Finite Group Databasebeta

← #28356637

Subgroups — #28356637

Order 13851.

948 conjugacy classes of subgroups; only the 268 normal subgroups are shown.

normal subgroups only

This group has 948 conjugacy classes of subgroups — too many to draw. Only its 268 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
1#17987544C313yesmaximal, complemented
2C3×#13095332C311yesmaximal, characteristic, complemented
3#17987527C316yesmaximal, complemented
4#17987523C316yesmaximal, complemented
5#17987520C316yesmaximal, complemented
6#17987508C313yesmaximal, complemented
7#17987502C313yesmaximal, complemented
8#17987501C314yesmaximal, complemented
9#17987500C312yesmaximal, complemented
10#17987498C312yesmaximal, complemented
11C19⋊C3×#733C312yesmaximal, complemented
12C19⋊C3×#732C311yesmaximal, characteristic, complemented
13C19×#6908C311yesmaximal, characteristic, complemented
14#13095333—312no—
15#13095333C32112yescomplemented
16#13095332—32no—
17#13095332—31no—
18#13095332—32no—
19#13095332—34no—
20#13095332—36no—
21#13095332C3216yescomplemented
22#13095331C3216yescomplemented
23C3×#10587025C3212yescomplemented
24C3×#10587022C3211yescharacteristic
25C3×#10587022C3212yescomplemented
26C3×#10587023—33no—
27C3×#10587023C3211yescharacteristic
28C3×#10587023C3212yescomplemented
293−1+2×C19⋊C3—36no—
303−1+2×C19⋊C3C3216yes—
31C3×C32⋊(C19⋊C3)C3211yescharacteristic
32H(3,𝔽3)×C19⋊C3C3213yes—
33C3×C9×C19⋊C3C3211yescharacteristic
34C3×C9×C19⋊C3C3212yescomplemented
35#13095322C3214yescomplemented
36#13095321C32112yescomplemented
37#13095320C3212yes—
38#13095319C3216yes—
39#13095318C32112yescomplemented
40#13095317C3216yescomplemented
41#13095316C3216yescomplemented
42#13095315C32112yescomplemented
43#13095314C3216yescomplemented
44#13095313C3216yescomplemented
45C19×#737C3213yescomplemented
46C32×C9×C19C3211yescharacteristic, complemented
47C19×#733C3212yescomplemented
48C19×#732C3211yescharacteristic
49C19×#731C3213yescomplemented
50C19×AΣL(1,𝔽27)C3213yescomplemented
51#10624936—191nomaximal, Sylow
52C33×C19C3311yescharacteristic
53C32×C19⋊C3—33no—
54C32×C19⋊C3C3312yes—
55C32×C19⋊C3C3311yescharacteristic
56C19×3−1+2—36no—
57C19×3−1+2C3316yes—
58C19×H(3,𝔽3)C3313yes—
59C3×C9×C19—32no—
60C3×C9×C19—31no—
61C3×C9×C19—33no—
62C3×C9×C19C3311yescharacteristic
63C3×C9×C19C3311yescharacteristic
64C3×C9×C19C3311yescharacteristic
65C32⋊(C19⋊C3)—36no—
66C32⋊(C19⋊C3)—32no—
67C32⋊(C19⋊C3)—31no—
68C32⋊(C19⋊C3)C3316yes—
69#10587025—312no—
70#10587025—34no—
71#10587025—32no—
72#10587025C33112yes—
73C3×#4294—36no—
74C3×#4294C3312yes—
75C3×#4294C3312yes—
76C3×#4294C3312yes—
77#10587023—36no—
78#10587023—36no—
79#10587023—34no—
80#10587023—32no—
81#10587023—312no—
82#10587023H(3,𝔽3)12yes—
83#10587023H(3,𝔽3)11yescharacteristic
84#10587023H(3,𝔽3)12yes—
85#10587023H(3,𝔽3)14yes—
86#10587022—36no—
87#10587022—32no—
88#10587022—31no—
89#10587022—36no—
90#10587022—312no—
91#10587022—34no—
92#10587022—32no—
93C9×C19⋊C3—32no—
94C9×C19⋊C3—31no—
95C9×C19⋊C3—36no—
96C9×C19⋊C3—36no—
97C9×C19⋊C3—34no—
98C9×C19⋊C3—32no—
99C9×C19⋊C3—312no—
1003−1+4—193no—
101C3×#737—191no—
102#6913—196no—
103#6913—196no—
104#6913—196no—
105#6910—193no—
106#6909—193no—
107#6908—192no—
108#6908—194no—
109#6908—192no—
110#6908C19⋊C311yescharacteristic, complemented
111C3×#733—192no—
112C3×#732—191no—
113C32×C19—33no—
114C32×C19—31no—
115C32×C19—91no—
116C32×C19C3411yescharacteristic
117C3×C19⋊C3—32no—
118C3×C19⋊C3—36no—
119C3×C19⋊C3—91no—
120C3×C19⋊C3—92no—
121C3×C19⋊C3—273no—
122C3×C19⋊C3C3×H(3,𝔽3)12yes—
123C3×C19⋊C3C3×H(3,𝔽3)11yescharacteristic
124C9×C19—31no—
125C9×C19—36no—
126C9×C19—31no—
127C9×C19C3×H(3,𝔽3)12yes—
128C9×C19C3×H(3,𝔽3)11yescharacteristic
129#4294—312no—
130#4294—32no—
131#4294—32no—
132#4294C3×H(3,𝔽3)14yes—
133#4294C3×H(3,𝔽3)12yes—
134#737—1912no—
135#737—196no—
136#737—196no—
137#737—571no—
138#737—572no—
139#737—572no—
140#737—574no—
141#737—576no—
142#737—5712no—
143#737C3×C19⋊C313yescomplemented
144C3×3−1+2—192no—
145C3×3−1+2—192no—
146C3×3−1+2—191no—
147C3×3−1+2—191no—
148C3×3−1+2—192no—
149C3×3−1+2—196no—
150C3×3−1+2—573no—
151C3×3−1+2—576no—
152C3×H(3,𝔽3)—193no—
153C3×H(3,𝔽3)—191no—
154C32×C9—191no—
155C32×C9—192no—
156C32×C9C3×C19⋊C311yescharacteristic, complemented
157#733—1912no—
158#733—194no—
159#733C3×C19⋊C312yescomplemented
160#732—196no—
161#732—192no—
162#732C3×C19⋊C311yescharacteristic
163#731—1912no—
164#731—196no—
165#731—196no—
166#731C3×C19⋊C313yescomplemented
167AΣL(1,𝔽27)—196no—
168AΣL(1,𝔽27)—1912no—
169AΣL(1,𝔽27)—196no—
170AΣL(1,𝔽27)C3×C19⋊C313yescomplemented
171C3×C19—31no—
172C3×C19—93no—
173C3×C19—91no—
174C3×C19C32×H(3,𝔽3)11yescharacteristic
175C19⋊C3—31no—
176C19⋊C3—32no—
177C19⋊C3—92no—
178C19⋊C3—96no—
179C33—191no—
180C33—192no—
181C33—573no—
182C33C32×C19⋊C311yescharacteristic
1833−1+2—36no—
1843−1+2—191no—
1853−1+2—192no—
1863−1+2—192no—
1873−1+2—194no—
1883−1+2—1912no—
1893−1+2—574no—
1903−1+2—572no—
1913−1+2—5712no—
1923−1+2—5712no—
1933−1+2—572no—
1943−1+2—571no—
1953−1+2—576no—
1963−1+2—576no—
1973−1+2—574no—
1983−1+2—572no—
1993−1+2—5712no—
2003−1+2—576no—
2013−1+2—572no—
2023−1+2—574no—
2033−1+2—576no—
2043−1+2C32×C19⋊C316yes—
205H(3,𝔽3)—196no—
206H(3,𝔽3)—572no—
207H(3,𝔽3)—571no—
208H(3,𝔽3)—576no—
209H(3,𝔽3)C32×C19⋊C313yes—
210C3×C9—31no—
211C3×C9—32no—
212C3×C9—33no—
213C3×C9—192no—
214C3×C9—192no—
215C3×C9—192no—
216C3×C9—574no—
217C3×C9—572no—
218C3×C9—5712no—
219C3×C9—572no—
220C3×C9—571no—
221C3×C9—576no—
222C3×C9—576no—
223C3×C9—576no—
224C3×C9C32×C19⋊C311yescharacteristic
225C3×C9C32×C19⋊C311yescharacteristic
226C3×C9C32×C19⋊C311yescharacteristic
227C19#1062493611yescharacteristic, complemented, Sylow
228C32—5133no—
229C32—31no—
230C32—33no—
231C32—91no—
232C32—192no—
233C32—191no—
234C32—576no—
235C32—572no—
236C32—1711no—
237C32—1712no—
238C32C33×C19⋊C311yescharacteristic
239C9—31no—
240C9—31no—
241C9—36no—
242C9—194no—
243C9—192no—
244C9—572no—
245C9—572no—
246C9—5712no—
247C9H(3,𝔽3)×C19⋊C311yescharacteristic
248C9H(3,𝔽3)×C19⋊C312yes—
249C3—31no—
250C3—93no—
251C3—91no—
252C3—571no—
253C3—572no—
254C3—1716no—
255C3—1712no—
256C3C3×H(3,𝔽3)×C19⋊C311yescharacteristic
subgroupG/H
centerC3C3×H(3,𝔽3)×C19⋊C3
commutator, cosocleC32×C19C34
FrattiniC32C33×C19⋊C3
FittingC19×#6908C3
socleC3×C19C32×H(3,𝔽3)
hypercenter#6908C19⋊C3
hypocenterC19#10624936
LCSG ▷ C32×C19 ▷ C3×C19 ▷ C19
UCSC1 ◁ C3 ◁ C3×C9 ◁ #6908

Complements

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

NH ≅ G/Ntype
1. #17987544C3semidirect
2. C3×#13095332C3semidirect
3. #17987527C3semidirect
4. #17987523C3semidirect
5. #17987520C3semidirect
6. #17987508C3semidirect
7. #17987502C3semidirect
8. #17987501C3semidirect
9. #17987500C3semidirect
10. #17987498C3semidirect
11. C19⋊C3×#733C3semidirect
12. C19⋊C3×#732C3semidirect
13. C19×#6908C3semidirect
15. #13095333C32semidirect
21. #13095332C32semidirect
22. #13095331C32semidirect
23. C3×#10587025C32semidirect
25. C3×#10587022C32semidirect
28. C3×#10587023C32semidirect
34. C3×C9×C19⋊C3C32semidirect
35. #13095322C32semidirect
36. #13095321C32semidirect
39. #13095318C32semidirect
40. #13095317C32semidirect
41. #13095316C32semidirect
42. #13095315C32semidirect
43. #13095314C32semidirect
44. #13095313C32semidirect
45. C19×#737C32semidirect
46. C32×C9×C19C32semidirect
47. C19×#733C32semidirect
49. C19×#731C32semidirect
50. C19×AΣL(1,𝔽27)C32semidirect
110. #6908C19⋊C3semidirect
143. #737C3×C19⋊C3semidirect
156. C32×C9C3×C19⋊C3semidirect
159. #733C3×C19⋊C3semidirect
166. #731C3×C19⋊C3semidirect
170. AΣL(1,𝔽27)C3×C19⋊C3semidirect
227. C19#10624936semidirect

Maximal subgroups

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

subgroupindex
#179875443
C3×#130953323
#179875273
#179875233
#179875203
#179875083
#179875023
#179875013
#179875003
#179874983
C19⋊C3×#7333
C19⋊C3×#7323
C19×#69083
#1062493619