Finite Group Databasebeta

← D3×C3⋊#11925892 #36345124

Subgroups — D3×C3⋊#11925892 #36345124

Order 21780.

616 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 98 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⋊(C3⋊#11925892)C211yesmaximal, characteristic, complemented
2C3×D3×#10597243C211yesmaximal, characteristic, complemented
3C3×C3⋊#11925892C211yesmaximal, characteristic, complemented
4C2×C3⋊#11925892—31nomaximal
5D3×#11925892—31nomaximal
6C32×#10597243C2211yescharacteristic, complemented, Hall
7D3×C3⋊(C11⋊D11)C511yesmaximal, characteristic, complemented, Hall
8C2×C3×#10597243—31no—
9D3×#10597243D311yescharacteristic, complemented
10C3⋊#11925892—31no—
11C3⋊#11925892—31no—
12C3⋊#11925892—61no—
13C3⋊#11925892D311yescharacteristic, direct product factor
14C3×#11925892—31no—
15C2×#11925892—91noHall
16C3⋊(C3⋊(C11⋊D11))C2×C511yescharacteristic, complemented
17C3×C3⋊(C11⋊D11)C2×C511yescharacteristic, complemented
18C3×D3×C112C2×C511yescharacteristic, complemented
19D3×C3⋊AGL(1,𝔽11)—1112nomaximal
20C3×#10597243—21no—
21C3×#10597243C2×D311yescharacteristic, complemented
22C3×#10597243C2×D311yescharacteristic, complemented
23C2×C3⋊(C11⋊D11)—31no—
24D3×C11⋊D11—31no—
25C2×#10597243—31no—
26#11925892—31no—
27#11925892—91no—
28C32×C112C22×C511yescharacteristic, complemented, Hall
29C3⋊(C3⋊AGL(1,𝔽11))—1112no—
30C3×C3⋊AGL(1,𝔽11)—1112no—
31C3×D3×C11⋊C5—1112no—
32C2×C3×C112—31no—
33C3⋊(C11⋊D11)—31no—
34C3⋊(C11⋊D11)—31no—
35C3⋊(C11⋊D11)—61no—
36C3⋊(C11⋊D11)C5×D311yescharacteristic, complemented
37D3×C112C5×D311yescharacteristic, complemented
38C3×C11⋊D11—31no—
39C2×C3⋊AGL(1,𝔽11)—3312no—
40D3×AGL(1,𝔽11)—3312no—
41#10597243D3211yescharacteristic, complemented, Hall
42C32×C11⋊C5—1112no—
43C2×C11⋊D11—91noHall
44D3×D33—1112no—
45C3×C112—21no—
46C3×C112C2×C5×D311yescharacteristic, complemented
47C3×C112C2×C5×D311yescharacteristic, complemented
48C2×C3×C11⋊C5—3312no—
49C3⋊AGL(1,𝔽11)—1112no—
50C3⋊AGL(1,𝔽11)—3312no—
51C3⋊AGL(1,𝔽11)—3312no—
52C3⋊AGL(1,𝔽11)—6612no—
53D3×C11⋊C5—1112no—
54C3×AGL(1,𝔽11)—3312no—
55C2×C112—31no—
56C11⋊D11—31no—
57C11⋊D11—91no—
58C2×AGL(1,𝔽11)—9912no—
59C3⋊D33—1112no—
60C3×D33—1112no—
61C3×D3×C11AGL(1,𝔽11)112yescomplemented
62C5×D32—1211noHall
63C3×C11⋊C5—1112no—
64C3×C11⋊C5—1112no—
65C3×C11⋊C5—2212no—
66C2×D33—3312no—
67D3×D11—3312no—
68C112C5×D3211yescharacteristic, complemented, Sylow
69C2×C11⋊C5—3312no—
70AGL(1,𝔽11)—3312no—
71AGL(1,𝔽11)—9912no—
72C32×C11C2×AGL(1,𝔽11)112yescomplemented
73C5×C3⋊D3—1211no—
74C3×C5×D3—1211no—
75C3×C5×D3—1211no—
76C2×C3×C11—312no—
77D33—1112no—
78D33—3312no—
79D33—3312no—
80D33—6612no—
81C3×D11—3312no—
82D3×C11C3⋊AGL(1,𝔽11)112yescomplemented
83C2×C5×D3—3631no—
84C2×C5×D3—3631no—
85C11⋊C5—1112no—
86C32×C5—1211noHall
87C2×D11—9912no—
88D32—1211noHall
89C3×C11—212no—
90C3×C11D3×AGL(1,𝔽11)112yescomplemented
91C3×C11C2×C3⋊AGL(1,𝔽11)112yescomplemented
92C2×C3×C5—3631no—
93C2×C3×C5—3631no—
94C5×D3—3631no—
95C5×D3—3631no—
96C5×D3—1211no—
97C5×D3—1211no—
98C5×D3—7261no—
99C2×C11—312no—
100D11—3312no—
101D11—9912no—
102C22×C5—10891noHall
103C3⋊D3—1211no—
104C3×D3—1211no—
105C3×D3#1192589211yescharacteristic, complemented
106C3×C5—1211no—
107C3×C5—1211no—
108C3×C5—2421no—
109C2×D3—3631no—
110C2×D3—3631no—
111C11D3×C3⋊AGL(1,𝔽11)112yescomplemented
112C2×C5—10891no—
113C2×C5—3631no—
114C2×C5—3631no—
115C32C2×#1192589211yescharacteristic, complemented, Sylow
116C2×C3—31no—
117C2×C3—3631no—
118D3—3631no—
119D3—3631no—
120D3—1211no—
121D3—7261no—
122D3C3⋊#1192589211yescharacteristic, direct product factor
123C5—1211noSylow
124C22—10891noSylow
125C3—21no—
126C3D3×#1192589211yescharacteristic, complemented
127C3C2×C3⋊#1192589211yescharacteristic, complemented
128C2—31no—
129C2—10891no—
130C2—3631no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C112C22×C5
LCSG ▷ C32×C112
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3⋊(C3⋊#11925892)C2semidirect
2. C3×D3×#10597243C2semidirect
3. C3×C3⋊#11925892C2semidirect
6. C32×#10597243C22semidirect
7. D3×C3⋊(C11⋊D11)C5semidirect
9. D3×#10597243D3semidirect
13. C3⋊#11925892D3direct (N × H)
16. C3⋊(C3⋊(C11⋊D11))C2×C5semidirect
17. C3×C3⋊(C11⋊D11)C2×C5semidirect
18. C3×D3×C112C2×C5semidirect
21. C3×#10597243C2×D3semidirect
22. C3×#10597243C2×D3semidirect
28. C32×C112C22×C5semidirect
36. C3⋊(C11⋊D11)C5×D3semidirect
37. D3×C112C5×D3semidirect
41. #10597243D32semidirect
46. C3×C112C2×C5×D3semidirect
47. C3×C112C2×C5×D3semidirect
61. C3×D3×C11AGL(1,𝔽11)semidirect
68. C112C5×D32semidirect
72. C32×C11C2×AGL(1,𝔽11)semidirect
82. D3×C11C3⋊AGL(1,𝔽11)semidirect
90. C3×C11D3×AGL(1,𝔽11)semidirect
91. C3×C11C2×C3⋊AGL(1,𝔽11)semidirect
105. C3×D3#11925892semidirect
111. C11D3×C3⋊AGL(1,𝔽11)semidirect
115. C32C2×#11925892semidirect
122. D3C3⋊#11925892direct (N × H)
126. C3D3×#11925892semidirect
127. C3C2×C3⋊#11925892semidirect

Maximal subgroups

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

subgroupindex
C3⋊(C3⋊#11925892)2
C3×D3×#105972432
C3×C3⋊#119258922
C2×C3⋊#119258923
D3×#119258923
D3×C3⋊(C11⋊D11)5
D3×C3⋊AGL(1,𝔽11)11