Finite Group Databasebeta

← C7×C3⋊D3×D119 #44472987

Subgroups — C7×C3⋊D3×D119 #44472987

Order 29988.

312 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 72 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×D119C211yesmaximal, characteristic, complemented
2C72×C17×C3⋊D3C211yesmaximal, characteristic, complemented
3C7×C3⋊D357C211yesmaximal, characteristic, complemented
4D3×C7×D119—34nomaximal
5C32×C72×C17C2211yescharacteristic, complemented, Hall
6C7×D357—34no—
7D3×C72×C17—34no—
8C3×C7×D119D314yescomplemented
9C3⋊D3×D119C711yesmaximal, characteristic, direct product factor
10C7×C3⋊D3×D17—71nomaximal
11C2×C7×D119—91noHall
12C3×C72×C17C2×D314yescomplemented
13C3⋊D357C2×C711yescharacteristic, complemented
14C7×C3⋊D51—71no—
15C7×C17×C3⋊D3—23no—
16C7×C17×C3⋊D3D711yescharacteristic, complemented
17C7×C17×C3⋊D3C2×C711yescharacteristic, complemented
18C32×D119C2×C711yescharacteristic, complemented
19C32×C7×D17—71no—
20C7×D7×C3⋊D3—171nomaximal, Hall
21C2×C72×C17—91no—
22C7×D119—91no—
23C7×D119C3⋊D311yescharacteristic, direct product factor
24D3×D119—34no—
25D3×C7×D17—214no—
26C32×C7×C17—23no—
27C32×C7×C17C2×D711yescharacteristic, complemented
28C32×C7×C17C22×C711yescharacteristic, complemented
29C7×C3⋊D21—171no—
30C72×C3⋊D3D1711yescharacteristic, complemented
31C32×C7×D7—171no—
32C72×C17C2×C3⋊D311yescharacteristic, complemented, Hall
33D357—34no—
34C7×D51—214no—
35D3×C7×C17—34no—
36D3×C7×C17—34no—
37D3×C7×C17—612no—
38C3×D119D3×C714yescomplemented
39C3×C7×D17—74no—
40C3⋊D3×D17—71noHall
41D3×C7×D7—514no—
42C2×D119—91no—
43C2×C7×D17—631no—
44C32×C72C2×D1711yescharacteristic, complemented, Hall
45C3×C7×C17—212no—
46C3×C7×C17D3×D714yescomplemented
47C3×C7×C17C2×D3×C714yescomplemented
48C3⋊D51—71no—
49C17×C3⋊D3C7×D711yescharacteristic, complemented
50C32×D17—71no—
51C7×D21—514no—
52D3×C72—34no—
53C3×C7×D7—174no—
54C2×C7×C3⋊D3—1191no—
55D7×C3⋊D3—171no—
56C2×C7×C17—91no—
57C2×C7×C17—91no—
58C2×C7×C17—183no—
59D119—91no—
60D119C7×C3⋊D311yescharacteristic, direct product factor
61C7×D17—71no—
62C7×D17—631no—
63D3×D17—214no—
64C2×C7×D7—1531noHall
65C32×C17C2×C7×D711yescharacteristic, complemented, Hall
66C3×C72D3×D1714yescomplemented
67C2×C32×C7—1191no—
68C3⋊D21—171no—
69C7×C3⋊D3—23no—
70C7×C3⋊D3—1191no—
71C7×C3⋊D3C7×D1711yescharacteristic, complemented
72C7×C3⋊D3D11911yescharacteristic, direct product factor
73C32×D7—171no—
74C7×C17—23no—
75C7×C17D7×C3⋊D311yescharacteristic, complemented
76C7×C17C2×C7×C3⋊D311yescharacteristic, complemented
77D51—214no—
78C3×D17—74no—
79D3×C17—34no—
80C2×C72—91no—
81C7×D7—171no—
82C7×D7—1531no—
83C2×D3×C7—3574no—
84D3×D7—514no—
85C2×D17—631noHall
86C32×C7—23no—
87C32×C7C2×C7×D1711yescharacteristic, complemented
88C32×C7C2×D11911yescharacteristic, complemented
89C3×C17D3×C7×D714yescomplemented
90C72C3⋊D3×D1711yescharacteristic, complemented, Sylow
91C2×C3×C7—1194no—
92D21—514no—
93C3×D7—174no—
94D3×C7—34no—
95D3×C7—34no—
96D3×C7—612no—
97D3×C7—3574no—
98C2×C3⋊D3—1191noHall
99C2×C17—91no—
100D17—71no—
101D17—631no—
102C22×C7—10711no—
103C2×D7—1531no—
104C3×C7—212no—
105C3×C7D3×C7×D1714yescomplemented
106C3×C7D3×D11914yescomplemented
107C2×C32—1191no—
108C3⋊D3—1191no—
109C3⋊D3C7×D11911yescharacteristic, direct product factor
110C17C7×D7×C3⋊D311yescharacteristic, complemented, Sylow
111C2×C7—91no—
112C2×C7—91no—
113C2×C7—183no—
114C2×C7—10711no—
115C2×C7—1191no—
116D7—171no—
117D7—1531no—
118C2×D3—3574no—
119C32C2×C7×D11911yescharacteristic, complemented, Sylow
120C7—23no—
121C7C7×C3⋊D3×D1711yescharacteristic, complemented
122C7C3⋊D3×D11911yescharacteristic, direct product factor
123C2×C3—1194no—
124D3—34no—
125D3—3574no—
126C22—10711noSylow
127C3D3×C7×D11914yescomplemented
128C2—91no—
129C2—10711no—
130C2—1191no—
subgroupG/H
center, hypercenterC7C3⋊D3×D119
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×D119C2semidirect
2. C72×C17×C3⋊D3C2semidirect
3. C7×C3⋊D357C2semidirect
5. C32×C72×C17C22semidirect
8. C3×C7×D119D3semidirect
9. C3⋊D3×D119C7direct (N × H)
12. C3×C72×C17C2×D3semidirect
13. C3⋊D357C2×C7semidirect
16. C7×C17×C3⋊D3D7semidirect
17. C7×C17×C3⋊D3C2×C7semidirect
18. C32×D119C2×C7semidirect
23. C7×D119C3⋊D3direct (N × H)
27. C32×C7×C17C2×D7semidirect
28. C32×C7×C17C22×C7semidirect
30. C72×C3⋊D3D17semidirect
32. C72×C17C2×C3⋊D3semidirect
38. C3×D119D3×C7semidirect
44. C32×C72C2×D17semidirect
46. C3×C7×C17D3×D7semidirect
47. C3×C7×C17C2×D3×C7semidirect
49. C17×C3⋊D3C7×D7semidirect
60. D119C7×C3⋊D3direct (N × H)
65. C32×C17C2×C7×D7semidirect
66. C3×C72D3×D17semidirect
71. C7×C3⋊D3C7×D17semidirect
72. C7×C3⋊D3D119direct (N × H)
75. C7×C17D7×C3⋊D3semidirect
76. C7×C17C2×C7×C3⋊D3semidirect
87. C32×C7C2×C7×D17semidirect
88. C32×C7C2×D119semidirect
89. C3×C17D3×C7×D7semidirect
90. C72C3⋊D3×D17semidirect
105. C3×C7D3×C7×D17semidirect
106. C3×C7D3×D119semidirect
109. C3⋊D3C7×D119direct (N × H)
110. C17C7×D7×C3⋊D3semidirect
119. C32C2×C7×D119semidirect
121. C7C7×C3⋊D3×D17semidirect
122. C7C3⋊D3×D119direct (N × H)
127. C3D3×C7×D119semidirect

Maximal subgroups

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

subgroupindex
C32×C7×D1192
C72×C17×C3⋊D32
C7×C3⋊D3572
D3×C7×D1193
C3⋊D3×D1197
C7×C3⋊D3×D177
C7×D7×C3⋊D317