Finite Group Databasebeta

← #14517031

Subgroups — #14517031

Order 1944.

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

normal subgroups only

This group has 493 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×#6291—31nomaximal
5#6195⋊C3—32nomaximal
6#6291⋊C3—31nomaximal
7#10619679—31nomaximal
8C2×C3×AΣL(1,𝔽27)C2211yescharacteristic
9C3⋊#4183—21no—
10D3×AΣL(1,𝔽27)—21no—
11C2×C3×C3⋊(C3⋊D3)—31no—
12C2×C33×D3D311yescharacteristic, complemented
13C32×C3⋊Dic3—31no—
14C2×C3⋊AGL(1,ℤ/9)—32no—
15C2×C3⋊((C3⋊D3)⋊C3)—31no—
16C2×D3×3−1+2D312yescomplemented
17C2×D3×H(3,𝔽3)D311yescharacteristic, complemented
18C3×3−1+2⋊C4—32no—
19C3×(C3⋊Dic3)⋊C3—31no—
20C22×AΣL(1,𝔽27)—31no—
21C2×#4183—31no—
22C2×#4183—61no—
23C2×#4183—62no—
24C2×#4183—61no—
25#66330D311yescharacteristic, complemented
26C3×AΣL(1,𝔽27)D411yescharacteristic, complemented, Sylow
27C3×#638—91no—
28#6291—31no—
29#6291—31no—
30C3×#626—93no—
31C3×#626—91no—
32#611⋊C3—92no—
33#638⋊C3—91no—
34#6195—32no—
35C2×C34C2×D311yescharacteristic
36C3×C3⋊(C3⋊D3)—61no—
37C33×D3—21no—
38C2×C3×3−1+2C2×D312yes—
39C2×C3×H(3,𝔽3)C2×D311yescharacteristic
40C3⋊AGL(1,ℤ/9)—62no—
41C3⋊((C3⋊D3)⋊C3)—61no—
42D3×3−1+2—22no—
43D3×H(3,𝔽3)—21no—
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—62no—
50#4183—64no—
51#4183—62no—
52#4183—61no—
53C22×C33—31no—
54C2×C3⋊(C3⋊D3)—31no—
55C2×C3⋊(C3⋊D3)—31no—
56C2×C3×C3⋊D3—93no—
57C2×C3×C3⋊D3—91no—
58C2×C3×C3⋊D3—91no—
59C2×C3×C3⋊D3—181no—
60C2×C3×C3⋊D3—183no—
61C2×C32×D3—31no—
62C2×C32×D3—33no—
63C2×C32×D3—31no—
64C2×C32×D3C3⋊D311yescharacteristic
65C3×C3⋊Dic3—31no—
66C3×C3⋊Dic3—31no—
67C3×C3⋊Dic3—31no—
68C3×C3⋊Dic3—61no—
69C32×Dic3—93no—
70C32×Dic3—91no—
71C22×3−1+2—32no—
72C22×H(3,𝔽3)—31no—
73C2×C3⋊D9—32no—
74C2×AGL(1,ℤ/9)—92no—
75C2×AGL(1,ℤ/9)—182no—
76C2×(C3⋊D3)⋊C3—91no—
77C2×(C3⋊D3)⋊C3—181no—
78C2×D3×C9—32no—
793−1+2⋊C4—32no—
803−1+2⋊C4—62no—
81(C3⋊Dic3)⋊C3—31no—
82(C3⋊Dic3)⋊C3—61no—
83C3×Dic9—32no—
84C34#6711yescharacteristic, complemented
85C3×3−1+2#6712yescomplemented
86C3×H(3,𝔽3)#6711yescharacteristic, complemented
87AΣL(1,𝔽27)—21no—
88AΣL(1,𝔽27)—22no—
89AΣL(1,𝔽27)—21no—
90AΣL(1,𝔽27)D1211yescharacteristic, complemented
91#638—91no—
92#638—91no—
93C3×#67—271no—
94C3×#67—273no—
95C3×D12—271no—
96#626—93no—
97#626—91no—
98#626—271no—
99#611—92no—
100C2×C33—21no—
101C2×C33—31no—
102C2×C33—33no—
103C2×C33—31no—
104C2×C33—61no—
105C2×C33—63no—
106C2×C33—61no—
107C2×C33D3211yescharacteristic
108C2×C33C2×C3⋊D311yescharacteristic
109C3⋊(C3⋊D3)—61no—
110C3⋊(C3⋊D3)—61no—
111C3×C3⋊D3—182no—
112C3×C3⋊D3—183no—
113C3×C3⋊D3—186no—
114C3×C3⋊D3—181no—
115C3×C3⋊D3—181no—
116C32×D3—21no—
117C32×D3—61no—
118C32×D3—61no—
119C32×D3—63no—
120C2×3−1+2—22no—
121C2×3−1+2—62no—
122C2×3−1+2—62no—
123C2×3−1+2D3212yes—
124C2×H(3,𝔽3)—21no—
125C2×H(3,𝔽3)—61no—
126C2×H(3,𝔽3)—61no—
127C2×H(3,𝔽3)D3211yescharacteristic
128C2×C3×C9—32no—
129C3⋊D9—62no—
130AGL(1,ℤ/9)—184no—
131AGL(1,ℤ/9)—182no—
132(C3⋊D3)⋊C3—182no—
133(C3⋊D3)⋊C3—181no—
134D3×C9—62no—
135C22×C32—31no—
136C22×C32—91no—
137C22×C32—91no—
138C22×C32—93no—
139C2×C3⋊D3—91no—
140C2×C3⋊D3—93no—
141C2×C3⋊D3—91no—
142C2×C3⋊D3—91no—
143C2×C3⋊D3—183no—
144C2×C3⋊D3—181no—
145C2×C3⋊D3—181no—
146C2×C3⋊D3—271no—
147C2×C3⋊D3—541no—
148C2×C3×D3—31no—
149C2×C3×D3—33no—
150C2×C3×D3—91no—
151C2×C3×D3—271no—
152C2×C3×D3—273no—
153C2×C3×D3—271no—
154C2×C3×D3—541no—
155C2×C3×D3—543no—
156C2×C3×D3#27211yescharacteristic
157C32×C4—271no—
158C3⋊Dic3—31no—
159C3⋊Dic3—31no—
160C3×Dic3—93no—
161C3×Dic3—93no—
162C3×Dic3—91no—
163C3×Dic3—91no—
164C3×Dic3—181no—
165C3×Dic3—183no—
166C3×Dic3—271no—
167C22×C9—92no—
168C2×D9—92no—
169C2×D9—182no—
170Dic9—32no—
171C33—21no—
172C33—31no—
173C33—33no—
174C33—31no—
175C33—61no—
176C33—63no—
177C33#62611yescharacteristic, complemented
178C33#63811yescharacteristic
1793−1+2—22no—
1803−1+2—62no—
1813−1+2#62612yescomplemented
182H(3,𝔽3)—21no—
183H(3,𝔽3)—61no—
184H(3,𝔽3)#62611yescharacteristic, complemented
185C3×C9—32no—
186C3×D4—811no—
187#67—271no—
188#67—273no—
189#67—811no—
190D12—271no—
191C2×C32—21no—
192C2×C32—31no—
193C2×C32—33no—
194C2×C32—31no—
195C2×C32—33no—
196C2×C32—31no—
197C2×C32—63no—
198C2×C32—61no—
199C2×C32—63no—
200C2×C32—63no—
201C2×C32—61no—
202C2×C32—61no—
203C2×C32—61no—
204C2×C32—91no—
205C2×C32—123no—
206C2×C32—181no—
207C2×C32—181no—
208C2×C32—181no—
209C2×C32—183no—
210C2×C32C2×#27211yescharacteristic
211C2×C32D3×C3⋊D311yescharacteristic
212C3⋊D3—181no—
213C3⋊D3—183no—
214C3⋊D3—186no—
215C3⋊D3—182no—
216C3⋊D3—181no—
217C3⋊D3—181no—
218C3⋊D3—182no—
219C3⋊D3—541no—
220C3⋊D3—542no—
221C3×D3—21no—
222C3×D3—61no—
223C3×D3—63no—
224C3×D3—181no—
225C3×D3—543no—
226C3×D3—541no—
227C3×D3—542no—
228C3×D3—546no—
229C3×D3—541no—
230C2×C9—32no—
231C2×C9—62no—
232C2×C9—182no—
233D9—182no—
234D9—184no—
235C22×C3—31no—
236C22×C3—93no—
237C22×C3—91no—
238C22×C3—271no—
239C22×C3—811no—
240C2×D3—273no—
241C2×D3—271no—
242C2×D3—271no—
243C2×D3—541no—
244C2×D3—543no—
245C2×D3—811no—
246C2×D3—1621no—
247C2×D3#418311yescharacteristic, complemented
248C3×C4—271no—
249C3×C4—271no—
250C3×C4—541no—
251Dic3—93no—
252Dic3—91no—
253Dic3—271no—
254C32—21no—
255C32—33no—
256C32—31no—
257C32—31no—
258C32—33no—
259C32—31no—
260C32—61no—
261C32—63no—
262C32—63no—
263C32—63no—
264C32—61no—
265C32—61no—
266C32—91no—
267C32—123no—
268C32—181no—
269C32#623511yescharacteristic
270C32#629111yescharacteristic
271C9—32no—
272C9—62no—
273D4—811noSylow
274C2×C3—21no—
275C2×C3—33no—
276C2×C3—31no—
277C2×C3—61no—
278C2×C3—61no—
279C2×C3—63no—
280C2×C3—91no—
281C2×C3—181no—
282C2×C3—183no—
283C2×C3—181no—
284C2×C3—541no—
285C2×C3—1621no—
286C2×C3C2×#418311yescharacteristic
287C2×C3D3×#27211yescharacteristic
288D3—21no—
289D3—542no—
290D3—543no—
291D3—546no—
292D3—541no—
293D3—541no—
294D3—1621no—
295D3—1622no—
296C22—31no—
297C22—811no—
298C4—271no—
299C3—21no—
300C3—33no—
301C3—31no—
302C3—63no—
303C3—61no—
304C3—91no—
305C3—181no—
306C3#1061967911yescharacteristic, complemented
307C3#1061989211yescharacteristic
308C2—61no—
309C2—1621no—
310C2D3×#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
16. C2×D3×3−1+2D3semidirect
17. C2×D3×H(3,𝔽3)D3semidirect
25. #66330D3semidirect
26. C3×AΣL(1,𝔽27)D4semidirect
84. C34#67semidirect
85. C3×3−1+2#67semidirect
86. C3×H(3,𝔽3)#67semidirect
90. AΣL(1,𝔽27)D12semidirect
177. C33#626semidirect
181. 3−1+2#626semidirect
184. H(3,𝔽3)#626semidirect
247. C2×D3#4183semidirect
306. 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×#62913
#6195⋊C33
#6291⋊C33
#106196793