Finite Group Databasebeta

← C9×#3460 #11768181

Subgroups — C9×#3460 #11768181

Order 1152.

1710 conjugacy classes of subgroups.

The subgroup lattice has 447 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#544C211yesmaximal, characteristic, complemented
2C9×#542C214yesmaximal, complemented
3C9×#540C214yesmaximal, complemented
4C9×#538C214yesmaximal, complemented
5C9×#537C211yesmaximal, characteristic, complemented
6C9×#535C212yesmaximal, complemented
7C9×#532C214yesmaximal, complemented
8C9×#529C214yesmaximal, complemented
9C9×#525C214yesmaximal, complemented
10C4×C9×#41C212yesmaximal, complemented
11C2×C4×D4×C9C211yesmaximal, characteristic, complemented
12C3×#3460C311yesmaximal, characteristic
13C2×C9×#41C2212yes—
14C2×C9×#41C2214yescomplemented
15C22×D4×C9C2211yescharacteristic
16C23×C4×C9C2212yes—
17C9×C4⋊Q8C2214yescomplemented
18C9×#127C2214yes—
19C9×#126C2218yescomplemented
20C9×#125C2214yescomplemented
21C9×#124C2214yes—
22C9×#124C2218yescomplemented
23C9×#123C2218yescomplemented
24C9×#123C2218yescomplemented
25C9×C22⋊Q8C2214yes—
26C9×C22⋊Q8C2214yescomplemented
27C9×C22⋊Q8C2214yescomplemented
28C9×#121C2214yes—
29C9×#121C2214yes—
30C9×#121C2214yes—
31C9×#121C2214yescomplemented
32C9×#121C2214yescomplemented
33C9×#121C2218yescomplemented
34C9×#120C2218yes—
35C4×Q8×C9C2212yescomplemented
36C4×Q8×C9C2212yescomplemented
37C4×D4×C9C2214yes—
38C4×D4×C9C2214yes—
39C4×D4×C9C2214yes—
40C4×D4×C9C2214yes—
41C4×D4×C9C2218yescomplemented
42C4×D4×C9C2212yescomplemented
43C4×D4×C9C2212yescomplemented
44C9×#117C2212yes—
45C9×#117C2214yescomplemented
46C9×#117C2214yescomplemented
47C2×C9×C4⋊C4C2211yescharacteristic
48C2×C9×C22⋊C4C2212yes—
49C2×C42×C9C2211yescharacteristic
50C2×C42×C9C2214yescomplemented
51C3×#544C2×C311yescharacteristic
52C3×#542C2×C314yes—
53C3×#540C2×C314yes—
54C3×#538C2×C314yes—
55C3×#537C2×C311yescharacteristic
56C3×#535C2×C312yes—
57C3×#532C2×C314yes—
58C3×#529C2×C314yes—
59C3×#525C2×C314yes—
60C3×C4×#41C2×C312yes—
61C2×C3×C4×D4C2×C311yescharacteristic
62C24×C9C2312yes—
63C9×#41—28no—
64C9×#41—48no—
65C2×Q8×C9C2312yes—
66C2×Q8×C9C2314yes—
67C2×D4×C9—24no—
68C2×D4×C9C2314yes—
69C2×D4×C9C2314yes—
70C2×D4×C9C2312yes—
71C2×D4×C9C2318yes—
72C2×D4×C9C2318yes—
73C2×D4×C9C2314yes—
74C22×C4×C9—44no—
75C22×C4×C9C2314yes—
76C22×C4×C9C2311yescharacteristic
77C22×C4×C9C2314yes—
78C22×C4×C9C2314yes—
79C22×C4×C9C2311yescharacteristic
80C22×C4×C9C2314yes—
81C22×C4×C9C2312yes—
82C22×C4×C9C2314yes—
83C22×C4×C9C2311yescharacteristic
84C9×C4⋊C4C2314yes—
85C9×C4⋊C4C2312yes—
86C9×C4⋊C4C2312yes—
87C9×C4⋊C4C2314yes—
88C9×C4⋊C4C2314yes—
89C9×C4⋊C4C2314yes—
90C9×C4⋊C4C2314yes—
91C9×C4⋊C4C2318yes—
92C9×C22⋊C4C2318yes—
93C9×C22⋊C4C2314yes—
94C9×C22⋊C4C2314yes—
95C9×C22⋊C4C2314yes—
96C9×C22⋊C4C2318yes—
97C9×C22⋊C4C2318yes—
98C9×C22⋊C4C2318yes—
99C42×C9C2312yes—
100C42×C9C2314yes—
101C42×C9C2314yes—
102C42×C9C2312yes—
103C42×C9C2314yes—
104#3460C911yescharacteristic, direct product factor, Sylow
105C2×C3×#41C22×C312yes—
106C2×C3×#41C22×C314yes—
107C22×C3×D4C22×C311yescharacteristic
108C23×C3×C4C22×C312yes—
109C3×C4⋊Q8C22×C314yes—
110C3×#127C22×C314yes—
111C3×#126C22×C318yes—
112C3×#125C22×C314yes—
113C3×#124C22×C314yes—
114C3×#124C22×C318yes—
115C3×#123C22×C318yes—
116C3×#123C22×C318yes—
117C3×C22⋊Q8C22×C314yes—
118C3×C22⋊Q8C22×C314yes—
119C3×C22⋊Q8C22×C314yes—
120C3×#121C22×C314yes—
121C3×#121C22×C314yes—
122C3×#121C22×C314yes—
123C3×#121C22×C314yes—
124C3×#121C22×C314yes—
125C3×#121C22×C318yes—
126C3×#120C22×C318yes—
127C3×C4×Q8C22×C312yes—
128C3×C4×Q8C22×C312yes—
129C3×C4×D4C22×C314yes—
130C3×C4×D4C22×C314yes—
131C3×C4×D4C22×C314yes—
132C3×C4×D4C22×C314yes—
133C3×C4×D4C22×C312yes—
134C3×C4×D4C22×C312yes—
135C3×C4×D4C22×C318yes—
136C3×#117C22×C312yes—
137C3×#117C22×C314yes—
138C3×#117C22×C314yes—
139C2×C3×C4⋊C4C22×C311yescharacteristic
140C2×C3×C22⋊C4C22×C312yes—
141C2×C3×C42C22×C311yescharacteristic
142C2×C3×C42C22×C314yes—
143C23×C9—24no—
144C23×C9—42no—
145C23×C9—42no—
146C23×C9C2414yes—
147C23×C9C2414yes—
148C23×C9C2411yescharacteristic
149Q8×C9—24no—
150Q8×C9—44no—
151D4×C9—28no—
152D4×C9—28no—
153D4×C9—24no—
154D4×C9—48no—
155D4×C9—44no—
156D4×C9—48no—
157C2×C4×C9—28no—
158C2×C4×C9—22no—
159C2×C4×C9—28no—
160C2×C4×C9—28no—
161C2×C4×C9—44no—
162C2×C4×C9—42no—
163C2×C4×C9—41no—
164C2×C4×C9—44no—
165C2×C4×C9#4114yescomplemented
166C2×C4×C9C2412yes—
167C2×C4×C9C2414yes—
168C2×C4×C9C2414yes—
169C2×C4×C9C2411yescharacteristic
170C2×C4×C9C2414yes—
171C2×C4×C9C2414yes—
172C2×C4×C9C2412yes—
173C2×C4×C9C2411yescharacteristic
174#544C2×C911yescharacteristic, complemented
175#542C2×C914yescomplemented
176#540C2×C914yescomplemented
177#538C2×C914yescomplemented
178#537C2×C911yescharacteristic, complemented
179#535C2×C912yescomplemented
180#532C2×C914yescomplemented
181#529C2×C914yescomplemented
182#525C2×C914yescomplemented
183C4×#41C2×C912yescomplemented
184C2×C4×D4C2×C911yescharacteristic, complemented
185C24×C3C23×C312yes—
186C3×#41—28no—
187C3×#41—48no—
188C2×C3×Q8C23×C312yes—
189C2×C3×Q8C23×C314yes—
190C2×C3×D4—24no—
191C2×C3×D4C23×C314yes—
192C2×C3×D4C23×C314yes—
193C2×C3×D4C23×C312yes—
194C2×C3×D4C23×C318yes—
195C2×C3×D4C23×C318yes—
196C2×C3×D4C23×C314yes—
197C22×C3×C4—44no—
198C22×C3×C4C23×C314yes—
199C22×C3×C4C23×C311yescharacteristic
200C22×C3×C4C23×C314yes—
201C22×C3×C4C23×C314yes—
202C22×C3×C4C23×C311yescharacteristic
203C22×C3×C4C23×C314yes—
204C22×C3×C4C23×C312yes—
205C22×C3×C4C23×C314yes—
206C22×C3×C4C23×C311yescharacteristic
207C3×C4⋊C4C23×C314yes—
208C3×C4⋊C4C23×C312yes—
209C3×C4⋊C4C23×C312yes—
210C3×C4⋊C4C23×C314yes—
211C3×C4⋊C4C23×C314yes—
212C3×C4⋊C4C23×C314yes—
213C3×C4⋊C4C23×C314yes—
214C3×C4⋊C4C23×C318yes—
215C3×C22⋊C4C23×C318yes—
216C3×C22⋊C4C23×C314yes—
217C3×C22⋊C4C23×C314yes—
218C3×C22⋊C4C23×C314yes—
219C3×C22⋊C4C23×C318yes—
220C3×C22⋊C4C23×C318yes—
221C3×C22⋊C4C23×C318yes—
222C3×C42C23×C312yes—
223C3×C42C23×C312yes—
224C3×C42C23×C314yes—
225C3×C42C23×C314yes—
226C3×C42C23×C314yes—
227C22×C9—21no—
228C22×C9—21no—
229C22×C9—24no—
230C22×C9—24no—
231C22×C9—24no—
232C22×C9—24no—
233C22×C9—24no—
234C22×C9—24no—
235C22×C9—48no—
236C22×C9C2×#4112yes—
237C22×C9C2511yescharacteristic
238C4×C9—24no—
239C4×C9—21no—
240C4×C9—24no—
241C4×C9—24no—
242C4×C9—22no—
243C4×C9—24no—
244C4×C9C2×#4114yes—
245C4×C9H(5,𝔽2)12yes—
246C2×#41C22×C912yes—
247C2×#41C22×C914yescomplemented
248C22×D4C22×C911yescharacteristic
249C23×C4C22×C912yes—
250C4⋊Q8C22×C914yescomplemented
251#127C22×C914yes—
252#126C22×C918yescomplemented
253#125C22×C914yescomplemented
254#124C22×C914yes—
255#124C22×C918yescomplemented
256#123C22×C918yescomplemented
257#123C22×C918yescomplemented
258C22⋊Q8C22×C914yes—
259C22⋊Q8C22×C914yescomplemented
260C22⋊Q8C22×C914yescomplemented
261#121C22×C914yes—
262#121C22×C914yes—
263#121C22×C914yes—
264#121C22×C914yescomplemented
265#121C22×C914yescomplemented
266#121C22×C918yescomplemented
267#120C22×C918yes—
268C4×Q8C22×C912yescomplemented
269C4×Q8C22×C912yescomplemented
270C4×D4C22×C914yes—
271C4×D4C22×C914yes—
272C4×D4C22×C914yes—
273C4×D4C22×C914yes—
274C4×D4C22×C912yescomplemented
275C4×D4C22×C912yescomplemented
276C4×D4C22×C918yescomplemented
277#117C22×C912yes—
278#117C22×C914yescomplemented
279#117C22×C914yescomplemented
280C2×C4⋊C4C22×C911yescharacteristic
281C2×C22⋊C4C22×C912yes—
282C2×C42C22×C911yescharacteristic
283C2×C42C22×C914yescomplemented
284C23×C3—24no—
285C23×C3—42no—
286C23×C3—42no—
287C23×C3C24×C314yes—
288C23×C3C24×C314yes—
289C23×C3C24×C311yescharacteristic
290C3×Q8—24no—
291C3×Q8—44no—
292C3×D4—28no—
293C3×D4—28no—
294C3×D4—24no—
295C3×D4—48no—
296C3×D4—44no—
297C3×D4—48no—
298C2×C3×C4—28no—
299C2×C3×C4—22no—
300C2×C3×C4—28no—
301C2×C3×C4—28no—
302C2×C3×C4—44no—
303C2×C3×C4—42no—
304C2×C3×C4—41no—
305C2×C3×C4—44no—
306C2×C3×C4C3×#4114yes—
307C2×C3×C4C24×C312yes—
308C2×C3×C4C24×C314yes—
309C2×C3×C4C24×C314yes—
310C2×C3×C4C24×C311yescharacteristic
311C2×C3×C4C24×C314yes—
312C2×C3×C4C24×C314yes—
313C2×C3×C4C24×C312yes—
314C2×C3×C4C24×C311yescharacteristic
315C2×C9—22no—
316C2×C9—44no—
317C2×C9—44no—
318C2×C9C22×#4111yescharacteristic
319C2×C9C2×H(5,𝔽2)11yescharacteristic
320C2×C9#58511yescharacteristic
321C24C23×C912yes—
322#41—28no—
323#41—48no—
324C2×Q8C23×C912yes—
325C2×Q8C23×C914yes—
326C2×D4—24no—
327C2×D4C23×C914yes—
328C2×D4C23×C914yes—
329C2×D4C23×C912yes—
330C2×D4C23×C918yes—
331C2×D4C23×C918yes—
332C2×D4C23×C914yes—
333C22×C4—44no—
334C22×C4C23×C911yescharacteristic
335C22×C4C23×C914yes—
336C22×C4C23×C914yes—
337C22×C4C23×C914yes—
338C22×C4C23×C911yescharacteristic
339C22×C4C23×C914yes—
340C22×C4C23×C912yes—
341C22×C4C23×C914yes—
342C22×C4C23×C911yescharacteristic
343C4⋊C4C23×C914yes—
344C4⋊C4C23×C912yes—
345C4⋊C4C23×C912yes—
346C4⋊C4C23×C914yes—
347C4⋊C4C23×C914yes—
348C4⋊C4C23×C914yes—
349C4⋊C4C23×C914yes—
350C4⋊C4C23×C918yes—
351C22⋊C4C23×C918yes—
352C22⋊C4C23×C914yes—
353C22⋊C4C23×C914yes—
354C22⋊C4C23×C914yes—
355C22⋊C4C23×C918yes—
356C22⋊C4C23×C918yes—
357C22⋊C4C23×C918yes—
358C42C23×C912yes—
359C42C23×C912yes—
360C42C23×C914yes—
361C42C23×C914yes—
362C42C23×C914yes—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—24no—
366C22×C3—24no—
367C22×C3—24no—
368C22×C3—24no—
369C22×C3—24no—
370C22×C3—24no—
371C22×C3—48no—
372C22×C3C2×C3×#4112yes—
373C22×C3C25×C311yescharacteristic
374C3×C4—24no—
375C3×C4—21no—
376C3×C4—24no—
377C3×C4—24no—
378C3×C4—22no—
379C3×C4—24no—
380C3×C4C2×C3×#4114yes—
381C3×C4C3×H(5,𝔽2)12yes—
382C9#346011yescharacteristic, direct product factor, Sylow
383C23—24no—
384C23—42no—
385C23—42no—
386C23C24×C914yes—
387C23C24×C914yes—
388C23C24×C911yescharacteristic
389Q8—24no—
390Q8—44no—
391D4—28no—
392D4—28no—
393D4—24no—
394D4—44no—
395D4—48no—
396D4—48no—
397C2×C4—28no—
398C2×C4—22no—
399C2×C4—28no—
400C2×C4—28no—
401C2×C4—44no—
402C2×C4—42no—
403C2×C4—41no—
404C2×C4—44no—
405C2×C4C9×#4114yescomplemented
406C2×C4C24×C912yes—
407C2×C4C24×C914yes—
408C2×C4C24×C914yes—
409C2×C4C24×C911yescharacteristic
410C2×C4C24×C914yes—
411C2×C4C24×C914yes—
412C2×C4C24×C912yes—
413C2×C4C24×C911yescharacteristic
414C2×C3—22no—
415C2×C3—44no—
416C2×C3—44no—
417C2×C3C22×C3×#4111yescharacteristic
418C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
419C2×C3C3×#58511yescharacteristic
420C22—21no—
421C22—21no—
422C22—24no—
423C22—24no—
424C22—24no—
425C22—24no—
426C22—24no—
427C22—24no—
428C22—48no—
429C22C2×C9×#4112yes—
430C22C25×C911yescharacteristic
431C4—24no—
432C4—21no—
433C4—24no—
434C4—24no—
435C4—22no—
436C4—24no—
437C4C2×C9×#4114yes—
438C4C9×H(5,𝔽2)12yes—
439C3C3×#346011yescharacteristic
440C2—22no—
441C2—44no—
442C2—44no—
443C2C22×C9×#4111yescharacteristic
444C2C2×C9×H(5,𝔽2)11yescharacteristic
445C2C9×#58511yescharacteristic
subgroupG/H
centerC2×C4×C9C24
commutatorC22C25×C9
Frattini, socle, cosocleC22×C3C25×C3
prime radicalC3×#3460C3
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C9 ◁ G

Complements

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

NH ≅ G/Ntype
1. C9×#544C2semidirect
2. C9×#542C2semidirect
3. C9×#540C2semidirect
4. C9×#538C2semidirect
5. C9×#537C2semidirect
6. C9×#535C2semidirect
7. C9×#532C2semidirect
8. C9×#529C2semidirect
9. C9×#525C2semidirect
10. C4×C9×#41C2semidirect
11. C2×C4×D4×C9C2semidirect
14. C2×C9×#41C22semidirect
17. C9×C4⋊Q8C22semidirect
19. C9×#126C22semidirect
20. C9×#125C22semidirect
22. C9×#124C22semidirect
23. C9×#123C22semidirect
24. C9×#123C22semidirect
26. C9×C22⋊Q8C22semidirect
27. C9×C22⋊Q8C22semidirect
31. C9×#121C22semidirect
32. C9×#121C22semidirect
33. C9×#121C22semidirect
35. C4×Q8×C9C22semidirect
36. C4×Q8×C9C22semidirect
41. C4×D4×C9C22semidirect
42. C4×D4×C9C22semidirect
43. C4×D4×C9C22semidirect
45. C9×#117C22semidirect
46. C9×#117C22semidirect
50. C2×C42×C9C22semidirect
104. #3460C9direct (N × H)
165. C2×C4×C9#41semidirect
174. #544C2×C9semidirect
175. #542C2×C9semidirect
176. #540C2×C9semidirect
177. #538C2×C9semidirect
178. #537C2×C9semidirect
179. #535C2×C9semidirect
180. #532C2×C9semidirect
181. #529C2×C9semidirect
182. #525C2×C9semidirect
183. C4×#41C2×C9semidirect
184. C2×C4×D4C2×C9semidirect
247. C2×#41C22×C9semidirect
250. C4⋊Q8C22×C9semidirect
252. #126C22×C9semidirect
253. #125C22×C9semidirect
255. #124C22×C9semidirect
256. #123C22×C9semidirect
257. #123C22×C9semidirect
259. C22⋊Q8C22×C9semidirect
260. C22⋊Q8C22×C9semidirect
264. #121C22×C9semidirect
265. #121C22×C9semidirect
266. #121C22×C9semidirect
268. C4×Q8C22×C9semidirect
269. C4×Q8C22×C9semidirect
274. C4×D4C22×C9semidirect
275. C4×D4C22×C9semidirect
276. C4×D4C22×C9semidirect
278. #117C22×C9semidirect
279. #117C22×C9semidirect
283. C2×C42C22×C9semidirect
382. C9#3460direct (N × H)
405. C2×C4C9×#41semidirect

Maximal subgroups

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

subgroupindex
C9×#5442
C9×#5422
C9×#5402
C9×#5382
C9×#5372
C9×#5352
C9×#5322
C9×#5292
C9×#5252
C4×C9×#412
C2×C4×D4×C92
C3×#34603