Finite Group Databasebeta

← #44535378

Subgroups — #44535378

Order 31347.

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#23782921C313yesmaximal, complemented
2C3×#16812525C311yesmaximal, characteristic, complemented
3#23782904C316yesmaximal, complemented
4#23782900C316yesmaximal, complemented
5#23782897C316yesmaximal, complemented
6#23782885C313yesmaximal, complemented
7#23782879C313yesmaximal, complemented
8#23782878C314yesmaximal, complemented
9#23782877C312yesmaximal, complemented
10#23782875C312yesmaximal, complemented
11#733×C43⋊C3C312yesmaximal, complemented
12#732×C43⋊C3C311yesmaximal, characteristic, complemented
13C43×#6908C311yesmaximal, characteristic, complemented
14#16812526—312no—
15#16812526C32112yescomplemented
16#16812525—32no—
17#16812525—31no—
18#16812525—32no—
19#16812525—34no—
20#16812525—36no—
21#16812525C3216yescomplemented
22#16812524C3216yescomplemented
23C3×#11923958C3212yescomplemented
24C3×#11923957C3211yescharacteristic
25C3×#11923957C3212yescomplemented
26C3×#11923956—33no—
27C3×#11923956C3211yescharacteristic
28C3×#11923956C3212yescomplemented
293−1+2×C43⋊C3—36no—
303−1+2×C43⋊C3C3216yes—
31C3×C32⋊(C43⋊C3)C3211yescharacteristic
32H(3,𝔽3)×C43⋊C3C3213yes—
33C3×C9×C43⋊C3C3211yescharacteristic
34C3×C9×C43⋊C3C3212yescomplemented
35#16812515C3214yescomplemented
36#16812514C32112yescomplemented
37#16812513C3212yes—
38#16812512C3216yes—
39#16812511C32112yescomplemented
40#16812510C3216yescomplemented
41#16812509C3216yescomplemented
42#16812508C32112yescomplemented
43#16812507C3216yescomplemented
44#16812506C3216yescomplemented
45C43×#737C3213yescomplemented
46C32×C9×C43C3211yescharacteristic, complemented
47C43×#733C3212yescomplemented
48C43×#732C3211yescharacteristic
49C43×#731C3213yescomplemented
50C43×AΣL(1,𝔽27)C3213yescomplemented
51C32×C43⋊C3—33no—
52C32×C43⋊C3C3312yes—
53C32×C43⋊C3C3311yescharacteristic
54#11923958—312no—
55#11923958—34no—
56#11923958—32no—
57#11923958C33112yes—
58#11923957—36no—
59#11923957—32no—
60#11923957—31no—
61#11923957—36no—
62#11923957—312no—
63#11923957—34no—
64#11923957—32no—
65#11923956—36no—
66#11923956—36no—
67#11923956—32no—
68#11923956—34no—
69#11923956—312no—
70#11923956H(3,𝔽3)12yes—
71#11923956H(3,𝔽3)11yescharacteristic
72#11923956H(3,𝔽3)12yes—
73#11923956H(3,𝔽3)14yes—
74C32⋊(C43⋊C3)—36no—
75C32⋊(C43⋊C3)—32no—
76C32⋊(C43⋊C3)—31no—
77C32⋊(C43⋊C3)C3316yes—
78C3×C43⋊C9—36no—
79C3×C43⋊C9C3312yes—
80C3×C43⋊C9C3312yes—
81C3×C43⋊C9C3312yes—
82C9×C43⋊C3—32no—
83C9×C43⋊C3—31no—
84C9×C43⋊C3—36no—
85C9×C43⋊C3—36no—
86C9×C43⋊C3—34no—
87C9×C43⋊C3—32no—
88C9×C43⋊C3—312no—
89C33×C43C3311yescharacteristic
903−1+2×C43—36no—
913−1+2×C43C3316yes—
92H(3,𝔽3)×C43C3313yes—
93C3×C9×C43—31no—
94C3×C9×C43—32no—
95C3×C9×C43—33no—
96C3×C9×C43C3311yescharacteristic
97C3×C9×C43C3311yescharacteristic
98C3×C9×C43C3311yescharacteristic
99#10624936—431nomaximal, Sylow
100C32×C43—31no—
101C32×C43—33no—
102C32×C43—91no—
103C32×C43C3411yescharacteristic
104C3×C43⋊C3—32no—
105C3×C43⋊C3—36no—
106C3×C43⋊C3—91no—
107C3×C43⋊C3—92no—
108C3×C43⋊C3—273no—
109C3×C43⋊C3C3×H(3,𝔽3)12yes—
110C3×C43⋊C3C3×H(3,𝔽3)11yescharacteristic
111C9×C43—31no—
112C9×C43—31no—
113C9×C43—36no—
114C9×C43C3×H(3,𝔽3)11yescharacteristic
115C9×C43C3×H(3,𝔽3)12yes—
116C43⋊C9—312no—
117C43⋊C9—32no—
118C43⋊C9—32no—
119C43⋊C9C3×H(3,𝔽3)14yes—
120C43⋊C9C3×H(3,𝔽3)12yes—
1213−1+4—433no—
122C3×#737—431no—
123#6913—436no—
124#6913—436no—
125#6913—436no—
126#6910—433no—
127#6909—433no—
128#6908—432no—
129#6908—434no—
130#6908—432no—
131#6908C43⋊C311yescharacteristic, complemented
132C3×#733—432no—
133C3×#732—431no—
134C3×C43—31no—
135C3×C43—93no—
136C3×C43—91no—
137C3×C43C32×H(3,𝔽3)11yescharacteristic
138C43⋊C3—31no—
139C43⋊C3—32no—
140C43⋊C3—92no—
141C43⋊C3—96no—
142#737—4312no—
143#737—436no—
144#737—436no—
145#737—1291no—
146#737—1292no—
147#737—1292no—
148#737—1294no—
149#737—1296no—
150#737—12912no—
151#737C3×C43⋊C313yescomplemented
152C3×3−1+2—432no—
153C3×3−1+2—432no—
154C3×3−1+2—431no—
155C3×3−1+2—431no—
156C3×3−1+2—432no—
157C3×3−1+2—436no—
158C3×3−1+2—1293no—
159C3×3−1+2—1296no—
160C3×H(3,𝔽3)—433no—
161C3×H(3,𝔽3)—431no—
162C32×C9—431no—
163C32×C9—432no—
164C32×C9C3×C43⋊C311yescharacteristic, complemented
165#733—4312no—
166#733—434no—
167#733C3×C43⋊C312yescomplemented
168#732—436no—
169#732—432no—
170#732C3×C43⋊C311yescharacteristic
171#731—4312no—
172#731—436no—
173#731—436no—
174#731C3×C43⋊C313yescomplemented
175AΣL(1,𝔽27)—436no—
176AΣL(1,𝔽27)—4312no—
177AΣL(1,𝔽27)—436no—
178AΣL(1,𝔽27)C3×C43⋊C313yescomplemented
179C43#1062493611yescharacteristic, complemented, Sylow
180C33—431no—
181C33—432no—
182C33—1293no—
183C33C32×C43⋊C311yescharacteristic
1843−1+2—36no—
1853−1+2—431no—
1863−1+2—432no—
1873−1+2—432no—
1883−1+2—434no—
1893−1+2—4312no—
1903−1+2—1294no—
1913−1+2—1292no—
1923−1+2—12912no—
1933−1+2—12912no—
1943−1+2—1296no—
1953−1+2—1292no—
1963−1+2—1291no—
1973−1+2—1296no—
1983−1+2—1294no—
1993−1+2—1292no—
2003−1+2—12912no—
2013−1+2—1292no—
2023−1+2—1294no—
2033−1+2—1296no—
2043−1+2—1296no—
2053−1+2C32×C43⋊C316yes—
206H(3,𝔽3)—436no—
207H(3,𝔽3)—1292no—
208H(3,𝔽3)—1291no—
209H(3,𝔽3)—1296no—
210H(3,𝔽3)C32×C43⋊C313yes—
211C3×C9—31no—
212C3×C9—32no—
213C3×C9—33no—
214C3×C9—432no—
215C3×C9—432no—
216C3×C9—432no—
217C3×C9—1294no—
218C3×C9—1292no—
219C3×C9—12912no—
220C3×C9—1292no—
221C3×C9—1291no—
222C3×C9—1296no—
223C3×C9—1296no—
224C3×C9—1296no—
225C3×C9C32×C43⋊C311yescharacteristic
226C3×C9C32×C43⋊C311yescharacteristic
227C3×C9C32×C43⋊C311yescharacteristic
228C32—31no—
229C32—33no—
230C32—91no—
231C32—432no—
232C32—431no—
233C32—1296no—
234C32—1292no—
235C32—3871no—
236C32—3872no—
237C32—11613no—
238C32C33×C43⋊C311yescharacteristic
239C9—31no—
240C9—31no—
241C9—36no—
242C9—434no—
243C9—432no—
244C9—1292no—
245C9—1292no—
246C9—12912no—
247C9H(3,𝔽3)×C43⋊C311yescharacteristic
248C9H(3,𝔽3)×C43⋊C312yes—
249C3—31no—
250C3—91no—
251C3—93no—
252C3—1292no—
253C3—1291no—
254C3—3872no—
255C3—3876no—
256C3C3×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#10624936
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. C3×#16812525C3semidirect
3. #23782904C3semidirect
4. #23782900C3semidirect
5. #23782897C3semidirect
6. #23782885C3semidirect
7. #23782879C3semidirect
8. #23782878C3semidirect
9. #23782877C3semidirect
10. #23782875C3semidirect
11. #733×C43⋊C3C3semidirect
12. #732×C43⋊C3C3semidirect
13. C43×#6908C3semidirect
15. #16812526C32semidirect
21. #16812525C32semidirect
22. #16812524C32semidirect
23. C3×#11923958C32semidirect
25. C3×#11923957C32semidirect
28. C3×#11923956C32semidirect
34. C3×C9×C43⋊C3C32semidirect
35. #16812515C32semidirect
36. #16812514C32semidirect
39. #16812511C32semidirect
40. #16812510C32semidirect
41. #16812509C32semidirect
42. #16812508C32semidirect
43. #16812507C32semidirect
44. #16812506C32semidirect
45. C43×#737C32semidirect
46. C32×C9×C43C32semidirect
47. C43×#733C32semidirect
49. C43×#731C32semidirect
50. C43×AΣL(1,𝔽27)C32semidirect
131. #6908C43⋊C3semidirect
151. #737C3×C43⋊C3semidirect
164. C32×C9C3×C43⋊C3semidirect
167. #733C3×C43⋊C3semidirect
174. #731C3×C43⋊C3semidirect
178. AΣL(1,𝔽27)C3×C43⋊C3semidirect
179. C43#10624936semidirect

Maximal subgroups

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

subgroupindex
#237829213
C3×#168125253
#237829043
#237829003
#237828973
#237828853
#237828793
#237828783
#237828773
#237828753
#733×C43⋊C33
#732×C43⋊C33
C43×#69083
#1062493643