Finite Group Databasebeta

← #11887176

Subgroups — #11887176

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#10589931C211yesmaximal, characteristic
2#10589741C211yesmaximal, characteristic, complemented
3C9×#452C211yesmaximal, characteristic, complemented
4#10588917C211yesmaximal, characteristic, complemented
5#10588868C211yesmaximal, characteristic, complemented
6#10588865C211yesmaximal, characteristic, complemented
7#10588849C211yesmaximal, characteristic, complemented
8SD16×Dic9C211yesmaximal, characteristic, complemented
9#10588731C211yesmaximal, characteristic, complemented
10#10588485C211yesmaximal, characteristic, complemented
11#10588480C211yesmaximal, characteristic, complemented
12D9×#102C211yesmaximal, characteristic, complemented
13#10588446C211yesmaximal, characteristic, complemented
14#10588419C211yesmaximal, characteristic, complemented
15#611⋊C8C211yesmaximal, characteristic, complemented
16#80246—31nomaximal
17C2×C9×#41C2211yescharacteristic
18C2×D4×D9C2211yescharacteristic
19C2×C9×Q16C2211yescharacteristic, complemented
20C2×C9×SD16C2211yescharacteristic
21C9×C22⋊Q8C2211yescharacteristic, complemented
22#63509C2211yescharacteristic
23#63508C2211yescharacteristic
24#63508C2211yescharacteristic
25Q8×Dic9C2211yescharacteristic, complemented
26C2×#3675C2211yescharacteristic
27#63501—21no—
28#63499—21no—
29D4×Dic9C2211yescharacteristic
30#63492C2211yescharacteristic
31#63491—21no—
32C4×#611C2211yescharacteristic
33C2×(C2×D9)⋊C4—21no—
34#63488C2211yescharacteristic, complemented
35C22×C9⋊C8C2211yescharacteristic, complemented
36C2×C8×D9C2211yescharacteristic
37#63454—21no—
38C4⋊C4×D9C2211yescharacteristic
39#63452C2211yescharacteristic, complemented
40#63451—21no—
41#63445—21no—
42#63441—21no—
43C9×#103C2211yescharacteristic, complemented
44C9×#102C2211yescharacteristic
45C9×C22⋊C8C2211yescharacteristic, complemented
46#63395C2211yescharacteristic, complemented
47#63395C2211yescharacteristic, complemented
48#63395C2211yescharacteristic, complemented
49#63392C2211yescharacteristic
50#63392C2211yescharacteristic
51#63380C2211yescharacteristic
52#63380C2211yescharacteristic
53(C2×D9)⋊C8C2211yescharacteristic
54#63378C2211yescharacteristic, complemented
55#63377C2211yescharacteristic, complemented
56Dic9⋊C8C2211yescharacteristic, complemented
57C8×Dic9C2211yescharacteristic, complemented
58#63369C2211yescharacteristic
59#63367C2211yescharacteristic, complemented
60#5829—31no—
61#5639—31no—
62C3×#452D311yescharacteristic
63#5233—31no—
64#5188—31no—
65#5185—31no—
66#5169—31no—
67Dic3×SD16—31no—
68#5048—31no—
69#4805—31no—
70#4800—31no—
71D3×#102—31no—
72#4766—31no—
73#4737—31no—
74#67⋊C8—31no—
75C23×D9—21no—
76C9×#41—22no—
77C9×#41—41no—
78C2×Q8×C9C2311yescharacteristic
79C2×Q8×C9C2311yescharacteristic
80C2×D4×C9—21no—
81C2×D4×C9C2311yescharacteristic
82C22×C4×C9—21no—
83C22×C4×C9C2311yescharacteristic
84C2×#611—21no—
85C2×#611—21no—
86C2×#611D411yescharacteristic
87C22×Dic9—21no—
88D4×D9—22no—
89D4×D9—41no—
90C2×D36C2311yescharacteristic
91C2×C4×D9—21no—
92C2×C4×D9C2311yescharacteristic
93C9×Q16—41no—
94C9×SD16—22no—
95C2×C8×C9C2311yescharacteristic
96C2×C8×C9C2311yescharacteristic
97C9×C4⋊C4—21no—
98C9×C4⋊C4C2311yescharacteristic
99C9×C22⋊C4—21no—
100#3676—21no—
101#3676—21no—
102#3676D411yescharacteristic
103#3675—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)⋊C4D411yescharacteristic
110C4⋊Dic9—21no—
111C4⋊Dic9—21no—
112C4⋊Dic9C2311yescharacteristic
113C4⋊Dic9C2311yescharacteristic
114C4⋊Dic9C2311yescharacteristic
115Dic9⋊C4—21no—
116Dic9⋊C4—21no—
117Dic9⋊C4—21no—
118Dic9⋊C4—21no—
119Dic9⋊C4D411yescharacteristic
120C4×Dic9—21no—
121C4×Dic9—21no—
122C4×Dic9C2311yescharacteristic
123C2×C9⋊C8—41no—
124C2×C9⋊C8C2311yescharacteristic
125C2×C9⋊C8C2311yescharacteristic
126C8×D9—41no—
127#3296—91noSylow
128C2×C3×#41C2×D311yescharacteristic
129C2×D3×D4—31no—
130C2×C3×Q16C2×D311yescharacteristic
131C2×C3×SD16C2×D311yescharacteristic
132C3×C22⋊Q8C2×D311yescharacteristic
133#947—31no—
134#946—31no—
135#946—31no—
136Q8×Dic3—31no—
137C2×#215—31no—
138#939—61no—
139#937—61no—
140D4×Dic3—31no—
141#930—31no—
142#929—61no—
143C4×#67—31no—
144C2×(C2×D3)⋊C4—61no—
145#926—31no—
146C22×C3⋊C8—31no—
147C2×D3×C8—31no—
148#892—61no—
149D3×C4⋊C4—31no—
150#890—31no—
151#889—61no—
152#883—61no—
153#879—61no—
154C3×#103C2×D311yescharacteristic
155C3×#102C2×D311yescharacteristic
156C3×C22⋊C8C2×D311yescharacteristic
157#835—31no—
158#835—31no—
159#835—31no—
160#832—31no—
161#832—31no—
162#821—31no—
163#821—31no—
164(C2×D3)⋊C8—31no—
165#818—31no—
166#817—31no—
167Dic3⋊C8—31no—
168C8×Dic3—31no—
169#809—31no—
170#808—31no—
171C23×C9—21no—
172C23×C9C2×D411yescharacteristic
173C22×D9—21no—
174C22×D9—42no—
175C22×D9—42no—
176C22×D9—81no—
177C22×D9C2×D411yescharacteristic
178Q8×C9—21no—
179Q8×C9—21no—
180Q8×C9—21no—
181Q8×C9—21no—
182D4×C9—21no—
183D4×C9—42no—
184D4×C9#4112yes—
185C2×C4×C9—21no—
186C2×C4×C9—21no—
187C2×C4×C9—21no—
188C2×C4×C9—21no—
189C2×C4×C9—21no—
190C2×C4×C9—42no—
191C2×C4×C9C2×D411yescharacteristic
192C2×C4×C9C2411yescharacteristic
193#611—22no—
194#611—42no—
195#611—81no—
196C2×Dic9—21no—
197C2×Dic9—21no—
198C2×Dic9—21no—
199C2×Dic9—81no—
200C2×Dic9C2×D411yescharacteristic
201C2×Dic9C2×D411yescharacteristic
202C2×Dic9C2×D411yescharacteristic
203D36—21no—
204D36—21no—
205C4×D9—21no—
206C4×D9—21no—
207C4×D9—42no—
208C8×C9—21no—
209C8×C9—21no—
210C9⋊C8—21no—
211C9⋊C8—21no—
212#552—91no—
213#546—91no—
214#488—91no—
215#483—91no—
216#482—91no—
217#478—91no—
218#467—91no—
219#465—91no—
220#464—91no—
221#452D911yescharacteristic, complemented
222#450—91no—
223C4×SD16—91no—
224C8×D4—91no—
225#416—91no—
226C2×#102—91no—
227C23×D3—61no—
228C3×#41—22no—
229C3×#41—41no—
230C2×C3×Q8C22×D311yescharacteristic
231C2×C3×Q8C22×D311yescharacteristic
232C2×C3×D4—21no—
233C2×C3×D4C22×D311yescharacteristic
234C22×C3×C4—21no—
235C22×C3×C4C22×D311yescharacteristic
236C2×#67—31no—
237C2×#67—61no—
238C2×#67—61no—
239C22×Dic3—61no—
240D3×D4—62no—
241D3×D4—121no—
242C2×D12—31no—
243C2×C4×D3—31no—
244C2×C4×D3—61no—
245C3×Q16—41no—
246C3×SD16—22no—
247C2×C3×C8C22×D311yescharacteristic
248C2×C3×C8C22×D311yescharacteristic
249C3×C4⋊C4—21no—
250C3×C4⋊C4C22×D311yescharacteristic
251C3×C22⋊C4—21no—
252#217—31no—
253#217—61no—
254#217—61no—
255#215—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—
262C4⋊Dic3—31no—
263C4⋊Dic3—31no—
264C4⋊Dic3—31no—
265C4⋊Dic3—61no—
266C4⋊Dic3—61no—
267Dic3⋊C4—31no—
268Dic3⋊C4—61no—
269Dic3⋊C4—61no—
270Dic3⋊C4—61no—
271Dic3⋊C4—61no—
272C4×Dic3—31no—
273C4×Dic3—61no—
274C4×Dic3—61no—
275C2×C3⋊C8—31no—
276C2×C3⋊C8—31no—
277C2×C3⋊C8—121no—
278D3×C8—121no—
279C22×C9—22no—
280C22×C9—21no—
281C22×C9—21no—
282C22×C9—21no—
283C22×C9—41no—
284C22×C9—41no—
285C22×C9C22×D411yescharacteristic
286C2×D9—21no—
287C2×D9—21no—
288C2×D9—41no—
289C2×D9—41no—
290C2×D9—41no—
291C2×D9—84no—
292C2×D9#13512yes—
293C4×C9—21no—
294C4×C9—41no—
295C4×C9—41no—
296C4×C9—41no—
297C4×C9C2×#4111yescharacteristic
298C4×C9H(5,𝔽2)11yescharacteristic
299Dic9—21no—
300Dic9—21no—
301Dic9—21no—
302Dic9—41no—
303Dic9—41no—
304Dic9—41no—
305C2×#41C2×D911yescharacteristic
306C22×D4—91no—
307C2×Q16C2×D911yescharacteristic, complemented
308C2×SD16—91no—
309C2×SD16C2×D911yescharacteristic
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, complemented
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⋊C4—91no—
330C2×C22⋊C4—181no—
331#107—91no—
332#106—91no—
333#106—91no—
334C4⋊C8—91no—
335#103—91no—
336#103—91no—
337#103—91no—
338#103C2×D911yescharacteristic, complemented
339#102—91no—
340#102—91no—
341#102—91no—
342#102—91no—
343#102—91no—
344#102C2×D911yescharacteristic
345C22⋊C8—91no—
346C22⋊C8C2×D911yescharacteristic, complemented
347C4×C8—91no—
348C23×C3—21no—
349C23×C3D3×D411yescharacteristic
350C22×D3—31no—
351C22×D3—61no—
352C22×D3—122no—
353C22×D3—122no—
354C22×D3—241no—
355C3×Q8—21no—
356C3×Q8—21no—
357C3×Q8—21no—
358C3×Q8—21no—
359C3×D4—21no—
360C3×D4—42no—
361C3×D4#23712yes—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—42no—
368C2×C3×C4D3×D411yescharacteristic
369C2×C3×C4C23×D311yescharacteristic
370#67—62no—
371#67—122no—
372#67—241no—
373C2×Dic3—31no—
374C2×Dic3—31no—
375C2×Dic3—31no—
376C2×Dic3—61no—
377C2×Dic3—61no—
378C2×Dic3—61no—
379C2×Dic3—241no—
380D12—61no—
381D12—61no—
382C4×D3—61no—
383C4×D3—61no—
384C4×D3—122no—
385C3×C8—21no—
386C3×C8—21no—
387C3⋊C8—61no—
388C3⋊C8—61no—
389C2×C9—42no—
390C2×C9—41no—
391C2×C9#54611yescharacteristic
392C2×C9C2×#13511yescharacteristic
393C2×C9#57711yescharacteristic
394D9—22no—
395D9—81no—
396C24—181no—
397#41—22no—
398#41—41no—
399C2×Q8C22×D911yescharacteristic
400C2×Q8C22×D911yescharacteristic
401C2×D4—21no—
402C2×D4—91no—
403C2×D4—91no—
404C2×D4—181no—
405C2×D4—182no—
406C2×D4—181no—
407C2×D4—361no—
408C2×D4C22×D911yescharacteristic
409C22×C4—21no—
410C22×C4—91no—
411C22×C4—181no—
412C22×C4—181no—
413C22×C4C22×D911yescharacteristic
414Q16—41no—
415SD16—22no—
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—91no—
425C4⋊C4—91no—
426C4⋊C4—91no—
427C4⋊C4—91no—
428C4⋊C4—181no—
429C4⋊C4—181no—
430C4⋊C4—181no—
431C4⋊C4—181no—
432C4⋊C4—181no—
433C4⋊C4—181no—
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—22no—
451C22×C3—21no—
452C22×C3—41no—
453C22×C3—41no—
454C22×C3C2×D3×D411yescharacteristic
455C2×D3—32no—
456C2×D3—61no—
457C2×D3—61no—
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×C4C2×#23711yescharacteristic
467C3×C4#100411yescharacteristic
468Dic3—61no—
469Dic3—61no—
470Dic3—61no—
471Dic3—121no—
472Dic3—121no—
473Dic3—121no—
474C9#329611yescharacteristic, complemented, Sylow
475C23—21no—
476C23—91no—
477C23—181no—
478C23—362no—
479C23—362no—
480C23—721no—
481C23D4×D911yescharacteristic
482Q8—21no—
483Q8—21no—
484Q8—21no—
485Q8—21no—
486D4—21no—
487D4—42no—
488D4—182no—
489D4—181no—
490D4—181no—
491D4—362no—
492D4—721no—
493D4#369912yes—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—42no—
500C2×C4—91no—
501C2×C4—91no—
502C2×C4—91no—
503C2×C4—181no—
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—42no—
517C2×C3—41no—
518C2×C3#559111yescharacteristic
519C2×C3D3×#13511yescharacteristic
520C2×C3#577811yescharacteristic
521D3—62no—
522D3—241no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—22no—
527C22—41no—
528C22—41no—
529C22—92no—
530C22—181no—
531C22—181no—
532C22—361no—
533C22—361no—
534C22—361no—
535C22—724no—
536C22C2×D4×D911yescharacteristic
537C4—21no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—181no—
542C4—181no—
543C4—181no—
544C4—361no—
545C4—361no—
546C4—361no—
547C4C2×#369911yescharacteristic
548C4#6371011yescharacteristic
549C3#8024611yescharacteristic
550C2—41no—
551C2—42no—
552C2—182no—
553C2—721no—
554C2#1058969311yescharacteristic
555C2D9×#13511yescharacteristic
556C2#1058988011yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#452C2
socleC22×C3C2×D3×D4
prime radical#10589931C2
hypercenter#452D9
hypocenterC9#3296
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
2. #10589741C2semidirect
3. C9×#452C2semidirect
4. #10588917C2semidirect
5. #10588868C2semidirect
6. #10588865C2semidirect
7. #10588849C2semidirect
8. SD16×Dic9C2semidirect
9. #10588731C2semidirect
10. #10588485C2semidirect
11. #10588480C2semidirect
12. D9×#102C2semidirect
13. #10588446C2semidirect
14. #10588419C2semidirect
15. #611⋊C8C2semidirect
19. C2×C9×Q16C22semidirect
21. C9×C22⋊Q8C22semidirect
25. Q8×Dic9C22semidirect
34. #63488C22semidirect
35. C22×C9⋊C8C22semidirect
39. #63452C22semidirect
43. C9×#103C22semidirect
45. C9×C22⋊C8C22semidirect
46. #63395C22semidirect
47. #63395C22semidirect
48. #63395C22semidirect
54. #63378C22semidirect
55. #63377C22semidirect
56. Dic9⋊C8C22semidirect
57. C8×Dic9C22semidirect
59. #63367C22semidirect
221. #452D9semidirect
307. C2×Q16C2×D9semidirect
320. C22⋊Q8C2×D9semidirect
338. #103C2×D9semidirect
346. C22⋊C8C2×D9semidirect
474. C9#3296semidirect

Maximal subgroups

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

subgroupindex
#105899312
#105897412
C9×#4522
#105889172
#105888682
#105888652
#105888492
SD16×Dic92
#105887312
#105884852
#105884802
D9×#1022
#105884462
#105884192
#611⋊C82
#802463