Finite Group Databasebeta

← #14518026

Subgroups — #14518026

Order 1944.

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

normal subgroups only

This group has 222 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#11757798C211yesmaximal, characteristic, complemented
2C3⋊(C3⋊((C22⋊C9)⋊C2))C311yesmaximal, characteristic, complemented
3#10620047—31nomaximal
4#10619744—31nomaximal
5#10619743—31nomaximal
6#10619642—31nomaximal
7#92330—41nomaximal
8C32×C22⋊C9C2×C311yescharacteristic, complemented
9#66440—21no—
10#66437D311yescharacteristic, complemented
11C22×AΣL(1,𝔽27)D311yescharacteristic
12C2×#4175—31no—
13#66368—21no—
14#66365—21no—
15#66364—21no—
16#66362D311yescharacteristic, complemented
17#66361D311yescharacteristic, complemented
18#66322—31no—
19#6908—41noSylow
20#6312—31no—
21C3⋊((C22⋊C9)⋊C2)—31no—
22C3⋊((C22⋊C9)⋊C2)—31no—
23C3⋊((C22⋊C9)⋊C2)—31no—
24C3⋊((C22⋊C9)⋊C2)—92no—
25C3⋊((C22⋊C9)⋊C2)—91no—
26C3×(C22⋊C9)⋊C2—91no—
27((C22⋊C9)⋊C2)⋊C3—92no—
28#638⋊C3—91no—
29C3⋊(C3⋊D9)—41no—
30#4207—121no—
31C2×AΣL(1,𝔽27)—31no—
32#4179—121no—
33#4177—121no—
34#4175—61no—
35C22×C33C3×D311yescharacteristic
36C2×C3⋊(C3⋊D3)—31no—
37C3⋊(C3⋊Dic3)—31no—
38C22×3−1+2—21no—
39C22×H(3,𝔽3)C3⋊D311yescharacteristic
40C2×(C3⋊D3)⋊C3—91no—
41C22⋊H(3,𝔽3)—21no—
42#1094—21no—
43#1094—21no—
44#1094—32no—
45C3×C22⋊C9—31no—
46C3×C22⋊C9—32no—
47C3×C22⋊C9—31no—
48C3×C22⋊C9C3×D311yescharacteristic
49C3×C22⋊C9C3×D311yescharacteristic
50C3×C22⋊C9C3×D311yescharacteristic
51C9⋊A4—62no—
52C9×A4—61no—
53(C3⋊Dic3)⋊C3—91no—
54#737—41no—
55#737—81no—
56C32×C9—41no—
57#733—81no—
58#732—41no—
59#731—41no—
60#731—81no—
61AΣL(1,𝔽27)—81no—
62AΣL(1,𝔽27)S411yescharacteristic
63#638—91no—
64#638—271no—
65#638—273no—
66C3×#67—271no—
67(C22⋊C9)⋊C2—92no—
68(C22⋊C9)⋊C2—91no—
69(C22⋊C9)⋊C2—271no—
70(C22⋊C9)⋊C2—271no—
71C2×C33—31no—
72C3⋊(C3⋊D3)—61no—
73C2×3−1+2—61no—
74C2×H(3,𝔽3)—31no—
75C3⋊D9—121no—
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—33no—
85C22×C32—31no—
86C22×C32C3×C3⋊D311yescharacteristic
87C2×C3⋊D3—91no—
88C2×C3⋊D3—271no—
89C2×C3⋊D3—273no—
90C2×C3×D3—271no—
91C3×A4—61no—
92C3⋊Dic3—91no—
93C3⋊Dic3—271no—
94C3⋊Dic3—273no—
95C3×Dic3—271no—
96C22×C9—61no—
97C22⋊C9—31no—
98C22⋊C9—31no—
99C22⋊C9—61no—
100C22⋊C9—61no—
101C22⋊C9(C3⋊D3)⋊C311yescharacteristic
102C22⋊C9(C3⋊D3)⋊C312yes—
103C33C3×S411yescharacteristic
1043−1+2—21no—
1053−1+2—81no—
1063−1+2—81no—
1073−1+2—122no—
1083−1+2—242no—
109H(3,𝔽3)—81no—
110H(3,𝔽3)C3⋊S411yescharacteristic
111C3×C9—41no—
112C3×C9—41no—
113C3×C9—41no—
114C3×C9—121no—
115C3×C9—122no—
116C3×C9—121no—
117C3×C9—241no—
118C3×D4—811no—
119#67—271no—
120#67—811no—
121#67—813no—
122C2×C32—31no—
123C2×C32—91no—
124C2×C32—91no—
125C2×C32—93no—
126C3⋊D3—181no—
127C3⋊D3—541no—
128C3⋊D3—543no—
129C3×D3—541no—
130C2×C9—181no—
131D9—361no—
132D9—362no—
133D9—1081no—
134D9—1081no—
135C22×C3—33no—
136C22×C3—31no—
137C22×C3—91no—
138C22×C3—811no—
139C22×C3C3⋊((C3⋊D3)⋊C3)11yescharacteristic
140C2×D3—271no—
141C2×D3—811no—
142C2×D3—813no—
143A4—181no—
144C3×C4—811no—
145Dic3—271no—
146Dic3—811no—
147Dic3—813no—
148C32—33no—
149C32—31no—
150C32—31no—
151C32—241no—
152C32C3×C3⋊S411yescharacteristic
153C9—41no—
154C9—42no—
155C9—61no—
156C9—121no—
157C9—121no—
158C9—241no—
159C9—241no—
160D4—811noSylow
161C2×C3—31no—
162C2×C3—91no—
163C2×C3—93no—
164C2×C3—271no—
165C2×C3—1621no—
166D3—541no—
167D3—1621no—
168D3—1623no—
169C22—811no—
170C22#9233011yescharacteristic, complemented
171C4—811no—
172C3—33no—
173C3—31no—
174C3—91no—
175C3—721no—
176C3A4⋊((C3⋊D3)⋊C3)11yescharacteristic
177C2—31no—
178C2—1621no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC32×C22⋊C9C2×C3
FrattiniC32C3×C3⋊S4
FittingC22×AΣL(1,𝔽27)D3
socleC22×C3C3⋊((C3⋊D3)⋊C3)
LCSG ▷ C32×C22⋊C9
UCSC1

Complements

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

NH ≅ G/Ntype
1. #11757798C2semidirect
2. C3⋊(C3⋊((C22⋊C9)⋊C2))C3semidirect
8. C32×C22⋊C9C2×C3semidirect
10. #66437D3semidirect
16. #66362D3semidirect
17. #66361D3semidirect
170. C22#92330semidirect

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
#106200473
#106197443
#106197433
#106196423
#923304