Finite Group Databasebeta

← C3×D49×AGL(1,𝔽11) #44568340

Subgroups — C3×D49×AGL(1,𝔽11) #44568340

Order 32340.

120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 44 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
1C3×C49⋊AGL(1,𝔽11)C211yesmaximal, characteristic, complemented
2C3×C11⋊C5×D49C211yesmaximal, characteristic, complemented
3C3×C49×AGL(1,𝔽11)C211yesmaximal, characteristic, complemented
4D49×AGL(1,𝔽11)C311yesmaximal, characteristic, direct product factor, Hall
5C3×C49×C11⋊C5C2211yescharacteristic, complemented, Hall
6C3×D11×D49C511yesmaximal, characteristic, complemented, Hall
7C49⋊AGL(1,𝔽11)C2×C311yescharacteristic, complemented
8C11⋊C5×D49C2×C311yescharacteristic, complemented
9C49×AGL(1,𝔽11)C2×C311yescharacteristic, complemented
10C3×D7×AGL(1,𝔽11)—71nomaximal
11C3×D539C2×C511yescharacteristic, complemented
12C3×C11×D49C2×C511yescharacteristic, complemented
13C3×D11×C49C2×C511yescharacteristic, complemented
14C2×C3×C5×D49—111nomaximal, Hall
15C49×C11⋊C5C22×C311yescharacteristic, complemented, Hall
16C3×C7⋊AGL(1,𝔽11)—71no—
17C3×D7×C11⋊C5—71no—
18C3×C7×AGL(1,𝔽11)D711yescharacteristic
19D11×D49C3×C511yescharacteristic, complemented, Hall
20C3×C11×C49C22×C511yescharacteristic, complemented, Hall
21D7×AGL(1,𝔽11)—71no—
22C2×C3×C5×C49—111no—
23C3×C5×D49—111no—
24C3×C5×D49—111no—
25C3×C7×C11⋊C5C2×D711yescharacteristic
26D539C2×C3×C511yescharacteristic, complemented
27D11×C49C2×C3×C511yescharacteristic, complemented
28C11×D49C2×C3×C511yescharacteristic, complemented
29C2×C5×D49—111noHall
30C3×D7×D11—71no—
31C7⋊AGL(1,𝔽11)—71no—
32D7×C11⋊C5—71no—
33C7×AGL(1,𝔽11)C3×D711yescharacteristic
34C3×C5×C49—111noHall
35C2×C3×AGL(1,𝔽11)—491noHall
36C2×C3×D49—551noHall
37C11×C49C22×C3×C511yescharacteristic, complemented, Hall
38C2×C5×C49—111no—
39C5×D49—111no—
40C5×D49—111no—
41C3×D77—71no—
42C3×C11×D7—71no—
43C3×C7×D11C5×D711yescharacteristic
44C2×C3×C5×D7—771no—
45C7×C11⋊C5C2×C3×D711yescharacteristic
46C2×C3×C11⋊C5—491no—
47C3×AGL(1,𝔽11)—491no—
48C3×AGL(1,𝔽11)D4911yescharacteristic, direct product factor
49D7×D11—71no—
50C2×C3×C49—551no—
51C3×D49—551no—
52C3×D49AGL(1,𝔽11)11yescharacteristic, direct product factor
53C5×C49—111noHall
54C3×C7×C11C2×C5×D711yescharacteristic
55C2×AGL(1,𝔽11)—491noHall
56C2×C3×C5×C7—111no—
57C3×C5×D7—771no—
58C3×C5×D7—771no—
59C2×D49—551noHall
60C3×C11⋊C5C2×D4911yescharacteristic, complemented, Hall
61D77—71no—
62C7×D11C3×C5×D711yescharacteristic
63C11×D7—71no—
64C3×C49C2×AGL(1,𝔽11)11yescharacteristic, complemented, Hall
65C2×C5×D7—771no—
66C2×C3×D11—491noHall
67C2×C11⋊C5—491no—
68AGL(1,𝔽11)—491no—
69AGL(1,𝔽11)C3×D4911yescharacteristic, direct product factor
70C3×C5×C7—111no—
71C2×C49—551no—
72D49—551no—
73D49C3×AGL(1,𝔽11)11yescharacteristic, direct product factor
74C2×C3×D7—3851no—
75C7×C11C2×C3×C5×D711yescharacteristic
76C2×C5×C7—111no—
77C5×D7—771no—
78C5×D7—771no—
79C2×C3×C11—491no—
80C3×D11—491no—
81C3×D11C5×D4911yescharacteristic, complemented
82C22×C3×C5—5391noHall
83C11⋊C5C2×C3×D4911yescharacteristic, complemented, Hall
84C49C2×C3×AGL(1,𝔽11)11yescharacteristic, complemented, Sylow
85C2×D11—491noHall
86C2×C3×C7—551no—
87C3×D7—71no—
88C3×D7—3851no—
89C5×C7—111no—
90C3×C11C2×C5×D4911yescharacteristic, complemented, Hall
91C2×C3×C5—111no—
92C2×C3×C5—5391no—
93C2×C3×C5—5391no—
94C2×D7—3851no—
95C2×C11—491no—
96D11—491no—
97D11C3×C5×D4911yescharacteristic, complemented
98C3×C7D7×AGL(1,𝔽11)11yescharacteristic
99C22×C5—5391noHall
100C3×C5—111noHall
101C2×C7—551no—
102D7—71no—
103D7—3851no—
104C22×C3—26951noHall
105C11C2×C3×C5×D4911yescharacteristic, complemented, Sylow
106C2×C5—111no—
107C2×C5—5391no—
108C2×C5—5391no—
109C7C3×D7×AGL(1,𝔽11)11yescharacteristic
110C2×C3—491no—
111C2×C3—551no—
112C2×C3—26951no—
113C5—111noSylow
114C22—26951noSylow
115C3D49×AGL(1,𝔽11)11yescharacteristic, direct product factor, Sylow
116C2—491no—
117C2—551no—
118C2—26951no—
subgroupG/H
center, hypercenterC3D49×AGL(1,𝔽11)
commutator, cosocle, hypocenterC11×C49C22×C3×C5
FrattiniC7C3×D7×AGL(1,𝔽11)
FittingC3×C11×C49C22×C5
socleC3×C7×C11C2×C5×D7
LCSG ▷ C11×C49
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×C49⋊AGL(1,𝔽11)C2semidirect
2. C3×C11⋊C5×D49C2semidirect
3. C3×C49×AGL(1,𝔽11)C2semidirect
4. D49×AGL(1,𝔽11)C3direct (N × H)
5. C3×C49×C11⋊C5C22semidirect
6. C3×D11×D49C5semidirect
7. C49⋊AGL(1,𝔽11)C2×C3semidirect
8. C11⋊C5×D49C2×C3semidirect
9. C49×AGL(1,𝔽11)C2×C3semidirect
11. C3×D539C2×C5semidirect
12. C3×C11×D49C2×C5semidirect
13. C3×D11×C49C2×C5semidirect
15. C49×C11⋊C5C22×C3semidirect
19. D11×D49C3×C5semidirect
20. C3×C11×C49C22×C5semidirect
26. D539C2×C3×C5semidirect
27. D11×C49C2×C3×C5semidirect
28. C11×D49C2×C3×C5semidirect
37. C11×C49C22×C3×C5semidirect
48. C3×AGL(1,𝔽11)D49direct (N × H)
52. C3×D49AGL(1,𝔽11)direct (N × H)
60. C3×C11⋊C5C2×D49semidirect
64. C3×C49C2×AGL(1,𝔽11)semidirect
69. AGL(1,𝔽11)C3×D49direct (N × H)
73. D49C3×AGL(1,𝔽11)direct (N × H)
81. C3×D11C5×D49semidirect
83. C11⋊C5C2×C3×D49semidirect
84. C49C2×C3×AGL(1,𝔽11)semidirect
90. C3×C11C2×C5×D49semidirect
97. D11C3×C5×D49semidirect
105. C11C2×C3×C5×D49semidirect
115. C3D49×AGL(1,𝔽11)direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C49⋊AGL(1,𝔽11)2
C3×C11⋊C5×D492
C3×C49×AGL(1,𝔽11)2
D49×AGL(1,𝔽11)3
C3×D11×D495
C3×D7×AGL(1,𝔽11)7
C2×C3×C5×D4911