Finite Group Databasebeta

← #14518088

Subgroups — #14518088

Order 1944.

226 conjugacy classes of subgroups; only the 28 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 28 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)C311yesmaximal, characteristic, complemented
3#10619983—31nomaximal
4#10619745—31nomaximal
5#10619744—31nomaximal
6#10619743—31nomaximal
7#92330—41nomaximal
8C22×#737D311yescharacteristic, complemented
9C2×#4207—31no—
10#66436—21no—
11C3×C9×A4C2×C311yescharacteristic, complemented
12#66409—31no—
13#66366—21no—
14#66365—21no—
15#66364—21no—
16#66363D311yescharacteristic
17#66362D311yescharacteristic, complemented
18#66361D311yescharacteristic, complemented
19#6908—41noSylow
20C3⋊(C3⋊S4)—31no—
21C3⋊((C22⋊C9)⋊C2)—31no—
22C3⋊((C22⋊C9)⋊C2)—31no—
23C9⋊S4—91no—
24C9⋊S4—92no—
25#6233—31no—
26#611⋊C3—92no—
27#638⋊C3—91no—
28C3×#611—91no—
29C2×#737—31no—
30C3⋊(C3⋊D9)—41no—
31#4207—61no—
32#4179—121no—
33#4177—121no—
34#4175—121no—
35C32×A4C3×D311yescharacteristic
36C22×3−1+2—21no—
37C22×3−1+2—32no—
38C22×H(3,𝔽3)C3⋊D311yescharacteristic
39C22×C3×C9—31no—
40C22×C3×C9C3×D311yescharacteristic
41C2×C3⋊D9—31no—
42C2×AGL(1,ℤ/9)—92no—
43C2×(C3⋊D3)⋊C3—91no—
44C2×C3×D9—91no—
45C22⋊H(3,𝔽3)—21no—
46#1094—21no—
47#1094—21no—
48C3×C22⋊C9C3×D311yescharacteristic
49C3×C22⋊C9C3×D311yescharacteristic
50C9⋊A4—62no—
51C9×A4—31no—
52C9×A4—32no—
53C9×A4—61no—
54C3⋊Dic9—31no—
553−1+2⋊C4—92no—
56(C3⋊Dic3)⋊C3—91no—
57C3×Dic9—91no—
58#737—81no—
59#737S411yescharacteristic, complemented
60C32×C9—41no—
61#733—81no—
62#732—41no—
63#731—41no—
64#731—81no—
65AΣL(1,𝔽27)—41no—
66AΣL(1,𝔽27)—81no—
67C3⋊S4—271no—
68C3⋊S4—273no—
69#638—91no—
70C3×#67—271no—
71(C22⋊C9)⋊C2—271no—
72(C22⋊C9)⋊C2—271no—
73#611—91no—
74#611—92no—
75C3⋊(C3⋊D3)—121no—
76C2×3−1+2—32no—
77C2×3−1+2—62no—
78C2×3−1+2—61no—
79C2×H(3,𝔽3)—31no—
80C2×C3×C9—31no—
81C2×C3×C9—31no—
82C2×C3×C9—61no—
83C3⋊D9—61no—
84C3⋊D9—121no—
85C3⋊D9—121no—
86C3⋊D9—361no—
87C3⋊D9—362no—
88AGL(1,ℤ/9)—182no—
89(C3⋊D3)⋊C3—181no—
90C3×D9—181no—
91C22×C32—31no—
92C22×C32C3×C3⋊D311yescharacteristic
93C2×C3⋊D3—91no—
94C2×C3×D3—271no—
95C3×A4—31no—
96C3×A4—33no—
97C3×A4—61no—
98C3⋊Dic3—91no—
99C3×Dic3—271no—
100C22×C9—61no—
101C22×C9(C3⋊D3)⋊C311yescharacteristic
102C22×C9(C3⋊D3)⋊C312yes—
103C2×D9—91no—
104C2×D9—92no—
105C22⋊C9—31no—
106C22⋊C9—31no—
107C22⋊C9—61no—
108C22⋊C9—61no—
109Dic9—91no—
110Dic9—92no—
111C33—41no—
1123−1+2—21no—
1133−1+2—32no—
1143−1+2—81no—
1153−1+2—81no—
1163−1+2—242no—
117H(3,𝔽3)—81no—
118H(3,𝔽3)C3⋊S411yescharacteristic
119C3×C9—31no—
120C3×C9—41no—
121C3×C9—41no—
122C3×C9—121no—
123C3×C9—122no—
124C3×C9—241no—
125C3×C9C3×S411yescharacteristic
126S4—813no—
127C3×D4—811no—
128#67—271no—
129#67—811no—
130C2×C32—31no—
131C2×C32—31no—
132C2×C32—61no—
133C3⋊D3—181no—
134C3⋊D3—1081no—
135C3⋊D3—1083no—
136C3×D3—541no—
137C2×C9—31no—
138C2×C9—32no—
139C2×C9—61no—
140C2×C9—62no—
141D9—181no—
142D9—182no—
143D9—1081no—
144D9—1081no—
145C22×C3—31no—
146C22×C3—91no—
147C22×C3—811no—
148C22×C3C3⋊((C3⋊D3)⋊C3)11yescharacteristic
149C2×D3—271no—
150C2×D3—811no—
151A4—33no—
152A4—181no—
153C3×C4—811no—
154Dic3—271no—
155Dic3—811no—
156C32—31no—
157C32—123no—
158C32—121no—
159C32—241no—
160C32C3×C3⋊S411yescharacteristic
161C9—61no—
162C9—121no—
163C9—121no—
164C9—241no—
165C9—241no—
166C9(C3⋊S4)⋊C311yescharacteristic
167C9(C3⋊S4)⋊C312yes—
168D4—811noSylow
169C2×C3—31no—
170C2×C3—91no—
171C2×C3—91no—
172C2×C3—181no—
173C2×C3—1621no—
174D3—541no—
175D3—3243no—
176D3—1621no—
177C22—811no—
178C22#9233011yescharacteristic, complemented
179C4—811no—
180C3—31no—
181C3—91no—
182C3—123no—
183C3—721no—
184C3C3⋊((C3⋊S4)⋊C3)11yescharacteristic
185C2—31no—
186C2—1621no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC3×C9×A4C2×C3
FrattiniC32C3×C3⋊S4
FittingC22×#737D3
socleC22×C3C3⋊((C3⋊D3)⋊C3)
LCSG ▷ C3×C9×A4
UCSC1

Complements

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

NH ≅ G/Ntype
1. #11757862C2semidirect
2. C3⋊(C9⋊S4)C3semidirect
8. C22×#737D3semidirect
11. C3×C9×A4C2×C3semidirect
17. #66362D3semidirect
18. #66361D3semidirect
59. #737S4semidirect
178. C22#92330semidirect

Maximal subgroups

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

subgroupindex
#117578622
C3⋊(C9⋊S4)3
#106199833
#106197453
#106197443
#106197433
#923304