Finite Group Databasebeta

← D3×C72×D5×C11 #44568885

Subgroups — D3×C72×D5×C11 #44568885

Order 32340.

400 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 200 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×D3×C72×C11C211yesmaximal, characteristic, complemented
3C72×C11×D15C211yesmaximal, characteristic, complemented
4C2×C72×D5×C11—31nomaximal, Hall
5C3×C5×C72×C11C2211yescharacteristic, complemented, Hall
6C2×D3×C72×C11—51nomaximal, Hall
7C72×D5×C11—31no—
8C72×D5×C11D311yescharacteristic, direct product factor
9C2×C5×C72×C11—31no—
10D3×C7×D5×C11C718yesmaximal, direct product factor
11D3×C72×C11—51no—
12D3×C72×C11D511yescharacteristic, direct product factor
13C2×C3×C72×C11—51no—
14D3×C72×D5C1111yesmaximal, characteristic, direct product factor, Hall
15C5×C72×C11C2×D311yescharacteristic, complemented, Hall
16C7×C11×D15C2×C718yescomplemented
17C5×D3×C7×C11C2×C718yescomplemented
18C3×C7×D5×C11C2×C718yescomplemented
19C22×C72×C11—151noHall
20C3×C72×C11C2×D511yescharacteristic, complemented, Hall
21C2×C7×D5×C11—38no—
22C72×D15C2×C1111yescharacteristic, complemented
23C5×D3×C72C2×C1111yescharacteristic, complemented
24C3×C72×D5C2×C1111yescharacteristic, complemented
25C3×C5×C7×C11C22×C718yescomplemented
26C2×C72×C11—31no—
27C2×C72×C11—51no—
28C2×C72×C11—151no—
29C2×C72×D5—31noHall
30C2×D3×C7×C11—58no—
31C2×C5×C7×C11—38no—
32C7×D5×C11—38no—
33C7×D5×C11D3×C718yesdirect product factor
34C3×C5×C72C22×C1111yescharacteristic, complemented, Hall
35D3×D5×C11C7211yescharacteristic, direct product factor, Hall
36C2×D3×C72—51noHall
37C72×C11D3×D511yescharacteristic, direct product factor, Hall
38C2×C5×C72—31no—
39C72×D5—31no—
40C72×D5D3×C1111yescharacteristic, direct product factor
41C2×C3×C7×C11—58no—
42D3×C7×C11—58no—
43D3×C7×C11C7×D518yesdirect product factor
44D3×C7×D5C7×C1118yesdirect product factor
45C5×C7×C11C2×D3×C718yescomplemented
46C11×D15C2×C7211yescharacteristic, complemented
47C5×D3×C11C2×C7211yescharacteristic, complemented
48C3×D5×C11C2×C7211yescharacteristic, complemented
49C22×C7×C11—158no—
50C2×C3×C72—51no—
51D3×C72—51no—
52D3×C72D5×C1111yescharacteristic, direct product factor
53C5×C72C2×D3×C1111yescharacteristic, complemented, Hall
54C3×C7×C11C2×C7×D518yescomplemented
55C2×D5×C11—31noHall
56C7×D15C2×C7×C1118yescomplemented
57C5×D3×C7C2×C7×C1118yescomplemented
58C3×C7×D5C2×C7×C1118yescomplemented
59C22×C72—151noHall
60C3×C5×C11C22×C7211yescharacteristic, complemented, Hall
61C2×C7×C11—38no—
62C2×C7×C11—58no—
63C2×C7×C11—158no—
64C3×C72C2×D5×C1111yescharacteristic, complemented, Hall
65C2×C7×D5—38no—
66C2×D3×C11—51noHall
67C2×C5×C11—31no—
68D5×C11—31no—
69D5×C11D3×C7211yescharacteristic, direct product factor
70C3×C5×C7C22×C7×C1118yescomplemented
71C2×C72—31no—
72C2×C72—51no—
73C2×C72—151no—
74C2×D3×C7—58no—
75C7×C11D3×C7×D518yesdirect product factor
76C2×C5×C7—38no—
77C7×D5—38no—
78C7×D5D3×C7×C1118yesdirect product factor
79C2×C3×C11—51no—
80D3×C11—51no—
81D3×C11C72×D511yescharacteristic, direct product factor
82D3×D5C72×C1111yescharacteristic, direct product factor, Hall
83C5×C11C2×D3×C7211yescharacteristic, complemented, Hall
84C72D3×D5×C1111yescharacteristic, direct product factor, Sylow
85C22×C11—151noHall
86C2×C3×C7—58no—
87D3×C7—58no—
88D3×C7C7×D5×C1118yesdirect product factor
89C5×C7C2×D3×C7×C1118yescomplemented
90C3×C11C2×C72×D511yescharacteristic, complemented, Hall
91D15C2×C72×C1111yescharacteristic, complemented
92C3×D5C2×C72×C1111yescharacteristic, complemented
93C5×D3C2×C72×C1111yescharacteristic, complemented
94C22×C7—158no—
95C2×C11—31no—
96C2×C11—51no—
97C2×C11—151no—
98C3×C7C2×C7×D5×C1118yescomplemented
99C2×D5—31noHall
100C3×C5C22×C72×C1111yescharacteristic, complemented, Hall
101C2×C7—38no—
102C2×C7—58no—
103C2×C7—158no—
104C2×D3—51noHall
105C11D3×C72×D511yescharacteristic, direct product factor, Sylow
106C2×C5—31no—
107D5—31no—
108D5D3×C72×C1111yescharacteristic, direct product factor
109C7D3×C7×D5×C1118yesdirect product factor
110C2×C3—51no—
111D3—51no—
112D3C72×D5×C1111yescharacteristic, direct product factor
113C5C2×D3×C72×C1111yescharacteristic, complemented, Sylow
114C22—151noSylow
115C3C2×C72×D5×C1111yescharacteristic, complemented, Sylow
116C2—31no—
117C2—51no—
118C2—151no—
subgroupG/H
center, hypercenterC72×C11D3×D5
commutator, cosocle, hypocenterC3×C5C22×C72×C11
FrattiniC1G
Fitting, socleC3×C5×C72×C11C22
LCSG ▷ C3×C5
UCSC1 ◁ C72×C11

Complements

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

NH ≅ G/Ntype
1. C3×C72×D5×C11C2semidirect
2. C5×D3×C72×C11C2semidirect
3. C72×C11×D15C2semidirect
5. C3×C5×C72×C11C22semidirect
8. C72×D5×C11D3direct (N × H)
10. D3×C7×D5×C11C7direct (N × H)
12. D3×C72×C11D5direct (N × H)
14. D3×C72×D5C11direct (N × H)
15. C5×C72×C11C2×D3semidirect
16. C7×C11×D15C2×C7semidirect
17. C5×D3×C7×C11C2×C7semidirect
18. C3×C7×D5×C11C2×C7semidirect
20. C3×C72×C11C2×D5semidirect
22. C72×D15C2×C11semidirect
23. C5×D3×C72C2×C11semidirect
24. C3×C72×D5C2×C11semidirect
25. C3×C5×C7×C11C22×C7semidirect
33. C7×D5×C11D3×C7direct (N × H)
34. C3×C5×C72C22×C11semidirect
35. D3×D5×C11C72direct (N × H)
37. C72×C11D3×D5direct (N × H)
40. C72×D5D3×C11direct (N × H)
43. D3×C7×C11C7×D5direct (N × H)
44. D3×C7×D5C7×C11direct (N × H)
45. C5×C7×C11C2×D3×C7semidirect
46. C11×D15C2×C72semidirect
47. C5×D3×C11C2×C72semidirect
48. C3×D5×C11C2×C72semidirect
52. D3×C72D5×C11direct (N × H)
53. C5×C72C2×D3×C11semidirect
54. C3×C7×C11C2×C7×D5semidirect
56. C7×D15C2×C7×C11semidirect
57. C5×D3×C7C2×C7×C11semidirect
58. C3×C7×D5C2×C7×C11semidirect
60. C3×C5×C11C22×C72semidirect
64. C3×C72C2×D5×C11semidirect
69. D5×C11D3×C72direct (N × H)
70. C3×C5×C7C22×C7×C11semidirect
75. C7×C11D3×C7×D5direct (N × H)
78. C7×D5D3×C7×C11direct (N × H)
81. D3×C11C72×D5direct (N × H)
82. D3×D5C72×C11direct (N × H)
83. C5×C11C2×D3×C72semidirect
84. C72D3×D5×C11direct (N × H)
88. D3×C7C7×D5×C11direct (N × H)
89. C5×C7C2×D3×C7×C11semidirect
90. C3×C11C2×C72×D5semidirect
91. D15C2×C72×C11semidirect
92. C3×D5C2×C72×C11semidirect
93. C5×D3C2×C72×C11semidirect
98. C3×C7C2×C7×D5×C11semidirect
100. C3×C5C22×C72×C11semidirect
105. C11D3×C72×D5direct (N × H)
108. D5D3×C72×C11direct (N × H)
109. C7D3×C7×D5×C11direct (N × H)
112. D3C72×D5×C11direct (N × H)
113. C5C2×D3×C72×C11semidirect
115. C3C2×C72×D5×C11semidirect

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×D3×C72×C112
C72×C11×D152
C2×C72×D5×C113
C2×D3×C72×C115
D3×C7×D5×C117
D3×C72×D511