Finite Group Databasebeta

← C3×C7×C11×#1039 #37528400

Subgroups — C3×C7×C11×#1039 #37528400

Order 23100.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C52×C7×C11C211yesmaximal, characteristic
2C7×C11×#1039C311yesmaximal, characteristic, direct product factor, Hall
3C3×C52×C7×C11C411yescharacteristic, complemented, Hall
4C3×C7×C11×Dic5—56nomaximal
5C2×C52×C7×C11C2×C311yescharacteristic
6C3×C11×#1039C711yesmaximal, characteristic, direct product factor, Hall
7C2×C3×C5×C7×C11D516yes—
8C3×C7×#1039C1111yesmaximal, characteristic, direct product factor, Hall
9C52×C7×C11C3×C411yescharacteristic, complemented, Hall
10C2×C3×C52×C11C2×C711yescharacteristic
11C7×C11×Dic5—56no—
12C3×C5×C7×C11Dic516yescomplemented
13C11×#1039C3×C711yescharacteristic, direct product factor, Hall
14C2×C3×C52×C7C2×C1111yescharacteristic
15C3×C4×C7×C11—251noHall
16C3×C52×C11C4×C711yescharacteristic, complemented, Hall
17C2×C5×C7×C11C3×D516yes—
18C7×#1039C3×C1111yescharacteristic, direct product factor, Hall
19C3×C11×Dic5—56no—
20C2×C52×C11C2×C3×C711yescharacteristic
21C3×C52×C7C4×C1111yescharacteristic, complemented, Hall
22C2×C3×C7×C11C5⋊D511yescharacteristic
23C3×C7×Dic5—56no—
24C5×C7×C11C3×Dic516yescomplemented
25C2×C52×C7C2×C3×C1111yescharacteristic
26C2×C3×C5×C11C7×D516yes—
27C4×C7×C11—251noHall
28C3×#1039C7×C1111yescharacteristic, direct product factor, Hall
29C52×C11C3×C4×C711yescharacteristic, complemented, Hall
30C3×C7×C11#103911yescharacteristic, direct product factor, Hall
31C11×Dic5—56no—
32C2×C3×C5×C7D5×C1116yes—
33C52×C7C3×C4×C1111yescharacteristic, complemented, Hall
34C3×C5×C11C7×Dic516yescomplemented
35C2×C7×C11C3×C5⋊D511yescharacteristic
36C2×C3×C52C2×C7×C1111yescharacteristic
37C7×Dic5—56no—
38C3×C4×C11—251noHall
39C2×C5×C11C3×C7×D516yes—
40C3×C5×C7C11×Dic516yescomplemented
41#1039C3×C7×C1111yescharacteristic, direct product factor, Hall
42C3×C4×C7—251noHall
43C7×C11C3×#103911yescharacteristic, direct product factor, Hall
44C3×C52C4×C7×C1111yescharacteristic, complemented, Hall
45C2×C5×C7C3×D5×C1116yes—
46C2×C3×C11C7×C5⋊D511yescharacteristic
47C3×Dic5—56no—
48C5×C11C3×C7×Dic516yescomplemented
49C2×C52C2×C3×C7×C1111yescharacteristic
50C4×C11—251noHall
51C2×C3×C7C11×C5⋊D511yescharacteristic
52C5×C7C3×C11×Dic516yescomplemented
53C3×C11C7×#103911yescharacteristic, direct product factor, Hall
54C2×C3×C5C7×D5×C1116yes—
55C4×C7—251noHall
56C52C3×C4×C7×C1111yescharacteristic, complemented, Sylow
57C2×C11C3×C7×C5⋊D511yescharacteristic
58C3×C7C11×#103911yescharacteristic, direct product factor, Hall
59Dic5—56no—
60C3×C5C7×C11×Dic516yescomplemented
61C2×C7C3×C11×C5⋊D511yescharacteristic
62C3×C4—251noHall
63C11C3×C7×#103911yescharacteristic, direct product factor, Sylow
64C2×C5C3×C7×D5×C1116yes—
65C7C3×C11×#103911yescharacteristic, direct product factor, Sylow
66C2×C3C7×C11×C5⋊D511yescharacteristic
67C5C3×C7×C11×Dic516yescomplemented
68C4—251noSylow
69C3C7×C11×#103911yescharacteristic, direct product factor, Sylow
70C2C3×C7×C11×C5⋊D511yescharacteristic
subgroupG/H
center, hypercenterC2×C3×C7×C11C5⋊D5
commutator, hypocenterC52C3×C4×C7×C11
FrattiniC2C3×C7×C11×C5⋊D5
Fitting, socle, prime radicalC2×C3×C52×C7×C11C2
cosocleC2×C52C2×C3×C7×C11
LCSG ▷ C52
UCSC1 ◁ C2×C3×C7×C11

Complements

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

NH ≅ G/Ntype
2. C7×C11×#1039C3direct (N × H)
3. C3×C52×C7×C11C4semidirect
6. C3×C11×#1039C7direct (N × H)
8. C3×C7×#1039C11direct (N × H)
9. C52×C7×C11C3×C4semidirect
12. C3×C5×C7×C11Dic5semidirect
13. C11×#1039C3×C7direct (N × H)
16. C3×C52×C11C4×C7semidirect
18. C7×#1039C3×C11direct (N × H)
21. C3×C52×C7C4×C11semidirect
24. C5×C7×C11C3×Dic5semidirect
28. C3×#1039C7×C11direct (N × H)
29. C52×C11C3×C4×C7semidirect
30. C3×C7×C11#1039direct (N × H)
33. C52×C7C3×C4×C11semidirect
34. C3×C5×C11C7×Dic5semidirect
40. C3×C5×C7C11×Dic5semidirect
41. #1039C3×C7×C11direct (N × H)
43. C7×C11C3×#1039direct (N × H)
44. C3×C52C4×C7×C11semidirect
48. C5×C11C3×C7×Dic5semidirect
52. C5×C7C3×C11×Dic5semidirect
53. C3×C11C7×#1039direct (N × H)
56. C52C3×C4×C7×C11semidirect
58. C3×C7C11×#1039direct (N × H)
60. C3×C5C7×C11×Dic5semidirect
63. C11C3×C7×#1039direct (N × H)
65. C7C3×C11×#1039direct (N × H)
67. C5C3×C7×C11×Dic5semidirect
69. C3C7×C11×#1039direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C52×C7×C112
C7×C11×#10393
C3×C7×C11×Dic55
C3×C11×#10397
C3×C7×#103911