Finite Group Databasebeta

← C9×#3492 #11768213

Subgroups — C9×#3492 #11768213

Order 1152.

1686 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#554C214yesmaximal, complemented
2C9×#553C214yesmaximal, complemented
3C9×#552C214yesmaximal, complemented
4C9×#547C214yesmaximal, complemented
5C9×#544C211yesmaximal, characteristic, complemented
6C9×#539C214yesmaximal, complemented
7C9×#537C211yesmaximal, characteristic, complemented
8C9×#525C212yesmaximal, complemented
9C9×#525C214yesmaximal, complemented
10C9×#520C212yesmaximal, complemented
11C22×C9×C4⋊C4C211yesmaximal, characteristic, complemented
12C3×#3492C311yesmaximal, characteristic
13C2×C9×#41C2212yes—
14C2×C9×#41C2214yes—
15C23×C4×C9C2211yescharacteristic
16C23×C4×C9C2212yes—
17C9×C4⋊Q8C2214yescomplemented
18C9×#126C2218yescomplemented
19C9×#125C2218yescomplemented
20C9×#125C2214yescomplemented
21C9×#123C2214yes—
22C9×#123C2218yes—
23C9×#123C2218yescomplemented
24C9×C22⋊Q8C2214yes—
25C9×C22⋊Q8C2212yes—
26C9×C22⋊Q8C2212yes—
27C9×C22⋊Q8C2214yes—
28C9×C22⋊Q8C2214yescomplemented
29C9×C22⋊Q8C2218yescomplemented
30C9×#121C2214yes—
31C9×#121C2212yes—
32C9×#121C2214yes—
33C9×#121C2212yes—
34C9×#121C2214yescomplemented
35C9×#120C2214yes—
36C4×Q8×C9C2214yescomplemented
37C4×D4×C9C2218yes—
38C4×D4×C9C2214yes—
39C4×D4×C9C2218yes—
40C4×D4×C9C2214yes—
41C4×D4×C9C2214yescomplemented
42C9×#117C2212yes—
43C9×#117C2214yes—
44C9×#117C2214yescomplemented
45C2×C9×C4⋊C4C2211yescharacteristic
46C2×C9×C4⋊C4C2211yescharacteristic
47C2×C9×C4⋊C4C2212yes—
48C2×C9×C4⋊C4C2214yes—
49C2×C9×C4⋊C4C2214yes—
50C2×C9×C4⋊C4C2214yescomplemented
51C3×#554C2×C314yes—
52C3×#553C2×C314yes—
53C3×#552C2×C314yes—
54C3×#547C2×C314yes—
55C3×#544C2×C311yescharacteristic
56C3×#539C2×C314yes—
57C3×#537C2×C311yescharacteristic
58C3×#525C2×C312yes—
59C3×#525C2×C314yes—
60C3×#520C2×C312yes—
61C22×C3×C4⋊C4C2×C311yescharacteristic
62C24×C9C2311yescharacteristic
63C9×#41—28no—
64C9×#41—48no—
65C2×Q8×C9C2312yes—
66C2×Q8×C9C2314yes—
67C2×D4×C9C2314yes—
68C2×D4×C9C2314yes—
69C2×D4×C9C2314yes—
70C2×D4×C9C2312yes—
71C2×D4×C9C2314yes—
72C22×C4×C9—24no—
73C22×C4×C9—44no—
74C22×C4×C9C2314yes—
75C22×C4×C9C2312yes—
76C22×C4×C9C2312yes—
77C22×C4×C9C2311yescharacteristic
78C22×C4×C9C2314yes—
79C22×C4×C9C2312yes—
80C22×C4×C9C2314yes—
81C22×C4×C9C2312yes—
82C22×C4×C9C2318yes—
83C22×C4×C9C2311yescharacteristic
84C9×C4⋊C4C2314yes—
85C9×C4⋊C4C2314yes—
86C9×C4⋊C4C2318yes—
87C9×C4⋊C4C2312yes—
88C9×C4⋊C4C2318yes—
89C9×C4⋊C4C2312yes—
90C9×C4⋊C4C2314yes—
91C9×C4⋊C4C2314yes—
92C9×C4⋊C4C2314yes—
93C9×C4⋊C4C2318yes—
94C9×C4⋊C4C2314yes—
95C9×C22⋊C4C2314yes—
96C9×C22⋊C4C2314yes—
97C9×C22⋊C4C2318yes—
98C9×C22⋊C4C2314yes—
99C9×C22⋊C4C2318yes—
100C9×C22⋊C4C2314yes—
101C9×C22⋊C4C2314yes—
102C42×C9C2318yes—
103C42×C9C2314yes—
104#3492C911yescharacteristic, direct product factor, Sylow
105C2×C3×#41C22×C312yes—
106C2×C3×#41C22×C314yes—
107C23×C3×C4C22×C311yescharacteristic
108C23×C3×C4C22×C312yes—
109C3×C4⋊Q8C22×C314yes—
110C3×#126C22×C318yes—
111C3×#125C22×C318yes—
112C3×#125C22×C314yes—
113C3×#123C22×C314yes—
114C3×#123C22×C318yes—
115C3×#123C22×C318yes—
116C3×C22⋊Q8C22×C314yes—
117C3×C22⋊Q8C22×C312yes—
118C3×C22⋊Q8C22×C312yes—
119C3×C22⋊Q8C22×C314yes—
120C3×C22⋊Q8C22×C314yes—
121C3×C22⋊Q8C22×C318yes—
122C3×#121C22×C314yes—
123C3×#121C22×C312yes—
124C3×#121C22×C314yes—
125C3×#121C22×C312yes—
126C3×#121C22×C314yes—
127C3×#120C22×C314yes—
128C3×C4×Q8C22×C314yes—
129C3×C4×D4C22×C318yes—
130C3×C4×D4C22×C314yes—
131C3×C4×D4C22×C318yes—
132C3×C4×D4C22×C314yes—
133C3×C4×D4C22×C314yes—
134C3×#117C22×C312yes—
135C3×#117C22×C314yes—
136C3×#117C22×C314yes—
137C2×C3×C4⋊C4C22×C311yescharacteristic
138C2×C3×C4⋊C4C22×C311yescharacteristic
139C2×C3×C4⋊C4C22×C312yes—
140C2×C3×C4⋊C4C22×C314yes—
141C2×C3×C4⋊C4C22×C314yes—
142C2×C3×C4⋊C4C22×C314yes—
143C23×C9—22no—
144C23×C9—22no—
145C23×C9—22no—
146C23×C9C2414yes—
147C23×C9C2411yescharacteristic
148C23×C9C2411yescharacteristic
149C23×C9C2411yescharacteristic
150Q8×C9—24no—
151Q8×C9—44no—
152D4×C9—28no—
153D4×C9—28no—
154D4×C9—28no—
155D4×C9—24no—
156D4×C9—44no—
157C2×C4×C9—22no—
158C2×C4×C9—28no—
159C2×C4×C9—24no—
160C2×C4×C9—24no—
161C2×C4×C9—28no—
162C2×C4×C9—42no—
163C2×C4×C9—44no—
164C2×C4×C9—42no—
165C2×C4×C9—48no—
166C2×C4×C9#4114yescomplemented
167C2×C4×C9C2414yes—
168C2×C4×C9C2414yes—
169C2×C4×C9C2414yes—
170C2×C4×C9C2414yes—
171C2×C4×C9C2412yes—
172C2×C4×C9C2414yes—
173C2×C4×C9C2412yes—
174#554C2×C914yescomplemented
175#553C2×C914yescomplemented
176#552C2×C914yescomplemented
177#547C2×C914yescomplemented
178#544C2×C911yescharacteristic, complemented
179#539C2×C914yescomplemented
180#537C2×C911yescharacteristic, complemented
181#525C2×C912yescomplemented
182#525C2×C914yescomplemented
183#520C2×C912yescomplemented
184C22×C4⋊C4C2×C911yescharacteristic, complemented
185C24×C3C23×C311yescharacteristic
186C3×#41—28no—
187C3×#41—48no—
188C2×C3×Q8C23×C312yes—
189C2×C3×Q8C23×C314yes—
190C2×C3×D4C23×C314yes—
191C2×C3×D4C23×C314yes—
192C2×C3×D4C23×C312yes—
193C2×C3×D4C23×C314yes—
194C2×C3×D4C23×C314yes—
195C22×C3×C4—24no—
196C22×C3×C4—44no—
197C22×C3×C4C23×C314yes—
198C22×C3×C4C23×C312yes—
199C22×C3×C4C23×C312yes—
200C22×C3×C4C23×C311yescharacteristic
201C22×C3×C4C23×C314yes—
202C22×C3×C4C23×C312yes—
203C22×C3×C4C23×C314yes—
204C22×C3×C4C23×C312yes—
205C22×C3×C4C23×C318yes—
206C22×C3×C4C23×C311yescharacteristic
207C3×C4⋊C4C23×C314yes—
208C3×C4⋊C4C23×C314yes—
209C3×C4⋊C4C23×C318yes—
210C3×C4⋊C4C23×C312yes—
211C3×C4⋊C4C23×C318yes—
212C3×C4⋊C4C23×C312yes—
213C3×C4⋊C4C23×C314yes—
214C3×C4⋊C4C23×C314yes—
215C3×C4⋊C4C23×C314yes—
216C3×C4⋊C4C23×C318yes—
217C3×C4⋊C4C23×C314yes—
218C3×C22⋊C4C23×C314yes—
219C3×C22⋊C4C23×C314yes—
220C3×C22⋊C4C23×C318yes—
221C3×C22⋊C4C23×C314yes—
222C3×C22⋊C4C23×C318yes—
223C3×C22⋊C4C23×C314yes—
224C3×C22⋊C4C23×C314yes—
225C3×C42C23×C318yes—
226C3×C42C23×C314yes—
227C22×C9—28no—
228C22×C9—21no—
229C22×C9—21no—
230C22×C9—21no—
231C22×C9—21no—
232C22×C9—21no—
233C22×C9—21no—
234C22×C9—24no—
235C22×C9—24no—
236C22×C9—24no—
237C22×C9C2×#4112yes—
238C22×C9H(5,𝔽2)12yes—
239C22×C92−1+412yes—
240C22×C9C2511yescharacteristic
241C4×C9—22no—
242C4×C9—24no—
243C4×C9—24no—
244C4×C9—24no—
245C4×C9—24no—
246C4×C9—24no—
247C4×C9C2×#4114yes—
248C2×#41C22×C912yes—
249C2×#41C22×C914yes—
250C23×C4C22×C911yescharacteristic
251C23×C4C22×C912yes—
252C4⋊Q8C22×C914yescomplemented
253#126C22×C918yescomplemented
254#125C22×C918yescomplemented
255#125C22×C914yescomplemented
256#123C22×C914yes—
257#123C22×C918yes—
258#123C22×C918yescomplemented
259C22⋊Q8C22×C914yes—
260C22⋊Q8C22×C912yes—
261C22⋊Q8C22×C912yes—
262C22⋊Q8C22×C914yes—
263C22⋊Q8C22×C914yescomplemented
264C22⋊Q8C22×C918yescomplemented
265#121C22×C914yes—
266#121C22×C912yes—
267#121C22×C914yes—
268#121C22×C912yes—
269#121C22×C914yescomplemented
270#120C22×C914yes—
271C4×Q8C22×C914yescomplemented
272C4×D4C22×C918yes—
273C4×D4C22×C914yes—
274C4×D4C22×C918yes—
275C4×D4C22×C914yes—
276C4×D4C22×C914yescomplemented
277#117C22×C912yes—
278#117C22×C914yes—
279#117C22×C914yescomplemented
280C2×C4⋊C4C22×C911yescharacteristic
281C2×C4⋊C4C22×C911yescharacteristic
282C2×C4⋊C4C22×C912yes—
283C2×C4⋊C4C22×C914yes—
284C2×C4⋊C4C22×C914yes—
285C2×C4⋊C4C22×C914yescomplemented
286C23×C3—22no—
287C23×C3—22no—
288C23×C3—22no—
289C23×C3C24×C314yes—
290C23×C3C24×C311yescharacteristic
291C23×C3C24×C311yescharacteristic
292C23×C3C24×C311yescharacteristic
293C3×Q8—24no—
294C3×Q8—44no—
295C3×D4—28no—
296C3×D4—28no—
297C3×D4—28no—
298C3×D4—24no—
299C3×D4—44no—
300C2×C3×C4—22no—
301C2×C3×C4—28no—
302C2×C3×C4—24no—
303C2×C3×C4—24no—
304C2×C3×C4—28no—
305C2×C3×C4—42no—
306C2×C3×C4—44no—
307C2×C3×C4—42no—
308C2×C3×C4—48no—
309C2×C3×C4C3×#4114yes—
310C2×C3×C4C24×C314yes—
311C2×C3×C4C24×C314yes—
312C2×C3×C4C24×C314yes—
313C2×C3×C4C24×C314yes—
314C2×C3×C4C24×C312yes—
315C2×C3×C4C24×C314yes—
316C2×C3×C4C24×C312yes—
317C2×C9—22no—
318C2×C9—22no—
319C2×C9—22no—
320C2×C9—44no—
321C2×C9C22×#4111yescharacteristic
322C2×C9C2×H(5,𝔽2)11yescharacteristic
323C2×C9C2×2−1+411yescharacteristic
324C24C23×C911yescharacteristic
325#41—28no—
326#41—48no—
327C2×Q8C23×C912yes—
328C2×Q8C23×C914yes—
329C2×D4C23×C914yes—
330C2×D4C23×C914yes—
331C2×D4C23×C914yes—
332C2×D4C23×C912yes—
333C2×D4C23×C914yes—
334C22×C4—24no—
335C22×C4—44no—
336C22×C4C23×C914yes—
337C22×C4C23×C912yes—
338C22×C4C23×C912yes—
339C22×C4C23×C911yescharacteristic
340C22×C4C23×C914yes—
341C22×C4C23×C912yes—
342C22×C4C23×C914yes—
343C22×C4C23×C912yes—
344C22×C4C23×C918yes—
345C22×C4C23×C911yescharacteristic
346C4⋊C4C23×C914yes—
347C4⋊C4C23×C914yes—
348C4⋊C4C23×C918yes—
349C4⋊C4C23×C912yes—
350C4⋊C4C23×C918yes—
351C4⋊C4C23×C912yes—
352C4⋊C4C23×C914yes—
353C4⋊C4C23×C914yes—
354C4⋊C4C23×C914yes—
355C4⋊C4C23×C918yes—
356C4⋊C4C23×C914yes—
357C22⋊C4C23×C914yes—
358C22⋊C4C23×C914yes—
359C22⋊C4C23×C918yes—
360C22⋊C4C23×C914yes—
361C22⋊C4C23×C918yes—
362C22⋊C4C23×C914yes—
363C22⋊C4C23×C914yes—
364C42C23×C918yes—
365C42C23×C914yes—
366C22×C3—28no—
367C22×C3—21no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—24no—
374C22×C3—24no—
375C22×C3—24no—
376C22×C3C2×C3×#4112yes—
377C22×C3C3×H(5,𝔽2)12yes—
378C22×C3C3×2−1+412yes—
379C22×C3C25×C311yescharacteristic
380C3×C4—22no—
381C3×C4—24no—
382C3×C4—24no—
383C3×C4—24no—
384C3×C4—24no—
385C3×C4—24no—
386C3×C4C2×C3×#4114yes—
387C9#349211yescharacteristic, direct product factor, Sylow
388C23—22no—
389C23—22no—
390C23—22no—
391C23C24×C914yes—
392C23C24×C911yescharacteristic
393C23C24×C911yescharacteristic
394C23C24×C911yescharacteristic
395Q8—24no—
396Q8—44no—
397D4—28no—
398D4—28no—
399D4—28no—
400D4—24no—
401D4—44no—
402C2×C4—22no—
403C2×C4—28no—
404C2×C4—24no—
405C2×C4—24no—
406C2×C4—28no—
407C2×C4—42no—
408C2×C4—44no—
409C2×C4—42no—
410C2×C4—48no—
411C2×C4C9×#4114yescomplemented
412C2×C4C24×C914yes—
413C2×C4C24×C914yes—
414C2×C4C24×C914yes—
415C2×C4C24×C914yes—
416C2×C4C24×C912yes—
417C2×C4C24×C914yes—
418C2×C4C24×C912yes—
419C2×C3—22no—
420C2×C3—22no—
421C2×C3—22no—
422C2×C3—44no—
423C2×C3C22×C3×#4111yescharacteristic
424C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
425C2×C3C2×C3×2−1+411yescharacteristic
426C22—28no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—24no—
434C22—24no—
435C22—24no—
436C22C2×C9×#4112yes—
437C22C9×H(5,𝔽2)12yes—
438C22C9×2−1+412yes—
439C22C25×C911yescharacteristic
440C4—22no—
441C4—24no—
442C4—24no—
443C4—24no—
444C4—24no—
445C4—24no—
446C4C2×C9×#4114yes—
447C3C3×#349211yescharacteristic
448C2—22no—
449C2—22no—
450C2—22no—
451C2—44no—
452C2C22×C9×#4111yescharacteristic
453C2C2×C9×H(5,𝔽2)11yescharacteristic
454C2C2×C9×2−1+411yescharacteristic
subgroupG/H
centerC22×C9C25
commutatorC22C25×C9
Frattini, socle, cosocleC22×C3C25×C3
prime radicalC3×#3492C3
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C9 ◁ G

Complements

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

NH ≅ G/Ntype
1. C9×#554C2semidirect
2. C9×#553C2semidirect
3. C9×#552C2semidirect
4. C9×#547C2semidirect
5. C9×#544C2semidirect
6. C9×#539C2semidirect
7. C9×#537C2semidirect
8. C9×#525C2semidirect
9. C9×#525C2semidirect
10. C9×#520C2semidirect
11. C22×C9×C4⋊C4C2semidirect
17. C9×C4⋊Q8C22semidirect
18. C9×#126C22semidirect
19. C9×#125C22semidirect
20. C9×#125C22semidirect
23. C9×#123C22semidirect
28. C9×C22⋊Q8C22semidirect
29. C9×C22⋊Q8C22semidirect
34. C9×#121C22semidirect
36. C4×Q8×C9C22semidirect
41. C4×D4×C9C22semidirect
44. C9×#117C22semidirect
50. C2×C9×C4⋊C4C22semidirect
104. #3492C9direct (N × H)
166. C2×C4×C9#41semidirect
174. #554C2×C9semidirect
175. #553C2×C9semidirect
176. #552C2×C9semidirect
177. #547C2×C9semidirect
178. #544C2×C9semidirect
179. #539C2×C9semidirect
180. #537C2×C9semidirect
181. #525C2×C9semidirect
182. #525C2×C9semidirect
183. #520C2×C9semidirect
184. C22×C4⋊C4C2×C9semidirect
252. C4⋊Q8C22×C9semidirect
253. #126C22×C9semidirect
254. #125C22×C9semidirect
255. #125C22×C9semidirect
258. #123C22×C9semidirect
263. C22⋊Q8C22×C9semidirect
264. C22⋊Q8C22×C9semidirect
269. #121C22×C9semidirect
271. C4×Q8C22×C9semidirect
276. C4×D4C22×C9semidirect
279. #117C22×C9semidirect
285. C2×C4⋊C4C22×C9semidirect
387. C9#3492direct (N × H)
411. C2×C4C9×#41semidirect

Maximal subgroups

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

subgroupindex
C9×#5542
C9×#5532
C9×#5522
C9×#5472
C9×#5442
C9×#5392
C9×#5372
C9×#5252
C9×#5202
C22×C9×C4⋊C42
C3×#34923