Finite Group Databasebeta

← #10620047⋊C3 #14519198

Subgroups — #10620047⋊C3 #14519198

Order 1944.

440 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 56 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#11758099C211yesmaximal, characteristic, complemented
2C3⋊(((C22⋊C9)⋊C2)⋊C3)C311yesmaximal, characteristic, complemented
3#10620047C313yesmaximal, complemented
4C3×((C22⋊C9)⋊C2)⋊C3—33nomaximal
5C3×#638⋊C3—31nomaximal
6#4207⋊C3—41nomaximal
7C22×C3×H(3,𝔽3)D311yescharacteristic
8C2×C3×(C3⋊D3)⋊C3—31no—
9C3×#1094—21no—
10C3×#1094—23no—
11C3×#1094D313yescomplemented
12C3×#1094C2×C311yescharacteristic, complemented
13#66437—23no—
14#66437—26no—
15#66437—23no—
16#66437C2×C313yescomplemented
17C3×(C3⋊Dic3)⋊C3—31no—
183−1+4—41noSylow
19C3×#638—31no—
20C32×#67—91no—
21C3⋊((C22⋊C9)⋊C2)C3211yescharacteristic, complemented
22C3×(C22⋊C9)⋊C2—33no—
23((C22⋊C9)⋊C2)⋊C3—33no—
24((C22⋊C9)⋊C2)⋊C3—36no—
25#638⋊C3—33no—
26C2×C3×H(3,𝔽3)—31no—
27#4207—43no—
28C3⋊AGL(1,ℤ/9)—41no—
29C3×AGL(1,ℤ/9)—123no—
30C3×(C3⋊D3)⋊C3—61no—
31C22×C33—21no—
32C22×C33C3×D311yescharacteristic
33C22×C33C3⋊D311yescharacteristic
34C2×C3×C3⋊D3—31no—
35C2×C32×D3—91no—
36C3×C3⋊Dic3—31no—
37C32×Dic3—91no—
38C22×H(3,𝔽3)—23no—
39C22×H(3,𝔽3)C3×D313yes—
40C2×(C3⋊D3)⋊C3—33no—
41#1094—26no—
42#1094—26no—
43#1094—22no—
44#1094—21no—
45#1094—23no—
46#1094—26no—
47#1094—23no—
48#1094—23no—
49#1094—26no—
50#1094C3×D313yes—
51#1094C3×D316yescomplemented
52C3×C22⋊C9—23no—
53C3×C22⋊C9—23no—
54C3×C22⋊C9—23no—
55C3×C22⋊C9—21no—
56C3×C22⋊C9—23no—
57C3×C22⋊C9—23no—
58C3×C22⋊C9C3×D313yescomplemented
59C3×C22⋊C9C2×C3211yescharacteristic, complemented
60(C3⋊Dic3)⋊C3—33no—
61#737—43no—
62#737—83no—
63#737—86no—
64#737—83no—
65C3×3−1+2—41no—
66C3×3−1+2—43no—
67C3×3−1+2—83no—
68C3×3−1+2—81no—
69C3×H(3,𝔽3)S411yescharacteristic
70C32×D4—271no—
71#638—31no—
72C3×#67—93no—
73C3×#67—91no—
74C3×#67—271no—
75(C22⋊C9)⋊C2—33no—
76C2×C33—31no—
77C2×C33—31no—
78C2×C33—61no—
79C3×C3⋊D3—61no—
80C32×D3—181no—
81C2×H(3,𝔽3)—33no—
82C2×H(3,𝔽3)—63no—
83C3⋊D9—41no—
84AGL(1,ℤ/9)—123no—
85AGL(1,ℤ/9)—126no—
86(C3⋊D3)⋊C3—63no—
87C3×D9—123no—
88C22×C32—21no—
89C22×C32—23no—
90C22×C32—91no—
91C22×C32—91no—
92C22×C32—181no—
93C22×C32—271no—
94C22×C32C32×D311yescharacteristic
95C22×C32C3×C3⋊D313yes—
96C22×C32C3×C3⋊D311yescharacteristic
97C2×C3⋊D3—31no—
98C2×C3×D3—93no—
99C2×C3×D3—91no—
100C2×C3×D3—271no—
101C32×C4—271no—
102C3⋊Dic3—31no—
103C3×Dic3—93no—
104C3×Dic3—91no—
105C3×Dic3—271no—
106C22⋊C9—23no—
107C22⋊C9—26no—
108C22⋊C9—23no—
109C22⋊C9C32×D313yes—
110C33—21no—
111C33C3×S411yescharacteristic
112C33C3⋊S411yescharacteristic
1133−1+2—43no—
1143−1+2—46no—
1153−1+2—83no—
1163−1+2—86no—
1173−1+2—81no—
1183−1+2—86no—
1193−1+2—82no—
1203−1+2—86no—
1213−1+2—83no—
1223−1+2—83no—
1233−1+2—86no—
124H(3,𝔽3)—23no—
125H(3,𝔽3)C3×S413yes—
126C3×C9—41no—
127C3×C9—43no—
128C3×C9—83no—
129C3×C9—83no—
130C3×C9—83no—
131C3×C9—83no—
132C3×C9—81no—
133C3×C9—83no—
134C3×D4—271no—
135C3×D4—273no—
136#67—91no—
137#67—271no—
138C2×C32—31no—
139C2×C32—31no—
140C2×C32—33no—
141C2×C32—63no—
142C2×C32—61no—
143C2×C32—91no—
144C2×C32—91no—
145C2×C32—181no—
146C2×C32—181no—
147C2×C32—181no—
148C2×C32—182no—
149C2×C32—541no—
150C3⋊D3—61no—
151C3×D3—183no—
152C3×D3—181no—
153C3×D3—541no—
154D9—123no—
155C22×C3—31no—
156C22×C3—31no—
157C22×C3—33no—
158C22×C3—61no—
159C22×C3—63no—
160C22×C3—271no—
161C22×C3—273no—
162C22×C3C32×C3⋊D311yescharacteristic
163C2×D3—91no—
164C2×D3—271no—
165C3×C4—271no—
166C3×C4—273no—
167Dic3—91no—
168Dic3—271no—
169C32—21no—
170C32—23no—
171C32—91no—
172C32—91no—
173C32—181no—
174C32C32×S411yescharacteristic
175C32C3×C3⋊S413yes—
176C32C3×C3⋊S411yescharacteristic
177C9—43no—
178C9—83no—
179C9—86no—
180C9—83no—
181D4—271noSylow
182C2×C3—31no—
183C2×C3—31no—
184C2×C3—61no—
185C2×C3—91no—
186C2×C3—93no—
187C2×C3—181no—
188C2×C3—183no—
189C2×C3—541no—
190C2×C3—543no—
191D3—181no—
192D3—541no—
193C22—271no—
194C22#4207⋊C311yescharacteristic, complemented
195C4—271no—
196C3—31no—
197C3—31no—
198C3—33no—
199C3—61no—
200C3—63no—
201C3C32×C3⋊S411yescharacteristic
202C2—31no—
203C2—541no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC3×C22⋊C9C2×C32
FrattiniC3C32×C3⋊S4
FittingC22×C3×H(3,𝔽3)D3
socleC22×C3C32×C3⋊D3
LCSG ▷ C3×C22⋊C9
UCSC1

Complements

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

NH ≅ G/Ntype
1. #11758099C2semidirect
2. C3⋊(((C22⋊C9)⋊C2)⋊C3)C3semidirect
3. #10620047C3semidirect
11. C3×#1094D3semidirect
12. C3×#1094C2×C3semidirect
16. #66437C2×C3semidirect
21. C3⋊((C22⋊C9)⋊C2)C32semidirect
51. #1094C3×D3semidirect
58. C3×C22⋊C9C3×D3semidirect
59. C3×C22⋊C9C2×C32semidirect
194. C22#4207⋊C3semidirect

Maximal subgroups

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

subgroupindex
#117580992
C3⋊(((C22⋊C9)⋊C2)⋊C3)3
#106200473
C3×((C22⋊C9)⋊C2)⋊C33
C3×#638⋊C33
#4207⋊C34