Finite Group Databasebeta

← C5×C11×D21⋊D7 #44568849

Subgroups — C5×C11×D21⋊D7 #44568849

Order 32340.

208 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 60 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×C5×C11×C7⋊D7C211yesmaximal, characteristic, complemented
2C5×C7×C11×D21C212yesmaximal, complemented
3C5×C11×D72—31nomaximal, Hall
4C3×C5×C72×C11C2211yescharacteristic, complemented, Hall
5C11×D21⋊D7C511yesmaximal, characteristic, direct product factor, Hall
6C5×C11×C7⋊D7D311yescharacteristic, complemented
7C5×C7×C11×D7—32no—
8C5×D3×C11×D7—72nomaximal
9C7×C11×D21C2×C512yescomplemented
10C3×C11×C7⋊D7C2×C511yescharacteristic, complemented
11C5×D21⋊D7C1111yesmaximal, characteristic, direct product factor, Hall
12C5×C72×C11C2×D311yescharacteristic, complemented, Hall
13C5×C11×D21D712yescomplemented
14C5×D3×C7×C11—72no—
15C3×C5×C11×D7—72no—
16C3×C5×C11×D7—143no—
17C11×D72—31noHall
18C3×C72×C11C22×C511yescharacteristic, complemented, Hall
19C2×C5×C11×D7—212no—
20C5×C7×D21C2×C1112yescomplemented
21C3×C5×C7⋊D7C2×C1111yescharacteristic, complemented
22C3×C5×C7×C11—23no—
23C3×C5×C7×C11C2×D712yescomplemented
24C11×C7⋊D7C5×D311yescharacteristic, complemented
25C7×C11×D7—32no—
26C5×D72—31noHall
27D3×C11×D7—72no—
28C2×C5×C7×C11—212no—
29C5×C11×D7—32no—
30C5×C11×D7—72no—
31C5×C11×D7—143no—
32C3×C5×C72C22×C1111yescharacteristic, complemented, Hall
33C2×C5×D3×C11—491noHall
34D21⋊D7C5×C1111yescharacteristic, direct product factor, Hall
35C72×C11C2×C5×D311yescharacteristic, complemented, Hall
36C5×C7⋊D7D3×C1111yescharacteristic, complemented
37C5×C7×D7—32no—
38C11×D21C5×D712yescomplemented
39D3×C7×C11—72no—
40C3×C11×D7—72no—
41C3×C11×D7—143no—
42C5×D3×D7—72no—
43C5×C7×C11—23no—
44C5×C7×C11D3×D712yescomplemented
45C2×C3×C5×C11—491no—
46C5×D3×C11—72no—
47C2×C11×D7—212no—
48C7×D21C2×C5×C1112yescomplemented
49C3×C7⋊D7C2×C5×C1111yescharacteristic, complemented
50C5×C72C2×D3×C1111yescharacteristic, complemented, Hall
51C3×C7×C11—23no—
52C3×C7×C11C2×C5×D712yescomplemented
53C22×C5×C11—1471noHall
54C5×D21C11×D712yescomplemented
55C5×D3×C7—72no—
56C3×C5×D7—72no—
57C3×C5×D7—143no—
58D72—31noHall
59C3×C5×C11D7211yescharacteristic, complemented, Hall
60C2×C7×C11—212no—
61C11×D7—32no—
62C11×D7—72no—
63C11×D7—143no—
64C3×C72C22×C5×C1111yescharacteristic, complemented, Hall
65C2×C5×D7—212no—
66C2×D3×C11—491noHall
67C2×C5×C11—212no—
68C2×C5×C11—491no—
69C3×C5×C7—23no—
70C3×C5×C7C2×C11×D712yescomplemented
71C7⋊D7C5×D3×C1111yescharacteristic, complemented
72C7×D7—32no—
73D3×D7—72no—
74C7×C11—23no—
75C7×C11C5×D3×D712yescomplemented
76C2×C5×C7—212no—
77C5×D7—32no—
78C5×D7—72no—
79C5×D7—143no—
80C2×C3×C11—491no—
81D3×C11—72no—
82C2×C5×D3—491noHall
83C5×C11D21⋊D711yescharacteristic, direct product factor, Hall
84C72C2×C5×D3×C1111yescharacteristic, complemented, Sylow
85C22×C11—1471noHall
86D21C5×C11×D712yescomplemented
87C3×D7—72no—
88C3×D7—143no—
89D3×C7—72no—
90C5×C7—23no—
91C5×C7D3×C11×D712yescomplemented
92C3×C11C5×D7211yescharacteristic, complemented, Hall
93C2×C3×C5—491no—
94C5×D3—72no—
95C2×D7—212no—
96C2×C11—212no—
97C2×C11—491no—
98C3×C7—23no—
99C3×C7C2×C5×C11×D712yescomplemented
100C22×C5—1471noHall
101C3×C5C11×D7211yescharacteristic, complemented, Hall
102C2×C7—212no—
103D7—32no—
104D7—72no—
105D7—143no—
106C2×D3—491noHall
107C11C5×D21⋊D711yescharacteristic, direct product factor, Sylow
108C2×C5—212no—
109C2×C5—491no—
110C7—23no—
111C7C5×D3×C11×D712yescomplemented
112C2×C3—491no—
113D3—72no—
114C5C11×D21⋊D711yescharacteristic, direct product factor, Sylow
115C22—1471noSylow
116C3C5×C11×D7211yescharacteristic, complemented, Sylow
117C2—212no—
118C2—491no—
subgroupG/H
center, hypercenterC5×C11D21⋊D7
commutator, cosocle, hypocenterC3×C72C22×C5×C11
FrattiniC1G
Fitting, socleC3×C5×C72×C11C22
LCSG ▷ C3×C72
UCSC1 ◁ C5×C11

Complements

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

NH ≅ G/Ntype
1. C3×C5×C11×C7⋊D7C2semidirect
2. C5×C7×C11×D21C2semidirect
4. C3×C5×C72×C11C22semidirect
5. C11×D21⋊D7C5direct (N × H)
6. C5×C11×C7⋊D7D3semidirect
9. C7×C11×D21C2×C5semidirect
10. C3×C11×C7⋊D7C2×C5semidirect
11. C5×D21⋊D7C11direct (N × H)
12. C5×C72×C11C2×D3semidirect
13. C5×C11×D21D7semidirect
18. C3×C72×C11C22×C5semidirect
20. C5×C7×D21C2×C11semidirect
21. C3×C5×C7⋊D7C2×C11semidirect
23. C3×C5×C7×C11C2×D7semidirect
24. C11×C7⋊D7C5×D3semidirect
32. C3×C5×C72C22×C11semidirect
34. D21⋊D7C5×C11direct (N × H)
35. C72×C11C2×C5×D3semidirect
36. C5×C7⋊D7D3×C11semidirect
38. C11×D21C5×D7semidirect
44. C5×C7×C11D3×D7semidirect
48. C7×D21C2×C5×C11semidirect
49. C3×C7⋊D7C2×C5×C11semidirect
50. C5×C72C2×D3×C11semidirect
52. C3×C7×C11C2×C5×D7semidirect
54. C5×D21C11×D7semidirect
59. C3×C5×C11D72semidirect
64. C3×C72C22×C5×C11semidirect
70. C3×C5×C7C2×C11×D7semidirect
71. C7⋊D7C5×D3×C11semidirect
75. C7×C11C5×D3×D7semidirect
83. C5×C11D21⋊D7direct (N × H)
84. C72C2×C5×D3×C11semidirect
86. D21C5×C11×D7semidirect
91. C5×C7D3×C11×D7semidirect
92. C3×C11C5×D72semidirect
99. C3×C7C2×C5×C11×D7semidirect
101. C3×C5C11×D72semidirect
107. C11C5×D21⋊D7direct (N × H)
111. C7C5×D3×C11×D7semidirect
114. C5C11×D21⋊D7direct (N × H)
116. C3C5×C11×D72semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C11×C7⋊D72
C5×C7×C11×D212
C5×C11×D723
C11×D21⋊D75
C5×D3×C11×D77
C5×D21⋊D711