Finite Group Databasebeta

← C9×#4762 #13141724

Subgroups — C9×#4762 #13141724

Order 1728.

434 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#940C211yesmaximal, characteristic
2C2×C9×#214C211yesmaximal, characteristic, complemented
3C2×C9×#204C211yesmaximal, characteristic, complemented
4C9×#887C211yesmaximal, characteristic, complemented
5C3×C9×#102C211yesmaximal, characteristic, complemented
6C9×Dic3⋊C8C211yesmaximal, characteristic, complemented
7C9×#809C211yesmaximal, characteristic, complemented
8C3×#4762C311yesmaximal, characteristic
9C9×#460—31nomaximal
10C2×C3×D4×C9C2211yescharacteristic
11C2×C9×#67—21no—
12C2×C9×#67—21no—
13C2×C9×D12C2211yescharacteristic
14C2×C9×Dic6C2211yescharacteristic
15C2×C3×C8×C9C2211yescharacteristic
16C3×C9×C4⋊C4C2211yescharacteristic
17C9×#214—22no—
18C9×Dic3⋊C4—21no—
19C4×C9×Dic3—21no—
20C4×C9×Dic3C2211yescharacteristic
21C2×C9×C3⋊C8C2211yescharacteristic
22C9×#204—22no—
23C3×#940C2×C311yescharacteristic
24C2×C3×#214C2×C311yescharacteristic
25C2×C3×#204C2×C311yescharacteristic
26C3×#887C2×C311yescharacteristic
27C32×#102C2×C311yescharacteristic
28C3×Dic3⋊C8C2×C311yescharacteristic
29C3×#809C2×C311yescharacteristic
30C2×C9×SD16—31no—
31C2×C9×SD16—31no—
32C9×#127—31no—
33C4×Q8×C9—31no—
34C9×C4⋊C8—31no—
35C9×#102—21no—
36C9×#102—31no—
37C9×#102D311yescharacteristic, complemented
38C23×C3×C9—21no—
39C22×D3×C9—21no—
40C3×D4×C9—21no—
41C3×D4×C9—21no—
42C2×C3×C4×C9—21no—
43C2×C3×C4×C9C2311yescharacteristic
44C9×#67—42no—
45C9×#67—42no—
46C2×C9×Dic3—21no—
47C2×C9×Dic3D411yescharacteristic
48C2×C9×Dic3D411yescharacteristic
49C9×D12—21no—
50C9×D12—21no—
51C9×Dic6—21no—
52C9×Dic6D412yescomplemented
53C3×C8×C9—21no—
54C9×C3⋊C8—21no—
55C3×#460—31no—
56#4762C911yescharacteristic, direct product factor
57C2×C32×D4C22×C311yescharacteristic
58C2×C3×#67—21no—
59C2×C3×#67—21no—
60C2×C3×D12C22×C311yescharacteristic
61C2×C3×Dic6C22×C311yescharacteristic
62C2×C32×C8C22×C311yescharacteristic
63C32×C4⋊C4C22×C311yescharacteristic
64C3×#214—22no—
65C3×Dic3⋊C4—21no—
66C3×C4×Dic3—21no—
67C3×C4×Dic3C22×C311yescharacteristic
68C2×C3×C3⋊C8C22×C311yescharacteristic
69C3×#204—22no—
70C2×Q8×C9—31no—
71C2×D4×C9—21no—
72C2×D4×C9—31no—
73C2×D4×C9—61no—
74C2×D4×C9—61no—
75C2×D4×C9C2×D311yescharacteristic
76C9×SD16—62no—
77C9×SD16—62no—
78C2×C8×C9—21no—
79C2×C8×C9—31no—
80C2×C8×C9C2×D311yescharacteristic
81C9×C4⋊C4—21no—
82C9×C4⋊C4—61no—
83C9×C4⋊C4C2×D311yescharacteristic
84C42×C9—31no—
85C42×C9—61no—
86C22×C3×C9—41no—
87C22×C3×C9—41no—
88C22×C3×C9—41no—
89C22×C3×C9C2×D411yescharacteristic
90C2×D3×C9—41no—
91C2×D3×C9—41no—
92C2×D3×C9—41no—
93C3×C4×C9—41no—
94C3×C4×C9C2×D411yescharacteristic
95C3×C4×C9#4111yescharacteristic
96C9×Dic3—22no—
97C9×Dic3—21no—
98C9×Dic3SD1612yescomplemented
99C2×C3×SD16—31no—
100C2×C3×SD16—31no—
101C3×#127—31no—
102C3×C4×Q8—31no—
103#940C2×C911yescharacteristic
104C2×#214C2×C911yescharacteristic, complemented
105C2×#204C2×C911yescharacteristic, complemented
106#887C2×C911yescharacteristic, complemented
107C3×C4⋊C8—31no—
108C3×#102—21no—
109C3×#102—31no—
110C3×#102C2×C911yescharacteristic, complemented
111C3×#102C3×D311yescharacteristic
112Dic3⋊C8C2×C911yescharacteristic, complemented
113#809C2×C911yescharacteristic, complemented
114C23×C32—21no—
115C22×C3×D3—21no—
116C32×D4—21no—
117C32×D4—21no—
118C2×C32×C4—21no—
119C2×C32×C4C23×C311yescharacteristic
120C3×#67—42no—
121C3×#67—42no—
122C2×C3×Dic3—21no—
123C2×C3×Dic3C3×D411yescharacteristic
124C2×C3×Dic3C3×D411yescharacteristic
125C3×D12—21no—
126C3×D12—21no—
127C3×Dic6—21no—
128C3×Dic6C3×D412yes—
129C23×C9—21no—
130C23×C9—41no—
131C23×C9—61no—
132C32×C8—21no—
133C3×C3⋊C8—21no—
134Q8×C9—32no—
135Q8×C9—61no—
136D4×C9—22no—
137D4×C9—21no—
138D4×C9—21no—
139D4×C9—41no—
140D4×C9—61no—
141D4×C9—61no—
142D4×C9—122no—
143D4×C9—122no—
144C2×C4×C9—21no—
145C2×C4×C9—21no—
146C2×C4×C9—31no—
147C2×C4×C9—31no—
148C2×C4×C9—41no—
149C2×C4×C9—61no—
150C2×C4×C9C22×D311yescharacteristic
151C8×C9—21no—
152C8×C9—41no—
153C8×C9—61no—
154#460—31noSylow
155C2×C3×C9—81no—
156C2×C3×C9#12111yescharacteristic
157C2×C3×C9C2×SD1611yescharacteristic
158C2×C3×C9AGL(1,ℤ/8)11yescharacteristic
159D3×C9—81no—
160C2×C3×Q8—31no—
161C2×C3×D4—21no—
162C2×C3×D4—31no—
163C2×C3×D4—61no—
164C2×C3×D4—61no—
165C2×C3×D4C22×C911yescharacteristic
166C2×C3×D4C2×C3×D311yescharacteristic
167C2×#67—21no—
168C2×#67—21no—
169C2×D12C22×C911yescharacteristic
170C2×Dic6C22×C911yescharacteristic
171C3×SD16—62no—
172C3×SD16—62no—
173C2×C3×C8—21no—
174C2×C3×C8—31no—
175C2×C3×C8C22×C911yescharacteristic
176C2×C3×C8C2×C3×D311yescharacteristic
177C3×C4⋊C4—21no—
178C3×C4⋊C4—61no—
179C3×C4⋊C4C22×C911yescharacteristic
180C3×C4⋊C4C2×C3×D311yescharacteristic
181C3×C42—31no—
182C3×C42—61no—
183#214—22no—
184Dic3⋊C4—21no—
185C4×Dic3—21no—
186C4×Dic3C22×C911yescharacteristic
187C2×C3⋊C8C22×C911yescharacteristic
188#204—22no—
189C22×C32—41no—
190C22×C32—41no—
191C22×C32—41no—
192C22×C32C2×C3×D411yescharacteristic
193C2×C3×D3—41no—
194C2×C3×D3—41no—
195C2×C3×D3—41no—
196C32×C4—41no—
197C32×C4C2×C3×D411yescharacteristic
198C32×C4C3×#4111yescharacteristic
199C3×Dic3—22no—
200C3×Dic3—21no—
201C3×Dic3C3×SD1612yes—
202C22×C9—21no—
203C22×C9—42no—
204C22×C9—41no—
205C22×C9—41no—
206C22×C9—41no—
207C22×C9—81no—
208C22×C9—81no—
209C22×C9—121no—
210C22×C9—121no—
211C22×C9—121no—
212C22×C9D3×D411yescharacteristic
213C4×C9—21no—
214C4×C9—21no—
215C4×C9—32no—
216C4×C9—41no—
217C4×C9—62no—
218C4×C9—61no—
219C4×C9—81no—
220C4×C9#23511yescharacteristic
221C4×C9D3×D411yescharacteristic
222C2×SD16—31no—
223C2×SD16—31no—
224#127—31no—
225C4×Q8—31no—
226C4⋊C8—31no—
227#102—31no—
228#102D3×C911yescharacteristic, complemented
229C3×C9#46011yescharacteristic, complemented, Sylow
230C23×C3—21no—
231C23×C3—21no—
232C23×C3—41no—
233C23×C3—61no—
234C22×D3—21no—
235C3×Q8—32no—
236C3×Q8—61no—
237C3×D4—22no—
238C3×D4—21no—
239C3×D4—21no—
240C3×D4—21no—
241C3×D4—21no—
242C3×D4—41no—
243C3×D4—61no—
244C3×D4—61no—
245C3×D4—122no—
246C3×D4—122no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—31no—
251C2×C3×C4—31no—
252C2×C3×C4—41no—
253C2×C3×C4—61no—
254C2×C3×C4C23×C911yescharacteristic
255C2×C3×C4C22×C3×D311yescharacteristic
256#67—42no—
257#67—42no—
258C2×Dic3—21no—
259C2×Dic3D4×C911yescharacteristic
260C2×Dic3D4×C911yescharacteristic
261D12—21no—
262D12—21no—
263Dic6—21no—
264Dic6D4×C912yescomplemented
265C3×C8—21no—
266C3×C8—21no—
267C3×C8—41no—
268C3×C8—61no—
269C3⋊C8—21no—
270C2×C32—81no—
271C2×C32C3×#12111yescharacteristic
272C2×C32C2×C3×SD1611yescharacteristic
273C2×C32C3×AGL(1,ℤ/8)11yescharacteristic
274C3×D3—81no—
275C2×C9—21no—
276C2×C9—21no—
277C2×C9—21no—
278C2×C9—82no—
279C2×C9—81no—
280C2×C9—241no—
281C2×C9#88411yescharacteristic
282C2×C9#91111yescharacteristic
283C2×C9D3×SD1611yescharacteristic
284C2×Q8—31no—
285C2×D4—31no—
286C2×D4—61no—
287C2×D4—61no—
288C2×D4C2×D3×C911yescharacteristic
289SD16—62no—
290SD16—62no—
291C2×C8—31no—
292C2×C8C2×D3×C911yescharacteristic
293C4⋊C4—61no—
294C4⋊C4C2×D3×C911yescharacteristic
295C42—31no—
296C42—61no—
297C22×C3—21no—
298C22×C3—42no—
299C22×C3—41no—
300C22×C3—41no—
301C22×C3—41no—
302C22×C3—41no—
303C22×C3—41no—
304C22×C3—41no—
305C22×C3—81no—
306C22×C3—81no—
307C22×C3—121no—
308C22×C3—121no—
309C22×C3—121no—
310C22×C3C2×D4×C911yescharacteristic
311C22×C3C3×D3×D411yescharacteristic
312C2×D3—41no—
313C2×D3—41no—
314C2×D3—41no—
315C3×C4—21no—
316C3×C4—21no—
317C3×C4—32no—
318C3×C4—41no—
319C3×C4—41no—
320C3×C4—62no—
321C3×C4—61no—
322C3×C4—81no—
323C3×C4C2×D4×C911yescharacteristic
324C3×C4C9×#4111yescharacteristic
325C3×C4C3×#23511yescharacteristic
326C3×C4C3×D3×D411yescharacteristic
327Dic3—22no—
328Dic3—21no—
329Dic3C9×SD1612yescomplemented
330C32C3×#46011yescharacteristic
331C9—21no—
332C9#476211yescharacteristic, direct product factor
333C23—21no—
334C23—61no—
335Q8—32no—
336Q8—61no—
337D4—21no—
338D4—21no—
339D4—61no—
340D4—61no—
341D4—122no—
342D4—122no—
343C2×C4—21no—
344C2×C4—31no—
345C2×C4—31no—
346C2×C4—61no—
347C2×C4C22×D3×C911yescharacteristic
348C8—21no—
349C8—61no—
350C2×C3—21no—
351C2×C3—21no—
352C2×C3—21no—
353C2×C3—82no—
354C2×C3—81no—
355C2×C3—81no—
356C2×C3—241no—
357C2×C3C9×#12111yescharacteristic
358C2×C3C2×C9×SD1611yescharacteristic
359C2×C3C9×AGL(1,ℤ/8)11yescharacteristic
360C2×C3C3×#88411yescharacteristic
361C2×C3C3×#91111yescharacteristic
362C2×C3C3×D3×SD1611yescharacteristic
363D3—81no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—121no—
368C22—121no—
369C22—121no—
370C22D3×D4×C911yescharacteristic
371C4—32no—
372C4—41no—
373C4—61no—
374C4—62no—
375C4C9×#23511yescharacteristic
376C4D3×D4×C911yescharacteristic
377C3—21no—
378C3C9×#46011yescharacteristic, complemented
379C3C3×#476211yescharacteristic
380C2—81no—
381C2—241no—
382C2C9×#88411yescharacteristic
383C2C9×#91111yescharacteristic
384C2D3×C9×SD1611yescharacteristic
subgroupG/H
centerC22×C9D3×D4
commutatorC2×C3×C4C23×C9
FrattiniC2×C3×C4C22×C3×D3
FittingC3×C9×#102C2
socleC22×C32C2×C3×D4
prime radicalC3×#940C2×C3
cosocleC2×C32×C4C23×C3
hypercenterC9×#102D3
hypocenterC3C9×#460
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C9 ◁ C2×C4×C9 ◁ C9×#102

Complements

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

NH ≅ G/Ntype
2. C2×C9×#214C2semidirect
3. C2×C9×#204C2semidirect
4. C9×#887C2semidirect
5. C3×C9×#102C2semidirect
6. C9×Dic3⋊C8C2semidirect
7. C9×#809C2semidirect
37. C9×#102D3semidirect
52. C9×Dic6D4semidirect
56. #4762C9direct (N × H)
98. C9×Dic3SD16semidirect
104. C2×#214C2×C9semidirect
105. C2×#204C2×C9semidirect
106. #887C2×C9semidirect
110. C3×#102C2×C9semidirect
112. Dic3⋊C8C2×C9semidirect
113. #809C2×C9semidirect
228. #102D3×C9semidirect
229. C3×C9#460semidirect
264. Dic6D4×C9semidirect
329. Dic3C9×SD16semidirect
332. C9#4762direct (N × H)
378. C3C9×#460semidirect

Maximal subgroups

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

subgroupindex
C9×#9402
C2×C9×#2142
C2×C9×#2042
C9×#8872
C3×C9×#1022
C9×Dic3⋊C82
C9×#8092
C3×#47623
C9×#4603