Finite Group Databasebeta

← D11×C3⋊D231 #44479237

Subgroups — D11×C3⋊D231 #44479237

Order 30492.

360 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 76 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
2C11×C3⋊D231C211yesmaximal, characteristic, complemented
3C3⋊(C3⋊(C7⋊(C11⋊D11)))C211yesmaximal, characteristic, complemented
4D11×D231—34nomaximal
5C32×C7×C112C2211yescharacteristic, complemented, Hall
6C3⋊(C7⋊(C11⋊D11))—34no—
7C11×D231—34no—
8C3×C7×C11×D11D314yescomplemented
9D11×C3⋊D33—71nomaximal, Hall
10D11×D77—91noHall
11C2×C3⋊D231—111nomaximal
12D11×C3⋊D21—111nomaximal
13C3×C7×C112C2×D314yescomplemented
14C3⋊(C3⋊(C11⋊D11))—71no—
15C11×C3⋊D33—71no—
16C32×C11×D11D711yescharacteristic, complemented
17C7⋊(C11⋊D11)—91no—
18C11×D77—91no—
19C7×C11×D11C3⋊D311yescharacteristic, complemented
20D11×D33—214no—
21C2×C32×C7×C11—111no—
22C3⋊D231—111no—
23C3⋊D231—111no—
24C3⋊D231—225no—
25C3⋊D231D1111yescharacteristic, direct product factor
26C11×C3⋊D21—111no—
27C32×C7×D11D1111yescharacteristic, complemented
28C32×C112C2×D711yescharacteristic, complemented, Hall
29C2×D231—334no—
30D11×D21—334no—
31C7×C112C2×C3⋊D311yescharacteristic, complemented, Hall
32C3⋊(C11⋊D11)—214no—
33C11×D33—214no—
34C3×C11×D11D2114yescomplemented
35C32×C7×C11—25no—
36C32×C7×C11C2×D1111yescharacteristic, complemented
37C32×C7×C11C2×D1111yescharacteristic, complemented
38D112—631noHall
39C2×C3×C7×C11—114no—
40D231—34no—
41D231—334no—
42D231—334no—
43D231—6620no—
44C11×D21—334no—
45C3×C7×D11D3314yescomplemented
46C2×C3⋊D33—771no—
47C3⋊D3×D11—771no—
48C3×C112C2×D2114yescomplemented
49C2×D77—991no—
50D7×D11—991no—
51C2×C3⋊D21—1211noHall
52C11⋊D11—631no—
53C11×D11—631no—
54C11×D11C3⋊D2111yescharacteristic, complemented
55C3×C7×C11—220no—
56C3×C7×C11D3×D1114yescomplemented
57C3×C7×C11C2×D3314yescomplemented
58C2×C32×C11—111no—
59C3⋊D33—71no—
60C3⋊D33—771no—
61C3⋊D33—771no—
62C3⋊D33—1545no—
63C11×C3⋊D3—771no—
64C32×D11D7711yescharacteristic, complemented
65C2×C7×C11—111no—
66D77—91no—
67D77—991no—
68D77—991no—
69D77—1985no—
70C7×D11C3⋊D3311yescharacteristic, complemented
71C11×D7—991no—
72C2×D33—2314no—
73D3×D11—2314no—
74C2×C32×C7—111no—
75C3⋊D21—111no—
76C3⋊D21—1211no—
77C112C2×C3⋊D2111yescharacteristic, complemented, Sylow
78C32×C11—25no—
79C32×C11D7×D1111yescharacteristic, complemented
80C32×C11C2×D7711yescharacteristic, complemented
81C2×D21—3634no—
82C7×C11—25no—
83C7×C11C3⋊D3×D1111yescharacteristic, complemented
84C7×C11C2×C3⋊D3311yescharacteristic, complemented
85C2×C3×C11—114no—
86D33—214no—
87D33—46220no—
88D33—2314no—
89D33—2314no—
90C3×D11D23114yescomplemented
91D3×C11—2314no—
92C32×C7D11211yescharacteristic, complemented, Hall
93C2×D11—6931no—
94C2×D11—6931no—
95C2×C3×C7—114no—
96D21—334no—
97D21—3634no—
98C2×C3⋊D3—8471noHall
99C3×C11—220no—
100C3×C11D11×D2114yescomplemented
101C3×C11C2×D23114yescomplemented
102C2×D7—10891noHall
103C2×C11—111no—
104C2×C11—6931no—
105D11—631no—
106D11—13865no—
107D11—6931no—
108D11—6931no—
109D11C3⋊D23111yescharacteristic, direct product factor
110C3×C7D11×D3314yescomplemented
111C2×C32—111no—
112C3⋊D3—771no—
113C3⋊D3—8471no—
114C2×C7—111no—
115D7—10891no—
116D7—991no—
117C2×D3—25414no—
118C11—25no—
119C11D11×C3⋊D2111yescharacteristic, complemented
120C11C2×C3⋊D23111yescharacteristic, complemented
121C32D11×D7711yescharacteristic, complemented, Sylow
122C7D11×C3⋊D3311yescharacteristic, complemented, Sylow
123C2×C3—114no—
124D3—2314no—
125D3—25414no—
126C22—76231noSylow
127C3D11×D23114yescomplemented
128C2—111no—
129C2—6931no—
130C2—76231no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C7×C112C22
LCSG ▷ C32×C7×C112
UCSC1

Complements

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

NH ≅ G/Ntype
1. C32×C7×C11×D11C2semidirect
2. C11×C3⋊D231C2semidirect
3. C3⋊(C3⋊(C7⋊(C11⋊D11)))C2semidirect
5. C32×C7×C112C22semidirect
8. C3×C7×C11×D11D3semidirect
13. C3×C7×C112C2×D3semidirect
16. C32×C11×D11D7semidirect
19. C7×C11×D11C3⋊D3semidirect
25. C3⋊D231D11direct (N × H)
27. C32×C7×D11D11semidirect
28. C32×C112C2×D7semidirect
31. C7×C112C2×C3⋊D3semidirect
34. C3×C11×D11D21semidirect
36. C32×C7×C11C2×D11semidirect
37. C32×C7×C11C2×D11semidirect
45. C3×C7×D11D33semidirect
48. C3×C112C2×D21semidirect
54. C11×D11C3⋊D21semidirect
56. C3×C7×C11D3×D11semidirect
57. C3×C7×C11C2×D33semidirect
64. C32×D11D77semidirect
70. C7×D11C3⋊D33semidirect
77. C112C2×C3⋊D21semidirect
79. C32×C11D7×D11semidirect
80. C32×C11C2×D77semidirect
83. C7×C11C3⋊D3×D11semidirect
84. C7×C11C2×C3⋊D33semidirect
90. C3×D11D231semidirect
92. C32×C7D112semidirect
100. C3×C11D11×D21semidirect
101. C3×C11C2×D231semidirect
109. D11C3⋊D231direct (N × H)
110. C3×C7D11×D33semidirect
119. C11D11×C3⋊D21semidirect
120. C11C2×C3⋊D231semidirect
121. C32D11×D77semidirect
122. C7D11×C3⋊D33semidirect
127. C3D11×D231semidirect

Maximal subgroups

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

subgroupindex
C32×C7×C11×D112
C11×C3⋊D2312
C3⋊(C3⋊(C7⋊(C11⋊D11)))2
D11×D2313
D11×C3⋊D337
C2×C3⋊D23111
D11×C3⋊D2111