Finite Group Databasebeta

← #44535360

Subgroups — #44535360

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#23782924C311yesmaximal, characteristic, complemented
2#23782923C312yesmaximal, complemented
3C32×#11923958C311yesmaximal, characteristic, complemented
4#23782898C319yesmaximal, complemented
5#23782897C319yesmaximal, complemented
6#23782895C312yesmaximal, complemented
7#23782891C311yesmaximal, characteristic, complemented
8#23782888C312yesmaximal, complemented
9#23782886C311yesmaximal, characteristic, complemented
10#23782873C319yesmaximal, complemented
11C3×#16812507C312yesmaximal, complemented
12C3×C43×AΣL(1,𝔽27)C311yesmaximal, characteristic, complemented
13#16812526—36no—
14#16812526C32118yescomplemented
15#16812525—36no—
16#16812524—36no—
17#16812524C3219yescomplemented
18C3×#11923958—36no—
19C3×#11923958—33no—
20C3×#11923958—33no—
21C3×#11923958C3212yes—
22C3×#11923958C3212yes—
23C3×#11923958C3211yescharacteristic
24C3×#11923958C3211yescharacteristic
25C3×#11923958C3211yescharacteristic
26C3×#11923958C3213yescomplemented
27C3×#11923958C3213yescomplemented
283−1+2×C43⋊C3—36no—
29C3×C32⋊(C43⋊C3)C3212yes—
30C32×C43⋊C9C3213yescomplemented
31#16812514C32118yescomplemented
32#16812512C3219yescomplemented
33#16812511C32118yescomplemented
34#16812509C3219yescomplemented
35#16812507C3216yescomplemented
36#16812507C3216yescomplemented
37#16812507C3216yescomplemented
38C34×C43C3211yescharacteristic
39C3×3−1+2×C43C3212yes—
40C3×H(3,𝔽3)×C43C3211yescharacteristic
41C43×AΣL(1,𝔽27)C3213yescomplemented
42C43×AΣL(1,𝔽27)C3213yescomplemented
43C43×AΣL(1,𝔽27)C3213yescomplemented
44C32×C43⋊C3—32no—
45#11923958—32no—
46#11923958—32no—
47#11923958—31no—
48#11923958—31no—
49#11923958—32no—
50#11923958—32no—
51#11923958—32no—
52#11923958—32no—
53#11923958—39no—
54#11923958—39no—
55#11923958—318no—
56#11923958H(3,𝔽3)16yes—
57#11923958H(3,𝔽3)13yes—
58#11923958C3316yes—
59#11923958C3316yes—
60#11923957—318no—
61#11923956—318no—
62C32⋊(C43⋊C3)—32no—
63C32⋊(C43⋊C3)—32no—
64C32⋊(C43⋊C3)C3316yes—
65C3×C43⋊C9—32no—
66C3×C43⋊C9—32no—
67C3×C43⋊C9—39no—
68C3×C43⋊C9—39no—
69C3×C43⋊C9C3313yes—
70C3×C43⋊C9C3313yes—
71C3×C43⋊C9C3313yes—
72C9×C43⋊C3—318no—
73C33×C43—31no—
74C33×C43—32no—
75C33×C43—31no—
76C33×C43—93no—
77C33×C43C3311yescharacteristic
78C33×C43C3311yescharacteristic
79C33×C43C3311yescharacteristic
80C33×C43C3311yescharacteristic
813−1+2×C43—32no—
823−1+2×C43—32no—
833−1+2×C43C3316yes—
84H(3,𝔽3)×C43—32no—
85H(3,𝔽3)×C43C3313yes—
86C3×C9×C43—32no—
87#10624934—431nomaximal, Sylow
88C32×C43—31no—
89C32×C43—33no—
90C32×C43—33no—
91C32×C43—31no—
92C32×C43—31no—
93C32×C43—91no—
94C32×C43—96no—
95C32×C43—93no—
96C32×C43—91no—
97C32×C43—91no—
98C32×C43—271no—
99C32×C43C3×H(3,𝔽3)11yescharacteristic
100C32×C43C3×H(3,𝔽3)12yes—
101C32×C43C3411yescharacteristic
102C3×C43⋊C3—36no—
103C3×C43⋊C3—272no—
104C9×C43—36no—
105C43⋊C9—36no—
106C43⋊C9—36no—
107C43⋊C9—33no—
108C43⋊C9—33no—
109C43⋊C9C3×H(3,𝔽3)19yes—
1103−1+4—432no—
1113−1+4—431no—
112C32×3−1+2—431no—
113#6913—439no—
114#6913—439no—
115#6912—432no—
116#6911—431no—
117#6910—432no—
118#6910—431no—
119#6908—439no—
120C3×AΣL(1,𝔽27)—432no—
121C3×AΣL(1,𝔽27)C43⋊C311yescharacteristic, complemented
122C3×C43—32no—
123C3×C43—33no—
124C3×C43—31no—
125C3×C43—31no—
126C3×C43—91no—
127C3×C43—91no—
128C3×C43—93no—
129C3×C43C32×H(3,𝔽3)11yescharacteristic
130C43⋊C3—96no—
131C34C3×C43⋊C311yescharacteristic
132#737—4318no—
133#737—439no—
134#737—1296no—
135#737—1296no—
136#737—1296no—
137C3×3−1+2—431no—
138C3×3−1+2—433no—
139C3×3−1+2—433no—
140C3×3−1+2—431no—
141C3×3−1+2—431no—
142C3×3−1+2—432no—
143C3×3−1+2—432no—
144C3×3−1+2—1296no—
145C3×3−1+2—1293no—
146C3×3−1+2—1296no—
147C3×3−1+2—1293no—
148C3×3−1+2C3×C43⋊C312yes—
149C3×H(3,𝔽3)—432no—
150C3×H(3,𝔽3)C3×C43⋊C311yescharacteristic
151C32×C9—433no—
152#733—4318no—
153#732—439no—
154#731—4318no—
155#731—439no—
156AΣL(1,𝔽27)—436no—
157AΣL(1,𝔽27)—436no—
158AΣL(1,𝔽27)—436no—
159AΣL(1,𝔽27)C3×C43⋊C313yescomplemented
160AΣL(1,𝔽27)C3×C43⋊C313yescomplemented
161AΣL(1,𝔽27)C3×C43⋊C313yescomplemented
162C43#1062493411yescharacteristic, complemented, Sylow
163C33—31no—
164C33—32no—
165C33—31no—
166C33—93no—
167C33—1292no—
168C33C32×C43⋊C311yescharacteristic
169C33C32×C43⋊C311yescharacteristic
170C33C32×C43⋊C311yescharacteristic
171C33C32×C43⋊C311yescharacteristic
1723−1+2—32no—
1733−1+2—32no—
1743−1+2—433no—
1753−1+2—436no—
1763−1+2—436no—
1773−1+2—436no—
1783−1+2—12918no—
1793−1+2—12918no—
1803−1+2—1299no—
1813−1+2—1299no—
1823−1+2—12918no—
1833−1+2—1291no—
1843−1+2—1291no—
1853−1+2—1292no—
1863−1+2—1292no—
1873−1+2—1292no—
1883−1+2—1292no—
1893−1+2—1292no—
1903−1+2—1292no—
1913−1+2C32×C43⋊C316yes—
192H(3,𝔽3)—32no—
193H(3,𝔽3)—436no—
194H(3,𝔽3)—1292no—
195H(3,𝔽3)—1292no—
196H(3,𝔽3)C32×C43⋊C313yes—
197C3×C9—32no—
198C3×C9—433no—
199C3×C9—433no—
200C3×C9—433no—
201C3×C9—12918no—
202C3×C9—1299no—
203C3×C9—1299no—
204C3×C9—1292no—
205C3×C9—1292no—
206C32—33no—
207C32—31no—
208C32—33no—
209C32—31no—
210C32—31no—
211C32—91no—
212C32—93no—
213C32—96no—
214C32—91no—
215C32—91no—
216C32—271no—
217C32—1296no—
218C32—11612no—
219C32H(3,𝔽3)×C43⋊C311yescharacteristic
220C32H(3,𝔽3)×C43⋊C312yes—
221C32C33×C43⋊C311yescharacteristic
222C9—36no—
223C9—439no—
224C9—1293no—
225C9—1293no—
226C9—1296no—
227C9—1296no—
228C3—33no—
229C3—31no—
230C3—31no—
231C3—32no—
232C3—91no—
233C3—91no—
234C3—93no—
235C3—3876no—
236C3C3×H(3,𝔽3)×C43⋊C311yescharacteristic
subgroupG/H
centerC3C3×H(3,𝔽3)×C43⋊C3
commutator, cosocleC32×C43C34
FrattiniC32C33×C43⋊C3
FittingC3×C43×AΣL(1,𝔽27)C3
socleC3×C43C32×H(3,𝔽3)
hypercenterC3×AΣL(1,𝔽27)C43⋊C3
hypocenterC43#10624934
LCSG ▷ C32×C43 ▷ C3×C43 ▷ C43
UCSC1 ◁ C3 ◁ C33 ◁ C3×AΣL(1,𝔽27)

Complements

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

NH ≅ G/Ntype
1. #23782924C3semidirect
2. #23782923C3semidirect
3. C32×#11923958C3semidirect
4. #23782898C3semidirect
5. #23782897C3semidirect
6. #23782895C3semidirect
7. #23782891C3semidirect
8. #23782888C3semidirect
9. #23782886C3semidirect
10. #23782873C3semidirect
11. C3×#16812507C3semidirect
12. C3×C43×AΣL(1,𝔽27)C3semidirect
14. #16812526C32semidirect
17. #16812524C32semidirect
26. C3×#11923958C32semidirect
27. C3×#11923958C32semidirect
30. C32×C43⋊C9C32semidirect
31. #16812514C32semidirect
32. #16812512C32semidirect
33. #16812511C32semidirect
34. #16812509C32semidirect
35. #16812507C32semidirect
36. #16812507C32semidirect
37. #16812507C32semidirect
41. C43×AΣL(1,𝔽27)C32semidirect
42. C43×AΣL(1,𝔽27)C32semidirect
43. C43×AΣL(1,𝔽27)C32semidirect
121. C3×AΣL(1,𝔽27)C43⋊C3semidirect
159. AΣL(1,𝔽27)C3×C43⋊C3semidirect
160. AΣL(1,𝔽27)C3×C43⋊C3semidirect
161. AΣL(1,𝔽27)C3×C43⋊C3semidirect
162. C43#10624934semidirect

Maximal subgroups

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

subgroupindex
#237829243
#237829233
C32×#119239583
#237828983
#237828973
#237828953
#237828913
#237828883
#237828863
#237828733
C3×#168125073
C3×C43×AΣL(1,𝔽27)3
#1062493443