Finite Group Databasebeta

← C4×C5×C11×#3862 #44568513

Subgroups — C4×C5×C11×#3862 #44568513

Order 32340.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×C11×#3862C211yesmaximal, characteristic
2C4×C5×C72×C11C311yesmaximal, characteristic, complemented, Hall
3C5×C11×#3862C411yescharacteristic, direct product factor, Hall
4C4×C11×#3862C511yesmaximal, characteristic, direct product factor, Hall
5C2×C5×C72×C11C2×C311yescharacteristic
6C4×C5×C11×ΓL(1,𝔽8)—72nomaximal
7C2×C11×#3862C2×C511yescharacteristic
8C4×C5×#3862C1111yesmaximal, characteristic, direct product factor, Hall
9C5×C72×C11C3×C411yescharacteristic, complemented, Hall
10C2×C5×C11×ΓL(1,𝔽8)—72no—
11C4×C72×C11C3×C511yescharacteristic, complemented, Hall
12C11×#3862C4×C511yescharacteristic, direct product factor, Hall
13C4×C5×C7×C11—32no—
14C4×C5×C7×C11ΓL(1,𝔽8)12yescomplemented
15C2×C5×#3862C2×C1111yescharacteristic
16C5×C11×ΓL(1,𝔽8)—72no—
17C2×C72×C11C2×C3×C511yescharacteristic
18C4×C5×C72C3×C1111yescharacteristic, complemented, Hall
19C4×C11×ΓL(1,𝔽8)—72no—
20C2×C5×C7×C11—32no—
21C2×C5×C7×C11C2×ΓL(1,𝔽8)12yes—
22C5×#3862C4×C1111yescharacteristic, direct product factor, Hall
23C3×C4×C5×C11—491noHall
24C4×#3862C5×C1111yescharacteristic, direct product factor, Hall
25C72×C11C3×C4×C511yescharacteristic, complemented, Hall
26C2×C5×C72C2×C3×C1111yescharacteristic
27C2×C11×ΓL(1,𝔽8)—72no—
28C4×C5×ΓL(1,𝔽8)—72no—
29C5×C7×C11—32no—
30C5×C7×C11C4×ΓL(1,𝔽8)12yescomplemented
31C2×C3×C5×C11—491no—
32C4×C7×C11—32no—
33C4×C7×C11C5×ΓL(1,𝔽8)12yescomplemented
34C2×#3862C2×C5×C1111yescharacteristic
35C5×C72C3×C4×C1111yescharacteristic, complemented, Hall
36C11×ΓL(1,𝔽8)—72no—
37C4×C5×C11#386211yescharacteristic, direct product factor, Hall
38C2×C5×ΓL(1,𝔽8)—72no—
39C4×C72C3×C5×C1111yescharacteristic, complemented, Hall
40C3×C5×C11—491noHall
41C2×C7×C11—32no—
42C2×C7×C11C2×C5×ΓL(1,𝔽8)12yes—
43#3862C4×C5×C1111yescharacteristic, direct product factor, Hall
44C4×C5×C7—32no—
45C4×C5×C7C11×ΓL(1,𝔽8)12yescomplemented
46C3×C4×C11—491noHall
47C2×C5×C11C2×#386211yescharacteristic
48C5×ΓL(1,𝔽8)—72no—
49C2×C72C2×C3×C5×C1111yescharacteristic
50C4×ΓL(1,𝔽8)—72no—
51C7×C11—32no—
52C7×C11C4×C5×ΓL(1,𝔽8)12yescomplemented
53C2×C5×C7—32no—
54C2×C5×C7C2×C11×ΓL(1,𝔽8)12yes—
55C2×C3×C11—491no—
56C3×C4×C5—491noHall
57C5×C11C4×#386211yescharacteristic, direct product factor, Hall
58C72C3×C4×C5×C1111yescharacteristic, complemented, Sylow
59C4×C11C5×#386211yescharacteristic, direct product factor, Hall
60C2×ΓL(1,𝔽8)—72no—
61C5×C7—32no—
62C5×C7C4×C11×ΓL(1,𝔽8)12yescomplemented
63C3×C11—491noHall
64C2×C3×C5—491no—
65C4×C7—32no—
66C4×C7C5×C11×ΓL(1,𝔽8)12yescomplemented
67C2×C11C2×C5×#386211yescharacteristic
68ΓL(1,𝔽8)—72no—
69C4×C5C11×#386211yescharacteristic, direct product factor, Hall
70C3×C5—491noHall
71C2×C7—32no—
72C2×C7C2×C5×C11×ΓL(1,𝔽8)12yes—
73C3×C4—491noHall
74C11C4×C5×#386211yescharacteristic, direct product factor, Sylow
75C2×C5C2×C11×#386211yescharacteristic
76C7—32no—
77C7C4×C5×C11×ΓL(1,𝔽8)12yescomplemented
78C2×C3—491no—
79C5C4×C11×#386211yescharacteristic, direct product factor, Sylow
80C4C5×C11×#386211yescharacteristic, direct product factor, Sylow
81C3—491noSylow
82C2C2×C5×C11×#386211yescharacteristic
subgroupG/H
center, hypercenterC4×C5×C11#3862
commutator, hypocenterC72C3×C4×C5×C11
FrattiniC2C2×C5×C11×#3862
FittingC4×C5×C72×C11C3
socleC2×C5×C72×C11C2×C3
prime radicalC2×C5×C11×#3862C2
cosocleC2×C72C2×C3×C5×C11
LCSG ▷ C72
UCSC1 ◁ C4×C5×C11

Complements

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

NH ≅ G/Ntype
2. C4×C5×C72×C11C3semidirect
3. C5×C11×#3862C4direct (N × H)
4. C4×C11×#3862C5direct (N × H)
8. C4×C5×#3862C11direct (N × H)
9. C5×C72×C11C3×C4semidirect
11. C4×C72×C11C3×C5semidirect
12. C11×#3862C4×C5direct (N × H)
14. C4×C5×C7×C11ΓL(1,𝔽8)semidirect
18. C4×C5×C72C3×C11semidirect
22. C5×#3862C4×C11direct (N × H)
24. C4×#3862C5×C11direct (N × H)
25. C72×C11C3×C4×C5semidirect
30. C5×C7×C11C4×ΓL(1,𝔽8)semidirect
33. C4×C7×C11C5×ΓL(1,𝔽8)semidirect
35. C5×C72C3×C4×C11semidirect
37. C4×C5×C11#3862direct (N × H)
39. C4×C72C3×C5×C11semidirect
43. #3862C4×C5×C11direct (N × H)
45. C4×C5×C7C11×ΓL(1,𝔽8)semidirect
52. C7×C11C4×C5×ΓL(1,𝔽8)semidirect
57. C5×C11C4×#3862direct (N × H)
58. C72C3×C4×C5×C11semidirect
59. C4×C11C5×#3862direct (N × H)
62. C5×C7C4×C11×ΓL(1,𝔽8)semidirect
66. C4×C7C5×C11×ΓL(1,𝔽8)semidirect
69. C4×C5C11×#3862direct (N × H)
74. C11C4×C5×#3862direct (N × H)
77. C7C4×C5×C11×ΓL(1,𝔽8)semidirect
79. C5C4×C11×#3862direct (N × H)
80. C4C5×C11×#3862direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×C11×#38622
C4×C5×C72×C113
C4×C11×#38625
C4×C5×C11×ΓL(1,𝔽8)7
C4×C5×#386211