Finite Group Databasebeta

← #11887191

Subgroups — #11887191

Order 1152.

612 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589732C211yesmaximal, characteristic
2#10589615C211yesmaximal, characteristic, complemented
3C9×#483C211yesmaximal, characteristic, complemented
4#10588727C211yesmaximal, characteristic, complemented
5C2×#63369C211yesmaximal, characteristic, complemented
6#10588551C211yesmaximal, characteristic, complemented
7#10588546C211yesmaximal, characteristic, complemented
8#10588544C211yesmaximal, characteristic, complemented
9#10588532C211yesmaximal, characteristic, complemented
10#10588488C211yesmaximal, characteristic, complemented
11#10588484C211yesmaximal, characteristic, complemented
12#10588480C211yesmaximal, characteristic, complemented
13#10588478C211yesmaximal, characteristic, complemented
14#10588413C211yesmaximal, characteristic, complemented
15#611⋊C8C211yesmaximal, characteristic, complemented
16#81445—31nomaximal
17C2×#3701C2211yescharacteristic
18C22×D36C2211yescharacteristic
19C9×C22⋊Q8C2211yescharacteristic
20C2×C9×C4⋊C4C2211yescharacteristic
21#63509C2211yescharacteristic
22C2×#3674C2211yescharacteristic, complemented
23#63491—21no—
24C4×#611C2211yescharacteristic
25#63488—21no—
26#63486C2211yescharacteristic
27C22×C9⋊C8C2211yescharacteristic
28C2×#3664C2211yescharacteristic
29C2×#3664C2211yescharacteristic
30C2×C8×D9C2211yescharacteristic, complemented
31#63460—21no—
32#63459C2211yescharacteristic, complemented
33#63457—21no—
34#63457C2211yescharacteristic
35#63456—21no—
36#63455C2211yescharacteristic
37#63454C2211yescharacteristic, complemented
38#63452C2211yescharacteristic, complemented
39#63451—21no—
40#63449C2211yescharacteristic, complemented
41#63444—21no—
42C22⋊C4×D9—21no—
43C9×#106C2211yescharacteristic, complemented
44C9×#106C2211yescharacteristic, 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#63368C2211yescharacteristic, complemented
59#63366C2211yescharacteristic, complemented
60#5630—31no—
61#5513—31no—
62C3×#483D311yescharacteristic
63#5051—31no—
64C2×#809—31no—
65#4871—31no—
66#4866—31no—
67#4864—31no—
68#4852—31no—
69#4808—31no—
70#4804—31no—
71#4800—31no—
72#4798—31no—
73#4731—31no—
74#67⋊C8—31no—
75C23×D9—21no—
76C2×Q8×C9C2311yescharacteristic
77C22×C4×C9—21no—
78C22×C4×C9C2311yescharacteristic
79C2×#611D411yescharacteristic
80#3701—22no—
81#3701—41no—
82C2×D36—22no—
83C2×D36—21no—
84C2×D36—21no—
85C2×D36—21no—
86C2×D36—41no—
87C2×D36C2311yescharacteristic
88C2×D36C2311yescharacteristic
89C2×C4×D9—21no—
90C2×C4×D9—21no—
91C2×C4×D9C2311yescharacteristic
92C2×Dic18C2311yescharacteristic
93C2×C8×C9C2311yescharacteristic
94C2×C8×C9C2311yescharacteristic
95C9×C4⋊C4—21no—
96C9×C4⋊C4—21no—
97C9×C4⋊C4C2311yescharacteristic
98C9×C4⋊C4C2311yescharacteristic
99C9×C4⋊C4C2311yescharacteristic
100C9×C22⋊C4—21no—
101#3676—21no—
102#3676D411yescharacteristic
103#3674—41no—
104(C2×D9)⋊C4—21no—
105(C2×D9)⋊C4—21no—
106(C2×D9)⋊C4—21no—
107(C2×D9)⋊C4—21no—
108(C2×D9)⋊C4—21no—
109(C2×D9)⋊C4—21no—
110(C2×D9)⋊C4D411yescharacteristic
111C4⋊Dic9—21no—
112C4⋊Dic9—21no—
113C4⋊Dic9C2311yescharacteristic
114Dic9⋊C4—21no—
115Dic9⋊C4—21no—
116Dic9⋊C4—21no—
117Dic9⋊C4D411yescharacteristic
118C4×Dic9—21no—
119C4×Dic9—21no—
120C4×Dic9C2311yescharacteristic
121C2×C9⋊C8—41no—
122C2×C9⋊C8C2311yescharacteristic
123C2×C9⋊C8C2311yescharacteristic
124#3664—22no—
125#3664—41no—
126C8×D9—41no—
127#3296—91noSylow
128C2×#239—31no—
129C22×D12—31no—
130C3×C22⋊Q8C2×D311yescharacteristic
131C2×C3×C4⋊C4C2×D311yescharacteristic
132#947—31no—
133C2×#216—31no—
134#929—61no—
135C4×#67—31no—
136#926—61no—
137#924—31no—
138C22×C3⋊C8—31no—
139C2×#204—31no—
140C2×#204—31no—
141C2×D3×C8—31no—
142#898—61no—
143#897—31no—
144#895—31no—
145#895—61no—
146#894—61no—
147#893—31no—
148#892—31no—
149#890—31no—
150#889—61no—
151#887—31no—
152#882—61no—
153D3×C22⋊C4—61no—
154C3×#106C2×D311yescharacteristic
155C3×#106C2×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#810—31no—
166#809—31no—
167#809—31no—
168#809—31no—
169#809—31no—
170#807—31no—
171C23×C9C2×D411yescharacteristic
172C22×D9—21no—
173C22×D9—21no—
174C22×D9—42no—
175C22×D9—42no—
176C22×D9—81no—
177C22×D9C2×D411yescharacteristic
178Q8×C9—21no—
179Q8×C9—21no—
180C2×C4×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—42no—
187C2×C4×C9C2×D411yescharacteristic
188C2×C4×C9C2411yescharacteristic
189#611—22no—
190C2×Dic9—21no—
191C2×Dic9—21no—
192C2×Dic9C2×D411yescharacteristic
193C2×Dic9C2×D411yescharacteristic
194C2×Dic9C2×D411yescharacteristic
195D36—21no—
196D36—21no—
197D36—21no—
198D36—42no—
199D36—42no—
200D36—81no—
201D36#4112yes—
202C4×D9—21no—
203C4×D9—21no—
204C4×D9—42no—
205C4×D9—81no—
206Dic18—21no—
207Dic18—21no—
208C8×C9—21no—
209C8×C9—21no—
210C9⋊C8—21no—
211C9⋊C8—21no—
212#552—91no—
213#546—91no—
214#488—91no—
215#483D911yescharacteristic, complemented
216#482—91no—
217#478—91no—
218#467—91no—
219#465—91no—
220#464—91no—
221#452—91no—
222#450—91no—
223C4×SD16—91no—
224C8×D4—91no—
225#416—91no—
226C2×#102—91no—
227C23×D3—61no—
228C2×C3×Q8C22×D311yescharacteristic
229C22×C3×C4—21no—
230C22×C3×C4C22×D311yescharacteristic
231C2×#67—31no—
232#239—62no—
233#239—121no—
234C2×D12—31no—
235C2×D12—31no—
236C2×D12—62no—
237C2×D12—61no—
238C2×D12—61no—
239C2×D12—61no—
240C2×D12—121no—
241C2×C4×D3—31no—
242C2×C4×D3—61no—
243C2×C4×D3—61no—
244C2×Dic6—31no—
245C2×C3×C8C22×D311yescharacteristic
246C2×C3×C8C22×D311yescharacteristic
247C3×C4⋊C4—21no—
248C3×C4⋊C4—21no—
249C3×C4⋊C4C22×D311yescharacteristic
250C3×C4⋊C4C22×D311yescharacteristic
251C3×C4⋊C4C22×D311yescharacteristic
252C3×C22⋊C4—21no—
253#217—31no—
254#217—61no—
255#216—121no—
256(C2×D3)⋊C4—31no—
257(C2×D3)⋊C4—61no—
258(C2×D3)⋊C4—61no—
259(C2×D3)⋊C4—61no—
260(C2×D3)⋊C4—61no—
261(C2×D3)⋊C4—61no—
262(C2×D3)⋊C4—61no—
263C4⋊Dic3—31no—
264C4⋊Dic3—61no—
265C4⋊Dic3—61no—
266Dic3⋊C4—31no—
267Dic3⋊C4—61no—
268Dic3⋊C4—61no—
269Dic3⋊C4—61no—
270C4×Dic3—31no—
271C4×Dic3—61no—
272C4×Dic3—61no—
273C2×C3⋊C8—31no—
274C2×C3⋊C8—31no—
275C2×C3⋊C8—121no—
276#204—62no—
277#204—121no—
278D3×C8—121no—
279C22×C9—21no—
280C22×C9—21no—
281C22×C9#13512yes—
282C22×C9C22×D411yescharacteristic
283C2×D9—21no—
284C2×D9—22no—
285C2×D9—21no—
286C2×D9—21no—
287C2×D9—41no—
288C2×D9—41no—
289C2×D9—41no—
290C2×D9—41no—
291C2×D9—41no—
292C2×D9—84no—
293C4×C9—21no—
294C4×C9—41no—
295C4×C9—41no—
296C4×C9—41no—
297C4×C9—41no—
298C4×C9C2×#4111yescharacteristic
299C4×C9H(5,𝔽2)11yescharacteristic
300Dic9—21no—
301Dic9—21no—
302Dic9—21no—
303Dic9—41no—
304Dic9—41no—
305C2×#41—91no—
306C22×D4—91no—
307C2×Q16—91no—
308C2×SD16—91no—
309C2×SD16—91no—
310C22×C8—91no—
311C22×C8—91no—
312#126—181no—
313#125—91no—
314#125—181no—
315#124—91no—
316#123—181no—
317#123—181no—
318C22⋊Q8—91no—
319C22⋊Q8—91no—
320C22⋊Q8C2×D911yescharacteristic
321#121—91no—
322#121—181no—
323#120—181no—
324C4×Q8—91no—
325C4×D4—91no—
326C4×D4—91no—
327#117—91no—
328#117—181no—
329C2×C4⋊C4C2×D911yescharacteristic
330C2×C22⋊C4—181no—
331#107—91no—
332#106C2×D911yescharacteristic, complemented
333#106C2×D911yescharacteristic, complemented
334C4⋊C8—91no—
335#103—91no—
336#103—91no—
337#103C2×D911yescharacteristic, complemented
338#103C2×D911yescharacteristic, complemented
339#102—91no—
340#102—91no—
341#102—91no—
342#102—91no—
343#102—91no—
344#102—91no—
345C22⋊C8—91no—
346C22⋊C8C2×D911yescharacteristic
347C4×C8—91no—
348C23×C3D3×D411yescharacteristic
349C22×D3—31no—
350C22×D3—61no—
351C22×D3—61no—
352C22×D3—122no—
353C22×D3—122no—
354C22×D3—241no—
355C3×Q8—21no—
356C3×Q8—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—42no—
364C2×C3×C4D3×D411yescharacteristic
365C2×C3×C4C23×D311yescharacteristic
366#67—62no—
367C2×Dic3—31no—
368C2×Dic3—31no—
369C2×Dic3—31no—
370C2×Dic3—61no—
371C2×Dic3—61no—
372D12—32no—
373D12—61no—
374D12—61no—
375D12—61no—
376D12—122no—
377D12—122no—
378D12—241no—
379C4×D3—61no—
380C4×D3—61no—
381C4×D3—122no—
382C4×D3—241no—
383Dic6—61no—
384Dic6—61no—
385C3×C8—21no—
386C3×C8—21no—
387C3⋊C8—61no—
388C3⋊C8—61no—
389C2×C9—22no—
390C2×C9#54611yescharacteristic
391C2×C9C2×#13511yescharacteristic
392C2×C9#57711yescharacteristic
393D9—41no—
394D9—42no—
395D9—81no—
396C24—181no—
397#41—182no—
398#41—361no—
399C2×Q8—91no—
400C2×Q8C22×D911yescharacteristic
401C2×D4—91no—
402C2×D4—91no—
403C2×D4—91no—
404C2×D4—182no—
405C2×D4—181no—
406C2×D4—181no—
407C2×D4—181no—
408C2×D4—361no—
409C22×C4—21no—
410C22×C4—91no—
411C22×C4—181no—
412C22×C4—181no—
413C22×C4C22×D911yescharacteristic
414Q16—361no—
415SD16—182no—
416SD16—361no—
417C2×C8—91no—
418C2×C8—91no—
419C2×C8—361no—
420C2×C8—361no—
421C2×C8C22×D911yescharacteristic
422C2×C8C22×D911yescharacteristic
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—91no—
426C4⋊C4—91no—
427C4⋊C4—181no—
428C4⋊C4—181no—
429C4⋊C4—181no—
430C4⋊C4—181no—
431C4⋊C4—181no—
432C4⋊C4C22×D911yescharacteristic
433C4⋊C4C22×D911yescharacteristic
434C4⋊C4C22×D911yescharacteristic
435C22⋊C4—21no—
436C22⋊C4—91no—
437C22⋊C4—91no—
438C22⋊C4—181no—
439C22⋊C4—181no—
440C22⋊C4—181no—
441C22⋊C4—181no—
442C22⋊C4—181no—
443C22⋊C4—181no—
444C22⋊C4—181no—
445C42—91no—
446C42—181no—
447C42—181no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3#91612yes—
451C22×C3C2×D3×D411yescharacteristic
452C2×D3—61no—
453C2×D3—62no—
454C2×D3—61no—
455C2×D3—61no—
456C2×D3—121no—
457C2×D3—121no—
458C2×D3—121no—
459C2×D3—121no—
460C2×D3—121no—
461C2×D3—244no—
462C3×C4—21no—
463C3×C4—41no—
464C3×C4—41no—
465C3×C4—41no—
466C3×C4—41no—
467C3×C4D3×#4111yescharacteristic
468C3×C4#100911yescharacteristic
469Dic3—61no—
470Dic3—61no—
471Dic3—61no—
472Dic3—121no—
473Dic3—121no—
474C9#329611yescharacteristic, complemented, Sylow
475C23—91no—
476C23—181no—
477C23—181no—
478C23—362no—
479C23—362no—
480C23—721no—
481C23D4×D911yescharacteristic
482Q8—21no—
483Q8—21no—
484Q8—181no—
485Q8—181no—
486D4—92no—
487D4—182no—
488D4—181no—
489D4—181no—
490D4—181no—
491D4—362no—
492D4—362no—
493D4—721no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—42no—
501C2×C4—91no—
502C2×C4—91no—
503C2×C4—91no—
504C2×C4—181no—
505C2×C4—181no—
506C2×C4—181no—
507C2×C4—181no—
508C2×C4—362no—
509C2×C4—721no—
510C2×C4D4×D911yescharacteristic
511C2×C4C23×D911yescharacteristic
512C8—21no—
513C8—21no—
514C8—181no—
515C8—181no—
516C2×C3—22no—
517C2×C3#565411yescharacteristic
518C2×C3C2×#91611yescharacteristic
519C2×C3#577811yescharacteristic
520D3—121no—
521D3—122no—
522D3—241no—
523C22—21no—
524C22—21no—
525C22—181no—
526C22—182no—
527C22—181no—
528C22—181no—
529C22—361no—
530C22—361no—
531C22—361no—
532C22—361no—
533C22—361no—
534C22—724no—
535C22#6347812yes—
536C22C2×D4×D911yescharacteristic
537C4—21no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—181no—
543C4—181no—
544C4—181no—
545C4—361no—
546C4—361no—
547C4#41×D911yescharacteristic
548C4#6371511yescharacteristic
549C3#8144511yescharacteristic
550C2—22no—
551C2—361no—
552C2—362no—
553C2—721no—
554C2#1058975611yescharacteristic
555C2C2×#6347811yescharacteristic
556C2#1058988011yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#483C2
socleC22×C3C2×D3×D4
prime radical#10589732C2
hypercenter#483D9
hypocenterC9#3296
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
2. #10589615C2semidirect
3. C9×#483C2semidirect
4. #10588727C2semidirect
5. C2×#63369C2semidirect
6. #10588551C2semidirect
7. #10588546C2semidirect
8. #10588544C2semidirect
9. #10588532C2semidirect
10. #10588488C2semidirect
11. #10588484C2semidirect
12. #10588480C2semidirect
13. #10588478C2semidirect
14. #10588413C2semidirect
15. #611⋊C8C2semidirect
22. C2×#3674C22semidirect
30. C2×C8×D9C22semidirect
32. #63459C22semidirect
37. #63454C22semidirect
38. #63452C22semidirect
40. #63449C22semidirect
43. C9×#106C22semidirect
44. C9×#106C22semidirect
45. C9×#103C22semidirect
46. C9×#103C22semidirect
48. #63395C22semidirect
51. (C2×D9)⋊C8C22semidirect
52. Dic9⋊C8C22semidirect
53. C8×Dic9C22semidirect
58. #63368C22semidirect
59. #63366C22semidirect
215. #483D9semidirect
332. #106C2×D9semidirect
333. #106C2×D9semidirect
337. #103C2×D9semidirect
338. #103C2×D9semidirect
474. C9#3296semidirect

Maximal subgroups

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

subgroupindex
#105897322
#105896152
C9×#4832
#105887272
C2×#633692
#105885512
#105885462
#105885442
#105885322
#105884882
#105884842
#105884802
#105884782
#105884132
#611⋊C82
#814453