Finite Group Databasebeta

← #14518099

Subgroups — #14518099

Order 1944.

298 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 40 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#11757798C211yesmaximal, characteristic, complemented
2C3×C3⋊((C22⋊C9)⋊C2)—31nomaximal
3#66440⋊C2—32nomaximal
4#10620047—31nomaximal
5#10619762—32nomaximal
6#66364⋊C2—32nomaximal
7#66365⋊C2—32nomaximal
8#10619756—31nomaximal
9#10619755—31nomaximal
10#10619679—31nomaximal
11#92344—41nomaximal
12C32×C22⋊C9D311yescharacteristic, complemented
13#66440D312yescomplemented
14#66437D311yescharacteristic, complemented
15C22×AΣL(1,𝔽27)D311yescharacteristic, complemented
16C2×#4183—31no—
17#66368D312yescomplemented
18#66365D312yescomplemented
19#66364D312yescomplemented
20#66362D311yescharacteristic, complemented
21#66361D311yescharacteristic, complemented
22#66330—31no—
23#6908—41noSylow
24C3×#638—91no—
25C3⋊((C22⋊C9)⋊C2)—31no—
26C3⋊((C22⋊C9)⋊C2)—31no—
27C9⋊S4—32no—
28(C3⋊S4)⋊C3—92no—
29C3×(C22⋊C9)⋊C2—91no—
30C3×(C22⋊C9)⋊C2—91no—
31C3×(C22⋊C9)⋊C2—91no—
32((C22⋊C9)⋊C2)⋊C3—92no—
33((C22⋊C9)⋊C2)⋊C3—92no—
34#611⋊C3—92no—
35#638⋊C3—91no—
36#4207—121no—
37#4207—122no—
38C3×C3⋊D9—121no—
39C2×AΣL(1,𝔽27)—31no—
40#733⋊C2—122no—
41#4185—121no—
42#4184—121no—
43#4184—122no—
44#4183—61no—
45#4183—122no—
46C22×C33C3⋊D311yescharacteristic
47C2×C3×C3⋊D3—91no—
48C3×C3⋊Dic3—91no—
49C22×3−1+2C3⋊D312yes—
50C22×H(3,𝔽3)C3⋊D311yescharacteristic
51C2×AGL(1,ℤ/9)—92no—
52C2×(C3⋊D3)⋊C3—91no—
53C22⋊H(3,𝔽3)C3⋊D312yes—
54#1094—61no—
55#1094C3⋊D312yes—
56#1094C3⋊D312yes—
57C3×C22⋊C9—31no—
58C3×C22⋊C9—31no—
59C3×C22⋊C9—61no—
60C3×C22⋊C9C3⋊D311yescharacteristic
61C3×C22⋊C9C3⋊D311yescharacteristic
62C3×C22⋊C9C3⋊D311yescharacteristic
63C9⋊A4—62no—
64C9×A4—32no—
653−1+2⋊C4—92no—
66(C3⋊Dic3)⋊C3—91no—
67#737—42no—
68#737—41no—
69C32×C9—41no—
70#733—42no—
71#732—41no—
72#731—42no—
73#731—41no—
74AΣL(1,𝔽27)—42no—
75AΣL(1,𝔽27)S411yescharacteristic, complemented
76C3⋊S4—92no—
77#638—91no—
78#638—91no—
79C3×#67—273no—
80C3×#67—271no—
81(C22⋊C9)⋊C2—92no—
82(C22⋊C9)⋊C2—92no—
83(C22⋊C9)⋊C2—91no—
84(C22⋊C9)⋊C2—91no—
85(C22⋊C9)⋊C2—91no—
86#611—92no—
87C2×C33—31no—
88C3×C3⋊D3—181no—
89C2×3−1+2—32no—
90C2×H(3,𝔽3)—31no—
91C3⋊D9—122no—
92C3⋊D9—121no—
93C3⋊D9—121no—
94AGL(1,ℤ/9)—182no—
95AGL(1,ℤ/9)—362no—
96AGL(1,ℤ/9)—362no—
97(C3⋊D3)⋊C3—181no—
98(C3⋊D3)⋊C3—362no—
99C3×D9—361no—
100C3×D9—361no—
101C3×D9—361no—
102C22×C32—31no—
103C22×C32—33no—
104C22×C32—31no—
105C22×C32C3⋊(C3⋊D3)11yescharacteristic
106C2×C3⋊D3—91no—
107C2×C3⋊D3—91no—
108C2×C3×D3—271no—
109C2×C3×D3—273no—
110C3×A4—32no—
111C3⋊Dic3—91no—
112C3⋊Dic3—91no—
113C3×Dic3—271no—
114C3×Dic3—273no—
115C22×C9—32no—
116C2×D9—92no—
117C22⋊C9—21no—
118C22⋊C9—32no—
119C22⋊C9—31no—
120C22⋊C9—31no—
121C22⋊C9—32no—
122C22⋊C9#27211yescharacteristic
123Dic9—92no—
124C33C3⋊S411yescharacteristic
1253−1+2—42no—
1263−1+2—42no—
1273−1+2—242no—
1283−1+2—241no—
1293−1+2C3⋊S412yes—
130H(3,𝔽3)—42no—
131H(3,𝔽3)C3⋊S411yescharacteristic
132C3×C9—41no—
133C3×C9—41no—
134C3×C9—41no—
135C3×C9—122no—
136C3×C9—121no—
137C3×C9—121no—
138C3×C9—241no—
139S4—812no—
140C3×D4—811no—
141#67—273no—
142#67—271no—
143#67—811no—
144C2×C32—31no—
145C2×C32—91no—
146C2×C32—91no—
147C2×C32—93no—
148C3⋊D3—181no—
149C3⋊D3—181no—
150C3⋊D3—362no—
151C3×D3—543no—
152C3×D3—541no—
153C2×C9—92no—
154D9—182no—
155D9—361no—
156D9—361no—
157D9—361no—
158D9—362no—
159D9—362no—
160C22×C3—33no—
161C22×C3—31no—
162C22×C3—91no—
163C22×C3—811no—
164C22×C3C3⋊#27211yescharacteristic
165C2×D3—271no—
166C2×D3—273no—
167C2×D3—811no—
168A4—92no—
169C3×C4—811no—
170Dic3—271no—
171Dic3—273no—
172Dic3—811no—
173C32—33no—
174C32—31no—
175C32—31no—
176C32—122no—
177C32C3⋊(C3⋊S4)11yescharacteristic
178C9—32no—
179C9—41no—
180C9—81no—
181C9—121no—
182C9—121no—
183C9—122no—
184C9—122no—
185D4—811noSylow
186C2×C3—31no—
187C2×C3—93no—
188C2×C3—91no—
189C2×C3—271no—
190C2×C3—1621no—
191D3—543no—
192D3—541no—
193D3—3242no—
194D3—1621no—
195C22—811no—
196C22#9234411yescharacteristic, complemented
197C4—811no—
198C3—33no—
199C3—31no—
200C3—91no—
201C3—362no—
202C3A4⋊#27211yescharacteristic
203C2—31no—
204C2—1621no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenter#11757798C2
FrattiniC32C3⋊(C3⋊S4)
FittingC22×AΣL(1,𝔽27)D3
socleC22×C3C3⋊#272
LCSG ▷ #11757798
UCSC1

Complements

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

NH ≅ G/Ntype
1. #11757798C2semidirect
12. C32×C22⋊C9D3semidirect
13. #66440D3semidirect
14. #66437D3semidirect
15. C22×AΣL(1,𝔽27)D3semidirect
17. #66368D3semidirect
18. #66365D3semidirect
19. #66364D3semidirect
20. #66362D3semidirect
21. #66361D3semidirect
75. AΣL(1,𝔽27)S4semidirect
196. C22#92344semidirect

Maximal subgroups

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

subgroupindex
#117577982
C3×C3⋊((C22⋊C9)⋊C2)3
#66440⋊C23
#106200473
#106197623
#66364⋊C23
#66365⋊C23
#106197563
#106197553
#106196793
#923444