Finite Group Databasebeta

← C7×D95⋊(C3⋊D3) #37561607

Subgroups — C7×D95⋊(C3⋊D3) #37561607

Order 23940.

240 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 70 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×D95C211yesmaximal, characteristic, complemented
2C5×C7×C3⋊D57C211yesmaximal, characteristic, complemented
3C7×C19×C3⋊D15C211yesmaximal, characteristic, complemented
4C7×D15⋊D19—34nomaximal
5C32×C5×C7×C19C2211yescharacteristic, complemented, Hall
6C7×C3⋊D3×D19—51nomaximal, Hall
7C7×C19×D15—34no—
8C5×C7×D57—34no—
9C3×C7×D95D314yescomplemented
10D95⋊(C3⋊D3)C711yesmaximal, characteristic, direct product factor, Hall
11C7×D5×D19—91noHall
12C7×C3⋊D57D511yescharacteristic, complemented
13C7×C3⋊D3×C19—51no—
14C32×C7×D19—51no—
15C3×C5×C7×C19C2×D314yescomplemented
16C19×C3⋊D15C2×C711yescharacteristic, complemented
17C5×C3⋊D57C2×C711yescharacteristic, complemented
18C32×D95C2×C711yescharacteristic, complemented
19D3×C7×D19—154no—
20C7×D95C3⋊D311yescharacteristic, complemented
21C7×D5×C19—91no—
22C5×C7×D19—91no—
23C7×D5×C3⋊D3—191nomaximal, Hall
24C32×C7×C19C2×D511yescharacteristic, complemented, Hall
25D15⋊D19—34no—
26C32×C5×C19C22×C711yescharacteristic, complemented, Hall
27C7×D57—34no—
28D3×C7×C19—154no—
29C3×C7×D19—54no—
30C3⋊D3×D19—51noHall
31C5×C7×C19C2×C3⋊D311yescharacteristic, complemented, Hall
32C7×C3⋊D15D1911yescharacteristic, complemented
33C5×C7×C3⋊D3—191no—
34C32×C7×D5—191no—
35C19×D15—34no—
36C5×D57—34no—
37C3×D95D3×C714yescomplemented
38C2×C7×D19—451noHall
39D3×C7×D5—574no—
40C3×C7×C19D3×D514yescomplemented
41D5×D19—91noHall
42C3⋊D57C7×D511yescharacteristic, complemented
43C3⋊D3×C19—51no—
44C32×D19—51no—
45C32×C5×C7C2×D1911yescharacteristic, complemented, Hall
46C3×C5×C19C2×D3×C714yescomplemented
47C2×C7×C19—451no—
48C7×D19—51no—
49C7×D19—91no—
50C2×C7×C3⋊D3—951noHall
51D3×D19—154no—
52C7×D15—34no—
53C5×D3×C7—574no—
54C3×C7×D5—194no—
55D95C7×C3⋊D311yescharacteristic, complemented
56C5×D19—91no—
57D5×C19—91no—
58D5×C3⋊D3—191noHall
59C32×C19C2×C7×D511yescharacteristic, complemented, Hall
60C2×C7×D5—1711noHall
61C7×C19D5×C3⋊D311yescharacteristic, complemented, Hall
62C2×C32×C7—951no—
63C7×C3⋊D3—51no—
64C7×C3⋊D3—191no—
65D57—34no—
66C3×D19—54no—
67D3×C19—154no—
68C3×C5×C7D3×D1914yescomplemented
69C5×C19C2×C7×C3⋊D311yescharacteristic, complemented, Hall
70C3⋊D15C7×D1911yescharacteristic, complemented
71C5×C3⋊D3—191no—
72C32×D5—191no—
73C2×D3×C7—2854no—
74C2×D19—451noHall
75C2×C5×C7—1711no—
76C7×D5—91no—
77C7×D5—191no—
78C32×C7D5×D1911yescharacteristic, complemented, Hall
79D3×D5—574no—
80C3×C19D3×C7×D514yescomplemented
81C32×C5C2×C7×D1911yescharacteristic, complemented, Hall
82C2×C3×C7—954no—
83D3×C7—154no—
84D3×C7—574no—
85C2×C19—451no—
86D19—51no—
87D19—91no—
88C2×C3⋊D3—951noHall
89C5×C7C3⋊D3×D1911yescharacteristic, complemented, Hall
90D15—34no—
91C3×D5—194no—
92C5×D3—574no—
93C22×C7—8551noHall
94C3×C7D15⋊D1914yescomplemented
95C2×D5—1711noHall
96C19C7×D5×C3⋊D311yescharacteristic, complemented, Sylow
97C2×C32—951no—
98C3⋊D3—51no—
99C3⋊D3—191no—
100C3×C5D3×C7×D1914yescomplemented
101C2×C7—451no—
102C2×C7—951no—
103C2×C7—1711no—
104C2×D3—2854no—
105C2×C5—1711no—
106D5—91no—
107D5—191no—
108C32C7×D5×D1911yescharacteristic, complemented, Sylow
109C7D95⋊(C3⋊D3)11yescharacteristic, direct product factor, Sylow
110C2×C3—954no—
111D3—154no—
112D3—574no—
113C5C7×C3⋊D3×D1911yescharacteristic, complemented, Sylow
114C22—8551noSylow
115C3C7×D15⋊D1914yescomplemented
116C2—451no—
117C2—951no—
118C2—1711no—
subgroupG/H
center, hypercenterC7D95⋊(C3⋊D3)
commutator, cosocle, hypocenterC32×C5×C19C22×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C19C22
LCSG ▷ C32×C5×C19
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C32×C7×D95C2semidirect
2. C5×C7×C3⋊D57C2semidirect
3. C7×C19×C3⋊D15C2semidirect
5. C32×C5×C7×C19C22semidirect
9. C3×C7×D95D3semidirect
10. D95⋊(C3⋊D3)C7direct (N × H)
12. C7×C3⋊D57D5semidirect
15. C3×C5×C7×C19C2×D3semidirect
16. C19×C3⋊D15C2×C7semidirect
17. C5×C3⋊D57C2×C7semidirect
18. C32×D95C2×C7semidirect
20. C7×D95C3⋊D3semidirect
24. C32×C7×C19C2×D5semidirect
26. C32×C5×C19C22×C7semidirect
31. C5×C7×C19C2×C3⋊D3semidirect
32. C7×C3⋊D15D19semidirect
37. C3×D95D3×C7semidirect
40. C3×C7×C19D3×D5semidirect
42. C3⋊D57C7×D5semidirect
45. C32×C5×C7C2×D19semidirect
46. C3×C5×C19C2×D3×C7semidirect
55. D95C7×C3⋊D3semidirect
59. C32×C19C2×C7×D5semidirect
61. C7×C19D5×C3⋊D3semidirect
68. C3×C5×C7D3×D19semidirect
69. C5×C19C2×C7×C3⋊D3semidirect
70. C3⋊D15C7×D19semidirect
78. C32×C7D5×D19semidirect
80. C3×C19D3×C7×D5semidirect
81. C32×C5C2×C7×D19semidirect
89. C5×C7C3⋊D3×D19semidirect
94. C3×C7D15⋊D19semidirect
96. C19C7×D5×C3⋊D3semidirect
100. C3×C5D3×C7×D19semidirect
108. C32C7×D5×D19semidirect
109. C7D95⋊(C3⋊D3)direct (N × H)
113. C5C7×C3⋊D3×D19semidirect
115. C3C7×D15⋊D19semidirect

Maximal subgroups

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

subgroupindex
C32×C7×D952
C5×C7×C3⋊D572
C7×C19×C3⋊D152
C7×D15⋊D193
C7×C3⋊D3×D195
D95⋊(C3⋊D3)7
C7×D5×C3⋊D319