Finite Group Databasebeta

← #72277553

Subgroups — #72277553

Order 2916.

347 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 347 conjugacy classes of subgroups — too many to draw. Only its 37 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#13091481C211yesmaximal, characteristic, complemented
2#13091480C211yesmaximal, characteristic, complemented
3#13091479C211yesmaximal, characteristic, complemented
4#66431⋊C3—31nomaximal
5#92294⋊C2C311yesmaximal, characteristic, complemented
6#92265⋊C2—31nomaximal
7(((C3⋊D3)⋊C9)⋊C2)⋊C3—31nomaximal
8#10624884C2211yescharacteristic, complemented, Sylow
9C3⋊D3×3−1+2—31no—
10C3×C3⋊AGL(1,ℤ/9)—31no—
11C3×C3⋊AGL(1,ℤ/9)D311yescharacteristic
12#92314D311yescharacteristic, complemented
13#6899⋊C2—21no—
14#6895⋊C2—21no—
15#92302D311yescharacteristic
16#92296C2×C311yescharacteristic, complemented
17#92295C2×C311yescharacteristic, complemented
18#92294—21no—
19#92294C2×C311yescharacteristic, complemented
20#92265—31no—
21#92265—31no—
22#92265—61no—
23#92265—61no—
24#4169⋊C3—31no—
25#4169⋊C3—61no—
26#92259—31no—
27C3×#1113—91no—
28#66431—31no—
29D3×AGL(1,ℤ/9)—91no—
30D3×AGL(1,ℤ/9)—91no—
31D3×AGL(1,ℤ/9)—91no—
32((C3⋊D3)⋊C9)⋊C2—31no—
33D92—31no—
34C32×3−1+2C2×D311yescharacteristic
35#6900—21no—
36#6900—21no—
37#6900—41no—
38#6900C2×D311yescharacteristic, complemented
39#6899—21no—
40#6899—41no—
41#6899—41no—
42#6899—41no—
43#6899—41no—
44#6895—21no—
45#6895—41no—
46#6891—21no—
47#6891C2×D311yescharacteristic
48#6887—21no—
49#6887C22×C311yescharacteristic, complemented
50C32×C3⋊D3—31no—
51C32×C3⋊D3—31no—
52C32×C3⋊D3—91no—
53C3⋊AGL(1,ℤ/9)—31no—
54C3⋊AGL(1,ℤ/9)—31no—
55C3⋊AGL(1,ℤ/9)—31no—
56C3⋊AGL(1,ℤ/9)—61no—
57C3⋊AGL(1,ℤ/9)—61no—
58C9×C3⋊D3—31no—
59C9×C3⋊D3—61no—
60C3×C3⋊D9—31no—
61C3×C3⋊D9C3×D311yescharacteristic
62D3×3−1+2—91no—
63D3×3−1+2—91no—
64D3×3−1+2—91no—
65D3×3−1+2—181no—
66C3×AGL(1,ℤ/9)—31no—
67C3×AGL(1,ℤ/9)—31no—
68C3×AGL(1,ℤ/9)—61no—
69C3×AGL(1,ℤ/9)—61no—
70C3×AGL(1,ℤ/9)—91no—
71C3×AGL(1,ℤ/9)—181no—
72#4181C3×D311yescharacteristic
73C9⋊D9C3×D311yescharacteristic, complemented
74D9⋊C9—61no—
75D9⋊C9—61no—
76D9⋊C9—61no—
77D9⋊C9—61no—
78D9⋊C9—61no—
79D9⋊C9—61no—
80#4169—31no—
81#4169—61no—
82#4169—61no—
83#4169—61no—
84#4169—61no—
85(C3⋊D3)⋊C9—31no—
86(C3⋊D3)⋊C9—61no—
87C9×D9—31no—
88C9×D9—31no—
89C9×D9—61no—
90C9×D9—61no—
91#1113—91no—
92C3×D32—271no—
93C3×D32—271no—
94C3×D32—271no—
95C2×AGL(1,ℤ/9)—271no—
96C2×AGL(1,ℤ/9)—271no—
97D3×D9—91no—
98D3×D9—91no—
99D3×D9—91no—
100C34D3211yescharacteristic
101C3×3−1+2—21no—
102C3×3−1+2—21no—
103C3×3−1+2—21no—
104C3×3−1+2—21no—
105C3×3−1+2—31no—
106C3×3−1+2—41no—
107C3×3−1+2—41no—
108C3×3−1+2—61no—
109C3×3−1+2—61no—
110C3×3−1+2—121no—
111C3×3−1+2D3211yescharacteristic
112C3×3−1+2D3211yescharacteristic
113C32×C9—21no—
114C32×C9C2×C3×D311yescharacteristic
115C9⋊C9—21no—
116C9⋊C9—21no—
117C9⋊C9—21no—
118C9⋊C9—21no—
119C9⋊C9—21no—
120C9⋊C9—21no—
121C9⋊C9—41no—
122C9⋊C9—41no—
123C9⋊C9—41no—
124C9⋊C9—41no—
125C9⋊C9—41no—
126C9⋊C9—41no—
127C9⋊C9—41no—
128C9⋊C9—41no—
129C9⋊C9—41no—
130C9⋊C9—41no—
131C9⋊C9—41no—
132C9⋊C9—42no—
133C9⋊C9—41no—
134C9⋊C9—41no—
135C32⋊C9—21no—
136C32⋊C9—21no—
137C32⋊C9—21no—
138C32⋊C9—21no—
139C32⋊C9—21no—
140C32⋊C9—41no—
141C32⋊C9—41no—
142C32⋊C9—41no—
143C32⋊C9—41no—
144C32⋊C9C2×C3×D311yescharacteristic
145C92—21no—
146C92—21no—
147C92—41no—
148C92C2×C3×D311yescharacteristic, complemented
149C3×C3⋊D3—31no—
150C3×C3⋊D3—31no—
151C3×C3⋊D3—91no—
152C3×C3⋊D3—91no—
153C3×C3⋊D3—91no—
154C3×C3⋊D3—91no—
155C3×C3⋊D3—181no—
156C32×D3—91no—
157C32×D3—91no—
158C32×D3—91no—
159C32×D3—181no—
160C32×D3—271no—
161C32×D3—271no—
162C32×D3—271no—
163C32×D3—541no—
164C2×3−1+2—271no—
165C2×3−1+2—271no—
166C3⋊D9—31no—
167C3⋊D9—31no—
168C3⋊D9—61no—
169C3⋊D9AGL(1,ℤ/9)11yescharacteristic, complemented
170AGL(1,ℤ/9)—91no—
171AGL(1,ℤ/9)—91no—
172AGL(1,ℤ/9)—91no—
173AGL(1,ℤ/9)—181no—
174AGL(1,ℤ/9)—181no—
175AGL(1,ℤ/9)—181no—
176AGL(1,ℤ/9)—181no—
177AGL(1,ℤ/9)—182no—
178AGL(1,ℤ/9)—271no—
179AGL(1,ℤ/9)—541no—
180D3×C9—91no—
181D3×C9—91no—
182D3×C9—91no—
183D3×C9—181no—
184D3×C9—181no—
185D3×C9—181no—
186D3×C9—181no—
187D3×C9—182no—
188C3×D9—31no—
189C3×D9—31no—
190C3×D9—61no—
191C3×D9—61no—
192C3×D9—91no—
193C3×D9—181no—
194C2×C3×D3—811no—
195C2×C3×D3—811no—
196C2×C3×D3—811no—
197D32—271no—
198D32—271no—
199D32—271no—
200C2×D9—271no—
201C2×D9—271no—
202C33—21no—
203C33—31no—
204C33—61no—
205C33—91no—
206C33—181no—
207C33C3×D3211yescharacteristic
208C33#111311yescharacteristic
2093−1+2—31no—
2103−1+2—61no—
2113−1+2—61no—
2123−1+2—62no—
2133−1+2—61no—
2143−1+2—91no—
2153−1+2—121no—
2163−1+2—122no—
2173−1+2—121no—
2183−1+2—181no—
2193−1+2—181no—
2203−1+2—361no—
221C3×C9—21no—
222C3×C9—21no—
223C3×C9—21no—
224C3×C9—21no—
225C3×C9—21no—
226C3×C9—21no—
227C3×C9—21no—
228C3×C9—41no—
229C3×C9—41no—
230C3×C9—41no—
231C3×C9—41no—
232C3×C9—41no—
233C3×C9—41no—
234C3×C9—41no—
235C3×C9—62no—
236C3×C9—61no—
237C3×C9C2×AGL(1,ℤ/9)11yescharacteristic, complemented
238C3×C9C3×D3211yescharacteristic
239C3×C9C3×D3211yescharacteristic
240C2×C32—271no—
241C2×C32—271no—
242C2×C32—811no—
243C3⋊D3—31no—
244C3⋊D3—31no—
245C3⋊D3—91no—
246C3×D3—91no—
247C3×D3—91no—
248C3×D3—91no—
249C3×D3—181no—
250C3×D3—271no—
251C3×D3—271no—
252C3×D3—271no—
253C3×D3—271no—
254C3×D3—271no—
255C3×D3—271no—
256C3×D3—271no—
257C3×D3—271no—
258C3×D3—271no—
259C3×D3—541no—
260C3×D3—541no—
261C3×D3—541no—
262C3×D3—541no—
263C3×D3—541no—
264C3×D3—541no—
265C3×D3—542no—
266C2×C9—271no—
267C2×C9—271no—
268C2×C9—541no—
269C2×C9—541no—
270D9—31no—
271D9—31no—
272D9—61no—
273D9—61no—
274D9—91no—
275D9—181no—
276D9—271no—
277D9—541no—
278C22×C3—2431no—
279C2×D3—811no—
280C2×D3—811no—
281C2×D3—811no—
282C32—21no—
283C32—31no—
284C32—31no—
285C32—31no—
286C32—61no—
287C32—61no—
288C32—62no—
289C32—61no—
290C32—61no—
291C32—91no—
292C32—181no—
293C32—181no—
294C32—361no—
295C32D3×AGL(1,ℤ/9)11yescharacteristic
296C32C3×#111311yescharacteristic
297C9—21no—
298C9—21no—
299C9—31no—
300C9—41no—
301C9—61no—
302C9—61no—
303C9—61no—
304C9—61no—
305C9—121no—
306C9—121no—
307C9—121no—
308C9—121no—
309C9—121no—
310C9—121no—
311C9D3×AGL(1,ℤ/9)11yescharacteristic
312C2×C3—271no—
313C2×C3—271no—
314C2×C3—811no—
315C2×C3—811no—
316C2×C3—811no—
317C2×C3—811no—
318C2×C3—1621no—
319D3—91no—
320D3—91no—
321D3—91no—
322D3—181no—
323D3—271no—
324D3—271no—
325D3—271no—
326D3—541no—
327C22—2431noSylow
328C3—21no—
329C3—31no—
330C3—61no—
331C3—91no—
332C3—181no—
333C3#66431⋊C311yescharacteristic
334C3(#4207⋊C2)⋊C311yescharacteristic
335C2—271no—
336C2—271no—
337C2—811no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenter#6887C22×C3
Frattini, socleC32C3×#1113
Fitting#10624884C22
LCSG ▷ #6887
UCSC1

Complements

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

NH ≅ G/Ntype
1. #13091481C2semidirect
2. #13091480C2semidirect
3. #13091479C2semidirect
5. #92294⋊C2C3semidirect
8. #10624884C22semidirect
12. #92314D3semidirect
16. #92296C2×C3semidirect
17. #92295C2×C3semidirect
19. #92294C2×C3semidirect
38. #6900C2×D3semidirect
49. #6887C22×C3semidirect
73. C9⋊D9C3×D3semidirect
148. C92C2×C3×D3semidirect
169. C3⋊D9AGL(1,ℤ/9)semidirect
237. C3×C9C2×AGL(1,ℤ/9)semidirect

Maximal subgroups

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

subgroupindex
#130914812
#130914802
#130914792
#66431⋊C33
#92294⋊C23
#92265⋊C23
(((C3⋊D3)⋊C9)⋊C2)⋊C33