Finite Group Databasebeta

← C2×C3×C17×D165 #46778207

Subgroups — C2×C3×C17×D165 #46778207

Order 33660.

176 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 76 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×C17×D165C212yesmaximal, direct product factor
2C2×C32×C5×C11×C17C211yesmaximal, characteristic, complemented
3C2×C3×C17×D55—31nomaximal
4C2×C17×D165C311yesmaximal, characteristic, direct product factor
5C32×C5×C11×C17C2211yescharacteristic, complemented, Hall
6C2×C3×C17×D33—51nomaximal, Hall
7C17×D165C2×C312yesdirect product factor
8C3×C17×D55—32no—
9C2×C3×C5×C11×C17—21no—
10C2×C3×C5×C11×C17D311yescharacteristic, complemented
11C2×C3×C5×C11×C17C2×C311yescharacteristic, complemented
12C2×C17×D55—31noHall
13C3×C17×D33—52no—
14C2×C32×C11×C17D511yescharacteristic, complemented
15C2×C3×C17×D15—111nomaximal, Hall
16C3×C5×C11×C17—21no—
17C3×C5×C11×C17C2×D311yescharacteristic, complemented
18C3×C5×C11×C17C22×C311yescharacteristic, complemented
19C2×C3×C17×D11—151no—
20C2×C17×D33—51no—
21C2×C3×D165C1711yesmaximal, characteristic, direct product factor, Hall
22C2×C5×C11×C17C3×D311yescharacteristic, complemented
23C17×D55—32no—
24C32×C11×C17C2×D511yescharacteristic, complemented, Hall
25C2×C32×C5×C17D1111yescharacteristic, complemented
26C3×C17×D15—112no—
27C2×C3×C11×C17—21no—
28C2×C3×C11×C17C3×D511yescharacteristic, complemented
29C2×C3×C11×C17D1511yescharacteristic, complemented
30C17×D33—52no—
31C3×C17×D11—152no—
32C2×C17×D15—111no—
33C2×C3×D5×C17—331no—
34C2×C32×C5×C11C2×C1711yescharacteristic, complemented
35C3×D165C2×C1712yesdirect product factor
36C5×C11×C17C2×C3×D311yescharacteristic, complemented, Hall
37C32×C5×C17C2×D1111yescharacteristic, complemented, Hall
38C2×C17×D11—151noHall
39C2×D165C3×C1711yescharacteristic, direct product factor
40C2×C3×D55—31no—
41C2×C3×D3×C17—551noHall
42C3×C11×C17—21no—
43C3×C11×C17C2×C3×D511yescharacteristic, complemented
44C3×C11×C17C2×D1511yescharacteristic, complemented
45C2×C3×C5×C17—21no—
46C2×C3×C5×C17C3×D1111yescharacteristic, complemented
47C2×C3×C5×C17D3311yescharacteristic, complemented
48C17×D15—112no—
49C3×D5×C17—332no—
50C32×C5×C11C22×C1711yescharacteristic, complemented, Hall
51C2×C3×D33—51noHall
52C2×C11×C17C3×D1511yescharacteristic, complemented
53C17×D11—152no—
54C2×D5×C17—331noHall
55C2×C3×C5×C11—21no—
56C2×C3×C5×C11D3×C1711yescharacteristic, complemented
57C2×C3×C5×C11C2×C3×C1711yescharacteristic, complemented
58D165C2×C3×C1712yesdirect product factor
59C3×D55—32no—
60C2×C32×C17D5511yescharacteristic, complemented
61C3×D3×C17—552no—
62C3×C5×C17—21no—
63C3×C5×C17C2×C3×D1111yescharacteristic, complemented
64C3×C5×C17C2×D3311yescharacteristic, complemented
65C2×D55—31noHall
66C22×C3×C17—1651no—
67C2×D3×C17—551no—
68C2×C32×C11D5×C1711yescharacteristic, complemented
69C3×D33—52no—
70C11×C17C2×C3×D1511yescharacteristic, complemented, Hall
71C2×C3×D15—111noHall
72C2×C5×C17C3×D3311yescharacteristic, complemented
73D5×C17—332no—
74C3×C5×C11—21no—
75C3×C5×C11C2×D3×C1711yescharacteristic, complemented
76C3×C5×C11C22×C3×C1711yescharacteristic, complemented
77C32×C17C2×D5511yescharacteristic, complemented, Hall
78C2×D33—51no—
79C2×C3×D11—151no—
80C2×C5×C11C3×D3×C1711yescharacteristic, complemented
81D55—32no—
82C2×C3×C17—21no—
83C2×C3×C17—1652no—
84C2×C3×C17C3×D5511yescharacteristic, complemented
85C2×C3×C17D16511yescharacteristic, direct product factor
86D3×C17—552no—
87C32×C11C2×D5×C1711yescharacteristic, complemented, Hall
88C2×C32×C5C17×D1111yescharacteristic, complemented
89C3×D15—112no—
90C5×C17C2×C3×D3311yescharacteristic, complemented, Hall
91C22×C17—1651noHall
92C2×C3×C11—21no—
93C2×C3×C11C3×D5×C1711yescharacteristic, complemented
94C2×C3×C11C17×D1511yescharacteristic, complemented
95D33—52no—
96C3×D11—152no—
97C2×D15—111no—
98C2×C3×D5—331no—
99C5×C11C2×C3×D3×C1711yescharacteristic, complemented, Hall
100C3×C17—21no—
101C3×C17C2×C3×D5511yescharacteristic, complemented
102C3×C17C2×D16511yescharacteristic, direct product factor
103C32×C5C2×C17×D1111yescharacteristic, complemented, Hall
104C2×D11—151noHall
105C2×C3×D3—551noHall
106C2×C17—1652no—
107C2×C17C3×D16511yescharacteristic, direct product factor
108C3×C11—21no—
109C3×C11C2×C3×D5×C1711yescharacteristic, complemented
110C3×C11C2×C17×D1511yescharacteristic, complemented
111C2×C3×C5—21no—
112C2×C3×C5C3×C17×D1111yescharacteristic, complemented
113C2×C3×C5C17×D3311yescharacteristic, complemented
114D15—112no—
115C3×D5—332no—
116C2×C11C3×C17×D1511yescharacteristic, complemented
117D11—152no—
118C2×D5—331noHall
119C2×C32C17×D5511yescharacteristic, complemented
120C3×D3—552no—
121C17C2×C3×D16511yescharacteristic, direct product factor, Sylow
122C3×C5—21no—
123C3×C5C2×C17×D3311yescharacteristic, complemented
124C3×C5C2×C3×C17×D1111yescharacteristic, complemented
125C22×C3—1651no—
126C2×D3—551no—
127C11C2×C3×C17×D1511yescharacteristic, complemented, Sylow
128C2×C5C3×C17×D3311yescharacteristic, complemented
129D5—332no—
130C32C2×C17×D5511yescharacteristic, complemented, Sylow
131C2×C3—21no—
132C2×C3—1652no—
133C2×C3C3×C17×D5511yescharacteristic, complemented
134C2×C3C17×D16511yescharacteristic, direct product factor
135D3—552no—
136C5C2×C3×C17×D3311yescharacteristic, complemented, Sylow
137C22—1651noSylow
138C3—21no—
139C3C2×C17×D16511yescharacteristic, direct product factor
140C3C2×C3×C17×D5511yescharacteristic, complemented
141C2—1652no—
142C2C3×C17×D16511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C17D165
commutator, cosocle, hypocenterC3×C5×C11C22×C3×C17
FrattiniC1G
Fitting, socleC2×C32×C5×C11×C17C2
LCSG ▷ C3×C5×C11
UCSC1 ◁ C2×C3×C17

Complements

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

NH ≅ G/Ntype
1. C3×C17×D165C2direct (N × H)
2. C2×C32×C5×C11×C17C2semidirect
4. C2×C17×D165C3direct (N × H)
5. C32×C5×C11×C17C22semidirect
7. C17×D165C2×C3direct (N × H)
10. C2×C3×C5×C11×C17D3semidirect
11. C2×C3×C5×C11×C17C2×C3semidirect
14. C2×C32×C11×C17D5semidirect
17. C3×C5×C11×C17C2×D3semidirect
18. C3×C5×C11×C17C22×C3semidirect
21. C2×C3×D165C17direct (N × H)
22. C2×C5×C11×C17C3×D3semidirect
24. C32×C11×C17C2×D5semidirect
25. C2×C32×C5×C17D11semidirect
28. C2×C3×C11×C17C3×D5semidirect
29. C2×C3×C11×C17D15semidirect
34. C2×C32×C5×C11C2×C17semidirect
35. C3×D165C2×C17direct (N × H)
36. C5×C11×C17C2×C3×D3semidirect
37. C32×C5×C17C2×D11semidirect
39. C2×D165C3×C17direct (N × H)
43. C3×C11×C17C2×C3×D5semidirect
44. C3×C11×C17C2×D15semidirect
46. C2×C3×C5×C17C3×D11semidirect
47. C2×C3×C5×C17D33semidirect
50. C32×C5×C11C22×C17semidirect
52. C2×C11×C17C3×D15semidirect
56. C2×C3×C5×C11D3×C17semidirect
57. C2×C3×C5×C11C2×C3×C17semidirect
58. D165C2×C3×C17direct (N × H)
60. C2×C32×C17D55semidirect
63. C3×C5×C17C2×C3×D11semidirect
64. C3×C5×C17C2×D33semidirect
68. C2×C32×C11D5×C17semidirect
70. C11×C17C2×C3×D15semidirect
72. C2×C5×C17C3×D33semidirect
75. C3×C5×C11C2×D3×C17semidirect
76. C3×C5×C11C22×C3×C17semidirect
77. C32×C17C2×D55semidirect
80. C2×C5×C11C3×D3×C17semidirect
84. C2×C3×C17C3×D55semidirect
85. C2×C3×C17D165direct (N × H)
87. C32×C11C2×D5×C17semidirect
88. C2×C32×C5C17×D11semidirect
90. C5×C17C2×C3×D33semidirect
93. C2×C3×C11C3×D5×C17semidirect
94. C2×C3×C11C17×D15semidirect
99. C5×C11C2×C3×D3×C17semidirect
101. C3×C17C2×C3×D55semidirect
102. C3×C17C2×D165direct (N × H)
103. C32×C5C2×C17×D11semidirect
107. C2×C17C3×D165direct (N × H)
109. C3×C11C2×C3×D5×C17semidirect
110. C3×C11C2×C17×D15semidirect
112. C2×C3×C5C3×C17×D11semidirect
113. C2×C3×C5C17×D33semidirect
116. C2×C11C3×C17×D15semidirect
119. C2×C32C17×D55semidirect
121. C17C2×C3×D165direct (N × H)
123. C3×C5C2×C17×D33semidirect
124. C3×C5C2×C3×C17×D11semidirect
127. C11C2×C3×C17×D15semidirect
128. C2×C5C3×C17×D33semidirect
130. C32C2×C17×D55semidirect
133. C2×C3C3×C17×D55semidirect
134. C2×C3C17×D165direct (N × H)
136. C5C2×C3×C17×D33semidirect
139. C3C2×C17×D165direct (N × H)
140. C3C2×C3×C17×D55semidirect
142. C2C3×C17×D165direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C17×D1652
C2×C32×C5×C11×C172
C2×C3×C17×D553
C2×C17×D1653
C2×C3×C17×D335
C2×C3×C17×D1511
C2×C3×D16517