Finite Group Databasebeta

← #11887203

Subgroups — #11887203

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#10589652C211yesmaximal, characteristic
2#10589643C211yesmaximal, characteristic, complemented
3C8×D4×C9C211yesmaximal, characteristic, complemented
4#10588795C211yesmaximal, characteristic, complemented
5#10588794C211yesmaximal, characteristic, complemented
6C2×#63380C211yesmaximal, characteristic, complemented
7#10588788C211yesmaximal, characteristic, complemented
8#10588531C211yesmaximal, characteristic, complemented
9#10588529C211yesmaximal, characteristic, complemented
10#10588419C211yesmaximal, characteristic, complemented
11#10588415C211yesmaximal, characteristic, complemented
12#10588413C211yesmaximal, characteristic, complemented
13#10588401C211yesmaximal, characteristic, complemented
14#10588379C211yesmaximal, characteristic, complemented
15C4×#3664C211yesmaximal, characteristic, complemented
16#79440—31nomaximal
17C2×#3697C2211yescharacteristic
18C22×D36C2211yescharacteristic
19C22×C8×C9C2211yescharacteristic
20C22×C8×C9C2211yescharacteristic, complemented
21C4×D4×C9C2211yescharacteristic
22#63499—21no—
23#63497—21no—
24#63492C2211yescharacteristic
25#63488C2211yescharacteristic, complemented
26C2×C4⋊Dic9C2211yescharacteristic
27#63486C2211yescharacteristic
28#63486C2211yescharacteristic
29#63486C2211yescharacteristic, complemented
30C2×#3664C2211yescharacteristic
31C2×#3664C2211yescharacteristic
32C2×Dic36C2211yescharacteristic, complemented
33#63456—21no—
34#63451—21no—
35#63446—21no—
36C22⋊C4×D9—21no—
37#63441—21no—
38#63439—21no—
39#63437C2211yescharacteristic
40C4×D36C2211yescharacteristic
41#63432C2211yescharacteristic, complemented
42C4×Dic18C2211yescharacteristic, complemented
43C9×C4⋊C8C2211yescharacteristic, complemented
44C9×C22⋊C8C2211yescharacteristic
45C9×C22⋊C8C2211yescharacteristic, complemented
46C4×C8×C9C2211yescharacteristic, complemented
47#63380C2211yescharacteristic
48#63380C2211yescharacteristic
49#63380C2211yescharacteristic
50#63380C2211yescharacteristic
51#63380C2211yescharacteristic
52#63380C2211yescharacteristic
53#63378C2211yescharacteristic, complemented
54#63377C2211yescharacteristic, complemented
55#63377C2211yescharacteristic, complemented
56#63376C2211yescharacteristic, complemented
57#63376C2211yescharacteristic, complemented
58#63376C2211yescharacteristic, complemented
59#63376C2211yescharacteristic, complemented
60#5550—31no—
61#5541—31no—
62C3×C8×D4D311yescharacteristic
63#5116—31no—
64#5114—31no—
65#5113—31no—
66C2×#821—31no—
67#4847—31no—
68#4845—31no—
69#4737—31no—
70#4733—31no—
71#4731—31no—
72#4721—31no—
73#4697—31no—
74C4×#204—31no—
75C23×D9—21no—
76C2×D4×C9D411yescharacteristic
77C22×C4×C9C2311yescharacteristic
78C22×C4×C9C2311yescharacteristic
79C2×#611—21no—
80C2×#611—21no—
81C22×Dic9—21no—
82#3697—22no—
83#3697—41no—
84C2×D36—22no—
85C2×D36—21no—
86C2×D36—41no—
87C2×D36C2311yescharacteristic
88C2×D36C2311yescharacteristic
89C2×C4×D9—21no—
90C2×C4×D9—21no—
91C2×Dic18C2311yescharacteristic
92C2×Dic18C2311yescharacteristic
93C2×C8×C9—41no—
94C2×C8×C9—41no—
95C2×C8×C9C2311yescharacteristic
96C2×C8×C9C2311yescharacteristic
97C2×C8×C9C2311yescharacteristic
98C2×C8×C9C2311yescharacteristic
99C9×C4⋊C4D411yescharacteristic
100C9×C22⋊C4D411yescharacteristic
101C9×C22⋊C4D411yescharacteristic
102C42×C9C2311yescharacteristic
103#3676—21no—
104#3676—21no—
105#3676—21no—
106#3676—21no—
107(C2×D9)⋊C4—21no—
108(C2×D9)⋊C4—21no—
109(C2×D9)⋊C4—21no—
110(C2×D9)⋊C4—21no—
111C4⋊Dic9—21no—
112C4⋊Dic9C2311yescharacteristic
113C4⋊Dic9C2311yescharacteristic
114C4⋊Dic9C2311yescharacteristic
115C4⋊Dic9C2311yescharacteristic
116Dic9⋊C4—21no—
117Dic9⋊C4—21no—
118Dic9⋊C4—21no—
119Dic9⋊C4—21no—
120Dic9⋊C4—21no—
121Dic9⋊C4—21no—
122C4×Dic9—21no—
123C4×Dic9—21no—
124#3664—22no—
125#3664—41no—
126Dic36—41no—
127#3296—91noSylow
128C2×#235—31no—
129C22×D12—31no—
130C22×C3×C8C2×D311yescharacteristic
131C22×C3×C8C2×D311yescharacteristic
132C3×C4×D4C2×D311yescharacteristic
133#937—61no—
134#935—61no—
135#930—31no—
136#926—31no—
137C2×C4⋊Dic3—31no—
138#924—31no—
139#924—31no—
140#924—31no—
141C2×Dic12—31no—
142C2×#204—31no—
143C2×#204—31no—
144#894—61no—
145#889—61no—
146#884—61no—
147D3×C22⋊C4—61no—
148#879—61no—
149#877—61no—
150#875—31no—
151C4×D12—31no—
152#870—31no—
153C4×Dic6—31no—
154C3×C4⋊C8C2×D311yescharacteristic
155C3×C22⋊C8C2×D311yescharacteristic
156C3×C22⋊C8C2×D311yescharacteristic
157C3×C4×C8C2×D311yescharacteristic
158#821—31no—
159#821—31no—
160#821—31no—
161#821—31no—
162#821—31no—
163#821—31no—
164#818—31no—
165#817—31no—
166#817—31no—
167#816—31no—
168#816—31no—
169#816—31no—
170#816—31no—
171C23×C9C2×D411yescharacteristic
172C23×C9C2×D411yescharacteristic
173C22×D9—21no—
174C22×D9—21no—
175C22×D9—42no—
176C22×D9—42no—
177C22×D9—81no—
178D4×C9—22no—
179C2×C4×C9—21no—
180C2×C4×C9—21no—
181C2×C4×C9—21no—
182C2×C4×C9—21no—
183C2×C4×C9C2×D411yescharacteristic
184C2×C4×C9C2×D411yescharacteristic
185C2×C4×C9C2×D411yescharacteristic
186C2×C4×C9C2×D411yescharacteristic
187C2×C4×C9C2411yescharacteristic
188#611—42no—
189#611—81no—
190C2×Dic9—21no—
191C2×Dic9—21no—
192C2×Dic9—21no—
193C2×Dic9—21no—
194C2×Dic9—21no—
195C2×Dic9—21no—
196C2×Dic9—42no—
197D36—21no—
198D36—21no—
199D36—21no—
200D36—42no—
201D36#4112yes—
202C4×D9—42no—
203C4×D9—81no—
204Dic18—21no—
205Dic18—21no—
206Dic18—21no—
207Dic18—21no—
208C8×C9—21no—
209C8×C9—21no—
210C8×C9—21no—
211C8×C9—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×D4D911yescharacteristic, complemented
225#416—91no—
226C2×#102—91no—
227C23×D3—61no—
228C2×C3×D4D1211yescharacteristic
229C22×C3×C4C22×D311yescharacteristic
230C22×C3×C4C22×D311yescharacteristic
231C2×#67—61no—
232C2×#67—61no—
233C22×Dic3—61no—
234#235—62no—
235#235—121no—
236C2×D12—31no—
237C2×D12—31no—
238C2×D12—62no—
239C2×D12—61no—
240C2×D12—121no—
241C2×C4×D3—61no—
242C2×C4×D3—61no—
243C2×Dic6—31no—
244C2×Dic6—31no—
245C2×C3×C8—41no—
246C2×C3×C8—41no—
247C2×C3×C8C22×D311yescharacteristic
248C2×C3×C8C22×D311yescharacteristic
249C2×C3×C8C22×D311yescharacteristic
250C2×C3×C8C22×D311yescharacteristic
251C3×C4⋊C4D1211yescharacteristic
252C3×C22⋊C4D1211yescharacteristic
253C3×C22⋊C4D1211yescharacteristic
254C3×C42C22×D311yescharacteristic
255#217—61no—
256#217—61no—
257#217—61no—
258#217—61no—
259(C2×D3)⋊C4—61no—
260(C2×D3)⋊C4—61no—
261(C2×D3)⋊C4—61no—
262(C2×D3)⋊C4—61no—
263C4⋊Dic3—31no—
264C4⋊Dic3—31no—
265C4⋊Dic3—31no—
266C4⋊Dic3—31no—
267C4⋊Dic3—61no—
268Dic3⋊C4—61no—
269Dic3⋊C4—61no—
270Dic3⋊C4—61no—
271Dic3⋊C4—61no—
272Dic3⋊C4—61no—
273Dic3⋊C4—61no—
274C4×Dic3—61no—
275C4×Dic3—61no—
276Dic12—121no—
277#204—62no—
278#204—121no—
279C22×C9—21no—
280C22×C9—21no—
281C22×C9—21no—
282C22×C9—21no—
283C22×C9—21no—
284C22×C9#13512yes—
285C22×C9C22×D411yescharacteristic
286C2×D9—22no—
287C2×D9—41no—
288C2×D9—41no—
289C2×D9—41no—
290C2×D9—41no—
291C2×D9—41no—
292C2×D9—84no—
293C4×C9—21no—
294C4×C9—21no—
295C4×C9—21no—
296C4×C9—21no—
297C4×C9C2×#4111yescharacteristic
298C4×C9H(5,𝔽2)11yescharacteristic
299Dic9—41no—
300Dic9—41no—
301Dic9—41no—
302Dic9—41no—
303Dic9—41no—
304Dic9—41no—
305C2×#41—91no—
306C22×D4—91no—
307C2×Q16—91no—
308C2×SD16—91no—
309C2×SD16—91no—
310C22×C8C2×D911yescharacteristic
311C22×C8C2×D911yescharacteristic, complemented
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×D4C2×D911yescharacteristic
327#117—91no—
328#117—181no—
329C2×C4⋊C4—91no—
330C2×C22⋊C4—181no—
331#107—91no—
332#106—91no—
333#106—91no—
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#102—91no—
344#102—91no—
345C22⋊C8C2×D911yescharacteristic
346C22⋊C8C2×D911yescharacteristic, complemented
347C4×C8C2×D911yescharacteristic, complemented
348C23×C3C2×D1211yescharacteristic
349C23×C3C2×D1211yescharacteristic
350C22×D3—61no—
351C22×D3—61no—
352C22×D3—122no—
353C22×D3—122no—
354C22×D3—241no—
355C3×D4—22no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4C2×D1211yescharacteristic
361C2×C3×C4C2×D1211yescharacteristic
362C2×C3×C4C2×D1211yescharacteristic
363C2×C3×C4C2×D1211yescharacteristic
364C2×C3×C4C23×D311yescharacteristic
365#67—122no—
366#67—241no—
367C2×Dic3—61no—
368C2×Dic3—61no—
369C2×Dic3—61no—
370C2×Dic3—61no—
371C2×Dic3—61no—
372C2×Dic3—61no—
373C2×Dic3—122no—
374D12—32no—
375D12—61no—
376D12—61no—
377D12—61no—
378D12—122no—
379C4×D3—122no—
380C4×D3—241no—
381Dic6—61no—
382Dic6—61no—
383Dic6—61no—
384Dic6—61no—
385C3×C8—21no—
386C3×C8—21no—
387C3×C8—21no—
388C3×C8—21no—
389C2×C9—22no—
390C2×C9—41no—
391C2×C9#54611yescharacteristic
392C2×C9C2×#13511yescharacteristic
393C2×C9#57711yescharacteristic
394D9—42no—
395D9—81no—
396C24—181no—
397#41—182no—
398#41—361no—
399C2×Q8—91no—
400C2×Q8—91no—
401C2×D4—91no—
402C2×D4—91no—
403C2×D4—182no—
404C2×D4—181no—
405C2×D4—181no—
406C2×D4—181no—
407C2×D4—361no—
408C2×D4D3611yescharacteristic
409C22×C4—181no—
410C22×C4—181no—
411C22×C4—181no—
412C22×C4C22×D911yescharacteristic
413C22×C4C22×D911yescharacteristic
414Q16—361no—
415SD16—182no—
416SD16—361no—
417C2×C8—41no—
418C2×C8—41no—
419C2×C8C22×D911yescharacteristic
420C2×C8C22×D911yescharacteristic
421C2×C8C22×D911yescharacteristic
422C2×C8C22×D911yescharacteristic
423C4⋊C4—91no—
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⋊C4—181no—
434C4⋊C4D3611yescharacteristic
435C22⋊C4—181no—
436C22⋊C4—181no—
437C22⋊C4—181no—
438C22⋊C4—181no—
439C22⋊C4—181no—
440C22⋊C4—181no—
441C22⋊C4—181no—
442C22⋊C4—181no—
443C22⋊C4D3611yescharacteristic
444C22⋊C4D3611yescharacteristic
445C42—181no—
446C42—181no—
447C42C22×D911yescharacteristic
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—21no—
453C22×C3#90412yes—
454C22×C3C22×D1211yescharacteristic
455C2×D3—62no—
456C2×D3—121no—
457C2×D3—121no—
458C2×D3—121no—
459C2×D3—121no—
460C2×D3—121no—
461C2×D3—244no—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4#100411yescharacteristic
467C3×C4D3×#4111yescharacteristic
468Dic3—121no—
469Dic3—121no—
470Dic3—121no—
471Dic3—121no—
472Dic3—121no—
473Dic3—121no—
474C9#329611yescharacteristic, complemented, Sylow
475C23—181no—
476C23—181no—
477C23—362no—
478C23—362no—
479C23—721no—
480C23C2×D3611yescharacteristic
481C23C2×D3611yescharacteristic
482Q8—181no—
483Q8—181no—
484Q8—181no—
485Q8—181no—
486D4—22no—
487D4—92no—
488D4—181no—
489D4—181no—
490D4—181no—
491D4—362no—
492D4—362no—
493D4—721no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—181no—
499C2×C4—181no—
500C2×C4—181no—
501C2×C4—181no—
502C2×C4—181no—
503C2×C4—181no—
504C2×C4—362no—
505C2×C4—362no—
506C2×C4—721no—
507C2×C4C2×D3611yescharacteristic
508C2×C4C2×D3611yescharacteristic
509C2×C4C2×D3611yescharacteristic
510C2×C4C2×D3611yescharacteristic
511C2×C4C23×D911yescharacteristic
512C8—21no—
513C8—21no—
514C8—21no—
515C8—21no—
516C2×C3—22no—
517C2×C3—41no—
518C2×C3#555411yescharacteristic
519C2×C3C2×#90411yescharacteristic
520C2×C3#575111yescharacteristic
521D3—122no—
522D3—241no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22—21no—
528C22—182no—
529C22—361no—
530C22—361no—
531C22—361no—
532C22—361no—
533C22—361no—
534C22—724no—
535C22#6346712yes—
536C22C22×D3611yescharacteristic
537C4—21no—
538C4—21no—
539C4—21no—
540C4—21no—
541C4—361no—
542C4—361no—
543C4—361no—
544C4—361no—
545C4—361no—
546C4—361no—
547C4#6371011yescharacteristic
548C4#41×D911yescharacteristic
549C3#7944011yescharacteristic
550C2—22no—
551C2—41no—
552C2—362no—
553C2—721no—
554C2#1058965611yescharacteristic
555C2C2×#6346711yescharacteristic
556C2#1058985311yescharacteristic
subgroupG/H
centerC22C22×D36
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC8×D4×C9C2
socleC22×C3C22×D12
prime radical#10589652C2
hypercenterC8×D4D9
hypocenterC9#3296
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
2. #10589643C2semidirect
3. C8×D4×C9C2semidirect
4. #10588795C2semidirect
5. #10588794C2semidirect
6. C2×#63380C2semidirect
7. #10588788C2semidirect
8. #10588531C2semidirect
9. #10588529C2semidirect
10. #10588419C2semidirect
11. #10588415C2semidirect
12. #10588413C2semidirect
13. #10588401C2semidirect
14. #10588379C2semidirect
15. C4×#3664C2semidirect
20. C22×C8×C9C22semidirect
25. #63488C22semidirect
29. #63486C22semidirect
32. C2×Dic36C22semidirect
41. #63432C22semidirect
42. C4×Dic18C22semidirect
43. C9×C4⋊C8C22semidirect
45. C9×C22⋊C8C22semidirect
46. C4×C8×C9C22semidirect
53. #63378C22semidirect
54. #63377C22semidirect
55. #63377C22semidirect
56. #63376C22semidirect
57. #63376C22semidirect
58. #63376C22semidirect
59. #63376C22semidirect
224. C8×D4D9semidirect
311. C22×C8C2×D9semidirect
334. C4⋊C8C2×D9semidirect
346. C22⋊C8C2×D9semidirect
347. C4×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
#105896522
#105896432
C8×D4×C92
#105887952
#105887942
C2×#633802
#105887882
#105885312
#105885292
#105884192
#105884152
#105884132
#105884012
#105883792
C4×#36642
#794403