Finite Group Databasebeta

← D15⋊(C3⋊(C11⋊D11)) #36345345

Subgroups — D15⋊(C3⋊(C11⋊D11)) #36345345

Order 21780.

616 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 145 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×C112×D15C211yesmaximal, characteristic, complemented
2C3×C3⋊(C5⋊(C11⋊D11))C211yesmaximal, characteristic, complemented
3C5×C3⋊(C3⋊(C11⋊D11))C211yesmaximal, characteristic, complemented
4D15⋊(C11⋊D11)—31nomaximal
5D5×C3⋊(C11⋊D11)—31nomaximal
6C32×C5×C112C2211yescharacteristic, complemented, Hall
7D3×C3⋊(C11⋊D11)—51nomaximal, Hall
8C3⋊(C5⋊(C11⋊D11))D311yescharacteristic, complemented
9C112×D15D311yescharacteristic, complemented
10C5×C3⋊(C11⋊D11)—31no—
11C5×C3⋊(C11⋊D11)—31no—
12C5×C3⋊(C11⋊D11)—61no—
13C3×C5⋊(C11⋊D11)—31no—
14C3×D5×C112—31no—
15D5×C11⋊D11—91noHall
16C3⋊(C3⋊(C11⋊D11))D511yescharacteristic, complemented
17C3×C3⋊(C11⋊D11)—51no—
18C3×D3×C112—51no—
19D15⋊D33—1112nomaximal
20C3×C5×C112—21no—
21C3×C5×C112C2×D311yescharacteristic, complemented
22C3×C5×C112C2×D311yescharacteristic, complemented
23C2×C3⋊(C11⋊D11)—151no—
24D3×C11⋊D11—151no—
25C5⋊(C11⋊D11)—31no—
26D5×C112—31no—
27C5×C11⋊D11—91no—
28C32×C112C2×D511yescharacteristic, complemented, Hall
29C5×C3⋊D33—1112no—
30C3×D165—1112no—
31C3×C11×D15D11112yescomplemented
32C2×C3×C112—151no—
33C3⋊(C11⋊D11)—31no—
34C3⋊(C11⋊D11)—31no—
35C3⋊(C11⋊D11)—51no—
36C3⋊(C11⋊D11)—61no—
37D3×C112—51no—
38C3×C11⋊D11—151no—
39D15⋊D11—3312no—
40D5×D33—3312no—
41C5×C112D3211yescharacteristic, complemented, Hall
42C32×C5×C11C2×D11112yescomplemented
43C2×C11⋊D11—451noHall
44D3×D33—5512no—
45C3×C112—21no—
46C3×C112D3×D511yescharacteristic, complemented
47C3×C112D3×D511yescharacteristic, complemented
48D165—1112no—
49C11×D15D33112yescomplemented
50C5×D33—3312no—
51C5×D33—3312no—
52C5×D33—6612no—
53C3×D55—3312no—
54C3×D5×C11—312no—
55C2×C112—151no—
56C11⋊D11—91no—
57C11⋊D11—151no—
58D5×D11—9912no—
59C3⋊D33—1112no—
60C3×D33—5512no—
61C3×D3×C11—512no—
62(C3⋊D3)⋊D5—1211noHall
63C3×C5×C11—212no—
64C3×C5×C11D3×D11112yescomplemented
65C3×C5×C11C2×D33112yescomplemented
66C2×D33—16512no—
67D3×D11—16512no—
68C112(C3⋊D3)⋊D511yescharacteristic, complemented, Sylow
69D55—3312no—
70C5×D11—9912no—
71D5×C11—312no—
72C32×C11D5×D11112yescomplemented
73C5×C3⋊D3—1211no—
74C3×D15—1211no—
75C3×D15C11⋊D1111yescharacteristic, complemented
76C2×C3×C11—1512no—
77D33—3312no—
78D33—3312no—
79D33—5512no—
80D33—6612no—
81C3×D11—16512no—
82D3×C11—512no—
83D3×D5—3631no—
84D3×D5—3631no—
85C5×C11D3×D33112yescomplemented
86C32×C5C2×C11⋊D1111yescharacteristic, complemented, Hall
87C2×D11—49512no—
88D32—6051noHall
89C3×C11—212no—
90C3×C11D5×D33112yescomplemented
91C3×C11D15⋊D11112yescomplemented
92D15—1211no—
93D15C3⋊(C11⋊D11)11yescharacteristic, complemented
94C3×D5—31no—
95C3×D5—3631no—
96C5×D3—3631no—
97C5×D3—3631no—
98C5×D3—7261no—
99C2×C11—1512no—
100D11—9912no—
101D11—16512no—
102C2×D5—10891noHall
103C3⋊D3—1211no—
104C3×D3—51no—
105C3×D3—6051no—
106C3×C5—21no—
107C3×C5D3×C11⋊D1111yescharacteristic, complemented
108C3×C5C2×C3⋊(C11⋊D11)11yescharacteristic, complemented
109C2×D3—18151no—
110C2×D3—18151no—
111C11D15⋊D33112yescomplemented
112C2×C5—10891no—
113D5—31no—
114D5—3631no—
115C32D5×C11⋊D1111yescharacteristic, complemented, Sylow
116C2×C3—151no—
117C2×C3—18151no—
118D3—51no—
119D3—6051no—
120D3—3631no—
121D3—3631no—
122D3—7261no—
123C5D3×C3⋊(C11⋊D11)11yescharacteristic, complemented, Sylow
124C22—54451noSylow
125C3—21no—
126C3D5×C3⋊(C11⋊D11)11yescharacteristic, complemented
127C3D15⋊(C11⋊D11)11yescharacteristic, complemented
128C2—151no—
129C2—18151no—
130C2—10891no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C112C22
LCSG ▷ C32×C5×C112
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C112×D15C2semidirect
2. C3×C3⋊(C5⋊(C11⋊D11))C2semidirect
3. C5×C3⋊(C3⋊(C11⋊D11))C2semidirect
6. C32×C5×C112C22semidirect
8. C3⋊(C5⋊(C11⋊D11))D3semidirect
9. C112×D15D3semidirect
16. C3⋊(C3⋊(C11⋊D11))D5semidirect
21. C3×C5×C112C2×D3semidirect
22. C3×C5×C112C2×D3semidirect
28. C32×C112C2×D5semidirect
31. C3×C11×D15D11semidirect
41. C5×C112D32semidirect
42. C32×C5×C11C2×D11semidirect
46. C3×C112D3×D5semidirect
47. C3×C112D3×D5semidirect
49. C11×D15D33semidirect
64. C3×C5×C11D3×D11semidirect
65. C3×C5×C11C2×D33semidirect
68. C112(C3⋊D3)⋊D5semidirect
72. C32×C11D5×D11semidirect
75. C3×D15C11⋊D11semidirect
85. C5×C11D3×D33semidirect
86. C32×C5C2×C11⋊D11semidirect
90. C3×C11D5×D33semidirect
91. C3×C11D15⋊D11semidirect
93. D15C3⋊(C11⋊D11)semidirect
107. C3×C5D3×C11⋊D11semidirect
108. C3×C5C2×C3⋊(C11⋊D11)semidirect
111. C11D15⋊D33semidirect
115. C32D5×C11⋊D11semidirect
123. C5D3×C3⋊(C11⋊D11)semidirect
126. C3D5×C3⋊(C11⋊D11)semidirect
127. C3D15⋊(C11⋊D11)semidirect

Maximal subgroups

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

subgroupindex
C3×C112×D152
C3×C3⋊(C5⋊(C11⋊D11))2
C5×C3⋊(C3⋊(C11⋊D11))2
D15⋊(C11⋊D11)3
D5×C3⋊(C11⋊D11)3
D3×C3⋊(C11⋊D11)5
D15⋊D3311