Finite Group Databasebeta

← C7×D7×C3⋊D51 #44472986

Subgroups — C7×D7×C3⋊D51 #44472986

Order 29988.

312 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 80 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
1C32×C7×D7×C17C211yesmaximal, characteristic, complemented
2C72×C3⋊D51C211yesmaximal, characteristic, complemented
3C7×C3⋊D357C211yesmaximal, characteristic, complemented
4C7×D7×D51—34nomaximal
5C32×C72×C17C2211yescharacteristic, complemented, Hall
6C7×D357—34no—
7C72×D51—34no—
8C3×C7×D7×C17D314yescomplemented
9C2×C7×C3⋊D51—71nomaximal
10D7×C3⋊D51C711yesmaximal, characteristic, direct product factor
11C7×D7×D17—91noHall
12C3×C72×C17C2×D314yescomplemented
13C3⋊D357C2×C711yescharacteristic, complemented
14C7×C3⋊D51—23no—
15C7×C3⋊D51—71no—
16C7×C3⋊D51D711yescharacteristic, direct product factor
17C7×C3⋊D51C2×C711yescharacteristic, complemented
18C32×D7×C17C2×C711yescharacteristic, complemented
19C2×C32×C7×C17—71no—
20C7×D7×C3⋊D3—171nomaximal, Hall
21C7×D119—91no—
22C7×D7×C17C3⋊D311yescharacteristic, complemented
23C72×D17—91no—
24C2×C7×D51—214no—
25D7×D51—34no—
26C32×C7×C17—23no—
27C32×C7×C17C2×D711yescharacteristic, complemented
28C32×C7×C17C22×C711yescharacteristic, complemented
29C7×C3⋊D21—171no—
30C72×C3⋊D3—171no—
31C32×C7×D7D1711yescharacteristic, complemented
32C72×C17C2×C3⋊D311yescharacteristic, complemented, Hall
33C2×C3×C7×C17—74no—
34D357—34no—
35C7×D51—34no—
36C7×D51—34no—
37C7×D51—612no—
38C7×D51—214no—
39C3×D7×C17D3×C714yescomplemented
40C2×C3⋊D51—71noHall
41D3×C7×D7—514no—
42C2×C7×D17—631no—
43D7×D17—91no—
44C32×C72C2×D1711yescharacteristic, complemented, Hall
45C3×C7×C17—212no—
46C3×C7×C17D3×D714yescomplemented
47C3×C7×C17C2×D3×C714yescomplemented
48C2×C32×C17—71no—
49C3⋊D51—71no—
50C3⋊D51C7×D711yescharacteristic, direct product factor
51C7×D21—514no—
52D3×C72—514no—
53C3×C7×D7D5114yescomplemented
54C2×C7×C3⋊D3—1191no—
55D7×C3⋊D3—171no—
56C2×C7×C17—71no—
57D119—91no—
58C7×D17—91no—
59C7×D17—91no—
60C7×D17—183no—
61C7×D17—631no—
62D7×C17C7×C3⋊D311yescharacteristic, complemented
63C2×D51—214no—
64C2×C7×D7—1531noHall
65C32×C17C2×C7×D711yescharacteristic, complemented, Hall
66C3×C72C2×D5114yescomplemented
67C2×C32×C7—71no—
68C3⋊D21—171no—
69C7×C3⋊D3—171no—
70C7×C3⋊D3—171no—
71C7×C3⋊D3—343no—
72C7×C3⋊D3—1191no—
73C32×D7C7×D1711yescharacteristic, complemented
74C7×C17—23no—
75C7×C17D7×C3⋊D311yescharacteristic, complemented
76C7×C17C2×C7×C3⋊D311yescharacteristic, complemented
77C2×C3×C17—74no—
78D51—34no—
79D51—214no—
80C2×C72—1531no—
81C7×D7—1531no—
82C7×D7C3⋊D5111yescharacteristic, direct product factor
83C2×D3×C7—3574no—
84D3×D7—514no—
85C2×D17—631noHall
86C32×C7—23no—
87C32×C7D7×D1711yescharacteristic, complemented
88C32×C7C2×C7×D1711yescharacteristic, complemented
89C3×C17D3×C7×D714yescomplemented
90C72C2×C3⋊D5111yescharacteristic, complemented, Sylow
91C2×C3×C7—74no—
92D21—514no—
93C3×D7C7×D5114yescomplemented
94D3×C7—514no—
95D3×C7—514no—
96D3×C7—3574no—
97D3×C7—10212no—
98C2×C3⋊D3—1191noHall
99C2×C17—71no—
100D17—91no—
101D17—631no—
102C22×C7—10711no—
103C2×D7—1531no—
104C3×C7—212no—
105C3×C7D7×D5114yescomplemented
106C3×C7C2×C7×D5114yescomplemented
107C2×C32—71no—
108C3⋊D3—171no—
109C3⋊D3—1191no—
110C17C7×D7×C3⋊D311yescharacteristic, complemented, Sylow
111C2×C7—71no—
112C2×C7—10711no—
113C2×C7—3063no—
114C2×C7—1531no—
115C2×C7—1531no—
116D7—1531no—
117D7C7×C3⋊D5111yescharacteristic, direct product factor
118C2×D3—3574no—
119C32C7×D7×D1711yescharacteristic, complemented, Sylow
120C7—23no—
121C7D7×C3⋊D5111yescharacteristic, direct product factor
122C7C2×C7×C3⋊D5111yescharacteristic, complemented
123C2×C3—74no—
124D3—514no—
125D3—3574no—
126C22—10711noSylow
127C3C7×D7×D5114yescomplemented
128C2—71no—
129C2—10711no—
130C2—1531no—
subgroupG/H
center, hypercenterC7D7×C3⋊D51
commutator, cosocle, hypocenterC32×C7×C17C22×C7
FrattiniC1G
Fitting, socleC32×C72×C17C22
LCSG ▷ C32×C7×C17
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C32×C7×D7×C17C2semidirect
2. C72×C3⋊D51C2semidirect
3. C7×C3⋊D357C2semidirect
5. C32×C72×C17C22semidirect
8. C3×C7×D7×C17D3semidirect
10. D7×C3⋊D51C7direct (N × H)
12. C3×C72×C17C2×D3semidirect
13. C3⋊D357C2×C7semidirect
16. C7×C3⋊D51D7direct (N × H)
17. C7×C3⋊D51C2×C7semidirect
18. C32×D7×C17C2×C7semidirect
22. C7×D7×C17C3⋊D3semidirect
27. C32×C7×C17C2×D7semidirect
28. C32×C7×C17C22×C7semidirect
31. C32×C7×D7D17semidirect
32. C72×C17C2×C3⋊D3semidirect
39. C3×D7×C17D3×C7semidirect
44. C32×C72C2×D17semidirect
46. C3×C7×C17D3×D7semidirect
47. C3×C7×C17C2×D3×C7semidirect
50. C3⋊D51C7×D7direct (N × H)
53. C3×C7×D7D51semidirect
62. D7×C17C7×C3⋊D3semidirect
65. C32×C17C2×C7×D7semidirect
66. C3×C72C2×D51semidirect
73. C32×D7C7×D17semidirect
75. C7×C17D7×C3⋊D3semidirect
76. C7×C17C2×C7×C3⋊D3semidirect
82. C7×D7C3⋊D51direct (N × H)
87. C32×C7D7×D17semidirect
88. C32×C7C2×C7×D17semidirect
89. C3×C17D3×C7×D7semidirect
90. C72C2×C3⋊D51semidirect
93. C3×D7C7×D51semidirect
105. C3×C7D7×D51semidirect
106. C3×C7C2×C7×D51semidirect
110. C17C7×D7×C3⋊D3semidirect
117. D7C7×C3⋊D51direct (N × H)
119. C32C7×D7×D17semidirect
121. C7D7×C3⋊D51direct (N × H)
122. C7C2×C7×C3⋊D51semidirect
127. C3C7×D7×D51semidirect

Maximal subgroups

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

subgroupindex
C32×C7×D7×C172
C72×C3⋊D512
C7×C3⋊D3572
C7×D7×D513
C2×C7×C3⋊D517
D7×C3⋊D517
C7×D7×C3⋊D317