Finite Group Databasebeta

← C11⋊C5×#64418⋊C2 #44568547

Subgroups — C11⋊C5×#64418⋊C2 #44568547

Order 32340.

136 conjugacy classes of subgroups; only the 24 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 24 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11⋊C5×#64418C212yesmaximal, complemented
2C11⋊C5×#64425C211yesmaximal, characteristic, complemented
3D72×C11⋊C5—31nomaximal, Hall
4C11⋊C5×#3862C2211yescharacteristic, complemented, Hall
5C11×#64418⋊C2C511yesmaximal, characteristic, complemented, Hall
6C11⋊C5×C7⋊D7D311yescharacteristic, complemented
7C7×D7×C11⋊C5—32no—
8C11×#64418C2×C512yescomplemented
9C11×#64425C2×C511yescharacteristic, complemented
10C5×#64418⋊C2—111nomaximal, Hall
11C72×C11⋊C5C2×D311yescharacteristic, complemented, Hall
12AGL(1,𝔽7)×C11⋊C5—141no—
13C11×D72—31noHall
14C11×#3862C22×C511yescharacteristic, complemented, Hall
15C2×D7×C11⋊C5—212no—
16C5×#64425—111no—
17C5×#64418—112no—
18ΓL(1,𝔽8)×C11⋊C5—141no—
19C11×C7⋊D7C5×D311yescharacteristic, complemented
20C7×C11×D7—32no—
21C5×D72—331noHall
22C2×C7×C11⋊C5—212no—
23D7×C11⋊C5—32no—
24D7×C11⋊C5—141no—
25D7×C11⋊C5—212no—
26C5×#3862—111noHall
27C2×D3×C11⋊C5—491nomaximal, Hall
28#64418⋊C2C11⋊C511yescharacteristic, direct product factor, Hall
29C72×C11C2×C5×D311yescharacteristic, complemented, Hall
30C5×C7⋊D7—111no—
31C5×C7×D7—332no—
32C11×AGL(1,𝔽7)—141no—
33C7×C11⋊C5—21no—
34C7×C11⋊C5—32no—
35C2×C3×C11⋊C5—491no—
36D3×C11⋊C5—492no—
37C2×C11×D7—212no—
38#64425C2×C11⋊C511yescharacteristic, complemented
39#64418C2×C11⋊C512yescomplemented
40C5×C72—111noHall
41C11×ΓL(1,𝔽8)—141no—
42C22×C11⋊C5—1471noHall
43C5×AGL(1,𝔽7)—1541no—
44D72—31noHall
45C3×C11⋊C5—491noHall
46C2×C7×C11—212no—
47C11×D7—32no—
48C11×D7—141no—
49C11×D7—212no—
50#3862C22×C11⋊C511yescharacteristic, complemented, Hall
51C2×C5×D7—2312no—
52C2×D3×C11—491noHall
53C2×C11⋊C5—212no—
54C2×C11⋊C5—491no—
55C5×ΓL(1,𝔽8)—1541no—
56C7⋊D7D3×C11⋊C511yescharacteristic, complemented
57C7×D7—32no—
58C7×C11—21no—
59C7×C11—32no—
60C2×C5×C7—2312no—
61C5×D7—332no—
62C5×D7—1541no—
63C5×D7—2312no—
64C2×C3×C11—491no—
65D3×C11—492no—
66C2×C5×D3—5391noHall
67C11⋊C5#64418⋊C211yescharacteristic, direct product factor, Hall
68C72C2×D3×C11⋊C511yescharacteristic, complemented, Sylow
69C22×C11—1471noHall
70AGL(1,𝔽7)—141no—
71C5×C7—221no—
72C5×C7—332no—
73C3×C11—491noHall
74C2×C3×C5—5391no—
75C5×D3—5392no—
76C2×D7—212no—
77C2×C11—212no—
78C2×C11—491no—
79ΓL(1,𝔽8)—141no—
80C22×C5—16171noHall
81C3×C5—5391noHall
82C2×C7—212no—
83D7—32no—
84D7—141no—
85D7—212no—
86C2×D3—491noHall
87C11C5×#64418⋊C211yescharacteristic, complemented, Sylow
88C2×C5—5391no—
89C2×C5—2312no—
90C7—21no—
91C7—32no—
92C2×C3—491no—
93D3—492no—
94C5—111noSylow
95C22—1471noSylow
96C3—491noSylow
97C2—212no—
98C2—491no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, cosocle, hypocenterC11×#3862C22×C5
Fitting, socleC72×C11C2×C5×D3
LCSG ▷ C11×#3862
UCSC1

Complements

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

NH ≅ G/Ntype
1. C11⋊C5×#64418C2semidirect
2. C11⋊C5×#64425C2semidirect
4. C11⋊C5×#3862C22semidirect
5. C11×#64418⋊C2C5semidirect
6. C11⋊C5×C7⋊D7D3semidirect
8. C11×#64418C2×C5semidirect
9. C11×#64425C2×C5semidirect
11. C72×C11⋊C5C2×D3semidirect
14. C11×#3862C22×C5semidirect
19. C11×C7⋊D7C5×D3semidirect
28. #64418⋊C2C11⋊C5direct (N × H)
29. C72×C11C2×C5×D3semidirect
38. #64425C2×C11⋊C5semidirect
39. #64418C2×C11⋊C5semidirect
50. #3862C22×C11⋊C5semidirect
56. C7⋊D7D3×C11⋊C5semidirect
67. C11⋊C5#64418⋊C2direct (N × H)
68. C72C2×D3×C11⋊C5semidirect
87. C11C5×#64418⋊C2semidirect

Maximal subgroups

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

subgroupindex
C11⋊C5×#644182
C11⋊C5×#644252
D72×C11⋊C53
C11×#64418⋊C25
C5×#64418⋊C211
C2×D3×C11⋊C549