Finite Group Databasebeta

← C3×#66889 #11760564

Subgroups — C3×#66889 #11760564

Order 1056.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#4339C211yesmaximal, characteristic
2C3×C11×M16C211yesmaximal, characteristic, complemented
3C3×C4×Dic11C211yesmaximal, characteristic, complemented
4#66889C311yesmaximal, characteristic, direct product factor, Hall
5C2×C3×C4×C11C2211yescharacteristic
6C3×C22⋊D11—21no—
7C2×C3×Dic11—21no—
8C3×D44C411yescharacteristic, complemented
9C3×C4×D11—21no—
10C3×Dic22C411yescharacteristic, complemented
11C3×C8×C11—21no—
12#4339C2×C311yescharacteristic
13C11×M16C2×C311yescharacteristic, complemented
14C4×Dic11C2×C311yescharacteristic, complemented
15C22×C3×C11D411yescharacteristic
16C2×C3×D11—21no—
17C3×C4×C11C2×C411yescharacteristic
18C3×C4×C11D411yescharacteristic
19C3×Dic11—22no—
20C3×Dic11—21no—
21C3×#104—111nomaximal, Hall
22C2×C4×C11C22×C311yescharacteristic
23C22⋊D11—21no—
24C2×Dic11—21no—
25D44C3×C411yescharacteristic, complemented
26C4×D11—21no—
27Dic22C3×C411yescharacteristic, complemented
28C8×C11—21no—
29C2×C3×C11—21no—
30C2×C3×C11C22⋊C411yescharacteristic
31C3×D11—41no—
32C3×#41—111no—
33C3×M16D1111yescharacteristic, complemented
34C3×C42—111no—
35C22×C11C3×D411yescharacteristic
36C2×D11—21no—
37C4×C11C2×C3×C411yescharacteristic
38C4×C11C3×D411yescharacteristic
39Dic11—22no—
40Dic11—21no—
41C3×C11#10411yescharacteristic, complemented, Hall
42#104—111noSylow
43C3×Q8—111no—
44C3×D4—111no—
45C3×D4—221no—
46C2×C3×C4—221no—
47C2×C3×C4—221no—
48C2×C3×C4C2×D1111yescharacteristic
49C3×C8—21no—
50C2×C11—21no—
51C2×C11C3×C22⋊C411yescharacteristic
52D11—41no—
53#41—111no—
54M16C3×D1111yescharacteristic, complemented
55C42—111no—
56C22×C3—221no—
57C22×C3D4411yescharacteristic
58C3×C4—222no—
59C3×C4—221no—
60C3×C4C4×D1111yescharacteristic
61C3×C4C22⋊D1111yescharacteristic
62C11C3×#10411yescharacteristic, complemented, Sylow
63Q8—111no—
64D4—111no—
65D4—221no—
66C2×C4—221no—
67C2×C4—221no—
68C2×C4C2×C3×D1111yescharacteristic
69C8—21no—
70C2×C3—21no—
71C2×C3—441no—
72C2×C3(C2×D11)⋊C411yescharacteristic
73C22—221no—
74C22C3×D4411yescharacteristic
75C4—222no—
76C4—221no—
77C4C3×C4×D1111yescharacteristic
78C4C3×C22⋊D1111yescharacteristic
79C3#6688911yescharacteristic, direct product factor, Sylow
80C2—21no—
81C2—441no—
82C2C3×(C2×D11)⋊C411yescharacteristic
subgroupG/H
centerC3×C4C22⋊D11
commutatorC4×C11C2×C3×C4
FrattiniC2×C4C2×C3×D11
FittingC3×C11×M16C2
socleC2×C3×C11C22⋊C4
prime radicalC3×#4339C2
cosocleC2×C4×C11C22×C3
hypercenterC3×M16D11
hypocenterC11C3×#104
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C3×M16

Complements

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

NH ≅ G/Ntype
2. C3×C11×M16C2semidirect
3. C3×C4×Dic11C2semidirect
4. #66889C3direct (N × H)
8. C3×D44C4semidirect
10. C3×Dic22C4semidirect
13. C11×M16C2×C3semidirect
14. C4×Dic11C2×C3semidirect
25. D44C3×C4semidirect
27. Dic22C3×C4semidirect
33. C3×M16D11semidirect
41. C3×C11#104semidirect
54. M16C3×D11semidirect
62. C11C3×#104semidirect
79. C3#66889direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#43392
C3×C11×M162
C3×C4×Dic112
#668893
C3×#10411