×D3×Q8C2semidirect
3. C32×SD16C2semidirect
4. C3×#215C2semidirect
5. C3×#214C2semidirect
6. C3×#204C2semidirect
7. C3×D3×C8C2semidirect
9. D3×SD16C3direct (N × H)
11. C32×Q8C22semidirect
18. C3×Dic6C22semidirect
19. C32×C8C22semidirect
20. C3×C3⋊C8C22semidirect
23. D3×Q8C2×C3semidirect
29. C3×SD16D3direct (N × H)
30. C3×SD16C2×C3semidirect
32. #215C2×C3semidirect
33. #214C2×C3semidirect
34. #204C2×C3semidirect
35. D3×C8C2×C3semidirect
50. C3×Q8C2×D3semidirect
51. C3×Q8C22×C3semidirect
64. Dic6C22×C3semidirect
67. C3×C8C2×D3semidirect
68. C3×C8C22×C3semidirect
69. C3⋊C8C22×C3semidirect
73. C3×D3SD16direct (N × H)
79. SD16C3×D3direct (N × H)
100. C32C2×SD16semidirect
104. Q8C2×C3×D3semidirect
111. C8C2×C3×D3semidirect
121. D3C3×SD16direct (N × H)
131. C3D3×SD16direct (N × H)
132. C3C2×C3×SD16semidirect

Maximal subgroups

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

subgroupindex
C3×D3×Q82
C3×D3×D42
C32×SD162
C3×#2152
C3×#2142
C3×#2042
C3×D3×C82
C2×C3×SD163
D3×SD163