Finite Group Databasebeta

← #14518123

Subgroups — #14518123

Order 1944.

292 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 41 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#11757862C211yesmaximal, characteristic, complemented
2C3×C9⋊S4—31nomaximal
3#10620045—32nomaximal
4#10619983—31nomaximal
5#66364⋊C2—32nomaximal
6#66365⋊C2—32nomaximal
7#66366⋊C2—32nomaximal
8#10619757—31nomaximal
9#10619756—31nomaximal
10#10619755—31nomaximal
11#92344—41nomaximal
12C22×#737D311yescharacteristic, complemented
13C2×#4207—31no—
14#66436D312yescomplemented
15C3×C9×A4D311yescharacteristic, complemented
16#66409—31no—
17#66366D312yescomplemented
18#66365D312yescomplemented
19#66364D312yescomplemented
20#66363D311yescharacteristic, complemented
21#66362D311yescharacteristic, complemented
22#66361D311yescharacteristic, complemented
23#6908—41noSylow
24C3×C3⋊S4—91no—
25C9⋊S4—32no—
26C9⋊S4—31no—
27(C3⋊S4)⋊C3—92no—
28C3×(C22⋊C9)⋊C2—91no—
29C3×(C22⋊C9)⋊C2—91no—
30((C22⋊C9)⋊C2)⋊C3—92no—
31((C22⋊C9)⋊C2)⋊C3—92no—
32#6233—31no—
33#611⋊C3—92no—
34#638⋊C3—91no—
35C3×#611—91no—
36C2×#737—31no—
37#4207—61no—
38#4207—122no—
39C3×C3⋊D9—121no—
40#733⋊C2—122no—
41#4185—121no—
42#4184—121no—
43#4184—122no—
44#4183—121no—
45#4183—122no—
46C32×A4C3⋊D311yescharacteristic
47C22×3−1+2—61no—
48C22×3−1+2C3⋊D312yes—
49C22×H(3,𝔽3)C3⋊D311yescharacteristic
50C22×C3×C9—31no—
51C22×C3×C9C3⋊D311yescharacteristic
52C2×C3⋊D9—31no—
53C2×AGL(1,ℤ/9)—92no—
54C2×(C3⋊D3)⋊C3—91no—
55C2×C3×D9—91no—
56C22⋊H(3,𝔽3)C3⋊D312yes—
57#1094C3⋊D312yes—
58#1094C3⋊D312yes—
59C3×C22⋊C9C3⋊D311yescharacteristic
60C3×C22⋊C9C3⋊D311yescharacteristic
61C9⋊A4—62no—
62C9×A4—31no—
63C9×A4—32no—
64C9×A4—61no—
65C3⋊Dic9—31no—
663−1+2⋊C4—92no—
67(C3⋊Dic3)⋊C3—91no—
68C3×Dic9—91no—
69#737—42no—
70#737S411yescharacteristic, complemented
71C32×C9—41no—
72#733—42no—
73#732—41no—
74#731—42no—
75#731—41no—
76AΣL(1,𝔽27)—42no—
77AΣL(1,𝔽27)—41no—
78C3⋊S4—91no—
79C3⋊S4—92no—
80C3×S4—273no—
81#638—91no—
82C3×#67—271no—
83(C22⋊C9)⋊C2—92no—
84(C22⋊C9)⋊C2—92no—
85(C22⋊C9)⋊C2—91no—
86(C22⋊C9)⋊C2—91no—
87#611—92no—
88#611—91no—
89C3×C3⋊D3—361no—
90C2×3−1+2—32no—
91C2×3−1+2—62no—
92C2×3−1+2—61no—
93C2×H(3,𝔽3)—31no—
94C2×C3×C9—31no—
95C2×C3×C9—31no—
96C2×C3×C9—61no—
97C3⋊D9—61no—
98C3⋊D9—121no—
99C3⋊D9—122no—
100AGL(1,ℤ/9)—182no—
101AGL(1,ℤ/9)—362no—
102AGL(1,ℤ/9)—362no—
103(C3⋊D3)⋊C3—181no—
104(C3⋊D3)⋊C3—362no—
105C3×D9—181no—
106C3×D9—361no—
107C3×D9—361no—
108C22×C32—31no—
109C22×C32C3⋊(C3⋊D3)11yescharacteristic
110C2×C3⋊D3—91no—
111C2×C3×D3—271no—
112C3×A4—31no—
113C3×A4—33no—
114C3×A4—32no—
115C3⋊Dic3—91no—
116C3×Dic3—271no—
117C22×C9—21no—
118C22×C9—32no—
119C22×C9#27211yescharacteristic
120C2×D9—91no—
121C2×D9—92no—
122C22⋊C9—31no—
123C22⋊C9—31no—
124C22⋊C9—32no—
125C22⋊C9—32no—
126Dic9—91no—
127Dic9—92no—
128C33—41no—
1293−1+2—42no—
1303−1+2—42no—
1313−1+2—61no—
1323−1+2—242no—
1333−1+2C3⋊S412yes—
134H(3,𝔽3)—42no—
135H(3,𝔽3)C3⋊S411yescharacteristic
136C3×C9—31no—
137C3×C9—41no—
138C3×C9—41no—
139C3×C9—121no—
140C3×C9—122no—
141C3×C9—241no—
142C3×C9C3⋊S411yescharacteristic
143S4—273no—
144S4—812no—
145C3×D4—811no—
146#67—271no—
147#67—811no—
148C2×C32—31no—
149C2×C32—31no—
150C2×C32—61no—
151C3⋊D3—181no—
152C3⋊D3—362no—
153C3⋊D3—361no—
154C3×D3—541no—
155C3×D3—1083no—
156C2×C9—32no—
157C2×C9—31no—
158C2×C9—61no—
159C2×C9—62no—
160D9—182no—
161D9—181no—
162D9—361no—
163D9—361no—
164D9—362no—
165D9—362no—
166C22×C3—31no—
167C22×C3—91no—
168C22×C3—811no—
169C22×C3C3⋊#27211yescharacteristic
170C2×D3—271no—
171C2×D3—811no—
172A4—33no—
173A4—92no—
174C3×C4—811no—
175Dic3—271no—
176Dic3—811no—
177C32—31no—
178C32—123no—
179C32—121no—
180C32—122no—
181C32C3⋊(C3⋊S4)11yescharacteristic
182C9—21no—
183C9—32no—
184C9—121no—
185C9—121no—
186C9—122no—
187C9—122no—
188C9#625811yescharacteristic
189D4—811noSylow
190C2×C3—31no—
191C2×C3—91no—
192C2×C3—91no—
193C2×C3—181no—
194C2×C3—1621no—
195D3—541no—
196D3—3242no—
197D3—1083no—
198D3—1621no—
199C22—811no—
200C22#9234411yescharacteristic, complemented
201C4—811no—
202C3—31no—
203C3—91no—
204C3—123no—
205C3—362no—
206C3C3⋊#625811yescharacteristic
207C2—31no—
208C2—1621no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenter#11757862C2
FrattiniC32C3⋊(C3⋊S4)
FittingC22×#737D3
socleC22×C3C3⋊#272
LCSG ▷ #11757862
UCSC1

Complements

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

NH ≅ G/Ntype
1. #11757862C2semidirect
12. C22×#737D3semidirect
14. #66436D3semidirect
15. C3×C9×A4D3semidirect
17. #66366D3semidirect
18. #66365D3semidirect
19. #66364D3semidirect
20. #66363D3semidirect
21. #66362D3semidirect
22. #66361D3semidirect
70. #737S4semidirect
200. C22#92344semidirect

Maximal subgroups

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

subgroupindex
#117578622
C3×C9⋊S43
#106200453
#106199833
#66364⋊C23
#66365⋊C23
#66366⋊C23
#106197573
#106197563
#106197553
#923444