Finite Group Databasebeta

← C9×#3493 #11768214

Subgroups — C9×#3493 #11768214

Order 1152.

1560 conjugacy classes of subgroups.

The subgroup lattice has 435 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#556C214yesmaximal, complemented
2C9×#555C214yesmaximal, complemented
3C9×#553C214yesmaximal, complemented
4C9×#552C214yesmaximal, complemented
5C9×#544C211yesmaximal, characteristic, complemented
6C9×#538C214yesmaximal, complemented
7C9×#537C211yesmaximal, characteristic, complemented
8C9×#529C214yesmaximal, complemented
9C9×#525C212yesmaximal, complemented
10C9×#520C212yesmaximal, complemented
11C2×C9×#117C211yesmaximal, characteristic, complemented
12C3×#3493C311yesmaximal, characteristic
13C2×C9×#41C2212yes—
14C23×C4×C9C2211yescharacteristic
15C9×C4⋊Q8C2214yescomplemented
16C9×#126C2218yes—
17C9×#126C2218yescomplemented
18C9×#125C2214yescomplemented
19C9×#125C2214yescomplemented
20C9×#124C2218yes—
21C9×#124C2214yescomplemented
22C9×#123C2214yes—
23C9×#123C2218yes—
24C9×C22⋊Q8C2212yes—
25C9×C22⋊Q8C2212yes—
26C9×C22⋊Q8C2214yes—
27C9×C22⋊Q8C2214yescomplemented
28C9×#121C2212yes—
29C9×#121C2212yes—
30C9×#121C2214yes—
31C9×#121C2218yes—
32C9×#121C2214yescomplemented
33C9×#120C2214yes—
34C4×Q8×C9C2214yescomplemented
35C4×Q8×C9C2214yescomplemented
36C4×D4×C9C2218yes—
37C4×D4×C9C2214yes—
38C4×D4×C9C2214yes—
39C4×D4×C9C2214yescomplemented
40C4×D4×C9C2214yescomplemented
41C9×#117C2212yes—
42C9×#117C2214yes—
43C9×#117C2214yes—
44C9×#117C2214yescomplemented
45C9×#117C2218yescomplemented
46C2×C9×C4⋊C4C2211yescharacteristic
47C2×C9×C4⋊C4C2211yescharacteristic
48C2×C9×C4⋊C4C2214yescomplemented
49C2×C9×C22⋊C4C2212yes—
50C2×C42×C9C2212yes—
51C3×#556C2×C314yes—
52C3×#555C2×C314yes—
53C3×#553C2×C314yes—
54C3×#552C2×C314yes—
55C3×#544C2×C311yescharacteristic
56C3×#538C2×C314yes—
57C3×#537C2×C311yescharacteristic
58C3×#529C2×C314yes—
59C3×#525C2×C312yes—
60C3×#520C2×C312yes—
61C2×C3×#117C2×C311yescharacteristic
62C24×C9C2311yescharacteristic
63C9×#41—28no—
64C2×Q8×C9C2312yes—
65C2×Q8×C9C2314yes—
66C2×D4×C9C2314yes—
67C2×D4×C9C2312yes—
68C2×D4×C9C2314yes—
69C2×D4×C9C2314yes—
70C2×D4×C9C2314yes—
71C22×C4×C9—24no—
72C22×C4×C9C2311yescharacteristic
73C22×C4×C9C2314yes—
74C22×C4×C9C2312yes—
75C22×C4×C9C2312yes—
76C22×C4×C9C2312yes—
77C22×C4×C9C2312yes—
78C22×C4×C9C2318yes—
79C22×C4×C9C2311yescharacteristic
80C9×C4⋊C4C2314yes—
81C9×C4⋊C4C2314yes—
82C9×C4⋊C4C2312yes—
83C9×C4⋊C4C2318yes—
84C9×C4⋊C4C2312yes—
85C9×C4⋊C4C2314yes—
86C9×C4⋊C4C2318yes—
87C9×C4⋊C4C2314yes—
88C9×C4⋊C4C2314yes—
89C9×C4⋊C4C2314yes—
90C9×C22⋊C4C2318yes—
91C9×C22⋊C4C2314yes—
92C9×C22⋊C4C2314yes—
93C9×C22⋊C4C2318yes—
94C9×C22⋊C4C2318yes—
95C9×C22⋊C4C2314yes—
96C9×C22⋊C4C2314yes—
97C9×C22⋊C4C2314yes—
98C42×C9C2314yes—
99C42×C9C2314yes—
100C42×C9C2314yes—
101C42×C9C2318yes—
102#3493C911yescharacteristic, direct product factor, Sylow
103C2×C3×#41C22×C312yes—
104C23×C3×C4C22×C311yescharacteristic
105C3×C4⋊Q8C22×C314yes—
106C3×#126C22×C318yes—
107C3×#126C22×C318yes—
108C3×#125C22×C314yes—
109C3×#125C22×C314yes—
110C3×#124C22×C318yes—
111C3×#124C22×C314yes—
112C3×#123C22×C314yes—
113C3×#123C22×C318yes—
114C3×C22⋊Q8C22×C312yes—
115C3×C22⋊Q8C22×C312yes—
116C3×C22⋊Q8C22×C314yes—
117C3×C22⋊Q8C22×C314yes—
118C3×#121C22×C312yes—
119C3×#121C22×C312yes—
120C3×#121C22×C314yes—
121C3×#121C22×C318yes—
122C3×#121C22×C314yes—
123C3×#120C22×C314yes—
124C3×C4×Q8C22×C314yes—
125C3×C4×Q8C22×C314yes—
126C3×C4×D4C22×C318yes—
127C3×C4×D4C22×C314yes—
128C3×C4×D4C22×C314yes—
129C3×C4×D4C22×C314yes—
130C3×C4×D4C22×C314yes—
131C3×#117C22×C314yes—
132C3×#117C22×C314yes—
133C3×#117C22×C312yes—
134C3×#117C22×C314yes—
135C3×#117C22×C318yes—
136C2×C3×C4⋊C4C22×C311yescharacteristic
137C2×C3×C4⋊C4C22×C311yescharacteristic
138C2×C3×C4⋊C4C22×C314yes—
139C2×C3×C22⋊C4C22×C312yes—
140C2×C3×C42C22×C312yes—
141C23×C9—22no—
142C23×C9—41no—
143C23×C9—41no—
144C23×C9C2412yes—
145C23×C9C2414yes—
146C23×C9C2411yescharacteristic
147Q8×C9—24no—
148Q8×C9—44no—
149D4×C9—28no—
150D4×C9—24no—
151D4×C9—44no—
152D4×C9—44no—
153D4×C9—44no—
154C2×C4×C9—22no—
155C2×C4×C9—24no—
156C2×C4×C9—24no—
157C2×C4×C9—28no—
158C2×C4×C9—42no—
159C2×C4×C9—48no—
160C2×C4×C9—42no—
161C2×C4×C9#4114yes—
162C2×C4×C9C2411yescharacteristic
163C2×C4×C9C2411yescharacteristic
164C2×C4×C9C2414yes—
165C2×C4×C9C2414yes—
166C2×C4×C9C2414yes—
167C2×C4×C9C2414yes—
168C2×C4×C9C2414yes—
169C2×C4×C9C2412yes—
170#556C2×C914yescomplemented
171#555C2×C914yescomplemented
172#553C2×C914yescomplemented
173#552C2×C914yescomplemented
174#544C2×C911yescharacteristic, complemented
175#538C2×C914yescomplemented
176#537C2×C911yescharacteristic, complemented
177#529C2×C914yescomplemented
178#525C2×C912yescomplemented
179#520C2×C912yescomplemented
180C2×#117C2×C911yescharacteristic, complemented
181C24×C3C23×C311yescharacteristic
182C3×#41—28no—
183C2×C3×Q8C23×C312yes—
184C2×C3×Q8C23×C314yes—
185C2×C3×D4C23×C314yes—
186C2×C3×D4C23×C312yes—
187C2×C3×D4C23×C314yes—
188C2×C3×D4C23×C314yes—
189C2×C3×D4C23×C314yes—
190C22×C3×C4—24no—
191C22×C3×C4C23×C311yescharacteristic
192C22×C3×C4C23×C314yes—
193C22×C3×C4C23×C312yes—
194C22×C3×C4C23×C312yes—
195C22×C3×C4C23×C312yes—
196C22×C3×C4C23×C312yes—
197C22×C3×C4C23×C318yes—
198C22×C3×C4C23×C311yescharacteristic
199C3×C4⋊C4C23×C314yes—
200C3×C4⋊C4C23×C312yes—
201C3×C4⋊C4C23×C314yes—
202C3×C4⋊C4C23×C318yes—
203C3×C4⋊C4C23×C312yes—
204C3×C4⋊C4C23×C314yes—
205C3×C4⋊C4C23×C318yes—
206C3×C4⋊C4C23×C314yes—
207C3×C4⋊C4C23×C314yes—
208C3×C4⋊C4C23×C314yes—
209C3×C22⋊C4C23×C318yes—
210C3×C22⋊C4C23×C314yes—
211C3×C22⋊C4C23×C314yes—
212C3×C22⋊C4C23×C318yes—
213C3×C22⋊C4C23×C318yes—
214C3×C22⋊C4C23×C314yes—
215C3×C22⋊C4C23×C314yes—
216C3×C22⋊C4C23×C314yes—
217C3×C42C23×C314yes—
218C3×C42C23×C314yes—
219C3×C42C23×C318yes—
220C3×C42C23×C314yes—
221C22×C9—21no—
222C22×C9—21no—
223C22×C9—22no—
224C22×C9—24no—
225C22×C9—24no—
226C22×C9—24no—
227C22×C9—22no—
228C22×C9—22no—
229C22×C9—44no—
230C22×C9C2×#4112yes—
231C22×C9C2511yescharacteristic
232C4×C9—21no—
233C4×C9—21no—
234C4×C9—24no—
235C4×C9—24no—
236C4×C9—24no—
237C4×C9—24no—
238C4×C9—24no—
239C4×C9C2×#4114yes—
240C2×#41C22×C912yes—
241C23×C4C22×C911yescharacteristic
242C4⋊Q8C22×C914yescomplemented
243#126C22×C918yes—
244#126C22×C918yescomplemented
245#125C22×C914yescomplemented
246#125C22×C914yescomplemented
247#124C22×C918yes—
248#124C22×C914yescomplemented
249#123C22×C914yes—
250#123C22×C918yes—
251C22⋊Q8C22×C912yes—
252C22⋊Q8C22×C912yes—
253C22⋊Q8C22×C914yes—
254C22⋊Q8C22×C914yescomplemented
255#121C22×C912yes—
256#121C22×C912yes—
257#121C22×C914yes—
258#121C22×C918yes—
259#121C22×C914yescomplemented
260#120C22×C914yes—
261C4×Q8C22×C914yescomplemented
262C4×Q8C22×C914yescomplemented
263C4×D4C22×C918yes—
264C4×D4C22×C914yes—
265C4×D4C22×C914yes—
266C4×D4C22×C914yescomplemented
267C4×D4C22×C914yescomplemented
268#117C22×C914yes—
269#117C22×C914yes—
270#117C22×C912yes—
271#117C22×C914yescomplemented
272#117C22×C918yescomplemented
273C2×C4⋊C4C22×C911yescharacteristic
274C2×C4⋊C4C22×C911yescharacteristic
275C2×C4⋊C4C22×C914yescomplemented
276C2×C22⋊C4C22×C912yes—
277C2×C42C22×C912yes—
278C23×C3—22no—
279C23×C3—41no—
280C23×C3—41no—
281C23×C3C24×C312yes—
282C23×C3C24×C314yes—
283C23×C3C24×C311yescharacteristic
284C3×Q8—24no—
285C3×Q8—44no—
286C3×D4—28no—
287C3×D4—24no—
288C3×D4—44no—
289C3×D4—44no—
290C3×D4—44no—
291C2×C3×C4—22no—
292C2×C3×C4—24no—
293C2×C3×C4—24no—
294C2×C3×C4—28no—
295C2×C3×C4—42no—
296C2×C3×C4—48no—
297C2×C3×C4—42no—
298C2×C3×C4C3×#4114yes—
299C2×C3×C4C24×C311yescharacteristic
300C2×C3×C4C24×C311yescharacteristic
301C2×C3×C4C24×C314yes—
302C2×C3×C4C24×C314yes—
303C2×C3×C4C24×C314yes—
304C2×C3×C4C24×C314yes—
305C2×C3×C4C24×C314yes—
306C2×C3×C4C24×C312yes—
307C2×C9—22no—
308C2×C9—44no—
309C2×C9—42no—
310C2×C9C22×#4111yescharacteristic
311C2×C9#58511yescharacteristic
312C2×C9#58511yescharacteristic
313C24C23×C911yescharacteristic
314#41—28no—
315C2×Q8C23×C912yes—
316C2×Q8C23×C914yes—
317C2×D4C23×C914yes—
318C2×D4C23×C912yes—
319C2×D4C23×C914yes—
320C2×D4C23×C914yes—
321C2×D4C23×C914yes—
322C22×C4—24no—
323C22×C4C23×C911yescharacteristic
324C22×C4C23×C914yes—
325C22×C4C23×C912yes—
326C22×C4C23×C912yes—
327C22×C4C23×C912yes—
328C22×C4C23×C912yes—
329C22×C4C23×C918yes—
330C22×C4C23×C911yescharacteristic
331C4⋊C4C23×C914yes—
332C4⋊C4C23×C914yes—
333C4⋊C4C23×C912yes—
334C4⋊C4C23×C918yes—
335C4⋊C4C23×C912yes—
336C4⋊C4C23×C914yes—
337C4⋊C4C23×C918yes—
338C4⋊C4C23×C914yes—
339C4⋊C4C23×C914yes—
340C4⋊C4C23×C914yes—
341C22⋊C4C23×C918yes—
342C22⋊C4C23×C914yes—
343C22⋊C4C23×C914yes—
344C22⋊C4C23×C918yes—
345C22⋊C4C23×C918yes—
346C22⋊C4C23×C914yes—
347C22⋊C4C23×C914yes—
348C22⋊C4C23×C914yes—
349C42C23×C914yes—
350C42C23×C914yes—
351C42C23×C914yes—
352C42C23×C918yes—
353C22×C3—21no—
354C22×C3—21no—
355C22×C3—22no—
356C22×C3—24no—
357C22×C3—24no—
358C22×C3—24no—
359C22×C3—22no—
360C22×C3—22no—
361C22×C3—44no—
362C22×C3C2×C3×#4112yes—
363C22×C3C25×C311yescharacteristic
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—24no—
367C3×C4—24no—
368C3×C4—24no—
369C3×C4—24no—
370C3×C4—24no—
371C3×C4C2×C3×#4114yes—
372C9#349311yescharacteristic, direct product factor, Sylow
373C23—22no—
374C23—41no—
375C23—41no—
376C23C24×C912yes—
377C23C24×C914yes—
378C23C24×C911yescharacteristic
379Q8—24no—
380Q8—44no—
381D4—28no—
382D4—24no—
383D4—44no—
384D4—44no—
385D4—44no—
386C2×C4—22no—
387C2×C4—24no—
388C2×C4—24no—
389C2×C4—28no—
390C2×C4—42no—
391C2×C4—48no—
392C2×C4—42no—
393C2×C4C9×#4114yes—
394C2×C4C24×C911yescharacteristic
395C2×C4C24×C911yescharacteristic
396C2×C4C24×C914yes—
397C2×C4C24×C914yes—
398C2×C4C24×C914yes—
399C2×C4C24×C914yes—
400C2×C4C24×C914yes—
401C2×C4C24×C912yes—
402C2×C3—22no—
403C2×C3—42no—
404C2×C3—44no—
405C2×C3C22×C3×#4111yescharacteristic
406C2×C3C3×#58511yescharacteristic
407C2×C3C3×#58511yescharacteristic
408C22—21no—
409C22—21no—
410C22—22no—
411C22—24no—
412C22—24no—
413C22—24no—
414C22—22no—
415C22—22no—
416C22—44no—
417C22C2×C9×#4112yes—
418C22C25×C911yescharacteristic
419C4—21no—
420C4—21no—
421C4—24no—
422C4—24no—
423C4—24no—
424C4—24no—
425C4—24no—
426C4C2×C9×#4114yes—
427C3C3×#349311yescharacteristic
428C2—22no—
429C2—42no—
430C2—44no—
431C2C22×C9×#4111yescharacteristic
432C2C9×#58511yescharacteristic
433C2C9×#58511yescharacteristic
subgroupG/H
centerC22×C9C25
commutatorC22C25×C9
Frattini, socle, cosocleC22×C3C25×C3
prime radicalC3×#3493C3
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C9 ◁ G

Complements

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

NH ≅ G/Ntype
1. C9×#556C2semidirect
2. C9×#555C2semidirect
3. C9×#553C2semidirect
4. C9×#552C2semidirect
5. C9×#544C2semidirect
6. C9×#538C2semidirect
7. C9×#537C2semidirect
8. C9×#529C2semidirect
9. C9×#525C2semidirect
10. C9×#520C2semidirect
11. C2×C9×#117C2semidirect
15. C9×C4⋊Q8C22semidirect
17. C9×#126C22semidirect
18. C9×#125C22semidirect
19. C9×#125C22semidirect
21. C9×#124C22semidirect
27. C9×C22⋊Q8C22semidirect
32. C9×#121C22semidirect
34. C4×Q8×C9C22semidirect
35. C4×Q8×C9C22semidirect
39. C4×D4×C9C22semidirect
40. C4×D4×C9C22semidirect
44. C9×#117C22semidirect
45. C9×#117C22semidirect
48. C2×C9×C4⋊C4C22semidirect
102. #3493C9direct (N × H)
170. #556C2×C9semidirect
171. #555C2×C9semidirect
172. #553C2×C9semidirect
173. #552C2×C9semidirect
174. #544C2×C9semidirect
175. #538C2×C9semidirect
176. #537C2×C9semidirect
177. #529C2×C9semidirect
178. #525C2×C9semidirect
179. #520C2×C9semidirect
180. C2×#117C2×C9semidirect
242. C4⋊Q8C22×C9semidirect
244. #126C22×C9semidirect
245. #125C22×C9semidirect
246. #125C22×C9semidirect
248. #124C22×C9semidirect
254. C22⋊Q8C22×C9semidirect
259. #121C22×C9semidirect
261. C4×Q8C22×C9semidirect
262. C4×Q8C22×C9semidirect
266. C4×D4C22×C9semidirect
267. C4×D4C22×C9semidirect
271. #117C22×C9semidirect
272. #117C22×C9semidirect
275. C2×C4⋊C4C22×C9semidirect
372. C9#3493direct (N × H)

Maximal subgroups

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

subgroupindex
C9×#5562
C9×#5552
C9×#5532
C9×#5522
C9×#5442
C9×#5382
C9×#5372
C9×#5292
C9×#5252
C9×#5202
C2×C9×#1172
C3×#34933