Finite Group Databasebeta

← #10620045⋊C3 #14519207

Subgroups — #10620045⋊C3 #14519207

Order 1944.

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

normal subgroups only

This group has 426 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#11758104C211yesmaximal, characteristic, complemented
2A4⋊AGL(1,ℤ/9)C311yesmaximal, characteristic, complemented
3#66440⋊C2C312yesmaximal, complemented
4#10620045C311yesmaximal, characteristic, complemented
5C3×(C3⋊S4)⋊C3—31nomaximal
6C3×((C22⋊C9)⋊C2)⋊C3—32nomaximal
7C3×#611⋊C3—31nomaximal
8#4207⋊C3—41nomaximal
9C22×C3×3−1+2D311yescharacteristic, complemented
10C2×C3×AGL(1,ℤ/9)—31no—
11C3×C22⋊H(3,𝔽3)D311yescharacteristic
12C3×#1094D312yescomplemented
13#66440—22no—
14#66440—22no—
15#66440—22no—
16#66440—22no—
17#66440C2×C312yescomplemented
18A4×3−1+2—21no—
19A4×3−1+2—21no—
20A4×3−1+2—22no—
21A4×3−1+2C2×C311yescharacteristic, complemented
22#66436—21no—
23#66436—21no—
24#66436—22no—
25#66436C2×C311yescharacteristic, complemented
26C3×3−1+2⋊C4—31no—
273−1+4—41noSylow
28C3×C3⋊S4—31no—
29C32×#67—91no—
30C9⋊S4C3211yescharacteristic, complemented
31(C3⋊S4)⋊C3—31no—
32(C3⋊S4)⋊C3—32no—
33C3×(C22⋊C9)⋊C2—32no—
34((C22⋊C9)⋊C2)⋊C3—32no—
35((C22⋊C9)⋊C2)⋊C3—32no—
36((C22⋊C9)⋊C2)⋊C3—32no—
37#611⋊C3—31no—
38#611⋊C3—32no—
39C3×#611—31no—
40C2×C3×3−1+2—31no—
41#4207—41no—
42#4207—42no—
43C3⋊AGL(1,ℤ/9)—41no—
44C3×AGL(1,ℤ/9)—61no—
45C3×AGL(1,ℤ/9)—122no—
46C3×(C3⋊D3)⋊C3—121no—
47C22×C33C3⋊D311yescharacteristic
48C2×C32×D3—91no—
49C32×A4—21no—
50C32×A4C3×D311yescharacteristic
51C32×Dic3—91no—
52C22×3−1+2—21no—
53C22×3−1+2—22no—
54C22×3−1+2C3×D311yescharacteristic
55C22×3−1+2C3×D312yescomplemented
56C22×C3×C9—21no—
57C22×C3×C9C3×D311yescharacteristic, complemented
58C2×AGL(1,ℤ/9)—31no—
59C2×AGL(1,ℤ/9)—32no—
60C2×C3×D9—31no—
61C22⋊H(3,𝔽3)—21no—
62C22⋊H(3,𝔽3)—22no—
63C22⋊H(3,𝔽3)C3×D311yescharacteristic
64C22⋊H(3,𝔽3)C3×D312yes—
65#1094—22no—
66#1094—22no—
67#1094—22no—
68#1094C3×D312yes—
69#1094C3×D312yescomplemented
70#1094C3×D312yescomplemented
71C3×C22⋊C9—22no—
72C3×C22⋊C9C3×D312yescomplemented
73C9⋊A4—22no—
74C9⋊A4—22no—
75C9⋊A4—22no—
76C9⋊A4—22no—
77C9⋊A4—22no—
78C9⋊A4—22no—
79C9⋊A4—22no—
80C9⋊A4—21no—
81C9⋊A4—22no—
82C9⋊A4—21no—
83C9⋊A4—22no—
84C9⋊A4—21no—
85C9⋊A4—22no—
86C9⋊A4—22no—
87C9⋊A4—22no—
88C9×A4—22no—
89C9×A4—22no—
90C9×A4—21no—
91C9×A4—21no—
92C9×A4—22no—
93C9×A4—21no—
94C9×A4—21no—
95C9×A4—21no—
96C9×A4—22no—
97C9×A4C2×C3211yescharacteristic, complemented
983−1+2⋊C4—31no—
993−1+2⋊C4—32no—
100C3×Dic9—31no—
101#737—42no—
102#737—41no—
103#737—81no—
104#737—82no—
105#737—82no—
106#737—82no—
107#737—82no—
108#737—82no—
109#737—81no—
110C3×3−1+2—42no—
111C3×3−1+2—41no—
112C3×3−1+2—82no—
113C3×3−1+2—81no—
114C3×3−1+2—81no—
115C3×3−1+2S411yescharacteristic, complemented
116C3×H(3,𝔽3)—41no—
117C3⋊S4—31no—
118C3×S4—271no—
119C32×D4—271no—
120C3×#67—91no—
121C3×#67—91no—
122C3×#67—92no—
123(C22⋊C9)⋊C2—32no—
124#611—31no—
125C2×C33—31no—
126C3×C3⋊D3—121no—
127C32×D3—181no—
128C2×3−1+2—31no—
129C2×3−1+2—32no—
130C2×3−1+2—61no—
131C2×3−1+2—62no—
132C2×C3×C9—31no—
133C2×C3×C9—61no—
134C3⋊D9—41no—
135AGL(1,ℤ/9)—61no—
136AGL(1,ℤ/9)—62no—
137AGL(1,ℤ/9)—122no—
138AGL(1,ℤ/9)—122no—
139AGL(1,ℤ/9)—122no—
140(C3⋊D3)⋊C3—121no—
141(C3⋊D3)⋊C3—122no—
142C3×D9—61no—
143C3×D9—122no—
144C22×C32—91no—
145C22×C32—271no—
146C22×C32C3×C3⋊D312yes—
147C22×C32C3×C3⋊D311yescharacteristic
148C22×C32C3×C3⋊D311yescharacteristic
149C2×C3×D3—91no—
150C2×C3×D3—92no—
151C2×C3×D3—91no—
152C3×A4—21no—
153C3×A4—21no—
154C3×A4—22no—
155C3×A4—91no—
156C3×A4—181no—
157C3×A4C32×D311yescharacteristic
158C32×C4—271no—
159C3×Dic3—91no—
160C3×Dic3—91no—
161C3×Dic3—92no—
162C22×C9—21no—
163C22×C9—22no—
164C22×C9—21no—
165C22×C9C32×D311yescharacteristic
166C2×D9—31no—
167C22⋊C9—22no—
168C22⋊C9—22no—
169C22⋊C9—22no—
170C22⋊C9—22no—
171C22⋊C9C32×D312yes—
172Dic9—31no—
173C33—41no—
174C33—81no—
175C33C3⋊S411yescharacteristic
1763−1+2—21no—
1773−1+2—22no—
1783−1+2—42no—
1793−1+2—42no—
1803−1+2—42no—
1813−1+2—82no—
1823−1+2—82no—
1833−1+2—82no—
1843−1+2—82no—
1853−1+2—81no—
1863−1+2—82no—
1873−1+2—82no—
1883−1+2—82no—
1893−1+2—82no—
1903−1+2—82no—
1913−1+2—82no—
1923−1+2—81no—
1933−1+2—82no—
1943−1+2—82no—
1953−1+2—82no—
1963−1+2—82no—
1973−1+2—81no—
1983−1+2—82no—
1993−1+2C3×S411yescharacteristic
2003−1+2C3×S412yescomplemented
201H(3,𝔽3)—41no—
202H(3,𝔽3)—42no—
203H(3,𝔽3)—81no—
204H(3,𝔽3)—82no—
205C3×C9—21no—
206C3×C9—41no—
207C3×C9—42no—
208C3×C9—82no—
209C3×C9—81no—
210C3×C9—81no—
211C3×C9—81no—
212C3×C9—82no—
213C3×C9—82no—
214C3×C9—82no—
215C3×C9—81no—
216C3×C9—82no—
217C3×C9—81no—
218C3×C9C3×S411yescharacteristic, complemented
219S4—271no—
220C3×D4—271no—
221C3×D4—272no—
222C3×D4—271no—
223#67—91no—
224C2×C32—31no—
225C2×C32—32no—
226C2×C32—31no—
227C2×C32—91no—
228C2×C32—181no—
229C2×C32—541no—
230C3⋊D3—121no—
231C3×D3—181no—
232C3×D3—182no—
233C3×D3—181no—
234C3×D3—1081no—
235C2×C9—31no—
236C2×C9—61no—
237C2×C9—61no—
238C2×C9—62no—
239D9—61no—
240D9—122no—
241C22×C3—31no—
242C22×C3—31no—
243C22×C3—32no—
244C22×C3—271no—
245C22×C3—271no—
246C22×C3—272no—
247C22×C3C32×C3⋊D311yescharacteristic
248C2×D3—91no—
249A4—31no—
250A4—61no—
251A4—61no—
252A4—62no—
253C3×C4—271no—
254C3×C4—272no—
255C3×C4—271no—
256Dic3—91no—
257C32—41no—
258C32—82no—
259C32—81no—
260C32—81no—
261C32—91no—
262C32—361no—
263C32—721no—
264C32C3×C3⋊S411yescharacteristic
265C32C3×C3⋊S412yes—
266C32C3×C3⋊S411yescharacteristic
267C9—21no—
268C9—22no—
269C9—21no—
270C9—42no—
271C9—82no—
272C9—82no—
273C9—82no—
274C9—82no—
275C9C32×S411yescharacteristic
276D4—271noSylow
277C2×C3—31no—
278C2×C3—31no—
279C2×C3—61no—
280C2×C3—91no—
281C2×C3—92no—
282C2×C3—541no—
283C2×C3—541no—
284C2×C3—542no—
285D3—181no—
286D3—1081no—
287C22—271no—
288C22#4207⋊C311yescharacteristic, complemented
289C4—271no—
290C3—31no—
291C3—31no—
292C3—32no—
293C3—121no—
294C3—241no—
295C3—242no—
296C3—241no—
297C3C32×C3⋊S411yescharacteristic
298C2—31no—
299C2—541no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC9×A4C2×C32
FrattiniC3C32×C3⋊S4
FittingC22×C3×3−1+2D3
socleC22×C3C32×C3⋊D3
LCSG ▷ C9×A4
UCSC1

Complements

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

NH ≅ G/Ntype
1. #11758104C2semidirect
2. A4⋊AGL(1,ℤ/9)C3semidirect
3. #66440⋊C2C3semidirect
4. #10620045C3semidirect
9. C22×C3×3−1+2D3semidirect
12. C3×#1094D3semidirect
17. #66440C2×C3semidirect
21. A4×3−1+2C2×C3semidirect
25. #66436C2×C3semidirect
30. C9⋊S4C32semidirect
55. C22×3−1+2C3×D3semidirect
57. C22×C3×C9C3×D3semidirect
69. #1094C3×D3semidirect
70. #1094C3×D3semidirect
72. C3×C22⋊C9C3×D3semidirect
97. C9×A4C2×C32semidirect
115. C3×3−1+2S4semidirect
200. 3−1+2C3×S4semidirect
218. C3×C9C3×S4semidirect
288. C22#4207⋊C3semidirect

Maximal subgroups

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

subgroupindex
#117581042
A4⋊AGL(1,ℤ/9)3
#66440⋊C23
#106200453
C3×(C3⋊S4)⋊C33
C3×((C22⋊C9)⋊C2)⋊C33
C3×#611⋊C33
#4207⋊C34