Finite Group Databasebeta

← #11887185

Subgroups — #11887185

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#10589908C211yesmaximal, characteristic
2#10589615C211yesmaximal, characteristic, complemented
3C2×C9×#102C211yesmaximal, characteristic, complemented
4#10588897C211yesmaximal, characteristic, complemented
5C8×#611C211yesmaximal, characteristic, complemented
6#10588788C211yesmaximal, characteristic, complemented
7#10588647C211yesmaximal, characteristic, complemented
8#10588464C211yesmaximal, characteristic, complemented
9#10588463C211yesmaximal, characteristic, complemented
10#10588458C211yesmaximal, characteristic, complemented
11#10588452C211yesmaximal, characteristic, complemented
12#10588448C211yesmaximal, characteristic, complemented
13#10588447C211yesmaximal, characteristic, complemented
14#10588446C211yesmaximal, characteristic, complemented
15#10588438C211yesmaximal, characteristic, complemented
16#78759—31nomaximal
17C22×D4×C9C2211yescharacteristic
18C2×#3699C2211yescharacteristic
19C22×C8×C9C2211yescharacteristic
20C2×C9×C4⋊C4C2211yescharacteristic
21#63515—21no—
22C2×#3676—21no—
23#63501—21no—
24#63500C2211yescharacteristic
25#63498C2211yescharacteristic
26#63497—21no—
27D4×Dic9C2211yescharacteristic
28C2×#3672C2211yescharacteristic
29C2×#3672C2211yescharacteristic
30#63491—21no—
31C4×#611C2211yescharacteristic
32#63488—21no—
33#63486C2211yescharacteristic
34#63486C2211yescharacteristic
35C2×C8×D9C2211yescharacteristic, complemented
36C2×Dic36C2211yescharacteristic, complemented
37#63460—21no—
38#63459C2211yescharacteristic, complemented
39#63454C2211yescharacteristic, complemented
40#63452C2211yescharacteristic, complemented
41#63451—21no—
42#63449C2211yescharacteristic, complemented
43C9×#102C2211yescharacteristic
44C9×#102C2211yescharacteristic
45C9×#102C2211yescharacteristic
46C9×#102C2211yescharacteristic
47#63392C2211yescharacteristic
48#63392C2211yescharacteristic
49#63389C2211yescharacteristic
50(C2×D9)⋊C8C2211yescharacteristic, complemented
51#63378C2211yescharacteristic, complemented
52#63376C2211yescharacteristic, complemented
53#63376C2211yescharacteristic, complemented
54Dic9⋊C8C2211yescharacteristic, complemented
55C8×Dic9C2211yescharacteristic, complemented
56#63368C2211yescharacteristic, complemented
57#63368C2211yescharacteristic, complemented
58#63367C2211yescharacteristic, complemented
59#63367C2211yescharacteristic, complemented
60#5806—31no—
61#5513—31no—
62C2×C3×#102D311yescharacteristic
63#5218—31no—
64#5116—31no—
65C8×#67—31no—
66#4971—31no—
67#4784—31no—
68#4783—31no—
69#4778—31no—
70#4772—31no—
71#4768—31no—
72#4767—31no—
73#4766—31no—
74#4758—31no—
75C24×C9—21no—
76C2×D4×C9—22no—
77C2×D4×C9—21no—
78C2×D4×C9—41no—
79C2×D4×C9C2311yescharacteristic
80C2×D4×C9C2311yescharacteristic
81C22×C4×C9—21no—
82C22×C4×C9C2311yescharacteristic
83C2×#611—21no—
84C2×#611—21no—
85C2×#611D411yescharacteristic
86C22×Dic9—21no—
87C22×Dic9—21no—
88#3699—22no—
89#3699—41no—
90C2×C4×D9C2311yescharacteristic
91C2×Dic18C2311yescharacteristic
92C2×Dic18C2311yescharacteristic
93C2×C8×C9—41no—
94C2×C8×C9C2311yescharacteristic
95C2×C8×C9C2311yescharacteristic
96C9×C4⋊C4—21no—
97C9×C4⋊C4C2311yescharacteristic
98C9×C4⋊C4C2311yescharacteristic
99#3676—21no—
100#3676—21no—
101#3676—21no—
102#3676—21no—
103#3676—21no—
104#3676—21no—
105#3676D411yescharacteristic
106#3672—22no—
107#3672—41no—
108(C2×D9)⋊C4—21no—
109(C2×D9)⋊C4—21no—
110(C2×D9)⋊C4D411yescharacteristic
111C4⋊Dic9—21no—
112C4⋊Dic9—21no—
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⋊C8C2311yescharacteristic
124C2×C9⋊C8C2311yescharacteristic
125C8×D9—41no—
126Dic36—41no—
127#3296—91noSylow
128C22×C3×D4C2×D311yescharacteristic
129C2×#237—31no—
130C22×C3×C8C2×D311yescharacteristic
131C2×C3×C4⋊C4C2×D311yescharacteristic
132#953—61no—
133C2×#217—61no—
134#939—61no—
135#938—31no—
136#936—31no—
137#935—61no—
138D4×Dic3—31no—
139C2×#214—31no—
140C2×#214—31no—
141#929—61no—
142C4×#67—31no—
143#926—61no—
144#924—31no—
145#924—31no—
146C2×Dic12—31no—
147C2×D3×C8—31no—
148#898—61no—
149#897—31no—
150#892—31no—
151#890—31no—
152#889—61no—
153#887—31no—
154C3×#102C2×D311yescharacteristic
155C3×#102C2×D311yescharacteristic
156C3×#102C2×D311yescharacteristic
157C3×#102C2×D311yescharacteristic
158#832—31no—
159#832—31no—
160#830—31no—
161(C2×D3)⋊C8—31no—
162#818—31no—
163#816—31no—
164#816—31no—
165Dic3⋊C8—31no—
166C8×Dic3—31no—
167#810—31no—
168#810—31no—
169#808—31no—
170#808—31no—
171C23×C9—21no—
172C23×C9—21no—
173C23×C9—42no—
174C23×C9—42no—
175C23×C9—81no—
176C23×C9C2×D411yescharacteristic
177C22×D9C2×D411yescharacteristic
178D4×C9—21no—
179D4×C9—21no—
180D4×C9—21no—
181D4×C9—42no—
182D4×C9#4112yes—
183C2×C4×C9—21no—
184C2×C4×C9—21no—
185C2×C4×C9—21no—
186C2×C4×C9—21no—
187C2×C4×C9—42no—
188C2×C4×C9C2×D411yescharacteristic
189C2×C4×C9C2411yescharacteristic
190#611—22no—
191#611—42no—
192#611—81no—
193C2×Dic9—21no—
194C2×Dic9—21no—
195C2×Dic9—21no—
196C2×Dic9—21no—
197C2×Dic9—42no—
198C2×Dic9—81no—
199C2×Dic9C2×D411yescharacteristic
200C2×Dic9C2×D411yescharacteristic
201C2×Dic9C2×D411yescharacteristic
202C4×D9—21no—
203C4×D9—21no—
204Dic18—21no—
205Dic18—21no—
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#483—91no—
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×#102D911yescharacteristic, complemented
227C24×C3—21no—
228C2×C3×D4—22no—
229C2×C3×D4—21no—
230C2×C3×D4—41no—
231C2×C3×D4C22×D311yescharacteristic
232C2×C3×D4C22×D311yescharacteristic
233C22×C3×C4—21no—
234C22×C3×C4C22×D311yescharacteristic
235C2×#67—31no—
236C2×#67—61no—
237C2×#67—61no—
238C22×Dic3—61no—
239C22×Dic3—61no—
240#237—62no—
241#237—121no—
242C2×C4×D3—31no—
243C2×Dic6—31no—
244C2×Dic6—31no—
245C2×C3×C8—41no—
246C2×C3×C8C22×D311yescharacteristic
247C2×C3×C8C22×D311yescharacteristic
248C3×C4⋊C4—21no—
249C3×C4⋊C4C22×D311yescharacteristic
250C3×C4⋊C4C22×D311yescharacteristic
251#217—31no—
252#217—61no—
253#217—61no—
254#217—61no—
255#217—61no—
256#217—61no—
257#217—61no—
258#214—62no—
259#214—121no—
260(C2×D3)⋊C4—31no—
261(C2×D3)⋊C4—61no—
262(C2×D3)⋊C4—61no—
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—
277Dic12—121no—
278D3×C8—121no—
279C22×C9—21no—
280C22×C9—21no—
281C22×C9—22no—
282C22×C9—41no—
283C22×C9—41no—
284C22×C9—41no—
285C22×C9—41no—
286C22×C9—41no—
287C22×C9—84no—
288C22×C9#13512yes—
289C22×C9C22×D411yescharacteristic
290C2×D9—21no—
291C2×D9—21no—
292C2×D9—21no—
293C4×C9—21no—
294C4×C9—41no—
295C4×C9—41no—
296C4×C9C2×#4111yescharacteristic
297C4×C9H(5,𝔽2)11yescharacteristic
298Dic9—21no—
299Dic9—21no—
300Dic9—21no—
301Dic9—41no—
302Dic9—41no—
303Dic9—41no—
304Dic9—41no—
305C2×#41—91no—
306C22×D4C2×D911yescharacteristic
307C2×Q16—91no—
308C2×SD16—91no—
309C2×SD16—91no—
310C22×C8—91no—
311C22×C8C2×D911yescharacteristic
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⋊Q8—91no—
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#106—91no—
333#106—91no—
334C4⋊C8—91no—
335#103—91no—
336#103—91no—
337#103—91no—
338#103—91no—
339#102—91no—
340#102—91no—
341#102C2×D911yescharacteristic
342#102C2×D911yescharacteristic
343#102C2×D911yescharacteristic
344#102C2×D911yescharacteristic
345C22⋊C8—91no—
346C22⋊C8—91no—
347C4×C8—91no—
348C23×C3—21no—
349C23×C3—21no—
350C23×C3—42no—
351C23×C3—42no—
352C23×C3—81no—
353C23×C3D3×D411yescharacteristic
354C22×D3—31no—
355C3×D4—21no—
356C3×D4—21no—
357C3×D4—21no—
358C3×D4—42no—
359C3×D4#23512yes—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—42no—
365C2×C3×C4D3×D411yescharacteristic
366C2×C3×C4C23×D311yescharacteristic
367#67—62no—
368#67—122no—
369#67—241no—
370C2×Dic3—31no—
371C2×Dic3—31no—
372C2×Dic3—31no—
373C2×Dic3—61no—
374C2×Dic3—61no—
375C2×Dic3—61no—
376C2×Dic3—61no—
377C2×Dic3—122no—
378C2×Dic3—241no—
379C4×D3—61no—
380C4×D3—61no—
381Dic6—61no—
382Dic6—61no—
383Dic6—61no—
384Dic6—61no—
385C3×C8—21no—
386C3×C8—21no—
387C3⋊C8—61no—
388C3⋊C8—61no—
389C2×C9—22no—
390C2×C9—42no—
391C2×C9—81no—
392C2×C9#54611yescharacteristic
393C2×C9C2×#13511yescharacteristic
394C2×C9#57711yescharacteristic
395D9—41no—
396C24—21no—
397#41—182no—
398#41—361no—
399C2×Q8—91no—
400C2×Q8—91no—
401C2×D4—22no—
402C2×D4—21no—
403C2×D4—41no—
404C2×D4—91no—
405C2×D4—181no—
406C2×D4—181no—
407C2×D4C22×D911yescharacteristic
408C2×D4C22×D911yescharacteristic
409C22×C4—21no—
410C22×C4—91no—
411C22×C4—181no—
412C22×C4—181no—
413C22×C4C22×D911yescharacteristic
414Q16—361no—
415SD16—182no—
416SD16—361no—
417C2×C8—41no—
418C2×C8—91no—
419C2×C8—91no—
420C2×C8—361no—
421C2×C8C22×D911yescharacteristic
422C2×C8C22×D911yescharacteristic
423C4⋊C4—21no—
424C4⋊C4—91no—
425C4⋊C4—91no—
426C4⋊C4—91no—
427C4⋊C4—181no—
428C4⋊C4—181no—
429C4⋊C4—181no—
430C4⋊C4—181no—
431C4⋊C4—181no—
432C4⋊C4—181no—
433C4⋊C4C22×D911yescharacteristic
434C4⋊C4C22×D911yescharacteristic
435C22⋊C4—91no—
436C22⋊C4—91no—
437C22⋊C4—181no—
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—41no—
452C22×C3—41no—
453C22×C3—41no—
454C22×C3—41no—
455C22×C3—41no—
456C22×C3—84no—
457C22×C3#91212yes—
458C22×C3C2×D3×D411yescharacteristic
459C2×D3—61no—
460C2×D3—61no—
461C2×D3—61no—
462C3×C4—21no—
463C3×C4—41no—
464C3×C4—41no—
465C3×C4C2×#23511yescharacteristic
466C3×C4#100411yescharacteristic
467Dic3—61no—
468Dic3—61no—
469Dic3—61no—
470Dic3—121no—
471Dic3—121no—
472Dic3—121no—
473Dic3—121no—
474C9#329611yescharacteristic, complemented, Sylow
475C23—21no—
476C23—21no—
477C23—42no—
478C23—42no—
479C23—81no—
480C23—91no—
481C23D4×D911yescharacteristic
482Q8—181no—
483Q8—181no—
484Q8—181no—
485Q8—181no—
486D4—21no—
487D4—21no—
488D4—21no—
489D4—42no—
490D4—182no—
491D4—362no—
492D4—721no—
493D4#369712yes—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—42no—
499C2×C4—91no—
500C2×C4—91no—
501C2×C4—91no—
502C2×C4—181no—
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—22no—
517C2×C3—42no—
518C2×C3—81no—
519C2×C3#549011yescharacteristic
520C2×C3C2×#91211yescharacteristic
521C2×C3#576211yescharacteristic
522D3—121no—
523C22—21no—
524C22—21no—
525C22—22no—
526C22—41no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—84no—
532C22—181no—
533C22—181no—
534C22—181no—
535C22#6347412yes—
536C22C2×D4×D911yescharacteristic
537C4—21no—
538C4—41no—
539C4—41no—
540C4—181no—
541C4—181no—
542C4—181no—
543C4—361no—
544C4—361no—
545C4—361no—
546C4—361no—
547C4C2×#369711yescharacteristic
548C4#6371011yescharacteristic
549C3#7875911yescharacteristic
550C2—22no—
551C2—42no—
552C2—81no—
553C2—361no—
554C2#1058959211yescharacteristic
555C2C2×#6347411yescharacteristic
556C2#1058986411yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC2×C9×#102C2
socleC22×C3C2×D3×D4
prime radical#10589908C2
hypercenterC2×#102D9
hypocenterC9#3296
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. #10589615C2semidirect
3. C2×C9×#102C2semidirect
4. #10588897C2semidirect
5. C8×#611C2semidirect
6. #10588788C2semidirect
7. #10588647C2semidirect
8. #10588464C2semidirect
9. #10588463C2semidirect
10. #10588458C2semidirect
11. #10588452C2semidirect
12. #10588448C2semidirect
13. #10588447C2semidirect
14. #10588446C2semidirect
15. #10588438C2semidirect
35. C2×C8×D9C22semidirect
36. C2×Dic36C22semidirect
38. #63459C22semidirect
39. #63454C22semidirect
40. #63452C22semidirect
42. #63449C22semidirect
50. (C2×D9)⋊C8C22semidirect
51. #63378C22semidirect
52. #63376C22semidirect
53. #63376C22semidirect
54. Dic9⋊C8C22semidirect
55. C8×Dic9C22semidirect
56. #63368C22semidirect
57. #63368C22semidirect
58. #63367C22semidirect
59. #63367C22semidirect
226. C2×#102D9semidirect
474. C9#3296semidirect

Maximal subgroups

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

subgroupindex
#105899082
#105896152
C2×C9×#1022
#105888972
C8×#6112
#105887882
#105886472
#105884642
#105884632
#105884582
#105884522
#105884482
#105884472
#105884462
#105884382
#787593