Finite Group Databasebeta

← #10619679⋊C3 #14517712

Subgroups — #10619679⋊C3 #14517712

Order 1944.

416 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 57 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
1C22×#6909C211yesmaximal, characteristic, complemented
2C2×#4183⋊C3C211yesmaximal, characteristic, complemented
3#66330⋊C3C211yesmaximal, characteristic, complemented
4C3×#611⋊C3—32nomaximal
5C3×#638⋊C3—31nomaximal
6C3×#638⋊C3—31nomaximal
7#10619679C311yesmaximal, characteristic, complemented
8C2×#6909—21no—
9C2×#6909C2211yescharacteristic
10#4183⋊C3—21no—
11C22×C3×3−1+2D312yescomplemented
12C22×C3×H(3,𝔽3)D311yescharacteristic, complemented
13C22×C3×H(3,𝔽3)D311yescharacteristic, complemented
14C2×C3×AGL(1,ℤ/9)—32no—
15C2×C3×(C3⋊D3)⋊C3—31no—
16C2×C3×(C3⋊D3)⋊C3—31no—
17C3×3−1+2⋊C4—32no—
18C3×(C3⋊Dic3)⋊C3—31no—
19C3×(C3⋊Dic3)⋊C3—31no—
20C22×AΣL(1,𝔽27)—21no—
21C22×AΣL(1,𝔽27)—22no—
22C22×AΣL(1,𝔽27)—21no—
23C22×AΣL(1,𝔽27)C2×C311yescharacteristic, complemented
24C2×#4183C2×C311yescharacteristic, complemented
25#66330C2×C311yescharacteristic, complemented
26#6909D411yescharacteristic, complemented, Sylow
27C3×#638—31no—
28C3×#638—31no—
29C32×#67—91no—
30#611⋊C3—32no—
31#611⋊C3—32no—
32#611⋊C3—32no—
33#638⋊C3—32no—
34#638⋊C3—32no—
35#638⋊C3—31no—
36#638⋊C3—31no—
37C3×#611—32no—
38C2×C3×3−1+2—22no—
39C2×C3×3−1+2C2×D312yes—
40C2×C3×H(3,𝔽3)—21no—
41C2×C3×H(3,𝔽3)—21no—
42C2×C3×H(3,𝔽3)C2×D311yescharacteristic
43C2×C3×H(3,𝔽3)C2×D311yescharacteristic
44C3×AGL(1,ℤ/9)—62no—
45C3×(C3⋊D3)⋊C3—61no—
46C3×(C3⋊D3)⋊C3—61no—
47C2×AΣL(1,𝔽27)—22no—
48C2×AΣL(1,𝔽27)—24no—
49C2×AΣL(1,𝔽27)—22no—
50C2×AΣL(1,𝔽27)—21no—
51C2×AΣL(1,𝔽27)—21no—
52C2×AΣL(1,𝔽27)—22no—
53C2×AΣL(1,𝔽27)—21no—
54C2×AΣL(1,𝔽27)C22×C311yescharacteristic
55#4183—21no—
56C22×C33—21no—
57C22×C33—31no—
58C22×C33C3×D311yescharacteristic, complemented
59C22×C33C3⋊D311yescharacteristic
60C2×C3×C3⋊D3—31no—
61C2×C3×C3⋊D3—31no—
62C2×C32×D3—91no—
63C3×C3⋊Dic3—31no—
64C3×C3⋊Dic3—31no—
65C32×Dic3—91no—
66C22×3−1+2—22no—
67C22×3−1+2—32no—
68C22×3−1+2—32no—
69C22×3−1+2C3×D312yescomplemented
70C22×H(3,𝔽3)—21no—
71C22×H(3,𝔽3)—32no—
72C22×H(3,𝔽3)—31no—
73C22×H(3,𝔽3)—32no—
74C22×H(3,𝔽3)C3×D311yescharacteristic
75C22×C3×C9—32no—
76C2×AGL(1,ℤ/9)—32no—
77C2×AGL(1,ℤ/9)—32no—
78C2×AGL(1,ℤ/9)—32no—
79C2×(C3⋊D3)⋊C3—32no—
80C2×(C3⋊D3)⋊C3—32no—
81C2×(C3⋊D3)⋊C3—31no—
82C2×(C3⋊D3)⋊C3—31no—
83C2×C3×D9—32no—
843−1+2⋊C4—32no—
853−1+2⋊C4—32no—
863−1+2⋊C4—32no—
87(C3⋊Dic3)⋊C3—32no—
88(C3⋊Dic3)⋊C3—32no—
89(C3⋊Dic3)⋊C3—31no—
90(C3⋊Dic3)⋊C3—31no—
91C3×Dic9—32no—
92C3×3−1+2#6712yescomplemented
93C3×H(3,𝔽3)#6711yescharacteristic, complemented
94C3×H(3,𝔽3)#6711yescharacteristic, complemented
95AΣL(1,𝔽27)—21no—
96AΣL(1,𝔽27)—22no—
97AΣL(1,𝔽27)—21no—
98AΣL(1,𝔽27)C3×D411yescharacteristic, complemented
99C32×D4—271no—
100#638—31no—
101#638—31no—
102C3×#67—92no—
103C3×#67—91no—
104C3×#67—91no—
105C3×#67—271no—
106C3×#67—271no—
107#611—32no—
108C2×C33—21no—
109C2×C33—22no—
110C2×C33—21no—
111C2×C33—21no—
112C2×C33—31no—
113C2×C33—61no—
114C2×C33C2×C3×D311yescharacteristic
115C2×C33C2×C3⋊D311yescharacteristic
116C3×C3⋊D3—61no—
117C3×C3⋊D3—61no—
118C32×D3—181no—
119C2×3−1+2—24no—
120C2×3−1+2—22no—
121C2×3−1+2—22no—
122C2×3−1+2—32no—
123C2×3−1+2—32no—
124C2×3−1+2—62no—
125C2×3−1+2—62no—
126C2×3−1+2C2×C3×D312yes—
127C2×H(3,𝔽3)—22no—
128C2×H(3,𝔽3)—21no—
129C2×H(3,𝔽3)—21no—
130C2×H(3,𝔽3)—32no—
131C2×H(3,𝔽3)—31no—
132C2×H(3,𝔽3)—32no—
133C2×H(3,𝔽3)—62no—
134C2×H(3,𝔽3)—62no—
135C2×H(3,𝔽3)—61no—
136C2×H(3,𝔽3)C2×C3×D311yescharacteristic
137C2×C3×C9—32no—
138C2×C3×C9—62no—
139AGL(1,ℤ/9)—62no—
140AGL(1,ℤ/9)—62no—
141AGL(1,ℤ/9)—62no—
142(C3⋊D3)⋊C3—62no—
143(C3⋊D3)⋊C3—62no—
144(C3⋊D3)⋊C3—61no—
145(C3⋊D3)⋊C3—61no—
146C3×D9—62no—
147C22×C32—31no—
148C22×C32—31no—
149C22×C32—61no—
150C22×C32—61no—
151C22×C32—91no—
152C22×C32—91no—
153C22×C32—91no—
154C22×C32—181no—
155C22×C32—181no—
156C22×C32—271no—
157C22×C32#27212yes—
158C22×C32#27211yescharacteristic
159C22×C32C3×C3⋊D311yescharacteristic
160C2×C3⋊D3—31no—
161C2×C3⋊D3—31no—
162C2×C3×D3—92no—
163C2×C3×D3—91no—
164C2×C3×D3—91no—
165C2×C3×D3—271no—
166C2×C3×D3—271no—
167C32×C4—271no—
168C3⋊Dic3—31no—
169C3⋊Dic3—31no—
170C3×Dic3—92no—
171C3×Dic3—91no—
172C3×Dic3—91no—
173C3×Dic3—271no—
174C3×Dic3—271no—
175C22×C9—32no—
176C22×C9—62no—
177C2×D9—32no—
178Dic9—32no—
179C33—21no—
180C33—31no—
181C33C3×#6711yescharacteristic, complemented
182C33#63811yescharacteristic
1833−1+2—22no—
1843−1+2—32no—
1853−1+2—32no—
1863−1+2C3×#6712yescomplemented
187H(3,𝔽3)—21no—
188H(3,𝔽3)—32no—
189H(3,𝔽3)—31no—
190H(3,𝔽3)—32no—
191H(3,𝔽3)C3×#6711yescharacteristic
192C3×C9—32no—
193C3×D4—271no—
194C3×D4—271no—
195C3×D4—272no—
196#67—91no—
197#67—271no—
198#67—271no—
199C2×C32—22no—
200C2×C32—21no—
201C2×C32—21no—
202C2×C32—31no—
203C2×C32—31no—
204C2×C32—61no—
205C2×C32—61no—
206C2×C32—62no—
207C2×C32—62no—
208C2×C32—61no—
209C2×C32—61no—
210C2×C32—91no—
211C2×C32—91no—
212C2×C32—91no—
213C2×C32—181no—
214C2×C32—181no—
215C2×C32—181no—
216C2×C32—181no—
217C2×C32—182no—
218C2×C32—181no—
219C2×C32—182no—
220C2×C32—541no—
221C2×C32C2×#27212yes—
222C2×C32C2×#27211yescharacteristic
223C2×C32C2×C3×C3⋊D311yescharacteristic
224C3⋊D3—61no—
225C3⋊D3—61no—
226C3×D3—182no—
227C3×D3—181no—
228C3×D3—181no—
229C3×D3—541no—
230C3×D3—541no—
231C2×C9—32no—
232C2×C9—62no—
233C2×C9—64no—
234C2×C9—62no—
235D9—62no—
236C22×C3—31no—
237C22×C3—31no—
238C22×C3—32no—
239C22×C3—91no—
240C22×C3—91no—
241C22×C3—181no—
242C22×C3—181no—
243C22×C3—271no—
244C22×C3—271no—
245C22×C3—272no—
246C22×C3C3×#27211yescharacteristic
247C2×D3—91no—
248C2×D3—271no—
249C2×D3—271no—
250C3×C4—271no—
251C3×C4—271no—
252C3×C4—272no—
253Dic3—91no—
254Dic3—271no—
255Dic3—271no—
256C32—31no—
257C32—31no—
258C32—61no—
259C32—61no—
260C32—91no—
261C32—91no—
262C32—91no—
263C32—181no—
264C32—181no—
265C32#623512yes—
266C32#623511yescharacteristic
267C32C3×#63811yescharacteristic
268C9—32no—
269C9—62no—
270D4—271noSylow
271C2×C3—21no—
272C2×C3—31no—
273C2×C3—31no—
274C2×C3—32no—
275C2×C3—62no—
276C2×C3—61no—
277C2×C3—61no—
278C2×C3—91no—
279C2×C3—91no—
280C2×C3—181no—
281C2×C3—181no—
282C2×C3—182no—
283C2×C3—182no—
284C2×C3—181no—
285C2×C3—181no—
286C2×C3—541no—
287C2×C3—541no—
288C2×C3—542no—
289C2×C3C2×C3×#27211yescharacteristic
290D3—181no—
291D3—541no—
292D3—541no—
293C22—271no—
294C22#4183⋊C311yescharacteristic, complemented
295C4—271no—
296C3—31no—
297C3—31no—
298C3—32no—
299C3—91no—
300C3—91no—
301C3—181no—
302C3—181no—
303C3C3×#623511yescharacteristic
304C2—21no—
305C2—541no—
306C2C2×#4183⋊C311yescharacteristic
subgroupG/H
centerC2C2×#4183⋊C3
commutator, cosocleC2×AΣL(1,𝔽27)C22×C3
FrattiniC2×C32C2×C3×C3⋊D3
FittingC22×#6909C2
socleC2×C3C2×C3×#272
hypercenterC22#4183⋊C3
hypocenterAΣL(1,𝔽27)C3×D4
LCSG ▷ C2×AΣL(1,𝔽27) ▷ AΣL(1,𝔽27)
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×#6909C2semidirect
2. C2×#4183⋊C3C2semidirect
3. #66330⋊C3C2semidirect
7. #10619679C3semidirect
11. C22×C3×3−1+2D3semidirect
12. C22×C3×H(3,𝔽3)D3semidirect
13. C22×C3×H(3,𝔽3)D3semidirect
23. C22×AΣL(1,𝔽27)C2×C3semidirect
24. C2×#4183C2×C3semidirect
25. #66330C2×C3semidirect
26. #6909D4semidirect
58. C22×C33C3×D3semidirect
69. C22×3−1+2C3×D3semidirect
92. C3×3−1+2#67semidirect
93. C3×H(3,𝔽3)#67semidirect
94. C3×H(3,𝔽3)#67semidirect
98. AΣL(1,𝔽27)C3×D4semidirect
181. C33C3×#67semidirect
186. 3−1+2C3×#67semidirect
294. C22#4183⋊C3semidirect

Maximal subgroups

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

subgroupindex
C22×#69092
C2×#4183⋊C32
#66330⋊C32
C3×#611⋊C33
C3×#638⋊C33
#106196793