Finite Group Databasebeta

← #44535358

Subgroups — #44535358

Order 31347.

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

normal subgroups only

This group has 980 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#23782921C313yesmaximal, complemented
2C32×#11923956C311yesmaximal, characteristic, complemented
3#23782907C314yesmaximal, complemented
4#23782903C316yesmaximal, complemented
5#23782902C312yesmaximal, complemented
6#23782900C316yesmaximal, complemented
7#23782894C312yesmaximal, complemented
8#23782890C311yesmaximal, characteristic, complemented
9#23782884C313yesmaximal, complemented
10#23782877C312yesmaximal, complemented
11#23782873C316yesmaximal, complemented
12AΣL(1,𝔽27)×C43⋊C3C313yesmaximal, complemented
13C43×#6908C311yesmaximal, characteristic, complemented
14C33×C43⋊C3C3211yescharacteristic
15#16812526—312no—
16#16812526C32112yescomplemented
17#16812525—36no—
18#16812525C3216yescomplemented
19#16812524C3216yescomplemented
20C3×#11923956—36no—
21C3×#11923956—33no—
22C3×#11923956—33no—
23C3×#11923956C3211yescharacteristic
24C3×#11923956C3211yescharacteristic
25C3×#11923956C3211yescharacteristic
26C3×#11923956C3212yescomplemented
27C3×#11923956C3212yescomplemented
28C3×#11923956C3212yescomplemented
293−1+2×C43⋊C3—36no—
303−1+2×C43⋊C3C3216yes—
31H(3,𝔽3)×C43⋊C3C3213yes—
32C32×C43⋊C9C3212yescomplemented
33#16812515C3214yescomplemented
34#16812514C32112yescomplemented
35#16812513C3212yescomplemented
36#16812512C3216yescomplemented
37#16812511C32112yescomplemented
38#16812510C3216yescomplemented
39#16812509C3216yescomplemented
40#16812508C32112yescomplemented
41#16812507C3216yescomplemented
42#16812506C3216yescomplemented
43C43×#737C3213yescomplemented
44C32×C9×C43C3211yescharacteristic, complemented
45C43×#733C3212yescomplemented
46C43×#732C3211yescharacteristic, complemented
47C43×#731C3213yescomplemented
48C43×AΣL(1,𝔽27)C3213yescomplemented
49C32×C43⋊C3—33no—
50C32×C43⋊C3—33no—
51C32×C43⋊C3—93no—
52C32×C43⋊C3C3312yes—
53C32×C43⋊C3C3311yescharacteristic
54#11923958—312no—
55#11923958C33112yes—
56#11923957—36no—
57#11923957—36no—
58#11923957—312no—
59#11923956—36no—
60#11923956—33no—
61#11923956—33no—
62#11923956—32no—
63#11923956—34no—
64#11923956—36no—
65#11923956—36no—
66#11923956—36no—
67#11923956—312no—
68#11923956H(3,𝔽3)16yes—
69#11923956H(3,𝔽3)13yes—
70C32⋊(C43⋊C3)—36no—
71C32⋊(C43⋊C3)C3316yes—
72C3×C43⋊C9—36no—
73C3×C43⋊C9—36no—
74C3×C43⋊C9C3312yes—
75C3×C43⋊C9C3312yes—
76C3×C43⋊C9C3312yes—
77C9×C43⋊C3—36no—
78C9×C43⋊C3—36no—
79C9×C43⋊C3—312no—
80C33×C43C3311yescharacteristic
813−1+2×C43—36no—
823−1+2×C43C3316yes—
83H(3,𝔽3)×C43C3313yes—
84C3×C9×C43—31no—
85C3×C9×C43—32no—
86C3×C9×C43—33no—
87C3×C9×C43C3311yescharacteristic
88C3×C9×C43C3311yescharacteristic
89C3×C9×C43C3311yescharacteristic
90#10624934—431nomaximal, Sylow
91C32×C43—31no—
92C32×C43—33no—
93C32×C43—33no—
94C32×C43C3411yescharacteristic
95C3×C43⋊C3—36no—
96C3×C43⋊C3—32no—
97C3×C43⋊C3—91no—
98C3×C43⋊C3—99no—
99C3×C43⋊C3—92no—
100C3×C43⋊C3—273no—
101C3×C43⋊C3C3×H(3,𝔽3)13yes—
102C9×C43—31no—
103C9×C43—31no—
104C9×C43—36no—
105C9×C43C3×H(3,𝔽3)11yescharacteristic
106C9×C43C3×H(3,𝔽3)12yes—
107C43⋊C9—312no—
108C43⋊C9—32no—
109C43⋊C9—32no—
110C43⋊C9C3×H(3,𝔽3)16yes—
1113−1+4—433no—
112C32×3−1+2—431no—
113#6913—436no—
114#6913—434no—
115#6913—432no—
116#6913—436no—
117#6912—432no—
118#6911—431no—
119#6910—433no—
120#6908—432no—
121#6908—436no—
122#6908C43⋊C311yescharacteristic, complemented
123C3×AΣL(1,𝔽27)—433no—
124C3×C43—33no—
125C3×C43—31no—
126C3×C43—93no—
127C3×C43C32×H(3,𝔽3)11yescharacteristic
128C43⋊C3—33no—
129C43⋊C3—92no—
130C43⋊C3—96no—
131C34—431no—
132#737—4312no—
133#737—436no—
134#737—436no—
135#737—1296no—
136#737—12912no—
137#737C3×C43⋊C313yescomplemented
138C3×3−1+2—431no—
139C3×3−1+2—432no—
140C3×3−1+2—432no—
141C3×3−1+2—431no—
142C3×3−1+2—431no—
143C3×3−1+2—432no—
144C3×3−1+2—436no—
145C3×3−1+2—1293no—
146C3×3−1+2—1296no—
147C3×3−1+2—1293no—
148C3×3−1+2—1296no—
149C3×H(3,𝔽3)—433no—
150C32×C9—432no—
151C32×C9C3×C43⋊C311yescharacteristic, complemented
152#733—4312no—
153#733—434no—
154#733C3×C43⋊C312yescomplemented
155#732—436no—
156#732—432no—
157#732C3×C43⋊C311yescharacteristic, complemented
158#731—4312no—
159#731—436no—
160#731—436no—
161#731C3×C43⋊C313yescomplemented
162AΣL(1,𝔽27)—436no—
163AΣL(1,𝔽27)—4312no—
164AΣL(1,𝔽27)—436no—
165AΣL(1,𝔽27)C3×C43⋊C313yescomplemented
166C43#1062493411yescharacteristic, complemented, Sylow
167C33—431no—
168C33—432no—
169C33—1293no—
170C33—1293no—
171C33—3873no—
172C33C32×C43⋊C311yescharacteristic
1733−1+2—36no—
1743−1+2—433no—
1753−1+2—436no—
1763−1+2—4312no—
1773−1+2—1296no—
1783−1+2—1296no—
1793−1+2—12912no—
1803−1+2—12912no—
1813−1+2—1293no—
1823−1+2—1293no—
1833−1+2—1296no—
1843−1+2—1296no—
1853−1+2—12912no—
1863−1+2—1292no—
1873−1+2—1294no—
1883−1+2—1296no—
1893−1+2—1296no—
1903−1+2C32×C43⋊C316yes—
191H(3,𝔽3)—436no—
192H(3,𝔽3)—1296no—
193H(3,𝔽3)C32×C43⋊C313yes—
194C3×C9—31no—
195C3×C9—32no—
196C3×C9—33no—
197C3×C9—432no—
198C3×C9—432no—
199C3×C9—432no—
200C3×C9—12912no—
201C3×C9—1296no—
202C3×C9—1296no—
203C3×C9—1296no—
204C3×C9—1296no—
205C3×C9C32×C43⋊C311yescharacteristic
206C3×C9C32×C43⋊C311yescharacteristic
207C3×C9C32×C43⋊C311yescharacteristic
208C32—33no—
209C32—31no—
210C32—33no—
211C32—433no—
212C32—1296no—
213C32—1292no—
214C32—3871no—
215C32—3879no—
216C32—3872no—
217C32—11613no—
218C32C33×C43⋊C311yescharacteristic
219C9—31no—
220C9—31no—
221C9—36no—
222C9—436no—
223C9—1292no—
224C9—1292no—
225C9—12912no—
226C9H(3,𝔽3)×C43⋊C311yescharacteristic
227C9H(3,𝔽3)×C43⋊C312yes—
228C3—33no—
229C3—31no—
230C3—93no—
231C3—1293no—
232C3—3872no—
233C3—3876no—
234C3C3×H(3,𝔽3)×C43⋊C311yescharacteristic
subgroupG/H
centerC3C3×H(3,𝔽3)×C43⋊C3
commutator, cosocleC32×C43C34
FrattiniC32C33×C43⋊C3
FittingC43×#6908C3
socleC3×C43C32×H(3,𝔽3)
hypercenter#6908C43⋊C3
hypocenterC43#10624934
LCSG ▷ C32×C43 ▷ C3×C43 ▷ C43
UCSC1 ◁ C3 ◁ C3×C9 ◁ #6908

Complements

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

NH ≅ G/Ntype
1. #23782921C3semidirect
2. C32×#11923956C3semidirect
3. #23782907C3semidirect
4. #23782903C3semidirect
5. #23782902C3semidirect
6. #23782900C3semidirect
7. #23782894C3semidirect
8. #23782890C3semidirect
9. #23782884C3semidirect
10. #23782877C3semidirect
11. #23782873C3semidirect
12. AΣL(1,𝔽27)×C43⋊C3C3semidirect
13. C43×#6908C3semidirect
16. #16812526C32semidirect
18. #16812525C32semidirect
19. #16812524C32semidirect
26. C3×#11923956C32semidirect
27. C3×#11923956C32semidirect
28. C3×#11923956C32semidirect
32. C32×C43⋊C9C32semidirect
33. #16812515C32semidirect
34. #16812514C32semidirect
35. #16812513C32semidirect
36. #16812512C32semidirect
37. #16812511C32semidirect
38. #16812510C32semidirect
39. #16812509C32semidirect
40. #16812508C32semidirect
41. #16812507C32semidirect
42. #16812506C32semidirect
43. C43×#737C32semidirect
44. C32×C9×C43C32semidirect
45. C43×#733C32semidirect
46. C43×#732C32semidirect
47. C43×#731C32semidirect
48. C43×AΣL(1,𝔽27)C32semidirect
122. #6908C43⋊C3semidirect
137. #737C3×C43⋊C3semidirect
151. C32×C9C3×C43⋊C3semidirect
154. #733C3×C43⋊C3semidirect
157. #732C3×C43⋊C3semidirect
161. #731C3×C43⋊C3semidirect
165. AΣL(1,𝔽27)C3×C43⋊C3semidirect
166. C43#10624934semidirect

Maximal subgroups

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

subgroupindex
#237829213
C32×#119239563
#237829073
#237829033
#237829023
#237829003
#237828943
#237828903
#237828843
#237828773
#237828733
AΣL(1,𝔽27)×C43⋊C33
C43×#69083
#1062493443