Finite Group Databasebeta

← C3×C11⋊C5×AGL(1,𝔽11) #31827608

Subgroups — C3×C11⋊C5×AGL(1,𝔽11) #31827608

Order 18150.

132 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 46 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×C11⋊C52C211yesmaximal, characteristic, complemented, Hall
2C11⋊C5×AGL(1,𝔽11)C311yesmaximal, characteristic, direct product factor, Hall
3C3×D11×C11⋊C5C511yesmaximal, characteristic, complemented
4C3×#11925898C511yesmaximal, characteristic, complemented
5C3×#11925897C511yesmaximal, characteristic, complemented
6C3×#11925896C511yesmaximal, characteristic, complemented
7C3×#11925895C511yesmaximal, characteristic, complemented
8C3×C11×AGL(1,𝔽11)C511yesmaximal, characteristic, complemented
9C11⋊C52C2×C311yescharacteristic, complemented, Hall
10C3×#10597244C2×C511yescharacteristic, complemented
11C3×#10597244C2×C511yescharacteristic, complemented
12C3×#10597245C2×C511yescharacteristic, complemented
13C3×#10597243C2×C511yescharacteristic, complemented
14C3×C11×C11⋊C5C2×C511yescharacteristic, complemented
15C3×C11×C11⋊C5C2×C511yescharacteristic, complemented
16C2×C3×C5×C11⋊C5—111nomaximal
17C3×C5×AGL(1,𝔽11)—111nomaximal
18D11×C11⋊C5C3×C511yescharacteristic, complemented
19#11925898C3×C511yescharacteristic, complemented
20#11925897C3×C511yescharacteristic, complemented
21#11925896C3×C511yescharacteristic, complemented
22#11925895C3×C511yescharacteristic, complemented
23C11×AGL(1,𝔽11)C3×C511yescharacteristic, complemented
24C3×C5×C11⋊C5—111no—
25C3×C5×C11⋊C5—111no—
26C3×C11×D11C5211yescharacteristic, complemented, Hall
27#10597245C2×C3×C511yescharacteristic, complemented
28#10597244C2×C3×C511yescharacteristic, complemented
29#10597244C2×C3×C511yescharacteristic, complemented
30#10597243C2×C3×C511yescharacteristic, complemented
31C11×C11⋊C5C2×C3×C511yescharacteristic, complemented
32C11×C11⋊C5C2×C3×C511yescharacteristic, complemented
33C2×C5×C11⋊C5—111no—
34C5×AGL(1,𝔽11)—111no—
35C3×C112C2×C5211yescharacteristic, complemented, Hall
36C2×C3×C5×C11—111no—
37C3×C5×D11—111no—
38C2×C3×C11⋊C5—111no—
39C2×C3×C11⋊C5—111no—
40C2×C3×C11⋊C5—111no—
41C2×C3×C11⋊C5—111no—
42C2×C3×C11⋊C5—111no—
43C3×AGL(1,𝔽11)—111no—
44C3×AGL(1,𝔽11)—111no—
45C3×AGL(1,𝔽11)—111no—
46C3×AGL(1,𝔽11)—111no—
47C3×AGL(1,𝔽11)C11⋊C511yescharacteristic, direct product factor
48C5×C11⋊C5—111no—
49C5×C11⋊C5—111no—
50C11×D11C3×C5211yescharacteristic, complemented, Hall
51C3×C5×C11—111no—
52C3×C5×C11—111no—
53C3×C11⋊C5—111no—
54C3×C11⋊C5—111no—
55C3×C11⋊C5—111no—
56C3×C11⋊C5—111no—
57C3×C11⋊C5—111no—
58C3×C11⋊C5—111no—
59C3×C11⋊C5—111no—
60C3×C11⋊C5—111no—
61C3×C11⋊C5—1101no—
62C3×C11⋊C5AGL(1,𝔽11)11yescharacteristic, direct product factor
63C3×C11⋊C5C2×C11⋊C511yescharacteristic, complemented
64C2×C3×C52—1211noHall
65C112C2×C3×C5211yescharacteristic, complemented, Sylow
66C2×C5×C11—111no—
67C5×D11—111no—
68C2×C11⋊C5—111no—
69C2×C11⋊C5—111no—
70C2×C11⋊C5—111no—
71C2×C11⋊C5—111no—
72C2×C11⋊C5—551no—
73AGL(1,𝔽11)—111no—
74AGL(1,𝔽11)—111no—
75AGL(1,𝔽11)—111no—
76AGL(1,𝔽11)—111no—
77AGL(1,𝔽11)C3×C11⋊C511yescharacteristic, direct product factor
78C3×C52—1211noHall
79C2×C3×C11—111no—
80C3×D11C5×C11⋊C511yescharacteristic, complemented
81C5×C11—111no—
82C5×C11—111no—
83C11⋊C5—111no—
84C11⋊C5—111no—
85C11⋊C5—111no—
86C11⋊C5—111no—
87C11⋊C5—111no—
88C11⋊C5—111no—
89C11⋊C5—111no—
90C11⋊C5—111no—
91C11⋊C5—1101no—
92C11⋊C5C3×AGL(1,𝔽11)11yescharacteristic, direct product factor
93C11⋊C5C2×C3×C11⋊C511yescharacteristic, complemented
94C2×C52—1211noHall
95C3×C11—101no—
96C3×C11C5×AGL(1,𝔽11)11yescharacteristic, complemented
97C3×C11C2×C5×C11⋊C511yescharacteristic, complemented
98C2×C3×C5—111no—
99C2×C3×C5—6051no—
100C2×C3×C5—1211no—
101C2×C3×C5—1211no—
102C2×C3×C5—1211no—
103C2×C3×C5—1211no—
104C52—1211noSylow
105C2×C11—551no—
106D11C3×C5×C11⋊C511yescharacteristic, complemented
107C3×C5—111no—
108C3×C5—111no—
109C3×C5—1211no—
110C3×C5—1211no—
111C3×C5—1211no—
112C3×C5—1211no—
113C11—101no—
114C11C3×C5×AGL(1,𝔽11)11yescharacteristic, complemented
115C11C2×C3×C5×C11⋊C511yescharacteristic, complemented
116C2×C5—111no—
117C2×C5—6051no—
118C2×C5—1211no—
119C2×C5—1211no—
120C2×C5—1211no—
121C2×C5—1211no—
122C2×C3—551noHall
123C5—111no—
124C5—111no—
125C5—1211no—
126C5—1211no—
127C5—1211no—
128C5—1211no—
129C3C11⋊C5×AGL(1,𝔽11)11yescharacteristic, direct product factor, Sylow
130C2—551noSylow
subgroupG/H
center, hypercenterC3C11⋊C5×AGL(1,𝔽11)
commutator, cosocle, hypocenterC112C2×C3×C52
FrattiniC1G
Fitting, socleC3×C112C2×C52
LCSG ▷ C112
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×C11⋊C52C2semidirect
2. C11⋊C5×AGL(1,𝔽11)C3direct (N × H)
3. C3×D11×C11⋊C5C5semidirect
4. C3×#11925898C5semidirect
5. C3×#11925897C5semidirect
6. C3×#11925896C5semidirect
7. C3×#11925895C5semidirect
8. C3×C11×AGL(1,𝔽11)C5semidirect
9. C11⋊C52C2×C3semidirect
10. C3×#10597244C2×C5semidirect
11. C3×#10597244C2×C5semidirect
12. C3×#10597245C2×C5semidirect
13. C3×#10597243C2×C5semidirect
14. C3×C11×C11⋊C5C2×C5semidirect
15. C3×C11×C11⋊C5C2×C5semidirect
18. D11×C11⋊C5C3×C5semidirect
19. #11925898C3×C5semidirect
20. #11925897C3×C5semidirect
21. #11925896C3×C5semidirect
22. #11925895C3×C5semidirect
23. C11×AGL(1,𝔽11)C3×C5semidirect
26. C3×C11×D11C52semidirect
27. #10597245C2×C3×C5semidirect
28. #10597244C2×C3×C5semidirect
29. #10597244C2×C3×C5semidirect
30. #10597243C2×C3×C5semidirect
31. C11×C11⋊C5C2×C3×C5semidirect
32. C11×C11⋊C5C2×C3×C5semidirect
35. C3×C112C2×C52semidirect
47. C3×AGL(1,𝔽11)C11⋊C5direct (N × H)
50. C11×D11C3×C52semidirect
62. C3×C11⋊C5AGL(1,𝔽11)direct (N × H)
63. C3×C11⋊C5C2×C11⋊C5semidirect
65. C112C2×C3×C52semidirect
77. AGL(1,𝔽11)C3×C11⋊C5direct (N × H)
80. C3×D11C5×C11⋊C5semidirect
92. C11⋊C5C3×AGL(1,𝔽11)direct (N × H)
93. C11⋊C5C2×C3×C11⋊C5semidirect
96. C3×C11C5×AGL(1,𝔽11)semidirect
97. C3×C11C2×C5×C11⋊C5semidirect
106. D11C3×C5×C11⋊C5semidirect
114. C11C3×C5×AGL(1,𝔽11)semidirect
115. C11C2×C3×C5×C11⋊C5semidirect
129. C3C11⋊C5×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×C11⋊C522
C11⋊C5×AGL(1,𝔽11)3
C3×D11×C11⋊C55
C3×#119258985
C3×#119258975
C3×#119258965
C3×#119258955
C3×C11×AGL(1,𝔽11)5
C2×C3×C5×C11⋊C511
C3×C5×AGL(1,𝔽11)11