Finite Group Databasebeta

← #14518032

Subgroups — #14518032

Order 1944.

205 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 205 conjugacy classes of subgroups — too many to draw. Only its 25 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#11757806C211yesmaximal, characteristic, complemented
2C3⋊(C9⋊S4)C311yesmaximal, characteristic, complemented
3#10620047—31nomaximal
4#10619745—31nomaximal
5#10619744—31nomaximal
6#10619650—31nomaximal
7#92330—41nomaximal
8#66437—21no—
9#66437D311yescharacteristic, complemented
10C3×C9×A4C2×C311yescharacteristic, complemented
11C22×#732D311yescharacteristic, complemented
12C2×#4179—31no—
13#66363—21no—
14#66363D311yescharacteristic
15#66361—21no—
16#66361D311yescharacteristic, complemented
17#66359—21no—
18#66326—31no—
19#6908—41noSylow
20C3⋊(C3⋊S4)—31no—
21C3⋊((C22⋊C9)⋊C2)—31no—
22C3⋊((C22⋊C9)⋊C2)—31no—
23C9⋊S4—92no—
24C9⋊S4—91no—
25C3×(C22⋊C9)⋊C2—91no—
26((C22⋊C9)⋊C2)⋊C3—92no—
27#6233—31no—
28#638⋊C3—91no—
29C3⋊(C3⋊D9)—41no—
30#4207—121no—
31C2×#732—31no—
32#4179—61no—
33#4177—121no—
34#4175—121no—
35C32×A4C3×D311yescharacteristic
36C22×H(3,𝔽3)—21no—
37C22×H(3,𝔽3)C3⋊D311yescharacteristic
38C22×C3×C9C3×D311yescharacteristic
39C2×C3⋊D9—31no—
40C2×(C3⋊D3)⋊C3—91no—
41#1094—21no—
42#1094—21no—
43#1094—21no—
44#1094—32no—
45#1094—62no—
46C3×C22⋊C9—31no—
47C3×C22⋊C9—61no—
48C3×C22⋊C9C3×D311yescharacteristic
49C3×C22⋊C9C3×D311yescharacteristic
50C9×A4—31no—
51C9×A4—32no—
52C3⋊Dic9—31no—
53(C3⋊Dic3)⋊C3—91no—
54#737—41no—
55#737—81no—
56C32×C9—41no—
57#733—81no—
58#732S411yescharacteristic, complemented
59#731—41no—
60#731—81no—
61AΣL(1,𝔽27)—41no—
62AΣL(1,𝔽27)—81no—
63C3⋊S4—271no—
64C3⋊S4—273no—
65#638—91no—
66C3×#67—271no—
67(C22⋊C9)⋊C2—92no—
68(C22⋊C9)⋊C2—91no—
69(C22⋊C9)⋊C2—271no—
70#611—271no—
71C3⋊(C3⋊D3)—121no—
72C2×H(3,𝔽3)—31no—
73C2×H(3,𝔽3)—61no—
74C2×C3×C9—31no—
75C3⋊D9—61no—
76C3⋊D9—121no—
77C3⋊D9—121no—
78C3⋊D9—361no—
79C3⋊D9—362no—
80AGL(1,ℤ/9)—362no—
81(C3⋊D3)⋊C3—181no—
82C3×D9—361no—
83C22×C32—31no—
84C22×C32—61no—
85C22×C32C3×C3⋊D311yescharacteristic
86C2×C3⋊D3—91no—
87C2×C3×D3—271no—
88C3×A4—31no—
89C3×A4—33no—
90C3⋊Dic3—91no—
91C3×Dic3—271no—
92C22×C9—31no—
93C2×D9—271no—
94C22⋊C9—31no—
95C22⋊C9—61no—
96C22⋊C9—61no—
97C22⋊C9—61no—
98C22⋊C9(C3⋊D3)⋊C311yescharacteristic
99C22⋊C9(C3⋊D3)⋊C312yes—
100Dic9—271no—
101C33—41no—
1023−1+2—81no—
1033−1+2—81no—
1043−1+2—81no—
1053−1+2—122no—
1063−1+2—242no—
107H(3,𝔽3)—21no—
108H(3,𝔽3)C3⋊S411yescharacteristic
109C3×C9—41no—
110C3×C9—41no—
111C3×C9—121no—
112C3×C9—122no—
113C3×C9—121no—
114C3×C9—241no—
115C3×C9C3×S411yescharacteristic
116S4—813no—
117C3×D4—811no—
118#67—271no—
119#67—811no—
120C2×C32—31no—
121C2×C32—91no—
122C2×C32—181no—
123C3⋊D3—181no—
124C3⋊D3—1081no—
125C3⋊D3—1083no—
126C3×D3—541no—
127C2×C9—91no—
128D9—361no—
129D9—362no—
130D9—541no—
131D9—1081no—
132C22×C3—31no—
133C22×C3—91no—
134C22×C3—181no—
135C22×C3—811no—
136C22×C3C3⋊((C3⋊D3)⋊C3)11yescharacteristic
137C2×D3—271no—
138C2×D3—811no—
139A4—33no—
140C3×C4—811no—
141Dic3—271no—
142Dic3—811no—
143C32—31no—
144C32—61no—
145C32—123no—
146C32—121no—
147C32C3×C3⋊S411yescharacteristic
148C9—31no—
149C9—41no—
150C9—42no—
151C9—121no—
152C9—241no—
153C9—241no—
154C9—241no—
155D4—811noSylow
156C2×C3—31no—
157C2×C3—91no—
158C2×C3—271no—
159C2×C3—541no—
160C2×C3—1621no—
161D3—541no—
162D3—3243no—
163D3—1621no—
164C22—811no—
165C22#9233011yescharacteristic, complemented
166C4—811no—
167C3—31no—
168C3—91no—
169C3—123no—
170C3—181no—
171C3A4⋊((C3⋊D3)⋊C3)11yescharacteristic
172C2—31no—
173C2—1621no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC3×C9×A4C2×C3
FrattiniC32C3×C3⋊S4
FittingC22×#732D3
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. #11757806C2semidirect
2. C3⋊(C9⋊S4)C3semidirect
9. #66437D3semidirect
10. C3×C9×A4C2×C3semidirect
11. C22×#732D3semidirect
16. #66361D3semidirect
58. #732S4semidirect
165. C22#92330semidirect

Maximal subgroups

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

subgroupindex
#117578062
C3⋊(C9⋊S4)3
#106200473
#106197453
#106197443
#106196503
#923304