Finite Group Databasebeta

← #45692717

Subgroups — #45692717

Order 33516.

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

normal subgroups only

This group has 230 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×C7×D399C211yesmaximal, characteristic, complemented
2C3×C3⋊(C7⋊D133)C211yesmaximal, characteristic, complemented
3C7×C19×C3⋊D21C211yesmaximal, characteristic, complemented
4D21⋊D133—31nomaximal
5D21×D133—31nomaximal
6C32×C72×C19C2211yescharacteristic, complemented, Hall
7C3⋊(C7⋊D133)D311yescharacteristic, complemented
8C7×D399D311yescharacteristic, complemented
9C7×C19×D21—31no—
10C7×C19×D21—31no—
11C7×C19×D21—61no—
12C3×C7⋊D133—31no—
13C3×C7×D133—31no—
14(C3⋊D3)⋊D133—71nomaximal
15D57⋊D21—71nomaximal
16D7×D133—91noHall
17C3×C72×C19—21no—
18C3×C72×C19C2×D311yescharacteristic, complemented
19C3×C72×C19C2×D311yescharacteristic, complemented
20C19×C3⋊D21D711yescharacteristic, complemented
21C7×C3⋊D3×C19—71no—
22C3×D399—71no—
23C3×D399—71no—
24C3×D399—143no—
25C3×D399D711yescharacteristic, complemented
26C3×C7×D57—71no—
27C7⋊D133—31no—
28C7×D133—31no—
29C7×D7×C19—91no—
30D21⋊D21—191nomaximal, Hall
31D21⋊D19—211no—
32D3×D133—211no—
33D3×D133—211no—
34D19×D21—211no—
35C32×C7×C19—23no—
36C32×C7×C19C2×D711yescharacteristic, complemented
37C32×C7×C19C2×D711yescharacteristic, complemented
38C72×C19D3211yescharacteristic, complemented, Hall
39C7×C3⋊D21D1911yescharacteristic, complemented
40C3×C3⋊(C7⋊D7)—191no—
41C3×C7×D21—191no—
42D399—71no—
43D399—71no—
44D399—143no—
45D399D2111yescharacteristic, complemented
46C19×D21—31no—
47C19×D21—31no—
48C19×D21—61no—
49C7×D57—71no—
50D3×C7×C19—211no—
51D3×C7×C19—211no—
52D3×C7×C19—421no—
53C3×D133—31no—
54C3×D133—211no—
55C3×D133—211no—
56C3×D133—423no—
57C3×C7×D19—211no—
58(C3⋊D3)⋊D19—491noHall
59D21⋊D7—571no—
60D7×D21—571no—
61C2×D133—631no—
62D7×D19—631no—
63C32×C72C2×D1911yescharacteristic, complemented, Hall
64C3×C7×C19—23no—
65C3×C7×C19—23no—
66C3×C7×C19—21no—
67C3×C7×C19—21no—
68C3×C7×C19—43no—
69C3×C7×C19D3×D711yescharacteristic, complemented
70C3×C7×C19D3×D711yescharacteristic, complemented
71C3×C7×C19D3×D711yescharacteristic, complemented
72C3×C7×C19C2×D2111yescharacteristic, complemented
73C3⋊D3×C19—71no—
74C3×D57—71no—
75C3×D57—491no—
76C3⋊(C7⋊D7)—191no—
77C7×D21—31no—
78C7×D21—31no—
79C7×D21—61no—
80C7×D21—191no—
81C3×C7⋊D7—571no—
82C3×C7×D7—571no—
83C2×C7×C19—631no—
84D133—31no—
85D133—211no—
86D133—211no—
87D133—423no—
88C7×D19—211no—
89D7×C19—91no—
90(C3⋊D3)⋊D7—1331no—
91D3×D21—1331no—
92D3×D19—1471no—
93D3×D19—1471no—
94D72—1711noHall
95C32×C19D7211yescharacteristic, complemented, Hall
96C3×C72—21no—
97C3×C72D3×D1911yescharacteristic, complemented
98C3×C72D3×D1911yescharacteristic, complemented
99C7×C19—23no—
100C7×C19D3×D2111yescharacteristic, complemented
101C7×C19(C3⋊D3)⋊D711yescharacteristic, complemented
102C3⋊D21D13311yescharacteristic, complemented
103C7×C3⋊D3—71no—
104C3×D21—2663no—
105C3×D21—191no—
106C3×D21—1331no—
107C3×D21—1331no—
108C3×D3×C7—1331no—
109D57—71no—
110D57—491no—
111C3×D19—211no—
112C3×D19—1471no—
113D3×C19—211no—
114D3×C19—211no—
115D3×C19—421no—
116C7⋊D7—571no—
117C7×D7—91no—
118C7×D7—571no—
119C2×D21—3991no—
120D3×D7—3991no—
121D3×D7—3991no—
122D3×D7—3991no—
123C2×D19—4411noHall
124C32×C7—23no—
125C32×C7D7×D1911yescharacteristic, complemented
126C32×C7C2×D13311yescharacteristic, complemented
127C3×C19—21no—
128C3×C19D7×D2111yescharacteristic, complemented
129C3×C19D21⋊D711yescharacteristic, complemented
130C72(C3⋊D3)⋊D1911yescharacteristic, complemented, Sylow
131C2×C3×C7—3991no—
132D21—31no—
133D21—31no—
134D21—61no—
135D21—2663no—
136D21—191no—
137D21—1331no—
138D21—1331no—
139C3×D7—7983no—
140C3×D7—571no—
141C3×D7—3991no—
142C3×D7—3991no—
143D3×C7—211no—
144D3×C7—211no—
145D3×C7—421no—
146D3×C7—1331no—
147C2×C19—631no—
148D19—211no—
149D19—1471no—
150D32—9311noHall
151C2×D7—11971no—
152C2×D7—11971no—
153C3×C7—21no—
154C3×C7—21no—
155C3×C7—23no—
156C3×C7—23no—
157C3×C7—43no—
158C3×C7D19×D2111yescharacteristic, complemented
159C3×C7D3×D13311yescharacteristic, complemented
160C3×C7D3×D13311yescharacteristic, complemented
161C3×C7D21⋊D1911yescharacteristic, complemented
162C19D21⋊D2111yescharacteristic, complemented, Sylow
163C3⋊D3—71no—
164C3×D3—1331no—
165C3×D3—9311no—
166C2×C7—631no—
167C2×C7—3991no—
168D7—91no—
169D7—7983no—
170D7—571no—
171D7—3991no—
172D7—3991no—
173C2×D3—27931no—
174C2×D3—27931no—
175C32D7×D13311yescharacteristic, complemented, Sylow
176C7—23no—
177C7D57⋊D2111yescharacteristic, complemented
178C7(C3⋊D3)⋊D13311yescharacteristic, complemented
179C2×C3—3991no—
180C2×C3—27931no—
181D3—211no—
182D3—211no—
183D3—421no—
184D3—1331no—
185D3—9311no—
186C22—83791noSylow
187C3—21no—
188C3D21×D13311yescharacteristic, complemented
189C3D21⋊D13311yescharacteristic, complemented
190C2—631no—
191C2—3991no—
192C2—27931no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C72×C19C22
LCSG ▷ C32×C72×C19
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C7×D399C2semidirect
2. C3×C3⋊(C7⋊D133)C2semidirect
3. C7×C19×C3⋊D21C2semidirect
6. C32×C72×C19C22semidirect
7. C3⋊(C7⋊D133)D3semidirect
8. C7×D399D3semidirect
18. C3×C72×C19C2×D3semidirect
19. C3×C72×C19C2×D3semidirect
20. C19×C3⋊D21D7semidirect
25. C3×D399D7semidirect
36. C32×C7×C19C2×D7semidirect
37. C32×C7×C19C2×D7semidirect
38. C72×C19D32semidirect
39. C7×C3⋊D21D19semidirect
45. D399D21semidirect
63. C32×C72C2×D19semidirect
69. C3×C7×C19D3×D7semidirect
70. C3×C7×C19D3×D7semidirect
71. C3×C7×C19D3×D7semidirect
72. C3×C7×C19C2×D21semidirect
95. C32×C19D72semidirect
97. C3×C72D3×D19semidirect
98. C3×C72D3×D19semidirect
100. C7×C19D3×D21semidirect
101. C7×C19(C3⋊D3)⋊D7semidirect
102. C3⋊D21D133semidirect
125. C32×C7D7×D19semidirect
126. C32×C7C2×D133semidirect
128. C3×C19D7×D21semidirect
129. C3×C19D21⋊D7semidirect
130. C72(C3⋊D3)⋊D19semidirect
158. C3×C7D19×D21semidirect
159. C3×C7D3×D133semidirect
160. C3×C7D3×D133semidirect
161. C3×C7D21⋊D19semidirect
162. C19D21⋊D21semidirect
175. C32D7×D133semidirect
177. C7D57⋊D21semidirect
178. C7(C3⋊D3)⋊D133semidirect
188. C3D21×D133semidirect
189. C3D21⋊D133semidirect

Maximal subgroups

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

subgroupindex
C3×C7×D3992
C3×C3⋊(C7⋊D133)2
C7×C19×C3⋊D212
D21⋊D1333
D21×D1333
(C3⋊D3)⋊D1337
D57⋊D217
D21⋊D2119