Finite Group Databasebeta

← #13091120

Subgroups — #13091120

Order 1458.

350 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 39 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#10624749C211yesmaximal, characteristic, complemented, Sylow
2#4207⋊C3—31nomaximal
3#92333—31nomaximal
4#4184⋊C3—31nomaximal
5#4184⋊C3—32nomaximal
6#4183⋊C3—32nomaximal
7#4183⋊C3—32nomaximal
8C3×#4183—32nomaximal
9#92302—31nomaximal
10#92300—31nomaximal
113−1+4D311yescharacteristic, complemented
12#6911D311yescharacteristic, complemented
13#6910D312yescomplemented
14#6910D311yescharacteristic, complemented
15#6909D312yescomplemented
16#6909D312yescomplemented
17C3×AΣL(1,𝔽27)D312yescomplemented
18#6891D311yescharacteristic, complemented
19C32⋊H(3,𝔽3)D311yescharacteristic, complemented
20C32×C3⋊D3—91no—
21C3⋊#272—31no—
22#4207—32no—
23#4207—31no—
24C3⋊AGL(1,ℤ/9)—31no—
25C3×AGL(1,ℤ/9)—92no—
26C3×AGL(1,ℤ/9)—91no—
27C3×AGL(1,ℤ/9)—92no—
28C3×AGL(1,ℤ/9)—92no—
29C3×(C3⋊D3)⋊C3—91no—
30C3×(C3⋊D3)⋊C3—91no—
31C3×(C3⋊D3)⋊C3—91no—
32C3×(C3⋊D3)⋊C3—92no—
33#4185—31no—
34#4184—32no—
35#4184—31no—
36#4183—32no—
37#4183—32no—
38#4183—32no—
39#4181—31no—
40C34C3⋊D311yescharacteristic
41#737—32no—
42#737—31no—
43#737—61no—
44#737—62no—
45C3×3−1+2—31no—
46C3×3−1+2—61no—
47C3×3−1+2C3⋊D311yescharacteristic
48C3×3−1+2C3⋊D312yes—
49C3×3−1+2C3⋊D312yes—
50C3×3−1+2C3⋊D312yes—
51C3×H(3,𝔽3)—31no—
52C3×H(3,𝔽3)—61no—
53C3×H(3,𝔽3)C3⋊D311yescharacteristic
54C3×H(3,𝔽3)C3⋊D311yescharacteristic
55C3×H(3,𝔽3)C3⋊D311yescharacteristic
56C3×H(3,𝔽3)C3⋊D312yes—
57#732—31no—
58#732—61no—
59#731—32no—
60#731—31no—
61#731—61no—
62#731—62no—
63AΣL(1,𝔽27)—32no—
64AΣL(1,𝔽27)—32no—
65AΣL(1,𝔽27)—32no—
66AΣL(1,𝔽27)—62no—
67AΣL(1,𝔽27)—62no—
68AΣL(1,𝔽27)—62no—
69C32⋊C9—31no—
70C32⋊C9—61no—
71C3×C3⋊D3—91no—
72C3×C3⋊D3—92no—
73C3×C3⋊D3—91no—
74C3×C3⋊D3—92no—
75C3×C3⋊D3—91no—
76C3×C3⋊D3—91no—
77C3×C3⋊D3—91no—
78C32×D3—273no—
79C32×D3—271no—
80#272—273no—
81C3⋊D9—31no—
82AGL(1,ℤ/9)—92no—
83AGL(1,ℤ/9)—92no—
84AGL(1,ℤ/9)—92no—
85AGL(1,ℤ/9)—92no—
86AGL(1,ℤ/9)—92no—
87AGL(1,ℤ/9)—92no—
88AGL(1,ℤ/9)—91no—
89AGL(1,ℤ/9)—92no—
90AGL(1,ℤ/9)—92no—
91AGL(1,ℤ/9)—92no—
92AGL(1,ℤ/9)—92no—
93(C3⋊D3)⋊C3—92no—
94(C3⋊D3)⋊C3—92no—
95(C3⋊D3)⋊C3—92no—
96(C3⋊D3)⋊C3—91no—
97(C3⋊D3)⋊C3—92no—
98(C3⋊D3)⋊C3—91no—
99(C3⋊D3)⋊C3—92no—
100(C3⋊D3)⋊C3—91no—
101(C3⋊D3)⋊C3—92no—
102C3×D9—92no—
103C3×D9—92no—
104C3×D9—92no—
105C3×D9—91no—
106C33—21no—
107C33—31no—
108C33—31no—
109C33—32no—
110C33—31no—
111C33—31no—
112C33—32no—
113C33—93no—
114C33#27211yescharacteristic
115C33C3⋊(C3⋊D3)11yescharacteristic
1163−1+2—22no—
1173−1+2—32no—
1183−1+2—31no—
1193−1+2—32no—
1203−1+2—32no—
1213−1+2—32no—
1223−1+2—32no—
1233−1+2—32no—
1243−1+2—32no—
1253−1+2—32no—
1263−1+2—32no—
1273−1+2—62no—
1283−1+2—62no—
1293−1+2—61no—
1303−1+2—62no—
1313−1+2—62no—
1323−1+2#27212yescomplemented
133H(3,𝔽3)—31no—
134H(3,𝔽3)—32no—
135H(3,𝔽3)—32no—
136H(3,𝔽3)—32no—
137H(3,𝔽3)—32no—
138H(3,𝔽3)—31no—
139H(3,𝔽3)—32no—
140H(3,𝔽3)—31no—
141H(3,𝔽3)—32no—
142H(3,𝔽3)—93no—
143H(3,𝔽3)—183no—
144C3×C9—21no—
145C3×C9—31no—
146C3×C9—32no—
147C3×C9—32no—
148C3×C9—32no—
149C3×C9—61no—
150C3×C9—61no—
151C3×C9—61no—
152C3×C9—61no—
153C3×C9#27211yescharacteristic, complemented
154C2×C32—811no—
155C3⋊D3—91no—
156C3⋊D3—91no—
157C3⋊D3—91no—
158C3⋊D3—92no—
159C3⋊D3—91no—
160C3×D3—273no—
161C3×D3—273no—
162C3×D3—276no—
163C3×D3—271no—
164C3×D3—272no—
165C3×D3—271no—
166C3×D3—811no—
167C3×D3—811no—
168C3×D3—811no—
169C3×D3—812no—
170D9—92no—
171D9—91no—
172D9—92no—
173D9—92no—
174C32—33no—
175C32—33no—
176C32—31no—
177C32—61no—
178C32—91no—
179C32—91no—
180C32—96no—
181C32—91no—
182C32—91no—
183C32—91no—
184C32—91no—
185C32—91no—
186C32—92no—
187C32—181no—
188C32—181no—
189C32—181no—
190C32—181no—
191C32—181no—
192C32—272no—
193C32C3⋊#27211yescharacteristic
194C32C3⋊#27212yes—
195C32C3⋊#27211yescharacteristic
196C9—32no—
197C9—31no—
198C9—61no—
199C9—62no—
200C9—92no—
201C9—92no—
202C2×C3—811no—
203C2×C3—812no—
204C2×C3—811no—
205D3—273no—
206D3—271no—
207D3—811no—
208D3—811no—
209D3—811no—
210D3—812no—
211C3—31no—
212C3—31no—
213C3—32no—
214C3—93no—
215C3—91no—
216C3—181no—
217C3—271no—
218C3—271no—
219C3—272no—
220C3#9233811yescharacteristic
221C2—811noSylow
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenter#10624749C2
FrattiniC33C3⋊(C3⋊D3)
socleC3#92338
LCSG ▷ #10624749
UCSC1

Complements

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

NH ≅ G/Ntype
1. #10624749C2semidirect
11. 3−1+4D3semidirect
12. #6911D3semidirect
13. #6910D3semidirect
14. #6910D3semidirect
15. #6909D3semidirect
16. #6909D3semidirect
17. C3×AΣL(1,𝔽27)D3semidirect
18. #6891D3semidirect
19. C32⋊H(3,𝔽3)D3semidirect
132. 3−1+2#272semidirect
153. C3×C9#272semidirect

Maximal subgroups

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

subgroupindex
#106247492
#4207⋊C33
#923333
#4184⋊C33
#4183⋊C33
C3×#41833
#923023
#923003