Finite Group Databasebeta

← C3×C11×C3⋊(C5⋊D35) #46831672

Subgroups — C3×C11×C3⋊(C5⋊D35) #46831672

Order 34650.

288 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 132 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×C52×C7×C11C211yesmaximal, characteristic, complemented, Hall
2C3×C11×C5⋊D35—31nomaximal
3C11×C3⋊(C5⋊D35)C311yesmaximal, characteristic, direct product factor
4C3×C11×D105—56nomaximal
5C3×C52×C7×C11—21no—
6C3×C52×C7×C11D311yescharacteristic, complemented
7C3×C52×C7×C11C2×C311yescharacteristic, complemented
8C3×C11×C3⋊(C5⋊D5)—71nomaximal, Hall
9C11×C5⋊D35—31noHall
10C32×C5×C7×C11D516yescomplemented
11C3×C3⋊(C5⋊D35)C1111yesmaximal, characteristic, direct product factor, Hall
12C32×C52×C11D711yescharacteristic, complemented, Hall
13C11×D105—56no—
14C3×C11×D35—156no—
15C52×C7×C11C3×D311yescharacteristic, complemented, Hall
16C11×C3⋊(C5⋊D5)—71no—
17C3×C11×C5⋊D5—211no—
18C32×C52×C7C2×C1111yescharacteristic, complemented, Hall
19C3×C11×D21—251noHall
20C3×C5×C7×C11—26no—
21C3×C5×C7×C11C3×D516yescomplemented
22C3×C5×C7×C11D1516yescomplemented
23C3⋊(C5⋊D35)C3×C1111yescharacteristic, direct product factor
24C3×C5⋊D35—31no—
25C3×C11×D15—356no—
26C3×C52×C11—21no—
27C3×C52×C11C3×D711yescharacteristic, complemented
28C3×C52×C11D2111yescharacteristic, complemented
29C11×D35—156no—
30C32×C7×C11C5⋊D511yescharacteristic, complemented, Hall
31C3×D105—56no—
32C11×C5⋊D5—211noHall
33C3×C52×C7—21no—
34C3×C52×C7D3×C1111yescharacteristic, complemented
35C3×C52×C7C2×C3×C1111yescharacteristic, complemented
36C32×C5×C11D3516yescomplemented
37C11×D21—251no—
38C3×C11×D7—751no—
39C3×C3⋊(C5⋊D5)—71noHall
40C5×C7×C11C3×D1516yescomplemented
41C5⋊D35—31noHall
42C11×D15—356no—
43C3×D5×C11—1056no—
44C32×C5×C7D5×C1116yescomplemented
45C52×C11C3×D2111yescharacteristic, complemented, Hall
46C3×C7×C11—21no—
47C3×C7×C11C3×C5⋊D511yescharacteristic, complemented
48C3×C7×C11C3⋊(C5⋊D5)11yescharacteristic, complemented
49C32×C52C11×D711yescharacteristic, complemented, Hall
50D105—56no—
51C3×D35—156no—
52C3×D3×C11—1751noHall
53C52×C7C3×D3×C1111yescharacteristic, complemented, Hall
54C3×C5×C11—26no—
55C3×C5×C11C3×D3516yescomplemented
56C3×C5×C11D10516yescomplemented
57C11×D7—751noHall
58C3⋊(C5⋊D5)—71no—
59C3×C5⋊D5—211no—
60C3×D21—251noHall
61D5×C11—1056no—
62C3×C5×C7—26no—
63C3×C5×C7C3×D5×C1116yescomplemented
64C3×C5×C7C11×D1516yescomplemented
65C32×C11C5⋊D3511yescharacteristic, complemented, Hall
66C3×D15—356no—
67C7×C11C3×C3⋊(C5⋊D5)11yescharacteristic, complemented, Hall
68C3×C52—21no—
69C3×C52C3×C11×D711yescharacteristic, complemented
70C3×C52C11×D2111yescharacteristic, complemented
71D35—156no—
72C2×C3×C11—5251no—
73D3×C11—1751no—
74C32×C7C11×C5⋊D511yescharacteristic, complemented, Hall
75C5×C11C3×D10516yescomplemented
76C5⋊D5—211noHall
77C32×C5C11×D3516yescomplemented
78D21—251no—
79C3×D7—751no—
80C5×C7C3×C11×D1516yescomplemented
81C3×C11—21no—
82C3×C11C3×C5⋊D3511yescharacteristic, complemented
83C3×C11C3⋊(C5⋊D35)11yescharacteristic, direct product factor
84D15—356no—
85C3×D5—1056no—
86C52C3×C11×D2111yescharacteristic, complemented, Sylow
87C2×C11—5251noHall
88C3×C7—21no—
89C3×C7C3×C11×C5⋊D511yescharacteristic, complemented
90C3×C7C11×C3⋊(C5⋊D5)11yescharacteristic, complemented
91C3×D3—1751noHall
92C3×C5—26no—
93C3×C5C3×C11×D3516yescomplemented
94C3×C5C11×D10516yescomplemented
95D7—751noHall
96C11C3×C3⋊(C5⋊D35)11yescharacteristic, direct product factor, Sylow
97D5—1056no—
98C32C11×C5⋊D3511yescharacteristic, complemented, Sylow
99C7C3×C11×C3⋊(C5⋊D5)11yescharacteristic, complemented, Sylow
100C2×C3—5251no—
101D3—1751no—
102C5C3×C11×D10516yescomplemented
103C3—21no—
104C3C11×C3⋊(C5⋊D35)11yescharacteristic, direct product factor
105C3C3×C11×C5⋊D3511yescharacteristic, complemented
106C2—5251noSylow
subgroupG/H
center, hypercenterC3×C11C3⋊(C5⋊D35)
commutator, cosocle, hypocenterC3×C52×C7C2×C3×C11
FrattiniC1G
Fitting, socleC32×C52×C7×C11C2
LCSG ▷ C3×C52×C7
UCSC1 ◁ C3×C11

Complements

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

NH ≅ G/Ntype
1. C32×C52×C7×C11C2semidirect
3. C11×C3⋊(C5⋊D35)C3direct (N × H)
6. C3×C52×C7×C11D3semidirect
7. C3×C52×C7×C11C2×C3semidirect
10. C32×C5×C7×C11D5semidirect
11. C3×C3⋊(C5⋊D35)C11direct (N × H)
12. C32×C52×C11D7semidirect
15. C52×C7×C11C3×D3semidirect
18. C32×C52×C7C2×C11semidirect
21. C3×C5×C7×C11C3×D5semidirect
22. C3×C5×C7×C11D15semidirect
23. C3⋊(C5⋊D35)C3×C11direct (N × H)
27. C3×C52×C11C3×D7semidirect
28. C3×C52×C11D21semidirect
30. C32×C7×C11C5⋊D5semidirect
34. C3×C52×C7D3×C11semidirect
35. C3×C52×C7C2×C3×C11semidirect
36. C32×C5×C11D35semidirect
40. C5×C7×C11C3×D15semidirect
44. C32×C5×C7D5×C11semidirect
45. C52×C11C3×D21semidirect
47. C3×C7×C11C3×C5⋊D5semidirect
48. C3×C7×C11C3⋊(C5⋊D5)semidirect
49. C32×C52C11×D7semidirect
53. C52×C7C3×D3×C11semidirect
55. C3×C5×C11C3×D35semidirect
56. C3×C5×C11D105semidirect
63. C3×C5×C7C3×D5×C11semidirect
64. C3×C5×C7C11×D15semidirect
65. C32×C11C5⋊D35semidirect
67. C7×C11C3×C3⋊(C5⋊D5)semidirect
69. C3×C52C3×C11×D7semidirect
70. C3×C52C11×D21semidirect
74. C32×C7C11×C5⋊D5semidirect
75. C5×C11C3×D105semidirect
77. C32×C5C11×D35semidirect
80. C5×C7C3×C11×D15semidirect
82. C3×C11C3×C5⋊D35semidirect
83. C3×C11C3⋊(C5⋊D35)direct (N × H)
86. C52C3×C11×D21semidirect
89. C3×C7C3×C11×C5⋊D5semidirect
90. C3×C7C11×C3⋊(C5⋊D5)semidirect
93. C3×C5C3×C11×D35semidirect
94. C3×C5C11×D105semidirect
96. C11C3×C3⋊(C5⋊D35)direct (N × H)
98. C32C11×C5⋊D35semidirect
99. C7C3×C11×C3⋊(C5⋊D5)semidirect
102. C5C3×C11×D105semidirect
104. C3C11×C3⋊(C5⋊D35)direct (N × H)
105. C3C3×C11×C5⋊D35semidirect

Maximal subgroups

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

subgroupindex
C32×C52×C7×C112
C3×C11×C5⋊D353
C11×C3⋊(C5⋊D35)3
C3×C11×D1055
C3×C11×C3⋊(C5⋊D5)7
C3×C3⋊(C5⋊D35)11