Finite Group Databasebeta

← #11889208

Subgroups — #11889208

Order 1152.

603 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#10589743C211yesmaximal, characteristic, complemented
2#10589714C211yesmaximal, characteristic
3C9×#465C211yesmaximal, characteristic, complemented
4#10588849C211yesmaximal, characteristic, complemented
5#10588846C211yesmaximal, characteristic, complemented
6#10588794C211yesmaximal, characteristic, complemented
7#10588792C211yesmaximal, characteristic, complemented
8#10588730C211yesmaximal, characteristic, complemented
9#10588715C211yesmaximal, characteristic, complemented
10#10588550C211yesmaximal, characteristic, complemented
11#10588548C211yesmaximal, characteristic, complemented
12#10588497C211yesmaximal, characteristic, complemented
13#10588496C211yesmaximal, characteristic, complemented
14#10588450C211yesmaximal, characteristic, complemented
15#10588445C211yesmaximal, characteristic, complemented
16#80686—31nomaximal
17C2×D4×D9C2211yescharacteristic
18C2×#3697C2211yescharacteristic
19C2×C9×SD16C2211yescharacteristic
20C22×C8×C9C2211yescharacteristic, complemented
21C9×C22⋊Q8C2211yescharacteristic, complemented
22C9×#121C2211yescharacteristic
23#63508C2211yescharacteristic
24Q8×Dic9C2211yescharacteristic, complemented
25C2×#3675C2211yescharacteristic
26C2×#3674C2211yescharacteristic, complemented
27#63500—21no—
28#63499—21no—
29#63498C2211yescharacteristic
30C4×#611C2211yescharacteristic
31#63488C2211yescharacteristic, complemented
32C2×#3663C2211yescharacteristic
33#63460—21no—
34#63459C2211yescharacteristic
35#63455C2211yescharacteristic
36#63454C2211yescharacteristic
37#63450C2211yescharacteristic, complemented
38#63449—21no—
39#63447—21no—
40#63445—21no—
41C22⋊C4×D9—21no—
42#63441—21no—
43C9×#106C2211yescharacteristic, complemented
44C9×#103C2211yescharacteristic, complemented
45C9×#102C2211yescharacteristic
46#63392C2211yescharacteristic
47#63392C2211yescharacteristic
48#63389C2211yescharacteristic, complemented
49#63380C2211yescharacteristic
50#63380C2211yescharacteristic
51(C2×D9)⋊C8C2211yescharacteristic
52#63376C2211yescharacteristic, complemented
53#63376C2211yescharacteristic, complemented
54#63375C2211yescharacteristic, complemented
55Dic9⋊C8C2211yescharacteristic, complemented
56#63369C2211yescharacteristic
57#63368C2211yescharacteristic, complemented
58#63367C2211yescharacteristic, complemented
59#63366C2211yescharacteristic, complemented
60#5641—31no—
61#5612—31no—
62C3×#465D311yescharacteristic
63#5169—31no—
64#5166—31no—
65#5113—31no—
66#5111—31no—
67#5047—31no—
68#5035—31no—
69#4870—31no—
70#4868—31no—
71#4817—31no—
72#4816—31no—
73#4770—31no—
74#4765—31no—
75C23×D9—21no—
76C2×Q8×C9C2311yescharacteristic
77C2×D4×C9—21no—
78C2×D4×C9C2311yescharacteristic
79C22×C4×C9C2311yescharacteristic
80C2×#611—21no—
81C2×#611—21no—
82C2×#611D411yescharacteristic
83D4×D9—22no—
84D4×D9—41no—
85#3697—22no—
86#3697—41no—
87C2×D36C2311yescharacteristic
88C2×C4×D9—21no—
89C2×C4×D9—21no—
90C2×C4×D9C2311yescharacteristic
91C2×Dic18—21no—
92C2×Dic18C2311yescharacteristic
93C9×SD16—41no—
94C2×C8×C9—41no—
95C2×C8×C9C2311yescharacteristic
96C2×C8×C9C2311yescharacteristic
97C9×C4⋊C4—21no—
98C9×C4⋊C4C2311yescharacteristic
99C9×C4⋊C4C2311yescharacteristic
100C9×C22⋊C4—21no—
101C9×C22⋊C4—21no—
102#3676—21no—
103#3676—21no—
104#3676—21no—
105#3676D411yescharacteristic
106#3675—22no—
107#3674—41no—
108(C2×D9)⋊C4—21no—
109(C2×D9)⋊C4—21no—
110(C2×D9)⋊C4—21no—
111(C2×D9)⋊C4—21no—
112(C2×D9)⋊C4D411yescharacteristic
113C4⋊Dic9—21no—
114C4⋊Dic9—21no—
115C4⋊Dic9C2311yescharacteristic
116C4⋊Dic9C2311yescharacteristic
117Dic9⋊C4—21no—
118Dic9⋊C4—21no—
119Dic9⋊C4D411yescharacteristic
120C4×Dic9—21no—
121C4×Dic9—21no—
122C4×Dic9—21no—
123C4×Dic9C2311yescharacteristic
124C2×C9⋊C8C2311yescharacteristic
125C2×C9⋊C8C2311yescharacteristic
126#3663—41no—
127#3311—91noSylow
128C2×D3×D4—31no—
129C2×#235—31no—
130C2×C3×SD16C2×D311yescharacteristic
131C22×C3×C8C2×D311yescharacteristic
132C3×C22⋊Q8C2×D311yescharacteristic
133C3×#121C2×D311yescharacteristic
134#946—31no—
135Q8×Dic3—31no—
136C2×#216—31no—
137C2×#215—31no—
138#938—61no—
139#937—61no—
140#936—31no—
141C4×#67—31no—
142#926—31no—
143C2×ΓL(1,𝔽25)—31no—
144#898—61no—
145#897—31no—
146#893—31no—
147#892—31no—
148#888—31no—
149#887—61no—
150#885—61no—
151#883—61no—
152D3×C22⋊C4—61no—
153#879—61no—
154C3×#106C2×D311yescharacteristic
155C3×#103C2×D311yescharacteristic
156C3×#102C2×D311yescharacteristic
157#832—31no—
158#832—31no—
159#830—31no—
160#821—31no—
161#821—31no—
162(C2×D3)⋊C8—31no—
163#816—31no—
164#816—31no—
165#815—31no—
166Dic3⋊C8—31no—
167#810—31no—
168#809—31no—
169#808—31no—
170#807—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—
180D4×C9—21no—
181D4×C9—21no—
182D4×C9—81no—
183C2×C4×C9—21no—
184C2×C4×C9—21no—
185C2×C4×C9—21no—
186C2×C4×C9—21no—
187C2×C4×C9—21no—
188C2×C4×C9C2×D411yescharacteristic
189C2×C4×C9C2411yescharacteristic
190#611—41no—
191#611—42no—
192#611—42no—
193C2×Dic9—21no—
194C2×Dic9—21no—
195C2×Dic9—21no—
196C2×Dic9C2×D411yescharacteristic
197C2×Dic9C2×D411yescharacteristic
198C2×Dic9C2×D411yescharacteristic
199D36—21no—
200D36#4112yes—
201C4×D9—21no—
202C4×D9—21no—
203C4×D9—42no—
204C4×D9—81no—
205Dic18—21no—
206Dic18—21no—
207Dic18—42no—
208C8×C9—21no—
209C8×C9—21no—
210C9⋊C8—21no—
211C9⋊C8—21no—
212#556—91no—
213#546—91no—
214#489—91no—
215#485—91no—
216#482—91no—
217#476—91no—
218#470—91no—
219#465D911yescharacteristic, complemented
220#464—91no—
221#452—91no—
222#450—91no—
223#440—91no—
224#435—91no—
225#418—91no—
226#416—91no—
227C23×D3—61no—
228C2×C3×Q8C22×D311yescharacteristic
229C2×C3×D4—21no—
230C2×C3×D4C22×D311yescharacteristic
231C22×C3×C4C22×D311yescharacteristic
232C2×#67—31no—
233C2×#67—61no—
234C2×#67—61no—
235D3×D4—62no—
236D3×D4—121no—
237#235—62no—
238#235—121no—
239C2×D12—31no—
240C2×C4×D3—31no—
241C2×C4×D3—61no—
242C2×C4×D3—61no—
243C2×Dic6—31no—
244C2×Dic6—61no—
245C3×SD16—41no—
246C2×C3×C8—41no—
247C2×C3×C8C22×D311yescharacteristic
248C2×C3×C8C22×D311yescharacteristic
249C3×C4⋊C4—21no—
250C3×C4⋊C4C22×D311yescharacteristic
251C3×C4⋊C4C22×D311yescharacteristic
252C3×C22⋊C4—21no—
253C3×C22⋊C4—21no—
254#217—31no—
255#217—61no—
256#217—61no—
257#217—61no—
258#216—121no—
259#215—62no—
260(C2×D3)⋊C4—31no—
261(C2×D3)⋊C4—61no—
262(C2×D3)⋊C4—61no—
263(C2×D3)⋊C4—61no—
264(C2×D3)⋊C4—61no—
265C4⋊Dic3—31no—
266C4⋊Dic3—31no—
267C4⋊Dic3—61no—
268C4⋊Dic3—61no—
269Dic3⋊C4—31no—
270Dic3⋊C4—61no—
271Dic3⋊C4—61no—
272C4×Dic3—31no—
273C4×Dic3—61no—
274C4×Dic3—61no—
275C4×Dic3—61no—
276C2×C3⋊C8—31no—
277C2×C3⋊C8—31no—
278ΓL(1,𝔽25)—121no—
279C22×C9—21no—
280C22×C9—21no—
281C22×C9—21no—
282C22×C9—41no—
283C22×C9—41no—
284C22×C9—41no—
285C22×C9C22×D411yescharacteristic
286C2×D9—21no—
287C2×D9—22no—
288C2×D9—21no—
289C2×D9—21no—
290C2×D9—41no—
291C2×D9—41no—
292C2×D9—84no—
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×#41—91no—
306C22×D4—91no—
307C2×Q16—91no—
308C2×SD16—91no—
309C2×SD16C2×D911yescharacteristic
310C2×M16—91no—
311C22×C8C2×D911yescharacteristic, complemented
312C4⋊Q8—91no—
313#126—181no—
314#126—181no—
315#124—91no—
316#124—181no—
317#123—181no—
318C22⋊Q8—91no—
319C22⋊Q8—91no—
320C22⋊Q8C2×D911yescharacteristic, complemented
321#121—181no—
322#121C2×D911yescharacteristic
323#120—181no—
324C4×Q8—91no—
325C4×Q8—181no—
326C4×D4—91no—
327C4×D4—91no—
328#117—91no—
329#117—91no—
330C2×C22⋊C4—181no—
331#107—91no—
332#106—91no—
333#106C2×D911yescharacteristic, complemented
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⋊C8—91no—
347#97—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×D4—21no—
358C3×D4—21no—
359C3×D4—81no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4D3×D411yescharacteristic
366C2×C3×C4C23×D311yescharacteristic
367#67—121no—
368#67—122no—
369#67—122no—
370C2×Dic3—31no—
371C2×Dic3—31no—
372C2×Dic3—31no—
373C2×Dic3—61no—
374C2×Dic3—61no—
375C2×Dic3—61no—
376D12—32no—
377D12—61no—
378C4×D3—61no—
379C4×D3—61no—
380C4×D3—122no—
381C4×D3—241no—
382Dic6—61no—
383Dic6—61no—
384Dic6—122no—
385C3×C8—21no—
386C3×C8—21no—
387C3⋊C8—61no—
388C3⋊C8—61no—
389C2×C9—41no—
390C2×C9—81no—
391C2×C9#54611yescharacteristic
392C2×C9#57511yescharacteristic
393C2×C9#57711yescharacteristic
394D9—41no—
395D9—42no—
396C24—181no—
397#41—182no—
398#41—361no—
399C2×Q8—91no—
400C2×Q8—181no—
401C2×Q8C22×D911yescharacteristic
402C2×D4—21no—
403C2×D4—91no—
404C2×D4—91no—
405C2×D4—181no—
406C2×D4—182no—
407C2×D4—181no—
408C2×D4—361no—
409C2×D4C22×D911yescharacteristic
410C22×C4—91no—
411C22×C4—181no—
412C22×C4—181no—
413C22×C4C22×D911yescharacteristic
414Q16—361no—
415SD16—41no—
416SD16—182no—
417M16—361no—
418C2×C8—41no—
419C2×C8—91no—
420C2×C8—91no—
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⋊C4C22×D911yescharacteristic
432C4⋊C4C22×D911yescharacteristic
433C22⋊C4—21no—
434C22⋊C4—21no—
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—
444C42—91no—
445C42—181no—
446C42—181no—
447C42—181no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—41no—
452C22×C3—41no—
453C22×C3—41no—
454C22×C3C2×D3×D411yescharacteristic
455C2×D3—61no—
456C2×D3—61no—
457C2×D3—61no—
458C2×D3—62no—
459C2×D3—121no—
460C2×D3—121no—
461C2×D3—244no—
462C3×C4—21no—
463C3×C4—41no—
464C3×C4—41no—
465C3×C4—41no—
466C3×C4#100411yescharacteristic
467C3×C4D3×#4111yescharacteristic
468Dic3—61no—
469Dic3—61no—
470Dic3—61no—
471Dic3—121no—
472Dic3—121no—
473Dic3—121no—
474C9#331111yescharacteristic, complemented, Sylow
475C23—21no—
476C23—91no—
477C23—181no—
478C23—362no—
479C23—362no—
480C23—721no—
481C23D4×D911yescharacteristic
482Q8—21no—
483Q8—21no—
484Q8—181no—
485Q8—181no—
486Q8—362no—
487D4—21no—
488D4—21no—
489D4—81no—
490D4—92no—
491D4—181no—
492D4—361no—
493D4—362no—
494D4—362no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
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—41no—
517C2×C3—81no—
518C2×C3#561011yescharacteristic
519C2×C3#576211yescharacteristic
520C2×C3#576811yescharacteristic
521D3—121no—
522D3—122no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—41no—
527C22—41no—
528C22—41no—
529C22—181no—
530C22—182no—
531C22—181no—
532C22—181no—
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—
547C4#6371011yescharacteristic
548C4#41×D911yescharacteristic
549C3#8068611yescharacteristic
550C2—41no—
551C2—81no—
552C2—361no—
553C2—362no—
554C2#1058971211yescharacteristic
555C2#1058986411yescharacteristic
556C2#1058987011yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#465C2
socleC22×C3C2×D3×D4
prime radical#10589714C2
hypercenter#465D9
hypocenterC9#3311
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. #10589743C2semidirect
3. C9×#465C2semidirect
4. #10588849C2semidirect
5. #10588846C2semidirect
6. #10588794C2semidirect
7. #10588792C2semidirect
8. #10588730C2semidirect
9. #10588715C2semidirect
10. #10588550C2semidirect
11. #10588548C2semidirect
12. #10588497C2semidirect
13. #10588496C2semidirect
14. #10588450C2semidirect
15. #10588445C2semidirect
20. C22×C8×C9C22semidirect
21. C9×C22⋊Q8C22semidirect
24. Q8×Dic9C22semidirect
26. C2×#3674C22semidirect
31. #63488C22semidirect
37. #63450C22semidirect
43. C9×#106C22semidirect
44. C9×#103C22semidirect
48. #63389C22semidirect
52. #63376C22semidirect
53. #63376C22semidirect
54. #63375C22semidirect
55. Dic9⋊C8C22semidirect
57. #63368C22semidirect
58. #63367C22semidirect
59. #63366C22semidirect
219. #465D9semidirect
311. C22×C8C2×D9semidirect
320. C22⋊Q8C2×D9semidirect
333. #106C2×D9semidirect
338. #103C2×D9semidirect
474. C9#3311semidirect

Maximal subgroups

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

subgroupindex
#105897432
#105897142
C9×#4652
#105888492
#105888462
#105887942
#105887922
#105887302
#105887152
#105885502
#105885482
#105884972
#105884962
#105884502
#105884452
#806863