Finite Group Databasebeta

← D5×C11×C3⋊(C7⋊D7) #44568913

Subgroups — D5×C11×C3⋊(C7⋊D7) #44568913

Order 32340.

400 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 128 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×C72×D5×C11C211yesmaximal, characteristic, complemented
2C5×C11×C3⋊(C7⋊D7)C211yesmaximal, characteristic, complemented
3C11×C3⋊(C5⋊(C7⋊D7))C211yesmaximal, characteristic, complemented
4D5×C11×C7⋊D7—31nomaximal, Hall
5C3×C5×C72×C11C2211yescharacteristic, complemented, Hall
6C2×C11×C3⋊(C7⋊D7)—51nomaximal, Hall
7C11×C5⋊(C7⋊D7)—31no—
8C72×D5×C11D311yescharacteristic, complemented
9C5×C11×C7⋊D7—31no—
10D5×C11×D21—78nomaximal
11C11×C3⋊(C7⋊D7)—51no—
12C11×C3⋊(C7⋊D7)D511yescharacteristic, direct product factor
13C2×C3×C72×C11—51no—
14D5×C3⋊(C7⋊D7)C1111yesmaximal, characteristic, direct product factor, Hall
15C5×C72×C11C2×D311yescharacteristic, complemented, Hall
16C11×D105—78no—
17C5×C11×D21—78no—
18C3×C7×D5×C11D718yescomplemented
19C2×C11×C7⋊D7—151noHall
20C3×C72×C11C2×D511yescharacteristic, complemented, Hall
21D5×C11×D7—218no—
22C3⋊(C5⋊(C7⋊D7))C2×C1111yescharacteristic, complemented
23C5×C3⋊(C7⋊D7)C2×C1111yescharacteristic, complemented
24C3×C72×D5C2×C1111yescharacteristic, complemented
25C3×C5×C7×C11C2×D718yescomplemented
26C2×C72×C11—51no—
27C11×C7⋊D7—31no—
28C11×C7⋊D7—151no—
29D5×C7⋊D7—31noHall
30C2×C11×D21—358no—
31C11×D35—218no—
32C7×D5×C11D2118yescomplemented
33C5×C11×D7—218no—
34C3×C5×C72C22×C1111yescharacteristic, complemented, Hall
35D3×D5×C11—491noHall
36C2×C3⋊(C7⋊D7)—51noHall
37C72×C11D3×D511yescharacteristic, complemented, Hall
38C5⋊(C7⋊D7)—31no—
39C72×D5D3×C1111yescharacteristic, complemented
40C5×C7⋊D7—31no—
41C2×C3×C7×C11—58no—
42C11×D21—78no—
43C11×D21—358no—
44D5×D21—78no—
45C5×C7×C11C2×D2118yescomplemented
46C11×D15—491no—
47C5×D3×C11—491no—
48C3×D5×C11C7⋊D711yescharacteristic, complemented
49C2×C11×D7—1058no—
50C2×C3×C72—51no—
51C3⋊(C7⋊D7)—51no—
52C3⋊(C7⋊D7)D5×C1111yescharacteristic, direct product factor
53C5×C72C2×D3×C1111yescharacteristic, complemented, Hall
54C3×C7×C11D5×D718yescomplemented
55C2×D5×C11—1471noHall
56D105—78no—
57C5×D21—78no—
58C3×C7×D5C11×D718yescomplemented
59C2×C7⋊D7—151noHall
60C3×C5×C11C2×C7⋊D711yescharacteristic, complemented, Hall
61C2×C7×C11—58no—
62C11×D7—218no—
63C11×D7—1058no—
64C3×C72C2×D5×C1111yescharacteristic, complemented, Hall
65D5×D7—218no—
66C2×D3×C11—2451noHall
67C2×C5×C11—1471no—
68D5×C11—1471no—
69D5×C11C3⋊(C7⋊D7)11yescharacteristic, direct product factor
70C3×C5×C7C2×C11×D718yescomplemented
71C2×C72—51no—
72C7⋊D7—31no—
73C7⋊D7—151no—
74C2×D21—358no—
75C7×C11D5×D2118yescomplemented
76D35—218no—
77C5×D7—218no—
78C7×D5C11×D2118yescomplemented
79C2×C3×C11—51no—
80D3×C11—491no—
81D3×C11—2451no—
82D3×D5—491noHall
83C5×C11C2×C3⋊(C7⋊D7)11yescharacteristic, complemented, Hall
84C72D3×D5×C1111yescharacteristic, complemented, Sylow
85C22×C11—7351noHall
86C2×C3×C7—58no—
87D21—78no—
88D21—358no—
89C5×C7C2×C11×D2118yescomplemented
90C3×C11D5×C7⋊D711yescharacteristic, complemented, Hall
91D15—491no—
92C3×D5C11×C7⋊D711yescharacteristic, complemented
93C5×D3—491no—
94C2×D7—1058no—
95C2×C11—51no—
96C2×C11—1471no—
97C2×C11—7351no—
98C3×C7D5×C11×D718yescomplemented
99C2×D5—1471noHall
100C3×C5C2×C11×C7⋊D711yescharacteristic, complemented, Hall
101C2×C7—58no—
102D7—218no—
103D7—1058no—
104C2×D3—2451noHall
105C11D5×C3⋊(C7⋊D7)11yescharacteristic, direct product factor, Sylow
106C2×C5—1471no—
107D5—1471no—
108D5C11×C3⋊(C7⋊D7)11yescharacteristic, direct product factor
109C7D5×C11×D2118yescomplemented
110C2×C3—51no—
111D3—491no—
112D3—2451no—
113C5C2×C11×C3⋊(C7⋊D7)11yescharacteristic, complemented, Sylow
114C22—7351noSylow
115C3D5×C11×C7⋊D711yescharacteristic, complemented, Sylow
116C2—51no—
117C2—1471no—
118C2—7351no—
subgroupG/H
center, hypercenterC11D5×C3⋊(C7⋊D7)
commutator, cosocle, hypocenterC3×C5×C72C22×C11
FrattiniC1G
Fitting, socleC3×C5×C72×C11C22
LCSG ▷ C3×C5×C72
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C3×C72×D5×C11C2semidirect
2. C5×C11×C3⋊(C7⋊D7)C2semidirect
3. C11×C3⋊(C5⋊(C7⋊D7))C2semidirect
5. C3×C5×C72×C11C22semidirect
8. C72×D5×C11D3semidirect
12. C11×C3⋊(C7⋊D7)D5direct (N × H)
14. D5×C3⋊(C7⋊D7)C11direct (N × H)
15. C5×C72×C11C2×D3semidirect
18. C3×C7×D5×C11D7semidirect
20. C3×C72×C11C2×D5semidirect
22. C3⋊(C5⋊(C7⋊D7))C2×C11semidirect
23. C5×C3⋊(C7⋊D7)C2×C11semidirect
24. C3×C72×D5C2×C11semidirect
25. C3×C5×C7×C11C2×D7semidirect
32. C7×D5×C11D21semidirect
34. C3×C5×C72C22×C11semidirect
37. C72×C11D3×D5semidirect
39. C72×D5D3×C11semidirect
45. C5×C7×C11C2×D21semidirect
48. C3×D5×C11C7⋊D7semidirect
52. C3⋊(C7⋊D7)D5×C11direct (N × H)
53. C5×C72C2×D3×C11semidirect
54. C3×C7×C11D5×D7semidirect
58. C3×C7×D5C11×D7semidirect
60. C3×C5×C11C2×C7⋊D7semidirect
64. C3×C72C2×D5×C11semidirect
69. D5×C11C3⋊(C7⋊D7)direct (N × H)
70. C3×C5×C7C2×C11×D7semidirect
75. C7×C11D5×D21semidirect
78. C7×D5C11×D21semidirect
83. C5×C11C2×C3⋊(C7⋊D7)semidirect
84. C72D3×D5×C11semidirect
89. C5×C7C2×C11×D21semidirect
90. C3×C11D5×C7⋊D7semidirect
92. C3×D5C11×C7⋊D7semidirect
98. C3×C7D5×C11×D7semidirect
100. C3×C5C2×C11×C7⋊D7semidirect
105. C11D5×C3⋊(C7⋊D7)direct (N × H)
108. D5C11×C3⋊(C7⋊D7)direct (N × H)
109. C7D5×C11×D21semidirect
113. C5C2×C11×C3⋊(C7⋊D7)semidirect
115. C3D5×C11×C7⋊D7semidirect

Maximal subgroups

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

subgroupindex
C3×C72×D5×C112
C5×C11×C3⋊(C7⋊D7)2
C11×C3⋊(C5⋊(C7⋊D7))2
D5×C11×C7⋊D73
C2×C11×C3⋊(C7⋊D7)5
D5×C11×D217
D5×C3⋊(C7⋊D7)11