Finite Group Databasebeta

← C2×C3×C11×D255 #46778206

Subgroups — C2×C3×C11×D255 #46778206

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×C11×D255C212yesmaximal, direct product factor
2C2×C32×C5×C11×C17C211yesmaximal, characteristic, complemented
3C2×C3×C11×D85—31nomaximal
4C2×C11×D255C311yesmaximal, characteristic, direct product factor
5C32×C5×C11×C17C2211yescharacteristic, complemented, Hall
6C2×C3×C11×D51—51nomaximal, Hall
7C11×D255C2×C312yesdirect product factor
8C3×C11×D85—32no—
9C2×C3×C5×C11×C17—21no—
10C2×C3×C5×C11×C17D311yescharacteristic, complemented
11C2×C3×C5×C11×C17C2×C311yescharacteristic, complemented
12C2×C11×D85—31noHall
13C3×C11×D51—52no—
14C2×C32×C11×C17D511yescharacteristic, complemented
15C2×C3×D255C1111yesmaximal, characteristic, direct product factor, Hall
16C3×C5×C11×C17—21no—
17C3×C5×C11×C17C2×D311yescharacteristic, complemented
18C3×C5×C11×C17C22×C311yescharacteristic, complemented
19C2×C3×C11×D17—151no—
20C2×C11×D51—51no—
21C2×C3×C11×D15—171nomaximal, Hall
22C2×C5×C11×C17C3×D311yescharacteristic, complemented
23C11×D85—32no—
24C32×C11×C17C2×D511yescharacteristic, complemented, Hall
25C2×C32×C5×C17C2×C1111yescharacteristic, complemented
26C3×D255C2×C1112yesdirect product factor
27C2×C3×C11×C17—21no—
28C2×C3×C11×C17C3×D511yescharacteristic, complemented
29C2×C3×C11×C17D1511yescharacteristic, complemented
30C11×D51—52no—
31C3×C11×D17—152no—
32C2×D255C3×C1111yescharacteristic, direct product factor
33C2×C3×D85—31no—
34C2×C32×C5×C11D1711yescharacteristic, complemented
35C3×C11×D15—172no—
36C5×C11×C17C2×C3×D311yescharacteristic, complemented, Hall
37C32×C5×C17C22×C1111yescharacteristic, complemented, Hall
38C2×C11×D17—151noHall
39C2×C11×D15—171no—
40C2×C3×D5×C11—511no—
41C2×C3×D51—51noHall
42C3×C11×C17—21no—
43C3×C11×C17C2×C3×D511yescharacteristic, complemented
44C3×C11×C17C2×D1511yescharacteristic, complemented
45C2×C3×C5×C17—21no—
46C2×C3×C5×C17D3×C1111yescharacteristic, complemented
47C2×C3×C5×C17C2×C3×C1111yescharacteristic, complemented
48D255C2×C3×C1112yesdirect product factor
49C3×D85—32no—
50C32×C5×C11C2×D1711yescharacteristic, complemented, Hall
51C2×C3×D3×C11—851noHall
52C2×C11×C17C3×D1511yescharacteristic, complemented
53C11×D17—152no—
54C2×D85—31noHall
55C2×C3×C5×C11—21no—
56C2×C3×C5×C11C3×D1711yescharacteristic, complemented
57C2×C3×C5×C11D5111yescharacteristic, complemented
58C11×D15—172no—
59C3×D5×C11—512no—
60C2×C32×C17D5×C1111yescharacteristic, complemented
61C3×D51—52no—
62C3×C5×C17—21no—
63C3×C5×C17C2×D3×C1111yescharacteristic, complemented
64C3×C5×C17C22×C3×C1111yescharacteristic, complemented
65C2×D5×C11—511noHall
66C2×D51—51no—
67C2×C3×D17—151no—
68C2×C32×C11D8511yescharacteristic, complemented
69C3×D3×C11—852no—
70C11×C17C2×C3×D1511yescharacteristic, complemented, Hall
71C2×C3×D15—171noHall
72C2×C5×C17C3×D3×C1111yescharacteristic, complemented
73D85—32no—
74C3×C5×C11—21no—
75C3×C5×C11C2×C3×D1711yescharacteristic, complemented
76C3×C5×C11C2×D5111yescharacteristic, complemented
77C32×C17C2×D5×C1111yescharacteristic, complemented, Hall
78C22×C3×C11—2551no—
79C2×D3×C11—851no—
80C2×C5×C11C3×D5111yescharacteristic, complemented
81D5×C11—512no—
82C2×C3×C17—21no—
83C2×C3×C17C3×D5×C1111yescharacteristic, complemented
84C2×C3×C17C11×D1511yescharacteristic, complemented
85D51—52no—
86C3×D17—152no—
87C32×C11C2×D8511yescharacteristic, complemented, Hall
88C2×C32×C5C11×D1711yescharacteristic, complemented
89C3×D15—172no—
90C5×C17C2×C3×D3×C1111yescharacteristic, complemented, Hall
91C2×D17—151noHall
92C2×C3×C11—21no—
93C2×C3×C11—2552no—
94C2×C3×C11C3×D8511yescharacteristic, complemented
95C2×C3×C11D25511yescharacteristic, direct product factor
96D3×C11—852no—
97C2×D15—171no—
98C2×C3×D5—511no—
99C5×C11C2×C3×D5111yescharacteristic, complemented, Hall
100C3×C17—21no—
101C3×C17C2×C3×D5×C1111yescharacteristic, complemented
102C3×C17C2×C11×D1511yescharacteristic, complemented
103C32×C5C2×C11×D1711yescharacteristic, complemented, Hall
104C22×C11—2551noHall
105C2×C3×D3—851noHall
106C2×C17C3×C11×D1511yescharacteristic, complemented
107D17—152no—
108C3×C11—21no—
109C3×C11C2×C3×D8511yescharacteristic, complemented
110C3×C11C2×D25511yescharacteristic, direct product factor
111C2×C3×C5—21no—
112C2×C3×C5C3×C11×D1711yescharacteristic, complemented
113C2×C3×C5C11×D5111yescharacteristic, complemented
114D15—172no—
115C3×D5—512no—
116C2×C11—2552no—
117C2×C11C3×D25511yescharacteristic, direct product factor
118C2×D5—511noHall
119C2×C32C11×D8511yescharacteristic, complemented
120C3×D3—852no—
121C17C2×C3×C11×D1511yescharacteristic, complemented, Sylow
122C3×C5—21no—
123C3×C5C2×C11×D5111yescharacteristic, complemented
124C3×C5C2×C3×C11×D1711yescharacteristic, complemented
125C22×C3—2551no—
126C2×D3—851no—
127C11C2×C3×D25511yescharacteristic, direct product factor, Sylow
128C2×C5C3×C11×D5111yescharacteristic, complemented
129D5—512no—
130C32C2×C11×D8511yescharacteristic, complemented, Sylow
131C2×C3—21no—
132C2×C3—2552no—
133C2×C3C3×C11×D8511yescharacteristic, complemented
134C2×C3C11×D25511yescharacteristic, direct product factor
135D3—852no—
136C5C2×C3×C11×D5111yescharacteristic, complemented, Sylow
137C22—2551noSylow
138C3—21no—
139C3C2×C11×D25511yescharacteristic, direct product factor
140C3C2×C3×C11×D8511yescharacteristic, complemented
141C2—2552no—
142C2C3×C11×D25511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C11D255
commutator, cosocle, hypocenterC3×C5×C17C22×C3×C11
FrattiniC1G
Fitting, socleC2×C32×C5×C11×C17C2
LCSG ▷ C3×C5×C17
UCSC1 ◁ C2×C3×C11

Complements

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

NH ≅ G/Ntype
1. C3×C11×D255C2direct (N × H)
2. C2×C32×C5×C11×C17C2semidirect
4. C2×C11×D255C3direct (N × H)
5. C32×C5×C11×C17C22semidirect
7. C11×D255C2×C3direct (N × H)
10. C2×C3×C5×C11×C17D3semidirect
11. C2×C3×C5×C11×C17C2×C3semidirect
14. C2×C32×C11×C17D5semidirect
15. C2×C3×D255C11direct (N × H)
17. C3×C5×C11×C17C2×D3semidirect
18. C3×C5×C11×C17C22×C3semidirect
22. C2×C5×C11×C17C3×D3semidirect
24. C32×C11×C17C2×D5semidirect
25. C2×C32×C5×C17C2×C11semidirect
26. C3×D255C2×C11direct (N × H)
28. C2×C3×C11×C17C3×D5semidirect
29. C2×C3×C11×C17D15semidirect
32. C2×D255C3×C11direct (N × H)
34. C2×C32×C5×C11D17semidirect
36. C5×C11×C17C2×C3×D3semidirect
37. C32×C5×C17C22×C11semidirect
43. C3×C11×C17C2×C3×D5semidirect
44. C3×C11×C17C2×D15semidirect
46. C2×C3×C5×C17D3×C11semidirect
47. C2×C3×C5×C17C2×C3×C11semidirect
48. D255C2×C3×C11direct (N × H)
50. C32×C5×C11C2×D17semidirect
52. C2×C11×C17C3×D15semidirect
56. C2×C3×C5×C11C3×D17semidirect
57. C2×C3×C5×C11D51semidirect
60. C2×C32×C17D5×C11semidirect
63. C3×C5×C17C2×D3×C11semidirect
64. C3×C5×C17C22×C3×C11semidirect
68. C2×C32×C11D85semidirect
70. C11×C17C2×C3×D15semidirect
72. C2×C5×C17C3×D3×C11semidirect
75. C3×C5×C11C2×C3×D17semidirect
76. C3×C5×C11C2×D51semidirect
77. C32×C17C2×D5×C11semidirect
80. C2×C5×C11C3×D51semidirect
83. C2×C3×C17C3×D5×C11semidirect
84. C2×C3×C17C11×D15semidirect
87. C32×C11C2×D85semidirect
88. C2×C32×C5C11×D17semidirect
90. C5×C17C2×C3×D3×C11semidirect
94. C2×C3×C11C3×D85semidirect
95. C2×C3×C11D255direct (N × H)
99. C5×C11C2×C3×D51semidirect
101. C3×C17C2×C3×D5×C11semidirect
102. C3×C17C2×C11×D15semidirect
103. C32×C5C2×C11×D17semidirect
106. C2×C17C3×C11×D15semidirect
109. C3×C11C2×C3×D85semidirect
110. C3×C11C2×D255direct (N × H)
112. C2×C3×C5C3×C11×D17semidirect
113. C2×C3×C5C11×D51semidirect
117. C2×C11C3×D255direct (N × H)
119. C2×C32C11×D85semidirect
121. C17C2×C3×C11×D15semidirect
123. C3×C5C2×C11×D51semidirect
124. C3×C5C2×C3×C11×D17semidirect
127. C11C2×C3×D255direct (N × H)
128. C2×C5C3×C11×D51semidirect
130. C32C2×C11×D85semidirect
133. C2×C3C3×C11×D85semidirect
134. C2×C3C11×D255direct (N × H)
136. C5C2×C3×C11×D51semidirect
139. C3C2×C11×D255direct (N × H)
140. C3C2×C3×C11×D85semidirect
142. C2C3×C11×D255direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C11×D2552
C2×C32×C5×C11×C172
C2×C3×C11×D853
C2×C11×D2553
C2×C3×C11×D515
C2×C3×D25511
C2×C3×C11×D1517