Finite Group Databasebeta

← #28356061

Subgroups — #28356061

Order 13851.

926 conjugacy classes of subgroups; only the 274 normal subgroups are shown.

normal subgroups only

This group has 926 conjugacy classes of subgroups — too many to draw. Only its 274 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×H(3,𝔽3)×C19⋊C3C311yesmaximal, characteristic
2#17987428C312yesmaximal, complemented
3#17987427C312yesmaximal, complemented
4#17987426C311yesmaximal, characteristic, complemented
5#17987425C311yesmaximal, characteristic, complemented
6#17987424C316yesmaximal, complemented
7#17987424C316yesmaximal, complemented
8#17987423C312yesmaximal, complemented
9#17987422C316yesmaximal, complemented
10#17987420C313yesmaximal, complemented
11#17987419C313yesmaximal, complemented
12#17987418C313yesmaximal, complemented
13C3×#13095303C311yesmaximal, characteristic, complemented
14C19⋊C3×C32⋊C9C312yesmaximal, complemented
15C19×C9⋊H(3,𝔽3)C311yesmaximal, characteristic, complemented
16C33×C19⋊C3C3213yes—
17C33×C19⋊C3C3211yescharacteristic
18C3×#10587025C3216yescomplemented
19C3×#10587022C3216yescomplemented
20C3×#10587022C3213yescomplemented
21C3×#10587023C3216yescomplemented
22C3×#10587023C3213yescomplemented
23C3×C32⋊(C19⋊C3)C3216yes—
24C3×C32⋊(C19⋊C3)C3211yescharacteristic
25C3×C32⋊(C19⋊C3)C3211yescharacteristic
26H(3,𝔽3)×C19⋊C3—39no—
27C32×#4294C3212yescomplemented
28C3×C9×C19⋊C3C3216yescomplemented
29C32⋊#4294C3212yescomplemented
30C32⋊#4294C3212yescomplemented
31C32⋊#4294C3216yescomplemented
32C32⋊#4294C3216yescomplemented
33#13095303C3216yes—
34#13095303C3211yescharacteristic
35#13095303C3211yescharacteristic
36#13095303C3211yescharacteristic
37#13095303C3216yescomplemented
38#13095303C3212yescomplemented
39#13095303C3212yescomplemented
40#13095303C3212yescomplemented
41#13095303C3213yescomplemented
42#13095303C3213yescomplemented
43#13095303C3216yescomplemented
44#13095303C3216yescomplemented
45#13095303C3216yescomplemented
46#13095303C3213yescomplemented
47#13095303C3216yescomplemented
48#13095303C3213yescomplemented
49C3×C19×3−1+2C3213yescomplemented
50C3×C19×H(3,𝔽3)C3211yescharacteristic
51C32×C9×C19C3211yescharacteristic, complemented
52C19×C32⋊C9C3212yescomplemented
53C19×C32⋊C9C3213yescomplemented
54C19×C32⋊C9C3213yescomplemented
55#10624883—191nomaximal, Sylow
56C33×C19C3313yes—
57C33×C19C3311yescharacteristic
58C32×C19⋊C3—39no—
59C32×C19⋊C3—91no—
60C32×C19⋊C3—93no—
61C32×C19⋊C3—91no—
62C32×C19⋊C3—91no—
63C32×C19⋊C3—93no—
64C32×C19⋊C3—93no—
65C32×C19⋊C33−1+219yescomplemented
66C32×C19⋊C3C3313yes—
67C32×C19⋊C3C3313yes—
68C32×C19⋊C3C3311yescharacteristic
69C32×C19⋊C3C3312yes—
70C19×3−1+2—93no—
71C19×H(3,𝔽3)—33no—
72C3×C9×C19—91no—
73C3×C9×C19C3311yescharacteristic
74C3×C9×C19C3311yescharacteristic
75C3×C9×C19C3316yes—
76C3×C9×C19C3311yescharacteristic
77C32⋊(C19⋊C3)—33no—
78C32⋊(C19⋊C3)—33no—
79C32⋊(C19⋊C3)—318no—
80#10587025—96no—
81C3×#4294—92no—
82C3×#4294C3312yes—
83C3×#4294C3316yes—
84C3×#4294C3316yes—
85C3×#4294C3312yes—
86C3×#4294C3312yes—
87#10587023—93no—
88#10587023—96no—
89#10587022—93no—
90#10587022—96no—
91C9×C19⋊C3—96no—
92C32×H(3,𝔽3)—191no—
93C9⋊H(3,𝔽3)—196no—
94C9⋊H(3,𝔽3)—192no—
95C9⋊H(3,𝔽3)—191no—
96C9⋊H(3,𝔽3)—191no—
97C9⋊H(3,𝔽3)—196no—
98C9⋊H(3,𝔽3)—196no—
99C9⋊H(3,𝔽3)—192no—
100C9⋊H(3,𝔽3)—192no—
101C9⋊H(3,𝔽3)C19⋊C311yescharacteristic, complemented
102#6891—193no—
103#6891—193no—
104#6891—193no—
105C3×C32⋊C9—191no—
106C3×C32⋊C9—192no—
107C32×C19—31no—
108C32×C19—31no—
109C32×C19—31no—
110C32×C19—33no—
111C32×C19—33no—
112C32×C19—33no—
113C32×C19—33no—
114C32×C19C3×3−1+213yes—
115C32×C19C3411yescharacteristic
116C3×C19⋊C3—32no—
117C3×C19⋊C3—31no—
118C3×C19⋊C3—31no—
119C3×C19⋊C3—31no—
120C3×C19⋊C3—32no—
121C3×C19⋊C3—32no—
122C3×C19⋊C3—33no—
123C3×C19⋊C3—33no—
124C3×C19⋊C3—33no—
125C3×C19⋊C3—33no—
126C3×C19⋊C3—33no—
127C3×C19⋊C3—33no—
128C3×C19⋊C3—33no—
129C3×C19⋊C3—33no—
130C3×C19⋊C3—99no—
131C3×C19⋊C3—927no—
132C3×C19⋊C3C3×3−1+216yes—
133C3×C19⋊C3C3×3−1+213yes—
134C9×C19—36no—
135C9×C19—31no—
136C9×C19—31no—
137C9×C19—31no—
138#4294—36no—
139#4294—36no—
140#4294—32no—
141#4294—32no—
142#4294—32no—
143C34—191no—
144C34—193no—
145C3×3−1+2—196no—
146C3×3−1+2—196no—
147C3×3−1+2—193no—
148C3×3−1+2—196no—
149C3×3−1+2—193no—
150C3×3−1+2C3×C19⋊C313yescomplemented
151C3×H(3,𝔽3)—196no—
152C3×H(3,𝔽3)—191no—
153C3×H(3,𝔽3)—191no—
154C3×H(3,𝔽3)—579no—
155C3×H(3,𝔽3)C3×C19⋊C311yescharacteristic
156C32×C9—192no—
157C32×C9—196no—
158C32×C9C3×C19⋊C311yescharacteristic, complemented
159C32⋊C9—192no—
160C32⋊C9—192no—
161C32⋊C9—196no—
162C32⋊C9—196no—
163C32⋊C9—191no—
164C32⋊C9—196no—
165C32⋊C9—191no—
166C32⋊C9—191no—
167C32⋊C9—192no—
168C32⋊C9—196no—
169C32⋊C9—192no—
170C32⋊C9—192no—
171C32⋊C9—193no—
172C32⋊C9—193no—
173C32⋊C9—196no—
174C32⋊C9—196no—
175C32⋊C9—196no—
176C32⋊C9—196no—
177C32⋊C9—193no—
178C32⋊C9—193no—
179C32⋊C9C3×C19⋊C312yescomplemented
180C32⋊C9C3×C19⋊C313yescomplemented
181C32⋊C9C3×C19⋊C313yescomplemented
182C3×C19—33no—
183C3×C19—93no—
184C3×C19C32×3−1+211yescharacteristic
185C3×C19H(5,𝔽3)11yescharacteristic
186C3×C193−1+411yescharacteristic
187C3×C193−1+411yescharacteristic
188C19⋊C3—33no—
189C19⋊C3—36no—
190C19⋊C3—93no—
191C19⋊C3—93no—
192C33—191no—
193C33—192no—
194C33—199no—
195C33—193no—
196C33—193no—
197C33—579no—
198C33—1711no—
199C33—1711no—
200C33—1711no—
201C33—1713no—
202C33—1713no—
203C33—1713no—
204C33C32×C19⋊C313yes—
205C33C32×C19⋊C311yescharacteristic
2063−1+2—93no—
2073−1+2—1713no—
2083−1+2—1716no—
2093−1+2—1713no—
2103−1+2—1716no—
2113−1+2—1716no—
212H(3,𝔽3)—33no—
213H(3,𝔽3)—5718no—
214H(3,𝔽3)—573no—
215H(3,𝔽3)—573no—
216C3×C9—91no—
217C3×C9—192no—
218C3×C9—196no—
219C3×C9—196no—
220C3×C9—192no—
221C3×C9—192no—
222C3×C9—1716no—
223C3×C9—1712no—
224C3×C9C32×C19⋊C311yescharacteristic
225C3×C9C32×C19⋊C316yes—
226C3×C9C32×C19⋊C311yescharacteristic
227C3×C9C32×C19⋊C311yescharacteristic
228C19#1062488311yescharacteristic, complemented, Sylow
229C32—31no—
230C32—31no—
231C32—31no—
232C32—33no—
233C32—33no—
234C32—33no—
235C32—33no—
236C32—196no—
237C32—193no—
238C32—572no—
239C32—571no—
240C32—571no—
241C32—572no—
242C32—571no—
243C32—572no—
244C32—573no—
245C32—573no—
246C32—573no—
247C32—573no—
248C32—573no—
249C32—573no—
250C32—573no—
251C32—573no—
252C32—1719no—
253C32—17127no—
254C323−1+2×C19⋊C313yes—
255C32C33×C19⋊C311yescharacteristic
256C9—31no—
257C9—31no—
258C9—31no—
259C9—36no—
260C9—576no—
261C9—576no—
262C9—572no—
263C9—572no—
264C9—572no—
265C3—33no—
266C3—93no—
267C3—573no—
268C3—576no—
269C3—1713no—
270C3—1713no—
271C3C3×3−1+2×C19⋊C311yescharacteristic
272C3C19⋊H(5,𝔽3)11yescharacteristic
273C3#1798754411yescharacteristic
274C3#1798754511yescharacteristic
subgroupG/H
center, FrattiniC32C33×C19⋊C3
commutator, socle, cosocleC32×C19C34
FittingC19×C9⋊H(3,𝔽3)C3
prime radicalC3×H(3,𝔽3)×C19⋊C3C3
hypercenterC9⋊H(3,𝔽3)C19⋊C3
hypocenterC19#10624883
LCSG ▷ C32×C19 ▷ C19
UCSC1 ◁ C32 ◁ C9⋊H(3,𝔽3)

Complements

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

NH ≅ G/Ntype
2. #17987428C3semidirect
3. #17987427C3semidirect
4. #17987426C3semidirect
5. #17987425C3semidirect
6. #17987424C3semidirect
7. #17987424C3semidirect
8. #17987423C3semidirect
9. #17987422C3semidirect
10. #17987420C3semidirect
11. #17987419C3semidirect
12. #17987418C3semidirect
13. C3×#13095303C3semidirect
14. C19⋊C3×C32⋊C9C3semidirect
15. C19×C9⋊H(3,𝔽3)C3semidirect
18. C3×#10587025C32semidirect
19. C3×#10587022C32semidirect
20. C3×#10587022C32semidirect
21. C3×#10587023C32semidirect
22. C3×#10587023C32semidirect
27. C32×#4294C32semidirect
28. C3×C9×C19⋊C3C32semidirect
29. C32⋊#4294C32semidirect
30. C32⋊#4294C32semidirect
31. C32⋊#4294C32semidirect
32. C32⋊#4294C32semidirect
37. #13095303C32semidirect
38. #13095303C32semidirect
39. #13095303C32semidirect
40. #13095303C32semidirect
41. #13095303C32semidirect
42. #13095303C32semidirect
43. #13095303C32semidirect
44. #13095303C32semidirect
45. #13095303C32semidirect
46. #13095303C32semidirect
47. #13095303C32semidirect
48. #13095303C32semidirect
49. C3×C19×3−1+2C32semidirect
51. C32×C9×C19C32semidirect
52. C19×C32⋊C9C32semidirect
53. C19×C32⋊C9C32semidirect
54. C19×C32⋊C9C32semidirect
65. C32×C19⋊C33−1+2semidirect
101. C9⋊H(3,𝔽3)C19⋊C3semidirect
150. C3×3−1+2C3×C19⋊C3semidirect
158. C32×C9C3×C19⋊C3semidirect
179. C32⋊C9C3×C19⋊C3semidirect
180. C32⋊C9C3×C19⋊C3semidirect
181. C32⋊C9C3×C19⋊C3semidirect
228. C19#10624883semidirect

Maximal subgroups

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

subgroupindex
C3×H(3,𝔽3)×C19⋊C33
#179874283
#179874273
#179874263
#179874253
#179874243
#179874233
#179874223
#179874203
#179874193
#179874183
C3×#130953033
C19⋊C3×C32⋊C93
C19×C9⋊H(3,𝔽3)3
#1062488319