Finite Group Databasebeta

← #13091164

Subgroups — #13091164

Order 1458.

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

normal subgroups only

This group has 300 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#10624763C211yesmaximal, characteristic, complemented, Sylow
2#4207⋊C3—31nomaximal
3#92333—31nomaximal
4#4184⋊C3—32nomaximal
5#4184⋊C3—31nomaximal
6#4183⋊C3—32nomaximal
7#4183⋊C3—32nomaximal
8C3×#733⋊C2—31nomaximal
9C3×#4185—31nomaximal
10C3×#4184—32nomaximal
113−1+4D311yescharacteristic, complemented
12#6911D311yescharacteristic, complemented
13#6910D312yescomplemented
14#6910D311yescharacteristic, complemented
15#6909D312yescomplemented
16#6909D312yescomplemented
17C3×#733D311yescharacteristic, complemented
18C3×#732D311yescharacteristic, complemented
19C3×#731D312yescomplemented
20#4207—32no—
21#4207—31no—
22C3⋊AGL(1,ℤ/9)—31no—
23C3×AGL(1,ℤ/9)—92no—
24C3×AGL(1,ℤ/9)—92no—
25C3×AGL(1,ℤ/9)—91no—
26C3×AGL(1,ℤ/9)—91no—
27C3×AGL(1,ℤ/9)—91no—
28C3×(C3⋊D3)⋊C3—92no—
29C3×(C3⋊D3)⋊C3—92no—
30C3×(C3⋊D3)⋊C3—91no—
31C32×D9—91no—
32#733⋊C2—31no—
33#4185—31no—
34#4185—31no—
35#4184—32no—
36#4184—32no—
37#4184—31no—
38#4183—32no—
39#4183—32no—
40#737—32no—
41#737—31no—
42#737—61no—
43#737—62no—
44C3×3−1+2—31no—
45C3×3−1+2—61no—
46C3×3−1+2C3⋊D312yes—
47C3×3−1+2C3⋊D311yescharacteristic
48C3×3−1+2C3⋊D312yes—
49C3×3−1+2C3⋊D311yescharacteristic
50C3×3−1+2C3⋊D311yescharacteristic
51C3×H(3,𝔽3)C3⋊D311yescharacteristic
52C3×H(3,𝔽3)C3⋊D312yes—
53C3×H(3,𝔽3)C3⋊D312yes—
54C32×C9C3⋊D311yescharacteristic
55#733—31no—
56#733—61no—
57#732—31no—
58#732—31no—
59#732—61no—
60#732—61no—
61#731—32no—
62#731—32no—
63#731—31no—
64#731—61no—
65#731—62no—
66#731—62no—
67AΣL(1,𝔽27)—32no—
68AΣL(1,𝔽27)—32no—
69AΣL(1,𝔽27)—62no—
70AΣL(1,𝔽27)—62no—
71C3×C3⋊D3—92no—
72C3×C3⋊D3—92no—
73C3×C3⋊D3—91no—
74C32×D3—271no—
75C3⋊D9—31no—
76AGL(1,ℤ/9)—92no—
77AGL(1,ℤ/9)—92no—
78AGL(1,ℤ/9)—92no—
79AGL(1,ℤ/9)—92no—
80AGL(1,ℤ/9)—92no—
81AGL(1,ℤ/9)—91no—
82AGL(1,ℤ/9)—91no—
83AGL(1,ℤ/9)—92no—
84AGL(1,ℤ/9)—92no—
85AGL(1,ℤ/9)—92no—
86AGL(1,ℤ/9)—91no—
87AGL(1,ℤ/9)—92no—
88(C3⋊D3)⋊C3—92no—
89(C3⋊D3)⋊C3—92no—
90(C3⋊D3)⋊C3—92no—
91(C3⋊D3)⋊C3—92no—
92(C3⋊D3)⋊C3—92no—
93(C3⋊D3)⋊C3—92no—
94(C3⋊D3)⋊C3—92no—
95(C3⋊D3)⋊C3—91no—
96C3×D9—92no—
97C3×D9—91no—
98C3×D9—92no—
99C3×D9—91no—
100C3×D9—91no—
101C3×D9—91no—
102C3×D9—91no—
103C3×D9—92no—
104C33—31no—
105C33—32no—
106C33—32no—
107C33C3⋊(C3⋊D3)11yescharacteristic
1083−1+2—21no—
1093−1+2—22no—
1103−1+2—32no—
1113−1+2—32no—
1123−1+2—32no—
1133−1+2—32no—
1143−1+2—32no—
1153−1+2—32no—
1163−1+2—32no—
1173−1+2—32no—
1183−1+2—31no—
1193−1+2—31no—
1203−1+2—62no—
1213−1+2—62no—
1223−1+2—61no—
1233−1+2—62no—
1243−1+2—61no—
1253−1+2—61no—
1263−1+2#27211yescharacteristic
1273−1+2#27212yes—
128H(3,𝔽3)—21no—
129H(3,𝔽3)—32no—
130H(3,𝔽3)—32no—
131H(3,𝔽3)—32no—
132H(3,𝔽3)—32no—
133H(3,𝔽3)—32no—
134H(3,𝔽3)—32no—
135H(3,𝔽3)—32no—
136H(3,𝔽3)#27211yescharacteristic
137C3×C9—31no—
138C3×C9—31no—
139C3×C9—32no—
140C3×C9—32no—
141C3×C9—31no—
142C3×C9—32no—
143C3×C9—31no—
144C3×C9—31no—
145C3×C9—31no—
146C3×C9—61no—
147C3×C9—61no—
148C3×C9—62no—
149C2×C32—811no—
150C3⋊D3—91no—
151C3⋊D3—92no—
152C3⋊D3—92no—
153C3×D3—271no—
154C3×D3—272no—
155C3×D3—271no—
156C3×D3—811no—
157C3×D3—812no—
158C3×D3—812no—
159D9—92no—
160D9—91no—
161D9—91no—
162D9—91no—
163D9—92no—
164D9—91no—
165C32—31no—
166C32—61no—
167C32—91no—
168C32—92no—
169C32—92no—
170C32—271no—
171C32—272no—
172C32—272no—
173C32C3⋊#27211yescharacteristic
174C32C3⋊#27212yes—
175C32C3⋊#27211yescharacteristic
176C9—32no—
177C9—31no—
178C9—61no—
179C9—62no—
180C9—91no—
181C9—91no—
182C9—92no—
183C9—91no—
184C2×C3—811no—
185C2×C3—812no—
186C2×C3—811no—
187D3—271no—
188D3—811no—
189D3—812no—
190D3—812no—
191C3—31no—
192C3—32no—
193C3—31no—
194C3—91no—
195C3—181no—
196C3—272no—
197C3—272no—
198C3#9233811yescharacteristic
199C2—811noSylow
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenter#10624763C2
FrattiniC33C3⋊(C3⋊D3)
socleC3#92338
LCSG ▷ #10624763
UCSC1

Complements

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

NH ≅ G/Ntype
1. #10624763C2semidirect
11. 3−1+4D3semidirect
12. #6911D3semidirect
13. #6910D3semidirect
14. #6910D3semidirect
15. #6909D3semidirect
16. #6909D3semidirect
17. C3×#733D3semidirect
18. C3×#732D3semidirect
19. C3×#731D3semidirect

Maximal subgroups

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

subgroupindex
#106247632
#4207⋊C33
#923333
#4184⋊C33
#4183⋊C33
C3×#733⋊C23
C3×#41853
C3×#41843