Finite Group Databasebeta

← C7×(C3⋊D3)⋊D119 #44472963

Subgroups — C7×(C3⋊D3)⋊D119 #44472963

Order 29988.

248 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 50 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
1C3×C7×D357C212yesmaximal, complemented
2C72×C17×C3⋊D3C211yesmaximal, characteristic, complemented
3D3×C7×D119—32nomaximal
4C32×C72×C17C2211yescharacteristic, complemented, Hall
5C7×D357D312yescomplemented
6D3×C72×C17—32no—
7D3×C72×C17—61no—
8C3×C7×D119—32no—
9(C3⋊D3)⋊D119C711yesmaximal, characteristic, direct product factor
10C7×(C3⋊D3)⋊D17—71nomaximal
11C2×C7×D119—91noHall
12C3×C72×C17—21no—
13C3×C72×C17C2×D312yescomplemented
14C7×C17×C3⋊D3—23no—
15C7×C17×C3⋊D3D711yescharacteristic, complemented
16C7×C17×C3⋊D3C2×C711yescharacteristic, complemented
17C3×D357C2×C712yescomplemented
18C3×C7×D51—72no—
19C7×(C3⋊D3)⋊D7—171nomaximal, Hall
20C2×C72×C17—91no—
21C7×D119—32no—
22D3×D119—32no—
23D3×C7×D17—212no—
24C32×C7×C17—23no—
25C32×C7×C17C2×D711yescharacteristic, complemented
26C32×C7×C17C22×C711yescharacteristic, complemented
27C72×C3⋊D3D1711yescharacteristic, complemented
28C3×C7×D21—172no—
29C72×C17D3211yescharacteristic, complemented, Hall
30D357D3×C712yescomplemented
31C7×D51—72no—
32D3×C7×C17—32no—
33D3×C7×C17—32no—
34D3×C7×C17—66no—
35D3×C7×C17—61no—
36D3×C7×C17—61no—
37D3×C7×C17—66no—
38C3×D119—32no—
39C3×C7×D17—212no—
40(C3⋊D3)⋊D17—71noHall
41D3×C7×D7—512no—
42C2×D119—91no—
43C2×C7×D17—631no—
44C32×C72C2×D1711yescharacteristic, complemented, Hall
45C3×C7×C17—26no—
46C3×C7×C17—21no—
47C3×C7×C17—21no—
48C3×C7×C17—26no—
49C3×C7×C17D3×D712yescomplemented
50C3×C7×C17C2×D3×C712yescomplemented
51C17×C3⋊D3C7×D711yescharacteristic, complemented
52C3×D51—72no—
53C7×D21—172no—
54D3×C72—32no—
55D3×C72—61no—
56C3×C7×D7—512no—
57(C3⋊D3)⋊D7—171no—
58D32×C7—1191no—
59C2×C7×C17—91no—
60C2×C7×C17—91no—
61C2×C7×C17—183no—
62D119—32no—
63C7×D17—212no—
64D3×D17—212no—
65C2×C7×D7—1531noHall
66C32×C17C2×C7×D711yescharacteristic, complemented, Hall
67C3×C72—21no—
68C3×C72D3×D1712yescomplemented
69C7×C3⋊D3—23no—
70C7×C3⋊D3C7×D1711yescharacteristic, complemented
71C7×C3⋊D3D11911yescharacteristic, complemented
72C3×D21—172no—
73C3×D3×C7—1192no—
74C7×C17—23no—
75C7×C17D32×C711yescharacteristic, complemented
76C7×C17(C3⋊D3)⋊D711yescharacteristic, complemented
77D51—72no—
78C3×D17—212no—
79D3×C17—32no—
80D3×C17—61no—
81C2×C72—91no—
82C7×D7—512no—
83C2×D3×C7—3572no—
84D3×D7—512no—
85C2×D17—631noHall
86C32×C7—23no—
87C32×C7C2×C7×D1711yescharacteristic, complemented
88C32×C7C2×D11911yescharacteristic, complemented
89C3×C17—21no—
90C3×C17D3×C7×D712yescomplemented
91C72(C3⋊D3)⋊D1711yescharacteristic, complemented, Sylow
92C2×C3×C7—3572no—
93D21—172no—
94C3×D7—512no—
95D3×C7—32no—
96D3×C7—32no—
97D3×C7—66no—
98D3×C7—61no—
99D3×C7—61no—
100D3×C7—66no—
101D3×C7—1192no—
102D32—1191noHall
103C2×C17—91no—
104D17—212no—
105C22×C7—10711no—
106C2×D7—1531no—
107C3×C7—26no—
108C3×C7—21no—
109C3×C7—21no—
110C3×C7—26no—
111C3×C7D3×C7×D1712yescomplemented
112C3×C7D3×D11912yescomplemented
113C3⋊D3C7×D11911yescharacteristic, complemented
114C3×D3—1192no—
115C17C7×(C3⋊D3)⋊D711yescharacteristic, complemented, Sylow
116C2×C7—91no—
117C2×C7—91no—
118C2×C7—183no—
119C2×C7—3572no—
120D7—512no—
121C2×D3—3572no—
122C32C2×C7×D11911yescharacteristic, complemented, Sylow
123C7—23no—
124C7C7×(C3⋊D3)⋊D1711yescharacteristic, complemented
125C7(C3⋊D3)⋊D11911yescharacteristic, direct product factor
126C2×C3—3572no—
127D3—32no—
128D3—61no—
129D3—1192no—
130C22—10711noSylow
131C3—21no—
132C3D3×C7×D11912yescomplemented
133C2—91no—
134C2—3572no—
subgroupG/H
center, hypercenterC7(C3⋊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. C3×C7×D357C2semidirect
2. C72×C17×C3⋊D3C2semidirect
4. C32×C72×C17C22semidirect
5. C7×D357D3semidirect
9. (C3⋊D3)⋊D119C7direct (N × H)
13. C3×C72×C17C2×D3semidirect
15. C7×C17×C3⋊D3D7semidirect
16. C7×C17×C3⋊D3C2×C7semidirect
17. C3×D357C2×C7semidirect
25. C32×C7×C17C2×D7semidirect
26. C32×C7×C17C22×C7semidirect
27. C72×C3⋊D3D17semidirect
29. C72×C17D32semidirect
30. D357D3×C7semidirect
44. C32×C72C2×D17semidirect
49. C3×C7×C17D3×D7semidirect
50. C3×C7×C17C2×D3×C7semidirect
51. C17×C3⋊D3C7×D7semidirect
66. C32×C17C2×C7×D7semidirect
68. C3×C72D3×D17semidirect
70. C7×C3⋊D3C7×D17semidirect
71. C7×C3⋊D3D119semidirect
75. C7×C17D32×C7semidirect
76. C7×C17(C3⋊D3)⋊D7semidirect
87. C32×C7C2×C7×D17semidirect
88. C32×C7C2×D119semidirect
90. C3×C17D3×C7×D7semidirect
91. C72(C3⋊D3)⋊D17semidirect
111. C3×C7D3×C7×D17semidirect
112. C3×C7D3×D119semidirect
113. C3⋊D3C7×D119semidirect
115. C17C7×(C3⋊D3)⋊D7semidirect
122. C32C2×C7×D119semidirect
124. C7C7×(C3⋊D3)⋊D17semidirect
125. C7(C3⋊D3)⋊D119direct (N × H)
132. C3D3×C7×D119semidirect

Maximal subgroups

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

subgroupindex
C3×C7×D3572
C72×C17×C3⋊D32
D3×C7×D1193
(C3⋊D3)⋊D1197
C7×(C3⋊D3)⋊D177
C7×(C3⋊D3)⋊D717