Finite Group Databasebeta

← C7×D115⋊(C3⋊D3) #44394646

Subgroups — C7×D115⋊(C3⋊D3) #44394646

Order 28980.

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×D115C211yesmaximal, characteristic, complemented
2C5×C7×C3⋊D69C211yesmaximal, characteristic, complemented
3C7×C23×C3⋊D15C211yesmaximal, characteristic, complemented
4C7×D15⋊D23—34nomaximal
5C32×C5×C7×C23C2211yescharacteristic, complemented, Hall
6C7×C3⋊D3×D23—51nomaximal, Hall
7C7×C23×D15—34no—
8C5×C7×D69—34no—
9C3×C7×D115D314yescomplemented
10D115⋊(C3⋊D3)C711yesmaximal, characteristic, direct product factor, Hall
11C7×D5×D23—91noHall
12C7×C3⋊D69D511yescharacteristic, complemented
13C7×C3⋊D3×C23—51no—
14C32×C7×D23—51no—
15C3×C5×C7×C23C2×D314yescomplemented
16C23×C3⋊D15C2×C711yescharacteristic, complemented
17C5×C3⋊D69C2×C711yescharacteristic, complemented
18C32×D115C2×C711yescharacteristic, complemented
19D3×C7×D23—154no—
20C7×D115C3⋊D311yescharacteristic, complemented
21C7×D5×C23—91no—
22C5×C7×D23—91no—
23C32×C7×C23C2×D511yescharacteristic, complemented, Hall
24D15⋊D23—34no—
25C7×D5×C3⋊D3—231nomaximal, Hall
26C32×C5×C23C22×C711yescharacteristic, complemented, Hall
27C7×D69—34no—
28D3×C7×C23—154no—
29C3×C7×D23—54no—
30C3⋊D3×D23—51noHall
31C5×C7×C23C2×C3⋊D311yescharacteristic, complemented, Hall
32C23×D15—34no—
33C5×D69—34no—
34C3×D115D3×C714yescomplemented
35C2×C7×D23—451noHall
36C7×C3⋊D15D2311yescharacteristic, complemented
37C5×C7×C3⋊D3—231no—
38C32×C7×D5—231no—
39C3×C7×C23D3×D514yescomplemented
40D5×D23—91noHall
41D3×C7×D5—694no—
42C3⋊D69C7×D511yescharacteristic, complemented
43C3⋊D3×C23—51no—
44C32×D23—51no—
45C3×C5×C23C2×D3×C714yescomplemented
46C2×C7×C23—451no—
47C7×D23—51no—
48C7×D23—91no—
49C32×C5×C7C2×D2311yescharacteristic, complemented, Hall
50D3×D23—154no—
51C2×C7×C3⋊D3—1151noHall
52D115C7×C3⋊D311yescharacteristic, complemented
53C5×D23—91no—
54D5×C23—91no—
55C7×D15—34no—
56C5×D3×C7—694no—
57C3×C7×D5—234no—
58C32×C23C2×C7×D511yescharacteristic, complemented, Hall
59D5×C3⋊D3—231noHall
60C7×C23D5×C3⋊D311yescharacteristic, complemented, Hall
61C2×C7×D5—2071noHall
62D69—34no—
63C3×D23—54no—
64D3×C23—154no—
65C2×C32×C7—1151no—
66C7×C3⋊D3—51no—
67C7×C3⋊D3—231no—
68C5×C23C2×C7×C3⋊D311yescharacteristic, complemented, Hall
69C3×C5×C7D3×D2314yescomplemented
70C2×D23—451noHall
71C3⋊D15C7×D2311yescharacteristic, complemented
72C5×C3⋊D3—231no—
73C32×D5—231no—
74C2×D3×C7—3454no—
75C2×C5×C7—2071no—
76C7×D5—91no—
77C7×D5—231no—
78C3×C23D3×C7×D514yescomplemented
79C32×C7D5×D2311yescharacteristic, complemented, Hall
80D3×D5—694no—
81C2×C23—451no—
82D23—51no—
83D23—91no—
84C32×C5C2×C7×D2311yescharacteristic, complemented, Hall
85C2×C3×C7—1154no—
86D3×C7—154no—
87D3×C7—694no—
88C2×C3⋊D3—1151noHall
89C5×C7C3⋊D3×D2311yescharacteristic, complemented, Hall
90D15—34no—
91C3×D5—234no—
92C5×D3—694no—
93C22×C7—10351noHall
94C23C7×D5×C3⋊D311yescharacteristic, complemented, Sylow
95C3×C7D15⋊D2314yescomplemented
96C2×D5—2071noHall
97C2×C32—1151no—
98C3⋊D3—51no—
99C3⋊D3—231no—
100C3×C5D3×C7×D2314yescomplemented
101C2×C7—451no—
102C2×C7—1151no—
103C2×C7—2071no—
104C2×D3—3454no—
105C2×C5—2071no—
106D5—91no—
107D5—231no—
108C32C7×D5×D2311yescharacteristic, complemented, Sylow
109C7D115⋊(C3⋊D3)11yescharacteristic, direct product factor, Sylow
110C2×C3—1154no—
111D3—154no—
112D3—694no—
113C5C7×C3⋊D3×D2311yescharacteristic, complemented, Sylow
114C22—10351noSylow
115C3C7×D15⋊D2314yescomplemented
116C2—451no—
117C2—1151no—
118C2—2071no—
subgroupG/H
center, hypercenterC7D115⋊(C3⋊D3)
commutator, cosocle, hypocenterC32×C5×C23C22×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C23C22
LCSG ▷ C32×C5×C23
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C32×C7×D115C2semidirect
2. C5×C7×C3⋊D69C2semidirect
3. C7×C23×C3⋊D15C2semidirect
5. C32×C5×C7×C23C22semidirect
9. C3×C7×D115D3semidirect
10. D115⋊(C3⋊D3)C7direct (N × H)
12. C7×C3⋊D69D5semidirect
15. C3×C5×C7×C23C2×D3semidirect
16. C23×C3⋊D15C2×C7semidirect
17. C5×C3⋊D69C2×C7semidirect
18. C32×D115C2×C7semidirect
20. C7×D115C3⋊D3semidirect
23. C32×C7×C23C2×D5semidirect
26. C32×C5×C23C22×C7semidirect
31. C5×C7×C23C2×C3⋊D3semidirect
34. C3×D115D3×C7semidirect
36. C7×C3⋊D15D23semidirect
39. C3×C7×C23D3×D5semidirect
42. C3⋊D69C7×D5semidirect
45. C3×C5×C23C2×D3×C7semidirect
49. C32×C5×C7C2×D23semidirect
52. D115C7×C3⋊D3semidirect
58. C32×C23C2×C7×D5semidirect
60. C7×C23D5×C3⋊D3semidirect
68. C5×C23C2×C7×C3⋊D3semidirect
69. C3×C5×C7D3×D23semidirect
71. C3⋊D15C7×D23semidirect
78. C3×C23D3×C7×D5semidirect
79. C32×C7D5×D23semidirect
84. C32×C5C2×C7×D23semidirect
89. C5×C7C3⋊D3×D23semidirect
94. C23C7×D5×C3⋊D3semidirect
95. C3×C7D15⋊D23semidirect
100. C3×C5D3×C7×D23semidirect
108. C32C7×D5×D23semidirect
109. C7D115⋊(C3⋊D3)direct (N × H)
113. C5C7×C3⋊D3×D23semidirect
115. C3C7×D15⋊D23semidirect

Maximal subgroups

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

subgroupindex
C32×C7×D1152
C5×C7×C3⋊D692
C7×C23×C3⋊D152
C7×D15⋊D233
C7×C3⋊D3×D235
D115⋊(C3⋊D3)7
C7×D5×C3⋊D323