Finite Group Databasebeta

← C11×D11×C3⋊D21 #44479236

Subgroups — C11×D11×C3⋊D21 #44479236

Order 30492.

360 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 80 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
1C32×C7×C11×D11C211yesmaximal, characteristic, complemented
2C112×C3⋊D21C211yesmaximal, characteristic, complemented
3C11×C3⋊D231C211yesmaximal, characteristic, complemented
4C11×D11×D21—34nomaximal
5C32×C7×C112C2211yescharacteristic, complemented, Hall
6C11×D231—34no—
7C112×D21—34no—
8C3×C7×C11×D11D314yescomplemented
9C11×C3⋊D3×D11—71nomaximal, Hall
10C11×D7×D11—91noHall
11C2×C11×C3⋊D21—111nomaximal
12D11×C3⋊D21C1111yesmaximal, characteristic, direct product factor
13C3×C7×C112C2×D314yescomplemented
14C11×C3⋊D33—71no—
15C112×C3⋊D3—71no—
16C32×C11×D11D711yescharacteristic, complemented
17C11×D77—91no—
18C112×D7—91no—
19C7×C11×D11C3⋊D311yescharacteristic, complemented
20D3×C11×D11—214no—
21C2×C32×C7×C11—111no—
22C3⋊D231C2×C1111yescharacteristic, complemented
23C11×C3⋊D21—25no—
24C11×C3⋊D21—111no—
25C11×C3⋊D21D1111yescharacteristic, direct product factor
26C11×C3⋊D21C2×C1111yescharacteristic, complemented
27C32×C7×D11C2×C1111yescharacteristic, complemented
28C32×C112C2×D711yescharacteristic, complemented, Hall
29C2×C11×D21—334no—
30D11×D21—34no—
31C7×C112C2×C3⋊D311yescharacteristic, complemented, Hall
32C11×D33—214no—
33D3×C112—214no—
34C3×C11×D11D2114yescomplemented
35C32×C7×C11—25no—
36C32×C7×C11C2×D1111yescharacteristic, complemented
37C32×C7×C11C22×C1111yescharacteristic, complemented
38C2×C11×D11—631noHall
39C2×C3×C7×C11—114no—
40D231—34no—
41C11×D21—34no—
42C11×D21—34no—
43C11×D21—620no—
44C11×D21—334no—
45C3×C7×D11D3×C1114yescomplemented
46C2×C11×C3⋊D3—771no—
47C3⋊D3×D11—71no—
48C3×C112C2×D2114yescomplemented
49C2×C11×D7—991no—
50D7×D11—91no—
51C2×C3⋊D21—111noHall
52C2×C112—631no—
53C11×D11—631no—
54C11×D11C3⋊D2111yescharacteristic, direct product factor
55C3×C7×C11—220no—
56C3×C7×C11D3×D1114yescomplemented
57C3×C7×C11C2×D3×C1114yescomplemented
58C2×C32×C11—111no—
59C3⋊D33—71no—
60C11×C3⋊D3—71no—
61C11×C3⋊D3—71no—
62C11×C3⋊D3—145no—
63C11×C3⋊D3—771no—
64C32×D11C11×D711yescharacteristic, complemented
65C2×C7×C11—111no—
66D77—91no—
67C7×D11C11×C3⋊D311yescharacteristic, complemented
68C11×D7—91no—
69C11×D7—91no—
70C11×D7—185no—
71C11×D7—991no—
72C2×D3×C11—2314no—
73D3×D11—214no—
74C2×C32×C7—111no—
75C3⋊D21—111no—
76C3⋊D21C11×D1111yescharacteristic, direct product factor
77C112C2×C3⋊D2111yescharacteristic, complemented, Sylow
78C32×C11—25no—
79C32×C11D7×D1111yescharacteristic, complemented
80C32×C11C2×C11×D711yescharacteristic, complemented
81C2×D21—334no—
82C7×C11—25no—
83C7×C11C3⋊D3×D1111yescharacteristic, complemented
84C7×C11C2×C11×C3⋊D311yescharacteristic, complemented
85C2×C3×C11—114no—
86D33—214no—
87C3×D11C11×D2114yescomplemented
88D3×C11—214no—
89D3×C11—214no—
90D3×C11—4220no—
91D3×C11—2314no—
92C32×C7C2×C11×D1111yescharacteristic, complemented, Hall
93C22×C11—6931no—
94C2×D11—631no—
95C2×C3×C7—114no—
96D21—34no—
97D21—334no—
98C2×C3⋊D3—771noHall
99C3×C11—220no—
100C3×C11D11×D2114yescomplemented
101C3×C11C2×C11×D2114yescomplemented
102C2×D7—991noHall
103C2×C11—111no—
104C2×C11—631no—
105C2×C11—631no—
106C2×C11—1265no—
107C2×C11—6931no—
108D11—631no—
109D11C11×C3⋊D2111yescharacteristic, direct product factor
110C3×C7D3×C11×D1114yescomplemented
111C2×C32—111no—
112C3⋊D3—71no—
113C3⋊D3—771no—
114C2×C7—111no—
115D7—91no—
116D7—991no—
117C2×D3—2314no—
118C11—25no—
119C11D11×C3⋊D2111yescharacteristic, direct product factor
120C11C2×C11×C3⋊D2111yescharacteristic, complemented
121C32C11×D7×D1111yescharacteristic, complemented, Sylow
122C7C11×C3⋊D3×D1111yescharacteristic, complemented, Sylow
123C2×C3—114no—
124D3—214no—
125D3—2314no—
126C22—6931noSylow
127C3C11×D11×D2114yescomplemented
128C2—111no—
129C2—631no—
130C2—6931no—
subgroupG/H
center, hypercenterC11D11×C3⋊D21
commutator, cosocle, hypocenterC32×C7×C11C22×C11
FrattiniC1G
Fitting, socleC32×C7×C112C22
LCSG ▷ C32×C7×C11
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C32×C7×C11×D11C2semidirect
2. C112×C3⋊D21C2semidirect
3. C11×C3⋊D231C2semidirect
5. C32×C7×C112C22semidirect
8. C3×C7×C11×D11D3semidirect
12. D11×C3⋊D21C11direct (N × H)
13. C3×C7×C112C2×D3semidirect
16. C32×C11×D11D7semidirect
19. C7×C11×D11C3⋊D3semidirect
22. C3⋊D231C2×C11semidirect
25. C11×C3⋊D21D11direct (N × H)
26. C11×C3⋊D21C2×C11semidirect
27. C32×C7×D11C2×C11semidirect
28. C32×C112C2×D7semidirect
31. C7×C112C2×C3⋊D3semidirect
34. C3×C11×D11D21semidirect
36. C32×C7×C11C2×D11semidirect
37. C32×C7×C11C22×C11semidirect
45. C3×C7×D11D3×C11semidirect
48. C3×C112C2×D21semidirect
54. C11×D11C3⋊D21direct (N × H)
56. C3×C7×C11D3×D11semidirect
57. C3×C7×C11C2×D3×C11semidirect
64. C32×D11C11×D7semidirect
67. C7×D11C11×C3⋊D3semidirect
76. C3⋊D21C11×D11direct (N × H)
77. C112C2×C3⋊D21semidirect
79. C32×C11D7×D11semidirect
80. C32×C11C2×C11×D7semidirect
83. C7×C11C3⋊D3×D11semidirect
84. C7×C11C2×C11×C3⋊D3semidirect
87. C3×D11C11×D21semidirect
92. C32×C7C2×C11×D11semidirect
100. C3×C11D11×D21semidirect
101. C3×C11C2×C11×D21semidirect
109. D11C11×C3⋊D21direct (N × H)
110. C3×C7D3×C11×D11semidirect
119. C11D11×C3⋊D21direct (N × H)
120. C11C2×C11×C3⋊D21semidirect
121. C32C11×D7×D11semidirect
122. C7C11×C3⋊D3×D11semidirect
127. C3C11×D11×D21semidirect

Maximal subgroups

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

subgroupindex
C32×C7×C11×D112
C112×C3⋊D212
C11×C3⋊D2312
C11×D11×D213
C11×C3⋊D3×D117
C2×C11×C3⋊D2111
D11×C3⋊D2111