Finite Group Databasebeta

← D33×D273 #49114955

Subgroups — D33×D273 #49114955

Order 36036.

176 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 46 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×C7×C13×D33C211yesmaximal, characteristic, complemented
2C3×C11×D273C211yesmaximal, characteristic, complemented
3C3⋊D3003C211yesmaximal, characteristic, complemented
4D33×D91—31nomaximal
5D11×D273—31nomaximal
6C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
7D3003—31no—
8D3003—31no—
9D3003—61no—
10C11×D273D311yescharacteristic, complemented
11C7×C13×D33D311yescharacteristic, complemented
12C3×C11×D91—31no—
13C3×C7×C13×D11—31no—
14D33×D39—71nomaximal, Hall
15D11×D91—91noHall
16D3×D273—111nomaximal, Hall
17C3×C7×C11×C13—21no—
18C3×C7×C11×C13C2×D311yescharacteristic, complemented
19C3×C7×C11×C13C2×D311yescharacteristic, complemented
20D21×D33—131nomaximal, Hall
21C3⋊D429—71no—
22C3×C13×D33D711yescharacteristic, complemented
23C3×C11×D39—71no—
24D1001—91no—
25C11×D91—31no—
26C7×C13×D11—31no—
27D11×D39—211no—
28D13×D33—211no—
29C3⋊D273—111no—
30C3×D273D1111yescharacteristic, complemented
31C3×D3×C7×C13—111no—
32C3⋊D231—131no—
33C3×C11×D21—131no—
34C3×C7×D33D1311yescharacteristic, complemented
35C32×C11×C13C2×D711yescharacteristic, complemented, Hall
36C2×D273—331no—
37D3×D91—331no—
38C7×C11×C13D3211yescharacteristic, complemented, Hall
39D7×D33—391no—
40D11×D21—391no—
41D429—211no—
42D429—211no—
43D429—421no—
44C13×D33D2111yescharacteristic, complemented
45C11×D39—71no—
46C3×C13×D11—31no—
47C3×C11×D13—211no—
48C32×C7×C13C2×D1111yescharacteristic, complemented, Hall
49C32×C7×C11C2×D1311yescharacteristic, complemented, Hall
50D11×D13—631noHall
51C2×C3×C7×C13—331no—
52D273—331no—
53D273—331no—
54D273—661no—
55D273D3311yescharacteristic, direct product factor
56D3×C7×C13—111no—
57C3×D91—31no—
58D3×D39—771noHall
59D231—391no—
60D231—391no—
61D231—781no—
62C11×D21—131no—
63C7×D33D3911yescharacteristic, complemented
64C3×C11×D7—391no—
65C3×C7×D11—31no—
66C3×C11×C13—21no—
67C3×C11×C13D3×D711yescharacteristic, complemented
68C3×C11×C13C2×D2111yescharacteristic, complemented
69D3×D33—911noHall
70C2×D91—991noHall
71D7×D11—1171noHall
72D143—631no—
73C11×D13—211no—
74C13×D11—31no—
75C3×C7×C13—21no—
76C3×C7×C13D3×D1111yescharacteristic, complemented
77C3×C7×C13C2×D3311yescharacteristic, complemented
78D3×D21—1431noHall
79C3⋊D39—771no—
80C3×D39—71no—
81C3×D3×C13—111no—
82C3×C7×C11—21no—
83C3×C7×C11D3×D1311yescharacteristic, complemented
84C3×C7×C11C2×D3911yescharacteristic, complemented
85C3⋊D33—911no—
86C3×D33D9111yescharacteristic, complemented
87C3×D3×C11—911no—
88C2×C7×C13—331no—
89D91—31no—
90D91—991no—
91C2×D39—2311no—
92D3×D13—2311no—
93D77—1171no—
94C7×D11—31no—
95C11×D7—391no—
96C11×C13D3×D2111yescharacteristic, complemented, Hall
97C2×D33—2731no—
98D3×D11—2731no—
99C3⋊D21—1431no—
100C3×D21—131no—
101C3×D3×C7—111no—
102C32×C13D7×D1111yescharacteristic, complemented, Hall
103C32×C11C2×D9111yescharacteristic, complemented, Hall
104C7×C13D3×D3311yescharacteristic, complemented, Hall
105C2×D21—4291no—
106D3×D7—4291no—
107C2×C3×C13—331no—
108D39—71no—
109D39—4621no—
110D39—2311no—
111D39—2311no—
112C3×D13—211no—
113D3×C13—111no—
114C7×C11D3×D3911yescharacteristic, complemented, Hall
115C2×C3×C11—2731no—
116D33—2731no—
117D33—2731no—
118D33—5461no—
119D33D27311yescharacteristic, direct product factor
120C3×D11—31no—
121D3×C11—911no—
122C32×C7D11×D1311yescharacteristic, complemented, Hall
123C2×D13—6931noHall
124C2×D11—8191noHall
125C2×C3×C7—331no—
126D21—131no—
127D21—8581no—
128D21—4291no—
129D21—4291no—
130C3×D7—391no—
131D3×C7—111no—
132C3×C13—21no—
133C3×C13D11×D2111yescharacteristic, complemented
134C3×C13D7×D3311yescharacteristic, complemented
135D32—10011noHall
136C3×C11—21no—
137C3×C11D3×D9111yescharacteristic, complemented
138C3×C11C2×D27311yescharacteristic, complemented
139C2×D7—12871noHall
140C2×C13—331no—
141D13—211no—
142D13—6931no—
143C2×C11—2731no—
144D11—31no—
145D11—8191no—
146C3×C7—21no—
147C3×C7D13×D3311yescharacteristic, complemented
148C3×C7D11×D3911yescharacteristic, complemented
149C3⋊D3—10011no—
150C3×D3—111no—
151C3×D3—911no—
152C2×C7—331no—
153D7—12871no—
154D7—391no—
155C13D21×D3311yescharacteristic, complemented, Sylow
156C2×D3—30031no—
157C2×D3—30031no—
158C11D3×D27311yescharacteristic, complemented, Sylow
159C32D11×D9111yescharacteristic, complemented, Sylow
160C7D33×D3911yescharacteristic, complemented, Sylow
161C2×C3—2731no—
162C2×C3—331no—
163D3—111no—
164D3—911no—
165D3—60061no—
166D3—30031no—
167D3—30031no—
168C22—90091noSylow
169C3—21no—
170C3D11×D27311yescharacteristic, complemented
171C3D33×D9111yescharacteristic, complemented
172C2—2731no—
173C2—331no—
174C2—90091no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C7×C11×C13C22
LCSG ▷ C32×C7×C11×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C7×C13×D33C2semidirect
2. C3×C11×D273C2semidirect
3. C3⋊D3003C2semidirect
6. C32×C7×C11×C13C22semidirect
10. C11×D273D3semidirect
11. C7×C13×D33D3semidirect
18. C3×C7×C11×C13C2×D3semidirect
19. C3×C7×C11×C13C2×D3semidirect
22. C3×C13×D33D7semidirect
30. C3×D273D11semidirect
34. C3×C7×D33D13semidirect
35. C32×C11×C13C2×D7semidirect
38. C7×C11×C13D32semidirect
44. C13×D33D21semidirect
48. C32×C7×C13C2×D11semidirect
49. C32×C7×C11C2×D13semidirect
55. D273D33direct (N × H)
63. C7×D33D39semidirect
67. C3×C11×C13D3×D7semidirect
68. C3×C11×C13C2×D21semidirect
76. C3×C7×C13D3×D11semidirect
77. C3×C7×C13C2×D33semidirect
83. C3×C7×C11D3×D13semidirect
84. C3×C7×C11C2×D39semidirect
86. C3×D33D91semidirect
96. C11×C13D3×D21semidirect
102. C32×C13D7×D11semidirect
103. C32×C11C2×D91semidirect
104. C7×C13D3×D33semidirect
114. C7×C11D3×D39semidirect
119. D33D273direct (N × H)
122. C32×C7D11×D13semidirect
133. C3×C13D11×D21semidirect
134. C3×C13D7×D33semidirect
137. C3×C11D3×D91semidirect
138. C3×C11C2×D273semidirect
147. C3×C7D13×D33semidirect
148. C3×C7D11×D39semidirect
155. C13D21×D33semidirect
158. C11D3×D273semidirect
159. C32D11×D91semidirect
160. C7D33×D39semidirect
170. C3D11×D273semidirect
171. C3D33×D91semidirect

Maximal subgroups

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

subgroupindex
C3×C7×C13×D332
C3×C11×D2732
C3⋊D30032
D33×D913
D11×D2733
D33×D397
D3×D27311
D21×D3313