Finite Group Databasebeta

← D51⋊D147 #44472464

Subgroups — D51⋊D147 #44472464

Order 29988.

132 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 35 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
1C17×C3⋊D147C211yesmaximal, characteristic, complemented
2C3×D2499C211yesmaximal, characteristic, complemented
3C3×C49×D51C211yesmaximal, characteristic, complemented
4D51⋊D49—31nomaximal
5D17×D147—31nomaximal
6C32×C17×C49C2211yescharacteristic, complemented, Hall
7D2499D311yescharacteristic, complemented
8C17×D147—31no—
9C17×D147—31no—
10C17×D147—61no—
11C49×D51D311yescharacteristic, complemented
12C3×D833—31no—
13C3×D17×C49—31no—
14D51⋊D21—71nomaximal
15D17×D49—91noHall
16C3×C17×C49—21no—
17C3×C17×C49C2×D311yescharacteristic, complemented
18C3×C17×C49C2×D311yescharacteristic, complemented
19C17×C3⋊D21—71no—
20C3×D357—71no—
21C3×C7×D51D711yescharacteristic
22D3×D147—171nomaximal, Hall
23D833—31no—
24D17×C49—31no—
25C17×D49—91no—
26D21⋊D17—211no—
27D17×D21—211no—
28C32×C7×C17C2×D711yescharacteristic
29C3⋊D147D1711yescharacteristic, complemented
30C3×D147—171no—
31C3×D3×C49—171no—
32C17×C49D3211yescharacteristic, complemented, Hall
33D357—71no—
34C17×D21—211no—
35C17×D21—211no—
36C17×D21—421no—
37C7×D51D2111yescharacteristic
38C3×D119—211no—
39C3×C7×D17—31no—
40(C3⋊D3)⋊D17—491noHall
41C2×D147—511no—
42D3×D49—511no—
43D7×D17—631no—
44C32×C49C2×D1711yescharacteristic, complemented, Hall
45C3×C7×C17—21no—
46C3×C7×C17D3×D711yescharacteristic
47C3×C7×C17C2×D2111yescharacteristic
48C17×C3⋊D3—491no—
49C3×D51—491no—
50C3×D51D4911yescharacteristic, complemented
51C2×C3×C49—511no—
52D147—31no—
53D147—31no—
54D147—61no—
55D147—171no—
56C3×D49—511no—
57D3×C49—171no—
58D3×D21—1191no—
59D119—211no—
60C7×D17—31no—
61D7×C17—631no—
62D3×D17—1471no—
63D3×D17—1471no—
64C2×D49—1531noHall
65C32×C17C2×D4911yescharacteristic, complemented, Hall
66C3×C49—21no—
67C3×C49D3×D1711yescharacteristic, complemented
68C3×C49D3×D1711yescharacteristic, complemented
69C3⋊D21—71no—
70C3×D21—1191no—
71C3×D3×C7—171no—
72C7×C17D3×D2111yescharacteristic
73D51—491no—
74D51D14711yescharacteristic, complemented
75C3×D17—31no—
76C3×D17—1471no—
77D3×C17—2941no—
78D3×C17—1471no—
79D3×C17—1471no—
80C2×C49—511no—
81D49—91no—
82D49—511no—
83C2×D21—3571no—
84D3×D7—3571no—
85C2×D17—4411noHall
86C32×C7D7×D1711yescharacteristic
87C3×C17—21no—
88C3×C17D3×D4911yescharacteristic, complemented
89C3×C17C2×D14711yescharacteristic, complemented
90C49(C3⋊D3)⋊D1711yescharacteristic, complemented, Sylow
91C2×C3×C7—511no—
92D21—211no—
93D21—211no—
94D21—421no—
95D21—1191no—
96C3×D7—3571no—
97D3×C7—171no—
98D32—8331noHall
99C2×C17—4411no—
100D17—31no—
101D17—1471no—
102C2×D7—10711no—
103C3×C7—21no—
104C3×C7D17×D2111yescharacteristic
105C3×C7D21⋊D1711yescharacteristic
106C3⋊D3—491no—
107C3×D3—171no—
108C3×D3—8331no—
109C17D3×D14711yescharacteristic, complemented, Sylow
110C2×C7—511no—
111D7—631no—
112D7—3571no—
113C2×D3—24991no—
114C2×D3—24991no—
115C32D17×D4911yescharacteristic, complemented, Sylow
116C7D51⋊D2111yescharacteristic
117C2×C3—511no—
118C2×C3—24991no—
119D3—171no—
120D3—2941no—
121D3—8331no—
122D3—1471no—
123D3—1471no—
124C22—74971noSylow
125C3—21no—
126C3D17×D14711yescharacteristic, complemented
127C3D51⋊D4911yescharacteristic, complemented
128C2—511no—
129C2—4411no—
130C2—24991no—
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC32×C17×C49C22
FrattiniC7D51⋊D21
socleC32×C7×C17C2×D7
LCSG ▷ C32×C17×C49
UCSC1

Complements

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

NH ≅ G/Ntype
1. C17×C3⋊D147C2semidirect
2. C3×D2499C2semidirect
3. C3×C49×D51C2semidirect
6. C32×C17×C49C22semidirect
7. D2499D3semidirect
11. C49×D51D3semidirect
17. C3×C17×C49C2×D3semidirect
18. C3×C17×C49C2×D3semidirect
29. C3⋊D147D17semidirect
32. C17×C49D32semidirect
44. C32×C49C2×D17semidirect
50. C3×D51D49semidirect
65. C32×C17C2×D49semidirect
67. C3×C49D3×D17semidirect
68. C3×C49D3×D17semidirect
74. D51D147semidirect
88. C3×C17D3×D49semidirect
89. C3×C17C2×D147semidirect
90. C49(C3⋊D3)⋊D17semidirect
109. C17D3×D147semidirect
115. C32D17×D49semidirect
126. C3D17×D147semidirect
127. C3D51⋊D49semidirect

Maximal subgroups

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

subgroupindex
C17×C3⋊D1472
C3×D24992
C3×C49×D512
D51⋊D493
D17×D1473
D51⋊D217
D3×D14717