Finite Group Databasebeta

← D147⋊D55 #44568417

Subgroups — D147⋊D55 #44568417

Order 32340.

120 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 34 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
2C5×C11×D147C211yesmaximal, characteristic, complemented
3C3×D2695C211yesmaximal, characteristic, complemented
4D49×D55—31nomaximal, Hall
5C3×C5×C11×C49C2211yescharacteristic, complemented, Hall
6D33⋊D49—51nomaximal, Hall
7D2695D311yescharacteristic, complemented
8C49×D55—31no—
9C5×C11×D49—31no—
10D21⋊D55—71nomaximal
11C11×D147D511yescharacteristic, complemented
12C49×D33—51no—
13C3×D539—51no—
14D15⋊D49—111nomaximal, Hall
15C5×C11×C49C2×D311yescharacteristic, complemented, Hall
16C7×D165D711yescharacteristic
17C5×C11×D21—71no—
18C3×D385—71no—
19D11×D49—151noHall
20C3×C11×C49C2×D511yescharacteristic, complemented, Hall
21D7×D55—211no—
22D15×C49—111no—
23C5×D147D1111yescharacteristic, complemented
24C3×D245—111no—
25C3×C5×C7×C11C2×D711yescharacteristic
26D539—51no—
27D11×C49—151no—
28C11×D49—31no—
29D5×D49—331noHall
30D21⋊D11—351no—
31D385—71no—
32C7×D55—31no—
33C5×C11×D7—211no—
34C3×C5×C49C2×D1111yescharacteristic, complemented, Hall
35D3×D55—491noHall
36D3×D49—551noHall
37C11×C49D3×D511yescharacteristic, complemented, Hall
38D245—111no—
39C5×D49—31no—
40D5×C49—331no—
41C11×D21—71no—
42C7×D33—51no—
43C3×D77—351no—
44D15⋊D7—771no—
45C5×C7×C11D3×D711yescharacteristic
46D165D4911yescharacteristic, complemented
47C5×D3×C11—491no—
48C3×D55—491no—
49D7×D11—1051no—
50D147D5511yescharacteristic, complemented
51C3×D49—551no—
52D3×C49—551no—
53C5×C49D3×D1111yescharacteristic, complemented, Hall
54C3×C7×C11D5×D711yescharacteristic
55C2×D55—1471noHall
56C7×D15—111no—
57C5×D21—71no—
58C3×D35—771no—
59C2×D49—1651noHall
60C3×C5×C11C2×D4911yescharacteristic, complemented, Hall
61D77—351no—
62C7×D11—151no—
63C11×D7—211no—
64C3×C49C2×D5511yescharacteristic, complemented, Hall
65D5×D7—2311no—
66D3×D11—2451noHall
67C2×C5×C11—1471no—
68D55—31no—
69D55—491no—
70C3×C5×C7D7×D1111yescharacteristic
71C2×C49—1651no—
72D49—31no—
73D49—551no—
74D3×D7—3851no—
75C7×C11D15⋊D711yescharacteristic
76D35—771no—
77C5×D7—211no—
78C7×D5—331no—
79D33—51no—
80C3×D11—2451no—
81D3×C11—491no—
82D3×D5—5391noHall
83C5×C11D3×D4911yescharacteristic, complemented, Hall
84C49D3×D5511yescharacteristic, complemented, Sylow
85C2×D11—7351noHall
86D21—71no—
87C3×D7—3851no—
88D3×C7—551no—
89C5×C7D21⋊D1111yescharacteristic
90C3×C11D5×D4911yescharacteristic, complemented, Hall
91D15—111no—
92C3×D5—5391no—
93C5×D3—491no—
94C2×D7—11551no—
95C2×C11—1471no—
96D11—151no—
97D11—2451no—
98C3×C7D7×D5511yescharacteristic
99C2×D5—16171noHall
100C3×C5D11×D4911yescharacteristic, complemented, Hall
101C2×C7—1651no—
102D7—211no—
103D7—3851no—
104C2×D3—26951noHall
105C11D15⋊D4911yescharacteristic, complemented, Sylow
106C2×C5—1471no—
107D5—5391no—
108D5—331no—
109C7D21⋊D5511yescharacteristic
110C2×C3—26951no—
111D3—491no—
112D3—551no—
113C5D33⋊D4911yescharacteristic, complemented, Sylow
114C22—80851noSylow
115C3D49×D5511yescharacteristic, complemented, Sylow
116C2—26951no—
117C2—1471no—
118C2—1651no—
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC3×C5×C11×C49C22
FrattiniC7D21⋊D55
socleC3×C5×C7×C11C2×D7
LCSG ▷ C3×C5×C11×C49
UCSC1

Complements

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

NH ≅ G/Ntype
1. C49×D165C2semidirect
2. C5×C11×D147C2semidirect
3. C3×D2695C2semidirect
5. C3×C5×C11×C49C22semidirect
7. D2695D3semidirect
11. C11×D147D5semidirect
15. C5×C11×C49C2×D3semidirect
20. C3×C11×C49C2×D5semidirect
23. C5×D147D11semidirect
34. C3×C5×C49C2×D11semidirect
37. C11×C49D3×D5semidirect
46. D165D49semidirect
50. D147D55semidirect
53. C5×C49D3×D11semidirect
60. C3×C5×C11C2×D49semidirect
64. C3×C49C2×D55semidirect
83. C5×C11D3×D49semidirect
84. C49D3×D55semidirect
90. C3×C11D5×D49semidirect
100. C3×C5D11×D49semidirect
105. C11D15⋊D49semidirect
113. C5D33⋊D49semidirect
115. C3D49×D55semidirect

Maximal subgroups

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

subgroupindex
C49×D1652
C5×C11×D1472
C3×D26952
D49×D553
D33⋊D495
D21⋊D557
D15⋊D4911