Finite Group Databasebeta

← C3×C7×C11×D75 #46831442

Subgroups — C3×C7×C11×D75 #46831442

Order 34650.

108 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 108 conjugacy classes of subgroups — too many to draw. Only its 56 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×C25C211yesmaximal, characteristic, complemented, Hall
2C7×C11×D75C311yesmaximal, characteristic, direct product factor
3C3×C7×C11×D25—31nomaximal
4C3×C7×C11×D15—51nomaximal
5C3×C7×C11×C25—21no—
6C3×C7×C11×C25D311yescharacteristic, complemented
7C3×C7×C11×C25C2×C311yescharacteristic, complemented
8C3×C11×D75C711yesmaximal, characteristic, direct product factor, Hall
9C7×C11×D25—31noHall
10C32×C5×C7×C11D511yescharacteristic
11C3×C7×D75C1111yesmaximal, characteristic, direct product factor, Hall
12C32×C11×C25C2×C711yescharacteristic, complemented, Hall
13C7×C11×D15—51no—
14C3×C7×D5×C11—151no—
15C7×C11×C25C3×D311yescharacteristic, complemented, Hall
16C11×D75C3×C711yescharacteristic, direct product factor
17C3×C11×D25—31no—
18C32×C7×C25C2×C1111yescharacteristic, complemented, Hall
19C3×D3×C7×C11—251noHall
20C3×C5×C7×C11—21no—
21C3×C5×C7×C11C3×D511yescharacteristic
22C3×C5×C7×C11D1511yescharacteristic
23C7×D75C3×C1111yescharacteristic, direct product factor
24C3×C7×D25—31no—
25C3×C11×D15—51no—
26C3×C11×C25—21no—
27C3×C11×C25D3×C711yescharacteristic, complemented
28C3×C11×C25C2×C3×C711yescharacteristic, complemented
29C7×D5×C11—151no—
30C32×C7×C11D2511yescharacteristic, complemented, Hall
31C3×C7×D15—51no—
32C11×D25—31noHall
33C3×C7×C25—21no—
34C3×C7×C25D3×C1111yescharacteristic, complemented
35C3×C7×C25C2×C3×C1111yescharacteristic, complemented
36C32×C5×C11C7×D511yescharacteristic
37C2×C3×C7×C11—751no—
38D3×C7×C11—251no—
39C3×D75C7×C1111yescharacteristic, direct product factor, Hall
40C5×C7×C11C3×D1511yescharacteristic
41C7×D25—31noHall
42C11×D15—51no—
43C3×D5×C11—151no—
44C32×C5×C7D5×C1111yescharacteristic
45C11×C25C3×D3×C711yescharacteristic, complemented, Hall
46C3×C7×C11—21no—
47C3×C7×C11C3×D2511yescharacteristic, complemented
48C3×C7×C11D7511yescharacteristic, direct product factor
49C32×C25C2×C7×C1111yescharacteristic, complemented, Hall
50C7×D15—51no—
51C3×C7×D5—151no—
52C3×D3×C11—251noHall
53C7×C25C3×D3×C1111yescharacteristic, complemented, Hall
54C3×C5×C11—21no—
55C3×C5×C11C3×C7×D511yescharacteristic
56C3×C5×C11C7×D1511yescharacteristic
57C2×C7×C11—751noHall
58D75C3×C7×C1111yescharacteristic, direct product factor
59C3×D25—31no—
60C3×D3×C7—251noHall
61D5×C11—151no—
62C3×C5×C7—21no—
63C3×C5×C7C3×D5×C1111yescharacteristic
64C3×C5×C7C11×D1511yescharacteristic
65C32×C11C7×D2511yescharacteristic, complemented, Hall
66C3×D15—51no—
67C7×C11C3×D7511yescharacteristic, direct product factor, Hall
68C3×C25—21no—
69C3×C25D3×C7×C1111yescharacteristic, complemented
70C3×C25C2×C3×C7×C1111yescharacteristic, complemented
71C7×D5—151no—
72C2×C3×C11—751no—
73D3×C11—251no—
74C32×C7C11×D2511yescharacteristic, complemented, Hall
75C5×C11C3×C7×D1511yescharacteristic
76D25—31noHall
77C32×C5C7×D5×C1111yescharacteristic
78C2×C3×C7—751no—
79D3×C7—251no—
80C5×C7C3×C11×D1511yescharacteristic
81C3×C11—21no—
82C3×C11C3×C7×D2511yescharacteristic, complemented
83C3×C11C7×D7511yescharacteristic, direct product factor
84D15—51no—
85C3×D5—151no—
86C25C3×D3×C7×C1111yescharacteristic, complemented, Sylow
87C2×C11—751noHall
88C3×C7—21no—
89C3×C7C3×C11×D2511yescharacteristic, complemented
90C3×C7C11×D7511yescharacteristic, direct product factor
91C3×D3—251noHall
92C3×C5—21no—
93C3×C5C3×C7×D5×C1111yescharacteristic
94C3×C5C7×C11×D1511yescharacteristic
95C2×C7—751noHall
96C11C3×C7×D7511yescharacteristic, direct product factor, Sylow
97D5—151no—
98C32C7×C11×D2511yescharacteristic, complemented, Sylow
99C7C3×C11×D7511yescharacteristic, direct product factor, Sylow
100C2×C3—751no—
101D3—251no—
102C5C3×C7×C11×D1511yescharacteristic
103C3—21no—
104C3C3×C7×C11×D2511yescharacteristic, complemented
105C3C7×C11×D7511yescharacteristic, direct product factor
106C2—751noSylow
subgroupG/H
center, hypercenterC3×C7×C11D75
commutator, cosocle, hypocenterC3×C25C2×C3×C7×C11
FrattiniC5C3×C7×C11×D15
FittingC32×C7×C11×C25C2
socleC32×C5×C7×C11D5
LCSG ▷ C3×C25
UCSC1 ◁ C3×C7×C11

Complements

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

NH ≅ G/Ntype
1. C32×C7×C11×C25C2semidirect
2. C7×C11×D75C3direct (N × H)
6. C3×C7×C11×C25D3semidirect
7. C3×C7×C11×C25C2×C3semidirect
8. C3×C11×D75C7direct (N × H)
11. C3×C7×D75C11direct (N × H)
12. C32×C11×C25C2×C7semidirect
15. C7×C11×C25C3×D3semidirect
16. C11×D75C3×C7direct (N × H)
18. C32×C7×C25C2×C11semidirect
23. C7×D75C3×C11direct (N × H)
27. C3×C11×C25D3×C7semidirect
28. C3×C11×C25C2×C3×C7semidirect
30. C32×C7×C11D25semidirect
34. C3×C7×C25D3×C11semidirect
35. C3×C7×C25C2×C3×C11semidirect
39. C3×D75C7×C11direct (N × H)
45. C11×C25C3×D3×C7semidirect
47. C3×C7×C11C3×D25semidirect
48. C3×C7×C11D75direct (N × H)
49. C32×C25C2×C7×C11semidirect
53. C7×C25C3×D3×C11semidirect
58. D75C3×C7×C11direct (N × H)
65. C32×C11C7×D25semidirect
67. C7×C11C3×D75direct (N × H)
69. C3×C25D3×C7×C11semidirect
70. C3×C25C2×C3×C7×C11semidirect
74. C32×C7C11×D25semidirect
82. C3×C11C3×C7×D25semidirect
83. C3×C11C7×D75direct (N × H)
86. C25C3×D3×C7×C11semidirect
89. C3×C7C3×C11×D25semidirect
90. C3×C7C11×D75direct (N × H)
96. C11C3×C7×D75direct (N × H)
98. C32C7×C11×D25semidirect
99. C7C3×C11×D75direct (N × H)
104. C3C3×C7×C11×D25semidirect
105. C3C7×C11×D75direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C7×C11×C252
C7×C11×D753
C3×C7×C11×D253
C3×C7×C11×D155
C3×C11×D757
C3×C7×D7511