Finite Group Databasebeta

← C3×C11×#11758266 #44568809

Subgroups — C3×C11×#11758266 #44568809

Order 32340.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C11×C5⋊(C7⋊D7)C211yesmaximal, characteristic
2C11×#11758266C311yesmaximal, characteristic, direct product factor, Hall
3C3×C5×C72×C11C411yescharacteristic, complemented, Hall
4C3×C11×#5997—51nomaximal, Hall
5C11×C5⋊(C7⋊D7)C2×C311yescharacteristic
6C3×C11×C7⋊D7—51no—
7C3×#11758266C1111yesmaximal, characteristic, direct product factor, Hall
8C5×C72×C11C3×C411yescharacteristic, complemented, Hall
9C3×C11×D35—144no—
10C11×#5997—51noHall
11C3×C72×C11AGL(1,𝔽5)11yescharacteristic, complemented, Hall
12C3×C5⋊(C7⋊D7)C2×C1111yescharacteristic
13C3×C5×C7×C11—24no—
14C11×C7⋊D7—51no—
15#11758266C3×C1111yescharacteristic, direct product factor, Hall
16C11×D35—144no—
17C3×C5×C72C4×C1111yescharacteristic, complemented, Hall
18C3×C11×AGL(1,𝔽5)—491nomaximal, Hall
19C3×#5997—51noHall
20C72×C11C3×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
21C5⋊(C7⋊D7)C2×C3×C1111yescharacteristic
22C3×C11×D7—704no—
23C5×C7×C11—24no—
24C3×D5×C11—491no—
25C3×C7⋊D7—51no—
26C5×C72C3×C4×C1111yescharacteristic, complemented, Hall
27C3×C7×C11—24no—
28C11×AGL(1,𝔽5)—491noHall
29C3×D35—144no—
30#5997—51noHall
31C3×C5×C11#599711yescharacteristic, complemented, Hall
32C11×D7—704no—
33C3×C72C11×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
34C3×C4×C11—2451noHall
35D5×C11—491no—
36C3×C5×C7—24no—
37C7⋊D7—51no—
38C7×C11—24no—
39D35—144no—
40C2×C3×C11—2451no—
41C3×AGL(1,𝔽5)—491noHall
42C5×C11C3×#599711yescharacteristic, complemented, Hall
43C72C3×C11×AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
44C4×C11—2451noHall
45C3×D7—704no—
46C5×C7—24no—
47C3×C11#1175826611yescharacteristic, direct product factor, Hall
48C3×D5—491no—
49C2×C11—2451no—
50C3×C7—24no—
51AGL(1,𝔽5)—491noHall
52C3×C5C11×#599711yescharacteristic, complemented, Hall
53D7—704no—
54C3×C4—2451noHall
55C11C3×#1175826611yescharacteristic, direct product factor, Sylow
56D5—491no—
57C7—24no—
58C2×C3—2451no—
59C5C3×C11×#599711yescharacteristic, complemented, Sylow
60C4—2451noSylow
61C3C11×#1175826611yescharacteristic, direct product factor, Sylow
62C2—2451no—
subgroupG/H
center, hypercenterC3×C11#11758266
commutator, hypocenterC5×C72C3×C4×C11
FrattiniC1G
Fitting, socleC3×C5×C72×C11C4
prime radicalC3×C11×C5⋊(C7⋊D7)C2
cosocleC5⋊(C7⋊D7)C2×C3×C11
LCSG ▷ C5×C72
UCSC1 ◁ C3×C11

Complements

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

NH ≅ G/Ntype
2. C11×#11758266C3direct (N × H)
3. C3×C5×C72×C11C4semidirect
7. C3×#11758266C11direct (N × H)
8. C5×C72×C11C3×C4semidirect
11. C3×C72×C11AGL(1,𝔽5)semidirect
15. #11758266C3×C11direct (N × H)
17. C3×C5×C72C4×C11semidirect
20. C72×C11C3×AGL(1,𝔽5)semidirect
26. C5×C72C3×C4×C11semidirect
31. C3×C5×C11#5997semidirect
33. C3×C72C11×AGL(1,𝔽5)semidirect
42. C5×C11C3×#5997semidirect
43. C72C3×C11×AGL(1,𝔽5)semidirect
47. C3×C11#11758266direct (N × H)
52. C3×C5C11×#5997semidirect
55. C11C3×#11758266direct (N × H)
59. C5C3×C11×#5997semidirect
61. C3C11×#11758266direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C11×C5⋊(C7⋊D7)2
C11×#117582663
C3×C11×#59975
C3×#1175826611
C3×C11×AGL(1,𝔽5)49