Finite Group Databasebeta

← #11878544

Subgroups — #11878544

Order 1152.

603 conjugacy classes of subgroups.

The subgroup lattice has 591 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#537C211yesmaximal, characteristic, complemented
2#10589935C211yesmaximal, characteristic, complemented
3#10588919C211yesmaximal, characteristic, complemented
4#10588918C211yesmaximal, characteristic, complemented
5#10588912C211yesmaximal, characteristic, complemented
6#10588731C211yesmaximal, characteristic, complemented
7#10588730C211yesmaximal, characteristic, complemented
8#10588728C211yesmaximal, characteristic, complemented
9#10588723C211yesmaximal, characteristic, complemented
10#10588722C211yesmaximal, characteristic, complemented
11#10588720C211yesmaximal, characteristic, complemented
12#10588717C211yesmaximal, characteristic, complemented
13#10588714C211yesmaximal, characteristic, complemented
14#10588651C211yesmaximal, characteristic, complemented
15#10588647C211yesmaximal, characteristic, complemented
16#83429—31nomaximal
17C2×C9×#41C2211yescharacteristic
18C2×C9×#41C2211yescharacteristic
19C2×#3697C2211yescharacteristic
20C9×C22⋊Q8—21no—
21C9×C22⋊Q8C2211yescharacteristic
22C9×C22⋊Q8C2211yescharacteristic
23C9×#121—21no—
24C9×#121—21no—
25C9×#121—21no—
26C9×#121C2211yescharacteristic
27C9×#121C2211yescharacteristic
28C2×C9×C4⋊C4C2211yescharacteristic
29#63508—21no—
30C2×#3675C2211yescharacteristic
31C2×#3674C2211yescharacteristic
32#63501—21no—
33#63501—21no—
34#63500—21no—
35C2×#3673C2211yescharacteristic
36C2×#3672C2211yescharacteristic
37#63492C2211yescharacteristic
38#63492C2211yescharacteristic
39C2×C4⋊Dic9C2211yescharacteristic
40#63486C2211yescharacteristic
41#63486C2211yescharacteristic
42C2×#3667C2211yescharacteristic
43C22×C9⋊C8C2211yescharacteristic
44#63395C2211yescharacteristic
45#63395C2211yescharacteristic
46#63392C2211yescharacteristic
47#63392C2211yescharacteristic
48#63389C2211yescharacteristic
49#63389C2211yescharacteristic
50#63389C2211yescharacteristic
51#63389C2211yescharacteristic
52#63369C2211yescharacteristic
53#63369C2211yescharacteristic
54#63368C2211yescharacteristic
55#63368C2211yescharacteristic
56#63367C2211yescharacteristic
57#63367C2211yescharacteristic
58#63367C2211yescharacteristic
59#63367C2211yescharacteristic
60C3×#537D311yescharacteristic
61#5833—31no—
62#5239—31no—
63#5238—31no—
64#5234—31no—
65#5052—31no—
66#5048—31no—
67#5047—31no—
68#5043—31no—
69#5041—31no—
70#5039—31no—
71#5037—31no—
72#5034—31no—
73#4971—31no—
74#4968—31no—
75C9×#41—41no—
76C9×#41—41no—
77C9×#41—41no—
78C9×#41—41no—
79C2×Q8×C9D411yescharacteristic
80C2×Q8×C9C2311yescharacteristic
81C2×D4×C9—21no—
82C2×D4×C9—21no—
83C2×D4×C9—21no—
84C2×D4×C9D411yescharacteristic
85C2×D4×C9D411yescharacteristic
86C2×D4×C9D411yescharacteristic
87C2×D4×C9C2311yescharacteristic
88C22×C4×C9—21no—
89C22×C4×C9—21no—
90C22×C4×C9C2311yescharacteristic
91C22×C4×C9C2311yescharacteristic
92C22×C4×C9C2311yescharacteristic
93C2×#611—21no—
94C2×#611—21no—
95C2×#611—21no—
96C22×Dic9—21no—
97#3697—41no—
98#3697—41no—
99C2×D36C2311yescharacteristic
100C2×C4×D9—21no—
101C2×Dic18C2311yescharacteristic
102C9×C4⋊C4—21no—
103C9×C4⋊C4—21no—
104C9×C4⋊C4—21no—
105C9×C4⋊C4C2311yescharacteristic
106C9×C4⋊C4C2311yescharacteristic
107C9×C22⋊C4—21no—
108C9×C22⋊C4—21no—
109C9×C22⋊C4—21no—
110C9×C22⋊C4—21no—
111#3676—21no—
112#3676—21no—
113#3675—41no—
114#3674—41no—
115#3673—41no—
116#3672—41no—
117(C2×D9)⋊C4—21no—
118(C2×D9)⋊C4—21no—
119C4⋊Dic9—21no—
120C4⋊Dic9C2311yescharacteristic
121C4⋊Dic9C2311yescharacteristic
122Dic9⋊C4—21no—
123Dic9⋊C4—21no—
124#3667—41no—
125C2×C9⋊C8—41no—
126C2×C9⋊C8C2311yescharacteristic
127C2×C9⋊C8C2311yescharacteristic
128C2×C9⋊C8C2311yescharacteristic
129C2×C9⋊C8C2311yescharacteristic
130#3204—91noSylow
131C2×C3×#41C2×D311yescharacteristic
132C2×C3×#41C2×D311yescharacteristic
133C2×#235—31no—
134C3×C22⋊Q8—21no—
135C3×C22⋊Q8C2×D311yescharacteristic
136C3×C22⋊Q8C2×D311yescharacteristic
137C3×#121—21no—
138C3×#121—21no—
139C3×#121—21no—
140C3×#121C2×D311yescharacteristic
141C3×#121C2×D311yescharacteristic
142C2×C3×C4⋊C4C2×D311yescharacteristic
143#946—61no—
144C2×#216—31no—
145C2×#215—31no—
146#939—61no—
147#939—61no—
148#938—61no—
149C2×#214—31no—
150C2×#213—31no—
151#930—31no—
152#930—31no—
153C2×C4⋊Dic3—31no—
154#924—31no—
155#924—31no—
156C2×#208—31no—
157C22×C3⋊C8—31no—
158#835—31no—
159#835—31no—
160#832—31no—
161#832—31no—
162#830—31no—
163#830—31no—
164#830—31no—
165#830—31no—
166#810—31no—
167#810—31no—
168#809—31no—
169#809—31no—
170#808—31no—
171#808—31no—
172#808—31no—
173#808—31no—
174C23×C9—21no—
175C23×C9C2×D411yescharacteristic
176C23×C9C2×D411yescharacteristic
177C23×C9C2×D411yescharacteristic
178C22×D9—21no—
179Q8×C9—21no—
180Q8×C9—21no—
181Q8×C9—41no—
182D4×C9—21no—
183D4×C9—21no—
184D4×C9—41no—
185D4×C9—41no—
186D4×C9—41no—
187D4×C9—42no—
188D4×C9—81no—
189D4×C9—81no—
190C2×C4×C9—21no—
191C2×C4×C9—21no—
192C2×C4×C9—21no—
193C2×C4×C9—21no—
194C2×C4×C9—21no—
195C2×C4×C9—21no—
196C2×C4×C9—21no—
197C2×C4×C9—21no—
198C2×C4×C9—21no—
199C2×C4×C9—42no—
200C2×C4×C9—81no—
201C2×C4×C9C2×D411yescharacteristic
202C2×C4×C9C2×D411yescharacteristic
203C2×C4×C9C2×D411yescharacteristic
204C2×C4×C9C2411yescharacteristic
205#611—42no—
206#611—81no—
207#611—81no—
208C2×Dic9—21no—
209C2×Dic9—21no—
210C2×Dic9—21no—
211C2×Dic9—81no—
212D36—21no—
213D36—21no—
214C4×D9—42no—
215Dic18—21no—
216Dic18—21no—
217C9⋊C8—21no—
218C9⋊C8—21no—
219C9⋊C8—21no—
220C9⋊C8—21no—
221#537—91no—
222#537D911yescharacteristic, complemented
223#483—91no—
224#483—91no—
225#481—91no—
226#481—91no—
227#470—91no—
228#469—91no—
229#465—91no—
230#465—91no—
231#452—91no—
232#452—91no—
233#449—91no—
234#449—91no—
235#408—91no—
236C3×#41—41no—
237C3×#41—41no—
238C3×#41—41no—
239C3×#41—41no—
240C2×C3×Q8#6711yescharacteristic
241C2×C3×Q8C22×D311yescharacteristic
242C2×C3×D4—21no—
243C2×C3×D4—21no—
244C2×C3×D4—21no—
245C2×C3×D4#6711yescharacteristic
246C2×C3×D4#6711yescharacteristic
247C2×C3×D4#6711yescharacteristic
248C2×C3×D4C22×D311yescharacteristic
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4C22×D311yescharacteristic
252C22×C3×C4C22×D311yescharacteristic
253C22×C3×C4C22×D311yescharacteristic
254C2×#67—61no—
255C2×#67—61no—
256C2×#67—61no—
257C22×Dic3—61no—
258#235—121no—
259#235—121no—
260C2×D12—31no—
261C2×C4×D3—61no—
262C2×Dic6—31no—
263C3×C4⋊C4—21no—
264C3×C4⋊C4—21no—
265C3×C4⋊C4—21no—
266C3×C4⋊C4C22×D311yescharacteristic
267C3×C4⋊C4C22×D311yescharacteristic
268C3×C22⋊C4—21no—
269C3×C22⋊C4—21no—
270C3×C22⋊C4—21no—
271C3×C22⋊C4—21no—
272#217—61no—
273#217—61no—
274#216—121no—
275#215—121no—
276#214—121no—
277#213—121no—
278(C2×D3)⋊C4—61no—
279(C2×D3)⋊C4—61no—
280C4⋊Dic3—31no—
281C4⋊Dic3—31no—
282C4⋊Dic3—61no—
283Dic3⋊C4—61no—
284Dic3⋊C4—61no—
285#208—121no—
286C2×C3⋊C8—31no—
287C2×C3⋊C8—31no—
288C2×C3⋊C8—31no—
289C2×C3⋊C8—31no—
290C2×C3⋊C8—121no—
291C22×C9—21no—
292C22×C9—21no—
293C22×C9—21no—
294C22×C9—21no—
295C22×C9—21no—
296C22×C9—21no—
297C22×C9—21no—
298C22×C9—21no—
299C22×C9—21no—
300C22×C9—41no—
301C22×C9—41no—
302C22×C9—41no—
303C22×C9C22×D411yescharacteristic
304C2×D9—41no—
305C2×D9—41no—
306C2×D9—41no—
307C4×C9—21no—
308C4×C9—21no—
309C4×C9—21no—
310C4×C9—41no—
311C4×C9—41no—
312C4×C9—41no—
313C4×C9H(5,𝔽2)11yescharacteristic
314C4×C9H(5,𝔽2)11yescharacteristic
315Dic9—41no—
316Dic9—41no—
317Dic9—41no—
318C2×#41—91no—
319C2×#41C2×D911yescharacteristic
320C2×#41C2×D911yescharacteristic
321C2×Q16—91no—
322C2×SD16—91no—
323C2×SD16—91no—
324C2×D8—91no—
325C2×M16—91no—
326C22×C8—91no—
327C22⋊Q8—21no—
328C22⋊Q8—91no—
329C22⋊Q8—91no—
330C22⋊Q8—181no—
331C22⋊Q8C2×D911yescharacteristic
332C22⋊Q8C2×D911yescharacteristic
333#121—21no—
334#121—21no—
335#121—21no—
336#121—91no—
337#121—91no—
338#121—181no—
339#121—181no—
340#121—181no—
341#121C2×D911yescharacteristic
342#121C2×D911yescharacteristic
343C2×C4⋊C4—91no—
344C2×C4⋊C4C2×D911yescharacteristic
345#106—91no—
346#106—91no—
347#106—91no—
348#106—91no—
349#103—91no—
350#103—91no—
351#103—91no—
352#103—91no—
353#102—91no—
354#102—91no—
355#102—91no—
356#102—91no—
357C22⋊C8—91no—
358C22⋊C8—91no—
359C22⋊C8—91no—
360C22⋊C8—91no—
361C23×C3—21no—
362C23×C3C2×#6711yescharacteristic
363C23×C3C2×#6711yescharacteristic
364C23×C3C2×#6711yescharacteristic
365C22×D3—61no—
366C3×Q8—21no—
367C3×Q8—21no—
368C3×Q8—41no—
369C3×D4—21no—
370C3×D4—21no—
371C3×D4—41no—
372C3×D4—41no—
373C3×D4—41no—
374C3×D4—42no—
375C3×D4—81no—
376C3×D4—81no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—42no—
387C2×C3×C4—81no—
388C2×C3×C4C2×#6711yescharacteristic
389C2×C3×C4C2×#6711yescharacteristic
390C2×C3×C4C2×#6711yescharacteristic
391C2×C3×C4C23×D311yescharacteristic
392#67—122no—
393#67—241no—
394#67—241no—
395C2×Dic3—61no—
396C2×Dic3—61no—
397C2×Dic3—61no—
398C2×Dic3—241no—
399D12—61no—
400D12—61no—
401C4×D3—122no—
402Dic6—61no—
403Dic6—61no—
404C3⋊C8—61no—
405C3⋊C8—61no—
406C3⋊C8—61no—
407C3⋊C8—61no—
408C2×C9—41no—
409C2×C9—41no—
410C2×C9—41no—
411C2×C9—81no—
412C2×C9#53411yescharacteristic
413C2×C9#57711yescharacteristic
414C2×C9#57711yescharacteristic
415D9—81no—
416#41—41no—
417#41—41no—
418#41—41no—
419#41—41no—
420#41—361no—
421#41—361no—
422C2×Q8—91no—
423C2×Q8#61111yescharacteristic
424C2×Q8C22×D911yescharacteristic
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—91no—
429C2×D4—181no—
430C2×D4—181no—
431C2×D4—181no—
432C2×D4#61111yescharacteristic
433C2×D4#61111yescharacteristic
434C2×D4#61111yescharacteristic
435C2×D4C22×D911yescharacteristic
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—181no—
439C22×C4—181no—
440C22×C4C22×D911yescharacteristic
441C22×C4C22×D911yescharacteristic
442C22×C4C22×D911yescharacteristic
443Q16—361no—
444SD16—361no—
445SD16—361no—
446D8—361no—
447M16—361no—
448C2×C8—91no—
449C2×C8—91no—
450C2×C8—91no—
451C2×C8—91no—
452C2×C8—361no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—91no—
457C4⋊C4—91no—
458C4⋊C4—181no—
459C4⋊C4—181no—
460C4⋊C4—181no—
461C4⋊C4C22×D911yescharacteristic
462C4⋊C4C22×D911yescharacteristic
463C22⋊C4—21no—
464C22⋊C4—21no—
465C22⋊C4—21no—
466C22⋊C4—21no—
467C22⋊C4—181no—
468C22⋊C4—181no—
469C22⋊C4—181no—
470C22⋊C4—181no—
471C22×C3—21no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—21no—
479C22×C3—21no—
480C22×C3—41no—
481C22×C3—41no—
482C22×C3—41no—
483C22×C3C22×#6711yescharacteristic
484C2×D3—121no—
485C2×D3—121no—
486C2×D3—121no—
487C3×C4—21no—
488C3×C4—21no—
489C3×C4—21no—
490C3×C4—41no—
491C3×C4—41no—
492C3×C4—41no—
493C3×C4#100411yescharacteristic
494C3×C4#100411yescharacteristic
495Dic3—121no—
496Dic3—121no—
497Dic3—121no—
498C9#320411yescharacteristic, complemented, Sylow
499C23—21no—
500C23—181no—
501C23C2×#61111yescharacteristic
502C23C2×#61111yescharacteristic
503C23C2×#61111yescharacteristic
504Q8—21no—
505Q8—21no—
506Q8—41no—
507Q8—181no—
508Q8—181no—
509D4—21no—
510D4—21no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—42no—
515D4—81no—
516D4—81no—
517D4—181no—
518D4—181no—
519D4—362no—
520D4—721no—
521D4—721no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—42no—
532C2×C4—81no—
533C2×C4—181no—
534C2×C4—181no—
535C2×C4—181no—
536C2×C4—362no—
537C2×C4—721no—
538C2×C4C2×#61111yescharacteristic
539C2×C4C2×#61111yescharacteristic
540C2×C4C2×#61111yescharacteristic
541C2×C4C23×D911yescharacteristic
542C8—181no—
543C8—181no—
544C8—181no—
545C8—181no—
546C2×C3—41no—
547C2×C3—41no—
548C2×C3—41no—
549C2×C3—81no—
550C2×C3#580411yescharacteristic
551C2×C3#583611yescharacteristic
552C2×C3#583711yescharacteristic
553D3—241no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—361no—
567C22—361no—
568C22—361no—
569C22C22×#61111yescharacteristic
570C4—21no—
571C4—21no—
572C4—21no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—361no—
577C4—361no—
578C4—361no—
579C4#6371011yescharacteristic
580C4#6371011yescharacteristic
581C3#8342911yescharacteristic
582C2—41no—
583C2—41no—
584C2—41no—
585C2—81no—
586C2—721no—
587C2#1058990611yescharacteristic
588C2#1058993811yescharacteristic
589C2#1058993911yescharacteristic
subgroupG/H
centerC22C22×#611
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#537C2
socleC22×C3C22×#67
hypercenter#537D9
hypocenterC9#3204
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C9×#537C2semidirect
2. #10589935C2semidirect
3. #10588919C2semidirect
4. #10588918C2semidirect
5. #10588912C2semidirect
6. #10588731C2semidirect
7. #10588730C2semidirect
8. #10588728C2semidirect
9. #10588723C2semidirect
10. #10588722C2semidirect
11. #10588720C2semidirect
12. #10588717C2semidirect
13. #10588714C2semidirect
14. #10588651C2semidirect
15. #10588647C2semidirect
222. #537D9semidirect
498. C9#3204semidirect

Maximal subgroups

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

subgroupindex
C9×#5372
#105899352
#105889192
#105889182
#105889122
#105887312
#105887302
#105887282
#105887232
#105887222
#105887202
#105887172
#105887142
#105886512
#105886472
#834293