Finite Group Databasebeta

← C11⋊C5×#64422 #30633503

Subgroups — C11⋊C5×#64422 #30633503

Order 16170.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11⋊C5×#3862C211yesmaximal, characteristic, complemented, Hall
2C7×D7×C11⋊C5C311yesmaximal, characteristic, complemented, Hall
3C11×#64422C511yesmaximal, characteristic, complemented, Hall
4C72×C11⋊C5C2×C311yescharacteristic, complemented, Hall
5AGL(1,𝔽7)×C11⋊C5—71nomaximal
6C2×ΓL(1,𝔽8)×C11⋊C5—71nomaximal
7C11×#3862C2×C511yescharacteristic, complemented, Hall
8C5×#64422—111nomaximal, Hall
9ΓL(1,𝔽8)×C11⋊C5—71no—
10ΓL(1,𝔽8)×C11⋊C5—71no—
11C7×C11×D7C3×C511yescharacteristic, complemented, Hall
12C2×C7×C11⋊C5—71no—
13D7×C11⋊C5ΓL(1,𝔽8)11yescharacteristic, complemented
14C5×#3862—111noHall
15C72×C11C2×C3×C511yescharacteristic, complemented, Hall
16C5×C7×D7—111noHall
17C2×C11×ΓL(1,𝔽8)—71no—
18C11×AGL(1,𝔽7)—71no—
19C7×C11⋊C5—61no—
20C7×C11⋊C5AGL(1,𝔽7)11yescharacteristic, complemented
21C7×C11⋊C5C2×ΓL(1,𝔽8)11yescharacteristic, complemented
22C2×C3×C11⋊C5—491noHall
23#64422C11⋊C511yescharacteristic, direct product factor, Hall
24C5×C72—111noHall
25C11×ΓL(1,𝔽8)—71no—
26C11×ΓL(1,𝔽8)—71no—
27C2×C5×ΓL(1,𝔽8)—771no—
28C5×AGL(1,𝔽7)—771no—
29C3×C11⋊C5—491noHall
30C2×C7×C11—71no—
31C11×D7C5×ΓL(1,𝔽8)11yescharacteristic, complemented
32#3862C2×C11⋊C511yescharacteristic, complemented, Hall
33C2×C11⋊C5—71noHall
34C5×ΓL(1,𝔽8)—771no—
35C5×ΓL(1,𝔽8)—771no—
36C7×D7C3×C11⋊C511yescharacteristic, complemented, Hall
37C7×C11—61no—
38C7×C11C5×AGL(1,𝔽7)11yescharacteristic, complemented
39C7×C11C2×C5×ΓL(1,𝔽8)11yescharacteristic, complemented
40C2×C5×C7—771no—
41C5×D7—111no—
42C2×C3×C11—491noHall
43C11⋊C5#6442211yescharacteristic, direct product factor, Hall
44C72C2×C3×C11⋊C511yescharacteristic, complemented, Sylow
45C2×ΓL(1,𝔽8)—71no—
46AGL(1,𝔽7)—71no—
47C5×C7—111no—
48C5×C7—111no—
49C5×C7—661no—
50C3×C11—491noHall
51C2×C3×C5—5391noHall
52C2×C11—71noHall
53ΓL(1,𝔽8)—71no—
54ΓL(1,𝔽8)—71no—
55C3×C5—5391noHall
56C2×C7—71no—
57D7ΓL(1,𝔽8)×C11⋊C511yescharacteristic, complemented
58C11C5×#6442211yescharacteristic, complemented, Sylow
59C2×C5—771noHall
60C7—61no—
61C7C2×ΓL(1,𝔽8)×C11⋊C511yescharacteristic, complemented
62C7AGL(1,𝔽7)×C11⋊C511yescharacteristic, complemented
63C2×C3—491noHall
64C5—111noSylow
65C3—491noSylow
66C2—71noSylow
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC72×C11C2×C3×C5
LCSG ▷ C72×C11
UCSC1

Complements

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

NH ≅ G/Ntype
1. C11⋊C5×#3862C2semidirect
2. C7×D7×C11⋊C5C3semidirect
3. C11×#64422C5semidirect
4. C72×C11⋊C5C2×C3semidirect
7. C11×#3862C2×C5semidirect
11. C7×C11×D7C3×C5semidirect
13. D7×C11⋊C5ΓL(1,𝔽8)semidirect
15. C72×C11C2×C3×C5semidirect
20. C7×C11⋊C5AGL(1,𝔽7)semidirect
21. C7×C11⋊C5C2×ΓL(1,𝔽8)semidirect
23. #64422C11⋊C5direct (N × H)
31. C11×D7C5×ΓL(1,𝔽8)semidirect
32. #3862C2×C11⋊C5semidirect
36. C7×D7C3×C11⋊C5semidirect
38. C7×C11C5×AGL(1,𝔽7)semidirect
39. C7×C11C2×C5×ΓL(1,𝔽8)semidirect
43. C11⋊C5#64422direct (N × H)
44. C72C2×C3×C11⋊C5semidirect
57. D7ΓL(1,𝔽8)×C11⋊C5semidirect
58. C11C5×#64422semidirect
61. C7C2×ΓL(1,𝔽8)×C11⋊C5semidirect
62. C7AGL(1,𝔽7)×C11⋊C5semidirect

Maximal subgroups

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

subgroupindex
C11⋊C5×#38622
C7×D7×C11⋊C53
C11×#644225
AGL(1,𝔽7)×C11⋊C57
C2×ΓL(1,𝔽8)×C11⋊C57
C5×#6442211