Finite Group Databasebeta

← C9×#3241 #11767962

Subgroups — C9×#3241 #11767962

Order 1152.

498 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#544C211yesmaximal, characteristic, complemented
2C9×#540C211yesmaximal, characteristic
3C9×#501C211yesmaximal, characteristic, complemented
4C9×#499C211yesmaximal, characteristic, complemented
5C9×#490C211yesmaximal, characteristic, complemented
6C9×#486C211yesmaximal, characteristic, complemented
7C9×#482C211yesmaximal, characteristic, complemented
8C9×#482C211yesmaximal, characteristic, complemented
9C9×#481C211yesmaximal, characteristic, complemented
10C9×#480C211yesmaximal, characteristic, complemented
11C9×#478C211yesmaximal, characteristic, complemented
12C9×#478C211yesmaximal, characteristic, complemented
13C9×#476C211yesmaximal, characteristic, complemented
14C9×#474C211yesmaximal, characteristic, complemented
15C9×#433C211yesmaximal, characteristic, complemented
16C3×#3241C311yesmaximal, characteristic
17C9×C4⋊Q8—21no—
18C9×C4⋊Q8C2211yescharacteristic
19C9×C4⋊Q8C2211yescharacteristic
20C9×#127C2211yescharacteristic
21C9×#125—21no—
22C9×#125C2211yescharacteristic
23C9×#125C2211yescharacteristic
24C9×#125C2211yescharacteristic
25C9×#123—21no—
26C9×#123—21no—
27C9×C22⋊Q8—21no—
28C9×C22⋊Q8—21no—
29C9×#121—21no—
30C9×#121—21no—
31C9×#121C2211yescharacteristic
32C9×#121C2211yescharacteristic
33C4×D4×C9C2211yescharacteristic
34C4×D4×C9C2211yescharacteristic
35C9×#117C2211yescharacteristic
36C9×#117C2211yescharacteristic
37C2×C9×C4⋊C4C2211yescharacteristic
38C9×#107C2211yescharacteristic
39C9×#107C2211yescharacteristic
40C9×#107C2211yescharacteristic
41C9×#107C2211yescharacteristic
42C9×#106C2211yescharacteristic
43C9×#106C2211yescharacteristic
44C9×#106C2211yescharacteristic
45C9×#106C2211yescharacteristic
46C9×C4⋊C8C2211yescharacteristic
47C9×C4⋊C8C2211yescharacteristic
48C9×#102C2211yescharacteristic
49C9×#102C2211yescharacteristic
50C9×#102C2211yescharacteristic
51C9×#102C2211yescharacteristic
52C9×#102C2211yescharacteristic
53C9×#102C2211yescharacteristic
54C9×#102C2211yescharacteristic
55C9×#102C2211yescharacteristic
56C9×C22⋊C8C2211yescharacteristic
57C9×C22⋊C8C2211yescharacteristic
58C9×#97C2211yescharacteristic
59C4×C8×C9C2211yescharacteristic
60C3×#544C2×C311yescharacteristic
61C3×#540C2×C311yescharacteristic
62C3×#501C2×C311yescharacteristic
63C3×#499C2×C311yescharacteristic
64C3×#490C2×C311yescharacteristic
65C3×#486C2×C311yescharacteristic
66C3×#482C2×C311yescharacteristic
67C3×#482C2×C311yescharacteristic
68C3×#481C2×C311yescharacteristic
69C3×#480C2×C311yescharacteristic
70C3×#478C2×C311yescharacteristic
71C3×#478C2×C311yescharacteristic
72C3×#476C2×C311yescharacteristic
73C3×#474C2×C311yescharacteristic
74C3×#433C2×C311yescharacteristic
75C2×Q8×C9—21no—
76C2×Q8×C9—21no—
77C2×D4×C9—21no—
78C2×D4×C9—21no—
79C2×D4×C9—21no—
80C2×D4×C9—21no—
81C2×D4×C9C2311yescharacteristic
82C2×D4×C9C2311yescharacteristic
83C22×C4×C9—21no—
84C22×C4×C9—21no—
85C22×C4×C9—21no—
86C22×C4×C9C2311yescharacteristic
87C2×C8×C9C2311yescharacteristic
88C2×C8×C9C2311yescharacteristic
89C2×C8×C9C2311yescharacteristic
90C2×C8×C9C2311yescharacteristic
91C9×C4⋊C4—21no—
92C9×C4⋊C4—21no—
93C9×C4⋊C4—21no—
94C9×C4⋊C4—21no—
95C9×C4⋊C4—21no—
96C9×C4⋊C4—21no—
97C9×C4⋊C4—21no—
98C9×C4⋊C4—21no—
99C9×C4⋊C4—21no—
100C9×C4⋊C4D411yescharacteristic
101C9×C4⋊C4D411yescharacteristic
102C9×C4⋊C4C2311yescharacteristic
103C9×C4⋊C4C2311yescharacteristic
104C9×C4⋊C4C2311yescharacteristic
105C9×C4⋊C4C2311yescharacteristic
106C9×C4⋊C4C2311yescharacteristic
107C9×C4⋊C4C2311yescharacteristic
108C9×C22⋊C4—21no—
109C9×C22⋊C4—21no—
110C9×C22⋊C4—21no—
111C9×C22⋊C4—21no—
112C9×C22⋊C4—21no—
113C9×C22⋊C4D411yescharacteristic
114C9×C22⋊C4D411yescharacteristic
115C42×C9—21no—
116C42×C9C2311yescharacteristic
117C42×C9C2311yescharacteristic
118#3241C911yescharacteristic, direct product factor, Sylow
119C3×C4⋊Q8—21no—
120C3×C4⋊Q8C22×C311yescharacteristic
121C3×C4⋊Q8C22×C311yescharacteristic
122C3×#127C22×C311yescharacteristic
123C3×#125—21no—
124C3×#125C22×C311yescharacteristic
125C3×#125C22×C311yescharacteristic
126C3×#125C22×C311yescharacteristic
127C3×#123—21no—
128C3×#123—21no—
129C3×C22⋊Q8—21no—
130C3×C22⋊Q8—21no—
131C3×#121—21no—
132C3×#121—21no—
133C3×#121C22×C311yescharacteristic
134C3×#121C22×C311yescharacteristic
135C3×C4×D4C22×C311yescharacteristic
136C3×C4×D4C22×C311yescharacteristic
137C3×#117C22×C311yescharacteristic
138C3×#117C22×C311yescharacteristic
139C2×C3×C4⋊C4C22×C311yescharacteristic
140C3×#107C22×C311yescharacteristic
141C3×#107C22×C311yescharacteristic
142C3×#107C22×C311yescharacteristic
143C3×#107C22×C311yescharacteristic
144C3×#106C22×C311yescharacteristic
145C3×#106C22×C311yescharacteristic
146C3×#106C22×C311yescharacteristic
147C3×#106C22×C311yescharacteristic
148C3×C4⋊C8C22×C311yescharacteristic
149C3×C4⋊C8C22×C311yescharacteristic
150C3×#102C22×C311yescharacteristic
151C3×#102C22×C311yescharacteristic
152C3×#102C22×C311yescharacteristic
153C3×#102C22×C311yescharacteristic
154C3×#102C22×C311yescharacteristic
155C3×#102C22×C311yescharacteristic
156C3×#102C22×C311yescharacteristic
157C3×#102C22×C311yescharacteristic
158C3×C22⋊C8C22×C311yescharacteristic
159C3×C22⋊C8C22×C311yescharacteristic
160C3×#97C22×C311yescharacteristic
161C3×C4×C8C22×C311yescharacteristic
162C23×C9—21no—
163C23×C9—21no—
164C23×C9C2×D411yescharacteristic
165Q8×C9—81no—
166Q8×C9—81no—
167D4×C9—21no—
168D4×C9—21no—
169D4×C9—21no—
170D4×C9—21no—
171D4×C9—81no—
172D4×C9—81no—
173D4×C9—81no—
174D4×C9—81no—
175C2×C4×C9—21no—
176C2×C4×C9—21no—
177C2×C4×C9—21no—
178C2×C4×C9—21no—
179C2×C4×C9—21no—
180C2×C4×C9—21no—
181C2×C4×C9—21no—
182C2×C4×C9—21no—
183C2×C4×C9—81no—
184C2×C4×C9—81no—
185C2×C4×C9—81no—
186C2×C4×C9C2×D411yescharacteristic
187C2×C4×C9C2×D411yescharacteristic
188C2×C4×C9C2×D411yescharacteristic
189C2×C4×C9C2×D411yescharacteristic
190C2×C4×C9C2×D411yescharacteristic
191C2×C4×C9C2411yescharacteristic
192C8×C9—21no—
193C8×C9—21no—
194C8×C9—21no—
195C8×C9—21no—
196#544C2×C911yescharacteristic, complemented
197#540C2×C911yescharacteristic
198#501C2×C911yescharacteristic, complemented
199#499C2×C911yescharacteristic, complemented
200#490C2×C911yescharacteristic, complemented
201#486C2×C911yescharacteristic, complemented
202#482C2×C911yescharacteristic, complemented
203#482C2×C911yescharacteristic, complemented
204#481C2×C911yescharacteristic, complemented
205#480C2×C911yescharacteristic, complemented
206#478C2×C911yescharacteristic, complemented
207#478C2×C911yescharacteristic, complemented
208#476C2×C911yescharacteristic, complemented
209#474C2×C911yescharacteristic, complemented
210#433C2×C911yescharacteristic, complemented
211C2×C3×Q8—21no—
212C2×C3×Q8—21no—
213C2×C3×D4—21no—
214C2×C3×D4—21no—
215C2×C3×D4—21no—
216C2×C3×D4—21no—
217C2×C3×D4C23×C311yescharacteristic
218C2×C3×D4C23×C311yescharacteristic
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4C23×C311yescharacteristic
223C2×C3×C8C23×C311yescharacteristic
224C2×C3×C8C23×C311yescharacteristic
225C2×C3×C8C23×C311yescharacteristic
226C2×C3×C8C23×C311yescharacteristic
227C3×C4⋊C4—21no—
228C3×C4⋊C4—21no—
229C3×C4⋊C4—21no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—21no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—21no—
235C3×C4⋊C4—21no—
236C3×C4⋊C4C3×D411yescharacteristic
237C3×C4⋊C4C3×D411yescharacteristic
238C3×C4⋊C4C23×C311yescharacteristic
239C3×C4⋊C4C23×C311yescharacteristic
240C3×C4⋊C4C23×C311yescharacteristic
241C3×C4⋊C4C23×C311yescharacteristic
242C3×C4⋊C4C23×C311yescharacteristic
243C3×C4⋊C4C23×C311yescharacteristic
244C3×C22⋊C4—21no—
245C3×C22⋊C4—21no—
246C3×C22⋊C4—21no—
247C3×C22⋊C4—21no—
248C3×C22⋊C4—21no—
249C3×C22⋊C4C3×D411yescharacteristic
250C3×C22⋊C4C3×D411yescharacteristic
251C3×C42—21no—
252C3×C42C23×C311yescharacteristic
253C3×C42C23×C311yescharacteristic
254C22×C9—21no—
255C22×C9—21no—
256C22×C9—21no—
257C22×C9—41no—
258C22×C9—41no—
259C22×C9—41no—
260C22×C9—41no—
261C22×C9—41no—
262C22×C9—41no—
263C22×C9C22×D411yescharacteristic
264C4×C9—21no—
265C4×C9—21no—
266C4×C9—21no—
267C4×C9—21no—
268C4×C9—21no—
269C4×C9—41no—
270C4×C9—41no—
271C4×C9—41no—
272C4×C9—41no—
273C4×C9—41no—
274C4×C9—41no—
275C4×C92−1+411yescharacteristic
276C4×C92−1+411yescharacteristic
277C4⋊Q8—21no—
278C4⋊Q8C22×C911yescharacteristic
279C4⋊Q8C22×C911yescharacteristic
280#127C22×C911yescharacteristic
281#125—21no—
282#125C22×C911yescharacteristic
283#125C22×C911yescharacteristic
284#125C22×C911yescharacteristic
285#123—21no—
286#123—21no—
287C22⋊Q8—21no—
288C22⋊Q8—21no—
289#121—21no—
290#121—21no—
291#121C22×C911yescharacteristic
292#121C22×C911yescharacteristic
293C4×D4C22×C911yescharacteristic
294C4×D4C22×C911yescharacteristic
295#117C22×C911yescharacteristic
296#117C22×C911yescharacteristic
297C2×C4⋊C4C22×C911yescharacteristic
298#107C22×C911yescharacteristic
299#107C22×C911yescharacteristic
300#107C22×C911yescharacteristic
301#107C22×C911yescharacteristic
302#106C22×C911yescharacteristic
303#106C22×C911yescharacteristic
304#106C22×C911yescharacteristic
305#106C22×C911yescharacteristic
306C4⋊C8C22×C911yescharacteristic
307C4⋊C8C22×C911yescharacteristic
308#102C22×C911yescharacteristic
309#102C22×C911yescharacteristic
310#102C22×C911yescharacteristic
311#102C22×C911yescharacteristic
312#102C22×C911yescharacteristic
313#102C22×C911yescharacteristic
314#102C22×C911yescharacteristic
315#102C22×C911yescharacteristic
316C22⋊C8C22×C911yescharacteristic
317C22⋊C8C22×C911yescharacteristic
318#97C22×C911yescharacteristic
319C4×C8C22×C911yescharacteristic
320C23×C3—21no—
321C23×C3—21no—
322C23×C3C2×C3×D411yescharacteristic
323C3×Q8—81no—
324C3×Q8—81no—
325C3×D4—21no—
326C3×D4—21no—
327C3×D4—21no—
328C3×D4—21no—
329C3×D4—81no—
330C3×D4—81no—
331C3×D4—81no—
332C3×D4—81no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—81no—
342C2×C3×C4—81no—
343C2×C3×C4—81no—
344C2×C3×C4C2×C3×D411yescharacteristic
345C2×C3×C4C2×C3×D411yescharacteristic
346C2×C3×C4C2×C3×D411yescharacteristic
347C2×C3×C4C2×C3×D411yescharacteristic
348C2×C3×C4C2×C3×D411yescharacteristic
349C2×C3×C4C24×C311yescharacteristic
350C3×C8—21no—
351C3×C8—21no—
352C3×C8—21no—
353C3×C8—21no—
354C2×C9—41no—
355C2×C9—81no—
356C2×C9—81no—
357C2×C9#53611yescharacteristic
358C2×C9#57611yescharacteristic
359C2×C9#57711yescharacteristic
360C2×Q8—21no—
361C2×Q8—21no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4C23×C911yescharacteristic
367C2×D4C23×C911yescharacteristic
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4C23×C911yescharacteristic
372C2×C8C23×C911yescharacteristic
373C2×C8C23×C911yescharacteristic
374C2×C8C23×C911yescharacteristic
375C2×C8C23×C911yescharacteristic
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4D4×C911yescharacteristic
386C4⋊C4D4×C911yescharacteristic
387C4⋊C4C23×C911yescharacteristic
388C4⋊C4C23×C911yescharacteristic
389C4⋊C4C23×C911yescharacteristic
390C4⋊C4C23×C911yescharacteristic
391C4⋊C4C23×C911yescharacteristic
392C4⋊C4C23×C911yescharacteristic
393C22⋊C4—21no—
394C22⋊C4—21no—
395C22⋊C4—21no—
396C22⋊C4—21no—
397C22⋊C4—21no—
398C22⋊C4D4×C911yescharacteristic
399C22⋊C4D4×C911yescharacteristic
400C42—21no—
401C42C23×C911yescharacteristic
402C42C23×C911yescharacteristic
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—41no—
407C22×C3—41no—
408C22×C3—41no—
409C22×C3—41no—
410C22×C3—41no—
411C22×C3—41no—
412C22×C3C22×C3×D411yescharacteristic
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—41no—
419C3×C4—41no—
420C3×C4—41no—
421C3×C4—41no—
422C3×C4—41no—
423C3×C4—41no—
424C3×C4C3×2−1+411yescharacteristic
425C3×C4C3×2−1+411yescharacteristic
426C9#324111yescharacteristic, direct product factor, Sylow
427C23—21no—
428C23—21no—
429C23C2×D4×C911yescharacteristic
430Q8—81no—
431Q8—81no—
432D4—21no—
433D4—21no—
434D4—21no—
435D4—21no—
436D4—81no—
437D4—81no—
438D4—81no—
439D4—81no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—81no—
449C2×C4—81no—
450C2×C4—81no—
451C2×C4C2×D4×C911yescharacteristic
452C2×C4C2×D4×C911yescharacteristic
453C2×C4C2×D4×C911yescharacteristic
454C2×C4C2×D4×C911yescharacteristic
455C2×C4C2×D4×C911yescharacteristic
456C2×C4C24×C911yescharacteristic
457C8—21no—
458C8—21no—
459C8—21no—
460C8—21no—
461C2×C3—41no—
462C2×C3—81no—
463C2×C3—81no—
464C2×C3C3×#53611yescharacteristic
465C2×C3C3×#57611yescharacteristic
466C2×C3C3×#57711yescharacteristic
467C22—21no—
468C22—21no—
469C22—21no—
470C22—41no—
471C22—41no—
472C22—41no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22C22×D4×C911yescharacteristic
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—21no—
482C4—41no—
483C4—41no—
484C4—41no—
485C4—41no—
486C4—41no—
487C4—41no—
488C4C9×2−1+411yescharacteristic
489C4C9×2−1+411yescharacteristic
490C3C3×#324111yescharacteristic
491C2—41no—
492C2—81no—
493C2—81no—
494C2C9×#53611yescharacteristic
495C2C9×#57611yescharacteristic
496C2C9×#57711yescharacteristic
subgroupG/H
centerC22×C9C22×D4
commutatorC2×C4C24×C9
Frattini, cosocleC2×C3×C4C24×C3
socleC22×C3C22×C3×D4
prime radicalC3×#540C2×C3
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C9 ◁ C9×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C9×#544C2semidirect
3. C9×#501C2semidirect
4. C9×#499C2semidirect
5. C9×#490C2semidirect
6. C9×#486C2semidirect
7. C9×#482C2semidirect
8. C9×#482C2semidirect
9. C9×#481C2semidirect
10. C9×#480C2semidirect
11. C9×#478C2semidirect
12. C9×#478C2semidirect
13. C9×#476C2semidirect
14. C9×#474C2semidirect
15. C9×#433C2semidirect
118. #3241C9direct (N × H)
196. #544C2×C9semidirect
198. #501C2×C9semidirect
199. #499C2×C9semidirect
200. #490C2×C9semidirect
201. #486C2×C9semidirect
202. #482C2×C9semidirect
203. #482C2×C9semidirect
204. #481C2×C9semidirect
205. #480C2×C9semidirect
206. #478C2×C9semidirect
207. #478C2×C9semidirect
208. #476C2×C9semidirect
209. #474C2×C9semidirect
210. #433C2×C9semidirect
426. C9#3241direct (N × H)

Maximal subgroups

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

subgroupindex
C9×#5442
C9×#5402
C9×#5012
C9×#4992
C9×#4902
C9×#4862
C9×#4822
C9×#4812
C9×#4802
C9×#4782
C9×#4762
C9×#4742
C9×#4332
C3×#32413