Finite Group Databasebeta

← C2×C3×C11×C17×D15 #46778205

Subgroups — C2×C3×C11×C17×D15 #46778205

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×C11×C17×D15C212yesmaximal, direct product factor
2C2×C32×C5×C11×C17C211yesmaximal, characteristic, complemented
3C2×C3×D5×C11×C17—31nomaximal
4C2×C11×C17×D15C311yesmaximal, characteristic, direct product factor
5C32×C5×C11×C17C2211yescharacteristic, complemented, Hall
6C2×C3×D3×C11×C17—51nomaximal, Hall
7C11×C17×D15C2×C312yesdirect product factor
8C3×D5×C11×C17—32no—
9C2×C3×C5×C11×C17—21no—
10C2×C3×C5×C11×C17D311yescharacteristic, complemented
11C2×C3×C5×C11×C17C2×C311yescharacteristic, complemented
12C2×D5×C11×C17—31noHall
13C3×D3×C11×C17—52no—
14C2×C32×C11×C17D511yescharacteristic, complemented
15C2×C3×C17×D15C1111yesmaximal, characteristic, direct product factor, Hall
16C3×C5×C11×C17—21no—
17C3×C5×C11×C17C2×D311yescharacteristic, complemented
18C3×C5×C11×C17C22×C311yescharacteristic, complemented
19C2×D3×C11×C17—51no—
20C22×C3×C11×C17—151no—
21C2×C3×C11×D15C1711yesmaximal, characteristic, direct product factor, Hall
22C2×C5×C11×C17C3×D311yescharacteristic, complemented
23D5×C11×C17—32no—
24C32×C11×C17C2×D511yescharacteristic, complemented, Hall
25C2×C32×C5×C17C2×C1111yescharacteristic, complemented
26C3×C17×D15C2×C1112yesdirect product factor
27C2×C3×C11×C17—21no—
28C2×C3×C11×C17—152no—
29C2×C3×C11×C17C3×D511yescharacteristic, complemented
30C2×C3×C11×C17D1511yescharacteristic, direct product factor
31D3×C11×C17—52no—
32C2×C17×D15C3×C1111yescharacteristic, direct product factor
33C2×C3×D5×C17—31no—
34C2×C32×C5×C11C2×C1711yescharacteristic, complemented
35C3×C11×D15C2×C1712yesdirect product factor
36C5×C11×C17C2×C3×D311yescharacteristic, complemented, Hall
37C32×C5×C17C22×C1111yescharacteristic, complemented, Hall
38C22×C11×C17—151noHall
39C2×C11×D15C3×C1711yescharacteristic, direct product factor
40C2×C3×D5×C11—31no—
41C2×C3×D3×C17—51noHall
42C3×C11×C17—21no—
43C3×C11×C17C2×C3×D511yescharacteristic, complemented
44C3×C11×C17C2×D1511yescharacteristic, direct product factor
45C2×C3×C5×C17—21no—
46C2×C3×C5×C17D3×C1111yescharacteristic, complemented
47C2×C3×C5×C17C2×C3×C1111yescharacteristic, complemented
48C17×D15C2×C3×C1112yesdirect product factor
49C3×D5×C17—32no—
50C32×C5×C11C22×C1711yescharacteristic, complemented, Hall
51C2×C3×D3×C11—51noHall
52C2×C11×C17—152no—
53C2×C11×C17C3×D1511yescharacteristic, direct product factor
54C2×D5×C17—31noHall
55C2×C3×C5×C11—21no—
56C2×C3×C5×C11D3×C1711yescharacteristic, complemented
57C2×C3×C5×C11C2×C3×C1711yescharacteristic, complemented
58C11×D15C2×C3×C1712yesdirect product factor
59C3×D5×C11—32no—
60C2×C32×C17D5×C1111yescharacteristic, complemented
61C3×D3×C17—52no—
62C3×C5×C17—21no—
63C3×C5×C17C2×D3×C1111yescharacteristic, complemented
64C3×C5×C17C22×C3×C1111yescharacteristic, complemented
65C2×D5×C11—31noHall
66C22×C3×C17—151no—
67C2×D3×C17—51no—
68C2×C32×C11D5×C1711yescharacteristic, complemented
69C3×D3×C11—52no—
70C11×C17C2×C3×D1511yescharacteristic, direct product factor, Hall
71C2×C3×D15C11×C1711yescharacteristic, direct product factor, Hall
72C2×C5×C17C3×D3×C1111yescharacteristic, complemented
73D5×C17—32no—
74C3×C5×C11—21no—
75C3×C5×C11C2×D3×C1711yescharacteristic, complemented
76C3×C5×C11C22×C3×C1711yescharacteristic, complemented
77C32×C17C2×D5×C1111yescharacteristic, complemented, Hall
78C22×C3×C11—151no—
79C2×D3×C11—51no—
80C2×C5×C11C3×D3×C1711yescharacteristic, complemented
81D5×C11—32no—
82C2×C3×C17—21no—
83C2×C3×C17—152no—
84C2×C3×C17C3×D5×C1111yescharacteristic, complemented
85C2×C3×C17C11×D1511yescharacteristic, direct product factor
86D3×C17—52no—
87C32×C11C2×D5×C1711yescharacteristic, complemented, Hall
88C2×C32×C5C2×C11×C1711yescharacteristic, complemented
89C3×D15C2×C11×C1712yesdirect product factor
90C5×C17C2×C3×D3×C1111yescharacteristic, complemented, Hall
91C22×C17—151noHall
92C2×C3×C11—21no—
93C2×C3×C11—152no—
94C2×C3×C11C3×D5×C1711yescharacteristic, complemented
95C2×C3×C11C17×D1511yescharacteristic, direct product factor
96D3×C11—52no—
97C2×D15C3×C11×C1711yescharacteristic, direct product factor
98C2×C3×D5—31no—
99C5×C11C2×C3×D3×C1711yescharacteristic, complemented, Hall
100C3×C17—21no—
101C3×C17C2×C3×D5×C1111yescharacteristic, complemented
102C3×C17C2×C11×D1511yescharacteristic, direct product factor
103C32×C5C22×C11×C1711yescharacteristic, complemented, Hall
104C22×C11—151noHall
105C2×C3×D3—51noHall
106C2×C17—152no—
107C2×C17C3×C11×D1511yescharacteristic, direct product factor
108C3×C11—21no—
109C3×C11C2×C3×D5×C1711yescharacteristic, complemented
110C3×C11C2×C17×D1511yescharacteristic, direct product factor
111C2×C3×C5—21no—
112C2×C3×C5D3×C11×C1711yescharacteristic, complemented
113C2×C3×C5C2×C3×C11×C1711yescharacteristic, complemented
114D15C2×C3×C11×C1712yesdirect product factor
115C3×D5—32no—
116C2×C11—152no—
117C2×C11C3×C17×D1511yescharacteristic, direct product factor
118C2×D5—31noHall
119C2×C32D5×C11×C1711yescharacteristic, complemented
120C3×D3—52no—
121C17C2×C3×C11×D1511yescharacteristic, direct product factor, Sylow
122C3×C5—21no—
123C3×C5C22×C3×C11×C1711yescharacteristic, complemented
124C3×C5C2×D3×C11×C1711yescharacteristic, complemented
125C22×C3—151no—
126C2×D3—51no—
127C11C2×C3×C17×D1511yescharacteristic, direct product factor, Sylow
128C2×C5C3×D3×C11×C1711yescharacteristic, complemented
129D5—32no—
130C32C2×D5×C11×C1711yescharacteristic, complemented, Sylow
131C2×C3—21no—
132C2×C3—152no—
133C2×C3C3×D5×C11×C1711yescharacteristic, complemented
134C2×C3C11×C17×D1511yescharacteristic, direct product factor
135D3—52no—
136C5C2×C3×D3×C11×C1711yescharacteristic, complemented, Sylow
137C22—151noSylow
138C3—21no—
139C3C2×C11×C17×D1511yescharacteristic, direct product factor
140C3C2×C3×D5×C11×C1711yescharacteristic, complemented
141C2—152no—
142C2C3×C11×C17×D1511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C11×C17D15
commutator, cosocle, hypocenterC3×C5C22×C3×C11×C17
FrattiniC1G
Fitting, socleC2×C32×C5×C11×C17C2
LCSG ▷ C3×C5
UCSC1 ◁ C2×C3×C11×C17

Complements

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

NH ≅ G/Ntype
1. C3×C11×C17×D15C2direct (N × H)
2. C2×C32×C5×C11×C17C2semidirect
4. C2×C11×C17×D15C3direct (N × H)
5. C32×C5×C11×C17C22semidirect
7. C11×C17×D15C2×C3direct (N × H)
10. C2×C3×C5×C11×C17D3semidirect
11. C2×C3×C5×C11×C17C2×C3semidirect
14. C2×C32×C11×C17D5semidirect
15. C2×C3×C17×D15C11direct (N × H)
17. C3×C5×C11×C17C2×D3semidirect
18. C3×C5×C11×C17C22×C3semidirect
21. C2×C3×C11×D15C17direct (N × H)
22. C2×C5×C11×C17C3×D3semidirect
24. C32×C11×C17C2×D5semidirect
25. C2×C32×C5×C17C2×C11semidirect
26. C3×C17×D15C2×C11direct (N × H)
29. C2×C3×C11×C17C3×D5semidirect
30. C2×C3×C11×C17D15direct (N × H)
32. C2×C17×D15C3×C11direct (N × H)
34. C2×C32×C5×C11C2×C17semidirect
35. C3×C11×D15C2×C17direct (N × H)
36. C5×C11×C17C2×C3×D3semidirect
37. C32×C5×C17C22×C11semidirect
39. C2×C11×D15C3×C17direct (N × H)
43. C3×C11×C17C2×C3×D5semidirect
44. C3×C11×C17C2×D15direct (N × H)
46. C2×C3×C5×C17D3×C11semidirect
47. C2×C3×C5×C17C2×C3×C11semidirect
48. C17×D15C2×C3×C11direct (N × H)
50. C32×C5×C11C22×C17semidirect
53. C2×C11×C17C3×D15direct (N × H)
56. C2×C3×C5×C11D3×C17semidirect
57. C2×C3×C5×C11C2×C3×C17semidirect
58. C11×D15C2×C3×C17direct (N × H)
60. C2×C32×C17D5×C11semidirect
63. C3×C5×C17C2×D3×C11semidirect
64. C3×C5×C17C22×C3×C11semidirect
68. C2×C32×C11D5×C17semidirect
70. C11×C17C2×C3×D15direct (N × H)
71. C2×C3×D15C11×C17direct (N × H)
72. C2×C5×C17C3×D3×C11semidirect
75. C3×C5×C11C2×D3×C17semidirect
76. C3×C5×C11C22×C3×C17semidirect
77. C32×C17C2×D5×C11semidirect
80. C2×C5×C11C3×D3×C17semidirect
84. C2×C3×C17C3×D5×C11semidirect
85. C2×C3×C17C11×D15direct (N × H)
87. C32×C11C2×D5×C17semidirect
88. C2×C32×C5C2×C11×C17semidirect
89. C3×D15C2×C11×C17direct (N × H)
90. C5×C17C2×C3×D3×C11semidirect
94. C2×C3×C11C3×D5×C17semidirect
95. C2×C3×C11C17×D15direct (N × H)
97. C2×D15C3×C11×C17direct (N × H)
99. C5×C11C2×C3×D3×C17semidirect
101. C3×C17C2×C3×D5×C11semidirect
102. C3×C17C2×C11×D15direct (N × H)
103. C32×C5C22×C11×C17semidirect
107. C2×C17C3×C11×D15direct (N × H)
109. C3×C11C2×C3×D5×C17semidirect
110. C3×C11C2×C17×D15direct (N × H)
112. C2×C3×C5D3×C11×C17semidirect
113. C2×C3×C5C2×C3×C11×C17semidirect
114. D15C2×C3×C11×C17direct (N × H)
117. C2×C11C3×C17×D15direct (N × H)
119. C2×C32D5×C11×C17semidirect
121. C17C2×C3×C11×D15direct (N × H)
123. C3×C5C22×C3×C11×C17semidirect
124. C3×C5C2×D3×C11×C17semidirect
127. C11C2×C3×C17×D15direct (N × H)
128. C2×C5C3×D3×C11×C17semidirect
130. C32C2×D5×C11×C17semidirect
133. C2×C3C3×D5×C11×C17semidirect
134. C2×C3C11×C17×D15direct (N × H)
136. C5C2×C3×D3×C11×C17semidirect
139. C3C2×C11×C17×D15direct (N × H)
140. C3C2×C3×D5×C11×C17semidirect
142. C2C3×C11×C17×D15direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C11×C17×D152
C2×C32×C5×C11×C172
C2×C3×D5×C11×C173
C2×C11×C17×D153
C2×C3×D3×C11×C175
C2×C3×C17×D1511
C2×C3×C11×D1517