Finite Group Databasebeta

← C9×#4825 #13141977

Subgroups — C9×#4825 #13141977

Order 1728.

500 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#1009C211yesmaximal, characteristic
2C9×#951C211yesmaximal, characteristic, complemented
3C9×#909C211yesmaximal, characteristic, complemented
4C9×#875C211yesmaximal, characteristic, complemented
5C3×C9×#104C211yesmaximal, characteristic, complemented
6C9×#823C211yesmaximal, characteristic, complemented
7C9×#805C211yesmaximal, characteristic, complemented
8C3×#4825C311yesmaximal, characteristic
9C9×#455—31nomaximal
10C3×C9×#41C2211yescharacteristic
11C9×#239—21no—
12D3×D4×C9—22no—
13D3×D4×C9—21no—
14C9×#235—21no—
15C9×#235C2211yescharacteristic
16C2×C9×D12—21no—
17C2×C9×D12C2211yescharacteristic
18C2×C9×Dic6C2211yescharacteristic, complemented
19C3×C9×M16C2211yescharacteristic, complemented
20C3×C42×C9C2211yescharacteristic, complemented
21C9×#216—21no—
22C9×#214—21no—
23C9×(C2×D3)⋊C4—22no—
24C9×#208C2211yescharacteristic, complemented
25C9×Dic12—21no—
26C9×#204—21no—
27C3×#1009C2×C311yescharacteristic
28C3×#951C2×C311yescharacteristic
29C3×#909C2×C311yescharacteristic
30C3×#875C2×C311yescharacteristic
31C9×H(5,𝔽2)—31no—
32C32×#104C2×C311yescharacteristic
33C3×#823C2×C311yescharacteristic
34C3×#805C2×C311yescharacteristic
35C9×#137—31no—
36C9×#137—31no—
37C9×#124—31no—
38C9×#104—21no—
39C9×#104—31no—
40C9×#104D311yescharacteristic, complemented
41C9×#100—31no—
42C22×D3×C9—22no—
43C22×D3×C9D412yes—
44C3×Q8×C9D411yescharacteristic
45C3×D4×C9—21no—
46C3×D4×C9D411yescharacteristic
47C2×C3×C4×C9—21no—
48C2×C3×C4×C9—21no—
49C2×C3×C4×C9C2311yescharacteristic
50C9×#67—22no—
51C9×#67—21no—
52C2×C9×Dic3—21no—
53C9×D12—22no—
54C9×D12—21no—
55C9×D12—21no—
56C9×D12D411yescharacteristic
57C4×D3×C9—22no—
58C4×D3×C9—21no—
59C9×Dic6—21no—
60C9×Dic6—21no—
61C9×Dic6D411yescharacteristic
62C3×C8×C9—21no—
63C9×C3⋊C8—21no—
64C3×#455—31no—
65#4825C911yescharacteristic, direct product factor
66C32×#41C22×C311yescharacteristic
67C3×#239—21no—
68C3×D3×D4—22no—
69C3×D3×D4—21no—
70C3×#235—21no—
71C3×#235C22×C311yescharacteristic
72C2×C3×D12—21no—
73C2×C3×D12C22×C311yescharacteristic
74C2×C3×Dic6C22×C311yescharacteristic
75C32×M16C22×C311yescharacteristic
76C32×C42C22×C311yescharacteristic
77C3×#216—21no—
78C3×#214—21no—
79C3×(C2×D3)⋊C4—22no—
80C3×#208C22×C311yescharacteristic
81C3×Dic12—21no—
82C3×#204—21no—
83C9×#41—21no—
84C9×#41—31no—
85C9×#41—61no—
86C9×#41—61no—
87C9×#41C2×D311yescharacteristic
88C2×Q8×C9—31no—
89C2×D4×C9—31no—
90C2×D4×C9—61no—
91C2×D4×C9—62no—
92C2×D4×C9—61no—
93C9×Q16—61no—
94C9×Q16—61no—
95C9×SD16—61no—
96C9×SD16—61no—
97C9×M16—21no—
98C9×M16—31no—
99C9×M16C2×D311yescharacteristic, complemented
100C9×C22⋊C4—62no—
101C42×C9—21no—
102C42×C9C2×D311yescharacteristic, complemented
103C22×C3×C9—21no—
104C22×C3×C9C2×D411yescharacteristic
105C2×D3×C9—22no—
106C2×D3×C9—21no—
107C2×D3×C9—42no—
108C2×D3×C9—82no—
109C3×C4×C9—21no—
110C3×C4×C9—41no—
111C3×C4×C9C2×D411yescharacteristic
112C3×C4×C9C2×D411yescharacteristic
113C9×Dic3—21no—
114C9×Dic3—41no—
115C3×H(5,𝔽2)—31no—
116#1009C2×C911yescharacteristic
117C3×#137—31no—
118C3×#137—31no—
119C3×#124—31no—
120#951C2×C911yescharacteristic, complemented
121#909C2×C911yescharacteristic, complemented
122#875C2×C911yescharacteristic, complemented
123C3×#104—21no—
124C3×#104—31no—
125C3×#104C2×C911yescharacteristic, complemented
126C3×#104C3×D311yescharacteristic
127C3×#100—31no—
128#823C2×C911yescharacteristic, complemented
129#805C2×C911yescharacteristic, complemented
130C22×C3×D3—22no—
131C22×C3×D3C3×D412yes—
132C32×Q8C3×D411yescharacteristic
133C32×D4—21no—
134C32×D4C3×D411yescharacteristic
135C2×C32×C4—21no—
136C2×C32×C4—21no—
137C2×C32×C4C23×C311yescharacteristic
138C3×#67—22no—
139C3×#67—21no—
140C2×C3×Dic3—21no—
141C3×D12—22no—
142C3×D12—21no—
143C3×D12—21no—
144C3×D12C3×D411yescharacteristic
145C3×C4×D3—22no—
146C3×C4×D3—21no—
147C3×Dic6—21no—
148C3×Dic6—21no—
149C3×Dic6C3×D411yescharacteristic
150C23×C9—32no—
151C23×C9—62no—
152C32×C8—21no—
153C3×C3⋊C8—21no—
154Q8×C9—21no—
155Q8×C9—31no—
156Q8×C9—61no—
157Q8×C9—61no—
158Q8×C9D1211yescharacteristic
159D4×C9—21no—
160D4×C9—21no—
161D4×C9—31no—
162D4×C9—41no—
163D4×C9—62no—
164D4×C9—62no—
165D4×C9—61no—
166D4×C9—61no—
167D4×C9—61no—
168D4×C9D1211yescharacteristic
169C2×C4×C9—21no—
170C2×C4×C9—21no—
171C2×C4×C9—21no—
172C2×C4×C9—41no—
173C2×C4×C9—41no—
174C2×C4×C9—62no—
175C2×C4×C9—61no—
176C2×C4×C9—61no—
177C2×C4×C9C22×D311yescharacteristic
178C8×C9—21no—
179C8×C9—41no—
180C8×C9—61no—
181#455—31noSylow
182C2×C3×C9—21no—
183C2×C3×C9—41no—
184C2×C3×C9#12011yescharacteristic
185D3×C9—42no—
186D3×C9—41no—
187C3×#41—21no—
188C3×#41—31no—
189C3×#41—61no—
190C3×#41—61no—
191C3×#41C22×C911yescharacteristic
192C3×#41C2×C3×D311yescharacteristic
193C2×C3×Q8—31no—
194C2×C3×D4—31no—
195C2×C3×D4—61no—
196C2×C3×D4—62no—
197C2×C3×D4—61no—
198#239—21no—
199D3×D4—22no—
200D3×D4—21no—
201#235—21no—
202#235C22×C911yescharacteristic
203C2×D12—21no—
204C2×D12C22×C911yescharacteristic
205C2×Dic6C22×C911yescharacteristic, complemented
206C3×Q16—61no—
207C3×Q16—61no—
208C3×SD16—61no—
209C3×SD16—61no—
210C3×M16—21no—
211C3×M16—31no—
212C3×M16C22×C911yescharacteristic, complemented
213C3×M16C2×C3×D311yescharacteristic
214C3×C22⋊C4—62no—
215C3×C42—21no—
216C3×C42C22×C911yescharacteristic, complemented
217C3×C42C2×C3×D311yescharacteristic
218#216—21no—
219#214—21no—
220(C2×D3)⋊C4—22no—
221#208C22×C911yescharacteristic, complemented
222Dic12—21no—
223#204—21no—
224C22×C32—21no—
225C22×C32C2×C3×D411yescharacteristic
226C2×C3×D3—22no—
227C2×C3×D3—21no—
228C2×C3×D3—42no—
229C2×C3×D3—82no—
230C32×C4—21no—
231C32×C4—41no—
232C32×C4C2×C3×D411yescharacteristic
233C32×C4C2×C3×D411yescharacteristic
234C3×Dic3—21no—
235C3×Dic3—41no—
236C22×C9—21no—
237C22×C9—21no—
238C22×C9—41no—
239C22×C9—61no—
240C22×C9—62no—
241C22×C9—122no—
242C22×C9—242no—
243C22×C9D3×D411yescharacteristic
244C4×C9—21no—
245C4×C9—21no—
246C4×C9—21no—
247C4×C9—41no—
248C4×C9—41no—
249C4×C9—42no—
250C4×C9—61no—
251C4×C9—121no—
252C4×C9C2×D1211yescharacteristic
253C4×C9D3×D411yescharacteristic
254H(5,𝔽2)—31no—
255#137—31no—
256#137—31no—
257#124—31no—
258#104—31no—
259#104D3×C911yescharacteristic, complemented
260#100—31no—
261C3×C9#45511yescharacteristic, complemented, Sylow
262C23×C3—32no—
263C23×C3—62no—
264C22×D3—22no—
265C22×D3D4×C912yes—
266C3×Q8—21no—
267C3×Q8—31no—
268C3×Q8—61no—
269C3×Q8—61no—
270C3×Q8D4×C911yescharacteristic
271C3×Q8C3×D1211yescharacteristic
272C3×D4—21no—
273C3×D4—21no—
274C3×D4—21no—
275C3×D4—31no—
276C3×D4—41no—
277C3×D4—62no—
278C3×D4—62no—
279C3×D4—61no—
280C3×D4—61no—
281C3×D4—61no—
282C3×D4D4×C911yescharacteristic
283C3×D4C3×D1211yescharacteristic
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—41no—
290C2×C3×C4—41no—
291C2×C3×C4—62no—
292C2×C3×C4—61no—
293C2×C3×C4—61no—
294C2×C3×C4C23×C911yescharacteristic
295C2×C3×C4C22×C3×D311yescharacteristic
296#67—22no—
297#67—21no—
298C2×Dic3—21no—
299D12—22no—
300D12—21no—
301D12—21no—
302D12D4×C911yescharacteristic
303C4×D3—22no—
304C4×D3—21no—
305Dic6—21no—
306Dic6—21no—
307Dic6D4×C911yescharacteristic
308C3×C8—21no—
309C3×C8—21no—
310C3×C8—41no—
311C3×C8—61no—
312C3⋊C8—21no—
313C2×C32—21no—
314C2×C32—41no—
315C2×C32C3×#12011yescharacteristic
316C3×D3—42no—
317C3×D3—41no—
318C2×C9—21no—
319C2×C9—21no—
320C2×C9—41no—
321C2×C9—41no—
322C2×C9—81no—
323C2×C9—122no—
324C2×C9—121no—
325C2×C9#88211yescharacteristic
326#41—31no—
327#41—61no—
328#41—61no—
329#41C2×D3×C911yescharacteristic
330C2×Q8—31no—
331C2×D4—31no—
332C2×D4—61no—
333C2×D4—62no—
334C2×D4—61no—
335Q16—61no—
336Q16—61no—
337SD16—61no—
338SD16—61no—
339M16—31no—
340M16C2×D3×C911yescharacteristic, complemented
341C22⋊C4—62no—
342C42C2×D3×C911yescharacteristic, complemented
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—41no—
347C22×C3—61no—
348C22×C3—62no—
349C22×C3—122no—
350C22×C3—242no—
351C22×C3C2×D4×C911yescharacteristic
352C22×C3C3×D3×D411yescharacteristic
353C2×D3—22no—
354C2×D3—21no—
355C2×D3—42no—
356C2×D3—82no—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—41no—
362C3×C4—41no—
363C3×C4—41no—
364C3×C4—42no—
365C3×C4—61no—
366C3×C4—121no—
367C3×C4C2×D4×C911yescharacteristic
368C3×C4C2×D4×C911yescharacteristic
369C3×C4C2×C3×D1211yescharacteristic
370C3×C4C3×D3×D411yescharacteristic
371Dic3—21no—
372Dic3—41no—
373C32C3×#45511yescharacteristic
374C9—21no—
375C9#482511yescharacteristic, direct product factor
376C23—32no—
377C23—62no—
378Q8—31no—
379Q8—61no—
380Q8—61no—
381Q8C9×D1211yescharacteristic
382D4—21no—
383D4—31no—
384D4—62no—
385D4—62no—
386D4—61no—
387D4—61no—
388D4—61no—
389D4C9×D1211yescharacteristic
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—62no—
393C2×C4—61no—
394C2×C4—61no—
395C2×C4C22×D3×C911yescharacteristic
396C8—21no—
397C8—61no—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—41no—
402C2×C3—41no—
403C2×C3—41no—
404C2×C3—81no—
405C2×C3—122no—
406C2×C3—121no—
407C2×C3C9×#12011yescharacteristic
408C2×C3C3×#88211yescharacteristic
409D3—42no—
410D3—41no—
411C22—21no—
412C22—61no—
413C22—62no—
414C22—122no—
415C22—242no—
416C22D3×D4×C911yescharacteristic
417C4—21no—
418C4—41no—
419C4—61no—
420C4—121no—
421C4C2×C9×D1211yescharacteristic
422C4D3×D4×C911yescharacteristic
423C3—21no—
424C3C9×#45511yescharacteristic, complemented
425C3C3×#482511yescharacteristic
426C2—21no—
427C2—41no—
428C2—122no—
429C2—121no—
430C2C9×#88211yescharacteristic
subgroupG/H
centerC2×C9#882
commutatorC2×C3×C4C23×C9
FrattiniC2×C3×C4C22×C3×D3
FittingC3×C9×#104C2
socleC2×C32C3×#120
prime radicalC3×#1009C2×C3
cosocleC2×C32×C4C23×C3
hypercenterC9×#104D3
hypocenterC3C9×#455
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C9 ◁ C2×C4×C9 ◁ C9×#104

Complements

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

NH ≅ G/Ntype
2. C9×#951C2semidirect
3. C9×#909C2semidirect
4. C9×#875C2semidirect
5. C3×C9×#104C2semidirect
6. C9×#823C2semidirect
7. C9×#805C2semidirect
18. C2×C9×Dic6C22semidirect
19. C3×C9×M16C22semidirect
20. C3×C42×C9C22semidirect
24. C9×#208C22semidirect
40. C9×#104D3semidirect
65. #4825C9direct (N × H)
99. C9×M16C2×D3semidirect
102. C42×C9C2×D3semidirect
120. #951C2×C9semidirect
121. #909C2×C9semidirect
122. #875C2×C9semidirect
125. C3×#104C2×C9semidirect
128. #823C2×C9semidirect
129. #805C2×C9semidirect
205. C2×Dic6C22×C9semidirect
212. C3×M16C22×C9semidirect
216. C3×C42C22×C9semidirect
221. #208C22×C9semidirect
259. #104D3×C9semidirect
261. C3×C9#455semidirect
340. M16C2×D3×C9semidirect
342. C42C2×D3×C9semidirect
375. C9#4825direct (N × H)
424. C3C9×#455semidirect

Maximal subgroups

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

subgroupindex
C9×#10092
C9×#9512
C9×#9092
C9×#8752
C3×C9×#1042
C9×#8232
C9×#8052
C3×#48253
C9×#4553