Finite Group Databasebeta

← C7×C3⋊D3×D95 #37561606

Subgroups — C7×C3⋊D3×D95 #37561606

Order 23940.

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

normal subgroups only

This group has 240 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×D95C211yesmaximal, characteristic, complemented
2C5×C7×C3⋊D3×C19C211yesmaximal, characteristic, complemented
3C7×C3⋊D285C211yesmaximal, characteristic, complemented
4D3×C7×D95—34nomaximal
5C32×C5×C7×C19C2211yescharacteristic, complemented, Hall
6C7×C3⋊D3×D19—51nomaximal, Hall
7C7×D285—34no—
8C5×D3×C7×C19—34no—
9C3×C7×D95D314yescomplemented
10C3⋊D3×D95C711yesmaximal, characteristic, direct product factor, Hall
11C2×C7×D95—91noHall
12C7×C3⋊D57—51no—
13C7×C3⋊D3×C19D511yescharacteristic, complemented
14C32×C7×D19—51no—
15C3×C5×C7×C19C2×D314yescomplemented
16C3⋊D285C2×C711yescharacteristic, complemented
17C5×C3⋊D3×C19C2×C711yescharacteristic, complemented
18C32×D95C2×C711yescharacteristic, complemented
19D3×C7×D19—154no—
20C2×C5×C7×C19—91no—
21C7×D95—91no—
22C7×D95C3⋊D311yescharacteristic, direct product factor
23C7×D5×C3⋊D3—191nomaximal, Hall
24C32×C7×C19C2×D511yescharacteristic, complemented, Hall
25D3×D95—34no—
26C32×C5×C19C22×C711yescharacteristic, complemented, Hall
27C7×D57—154no—
28D3×C7×C19—34no—
29C3×C7×D19—54no—
30C3⋊D3×D19—51noHall
31C5×C7×C19C2×C3⋊D311yescharacteristic, complemented, Hall
32C7×C3⋊D15—191no—
33C5×C7×C3⋊D3D1911yescharacteristic, complemented
34C32×C7×D5—191no—
35D285—34no—
36C5×D3×C19—34no—
37C3×D95D3×C714yescomplemented
38C2×C7×D19—451noHall
39D3×C7×D5—574no—
40C3×C7×C19D3×D514yescomplemented
41C2×D95—91noHall
42C3⋊D57—51no—
43C3⋊D3×C19C7×D511yescharacteristic, complemented
44C32×D19—51no—
45C32×C5×C7C2×D1911yescharacteristic, complemented, Hall
46C3×C5×C19C2×D3×C714yescomplemented
47C2×C7×C19—91no—
48C7×D19—51no—
49C7×D19—451no—
50C2×C7×C3⋊D3—951noHall
51D3×D19—154no—
52C7×D15—574no—
53C5×D3×C7—34no—
54C3×C7×D5—194no—
55C2×C5×C19—91no—
56D95—91no—
57D95C7×C3⋊D311yescharacteristic, direct product factor
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—951no—
64C7×C3⋊D3D9511yescharacteristic, direct product factor
65D57—154no—
66C3×D19—54no—
67D3×C19—34no—
68C3×C5×C7D3×D1914yescomplemented
69C5×C19C2×C7×C3⋊D311yescharacteristic, complemented, Hall
70C3⋊D15—191no—
71C5×C3⋊D3C7×D1911yescharacteristic, complemented
72C32×D5—191no—
73C2×D3×C7—2854no—
74C2×D19—451noHall
75C2×C5×C7—91no—
76C7×D5—191no—
77C7×D5—1711no—
78C32×C7C2×D9511yescharacteristic, complemented, Hall
79D3×D5—574no—
80C3×C19D3×C7×D514yescomplemented
81C32×C5C2×C7×D1911yescharacteristic, complemented, Hall
82C2×C3×C7—954no—
83D3×C7—34no—
84D3×C7—2854no—
85C2×C19—91no—
86D19—51no—
87D19—451no—
88C2×C3⋊D3—951noHall
89C5×C7C3⋊D3×D1911yescharacteristic, complemented, Hall
90D15—574no—
91C3×D5—194no—
92C5×D3—34no—
93C22×C7—8551noHall
94C3×C7D3×D9514yescomplemented
95C2×D5—1711noHall
96C19C7×D5×C3⋊D311yescharacteristic, complemented, Sylow
97C2×C32—951no—
98C3⋊D3—951no—
99C3⋊D3C7×D9511yescharacteristic, direct product factor
100C3×C5D3×C7×D1914yescomplemented
101C2×C7—91no—
102C2×C7—8551no—
103C2×C7—951no—
104C2×D3—2854no—
105C2×C5—91no—
106D5—191no—
107D5—1711no—
108C32C2×C7×D9511yescharacteristic, complemented, Sylow
109C7C3⋊D3×D9511yescharacteristic, direct product factor, Sylow
110C2×C3—954no—
111D3—34no—
112D3—2854no—
113C5C7×C3⋊D3×D1911yescharacteristic, complemented, Sylow
114C22—8551noSylow
115C3D3×C7×D9514yescomplemented
116C2—91no—
117C2—8551no—
118C2—951no—
subgroupG/H
center, hypercenterC7C3⋊D3×D95
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⋊D3×C19C2semidirect
3. C7×C3⋊D285C2semidirect
5. C32×C5×C7×C19C22semidirect
9. C3×C7×D95D3semidirect
10. C3⋊D3×D95C7direct (N × H)
13. C7×C3⋊D3×C19D5semidirect
15. C3×C5×C7×C19C2×D3semidirect
16. C3⋊D285C2×C7semidirect
17. C5×C3⋊D3×C19C2×C7semidirect
18. C32×D95C2×C7semidirect
22. C7×D95C3⋊D3direct (N × H)
24. C32×C7×C19C2×D5semidirect
26. C32×C5×C19C22×C7semidirect
31. C5×C7×C19C2×C3⋊D3semidirect
33. C5×C7×C3⋊D3D19semidirect
37. C3×D95D3×C7semidirect
40. C3×C7×C19D3×D5semidirect
43. C3⋊D3×C19C7×D5semidirect
45. C32×C5×C7C2×D19semidirect
46. C3×C5×C19C2×D3×C7semidirect
57. D95C7×C3⋊D3direct (N × H)
59. C32×C19C2×C7×D5semidirect
61. C7×C19D5×C3⋊D3semidirect
64. C7×C3⋊D3D95direct (N × H)
68. C3×C5×C7D3×D19semidirect
69. C5×C19C2×C7×C3⋊D3semidirect
71. C5×C3⋊D3C7×D19semidirect
78. C32×C7C2×D95semidirect
80. C3×C19D3×C7×D5semidirect
81. C32×C5C2×C7×D19semidirect
89. C5×C7C3⋊D3×D19semidirect
94. C3×C7D3×D95semidirect
96. C19C7×D5×C3⋊D3semidirect
99. C3⋊D3C7×D95direct (N × H)
100. C3×C5D3×C7×D19semidirect
108. C32C2×C7×D95semidirect
109. C7C3⋊D3×D95direct (N × H)
113. C5C7×C3⋊D3×D19semidirect
115. C3D3×C7×D95semidirect

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⋊D3×C192
C7×C3⋊D2852
D3×C7×D953
C7×C3⋊D3×D195
C3⋊D3×D957
C7×D5×C3⋊D319