Finite Group Databasebeta

← #11887345

Subgroups — #11887345

Order 1152.

630 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589732C211yesmaximal, characteristic, complemented
2#10589616C211yesmaximal, characteristic, complemented
3C9×#484C211yesmaximal, characteristic, complemented
4#10588731C211yesmaximal, characteristic, complemented
5C2×#63369C211yesmaximal, characteristic, complemented
6#10588571C211yesmaximal, characteristic, complemented
7#10588565C211yesmaximal, characteristic, complemented
8#10588563C211yesmaximal, characteristic, complemented
9#10588552C211yesmaximal, characteristic, complemented
10#10588499C211yesmaximal, characteristic, complemented
11#10588490C211yesmaximal, characteristic, complemented
12#10588484C211yesmaximal, characteristic, complemented
13#10588480C211yesmaximal, characteristic, complemented
14#10588414C211yesmaximal, characteristic, complemented
15#611⋊C8C211yesmaximal, characteristic, complemented
16#81485—31nomaximal
17C2×#3701C2211yescharacteristic
18C22×D36C2211yescharacteristic
19C9×C22⋊Q8C2211yescharacteristic
20C2×C9×C4⋊C4C2211yescharacteristic
21#63509C2211yescharacteristic
22C2×#3675C2211yescharacteristic, complemented
23#63492—21no—
24#63492C2211yescharacteristic
25C4×#611—21no—
26C4×#611C2211yescharacteristic
27C22×C9⋊C8C2211yescharacteristic
28C2×D72C2211yescharacteristic
29C2×D72C2211yescharacteristic
30C2×C8×D9C2211yescharacteristic, complemented
31#63460—21no—
32#63457—21no—
33#63457C2211yescharacteristic
34#63457C2211yescharacteristic, complemented
35#63456—21no—
36#63456—21no—
37#63455C2211yescharacteristic
38#63455C2211yescharacteristic, complemented
39#63454C2211yescharacteristic, complemented
40#63452C2211yescharacteristic, complemented
41#63444—21no—
42C22⋊C4×D9—21no—
43C9×#107C2211yescharacteristic, complemented
44C9×#107C2211yescharacteristic, complemented
45C9×#103C2211yescharacteristic, complemented
46C9×#103C2211yescharacteristic, complemented
47C9×C22⋊C8C2211yescharacteristic
48#63395C2211yescharacteristic, complemented
49#63380C2211yescharacteristic
50#63380C2211yescharacteristic
51(C2×D9)⋊C8C2211yescharacteristic, complemented
52Dic9⋊C8C2211yescharacteristic, complemented
53C8×Dic9C2211yescharacteristic, complemented
54#63369C2211yescharacteristic
55#63369C2211yescharacteristic
56#63369C2211yescharacteristic
57#63369C2211yescharacteristic
58#63369C2211yescharacteristic, complemented
59#63367C2211yescharacteristic, complemented
60#5630—31no—
61#5514—31no—
62C3×#484D311yescharacteristic
63#5048—31no—
64C2×#809—31no—
65#4891—31no—
66#4885—31no—
67#4883—31no—
68#4872—31no—
69#4819—31no—
70#4810—31no—
71#4804—31no—
72#4800—31no—
73#4732—31no—
74#67⋊C8—31no—
75C23×D9—21no—
76C2×Q8×C9C2311yescharacteristic
77C22×C4×C9—21no—
78C22×C4×C9C2311yescharacteristic
79C2×#611—21no—
80C2×#611D411yescharacteristic
81#3701—22no—
82#3701—41no—
83C2×D36—22no—
84C2×D36—21no—
85C2×D36—21no—
86C2×D36—21no—
87C2×D36—21no—
88C2×D36—41no—
89C2×D36C2311yescharacteristic
90C2×D36C2311yescharacteristic
91C2×D36C2311yescharacteristic
92C2×C4×D9—21no—
93C2×C4×D9—21no—
94C2×C4×D9—21no—
95C2×C4×D9C2311yescharacteristic
96C2×C8×C9C2311yescharacteristic
97C2×C8×C9C2311yescharacteristic
98C9×C4⋊C4—21no—
99C9×C4⋊C4—21no—
100C9×C4⋊C4C2311yescharacteristic
101C9×C4⋊C4C2311yescharacteristic
102C9×C4⋊C4C2311yescharacteristic
103C9×C22⋊C4—21no—
104#3676D411yescharacteristic
105#3675—41no—
106(C2×D9)⋊C4—21no—
107(C2×D9)⋊C4—21no—
108(C2×D9)⋊C4—21no—
109(C2×D9)⋊C4—21no—
110(C2×D9)⋊C4—21no—
111(C2×D9)⋊C4—21no—
112(C2×D9)⋊C4—21no—
113(C2×D9)⋊C4—21no—
114(C2×D9)⋊C4D411yescharacteristic
115C4⋊Dic9—21no—
116C4⋊Dic9C2311yescharacteristic
117Dic9⋊C4—21no—
118Dic9⋊C4D411yescharacteristic
119C4×Dic9—21no—
120C4×Dic9C2311yescharacteristic
121C2×C9⋊C8—41no—
122C2×C9⋊C8C2311yescharacteristic
123C2×C9⋊C8C2311yescharacteristic
124D72—22no—
125D72—41no—
126C8×D9—41no—
127#3297—91noSylow
128C2×#239—31no—
129C22×D12—31no—
130C3×C22⋊Q8C2×D311yescharacteristic
131C2×C3×C4⋊C4C2×D311yescharacteristic
132#947—31no—
133C2×#215—31no—
134#930—31no—
135#930—61no—
136C4×#67—31no—
137C4×#67—61no—
138C22×C3⋊C8—31no—
139C2×D24—31no—
140C2×D24—31no—
141C2×D3×C8—31no—
142#898—61no—
143#895—31no—
144#895—31no—
145#895—61no—
146#894—61no—
147#894—61no—
148#893—31no—
149#893—31no—
150#892—31no—
151#890—31no—
152#882—61no—
153D3×C22⋊C4—61no—
154C3×#107C2×D311yescharacteristic
155C3×#107C2×D311yescharacteristic
156C3×#103C2×D311yescharacteristic
157C3×#103C2×D311yescharacteristic
158C3×C22⋊C8C2×D311yescharacteristic
159#835—31no—
160#821—31no—
161#821—31no—
162(C2×D3)⋊C8—31no—
163Dic3⋊C8—31no—
164C8×Dic3—31no—
165#809—31no—
166#809—31no—
167#809—31no—
168#809—31no—
169#809—31no—
170#808—31no—
171C23×C9C2×D411yescharacteristic
172C22×D9—21no—
173C22×D9—21no—
174C22×D9—21no—
175C22×D9—42no—
176C22×D9—42no—
177C22×D9—81no—
178C22×D9C2×D411yescharacteristic
179Q8×C9—21no—
180Q8×C9—21no—
181C2×C4×C9—21no—
182C2×C4×C9—21no—
183C2×C4×C9—21no—
184C2×C4×C9—21no—
185C2×C4×C9—21no—
186C2×C4×C9—21no—
187C2×C4×C9—81no—
188C2×C4×C9C2×D411yescharacteristic
189C2×C4×C9C2411yescharacteristic
190#611—22no—
191#611—42no—
192C2×Dic9—21no—
193C2×Dic9C2×D411yescharacteristic
194C2×Dic9C2×D411yescharacteristic
195C2×Dic9C2×D411yescharacteristic
196D36—21no—
197D36—21no—
198D36—21no—
199D36—21no—
200D36—21no—
201D36—42no—
202D36—42no—
203D36—81no—
204D36—81no—
205D36#4112yes—
206C4×D9—21no—
207C4×D9—21no—
208C4×D9—42no—
209C4×D9—81no—
210C4×D9—81no—
211C8×C9—21no—
212C8×C9—21no—
213C9⋊C8—21no—
214C9⋊C8—21no—
215#553—91no—
216#546—91no—
217#488—91no—
218#484D911yescharacteristic, complemented
219#482—91no—
220#478—91no—
221#466—91no—
222#465—91no—
223#463—91no—
224#449—91no—
225#447—91no—
226C4×D8—91no—
227C8×D4—91no—
228#416—91no—
229C2×#102—91no—
230C23×D3—61no—
231C2×C3×Q8C22×D311yescharacteristic
232C22×C3×C4—21no—
233C22×C3×C4C22×D311yescharacteristic
234C2×#67—31no—
235C2×#67—61no—
236#239—62no—
237#239—121no—
238C2×D12—31no—
239C2×D12—31no—
240C2×D12—31no—
241C2×D12—62no—
242C2×D12—61no—
243C2×D12—61no—
244C2×D12—61no—
245C2×D12—61no—
246C2×D12—121no—
247C2×C4×D3—31no—
248C2×C4×D3—61no—
249C2×C4×D3—61no—
250C2×C4×D3—61no—
251C2×C3×C8C22×D311yescharacteristic
252C2×C3×C8C22×D311yescharacteristic
253C3×C4⋊C4—21no—
254C3×C4⋊C4—21no—
255C3×C4⋊C4C22×D311yescharacteristic
256C3×C4⋊C4C22×D311yescharacteristic
257C3×C4⋊C4C22×D311yescharacteristic
258C3×C22⋊C4—21no—
259#217—31no—
260#215—121no—
261(C2×D3)⋊C4—31no—
262(C2×D3)⋊C4—61no—
263(C2×D3)⋊C4—61no—
264(C2×D3)⋊C4—61no—
265(C2×D3)⋊C4—61no—
266(C2×D3)⋊C4—61no—
267(C2×D3)⋊C4—61no—
268(C2×D3)⋊C4—61no—
269(C2×D3)⋊C4—61no—
270C4⋊Dic3—31no—
271C4⋊Dic3—61no—
272Dic3⋊C4—31no—
273Dic3⋊C4—61no—
274C4×Dic3—31no—
275C4×Dic3—61no—
276C2×C3⋊C8—31no—
277C2×C3⋊C8—31no—
278C2×C3⋊C8—121no—
279D24—62no—
280D24—121no—
281D3×C8—121no—
282C22×C9—21no—
283C22×C9—21no—
284C22×C9#13512yes—
285C22×C9C22×D411yescharacteristic
286C2×D9—21no—
287C2×D9—22no—
288C2×D9—21no—
289C2×D9—21no—
290C2×D9—41no—
291C2×D9—41no—
292C2×D9—41no—
293C2×D9—41no—
294C2×D9—41no—
295C2×D9—41no—
296C2×D9—41no—
297C2×D9—41no—
298C2×D9—84no—
299C4×C9—21no—
300C4×C9—41no—
301C4×C9—41no—
302C4×C9—41no—
303C4×C9—41no—
304C4×C9C2×#4111yescharacteristic
305C4×C9H(5,𝔽2)11yescharacteristic
306Dic9—21no—
307Dic9—21no—
308Dic9—21no—
309Dic9—41no—
310C2×#41—91no—
311C22×D4—91no—
312C2×SD16—91no—
313C2×D8—91no—
314C2×D8—91no—
315C22×C8—91no—
316C22×C8—91no—
317#126—181no—
318#125—91no—
319#124—91no—
320#123—181no—
321#123—181no—
322C22⋊Q8C2×D911yescharacteristic
323#121—91no—
324#121—91no—
325#121—91no—
326#121—181no—
327#121—181no—
328#120—181no—
329C4×D4—91no—
330C4×D4—91no—
331C4×D4—91no—
332C4×D4—181no—
333#117—91no—
334C2×C4⋊C4C2×D911yescharacteristic
335C2×C22⋊C4—181no—
336#107C2×D911yescharacteristic, complemented
337#107C2×D911yescharacteristic, complemented
338#106—91no—
339C4⋊C8—91no—
340#103—91no—
341#103C2×D911yescharacteristic, complemented
342#103C2×D911yescharacteristic, complemented
343#102—91no—
344#102—91no—
345#102—91no—
346#102—91no—
347#102—91no—
348#102—91no—
349#102—91no—
350C22⋊C8—91no—
351C22⋊C8C2×D911yescharacteristic
352C4×C8—91no—
353C23×C3D3×D411yescharacteristic
354C22×D3—31no—
355C22×D3—61no—
356C22×D3—61no—
357C22×D3—61no—
358C22×D3—122no—
359C22×D3—122no—
360C22×D3—241no—
361C3×Q8—21no—
362C3×Q8—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—81no—
370C2×C3×C4D3×D411yescharacteristic
371C2×C3×C4C23×D311yescharacteristic
372#67—62no—
373#67—122no—
374C2×Dic3—31no—
375C2×Dic3—31no—
376C2×Dic3—31no—
377C2×Dic3—61no—
378D12—32no—
379D12—61no—
380D12—61no—
381D12—61no—
382D12—61no—
383D12—61no—
384D12—122no—
385D12—122no—
386D12—241no—
387D12—241no—
388C4×D3—61no—
389C4×D3—61no—
390C4×D3—122no—
391C4×D3—241no—
392C4×D3—241no—
393C3×C8—21no—
394C3×C8—21no—
395C3⋊C8—61no—
396C3⋊C8—61no—
397C2×C9—22no—
398C2×C9#54611yescharacteristic
399C2×C9C2×#13511yescharacteristic
400C2×C9#57611yescharacteristic
401D9—41no—
402D9—42no—
403D9—81no—
404D9—81no—
405C24—181no—
406#41—182no—
407#41—361no—
408C2×Q8C22×D911yescharacteristic
409C2×D4—91no—
410C2×D4—91no—
411C2×D4—91no—
412C2×D4—91no—
413C2×D4—182no—
414C2×D4—181no—
415C2×D4—181no—
416C2×D4—181no—
417C2×D4—181no—
418C2×D4—181no—
419C2×D4—361no—
420C22×C4—21no—
421C22×C4—91no—
422C22×C4—181no—
423C22×C4—181no—
424C22×C4—181no—
425C22×C4C22×D911yescharacteristic
426SD16—361no—
427D8—182no—
428D8—361no—
429C2×C8—91no—
430C2×C8—91no—
431C2×C8—361no—
432C2×C8—361no—
433C2×C8C22×D911yescharacteristic
434C2×C8C22×D911yescharacteristic
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—91no—
438C4⋊C4—91no—
439C4⋊C4—181no—
440C4⋊C4—181no—
441C4⋊C4C22×D911yescharacteristic
442C4⋊C4C22×D911yescharacteristic
443C4⋊C4C22×D911yescharacteristic
444C22⋊C4—21no—
445C22⋊C4—91no—
446C22⋊C4—91no—
447C22⋊C4—181no—
448C22⋊C4—181no—
449C22⋊C4—181no—
450C22⋊C4—181no—
451C22⋊C4—181no—
452C22⋊C4—181no—
453C22⋊C4—181no—
454C22⋊C4—181no—
455C42—91no—
456C42—181no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3#91912yes—
460C22×C3C2×D3×D411yescharacteristic
461C2×D3—61no—
462C2×D3—62no—
463C2×D3—61no—
464C2×D3—61no—
465C2×D3—121no—
466C2×D3—121no—
467C2×D3—121no—
468C2×D3—121no—
469C2×D3—121no—
470C2×D3—121no—
471C2×D3—121no—
472C2×D3—121no—
473C2×D3—244no—
474C3×C4—21no—
475C3×C4—41no—
476C3×C4—41no—
477C3×C4—41no—
478C3×C4—41no—
479C3×C4D3×#4111yescharacteristic
480C3×C4#100911yescharacteristic
481Dic3—61no—
482Dic3—61no—
483Dic3—61no—
484Dic3—121no—
485C9#329711yescharacteristic, complemented, Sylow
486C23—91no—
487C23—181no—
488C23—181no—
489C23—181no—
490C23—362no—
491C23—362no—
492C23—721no—
493C23D4×D911yescharacteristic
494Q8—21no—
495Q8—21no—
496D4—92no—
497D4—182no—
498D4—181no—
499D4—181no—
500D4—181no—
501D4—181no—
502D4—181no—
503D4—362no—
504D4—362no—
505D4—362no—
506D4—721no—
507D4—721no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—81no—
515C2×C4—91no—
516C2×C4—91no—
517C2×C4—91no—
518C2×C4—181no—
519C2×C4—181no—
520C2×C4—181no—
521C2×C4—362no—
522C2×C4—721no—
523C2×C4—721no—
524C2×C4D4×D911yescharacteristic
525C2×C4C23×D911yescharacteristic
526C8—21no—
527C8—21no—
528C8—181no—
529C8—181no—
530C2×C3—22no—
531C2×C3#565411yescharacteristic
532C2×C3C2×#91911yescharacteristic
533C2×C3#577411yescharacteristic
534D3—121no—
535D3—122no—
536D3—241no—
537D3—241no—
538C22—21no—
539C22—21no—
540C22—181no—
541C22—182no—
542C22—181no—
543C22—181no—
544C22—361no—
545C22—361no—
546C22—361no—
547C22—361no—
548C22—361no—
549C22—361no—
550C22—361no—
551C22—361no—
552C22—724no—
553C22#6348112yes—
554C22C2×D4×D911yescharacteristic
555C4—21no—
556C4—41no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—181no—
561C4—181no—
562C4—181no—
563C4—361no—
564C4#41×D911yescharacteristic
565C4#6371511yescharacteristic
566C3#8148511yescharacteristic
567C2—22no—
568C2—361no—
569C2—362no—
570C2—721no—
571C2—721no—
572C2#1058975611yescharacteristic
573C2C2×#6348111yescharacteristic
574C2#1058987611yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#484C2
socleC22×C3C2×D3×D4
hypercenter#484D9
hypocenterC9#3297
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
1. #10589732C2semidirect
2. #10589616C2semidirect
3. C9×#484C2semidirect
4. #10588731C2semidirect
5. C2×#63369C2semidirect
6. #10588571C2semidirect
7. #10588565C2semidirect
8. #10588563C2semidirect
9. #10588552C2semidirect
10. #10588499C2semidirect
11. #10588490C2semidirect
12. #10588484C2semidirect
13. #10588480C2semidirect
14. #10588414C2semidirect
15. #611⋊C8C2semidirect
22. C2×#3675C22semidirect
30. C2×C8×D9C22semidirect
34. #63457C22semidirect
38. #63455C22semidirect
39. #63454C22semidirect
40. #63452C22semidirect
43. C9×#107C22semidirect
44. C9×#107C22semidirect
45. C9×#103C22semidirect
46. C9×#103C22semidirect
48. #63395C22semidirect
51. (C2×D9)⋊C8C22semidirect
52. Dic9⋊C8C22semidirect
53. C8×Dic9C22semidirect
58. #63369C22semidirect
59. #63367C22semidirect
218. #484D9semidirect
336. #107C2×D9semidirect
337. #107C2×D9semidirect
341. #103C2×D9semidirect
342. #103C2×D9semidirect
485. C9#3297semidirect

Maximal subgroups

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

subgroupindex
#105897322
#105896162
C9×#4842
#105887312
C2×#633692
#105885712
#105885652
#105885632
#105885522
#105884992
#105884902
#105884842
#105884802
#105884142
#611⋊C82
#814853