Finite Group Databasebeta

← #14518101

Subgroups — #14518101

Order 1944.

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

normal subgroups only

This group has 280 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#11757802C211yesmaximal, characteristic, complemented
2#66440⋊C2—32nomaximal
3#10620047—31nomaximal
4C3×C9⋊S4—31nomaximal
5#66364⋊C2—32nomaximal
6#66366⋊C2—32nomaximal
7#10619757—31nomaximal
8#10619755—31nomaximal
9#10619751—32nomaximal
10#10619681—31nomaximal
11#92344—41nomaximal
12#66440D312yescomplemented
13#66437D311yescharacteristic, complemented
14C3×C9×A4D311yescharacteristic, complemented
15C22×#731D311yescharacteristic, complemented
16C2×#4184—31no—
17#66366D312yescomplemented
18#66364D312yescomplemented
19#66363D311yescharacteristic, complemented
20#66362D311yescharacteristic, complemented
21#66357D312yescomplemented
22#66331—31no—
23#6908—41noSylow
24C3×C3⋊S4—91no—
25C3⋊((C22⋊C9)⋊C2)—31no—
26C9⋊S4—31no—
27C9⋊S4—32no—
28(C3⋊S4)⋊C3—92no—
29C3×(C22⋊C9)⋊C2—91no—
30C3×(C22⋊C9)⋊C2—91no—
31((C22⋊C9)⋊C2)⋊C3—92no—
32((C22⋊C9)⋊C2)⋊C3—92no—
33#611⋊C3—92no—
34#638⋊C3—91no—
35C3×#611—91no—
36#4207—121no—
37#4207—122no—
38C3×C3⋊D9—121no—
39C2×#731—31no—
40#733⋊C2—122no—
41#4185—121no—
42#4184—61no—
43#4184—122no—
44#4183—121no—
45#4183—122no—
46C32×A4C3⋊D311yescharacteristic
47C22×3−1+2C3⋊D312yes—
48C22×H(3,𝔽3)C3⋊D311yescharacteristic
49C22×C3×C9C3⋊D311yescharacteristic
50C2×AGL(1,ℤ/9)—92no—
51C2×(C3⋊D3)⋊C3—91no—
52C2×C3×D9—91no—
53C22⋊H(3,𝔽3)C3⋊D312yes—
54#1094—61no—
55#1094C3⋊D312yes—
56#1094C3⋊D312yes—
57C3×C22⋊C9—31no—
58C3×C22⋊C9C3⋊D311yescharacteristic
59C3×C22⋊C9C3⋊D311yescharacteristic
60C9⋊A4—62no—
61C9×A4—31no—
62C9×A4—32no—
63C9×A4—61no—
643−1+2⋊C4—92no—
65(C3⋊Dic3)⋊C3—91no—
66C3×Dic9—91no—
67#737—42no—
68#737—41no—
69C32×C9—41no—
70#733—42no—
71#732—41no—
72#731—42no—
73#731S411yescharacteristic, complemented
74AΣL(1,𝔽27)—42no—
75AΣL(1,𝔽27)—41no—
76C3⋊S4—91no—
77C3⋊S4—92no—
78C3×S4—273no—
79#638—91no—
80C3×#67—271no—
81(C22⋊C9)⋊C2—92no—
82(C22⋊C9)⋊C2—92no—
83(C22⋊C9)⋊C2—91no—
84(C22⋊C9)⋊C2—91no—
85#611—91no—
86#611—92no—
87C3×C3⋊D3—361no—
88C2×3−1+2—32no—
89C2×H(3,𝔽3)—31no—
90C2×C3×C9—31no—
91C3⋊D9—121no—
92C3⋊D9—122no—
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—181no—
100C3×D9—361no—
101C3×D9—361no—
102C22×C32—31no—
103C22×C32C3⋊(C3⋊D3)11yescharacteristic
104C2×C3⋊D3—91no—
105C2×C3×D3—271no—
106C3×A4—31no—
107C3×A4—33no—
108C3×A4—32no—
109C3⋊Dic3—91no—
110C3×Dic3—271no—
111C22×C9—31no—
112C22×C9—32no—
113C2×D9—91no—
114C2×D9—92no—
115C22⋊C9—21no—
116C22⋊C9—31no—
117C22⋊C9—32no—
118C22⋊C9—32no—
119C22⋊C9#27211yescharacteristic
120Dic9—91no—
121Dic9—92no—
122C33—41no—
1233−1+2—42no—
1243−1+2—42no—
1253−1+2—242no—
1263−1+2—241no—
1273−1+2C3⋊S412yes—
128H(3,𝔽3)—42no—
129H(3,𝔽3)C3⋊S411yescharacteristic
130C3×C9—41no—
131C3×C9—41no—
132C3×C9—121no—
133C3×C9—122no—
134C3×C9—121no—
135C3×C9—241no—
136C3×C9C3⋊S411yescharacteristic
137S4—273no—
138S4—812no—
139C3×D4—811no—
140#67—271no—
141#67—811no—
142C2×C32—31no—
143C2×C32—91no—
144C3⋊D3—181no—
145C3⋊D3—362no—
146C3⋊D3—361no—
147C3×D3—541no—
148C3×D3—1083no—
149C2×C9—91no—
150C2×C9—92no—
151D9—181no—
152D9—182no—
153D9—361no—
154D9—361no—
155D9—362no—
156D9—362no—
157C22×C3—31no—
158C22×C3—91no—
159C22×C3—811no—
160C22×C3C3⋊#27211yescharacteristic
161C2×D3—271no—
162C2×D3—811no—
163A4—33no—
164A4—92no—
165C3×C4—811no—
166Dic3—271no—
167Dic3—811no—
168C32—31no—
169C32—123no—
170C32—121no—
171C32—122no—
172C32C3⋊(C3⋊S4)11yescharacteristic
173C9—31no—
174C9—32no—
175C9—41no—
176C9—81no—
177C9—121no—
178C9—122no—
179C9—122no—
180D4—811noSylow
181C2×C3—31no—
182C2×C3—91no—
183C2×C3—271no—
184C2×C3—1621no—
185D3—541no—
186D3—3242no—
187D3—1083no—
188D3—1621no—
189C22—811no—
190C22#9234411yescharacteristic, complemented
191C4—811no—
192C3—31no—
193C3—91no—
194C3—123no—
195C3—362no—
196C3A4⋊#27211yescharacteristic
197C2—31no—
198C2—1621no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenter#11757802C2
FrattiniC32C3⋊(C3⋊S4)
FittingC22×#731D3
socleC22×C3C3⋊#272
LCSG ▷ #11757802
UCSC1

Complements

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

NH ≅ G/Ntype
1. #11757802C2semidirect
12. #66440D3semidirect
13. #66437D3semidirect
14. C3×C9×A4D3semidirect
15. C22×#731D3semidirect
17. #66366D3semidirect
18. #66364D3semidirect
19. #66363D3semidirect
20. #66362D3semidirect
21. #66357D3semidirect
73. #731S4semidirect
190. C22#92344semidirect

Maximal subgroups

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

subgroupindex
#117578022
#66440⋊C23
#106200473
C3×C9⋊S43
#66364⋊C23
#66366⋊C23
#106197573
#106197553
#106197513
#106196813
#923444