Finite Group Databasebeta

← D11×D15×C49 #44568397

Subgroups — D11×D15×C49 #44568397

Order 32340.

120 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 48 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
1C49×D165C211yesmaximal, characteristic, complemented
2C11×D15×C49C211yesmaximal, characteristic, complemented
3C3×C5×D11×C49C211yesmaximal, characteristic, complemented
4D5×D11×C49—31nomaximal, Hall
5C3×C5×C11×C49C2211yescharacteristic, complemented, Hall
6D3×D11×C49—51nomaximal, Hall
7C49×D55—31no—
8D5×C11×C49—31no—
9C5×D11×C49D311yescharacteristic, complemented
10C7×D11×D15C711yesmaximal, characteristic
11C49×D33—51no—
12D3×C11×C49—51no—
13C3×D11×C49D511yescharacteristic, complemented
14C2×D15×C49—111nomaximal, Hall
15C5×C11×C49C2×D311yescharacteristic, complemented, Hall
16C7×D165C2×C711yescharacteristic
17C7×C11×D15C2×C711yescharacteristic
18C3×C5×C7×D11C2×C711yescharacteristic
19C2×D11×C49—151noHall
20C3×C11×C49C2×D511yescharacteristic, complemented, Hall
21C7×D5×D11—31no—
22C2×C3×C5×C49—111no—
23D15×C49—111no—
24D15×C49D1111yescharacteristic, direct product factor
25C3×C5×C7×C11C22×C711yescharacteristic
26C2×C11×C49—151no—
27D11×C49—151no—
28D11×C49D1511yescharacteristic, direct product factor
29C2×D5×C49—331noHall
30D3×C7×D11—51no—
31C7×D55—31no—
32C7×D5×C11—31no—
33C5×C7×D11D3×C711yescharacteristic
34C3×C5×C49C2×D1111yescharacteristic, complemented, Hall
35D11×D15C4911yescharacteristic, direct product factor, Hall
36C2×D3×C49—551noHall
37C11×C49C2×D1511yescharacteristic, complemented, Hall
38C2×C5×C49—111no—
39D5×C49—31no—
40D5×C49—331no—
41C7×D33—51no—
42D3×C7×C11—51no—
43C3×C7×D11C7×D511yescharacteristic
44C2×C7×D15—111no—
45C5×C7×C11C2×D3×C711yescharacteristic
46D165C2×C4911yescharacteristic, complemented
47C11×D15C2×C4911yescharacteristic, complemented
48C3×C5×D11C2×C4911yescharacteristic, complemented
49C2×C7×D11—151no—
50C2×C3×C49—111no—
51D3×C49—51no—
52D3×C49—551no—
53C5×C49D3×D1111yescharacteristic, complemented, Hall
54C3×C7×C11C2×C7×D511yescharacteristic
55D5×D11—31noHall
56C2×C3×C5×C7—111no—
57C7×D15—111no—
58C7×D15C7×D1111yescharacteristic
59C22×C49—1651noHall
60C3×C5×C11C22×C4911yescharacteristic, complemented, Hall
61C2×C7×C11—151no—
62C7×D11—151no—
63C7×D11C7×D1511yescharacteristic
64C3×C49D5×D1111yescharacteristic, complemented, Hall
65C2×C7×D5—331no—
66D3×D11—51noHall
67D55—31no—
68C5×D11D3×C4911yescharacteristic, complemented
69D5×C11—31no—
70C3×C5×C7C2×C7×D1111yescharacteristic
71C2×C49—111no—
72C2×C49—151no—
73C2×C49—1651no—
74C2×D3×C7—551no—
75C7×C11C2×C7×D1511yescharacteristic
76C2×C5×C7—111no—
77C7×D5—31no—
78C7×D5—331no—
79D33—51no—
80C3×D11D5×C4911yescharacteristic, complemented
81D3×C11—51no—
82C2×D15—111noHall
83C5×C11C2×D3×C4911yescharacteristic, complemented, Hall
84C49D11×D1511yescharacteristic, direct product factor, Sylow
85C2×D11—151noHall
86C2×C3×C7—111no—
87D3×C7—51no—
88D3×C7—551no—
89C5×C7D3×C7×D1111yescharacteristic
90C3×C11C2×D5×C4911yescharacteristic, complemented, Hall
91C2×C3×C5—111no—
92D15—111no—
93D15D11×C4911yescharacteristic, direct product factor
94C22×C7—1651no—
95C2×C11—151no—
96D11—151no—
97D11D15×C4911yescharacteristic, direct product factor
98C3×C7C7×D5×D1111yescharacteristic
99C2×D5—331noHall
100C3×C5C2×D11×C4911yescharacteristic, complemented, Hall
101C2×C7—111no—
102C2×C7—151no—
103C2×C7—1651no—
104C2×D3—551noHall
105C11C2×D15×C4911yescharacteristic, complemented, Sylow
106C2×C5—111no—
107D5—31no—
108D5—331no—
109C7C7×D11×D1511yescharacteristic
110C2×C3—111no—
111D3—51no—
112D3—551no—
113C5D3×D11×C4911yescharacteristic, complemented, Sylow
114C22—1651noSylow
115C3D5×D11×C4911yescharacteristic, complemented, Sylow
116C2—111no—
117C2—151no—
118C2—1651no—
subgroupG/H
center, hypercenterC49D11×D15
commutator, hypocenterC3×C5×C11C22×C49
FrattiniC7C7×D11×D15
FittingC3×C5×C11×C49C22
socle, cosocleC3×C5×C7×C11C22×C7
prime radicalC7×D11×D15C7
LCSG ▷ C3×C5×C11
UCSC1 ◁ C49

Complements

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

NH ≅ G/Ntype
1. C49×D165C2semidirect
2. C11×D15×C49C2semidirect
3. C3×C5×D11×C49C2semidirect
5. C3×C5×C11×C49C22semidirect
9. C5×D11×C49D3semidirect
13. C3×D11×C49D5semidirect
15. C5×C11×C49C2×D3semidirect
20. C3×C11×C49C2×D5semidirect
24. D15×C49D11direct (N × H)
28. D11×C49D15direct (N × H)
34. C3×C5×C49C2×D11semidirect
35. D11×D15C49direct (N × H)
37. C11×C49C2×D15semidirect
46. D165C2×C49semidirect
47. C11×D15C2×C49semidirect
48. C3×C5×D11C2×C49semidirect
53. C5×C49D3×D11semidirect
60. C3×C5×C11C22×C49semidirect
64. C3×C49D5×D11semidirect
68. C5×D11D3×C49semidirect
80. C3×D11D5×C49semidirect
83. C5×C11C2×D3×C49semidirect
84. C49D11×D15direct (N × H)
90. C3×C11C2×D5×C49semidirect
93. D15D11×C49direct (N × H)
97. D11D15×C49direct (N × H)
100. C3×C5C2×D11×C49semidirect
105. C11C2×D15×C49semidirect
113. C5D3×D11×C49semidirect
115. C3D5×D11×C49semidirect

Maximal subgroups

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

subgroupindex
C49×D1652
C11×D15×C492
C3×C5×D11×C492
D5×D11×C493
D3×D11×C495
C7×D11×D157
C2×D15×C4911