Finite Group Databasebeta

← C3×D5×D11×C49 #44568381

Subgroups — C3×D5×D11×C49 #44568381

Order 32340.

120 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 60 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
1C3×C49×D55C211yesmaximal, characteristic, complemented
2C3×D5×C11×C49C211yesmaximal, characteristic, complemented
3C3×C5×D11×C49C211yesmaximal, characteristic, complemented
4D5×D11×C49C311yesmaximal, characteristic, direct product factor, Hall
5C3×C5×C11×C49C2211yescharacteristic, complemented, Hall
6C2×C3×D11×C49—51nomaximal, Hall
7C49×D55C2×C311yescharacteristic, complemented
8D5×C11×C49C2×C311yescharacteristic, complemented
9C5×D11×C49C2×C311yescharacteristic, complemented
10C3×C7×D5×D11C711yesmaximal, characteristic
11C3×D11×C49—51no—
12C3×D11×C49D511yescharacteristic, direct product factor
13C2×C3×C11×C49—51no—
14C2×C3×D5×C49—111nomaximal, Hall
15C5×C11×C49C22×C311yescharacteristic, complemented, Hall
16C3×C7×D55C2×C711yescharacteristic
17C3×C7×D5×C11C2×C711yescharacteristic
18C3×C5×C7×D11C2×C711yescharacteristic
19C2×D11×C49—51noHall
20C3×C11×C49C2×D511yescharacteristic, complemented, Hall
21C7×D5×D11C3×C711yescharacteristic
22C2×C3×C5×C49—111no—
23C3×D5×C49—111no—
24C3×D5×C49D1111yescharacteristic, direct product factor
25C3×C5×C7×C11C22×C711yescharacteristic
26C2×C11×C49—51no—
27D11×C49—51no—
28D11×C49C3×D511yescharacteristic, direct product factor
29C2×D5×C49—111noHall
30C2×C3×C7×D11—51no—
31C7×D55C2×C3×C711yescharacteristic
32C7×D5×C11C2×C3×C711yescharacteristic
33C5×C7×D11C2×C3×C711yescharacteristic
34C3×C5×C49C2×D1111yescharacteristic, complemented, Hall
35C3×D5×D11C4911yescharacteristic, direct product factor, Hall
36C22×C3×C49—551noHall
37C11×C49C2×C3×D511yescharacteristic, complemented, Hall
38C2×C5×C49—111no—
39D5×C49—111no—
40D5×C49C3×D1111yescharacteristic, direct product factor
41C2×C3×C7×C11—51no—
42C3×C7×D11—51no—
43C3×C7×D11C7×D511yescharacteristic
44C2×C3×C7×D5—111no—
45C5×C7×C11C22×C3×C711yescharacteristic
46C3×D55C2×C4911yescharacteristic, complemented
47C3×D5×C11C2×C4911yescharacteristic, complemented
48C3×C5×D11C2×C4911yescharacteristic, complemented
49C2×C7×D11—51no—
50C2×C3×C49—51no—
51C2×C3×C49—111no—
52C2×C3×C49—551no—
53C5×C49C2×C3×D1111yescharacteristic, complemented, Hall
54C3×C7×C11C2×C7×D511yescharacteristic
55D5×D11C3×C4911yescharacteristic, direct product factor, Hall
56C2×C3×C5×C7—111no—
57C3×C7×D5—111no—
58C3×C7×D5C7×D1111yescharacteristic
59C22×C49—551noHall
60C3×C5×C11C22×C4911yescharacteristic, complemented, Hall
61C2×C7×C11—51no—
62C7×D11—51no—
63C7×D11C3×C7×D511yescharacteristic
64C3×C49D5×D1111yescharacteristic, direct product factor, Hall
65C2×C7×D5—111no—
66C2×C3×D11—51noHall
67D55C2×C3×C4911yescharacteristic, complemented
68C5×D11C2×C3×C4911yescharacteristic, complemented
69D5×C11C2×C3×C4911yescharacteristic, complemented
70C3×C5×C7C2×C7×D1111yescharacteristic
71C2×C49—51no—
72C2×C49—111no—
73C2×C49—551no—
74C22×C3×C7—551no—
75C7×C11C2×C3×C7×D511yescharacteristic
76C2×C5×C7—111no—
77C7×D5—111no—
78C7×D5C3×C7×D1111yescharacteristic
79C2×C3×C11—51no—
80C3×D11—51no—
81C3×D11D5×C4911yescharacteristic, direct product factor
82C2×C3×D5—111noHall
83C5×C11C22×C3×C4911yescharacteristic, complemented, Hall
84C49C3×D5×D1111yescharacteristic, direct product factor, Sylow
85C2×D11—51noHall
86C2×C3×C7—51no—
87C2×C3×C7—111no—
88C2×C3×C7—551no—
89C5×C7C2×C3×C7×D1111yescharacteristic
90C3×C11C2×D5×C4911yescharacteristic, complemented, Hall
91C2×C3×C5—111no—
92C3×D5—111no—
93C3×D5D11×C4911yescharacteristic, direct product factor
94C22×C7—551no—
95C2×C11—51no—
96D11—51no—
97D11C3×D5×C4911yescharacteristic, direct product factor
98C3×C7C7×D5×D1111yescharacteristic
99C2×D5—111noHall
100C3×C5C2×D11×C4911yescharacteristic, complemented, Hall
101C2×C7—51no—
102C2×C7—111no—
103C2×C7—551no—
104C22×C3—551noHall
105C11C2×C3×D5×C4911yescharacteristic, complemented, Sylow
106C2×C5—111no—
107D5—111no—
108D5C3×D11×C4911yescharacteristic, direct product factor
109C7C3×C7×D5×D1111yescharacteristic
110C2×C3—51no—
111C2×C3—111no—
112C2×C3—551no—
113C5C2×C3×D11×C4911yescharacteristic, complemented, Sylow
114C22—551noSylow
115C3D5×D11×C4911yescharacteristic, direct product factor, Sylow
116C2—51no—
117C2—111no—
118C2—551no—
subgroupG/H
center, hypercenterC3×C49D5×D11
commutator, hypocenterC5×C11C22×C3×C49
FrattiniC7C3×C7×D5×D11
FittingC3×C5×C11×C49C22
socleC3×C5×C7×C11C22×C7
prime radicalC3×C7×D5×D11C7
cosocleC5×C7×C11C22×C3×C7
LCSG ▷ C5×C11
UCSC1 ◁ C3×C49

Complements

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

NH ≅ G/Ntype
1. C3×C49×D55C2semidirect
2. C3×D5×C11×C49C2semidirect
3. C3×C5×D11×C49C2semidirect
4. D5×D11×C49C3direct (N × H)
5. C3×C5×C11×C49C22semidirect
7. C49×D55C2×C3semidirect
8. D5×C11×C49C2×C3semidirect
9. C5×D11×C49C2×C3semidirect
12. C3×D11×C49D5direct (N × H)
15. C5×C11×C49C22×C3semidirect
20. C3×C11×C49C2×D5semidirect
24. C3×D5×C49D11direct (N × H)
28. D11×C49C3×D5direct (N × H)
34. C3×C5×C49C2×D11semidirect
35. C3×D5×D11C49direct (N × H)
37. C11×C49C2×C3×D5semidirect
40. D5×C49C3×D11direct (N × H)
46. C3×D55C2×C49semidirect
47. C3×D5×C11C2×C49semidirect
48. C3×C5×D11C2×C49semidirect
53. C5×C49C2×C3×D11semidirect
55. D5×D11C3×C49direct (N × H)
60. C3×C5×C11C22×C49semidirect
64. C3×C49D5×D11direct (N × H)
67. D55C2×C3×C49semidirect
68. C5×D11C2×C3×C49semidirect
69. D5×C11C2×C3×C49semidirect
81. C3×D11D5×C49direct (N × H)
83. C5×C11C22×C3×C49semidirect
84. C49C3×D5×D11direct (N × H)
90. C3×C11C2×D5×C49semidirect
93. C3×D5D11×C49direct (N × H)
97. D11C3×D5×C49direct (N × H)
100. C3×C5C2×D11×C49semidirect
105. C11C2×C3×D5×C49semidirect
108. D5C3×D11×C49direct (N × H)
113. C5C2×C3×D11×C49semidirect
115. C3D5×D11×C49direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C49×D552
C3×D5×C11×C492
C3×C5×D11×C492
D5×D11×C493
C2×C3×D11×C495
C3×C7×D5×D117
C2×C3×D5×C4911