Finite Group Databasebeta

← D147⋊D51 #44472467

Subgroups — D147⋊D51 #44472467

Order 29988.

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

normal subgroups only

This group has 132 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×C3⋊D51C211yesmaximal, characteristic, complemented
2C3×D2499C211yesmaximal, characteristic, complemented
3C3×C17×D147C211yesmaximal, characteristic, complemented
4D51⋊D49—31nomaximal
5D49×D51—31nomaximal
6C32×C17×C49C2211yescharacteristic, complemented, Hall
7D2499D311yescharacteristic, complemented
8C17×D147D311yescharacteristic, complemented
9C49×D51—31no—
10C49×D51—31no—
11C49×D51—61no—
12C3×D833—31no—
13C3×C17×D49—31no—
14D21⋊D51—71nomaximal
15D17×D49—91noHall
16C3×C17×C49—21no—
17C3×C17×C49C2×D311yescharacteristic, complemented
18C3×C17×C49C2×D311yescharacteristic, complemented
19C7×C3⋊D51D711yescharacteristic
20C3×D357—71no—
21C3×C17×D21—71no—
22(C3⋊D3)⋊D49—171nomaximal, Hall
23D833—31no—
24D17×C49—91no—
25C17×D49—31no—
26D21⋊D17—211no—
27D7×D51—211no—
28C32×C7×C17C2×D711yescharacteristic
29C3⋊D3×C49—171no—
30C3×D147—171no—
31C3×D147D1711yescharacteristic, complemented
32C17×C49D3211yescharacteristic, complemented, Hall
33D357—71no—
34C17×D21—71no—
35C7×D51—31no—
36C7×D51—31no—
37C7×D51—61no—
38C3×D119—211no—
39C3×D7×C17—211no—
40D3×D51—491noHall
41D3×D49—511no—
42D3×D49—511no—
43D7×D17—631no—
44C32×C49C2×D1711yescharacteristic, complemented, Hall
45C3×C7×C17—21no—
46C3×C7×C17D3×D711yescharacteristic
47C3×C7×C17D3×D711yescharacteristic
48C3⋊D51D4911yescharacteristic, complemented
49C3×D51—491no—
50C3×D3×C17—491no—
51D147—171no—
52D147D5111yescharacteristic, complemented
53C3×D49—31no—
54C3×D49—511no—
55D3×C49—511no—
56D3×C49—511no—
57D3×C49—1021no—
58(C3⋊D3)⋊D7—1191no—
59D119—211no—
60C7×D17—91no—
61D7×C17—211no—
62C2×D51—1471no—
63D3×D17—1471no—
64C2×D49—1531noHall
65C32×C17C2×D4911yescharacteristic, complemented, Hall
66C3×C49—21no—
67C3×C49D3×D1711yescharacteristic, complemented
68C3×C49C2×D5111yescharacteristic, complemented
69C7×C3⋊D3—171no—
70C3×D21—71no—
71C3×D21—1191no—
72C7×C17(C3⋊D3)⋊D711yescharacteristic
73C2×C3×C17—1471no—
74D51—31no—
75D51—31no—
76D51—61no—
77D51—491no—
78C3×D17—1471no—
79D3×C17—491no—
80C2×C49—1531no—
81D49—31no—
82D49—511no—
83D3×D7—3571no—
84D3×D7—3571no—
85C2×D17—4411noHall
86C32×C7D7×D1711yescharacteristic
87C3×C17—21no—
88C3×C17D3×D4911yescharacteristic, complemented
89C3×C17D3×D4911yescharacteristic, complemented
90C49D3×D5111yescharacteristic, complemented, Sylow
91D21—71no—
92D21—1191no—
93C3×D7—211no—
94C3×D7—3571no—
95D3×C7—511no—
96D3×C7—511no—
97D3×C7—1021no—
98D32—8331noHall
99C2×C17—1471no—
100D17—91no—
101D17—1471no—
102C2×D7—10711no—
103C3×C7—21no—
104C3×C7D7×D5111yescharacteristic
105C3×C7D21⋊D1711yescharacteristic
106C3⋊D3—171no—
107C3×D3—491no—
108C3×D3—8331no—
109C17(C3⋊D3)⋊D4911yescharacteristic, complemented, Sylow
110C2×C7—1531no—
111D7—211no—
112D7—3571no—
113C2×D3—24991no—
114C2×D3—24991no—
115C32D17×D4911yescharacteristic, complemented, Sylow
116C7D21⋊D5111yescharacteristic
117C2×C3—1471no—
118C2×C3—24991no—
119D3—491no—
120D3—511no—
121D3—511no—
122D3—8331no—
123D3—1021no—
124C22—74971noSylow
125C3—21no—
126C3D49×D5111yescharacteristic, complemented
127C3D51⋊D4911yescharacteristic, complemented
128C2—1471no—
129C2—1531no—
130C2—24991no—
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC32×C17×C49C22
FrattiniC7D21⋊D51
socleC32×C7×C17C2×D7
LCSG ▷ C32×C17×C49
UCSC1

Complements

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

NH ≅ G/Ntype
1. C49×C3⋊D51C2semidirect
2. C3×D2499C2semidirect
3. C3×C17×D147C2semidirect
6. C32×C17×C49C22semidirect
7. D2499D3semidirect
8. C17×D147D3semidirect
17. C3×C17×C49C2×D3semidirect
18. C3×C17×C49C2×D3semidirect
31. C3×D147D17semidirect
32. C17×C49D32semidirect
44. C32×C49C2×D17semidirect
48. C3⋊D51D49semidirect
52. D147D51semidirect
65. C32×C17C2×D49semidirect
67. C3×C49D3×D17semidirect
68. C3×C49C2×D51semidirect
88. C3×C17D3×D49semidirect
89. C3×C17D3×D49semidirect
90. C49D3×D51semidirect
109. C17(C3⋊D3)⋊D49semidirect
115. C32D17×D49semidirect
126. C3D49×D51semidirect
127. C3D51⋊D49semidirect

Maximal subgroups

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

subgroupindex
C49×C3⋊D512
C3×D24992
C3×C17×D1472
D51⋊D493
D49×D513
D21⋊D517
(C3⋊D3)⋊D4917