Finite Group Databasebeta

← #11889181

Subgroups — #11889181

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#10589834C211yesmaximal, characteristic, complemented
2#10589656C211yesmaximal, characteristic
3C9×#476C211yesmaximal, characteristic, complemented
4#10588774C211yesmaximal, characteristic, complemented
5#10588694C211yesmaximal, characteristic, complemented
6#10588548C211yesmaximal, characteristic, complemented
7#10588547C211yesmaximal, characteristic, complemented
8#10588546C211yesmaximal, characteristic, complemented
9#10588544C211yesmaximal, characteristic, complemented
10#10588529C211yesmaximal, characteristic, complemented
11#10588520C211yesmaximal, characteristic, complemented
12#10588463C211yesmaximal, characteristic, complemented
13#10588456C211yesmaximal, characteristic, complemented
14#10588452C211yesmaximal, characteristic, complemented
15#10588450C211yesmaximal, characteristic, complemented
16#81078—31nomaximal
17C2×#3699C2211yescharacteristic
18C2×D4×D9C2211yescharacteristic
19C9×C4⋊Q8C2211yescharacteristic, complemented
20C4×D4×C9C2211yescharacteristic
21#63509—21no—
22Q8×Dic9—21no—
23C2×#3672C2211yescharacteristic
24#63492—21no—
25C2×(C2×D9)⋊C4—21no—
26C2×#3664C2211yescharacteristic
27C2×#3663C2211yescharacteristic
28C2×C8×D9C2211yescharacteristic, complemented
29C2×Dic36C2211yescharacteristic, complemented
30#63460—21no—
31#63460—21no—
32#63459C2211yescharacteristic
33#63459C2211yescharacteristic
34#63459C2211yescharacteristic, complemented
35#63457C2211yescharacteristic
36#63454C2211yescharacteristic
37#63454C2211yescharacteristic, complemented
38#63448—21no—
39#63444—21no—
40#63437C2211yescharacteristic
41C4×D36C2211yescharacteristic
42C4×Dic18C2211yescharacteristic, complemented
43C9×#106C2211yescharacteristic, complemented
44C9×#106C2211yescharacteristic, complemented
45C9×C4⋊C8C2211yescharacteristic, complemented
46C9×#102C2211yescharacteristic
47C9×#102C2211yescharacteristic
48#63392C2211yescharacteristic
49#63380C2211yescharacteristic
50(C2×D9)⋊C8C2211yescharacteristic
51(C2×D9)⋊C8C2211yescharacteristic, complemented
52#63376C2211yescharacteristic, complemented
53#63369C2211yescharacteristic
54#63369C2211yescharacteristic
55#63368C2211yescharacteristic, complemented
56#63368C2211yescharacteristic, complemented
57#63368C2211yescharacteristic, complemented
58#63366C2211yescharacteristic, complemented
59#63362C2211yescharacteristic, complemented
60#5732—31no—
61#5554—31no—
62C3×#476D311yescharacteristic
63#5089—31no—
64#5018—31no—
65#4868—31no—
66#4867—31no—
67#4866—31no—
68#4864—31no—
69#4845—31no—
70#4836—31no—
71#4783—31no—
72#4776—31no—
73#4772—31no—
74#4770—31no—
75C23×D9—21no—
76C2×Q8×C9—21no—
77C2×D4×C9C2311yescharacteristic
78C22×C4×C9—21no—
79C2×#611—21no—
80C2×#611—21no—
81C22×Dic9—21no—
82#3699—22no—
83#3699—41no—
84D4×D9—22no—
85D4×D9—41no—
86C2×D36—21no—
87C2×D36D411yescharacteristic
88C2×D36C2311yescharacteristic
89C2×C4×D9C2311yescharacteristic
90C2×C4×D9C2311yescharacteristic
91C2×Dic18C2311yescharacteristic
92C2×Dic18C2311yescharacteristic
93C2×C8×C9C2311yescharacteristic
94C2×C8×C9C2311yescharacteristic
95C9×C4⋊C4—21no—
96C9×C4⋊C4C2311yescharacteristic
97C9×C4⋊C4C2311yescharacteristic
98C9×C4⋊C4C2311yescharacteristic
99C9×C22⋊C4—21no—
100C42×C9C2311yescharacteristic
101#3672—22no—
102(C2×D9)⋊C4—21no—
103(C2×D9)⋊C4—21no—
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
111(C2×D9)⋊C4D411yescharacteristic
112C4⋊Dic9—21no—
113C4⋊Dic9—21no—
114C4⋊Dic9—21no—
115C4⋊Dic9D411yescharacteristic
116C4⋊Dic9C2311yescharacteristic
117Dic9⋊C4—21no—
118C4×Dic9—21no—
119C4×Dic9—21no—
120C4×Dic9—21no—
121C2×C9⋊C8C2311yescharacteristic
122C2×C9⋊C8C2311yescharacteristic
123#3664—41no—
124#3663—41no—
125C8×D9—41no—
126Dic36—41no—
127#3311—91noSylow
128C2×#237—31no—
129C2×D3×D4—31no—
130C3×C4⋊Q8C2×D311yescharacteristic
131C3×C4×D4C2×D311yescharacteristic
132#947—61no—
133Q8×Dic3—61no—
134C2×#214—31no—
135#930—61no—
136C2×(C2×D3)⋊C4—61no—
137C2×Dic12—31no—
138C2×#204—31no—
139C2×ΓL(1,𝔽25)—31no—
140C2×D3×C8—31no—
141#898—61no—
142#898—61no—
143#897—31no—
144#897—31no—
145#897—31no—
146#895—31no—
147#892—31no—
148#892—31no—
149#886—61no—
150#882—61no—
151#875—31no—
152C4×D12—31no—
153C4×Dic6—31no—
154C3×#106C2×D311yescharacteristic
155C3×#106C2×D311yescharacteristic
156C3×C4⋊C8C2×D311yescharacteristic
157C3×#102C2×D311yescharacteristic
158C3×#102C2×D311yescharacteristic
159#832—31no—
160#821—31no—
161(C2×D3)⋊C8—31no—
162(C2×D3)⋊C8—31no—
163#816—31no—
164#810—31no—
165#810—31no—
166#810—31no—
167#809—31no—
168#809—31no—
169#807—31no—
170#803—31no—
171C23×C9—21no—
172C22×D9—21no—
173C22×D9—42no—
174C22×D9—42no—
175C22×D9—81no—
176C22×D9C2×D411yescharacteristic
177C22×D9C2×D411yescharacteristic
178Q8×C9—42no—
179D4×C9—21no—
180D4×C9#4112yes—
181C2×C4×C9—21no—
182C2×C4×C9—21no—
183C2×C4×C9—21no—
184C2×C4×C9—81no—
185C2×C4×C9C2×D411yescharacteristic
186C2×C4×C9C2×D411yescharacteristic
187C2×C4×C9C2411yescharacteristic
188#611—42no—
189#611—42no—
190C2×Dic9—21no—
191C2×Dic9—21no—
192C2×Dic9—21no—
193C2×Dic9—42no—
194C2×Dic9C2×D411yescharacteristic
195C2×Dic9C2×D411yescharacteristic
196D36—21no—
197D36—21no—
198D36—41no—
199D36—81no—
200C4×D9—21no—
201C4×D9—21no—
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#556—91no—
213#546—91no—
214#489—91no—
215#485—91no—
216#482—91no—
217#476D911yescharacteristic, complemented
218#470—91no—
219#465—91no—
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×Q8—21no—
229C2×C3×D4C22×D311yescharacteristic
230C22×C3×C4—21no—
231C2×#67—61no—
232C2×#67—61no—
233C22×Dic3—61no—
234#237—62no—
235#237—121no—
236D3×D4—62no—
237D3×D4—121no—
238C2×D12—31no—
239C2×D12—31no—
240C2×D12—61no—
241C2×C4×D3—31no—
242C2×C4×D3—31no—
243C2×Dic6—31no—
244C2×Dic6—31no—
245C2×C3×C8C22×D311yescharacteristic
246C2×C3×C8C22×D311yescharacteristic
247C3×C4⋊C4—21no—
248C3×C4⋊C4C22×D311yescharacteristic
249C3×C4⋊C4C22×D311yescharacteristic
250C3×C4⋊C4C22×D311yescharacteristic
251C3×C22⋊C4—21no—
252C3×C42C22×D311yescharacteristic
253#214—62no—
254(C2×D3)⋊C4—31no—
255(C2×D3)⋊C4—31no—
256(C2×D3)⋊C4—61no—
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—
263(C2×D3)⋊C4—61no—
264C4⋊Dic3—31no—
265C4⋊Dic3—31no—
266C4⋊Dic3—61no—
267C4⋊Dic3—61no—
268C4⋊Dic3—61no—
269Dic3⋊C4—61no—
270C4×Dic3—61no—
271C4×Dic3—61no—
272C4×Dic3—61no—
273C2×C3⋊C8—31no—
274C2×C3⋊C8—31no—
275Dic12—121no—
276#204—121no—
277ΓL(1,𝔽25)—121no—
278D3×C8—121no—
279C22×C9—22no—
280C22×C9—41no—
281C22×C9—41no—
282C22×C9C22×D411yescharacteristic
283C2×D9—21no—
284C2×D9—21no—
285C2×D9—21no—
286C2×D9—21no—
287C2×D9—21no—
288C2×D9—21no—
289C2×D9—41no—
290C2×D9—41no—
291C2×D9—41no—
292C2×D9—84no—
293C4×C9—21no—
294C4×C9—21no—
295C4×C9—41no—
296C4×C9—41no—
297C4×C9—41no—
298C4×C9C2×#4111yescharacteristic
299C4×C9H(5,𝔽2)11yescharacteristic
300Dic9—21no—
301Dic9—21no—
302Dic9—41no—
303Dic9—41no—
304Dic9—41no—
305C2×#41—91no—
306C22×D4—91no—
307C2×Q16—91no—
308C2×SD16—91no—
309C2×SD16—91no—
310C2×M16—91no—
311C22×C8—91no—
312C4⋊Q8C2×D911yescharacteristic, complemented
313#126—181no—
314#126—181no—
315#124—91no—
316#124—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×Q8—181no—
326C4×D4—91no—
327C4×D4C2×D911yescharacteristic
328#117—91no—
329#117—91no—
330C2×C22⋊C4—181no—
331#107—91no—
332#106C2×D911yescharacteristic, complemented
333#106C2×D911yescharacteristic, complemented
334C4⋊C8C2×D911yescharacteristic, complemented
335#103—91no—
336#103—91no—
337#103—91no—
338#103—91no—
339#102—91no—
340#102—91no—
341#102—91no—
342#102—91no—
343#102C2×D911yescharacteristic
344#102C2×D911yescharacteristic
345C22⋊C8—91no—
346C22⋊C8—91no—
347#97—91no—
348C23×C3—21no—
349C22×D3—31no—
350C22×D3—31no—
351C22×D3—61no—
352C22×D3—122no—
353C22×D3—122no—
354C22×D3—241no—
355C3×Q8—42no—
356C3×D4—21no—
357C3×D4#23912yes—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—81no—
362C2×C3×C4D3×D411yescharacteristic
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4C23×D311yescharacteristic
365#67—122no—
366#67—122no—
367C2×Dic3—31no—
368C2×Dic3—31no—
369C2×Dic3—61no—
370C2×Dic3—61no—
371C2×Dic3—61no—
372C2×Dic3—122no—
373D12—61no—
374D12—61no—
375D12—121no—
376D12—241no—
377C4×D3—61no—
378C4×D3—61no—
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—42no—
390C2×C9#54611yescharacteristic
391C2×C9#57511yescharacteristic
392C2×C9#57711yescharacteristic
393D9—41no—
394D9—41no—
395D9—81no—
396C24—181no—
397#41—182no—
398#41—361no—
399C2×Q8—21no—
400C2×Q8—91no—
401C2×Q8—91no—
402C2×D4—91no—
403C2×D4—91no—
404C2×D4—181no—
405C2×D4—181no—
406C2×D4—182no—
407C2×D4—181no—
408C2×D4—361no—
409C2×D4C22×D911yescharacteristic
410C22×C4—21no—
411C22×C4—91no—
412C22×C4—91no—
413C22×C4—181no—
414Q16—361no—
415SD16—182no—
416SD16—361no—
417M16—361no—
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—181no—
427C4⋊C4—181no—
428C4⋊C4—181no—
429C4⋊C4—181no—
430C4⋊C4C22×D911yescharacteristic
431C4⋊C4C22×D911yescharacteristic
432C4⋊C4C22×D911yescharacteristic
433C22⋊C4—21no—
434C22⋊C4—91no—
435C22⋊C4—91no—
436C22⋊C4—181no—
437C22⋊C4—181no—
438C22⋊C4—181no—
439C22⋊C4—181no—
440C22⋊C4—181no—
441C22⋊C4—181no—
442C22⋊C4—181no—
443C22⋊C4—181no—
444C42—181no—
445C42—181no—
446C42—181no—
447C42C22×D911yescharacteristic
448C22×C3—22no—
449C22×C3—41no—
450C22×C3—41no—
451C22×C3C2×D3×D411yescharacteristic
452C2×D3—61no—
453C2×D3—61no—
454C2×D3—61no—
455C2×D3—61no—
456C2×D3—61no—
457C2×D3—61no—
458C2×D3—121no—
459C2×D3—121no—
460C2×D3—121no—
461C2×D3—244no—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—41no—
465C3×C4—41no—
466C3×C4—41no—
467C3×C4C2×#23911yescharacteristic
468C3×C4#100911yescharacteristic
469Dic3—61no—
470Dic3—61no—
471Dic3—121no—
472Dic3—121no—
473Dic3—121no—
474C9#331111yescharacteristic, complemented, Sylow
475C23—21no—
476C23—91no—
477C23—91no—
478C23—181no—
479C23—362no—
480C23—362no—
481C23—721no—
482Q8—42no—
483Q8—181no—
484Q8—181no—
485Q8—181no—
486Q8—181no—
487D4—21no—
488D4—181no—
489D4—181no—
490D4—361no—
491D4—362no—
492D4—362no—
493D4—721no—
494D4#370112yes—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—81no—
499C2×C4—91no—
500C2×C4—91no—
501C2×C4—181no—
502C2×C4—181no—
503C2×C4—181no—
504C2×C4—181no—
505C2×C4—181no—
506C2×C4—181no—
507C2×C4—181no—
508C2×C4—362no—
509C2×C4D4×D911yescharacteristic
510C2×C4D4×D911yescharacteristic
511C2×C4C23×D911yescharacteristic
512C8—21no—
513C8—21no—
514C8—181no—
515C8—181no—
516C2×C3—42no—
517C2×C3#563011yescharacteristic
518C2×C3#576211yescharacteristic
519C2×C3#577311yescharacteristic
520D3—121no—
521D3—121no—
522D3—241no—
523C22—22no—
524C22—41no—
525C22—41no—
526C22—181no—
527C22—181no—
528C22—181no—
529C22—181no—
530C22—181no—
531C22—181no—
532C22—361no—
533C22—361no—
534C22—361no—
535C22—724no—
536C22C2×D4×D911yescharacteristic
537C4—21no—
538C4—21no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—181no—
543C4—181no—
544C4—361no—
545C4—361no—
546C4—361no—
547C4C2×#370111yescharacteristic
548C4#6371511yescharacteristic
549C3#8107811yescharacteristic
550C2—42no—
551C2—361no—
552C2—361no—
553C2—721no—
554C2#1058973211yescharacteristic
555C2#1058986411yescharacteristic
556C2#1058987511yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#476C2
socleC22×C3C2×D3×D4
prime radical#10589656C2
hypercenter#476D9
hypocenterC9#3311
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #10589834C2semidirect
3. C9×#476C2semidirect
4. #10588774C2semidirect
5. #10588694C2semidirect
6. #10588548C2semidirect
7. #10588547C2semidirect
8. #10588546C2semidirect
9. #10588544C2semidirect
10. #10588529C2semidirect
11. #10588520C2semidirect
12. #10588463C2semidirect
13. #10588456C2semidirect
14. #10588452C2semidirect
15. #10588450C2semidirect
19. C9×C4⋊Q8C22semidirect
28. C2×C8×D9C22semidirect
29. C2×Dic36C22semidirect
34. #63459C22semidirect
37. #63454C22semidirect
42. C4×Dic18C22semidirect
43. C9×#106C22semidirect
44. C9×#106C22semidirect
45. C9×C4⋊C8C22semidirect
51. (C2×D9)⋊C8C22semidirect
52. #63376C22semidirect
55. #63368C22semidirect
56. #63368C22semidirect
57. #63368C22semidirect
58. #63366C22semidirect
59. #63362C22semidirect
217. #476D9semidirect
312. C4⋊Q8C2×D9semidirect
332. #106C2×D9semidirect
333. #106C2×D9semidirect
334. C4⋊C8C2×D9semidirect
474. C9#3311semidirect

Maximal subgroups

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

subgroupindex
#105898342
#105896562
C9×#4762
#105887742
#105886942
#105885482
#105885472
#105885462
#105885442
#105885292
#105885202
#105884632
#105884562
#105884522
#105884502
#810783