Finite Group Databasebeta

← #11887080

Subgroups — #11887080

Order 1152.

693 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589737C211yesmaximal, characteristic, complemented
2#10589711C211yesmaximal, characteristic
3C9×#465C211yesmaximal, characteristic, complemented
4#10588849C211yesmaximal, characteristic, complemented
5#10588843C211yesmaximal, characteristic, complemented
6C2×#63380C211yesmaximal, characteristic, complemented
7C8×#611C211yesmaximal, characteristic, complemented
8#10588729C211yesmaximal, characteristic, complemented
9#10588714C211yesmaximal, characteristic, complemented
10#10588550C211yesmaximal, characteristic, complemented
11#10588543C211yesmaximal, characteristic, complemented
12#10588487C211yesmaximal, characteristic, complemented
13#10588468C211yesmaximal, characteristic, complemented
14D9×#102C211yesmaximal, characteristic, complemented
15#10588440C211yesmaximal, characteristic, complemented
16#80680—31nomaximal
17C2×D4×D9—21no—
18C2×D4×D9C2211yescharacteristic
19C22×D36C2211yescharacteristic
20C2×C9×SD16C2211yescharacteristic, complemented
21C22×C8×C9C2211yescharacteristic, complemented
22C9×C22⋊Q8C2211yescharacteristic, complemented
23C9×#121C2211yescharacteristic
24#63508C2211yescharacteristic, complemented
25Q8×Dic9C2211yescharacteristic, complemented
26C2×#3675C2211yescharacteristic
27C2×#3675C2211yescharacteristic, complemented
28#63502C2211yescharacteristic
29#63499—21no—
30C4×#611C2211yescharacteristic
31C2×C4⋊Dic9C2211yescharacteristic, complemented
32C2×C8×D9C2211yescharacteristic, complemented
33#63459—21no—
34#63457C2211yescharacteristic
35#63455C2211yescharacteristic
36C4⋊C4×D9C2211yescharacteristic, complemented
37#63451—21no—
38#63450C2211yescharacteristic, complemented
39#63446—21no—
40#63444—21no—
41#611⋊C4—21no—
42#63440—21no—
43C9×#106C2211yescharacteristic, complemented
44C9×#103C2211yescharacteristic, complemented
45C9×#102C2211yescharacteristic, complemented
46#63392C2211yescharacteristic, complemented
47#63392C2211yescharacteristic, complemented
48#63389C2211yescharacteristic, complemented
49#63380C2211yescharacteristic
50#63380C2211yescharacteristic
51#63380C2211yescharacteristic, complemented
52#63380C2211yescharacteristic, complemented
53(C2×D9)⋊C8C2211yescharacteristic, complemented
54Dic9⋊C8C2211yescharacteristic, complemented
55C8×Dic9C2211yescharacteristic, complemented
56#63369C2211yescharacteristic
57#63369C2211yescharacteristic, complemented
58#63367C2211yescharacteristic, complemented
59#63367C2211yescharacteristic, complemented
60#5635—31no—
61#5609—31no—
62C3×#465D311yescharacteristic
63#5169—31no—
64#5163—31no—
65C2×#821—31no—
66C8×#67—31no—
67#5046—31no—
68#5034—31no—
69#4870—31no—
70#4863—31no—
71#4807—31no—
72#4788—31no—
73D3×#102—31no—
74#4760—31no—
75C23×D9—21no—
76C23×D9—21no—
77C2×Q8×C9C2311yescharacteristic
78C2×D4×C9—21no—
79C2×D4×C9C2311yescharacteristic
80C22×C4×C9C2311yescharacteristic
81C2×#611—21no—
82C2×#611—21no—
83C2×#611—21no—
84C2×#611D411yescharacteristic
85C22×Dic9—21no—
86D4×D9—22no—
87D4×D9—41no—
88D4×D9—44no—
89C2×D36—22no—
90C2×D36—21no—
91C2×D36—21no—
92C2×D36—41no—
93C2×D36C2311yescharacteristic
94C2×D36C2311yescharacteristic
95C2×C4×D9—21no—
96C2×C4×D9—21no—
97C2×C4×D9C2311yescharacteristic
98C2×Dic18—21no—
99C9×SD16—41no—
100C2×C8×C9—41no—
101C2×C8×C9C2311yescharacteristic
102C2×C8×C9C2311yescharacteristic
103C9×C4⋊C4—21no—
104C9×C4⋊C4C2311yescharacteristic
105C9×C4⋊C4C2311yescharacteristic
106C9×C22⋊C4—21no—
107C9×C22⋊C4—21no—
108#3676D411yescharacteristic
109#3675—22no—
110#3675—41no—
111(C2×D9)⋊C4—21no—
112(C2×D9)⋊C4—21no—
113(C2×D9)⋊C4—21no—
114(C2×D9)⋊C4D411yescharacteristic
115C4⋊Dic9—21no—
116C4⋊Dic9—21no—
117C4⋊Dic9C2311yescharacteristic
118C4⋊Dic9C2311yescharacteristic
119Dic9⋊C4—21no—
120Dic9⋊C4—21no—
121Dic9⋊C4—21no—
122Dic9⋊C4D411yescharacteristic
123C4×Dic9—21no—
124C4×Dic9C2311yescharacteristic
125C2×C9⋊C8C2311yescharacteristic
126C2×C9⋊C8C2311yescharacteristic
127C8×D9—41no—
128#3295—91noSylow
129C2×D3×D4—31no—
130C2×D3×D4—61no—
131C22×D12—31no—
132C2×C3×SD16C2×D311yescharacteristic
133C22×C3×C8C2×D311yescharacteristic
134C3×C22⋊Q8C2×D311yescharacteristic
135C3×#121C2×D311yescharacteristic
136#946—31no—
137Q8×Dic3—31no—
138C2×#215—31no—
139C2×#215—31no—
140#940—31no—
141#937—61no—
142C4×#67—31no—
143C2×C4⋊Dic3—31no—
144C2×D3×C8—31no—
145#897—61no—
146#895—31no—
147#893—31no—
148D3×C4⋊C4—31no—
149#889—61no—
150#888—31no—
151#884—61no—
152#882—61no—
153#67⋊C4—61no—
154#878—61no—
155C3×#106C2×D311yescharacteristic
156C3×#103C2×D311yescharacteristic
157C3×#102C2×D311yescharacteristic
158#832—31no—
159#832—31no—
160#830—31no—
161#821—31no—
162#821—31no—
163#821—31no—
164#821—31no—
165(C2×D3)⋊C8—31no—
166Dic3⋊C8—31no—
167C8×Dic3—31no—
168#809—31no—
169#809—31no—
170#808—31no—
171#808—31no—
172C23×C9—21no—
173C23×C9C2×D411yescharacteristic
174C22×D9—21no—
175C22×D9—21no—
176C22×D9—42no—
177C22×D9—42no—
178C22×D9—42no—
179C22×D9—42no—
180C22×D9—81no—
181C22×D9—81no—
182C22×D9C2×D411yescharacteristic
183Q8×C9—21no—
184Q8×C9—21no—
185D4×C9—21no—
186D4×C9—21no—
187D4×C9—42no—
188C2×C4×C9—21no—
189C2×C4×C9—21no—
190C2×C4×C9—21no—
191C2×C4×C9—21no—
192C2×C4×C9—21no—
193C2×C4×C9C2×D411yescharacteristic
194C2×C4×C9C2411yescharacteristic
195#611—42no—
196#611—42no—
197#611—81no—
198#611SD1614yescomplemented
199C2×Dic9—21no—
200C2×Dic9—21no—
201C2×Dic9—81no—
202C2×Dic9C2×D411yescharacteristic
203C2×Dic9C2×D411yescharacteristic
204C2×Dic9C2×D411yescharacteristic
205D36—21no—
206D36—21no—
207D36—21no—
208D36—42no—
209D36—42no—
210D36#4112yes—
211C4×D9—21no—
212C4×D9—21no—
213C4×D9—42no—
214C4×D9—81no—
215Dic18—81no—
216C8×C9—21no—
217C8×C9—21no—
218C9⋊C8—21no—
219C9⋊C8—21no—
220#554—91no—
221D42—91no—
222#486—91no—
223#481—91no—
224#481—91no—
225#476—91no—
226#465—91no—
227#465D911yescharacteristic, complemented
228#460—91no—
229#450—91no—
230#450—91no—
231C4×SD16—91no—
232C8×D4—91no—
233C2×#102—91no—
234C2×#102—91no—
235C23×D3—61no—
236C23×D3—61no—
237C2×C3×Q8C22×D311yescharacteristic
238C2×C3×D4—21no—
239C2×C3×D4C22×D311yescharacteristic
240C22×C3×C4C22×D311yescharacteristic
241C2×#67—31no—
242C2×#67—61no—
243C2×#67—61no—
244C2×#67—61no—
245C22×Dic3—61no—
246D3×D4—62no—
247D3×D4—121no—
248D3×D4—124no—
249C2×D12—31no—
250C2×D12—31no—
251C2×D12—62no—
252C2×D12—61no—
253C2×D12—61no—
254C2×D12—121no—
255C2×C4×D3—31no—
256C2×C4×D3—61no—
257C2×C4×D3—61no—
258C2×Dic6—61no—
259C3×SD16—41no—
260C2×C3×C8—41no—
261C2×C3×C8C22×D311yescharacteristic
262C2×C3×C8C22×D311yescharacteristic
263C3×C4⋊C4—21no—
264C3×C4⋊C4C22×D311yescharacteristic
265C3×C4⋊C4C22×D311yescharacteristic
266C3×C22⋊C4—21no—
267C3×C22⋊C4—21no—
268#217—31no—
269#215—62no—
270#215—121no—
271(C2×D3)⋊C4—31no—
272(C2×D3)⋊C4—61no—
273(C2×D3)⋊C4—61no—
274(C2×D3)⋊C4—61no—
275C4⋊Dic3—31no—
276C4⋊Dic3—31no—
277C4⋊Dic3—61no—
278C4⋊Dic3—61no—
279Dic3⋊C4—31no—
280Dic3⋊C4—61no—
281Dic3⋊C4—61no—
282Dic3⋊C4—61no—
283C4×Dic3—31no—
284C4×Dic3—61no—
285C2×C3⋊C8—31no—
286C2×C3⋊C8—31no—
287D3×C8—121no—
288C22×C9—21no—
289C22×C9—21no—
290C22×C9—41no—
291C22×C9—41no—
292C22×C9—41no—
293C22×C9C2×SD1612yes—
294C22×C9C22×D411yescharacteristic
295C2×D9—21no—
296C2×D9—21no—
297C2×D9—22no—
298C2×D9—41no—
299C2×D9—41no—
300C2×D9—41no—
301C2×D9—41no—
302C2×D9—41no—
303C2×D9—84no—
304C2×D9—84no—
305C2×D9C2×SD1612yes—
306C4×C9—21no—
307C4×C9—41no—
308C4×C9—41no—
309C4×C9—41no—
310C4×C9C2×#4111yescharacteristic
311C4×C9H(5,𝔽2)11yescharacteristic
312Dic9—21no—
313Dic9—21no—
314Dic9—41no—
315Dic9—41no—
316Dic9C2×SD1612yes—
317C22×D4—91no—
318C22×D4—91no—
319C22×D4—181no—
320C2×SD16—91no—
321C2×SD16—91no—
322C2×SD16C2×D911yescharacteristic, complemented
323C22×C8—91no—
324C22×C8C2×D911yescharacteristic, complemented
325C4⋊Q8—91no—
326#127—91no—
327#125—181no—
328C22⋊Q8—91no—
329C22⋊Q8—181no—
330C22⋊Q8—181no—
331C22⋊Q8C2×D911yescharacteristic, complemented
332#121—91no—
333#121—181no—
334#121C2×D911yescharacteristic
335#120—181no—
336#120—181no—
337C4×Q8—91no—
338C4×D4—91no—
339C4×D4—91no—
340C4×D4—181no—
341C2×C4⋊C4—91no—
342C2×C4⋊C4—91no—
343#106—91no—
344#106—91no—
345#106C2×D911yescharacteristic, complemented
346C4⋊C8—91no—
347#103C2×D911yescharacteristic, complemented
348#102—91no—
349#102—91no—
350#102—91no—
351#102—91no—
352#102—91no—
353#102—91no—
354#102—91no—
355#102—91no—
356#102C2×D911yescharacteristic, complemented
357C22⋊C8—91no—
358C22⋊C8—91no—
359C4×C8—91no—
360C23×C3—21no—
361C23×C3D3×D411yescharacteristic
362C22×D3—31no—
363C22×D3—61no—
364C22×D3—61no—
365C22×D3—122no—
366C22×D3—122no—
367C22×D3—122no—
368C22×D3—122no—
369C22×D3—241no—
370C22×D3—241no—
371C3×Q8—21no—
372C3×Q8—21no—
373C3×D4—21no—
374C3×D4—21no—
375C3×D4—42no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4D3×D411yescharacteristic
382C2×C3×C4C23×D311yescharacteristic
383#67—34no—
384#67—122no—
385#67—122no—
386#67—241no—
387C2×Dic3—31no—
388C2×Dic3—31no—
389C2×Dic3—31no—
390C2×Dic3—61no—
391C2×Dic3—61no—
392C2×Dic3—241no—
393D12—32no—
394D12—61no—
395D12—61no—
396D12—61no—
397D12—122no—
398D12—122no—
399C4×D3—61no—
400C4×D3—61no—
401C4×D3—122no—
402C4×D3—241no—
403Dic6—241no—
404C3×C8—21no—
405C3×C8—21no—
406C3⋊C8—61no—
407C3⋊C8—61no—
408C2×C9—22no—
409C2×C9—81no—
410C2×C9#54611yescharacteristic
411C2×C9C22×SD1611yescharacteristic
412C2×C9#57611yescharacteristic
413D9—22no—
414D9—42no—
415D9—81no—
416C24—181no—
417C24—181no—
418C2×Q8—181no—
419C2×Q8C22×D911yescharacteristic
420C2×D4—21no—
421C2×D4—91no—
422C2×D4—91no—
423C2×D4—91no—
424C2×D4—182no—
425C2×D4—181no—
426C2×D4—181no—
427C2×D4—181no—
428C2×D4—181no—
429C2×D4—182no—
430C2×D4—181no—
431C2×D4—361no—
432C2×D4—361no—
433C2×D4—364no—
434C2×D4C22×D911yescharacteristic
435C22×C4—91no—
436C22×C4—181no—
437C22×C4—181no—
438C22×C4—181no—
439C22×C4C22×D911yescharacteristic
440SD16—41no—
441SD16—182no—
442SD16—361no—
443C2×C8—41no—
444C2×C8—91no—
445C2×C8—91no—
446C2×C8—361no—
447C2×C8C22×D911yescharacteristic
448C2×C8C22×D911yescharacteristic
449C4⋊C4—21no—
450C4⋊C4—91no—
451C4⋊C4—91no—
452C4⋊C4—91no—
453C4⋊C4—181no—
454C4⋊C4—181no—
455C4⋊C4—181no—
456C4⋊C4—181no—
457C4⋊C4—181no—
458C4⋊C4C22×D911yescharacteristic
459C4⋊C4C22×D911yescharacteristic
460C22⋊C4—21no—
461C22⋊C4—21no—
462C22⋊C4—91no—
463C22⋊C4—91no—
464C22⋊C4—181no—
465C22⋊C4—181no—
466C22⋊C4—181no—
467C42—91no—
468C42—181no—
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—41no—
472C22×C3—41no—
473C22×C3—41no—
474C22×C3D3×SD1612yes—
475C22×C3C2×D3×D411yescharacteristic
476C2×D3—32no—
477C2×D3—61no—
478C2×D3—61no—
479C2×D3—62no—
480C2×D3—121no—
481C2×D3—121no—
482C2×D3—121no—
483C2×D3—121no—
484C2×D3—121no—
485C2×D3—244no—
486C2×D3—244no—
487C3×C4—21no—
488C3×C4—41no—
489C3×C4—41no—
490C3×C4—41no—
491C3×C4#100411yescharacteristic
492C3×C4D3×#4111yescharacteristic
493Dic3—32no—
494Dic3—61no—
495Dic3—61no—
496Dic3—121no—
497Dic3—121no—
498C9#329511yescharacteristic, complemented, Sylow
499C23—21no—
500C23—91no—
501C23—181no—
502C23—181no—
503C23—362no—
504C23—362no—
505C23—362no—
506C23—362no—
507C23—721no—
508C23—721no—
509C23D4×D911yescharacteristic
510Q8—21no—
511Q8—21no—
512Q8—721no—
513D4—21no—
514D4—21no—
515D4—42no—
516D4—94no—
517D4—92no—
518D4—181no—
519D4—181no—
520D4—181no—
521D4—362no—
522D4—362no—
523D4—362no—
524D4—362no—
525D4—721no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—91no—
532C2×C4—91no—
533C2×C4—91no—
534C2×C4—181no—
535C2×C4—181no—
536C2×C4—181no—
537C2×C4—181no—
538C2×C4—362no—
539C2×C4—721no—
540C2×C4—721no—
541C2×C4D4×D911yescharacteristic
542C2×C4C23×D911yescharacteristic
543C8—21no—
544C8—21no—
545C8—181no—
546C8—181no—
547C2×C3—22no—
548C2×C3—81no—
549C2×C3#561011yescharacteristic
550C2×C3C2×D3×SD1611yescharacteristic
551C2×C3#576911yescharacteristic
552D3—62no—
553D3—122no—
554D3—241no—
555C22—21no—
556C22—21no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—92no—
561C22—181no—
562C22—181no—
563C22—182no—
564C22—361no—
565C22—361no—
566C22—361no—
567C22—361no—
568C22—361no—
569C22—724no—
570C22—724no—
571C22SD16×D912yes—
572C22C2×D4×D911yescharacteristic
573C4—21no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—92no—
578C4—181no—
579C4—181no—
580C4—361no—
581C4—361no—
582C4#6371011yescharacteristic
583C4#41×D911yescharacteristic
584C3#8068011yescharacteristic
585C2—22no—
586C2—81no—
587C2—182no—
588C2—362no—
589C2—721no—
590C2#1058971211yescharacteristic
591C2C2×SD16×D911yescharacteristic
592C2#1058987111yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#465C2
socleC22×C3C2×D3×D4
prime radical#10589711C2
hypercenter#465D9
hypocenterC9#3295
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #10589737C2semidirect
3. C9×#465C2semidirect
4. #10588849C2semidirect
5. #10588843C2semidirect
6. C2×#63380C2semidirect
7. C8×#611C2semidirect
8. #10588729C2semidirect
9. #10588714C2semidirect
10. #10588550C2semidirect
11. #10588543C2semidirect
12. #10588487C2semidirect
13. #10588468C2semidirect
14. D9×#102C2semidirect
15. #10588440C2semidirect
20. C2×C9×SD16C22semidirect
21. C22×C8×C9C22semidirect
22. C9×C22⋊Q8C22semidirect
24. #63508C22semidirect
25. Q8×Dic9C22semidirect
27. C2×#3675C22semidirect
31. C2×C4⋊Dic9C22semidirect
32. C2×C8×D9C22semidirect
36. C4⋊C4×D9C22semidirect
38. #63450C22semidirect
43. C9×#106C22semidirect
44. C9×#103C22semidirect
45. C9×#102C22semidirect
46. #63392C22semidirect
47. #63392C22semidirect
48. #63389C22semidirect
51. #63380C22semidirect
52. #63380C22semidirect
53. (C2×D9)⋊C8C22semidirect
54. Dic9⋊C8C22semidirect
55. C8×Dic9C22semidirect
57. #63369C22semidirect
58. #63367C22semidirect
59. #63367C22semidirect
198. #611SD16semidirect
227. #465D9semidirect
322. C2×SD16C2×D9semidirect
324. C22×C8C2×D9semidirect
331. C22⋊Q8C2×D9semidirect
345. #106C2×D9semidirect
347. #103C2×D9semidirect
356. #102C2×D9semidirect
498. C9#3295semidirect

Maximal subgroups

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

subgroupindex
#105897372
#105897112
C9×#4652
#105888492
#105888432
C2×#633802
C8×#6112
#105887292
#105887142
#105885502
#105885432
#105884872
#105884682
D9×#1022
#105884402
#806803