Finite Group Databasebeta

← C11×C3⋊D3×D77 #44479242

Subgroups — C11×C3⋊D3×D77 #44479242

Order 30492.

360 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 72 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×C11×D77C211yesmaximal, characteristic, complemented
2C7×C112×C3⋊D3C211yesmaximal, characteristic, complemented
3C11×C3⋊D231C211yesmaximal, characteristic, complemented
4D3×C11×D77—34nomaximal
5C32×C7×C112C2211yescharacteristic, complemented, Hall
6C11×D231—34no—
7D3×C7×C112—34no—
8C3×C11×D77D314yescomplemented
9C11×C3⋊D3×D11—71nomaximal, Hall
10C2×C11×D77—91noHall
11C3⋊D3×D77C1111yesmaximal, characteristic, direct product factor
12C11×D7×C3⋊D3—111nomaximal
13C3×C7×C112C2×D314yescomplemented
14C11×C3⋊D33—71no—
15C112×C3⋊D3D711yescharacteristic, complemented
16C32×C11×D11—71no—
17C2×C7×C112—91no—
18C11×D77—91no—
19C11×D77C3⋊D311yescharacteristic, direct product factor
20D3×C11×D11—214no—
21C3⋊D231C2×C1111yescharacteristic, complemented
22C11×C3⋊D21—111no—
23C7×C11×C3⋊D3—25no—
24C7×C11×C3⋊D3D1111yescharacteristic, complemented
25C7×C11×C3⋊D3C2×C1111yescharacteristic, complemented
26C32×D77C2×C1111yescharacteristic, complemented
27C32×C11×D7—111no—
28C32×C112C2×D711yescharacteristic, complemented, Hall
29D3×D77—34no—
30D3×C11×D7—334no—
31C7×C112C2×C3⋊D311yescharacteristic, complemented, Hall
32C11×D33—214no—
33D3×C112—34no—
34C3×C11×D11—74no—
35C32×C7×C11—25no—
36C32×C7×C11C2×D1111yescharacteristic, complemented
37C32×C7×C11C22×C1111yescharacteristic, complemented
38C2×C11×D11—631noHall
39D231—34no—
40C11×D21—334no—
41D3×C7×C11—34no—
42D3×C7×C11—34no—
43D3×C7×C11—620no—
44C3×D77D3×C1114yescomplemented
45C3×C11×D7—114no—
46C2×C11×C3⋊D3—771no—
47C3⋊D3×D11—71no—
48C3×C112D3×D714yescomplemented
49C2×D77—91no—
50C2×C11×D7—991no—
51D7×C3⋊D3—111noHall
52C2×C112—91no—
53C11×D11—71no—
54C11×D11—631no—
55C3×C7×C11—220no—
56C3×C7×C11D3×D1114yescomplemented
57C3×C7×C11C2×D3×C1114yescomplemented
58C2×C32×C11—771no—
59C3⋊D33—71no—
60C11×C3⋊D3—25no—
61C11×C3⋊D3—771no—
62C11×C3⋊D3C11×D711yescharacteristic, complemented
63C11×C3⋊D3D7711yescharacteristic, direct product factor
64C32×D11—71no—
65C2×C7×C11—91no—
66C2×C7×C11—91no—
67C2×C7×C11—185no—
68D77—91no—
69D77C11×C3⋊D311yescharacteristic, direct product factor
70C11×D7—111no—
71C11×D7—991no—
72C2×D3×C11—2314no—
73D3×D11—214no—
74C3⋊D21—111no—
75C7×C3⋊D3C11×D1111yescharacteristic, complemented
76C32×D7—111no—
77C112D7×C3⋊D311yescharacteristic, complemented, Sylow
78C32×C11—25no—
79C32×C11C2×C11×D711yescharacteristic, complemented
80C32×C11C2×D7711yescharacteristic, complemented
81D3×D7—334no—
82C7×C11—25no—
83C7×C11C3⋊D3×D1111yescharacteristic, complemented
84C7×C11C2×C11×C3⋊D311yescharacteristic, complemented
85C2×C3×C11—774no—
86D33—214no—
87C3×D11—74no—
88D3×C11—34no—
89D3×C11—34no—
90D3×C11—620no—
91D3×C11—2314no—
92C32×C7C2×C11×D1111yescharacteristic, complemented, Hall
93C22×C11—6931no—
94C2×D11—631no—
95D21—334no—
96C3×D7—114no—
97D3×C7—34no—
98C2×C3⋊D3—771noHall
99C3×C11—220no—
100C3×C11D3×C11×D714yescomplemented
101C3×C11D3×D7714yescomplemented
102C2×D7—991noHall
103C2×C11—91no—
104C2×C11—91no—
105C2×C11—185no—
106C2×C11—771no—
107C2×C11—6931no—
108D11—71no—
109D11—631no—
110C3×C7D3×C11×D1114yescomplemented
111C2×C32—771no—
112C3⋊D3—771no—
113C3⋊D3C11×D7711yescharacteristic, direct product factor
114C2×C7—91no—
115D7—111no—
116D7—991no—
117C2×D3—2314no—
118C11—25no—
119C11C11×D7×C3⋊D311yescharacteristic, complemented
120C11C3⋊D3×D7711yescharacteristic, direct product factor
121C32C2×C11×D7711yescharacteristic, complemented, Sylow
122C7C11×C3⋊D3×D1111yescharacteristic, complemented, Sylow
123C2×C3—774no—
124D3—34no—
125D3—2314no—
126C22—6931noSylow
127C3D3×C11×D7714yescomplemented
128C2—91no—
129C2—771no—
130C2—6931no—
subgroupG/H
center, hypercenterC11C3⋊D3×D77
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×C11×D77C2semidirect
2. C7×C112×C3⋊D3C2semidirect
3. C11×C3⋊D231C2semidirect
5. C32×C7×C112C22semidirect
8. C3×C11×D77D3semidirect
11. C3⋊D3×D77C11direct (N × H)
13. C3×C7×C112C2×D3semidirect
15. C112×C3⋊D3D7semidirect
19. C11×D77C3⋊D3direct (N × H)
21. C3⋊D231C2×C11semidirect
24. C7×C11×C3⋊D3D11semidirect
25. C7×C11×C3⋊D3C2×C11semidirect
26. C32×D77C2×C11semidirect
28. C32×C112C2×D7semidirect
31. C7×C112C2×C3⋊D3semidirect
36. C32×C7×C11C2×D11semidirect
37. C32×C7×C11C22×C11semidirect
44. C3×D77D3×C11semidirect
48. C3×C112D3×D7semidirect
56. C3×C7×C11D3×D11semidirect
57. C3×C7×C11C2×D3×C11semidirect
62. C11×C3⋊D3C11×D7semidirect
63. C11×C3⋊D3D77direct (N × H)
69. D77C11×C3⋊D3direct (N × H)
75. C7×C3⋊D3C11×D11semidirect
77. C112D7×C3⋊D3semidirect
79. C32×C11C2×C11×D7semidirect
80. C32×C11C2×D77semidirect
83. C7×C11C3⋊D3×D11semidirect
84. C7×C11C2×C11×C3⋊D3semidirect
92. C32×C7C2×C11×D11semidirect
100. C3×C11D3×C11×D7semidirect
101. C3×C11D3×D77semidirect
110. C3×C7D3×C11×D11semidirect
113. C3⋊D3C11×D77direct (N × H)
119. C11C11×D7×C3⋊D3semidirect
120. C11C3⋊D3×D77direct (N × H)
121. C32C2×C11×D77semidirect
122. C7C11×C3⋊D3×D11semidirect
127. C3D3×C11×D77semidirect

Maximal subgroups

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

subgroupindex
C32×C11×D772
C7×C112×C3⋊D32
C11×C3⋊D2312
D3×C11×D773
C11×C3⋊D3×D117
C3⋊D3×D7711
C11×D7×C3⋊D311