Finite Group Databasebeta

← #11870863

Subgroups — #11870863

Order 1152.

681 conjugacy classes of subgroups.

The subgroup lattice has 555 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589793C211yesmaximal, characteristic, complemented
2C4×D4×D9C211yesmaximal, characteristic, complemented
3C9×#478C211yesmaximal, characteristic, complemented
4#10588747C211yesmaximal, characteristic, complemented
5#10588699C211yesmaximal, characteristic, complemented
6#10588564C211yesmaximal, characteristic, complemented
7#10588552C211yesmaximal, characteristic, complemented
8#10588543C211yesmaximal, characteristic, complemented
9#10588532C211yesmaximal, characteristic, complemented
10#10588528C211yesmaximal, characteristic, complemented
11#10588517C211yesmaximal, characteristic, complemented
12#10588456C211yesmaximal, characteristic, complemented
13#10588453C211yesmaximal, characteristic
14#10588438C211yesmaximal, characteristic, complemented
15#10588436C211yesmaximal, characteristic, complemented
16#81141—31nomaximal
17C2×D4×D9C2211yescharacteristic
18C22×C4×D9—21no—
19C9×#125C2211yescharacteristic, complemented
20C4×D4×C9C2211yescharacteristic
21D4×Dic9C2211yescharacteristic
22C2×#3673C2211yescharacteristic
23C2×#3672C2211yescharacteristic
24C4×#611—21no—
25C2×D72C2211yescharacteristic
26C2×#3664C2211yescharacteristic
27#63460—21no—
28#63459C2211yescharacteristic
29#63457C2211yescharacteristic
30#63456—21no—
31#63455—21no—
32#63455C2211yescharacteristic
33#63455C2211yescharacteristic, complemented
34#63454—21no—
35C4⋊C4×D9C2211yescharacteristic
36#63449C2211yescharacteristic, complemented
37#611⋊C4—21no—
38C22⋊C4×D9—21no—
39#63437C2211yescharacteristic, complemented
40C4×D36C2211yescharacteristic
41C42×D9C2211yescharacteristic
42C9×#107C2211yescharacteristic, complemented
43C9×#106C2211yescharacteristic, complemented
44C9×C4⋊C8C2211yescharacteristic, complemented
45C9×#102C2211yescharacteristic
46C9×#102C2211yescharacteristic
47#63380C2211yescharacteristic, complemented
48(C2×D9)⋊C8C2211yescharacteristic
49(C2×D9)⋊C8C2211yescharacteristic
50#63376C2211yescharacteristic, complemented
51C8×Dic9C2211yescharacteristic, complemented
52C8×Dic9C2211yescharacteristic, complemented
53#63369C2211yescharacteristic
54#63369C2211yescharacteristic
55#63369C2211yescharacteristic, complemented
56#63368C2211yescharacteristic, complemented
57#63367C2211yescharacteristic, complemented
58#63366C2211yescharacteristic, complemented
59C4⋊(C9⋊C8)C2211yescharacteristic, complemented
60#5691—31no—
61C4×D3×D4—31no—
62C3×#478D311yescharacteristic
63#5066—31no—
64#5016—31no—
65#4884—31no—
66#4872—31no—
67#4863—31no—
68#4852—31no—
69#4844—31no—
70#4833—31no—
71#4776—31no—
72#4773—31no—
73#4758—31no—
74#4756—31no—
75C23×D9—21no—
76C2×D4×C9C2311yescharacteristic
77C22×C4×C9—21no—
78C2×#611—21no—
79C22×Dic9—21no—
80D4×D9—22no—
81D4×D9—22no—
82C2×D36—21no—
83C2×D36C2311yescharacteristic
84C2×D36C2311yescharacteristic
85C2×C4×D9—21no—
86C2×C4×D9—21no—
87C2×C4×D9—21no—
88C2×C4×D9—21no—
89C2×C4×D9—44no—
90C2×C4×D9D411yescharacteristic
91C2×C4×D9D411yescharacteristic
92C2×C4×D9C2311yescharacteristic
93C2×Dic18C2311yescharacteristic
94C2×C8×C9C2311yescharacteristic
95C2×C8×C9C2311yescharacteristic
96C9×C4⋊C4—21no—
97C9×C4⋊C4—21no—
98C9×C4⋊C4C2311yescharacteristic
99C9×C4⋊C4C2311yescharacteristic
100C9×C4⋊C4C2311yescharacteristic
101C9×C22⋊C4—21no—
102C42×C9C2311yescharacteristic
103#3676—21no—
104#3673—22no—
105#3672—22no—
106(C2×D9)⋊C4—21no—
107(C2×D9)⋊C4—21no—
108(C2×D9)⋊C4—21no—
109(C2×D9)⋊C4—21no—
110(C2×D9)⋊C4—21no—
111(C2×D9)⋊C4—21no—
112(C2×D9)⋊C4—21no—
113C4⋊Dic9—21no—
114C4⋊Dic9C2311yescharacteristic
115Dic9⋊C4—21no—
116Dic9⋊C4—21no—
117C4×Dic9—21no—
118C4×Dic9D411yescharacteristic
119C4×Dic9D411yescharacteristic
120C4×Dic9C2311yescharacteristic
121C2×C9⋊C8C2311yescharacteristic
122C2×C9⋊C8C2311yescharacteristic
123D72—22no—
124#3664—22no—
125#3105—91noSylow
126C2×D3×D4—31no—
127C22×C4×D3—61no—
128C3×#125C2×D311yescharacteristic
129C3×C4×D4C2×D311yescharacteristic
130D4×Dic3—31no—
131C2×#214—31no—
132C2×#213—31no—
133C4×#67—61no—
134C2×D24—31no—
135C2×#204—31no—
136#898—61no—
137#897—31no—
138#895—31no—
139#894—61no—
140#893—31no—
141#893—31no—
142#893—61no—
143#892—61no—
144D3×C4⋊C4—31no—
145#887—31no—
146#67⋊C4—61no—
147D3×C22⋊C4—61no—
148#875—31no—
149C4×D12—31no—
150C42×D3—31no—
151C3×#107C2×D311yescharacteristic
152C3×#106C2×D311yescharacteristic
153C3×C4⋊C8C2×D311yescharacteristic
154C3×#102C2×D311yescharacteristic
155C3×#102C2×D311yescharacteristic
156#821—31no—
157(C2×D3)⋊C8—31no—
158(C2×D3)⋊C8—31no—
159#816—31no—
160C8×Dic3—31no—
161C8×Dic3—31no—
162#810—31no—
163#809—31no—
164#809—31no—
165#809—31no—
166#808—31no—
167#807—31no—
168C4⋊(C3⋊C8)—31no—
169C23×C9—21no—
170C22×D9—24no—
171C22×D9—21no—
172C22×D9—21no—
173C22×D9—42no—
174C22×D9—42no—
175C22×D9C2×D411yescharacteristic
176D4×C9—21no—
177D4×C9#4112yes—
178C2×C4×C9—21no—
179C2×C4×C9—21no—
180C2×C4×C9—21no—
181C2×C4×C9—42no—
182C2×C4×C9C2×D411yescharacteristic
183C2×C4×C9C2×D411yescharacteristic
184C2×C4×C9C2411yescharacteristic
185#611—24no—
186C2×Dic9—21no—
187C2×Dic9—21no—
188C2×Dic9—42no—
189C2×Dic9C2×D411yescharacteristic
190C2×Dic9C2×D411yescharacteristic
191C2×Dic9C2×D411yescharacteristic
192D36—21no—
193D36—21no—
194D36—21no—
195D36—42no—
196D36#4112yes—
197C4×D9—22no—
198C4×D9—21no—
199C4×D9—21no—
200C4×D9—22no—
201C4×D9—42no—
202C4×D9—42no—
203C4×D9—42no—
204C4×D9—42no—
205Dic18—21no—
206Dic18—21no—
207C8×C9—21no—
208C8×C9—21no—
209C9⋊C8—21no—
210C9⋊C8—21no—
211#529—91no—
212C2×C4×D4—91no—
213#484—91no—
214#481—91no—
215#478—91no—
216#478D911yescharacteristic, complemented
217#463—91no—
218#463—91no—
219#450—91no—
220#447—91no—
221C4×SD16—91no—
222C4×SD16—91no—
223C4×D8—91no—
224C4×D8—91no—
225#431—91no—
226C23×D3—61no—
227C2×C3×D4C22×D311yescharacteristic
228C22×C3×C4—21no—
229C2×#67—61no—
230C22×Dic3—61no—
231D3×D4—62no—
232D3×D4—62no—
233C2×D12—31no—
234C2×D12—31no—
235C2×D12—61no—
236C2×C4×D3—31no—
237C2×C4×D3—31no—
238C2×C4×D3—31no—
239C2×C4×D3—61no—
240C2×C4×D3—61no—
241C2×C4×D3—61no—
242C2×C4×D3—61no—
243C2×C4×D3—124no—
244C2×Dic6—31no—
245C2×C3×C8C22×D311yescharacteristic
246C2×C3×C8C22×D311yescharacteristic
247C3×C4⋊C4—21no—
248C3×C4⋊C4—21no—
249C3×C4⋊C4C22×D311yescharacteristic
250C3×C4⋊C4C22×D311yescharacteristic
251C3×C4⋊C4C22×D311yescharacteristic
252C3×C22⋊C4—21no—
253C3×C42C22×D311yescharacteristic
254#217—61no—
255#214—62no—
256#213—62no—
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—61no—
266Dic3⋊C4—61no—
267Dic3⋊C4—61no—
268C4×Dic3—31no—
269C4×Dic3—31no—
270C4×Dic3—31no—
271C4×Dic3—61no—
272C2×C3⋊C8—31no—
273C2×C3⋊C8—31no—
274D24—62no—
275#204—62no—
276C22×C9—22no—
277C22×C9—41no—
278C22×C9—41no—
279C22×C9C22×D411yescharacteristic
280C2×D9—21no—
281C2×D9—21no—
282C2×D9—22no—
283C2×D9—48no—
284C2×D9—41no—
285C2×D9—41no—
286C2×D9—41no—
287C2×D9—41no—
288C2×D9—41no—
289C2×D9#13512yes—
290C4×C9—21no—
291C4×C9—21no—
292C4×C9—41no—
293C4×C9—41no—
294C4×C9—41no—
295C4×C9C2×#4111yescharacteristic
296C4×C9C2×#4111yescharacteristic
297Dic9—21no—
298Dic9—21no—
299Dic9—41no—
300Dic9—41no—
301Dic9AGL(1,ℤ/8)12yes—
302C22×D4—91no—
303C23×C4—181no—
304C2×SD16—91no—
305C2×SD16—91no—
306C2×D8—91no—
307C2×D8—91no—
308#126—181no—
309#125C2×D911yescharacteristic, complemented
310#124—91no—
311#123—181no—
312C22⋊Q8—91no—
313#121—91no—
314C4×Q8—91no—
315C4×D4—91no—
316C4×D4—91no—
317C4×D4—91no—
318C4×D4—91no—
319C4×D4—181no—
320C4×D4—181no—
321C4×D4—181no—
322C4×D4C2×D911yescharacteristic
323#117—181no—
324C2×C4⋊C4—91no—
325C2×C22⋊C4—181no—
326C2×C42—91no—
327#107—91no—
328#107C2×D911yescharacteristic, complemented
329#106—91no—
330#106C2×D911yescharacteristic, complemented
331C4⋊C8—91no—
332C4⋊C8C2×D911yescharacteristic, complemented
333#103—91no—
334#103—91no—
335#102—91no—
336#102—91no—
337#102—91no—
338#102—91no—
339#102C2×D911yescharacteristic
340#102C2×D911yescharacteristic
341C22⋊C8—91no—
342C22⋊C8—91no—
343C4×C8—91no—
344C4×C8—91no—
345C23×C3—21no—
346C22×D3—31no—
347C22×D3—64no—
348C22×D3—61no—
349C22×D3—61no—
350C22×D3—122no—
351C22×D3—122no—
352C3×D4—21no—
353C3×D4#23912yes—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—42no—
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4C23×D311yescharacteristic
361#67—64no—
362C2×Dic3—31no—
363C2×Dic3—31no—
364C2×Dic3—31no—
365C2×Dic3—61no—
366C2×Dic3—61no—
367C2×Dic3—122no—
368D12—32no—
369D12—61no—
370D12—61no—
371D12—61no—
372D12—122no—
373C4×D3—62no—
374C4×D3—62no—
375C4×D3—61no—
376C4×D3—61no—
377C4×D3—122no—
378C4×D3—122no—
379C4×D3—122no—
380C4×D3—122no—
381Dic6—61no—
382Dic6—61no—
383C3×C8—21no—
384C3×C8—21no—
385C3⋊C8—61no—
386C3⋊C8—61no—
387C2×C9—42no—
388C2×C9#52511yescharacteristic
389C2×C9C2×#13511yescharacteristic
390C2×C9C2×AGL(1,ℤ/8)11yescharacteristic
391D9—22no—
392D9—42no—
393D9—81no—
394C24—181no—
395C2×Q8—91no—
396C2×D4—91no—
397C2×D4—91no—
398C2×D4—181no—
399C2×D4—181no—
400C2×D4—182no—
401C2×D4—182no—
402C2×D4C22×D911yescharacteristic
403C22×C4—21no—
404C22×C4—91no—
405C22×C4—91no—
406C22×C4—91no—
407C22×C4—181no—
408C22×C4—181no—
409C22×C4—181no—
410C22×C4—181no—
411C22×C4—181no—
412C22×C4—364no—
413SD16—182no—
414SD16—182no—
415D8—182no—
416D8—182no—
417C2×C8—91no—
418C2×C8—91no—
419C2×C8C22×D911yescharacteristic
420C2×C8C22×D911yescharacteristic
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—91no—
424C4⋊C4—181no—
425C4⋊C4—181no—
426C4⋊C4—181no—
427C4⋊C4C22×D911yescharacteristic
428C4⋊C4C22×D911yescharacteristic
429C4⋊C4C22×D911yescharacteristic
430C22⋊C4—21no—
431C22⋊C4—181no—
432C22⋊C4—181no—
433C22⋊C4—181no—
434C22⋊C4—181no—
435C22⋊C4—181no—
436C22⋊C4—181no—
437C22⋊C4—181no—
438C22⋊C4—181no—
439C42—91no—
440C42—91no—
441C42—91no—
442C42—181no—
443C42C22×D911yescharacteristic
444C22×C3—22no—
445C22×C3—41no—
446C22×C3—41no—
447C22×C3C2×D3×D411yescharacteristic
448C2×D3—32no—
449C2×D3—61no—
450C2×D3—61no—
451C2×D3—62no—
452C2×D3—128no—
453C2×D3—121no—
454C2×D3—121no—
455C2×D3—121no—
456C2×D3—121no—
457C2×D3—121no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—41no—
461C3×C4—41no—
462C3×C4—41no—
463C3×C4C2×#23911yescharacteristic
464C3×C4D3×#4111yescharacteristic
465Dic3—32no—
466Dic3—61no—
467Dic3—61no—
468Dic3—121no—
469Dic3—121no—
470C9#310511yescharacteristic, complemented, Sylow
471C23—21no—
472C23—91no—
473C23—184no—
474C23—181no—
475C23—181no—
476C23—362no—
477C23—362no—
478Q8—181no—
479Q8—181no—
480D4—21no—
481D4—92no—
482D4—184no—
483D4—181no—
484D4—181no—
485D4—181no—
486D4—362no—
487D4#370112yes—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—42no—
492C2×C4—91no—
493C2×C4—91no—
494C2×C4—91no—
495C2×C4—182no—
496C2×C4—182no—
497C2×C4—181no—
498C2×C4—181no—
499C2×C4—181no—
500C2×C4—181no—
501C2×C4—362no—
502C2×C4—362no—
503C2×C4—362no—
504C2×C4—362no—
505C2×C4—362no—
506C2×C4D4×D911yescharacteristic
507C2×C4D4×D911yescharacteristic
508C2×C4C23×D911yescharacteristic
509C8—21no—
510C8—21no—
511C8—181no—
512C8—181no—
513C2×C3—42no—
514C2×C3#562711yescharacteristic
515C2×C3D3×#13511yescharacteristic
516C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
517D3—62no—
518D3—122no—
519D3—241no—
520C22—22no—
521C22—41no—
522C22—41no—
523C22—92no—
524C22—181no—
525C22—181no—
526C22—182no—
527C22—368no—
528C22—361no—
529C22—361no—
530C22—361no—
531C22—361no—
532C22—361no—
533C22C2×D4×D911yescharacteristic
534C4—21no—
535C4—21no—
536C4—41no—
537C4—41no—
538C4—41no—
539C4—92no—
540C4—181no—
541C4—181no—
542C4—361no—
543C4—361no—
544C4C2×#370111yescharacteristic
545C4#41×D911yescharacteristic
546C3#8114111yescharacteristic
547C2—42no—
548C2—182no—
549C2—362no—
550C2—721no—
551C2#1058972911yescharacteristic
552C2D9×#13511yescharacteristic
553C2D9×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#478C2
socleC22×C3C2×D3×D4
prime radical#10588453C2
hypercenter#478D9
hypocenterC9#3105
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #10589793C2semidirect
2. C4×D4×D9C2semidirect
3. C9×#478C2semidirect
4. #10588747C2semidirect
5. #10588699C2semidirect
6. #10588564C2semidirect
7. #10588552C2semidirect
8. #10588543C2semidirect
9. #10588532C2semidirect
10. #10588528C2semidirect
11. #10588517C2semidirect
12. #10588456C2semidirect
14. #10588438C2semidirect
15. #10588436C2semidirect
19. C9×#125C22semidirect
33. #63455C22semidirect
36. #63449C22semidirect
39. #63437C22semidirect
42. C9×#107C22semidirect
43. C9×#106C22semidirect
44. C9×C4⋊C8C22semidirect
47. #63380C22semidirect
50. #63376C22semidirect
51. C8×Dic9C22semidirect
52. C8×Dic9C22semidirect
55. #63369C22semidirect
56. #63368C22semidirect
57. #63367C22semidirect
58. #63366C22semidirect
59. C4⋊(C9⋊C8)C22semidirect
216. #478D9semidirect
309. #125C2×D9semidirect
328. #107C2×D9semidirect
330. #106C2×D9semidirect
332. C4⋊C8C2×D9semidirect
470. C9#3105semidirect

Maximal subgroups

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

subgroupindex
#105897932
C4×D4×D92
C9×#4782
#105887472
#105886992
#105885642
#105885522
#105885432
#105885322
#105885282
#105885172
#105884562
#105884532
#105884382
#105884362
#811413