Finite Group Databasebeta

← #14517030

Subgroups — #14517030

Order 1944.

455 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 455 conjugacy classes of subgroups — too many to draw. Only its 44 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
1C2×C3×#4183C211yesmaximal, characteristic, complemented
2C2×D3×AΣL(1,𝔽27)C211yesmaximal, characteristic, complemented
3C3⋊#66330C211yesmaximal, characteristic, complemented
4C3×#6290—31nomaximal
5#6194⋊C3—32nomaximal
6#6290⋊C3—31nomaximal
7#10619679—31nomaximal
8C2×C3×AΣL(1,𝔽27)C2211yescharacteristic
9C3×#4183—21no—
10D3×AΣL(1,𝔽27)—21no—
11C2×C32×C3⋊D3—31no—
12C2×C33×D3D311yescharacteristic, complemented
13C3×C3⋊(C3⋊Dic3)—31no—
14C2×D3×3−1+2D312yescomplemented
15C2×C3×AGL(1,ℤ/9)—32no—
16C2×D3×H(3,𝔽3)D311yescharacteristic, complemented
17C2×C3×(C3⋊D3)⋊C3—31no—
18C3⋊(3−1+2⋊C4)—32no—
19C3⋊((C3⋊Dic3)⋊C3)—31no—
20C22×AΣL(1,𝔽27)—31no—
21C2×#4183D311yescharacteristic, complemented
22#66330—31no—
23#66330—61no—
24#66330—62no—
25#66330—61no—
26C3×AΣL(1,𝔽27)D411yescharacteristic, complemented, Sylow
27C3×#638—91no—
28#6290—31no—
29#6290—31no—
30C3×#625—93no—
31C3×#625—91no—
32#611⋊C3—92no—
33#638⋊C3—91no—
34#6194—32no—
35C2×C34C2×D311yescharacteristic
36C32×C3⋊D3—61no—
37C33×D3—21no—
38C2×C3×3−1+2C2×D312yes—
39C2×C3×H(3,𝔽3)C2×D311yescharacteristic
40D3×3−1+2—22no—
41C3×AGL(1,ℤ/9)—62no—
42D3×H(3,𝔽3)—21no—
43C3×(C3⋊D3)⋊C3—61no—
44C2×AΣL(1,𝔽27)—21no—
45C2×AΣL(1,𝔽27)—22no—
46C2×AΣL(1,𝔽27)—21no—
47C2×AΣL(1,𝔽27)—61no—
48C2×AΣL(1,𝔽27)C2×D311yescharacteristic
49#4183—21no—
50C22×C33—31no—
51C2×C3×C3⋊D3—31no—
52C2×C3×C3⋊D3—31no—
53C2×C3×C3⋊D3—31no—
54C2×C3×C3⋊D3—61no—
55C2×C32×D3—31no—
56C2×C32×D3—33no—
57C2×C32×D3—31no—
58C2×C32×D3—93no—
59C2×C32×D3—91no—
60C2×C32×D3C3⋊D311yescharacteristic
61C3⋊(C3⋊Dic3)—31no—
62C3⋊(C3⋊Dic3)—31no—
63C3×C3⋊Dic3—93no—
64C3×C3⋊Dic3—91no—
65C3×C3⋊Dic3—91no—
66C3×C3⋊Dic3—181no—
67C3×C3⋊Dic3—183no—
68C22×3−1+2—32no—
69C22×H(3,𝔽3)—31no—
70C2×AGL(1,ℤ/9)—32no—
71C2×AGL(1,ℤ/9)—62no—
72C2×(C3⋊D3)⋊C3—31no—
73C2×(C3⋊D3)⋊C3—61no—
74C2×D3×C9—32no—
75C2×C3×D9—32no—
76C3⋊Dic9—32no—
773−1+2⋊C4—92no—
783−1+2⋊C4—182no—
79(C3⋊Dic3)⋊C3—91no—
80(C3⋊Dic3)⋊C3—181no—
81C34#6711yescharacteristic, complemented
82C3×3−1+2#6712yescomplemented
83C3×H(3,𝔽3)#6711yescharacteristic, complemented
84AΣL(1,𝔽27)—21no—
85AΣL(1,𝔽27)—22no—
86AΣL(1,𝔽27)—21no—
87AΣL(1,𝔽27)#6711yescharacteristic, complemented
88#638—91no—
89#638—91no—
90C3×#67—271no—
91C3×#67—271no—
92C3×#67—273no—
93#625—93no—
94#625—91no—
95#625—271no—
96#611—92no—
97C2×C33—21no—
98C2×C33—31no—
99C2×C33—33no—
100C2×C33—31no—
101C2×C33—61no—
102C2×C33—63no—
103C2×C33—61no—
104C2×C33D3211yescharacteristic
105C2×C33C2×C3⋊D311yescharacteristic
106C3×C3⋊D3—61no—
107C3×C3⋊D3—62no—
108C3×C3⋊D3—61no—
109C3×C3⋊D3—61no—
110C32×D3—21no—
111C32×D3—61no—
112C32×D3—61no—
113C32×D3—63no—
114C32×D3—183no—
115C32×D3—181no—
116C2×3−1+2—22no—
117C2×3−1+2—62no—
118C2×3−1+2—62no—
119C2×3−1+2D3212yes—
120C2×H(3,𝔽3)—21no—
121C2×H(3,𝔽3)—61no—
122C2×H(3,𝔽3)—61no—
123C2×H(3,𝔽3)D3211yescharacteristic
124C2×C3×C9—32no—
125AGL(1,ℤ/9)—64no—
126AGL(1,ℤ/9)—62no—
127(C3⋊D3)⋊C3—62no—
128(C3⋊D3)⋊C3—61no—
129D3×C9—62no—
130C3×D9—62no—
131C22×C32—31no—
132C22×C32—91no—
133C22×C32—91no—
134C22×C32—93no—
135C22×C32—271no—
136C2×C3⋊D3—31no—
137C2×C3⋊D3—31no—
138C2×C3×D3—31no—
139C2×C3×D3—33no—
140C2×C3×D3—93no—
141C2×C3×D3—93no—
142C2×C3×D3—91no—
143C2×C3×D3—91no—
144C2×C3×D3—91no—
145C2×C3×D3—181no—
146C2×C3×D3—183no—
147C2×C3×D3—271no—
148C2×C3×D3#27211yescharacteristic
149C3⋊Dic3—91no—
150C3⋊Dic3—93no—
151C3⋊Dic3—91no—
152C3⋊Dic3—91no—
153C3⋊Dic3—183no—
154C3⋊Dic3—181no—
155C3⋊Dic3—181no—
156C3⋊Dic3—271no—
157C3⋊Dic3—541no—
158C3×Dic3—271no—
159C3×Dic3—273no—
160C3×Dic3—271no—
161C3×Dic3—541no—
162C3×Dic3—543no—
163C22×C9—92no—
164C2×D9—32no—
165Dic9—92no—
166Dic9—182no—
167C33—21no—
168C33—31no—
169C33—33no—
170C33—31no—
171C33—61no—
172C33—63no—
173C33#62511yescharacteristic, complemented
174C33#63811yescharacteristic
1753−1+2—22no—
1763−1+2—62no—
1773−1+2#62512yescomplemented
178H(3,𝔽3)—21no—
179H(3,𝔽3)—61no—
180H(3,𝔽3)#62511yescharacteristic, complemented
181C3×C9—32no—
182C3×D4—811no—
183#67—271no—
184#67—273no—
185#67—271no—
186#67—811no—
187C2×C32—21no—
188C2×C32—31no—
189C2×C32—33no—
190C2×C32—31no—
191C2×C32—33no—
192C2×C32—31no—
193C2×C32—63no—
194C2×C32—61no—
195C2×C32—63no—
196C2×C32—63no—
197C2×C32—61no—
198C2×C32—61no—
199C2×C32—61no—
200C2×C32—91no—
201C2×C32—123no—
202C2×C32—181no—
203C2×C32—181no—
204C2×C32—181no—
205C2×C32—183no—
206C2×C32—541no—
207C2×C32C2×#27211yescharacteristic
208C2×C32D3×C3⋊D311yescharacteristic
209C3⋊D3—61no—
210C3⋊D3—61no—
211C3×D3—21no—
212C3×D3—61no—
213C3×D3—63no—
214C3×D3—181no—
215C3×D3—182no—
216C3×D3—183no—
217C3×D3—183no—
218C3×D3—186no—
219C3×D3—181no—
220C3×D3—181no—
221C3×D3—541no—
222C2×C9—32no—
223C2×C9—62no—
224C2×C9—182no—
225D9—62no—
226C22×C3—31no—
227C22×C3—93no—
228C22×C3—91no—
229C22×C3—271no—
230C22×C3—271no—
231C22×C3—271no—
232C22×C3—541no—
233C2×D3—93no—
234C2×D3—91no—
235C2×D3—271no—
236C2×D3#418311yescharacteristic, complemented
237C3×C4—811no—
238Dic3—273no—
239Dic3—271no—
240Dic3—271no—
241Dic3—541no—
242Dic3—543no—
243Dic3—811no—
244Dic3—1621no—
245C32—21no—
246C32—33no—
247C32—31no—
248C32—33no—
249C32—31no—
250C32—31no—
251C32—61no—
252C32—63no—
253C32—63no—
254C32—63no—
255C32—61no—
256C32—61no—
257C32—91no—
258C32—123no—
259C32—181no—
260C32#623511yescharacteristic
261C32#629011yescharacteristic
262C9—32no—
263C9—62no—
264D4—811noSylow
265C2×C3—21no—
266C2×C3—33no—
267C2×C3—31no—
268C2×C3—61no—
269C2×C3—63no—
270C2×C3—61no—
271C2×C3—91no—
272C2×C3—181no—
273C2×C3—183no—
274C2×C3—181no—
275C2×C3—541no—
276C2×C3—541no—
277C2×C3—542no—
278C2×C3—541no—
279C2×C3C2×#418311yescharacteristic
280C2×C3D3×#27211yescharacteristic
281D3—21no—
282D3—183no—
283D3—181no—
284D3—541no—
285C22—31no—
286C22—271no—
287C4—811no—
288C3—21no—
289C3—33no—
290C3—31no—
291C3—61no—
292C3—63no—
293C3—91no—
294C3—181no—
295C3#1061967911yescharacteristic, complemented
296C3#1061989111yescharacteristic
297C2—61no—
298C2—541no—
299C2D3×#418311yescharacteristic
subgroupG/H
center, hypercenterC2D3×#4183
commutator, Fitting, cosocleC2×C3×AΣL(1,𝔽27)C22
FrattiniC2×C32D3×C3⋊D3
socleC2×C32C2×#272
hypocenterC3×AΣL(1,𝔽27)D4
LCSG ▷ C2×C3×AΣL(1,𝔽27) ▷ C3×AΣL(1,𝔽27)
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4183C2semidirect
2. C2×D3×AΣL(1,𝔽27)C2semidirect
3. C3⋊#66330C2semidirect
12. C2×C33×D3D3semidirect
14. C2×D3×3−1+2D3semidirect
16. C2×D3×H(3,𝔽3)D3semidirect
21. C2×#4183D3semidirect
26. C3×AΣL(1,𝔽27)D4semidirect
81. C34#67semidirect
82. C3×3−1+2#67semidirect
83. C3×H(3,𝔽3)#67semidirect
87. AΣL(1,𝔽27)#67semidirect
173. C33#625semidirect
177. 3−1+2#625semidirect
180. H(3,𝔽3)#625semidirect
236. C2×D3#4183semidirect
295. C3#10619679semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#41832
C2×D3×AΣL(1,𝔽27)2
C3⋊#663302
C3×#62903
#6194⋊C33
#6290⋊C33
#106196793