Finite Group Databasebeta

← C2×C3×C5×C17×D33 #46778203

Subgroups — C2×C3×C5×C17×D33 #46778203

Order 33660.

176 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 88 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×C17×D33C212yesmaximal, direct product factor
2C2×C32×C5×C11×C17C211yesmaximal, characteristic, complemented
3C2×C3×C5×C17×D11—31nomaximal
4C2×C5×C17×D33C311yesmaximal, characteristic, direct product factor
5C32×C5×C11×C17C2211yescharacteristic, complemented, Hall
6C2×C3×C17×D33C511yesmaximal, characteristic, direct product factor, Hall
7C5×C17×D33C2×C312yesdirect product factor
8C3×C5×C17×D11—32no—
9C2×C3×C5×C11×C17—21no—
10C2×C3×C5×C11×C17D311yescharacteristic, complemented
11C2×C3×C5×C11×C17C2×C311yescharacteristic, complemented
12C2×C5×C17×D11—31noHall
13C3×C17×D33C2×C512yesdirect product factor
14C2×C32×C11×C17C2×C511yescharacteristic, complemented
15C2×C3×C5×D3×C17—111nomaximal, Hall
16C3×C5×C11×C17—21no—
17C3×C5×C11×C17C2×D311yescharacteristic, complemented
18C3×C5×C11×C17C22×C311yescharacteristic, complemented
19C2×C3×C17×D11—31no—
20C2×C17×D33C3×C511yescharacteristic, direct product factor
21C2×C3×C5×D33C1711yesmaximal, characteristic, direct product factor, Hall
22C2×C5×C11×C17C3×D311yescharacteristic, complemented
23C5×C17×D11—32no—
24C32×C11×C17C22×C511yescharacteristic, complemented, Hall
25C2×C32×C5×C17D1111yescharacteristic, complemented
26C3×C5×D3×C17—112no—
27C2×C3×C11×C17—21no—
28C2×C3×C11×C17C5×D311yescharacteristic, complemented
29C2×C3×C11×C17C2×C3×C511yescharacteristic, complemented
30C17×D33C2×C3×C512yesdirect product factor
31C3×C17×D11—32no—
32C22×C3×C5×C17—331no—
33C2×C5×D3×C17—111no—
34C2×C32×C5×C11C2×C1711yescharacteristic, complemented
35C3×C5×D33C2×C1712yesdirect product factor
36C5×C11×C17C2×C3×D311yescharacteristic, complemented, Hall
37C32×C5×C17C2×D1111yescharacteristic, complemented, Hall
38C2×C17×D11—31noHall
39C2×C5×D33C3×C1711yescharacteristic, direct product factor
40C2×C3×C5×D11—31no—
41C2×C3×D3×C17—111noHall
42C3×C11×C17—21no—
43C3×C11×C17C2×C5×D311yescharacteristic, complemented
44C3×C11×C17C22×C3×C511yescharacteristic, complemented
45C2×C3×C5×C17—21no—
46C2×C3×C5×C17—332no—
47C2×C3×C5×C17C3×D1111yescharacteristic, complemented
48C2×C3×C5×C17D3311yescharacteristic, direct product factor
49C5×D3×C17—112no—
50C32×C5×C11C22×C1711yescharacteristic, complemented, Hall
51C2×C3×D33C5×C1711yescharacteristic, direct product factor, Hall
52C2×C11×C17C3×C5×D311yescharacteristic, complemented
53C17×D11—32no—
54C22×C5×C17—331noHall
55C2×C3×C5×C11—21no—
56C2×C3×C5×C11D3×C1711yescharacteristic, complemented
57C2×C3×C5×C11C2×C3×C1711yescharacteristic, complemented
58C5×D33C2×C3×C1712yesdirect product factor
59C3×C5×D11—32no—
60C2×C32×C17C5×D1111yescharacteristic, complemented
61C3×D3×C17—112no—
62C3×C5×C17—21no—
63C3×C5×C17C2×C3×D1111yescharacteristic, complemented
64C3×C5×C17C2×D3311yescharacteristic, direct product factor
65C2×C5×D11—31noHall
66C22×C3×C17—331no—
67C2×D3×C17—111no—
68C2×C32×C11C2×C5×C1711yescharacteristic, complemented
69C3×D33C2×C5×C1712yesdirect product factor
70C11×C17C2×C3×C5×D311yescharacteristic, complemented, Hall
71C2×C3×C5×D3—111noHall
72C2×C5×C17—332no—
73C2×C5×C17C3×D3311yescharacteristic, direct product factor
74C3×C5×C11—21no—
75C3×C5×C11C2×D3×C1711yescharacteristic, complemented
76C3×C5×C11C22×C3×C1711yescharacteristic, complemented
77C32×C17C2×C5×D1111yescharacteristic, complemented, Hall
78C2×D33C3×C5×C1711yescharacteristic, direct product factor
79C2×C3×D11—31no—
80C2×C5×C11C3×D3×C1711yescharacteristic, complemented
81C5×D11—32no—
82C2×C3×C17—21no—
83C2×C3×C17—332no—
84C2×C3×C17C3×C5×D1111yescharacteristic, complemented
85C2×C3×C17C5×D3311yescharacteristic, direct product factor
86D3×C17—112no—
87C32×C11C22×C5×C1711yescharacteristic, complemented, Hall
88C2×C32×C5C17×D1111yescharacteristic, complemented
89C3×C5×D3—112no—
90C5×C17C2×C3×D3311yescharacteristic, direct product factor, Hall
91C22×C17—331noHall
92C2×C3×C11—21no—
93C2×C3×C11C5×D3×C1711yescharacteristic, complemented
94C2×C3×C11C2×C3×C5×C1711yescharacteristic, complemented
95D33C2×C3×C5×C1712yesdirect product factor
96C3×D11—32no—
97C22×C3×C5—331no—
98C2×C5×D3—111no—
99C5×C11C2×C3×D3×C1711yescharacteristic, complemented, Hall
100C3×C17—21no—
101C3×C17C2×C3×C5×D1111yescharacteristic, complemented
102C3×C17C2×C5×D3311yescharacteristic, direct product factor
103C32×C5C2×C17×D1111yescharacteristic, complemented, Hall
104C2×D11—31noHall
105C2×C3×D3—111noHall
106C2×C17—332no—
107C2×C17C3×C5×D3311yescharacteristic, direct product factor
108C3×C11—21no—
109C3×C11C2×C5×D3×C1711yescharacteristic, complemented
110C3×C11C22×C3×C5×C1711yescharacteristic, complemented
111C2×C3×C5—21no—
112C2×C3×C5—332no—
113C2×C3×C5C3×C17×D1111yescharacteristic, complemented
114C2×C3×C5C17×D3311yescharacteristic, direct product factor
115C5×D3—112no—
116C2×C11C3×C5×D3×C1711yescharacteristic, complemented
117D11—32no—
118C22×C5—331noHall
119C2×C32C5×C17×D1111yescharacteristic, complemented
120C3×D3—112no—
121C17C2×C3×C5×D3311yescharacteristic, direct product factor, Sylow
122C3×C5—21no—
123C3×C5C2×C17×D3311yescharacteristic, direct product factor
124C3×C5C2×C3×C17×D1111yescharacteristic, complemented
125C22×C3—331no—
126C2×D3—111no—
127C11C2×C3×C5×D3×C1711yescharacteristic, complemented, Sylow
128C2×C5—332no—
129C2×C5C3×C17×D3311yescharacteristic, direct product factor
130C32C2×C5×C17×D1111yescharacteristic, complemented, Sylow
131C2×C3—21no—
132C2×C3—332no—
133C2×C3C3×C5×C17×D1111yescharacteristic, complemented
134C2×C3C5×C17×D3311yescharacteristic, direct product factor
135D3—112no—
136C5C2×C3×C17×D3311yescharacteristic, direct product factor, Sylow
137C22—331noSylow
138C3—21no—
139C3C2×C5×C17×D3311yescharacteristic, direct product factor
140C3C2×C3×C5×C17×D1111yescharacteristic, complemented
141C2—332no—
142C2C3×C5×C17×D3311yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C5×C17D33
commutator, cosocle, hypocenterC3×C11C22×C3×C5×C17
FrattiniC1G
Fitting, socleC2×C32×C5×C11×C17C2
LCSG ▷ C3×C11
UCSC1 ◁ C2×C3×C5×C17

Complements

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

NH ≅ G/Ntype
1. C3×C5×C17×D33C2direct (N × H)
2. C2×C32×C5×C11×C17C2semidirect
4. C2×C5×C17×D33C3direct (N × H)
5. C32×C5×C11×C17C22semidirect
6. C2×C3×C17×D33C5direct (N × H)
7. C5×C17×D33C2×C3direct (N × H)
10. C2×C3×C5×C11×C17D3semidirect
11. C2×C3×C5×C11×C17C2×C3semidirect
13. C3×C17×D33C2×C5direct (N × H)
14. C2×C32×C11×C17C2×C5semidirect
17. C3×C5×C11×C17C2×D3semidirect
18. C3×C5×C11×C17C22×C3semidirect
20. C2×C17×D33C3×C5direct (N × H)
21. C2×C3×C5×D33C17direct (N × H)
22. C2×C5×C11×C17C3×D3semidirect
24. C32×C11×C17C22×C5semidirect
25. C2×C32×C5×C17D11semidirect
28. C2×C3×C11×C17C5×D3semidirect
29. C2×C3×C11×C17C2×C3×C5semidirect
30. C17×D33C2×C3×C5direct (N × H)
34. C2×C32×C5×C11C2×C17semidirect
35. C3×C5×D33C2×C17direct (N × H)
36. C5×C11×C17C2×C3×D3semidirect
37. C32×C5×C17C2×D11semidirect
39. C2×C5×D33C3×C17direct (N × H)
43. C3×C11×C17C2×C5×D3semidirect
44. C3×C11×C17C22×C3×C5semidirect
47. C2×C3×C5×C17C3×D11semidirect
48. C2×C3×C5×C17D33direct (N × H)
50. C32×C5×C11C22×C17semidirect
51. C2×C3×D33C5×C17direct (N × H)
52. C2×C11×C17C3×C5×D3semidirect
56. C2×C3×C5×C11D3×C17semidirect
57. C2×C3×C5×C11C2×C3×C17semidirect
58. C5×D33C2×C3×C17direct (N × H)
60. C2×C32×C17C5×D11semidirect
63. C3×C5×C17C2×C3×D11semidirect
64. C3×C5×C17C2×D33direct (N × H)
68. C2×C32×C11C2×C5×C17semidirect
69. C3×D33C2×C5×C17direct (N × H)
70. C11×C17C2×C3×C5×D3semidirect
73. C2×C5×C17C3×D33direct (N × H)
75. C3×C5×C11C2×D3×C17semidirect
76. C3×C5×C11C22×C3×C17semidirect
77. C32×C17C2×C5×D11semidirect
78. C2×D33C3×C5×C17direct (N × H)
80. C2×C5×C11C3×D3×C17semidirect
84. C2×C3×C17C3×C5×D11semidirect
85. C2×C3×C17C5×D33direct (N × H)
87. C32×C11C22×C5×C17semidirect
88. C2×C32×C5C17×D11semidirect
90. C5×C17C2×C3×D33direct (N × H)
93. C2×C3×C11C5×D3×C17semidirect
94. C2×C3×C11C2×C3×C5×C17semidirect
95. D33C2×C3×C5×C17direct (N × H)
99. C5×C11C2×C3×D3×C17semidirect
101. C3×C17C2×C3×C5×D11semidirect
102. C3×C17C2×C5×D33direct (N × H)
103. C32×C5C2×C17×D11semidirect
107. C2×C17C3×C5×D33direct (N × H)
109. C3×C11C2×C5×D3×C17semidirect
110. C3×C11C22×C3×C5×C17semidirect
113. C2×C3×C5C3×C17×D11semidirect
114. C2×C3×C5C17×D33direct (N × H)
116. C2×C11C3×C5×D3×C17semidirect
119. C2×C32C5×C17×D11semidirect
121. C17C2×C3×C5×D33direct (N × H)
123. C3×C5C2×C17×D33direct (N × H)
124. C3×C5C2×C3×C17×D11semidirect
127. C11C2×C3×C5×D3×C17semidirect
129. C2×C5C3×C17×D33direct (N × H)
130. C32C2×C5×C17×D11semidirect
133. C2×C3C3×C5×C17×D11semidirect
134. C2×C3C5×C17×D33direct (N × H)
136. C5C2×C3×C17×D33direct (N × H)
139. C3C2×C5×C17×D33direct (N × H)
140. C3C2×C3×C5×C17×D11semidirect
142. C2C3×C5×C17×D33direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×C17×D332
C2×C32×C5×C11×C172
C2×C3×C5×C17×D113
C2×C5×C17×D333
C2×C3×C17×D335
C2×C3×C5×D3×C1711
C2×C3×C5×D3317