Finite Group Databasebeta

← C2×AGL(1,𝔽7)×C11⋊C5 #17987643

Subgroups — C2×AGL(1,𝔽7)×C11⋊C5 #17987643

Order 4620.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1AGL(1,𝔽7)×C11⋊C5C212yesmaximal, direct product factor
2C2×ΓL(1,𝔽8)×C11⋊C5C211yesmaximal, characteristic, complemented
3C2×D7×C11⋊C5C311yesmaximal, characteristic, complemented, Hall
4ΓL(1,𝔽8)×C11⋊C5C2211yescharacteristic, complemented, Hall
5C2×C11×AGL(1,𝔽7)C511yesmaximal, characteristic, complemented, Hall
6C2×C7×C11⋊C5C2×C311yescharacteristic, complemented
7D7×C11⋊C5C2×C312yescomplemented
8C22×C3×C11⋊C5—71nomaximal, Hall
9C2×C11×ΓL(1,𝔽8)C2×C511yescharacteristic, complemented
10C11×AGL(1,𝔽7)C2×C512yescomplemented
11C2×C5×AGL(1,𝔽7)—111nomaximal, Hall
12C7×C11⋊C5C22×C311yescharacteristic, complemented, Hall
13C2×C3×C11⋊C5—72no—
14C2×C3×C11⋊C5—71no—
15C2×C11×D7C3×C511yescharacteristic, complemented, Hall
16C11×ΓL(1,𝔽8)C22×C511yescharacteristic, complemented, Hall
17C22×C11⋊C5—71noHall
18C2×C5×ΓL(1,𝔽8)—111no—
19C5×AGL(1,𝔽7)—112no—
20C3×C11⋊C5—71noHall
21C2×C7×C11C2×C3×C511yescharacteristic, complemented
22C11×D7C2×C3×C512yescomplemented
23C2×C5×D7—111noHall
24C22×C3×C11—71noHall
25C2×C11⋊C5—72no—
26C2×C11⋊C5AGL(1,𝔽7)11yescharacteristic, direct product factor
27C5×ΓL(1,𝔽8)—111noHall
28C2×AGL(1,𝔽7)C11⋊C511yescharacteristic, direct product factor, Hall
29C7×C11C22×C3×C511yescharacteristic, complemented, Hall
30C2×C5×C7—111no—
31C5×D7—112no—
32C2×C3×C11—72no—
33C2×C3×C11—71no—
34C22×C3×C5—771noHall
35C11⋊C5C2×AGL(1,𝔽7)11yescharacteristic, direct product factor, Hall
36C22×C11—71noHall
37C2×ΓL(1,𝔽8)C2×C11⋊C511yescharacteristic, complemented
38AGL(1,𝔽7)C2×C11⋊C512yesdirect product factor
39C5×C7—111noHall
40C3×C11—71noHall
41C2×C3×C5—771no—
42C2×C3×C5—772no—
43C2×D7C3×C11⋊C511yescharacteristic, complemented, Hall
44C2×C11—72no—
45C2×C11C5×AGL(1,𝔽7)11yescharacteristic, complemented
46ΓL(1,𝔽8)C22×C11⋊C511yescharacteristic, complemented, Hall
47C22×C5—771noHall
48C3×C5—771noHall
49C2×C7C2×C3×C11⋊C511yescharacteristic, complemented
50D7C2×C3×C11⋊C512yescomplemented
51C22×C3—71noHall
52C11C2×C5×AGL(1,𝔽7)11yescharacteristic, complemented, Sylow
53C2×C5—111no—
54C2×C5—772no—
55C7C22×C3×C11⋊C511yescharacteristic, complemented, Sylow
56C2×C3—72no—
57C2×C3—71no—
58C5—111noSylow
59C22—71noSylow
60C3—71noSylow
61C2—72no—
62C2AGL(1,𝔽7)×C11⋊C511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2AGL(1,𝔽7)×C11⋊C5
commutator, cosocle, hypocenterC7×C11C22×C3×C5
FrattiniC1G
Fitting, socleC2×C7×C11C2×C3×C5
LCSG ▷ C7×C11
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. AGL(1,𝔽7)×C11⋊C5C2direct (N × H)
2. C2×ΓL(1,𝔽8)×C11⋊C5C2semidirect
3. C2×D7×C11⋊C5C3semidirect
4. ΓL(1,𝔽8)×C11⋊C5C22semidirect
5. C2×C11×AGL(1,𝔽7)C5semidirect
6. C2×C7×C11⋊C5C2×C3semidirect
7. D7×C11⋊C5C2×C3semidirect
9. C2×C11×ΓL(1,𝔽8)C2×C5semidirect
10. C11×AGL(1,𝔽7)C2×C5semidirect
12. C7×C11⋊C5C22×C3semidirect
15. C2×C11×D7C3×C5semidirect
16. C11×ΓL(1,𝔽8)C22×C5semidirect
21. C2×C7×C11C2×C3×C5semidirect
22. C11×D7C2×C3×C5semidirect
26. C2×C11⋊C5AGL(1,𝔽7)direct (N × H)
28. C2×AGL(1,𝔽7)C11⋊C5direct (N × H)
29. C7×C11C22×C3×C5semidirect
35. C11⋊C5C2×AGL(1,𝔽7)direct (N × H)
37. C2×ΓL(1,𝔽8)C2×C11⋊C5semidirect
38. AGL(1,𝔽7)C2×C11⋊C5direct (N × H)
43. C2×D7C3×C11⋊C5semidirect
45. C2×C11C5×AGL(1,𝔽7)semidirect
46. ΓL(1,𝔽8)C22×C11⋊C5semidirect
49. C2×C7C2×C3×C11⋊C5semidirect
50. D7C2×C3×C11⋊C5semidirect
52. C11C2×C5×AGL(1,𝔽7)semidirect
55. C7C22×C3×C11⋊C5semidirect
62. C2AGL(1,𝔽7)×C11⋊C5direct (N × H)

Maximal subgroups

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

subgroupindex
AGL(1,𝔽7)×C11⋊C52
C2×ΓL(1,𝔽8)×C11⋊C52
C2×D7×C11⋊C53
C2×C11×AGL(1,𝔽7)5
C22×C3×C11⋊C57
C2×C5×AGL(1,𝔽7)11