Finite Group Databasebeta

← #46778151

Subgroups — #46778151

Order 33660.

176 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 43 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×D165C211yesmaximal, characteristic, complemented
2C3×D2805C211yesmaximal, characteristic, complemented
3C5×C11×C3⋊D51C211yesmaximal, characteristic, complemented
4D51⋊D55—31nomaximal
5D51×D55—31nomaximal
6C32×C5×C11×C17C2211yescharacteristic, complemented, Hall
7D33⋊D51—51nomaximal, Hall
8D2805D311yescharacteristic, complemented
9C17×D165D311yescharacteristic, complemented
10C5×C11×D51—31no—
11C5×C11×D51—31no—
12C5×C11×D51—61no—
13C3×D935—31no—
14C3×C17×D55—31no—
15D17×D55—91noHall
16C11×C3⋊D51D511yescharacteristic, complemented
17C3×D561—51no—
18C3×C17×D33—51no—
19D15⋊D51—111nomaximal, Hall
20C3×C5×C11×C17—21no—
21C3×C5×C11×C17C2×D311yescharacteristic, complemented
22C3×C5×C11×C17C2×D311yescharacteristic, complemented
23D33⋊D17—151no—
24D11×D51—151no—
25(C3⋊D3)⋊D55—171nomaximal, Hall
26D935—31no—
27C17×D55—31no—
28C5×C11×D17—91no—
29C32×C11×C17C2×D511yescharacteristic, complemented, Hall
30C5×C3⋊D51D1111yescharacteristic, complemented
31C3×D255—111no—
32C3×C17×D15—111no—
33D561—51no—
34C17×D33—51no—
35C11×D51—31no—
36C11×D51—31no—
37C11×D51—61no—
38C3×D187—151no—
39C3×C17×D11—151no—
40D15⋊D17—331no—
41D5×D51—331no—
42C5×C11×C3⋊D3—171no—
43C3×D165—171no—
44C3×D165D1711yescharacteristic, complemented
45C5×C11×C17D3211yescharacteristic, complemented, Hall
46C32×C5×C17C2×D1111yescharacteristic, complemented, Hall
47D11×D17—451noHall
48D3×D55—511no—
49D3×D55—511no—
50D3×D51—551noHall
51C3×C11×C17—21no—
52C3×C11×C17D3×D511yescharacteristic, complemented
53C3×C11×C17D3×D511yescharacteristic, complemented
54D255—111no—
55C17×D15—111no—
56C5×D51—31no—
57C5×D51—31no—
58C5×D51—61no—
59C3×D85—331no—
60C3×D5×C17—331no—
61C32×C5×C11C2×D1711yescharacteristic, complemented, Hall
62(C3⋊D3)⋊D11—851noHall
63D187—151no—
64C11×D17—91no—
65C17×D11—151no—
66D5×D17—991noHall
67D165—171no—
68D165D5111yescharacteristic, complemented
69C5×D3×C11—511no—
70C5×D3×C11—511no—
71C5×D3×C11—1021no—
72C3×D55—31no—
73C3×D55—511no—
74C3⋊D51D5511yescharacteristic, complemented
75C3×D51—551no—
76C3×D3×C17—551no—
77C3×C5×C17—21no—
78C3×C5×C17D3×D1111yescharacteristic, complemented
79C3×C5×C17D3×D1111yescharacteristic, complemented
80C2×D55—1531noHall
81C2×D51—1651no—
82D3×D17—1651no—
83C11×C3⋊D3—171no—
84C3×D33—51no—
85C3×D33—851no—
86C11×C17(C3⋊D3)⋊D511yescharacteristic, complemented, Hall
87(C3⋊D3)⋊D5—1871noHall
88D85—331no—
89C5×D17—91no—
90D5×C17—331no—
91C3×C5×C11—21no—
92C3×C5×C11D3×D1711yescharacteristic, complemented
93C3×C5×C11C2×D5111yescharacteristic, complemented
94C32×C17C2×D5511yescharacteristic, complemented, Hall
95D3×D11—2551no—
96D3×D11—2551no—
97C2×C5×C11—1531no—
98D55—31no—
99D55—511no—
100C2×C3×C17—1651no—
101D51—31no—
102D51—31no—
103D51—61no—
104D51—551no—
105C3×D17—1651no—
106D3×C17—551no—
107C32×C11D5×D1711yescharacteristic, complemented, Hall
108C5×C3⋊D3—171no—
109C3×D15—111no—
110C3×D15—1871no—
111C5×C17(C3⋊D3)⋊D1111yescharacteristic, complemented, Hall
112C2×D17—4951noHall
113D33—51no—
114D33—851no—
115C3×D11—151no—
116C3×D11—2551no—
117D3×C11—511no—
118D3×C11—511no—
119D3×C11—1021no—
120D3×D5—5611no—
121D3×D5—5611no—
122C5×C11D3×D5111yescharacteristic, complemented, Hall
123C3×C17—21no—
124C3×C17D3×D5511yescharacteristic, complemented
125C3×C17D3×D5511yescharacteristic, complemented
126C32×C5D11×D1711yescharacteristic, complemented, Hall
127C2×D11—7651noHall
128D32—9351noHall
129C2×C17—1651no—
130D17—91no—
131D17—1651no—
132C3×C11—21no—
133C3×C11D5×D5111yescharacteristic, complemented
134C3×C11D15⋊D1711yescharacteristic, complemented
135D15—111no—
136D15—1871no—
137C3×D5—331no—
138C3×D5—5611no—
139C5×D3—511no—
140C5×D3—511no—
141C5×D3—1021no—
142C2×C11—1531no—
143D11—151no—
144D11—2551no—
145C2×D5—16831noHall
146C3⋊D3—171no—
147C3×D3—551no—
148C3×D3—9351no—
149C17(C3⋊D3)⋊D5511yescharacteristic, complemented, Sylow
150C3×C5—21no—
151C3×C5D11×D5111yescharacteristic, complemented
152C3×C5D33⋊D1711yescharacteristic, complemented
153C2×D3—28051no—
154C2×D3—28051no—
155C11D15⋊D5111yescharacteristic, complemented, Sylow
156C2×C5—1531no—
157D5—331no—
158D5—5611no—
159C32D17×D5511yescharacteristic, complemented, Sylow
160C2×C3—1651no—
161C2×C3—28051no—
162D3—511no—
163D3—511no—
164D3—551no—
165D3—1021no—
166D3—9351no—
167C5D33⋊D5111yescharacteristic, complemented, Sylow
168C22—84151noSylow
169C3—21no—
170C3D51×D5511yescharacteristic, complemented
171C3D51⋊D5511yescharacteristic, complemented
172C2—1531no—
173C2—1651no—
174C2—28051no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C11×C17C22
LCSG ▷ C32×C5×C11×C17
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C17×D165C2semidirect
2. C3×D2805C2semidirect
3. C5×C11×C3⋊D51C2semidirect
6. C32×C5×C11×C17C22semidirect
8. D2805D3semidirect
9. C17×D165D3semidirect
16. C11×C3⋊D51D5semidirect
21. C3×C5×C11×C17C2×D3semidirect
22. C3×C5×C11×C17C2×D3semidirect
29. C32×C11×C17C2×D5semidirect
30. C5×C3⋊D51D11semidirect
44. C3×D165D17semidirect
45. C5×C11×C17D32semidirect
46. C32×C5×C17C2×D11semidirect
52. C3×C11×C17D3×D5semidirect
53. C3×C11×C17D3×D5semidirect
61. C32×C5×C11C2×D17semidirect
68. D165D51semidirect
74. C3⋊D51D55semidirect
78. C3×C5×C17D3×D11semidirect
79. C3×C5×C17D3×D11semidirect
86. C11×C17(C3⋊D3)⋊D5semidirect
92. C3×C5×C11D3×D17semidirect
93. C3×C5×C11C2×D51semidirect
94. C32×C17C2×D55semidirect
107. C32×C11D5×D17semidirect
111. C5×C17(C3⋊D3)⋊D11semidirect
122. C5×C11D3×D51semidirect
124. C3×C17D3×D55semidirect
125. C3×C17D3×D55semidirect
126. C32×C5D11×D17semidirect
133. C3×C11D5×D51semidirect
134. C3×C11D15⋊D17semidirect
149. C17(C3⋊D3)⋊D55semidirect
151. C3×C5D11×D51semidirect
152. C3×C5D33⋊D17semidirect
155. C11D15⋊D51semidirect
159. C32D17×D55semidirect
167. C5D33⋊D51semidirect
170. C3D51×D55semidirect
171. C3D51⋊D55semidirect

Maximal subgroups

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

subgroupindex
C3×C17×D1652
C3×D28052
C5×C11×C3⋊D512
D51⋊D553
D51×D553
D33⋊D515
D15⋊D5111
(C3⋊D3)⋊D5517