Finite Group Databasebeta

← #11871319

Subgroups — #11871319

Order 1152.

666 conjugacy classes of subgroups.

The subgroup lattice has 543 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589680C211yesmaximal, characteristic, complemented
2C4×D4×D9C211yesmaximal, characteristic
3C9×#440C211yesmaximal, characteristic, complemented
4#10588849C211yesmaximal, characteristic
5#10588842C211yesmaximal, characteristic, complemented
6#10588709C211yesmaximal, characteristic, complemented
7#10588694C211yesmaximal, characteristic, complemented
8#10588570C211yesmaximal, characteristic, complemented
9#10588564C211yesmaximal, characteristic, complemented
10#10588498C211yesmaximal, characteristic, complemented
11#10588491C211yesmaximal, characteristic, complemented
12#10588456C211yesmaximal, characteristic
13#10588439C211yesmaximal, characteristic, complemented
14#10588391C211yesmaximal, characteristic, complemented
15#10588386C211yesmaximal, characteristic, complemented
16#79779—31nomaximal
17C2×D4×D9C2211yescharacteristic
18C22×C4×D9—21no—
19C2×C9×SD16C2211yescharacteristic
20C4×Q8×C9C2211yescharacteristic, complemented
21C4×D4×C9C2211yescharacteristic
22#63508C2211yescharacteristic
23#63506C2211yescharacteristic, complemented
24C2×#3675C2211yescharacteristic
25D4×Dic9C2211yescharacteristic
26C2×#3672C2211yescharacteristic
27C4×#611—21no—
28C2×#3664C2211yescharacteristic
29#63459C2211yescharacteristic
30#63458—21no—
31#63455C2211yescharacteristic
32C4⋊C4×D9C2211yescharacteristic
33#63451—21no—
34#63450C2211yescharacteristic, complemented
35#611⋊C4—21no—
36C22⋊C4×D9—21no—
37C4×D36C2211yescharacteristic
38#63434—21no—
39C42×D9C2211yescharacteristic
40C4×Dic18—21no—
41C4×Dic18C2211yescharacteristic, complemented
42C9×#107C2211yescharacteristic, complemented
43C9×#103C2211yescharacteristic, complemented
44C9×#102C2211yescharacteristic
45C9×#97C2211yescharacteristic, complemented
46#63395C2211yescharacteristic, complemented
47#63392C2211yescharacteristic
48#63380C2211yescharacteristic
49(C2×D9)⋊C8C2211yescharacteristic
50(C2×D9)⋊C8C2211yescharacteristic
51#63378C2211yescharacteristic, complemented
52#63376C2211yescharacteristic, complemented
53Dic9⋊C8C2211yescharacteristic, complemented
54Dic9⋊C8C2211yescharacteristic, complemented
55#63369C2211yescharacteristic
56#63368C2211yescharacteristic, complemented
57#63366C2211yescharacteristic, complemented
58#63366C2211yescharacteristic, complemented
59#63362C2211yescharacteristic, complemented
60#5578—31no—
61C4×D3×D4—31no—
62C3×#440D311yescharacteristic
63#5169—31no—
64#5162—31no—
65#5026—31no—
66#5018—31no—
67#4890—31no—
68#4884—31no—
69#4818—31no—
70#4811—31no—
71#4776—31no—
72#4759—31no—
73#4710—31no—
74#4705—31no—
75C23×D9—21no—
76C2×Q8×C9C2311yescharacteristic
77C2×D4×C9C2311yescharacteristic
78C22×C4×C9—21no—
79C2×#611—21no—
80C22×Dic9—21no—
81D4×D9—22no—
82D4×D9—22no—
83C2×D36C2311yescharacteristic
84C2×C4×D9—21no—
85C2×C4×D9—21no—
86C2×C4×D9—21no—
87C2×C4×D9—44no—
88C2×C4×D9D411yescharacteristic
89C2×C4×D9D411yescharacteristic
90C2×C4×D9C2311yescharacteristic
91C2×Dic18—21no—
92C2×Dic18C2311yescharacteristic
93C9×SD16—22no—
94C2×C8×C9C2311yescharacteristic
95C2×C8×C9C2311yescharacteristic
96C9×C4⋊C4—21no—
97C9×C4⋊C4C2311yescharacteristic
98C9×C4⋊C4C2311yescharacteristic
99C9×C22⋊C4—21no—
100C42×C9—21no—
101C42×C9C2311yescharacteristic
102#3676—21no—
103#3675—22no—
104#3672—22no—
105(C2×D9)⋊C4—21no—
106(C2×D9)⋊C4—21no—
107(C2×D9)⋊C4—21no—
108(C2×D9)⋊C4—21no—
109C4⋊Dic9—21no—
110C4⋊Dic9C2311yescharacteristic
111C4⋊Dic9C2311yescharacteristic
112Dic9⋊C4—21no—
113Dic9⋊C4—21no—
114Dic9⋊C4—21no—
115Dic9⋊C4—21no—
116Dic9⋊C4—21no—
117Dic9⋊C4—21no—
118C4×Dic9—21no—
119C4×Dic9D411yescharacteristic
120C4×Dic9D411yescharacteristic
121C4×Dic9C2311yescharacteristic
122C2×C9⋊C8C2311yescharacteristic
123C2×C9⋊C8C2311yescharacteristic
124#3664—22no—
125#3110—91noSylow
126C2×D3×D4—31no—
127C22×C4×D3—61no—
128C2×C3×SD16C2×D311yescharacteristic
129C3×C4×Q8C2×D311yescharacteristic
130C3×C4×D4C2×D311yescharacteristic
131#946—31no—
132#944—31no—
133C2×#215—31no—
134D4×Dic3—31no—
135C2×#214—31no—
136C4×#67—61no—
137C2×#204—31no—
138#897—31no—
139#896—61no—
140#893—31no—
141D3×C4⋊C4—31no—
142#889—61no—
143#888—31no—
144#67⋊C4—61no—
145D3×C22⋊C4—61no—
146C4×D12—31no—
147#872—61no—
148C42×D3—31no—
149C4×Dic6—31no—
150C4×Dic6—61no—
151C3×#107C2×D311yescharacteristic
152C3×#103C2×D311yescharacteristic
153C3×#102C2×D311yescharacteristic
154C3×#97C2×D311yescharacteristic
155#835—31no—
156#832—31no—
157#821—31no—
158(C2×D3)⋊C8—31no—
159(C2×D3)⋊C8—31no—
160#818—31no—
161#816—31no—
162Dic3⋊C8—31no—
163Dic3⋊C8—31no—
164#810—31no—
165#809—31no—
166#807—31no—
167#807—31no—
168#803—31no—
169C23×C9—21no—
170C22×D9—24no—
171C22×D9—21no—
172C22×D9—42no—
173C22×D9—42no—
174C22×D9C2×D411yescharacteristic
175Q8×C9—21no—
176Q8×C9—21no—
177D4×C9—21no—
178D4×C9#4112yes—
179C2×C4×C9—21no—
180C2×C4×C9—21no—
181C2×C4×C9—21no—
182C2×C4×C9—42no—
183C2×C4×C9C2×D411yescharacteristic
184C2×C4×C9C2×D411yescharacteristic
185C2×C4×C9C2411yescharacteristic
186#611—24no—
187C2×Dic9—21no—
188C2×Dic9—21no—
189C2×Dic9—21no—
190C2×Dic9—42no—
191C2×Dic9C2×D411yescharacteristic
192C2×Dic9C2×D411yescharacteristic
193C2×Dic9C2×D411yescharacteristic
194D36—21no—
195D36#4112yes—
196C4×D9—22no—
197C4×D9—21no—
198C4×D9—21no—
199C4×D9—22no—
200C4×D9—42no—
201C4×D9—42no—
202C4×D9—42no—
203Dic18—21no—
204Dic18—21no—
205Dic18—42no—
206C8×C9—21no—
207C8×C9—21no—
208C9⋊C8—21no—
209C9⋊C8—21no—
210#533—91no—
211C2×C4×D4—91no—
212#484—91no—
213#484—91no—
214#474—91no—
215#474—91no—
216#461—91no—
217#461—91no—
218#450—91no—
219#450—91no—
220#440—91no—
221#440—91no—
222#440—91no—
223#440D911yescharacteristic, complemented
224#432—91no—
225C23×D3—61no—
226C2×C3×Q8C22×D311yescharacteristic
227C2×C3×D4C22×D311yescharacteristic
228C22×C3×C4—21no—
229C2×#67—61no—
230C22×Dic3—61no—
231D3×D4—62no—
232D3×D4—62no—
233C2×D12—31no—
234C2×C4×D3—31no—
235C2×C4×D3—31no—
236C2×C4×D3—31no—
237C2×C4×D3—61no—
238C2×C4×D3—61no—
239C2×C4×D3—61no—
240C2×C4×D3—124no—
241C2×Dic6—31no—
242C2×Dic6—61no—
243C3×SD16—22no—
244C2×C3×C8C22×D311yescharacteristic
245C2×C3×C8C22×D311yescharacteristic
246C3×C4⋊C4—21no—
247C3×C4⋊C4C22×D311yescharacteristic
248C3×C4⋊C4C22×D311yescharacteristic
249C3×C22⋊C4—21no—
250C3×C42—21no—
251C3×C42C22×D311yescharacteristic
252#217—61no—
253#215—62no—
254#214—62no—
255(C2×D3)⋊C4—61no—
256(C2×D3)⋊C4—61no—
257(C2×D3)⋊C4—61no—
258(C2×D3)⋊C4—61no—
259C4⋊Dic3—31no—
260C4⋊Dic3—31no—
261C4⋊Dic3—61no—
262Dic3⋊C4—61no—
263Dic3⋊C4—61no—
264Dic3⋊C4—61no—
265Dic3⋊C4—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—
274#204—62no—
275C22×C9—22no—
276C22×C9—41no—
277C22×C9—41no—
278C22×C9C22×D411yescharacteristic
279C2×D9—21no—
280C2×D9—21no—
281C2×D9—22no—
282C2×D9—48no—
283C2×D9—41no—
284C2×D9—41no—
285C2×D9#13712yes—
286C4×C9—21no—
287C4×C9—21no—
288C4×C9—41no—
289C4×C9—41no—
290C4×C9—41no—
291C4×C9C2×#4111yescharacteristic
292C4×C9C2×#4111yescharacteristic
293Dic9—21no—
294Dic9—21no—
295Dic9—41no—
296Dic9—41no—
297Dic9—41no—
298Dic9AGL(1,ℤ/8)12yes—
299C22×D4—91no—
300C23×C4—181no—
301C2×SD16—91no—
302C2×SD16—91no—
303C2×SD16—91no—
304C2×SD16C2×D911yescharacteristic
305C4⋊Q8—91no—
306C4⋊Q8—91no—
307#125—181no—
308C22⋊Q8—91no—
309C22⋊Q8—91no—
310C22⋊Q8—181no—
311C4×Q8—91no—
312C4×Q8—181no—
313C4×Q8C2×D911yescharacteristic, complemented
314C4×D4—91no—
315C4×D4—91no—
316C4×D4—91no—
317C4×D4—181no—
318C4×D4—181no—
319C4×D4C2×D911yescharacteristic
320#117—181no—
321C2×C4⋊C4—91no—
322C2×C22⋊C4—181no—
323C2×C42—91no—
324#107—91no—
325#107—91no—
326#107—91no—
327#107C2×D911yescharacteristic, complemented
328C4⋊C8—91no—
329C4⋊C8—91no—
330#103—91no—
331#103—91no—
332#103—91no—
333#103C2×D911yescharacteristic, complemented
334#102—91no—
335#102—91no—
336#102—91no—
337#102C2×D911yescharacteristic
338C22⋊C8—91no—
339C22⋊C8—91no—
340#97—91no—
341#97C2×D911yescharacteristic, complemented
342C23×C3—21no—
343C22×D3—31no—
344C22×D3—64no—
345C22×D3—61no—
346C22×D3—122no—
347C22×D3—122no—
348C3×Q8—21no—
349C3×Q8—21no—
350C3×D4—21no—
351C3×D4#23512yes—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—42no—
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4C23×D311yescharacteristic
359#67—64no—
360C2×Dic3—31no—
361C2×Dic3—31no—
362C2×Dic3—31no—
363C2×Dic3—61no—
364C2×Dic3—61no—
365C2×Dic3—61no—
366C2×Dic3—122no—
367D12—32no—
368D12—61no—
369C4×D3—62no—
370C4×D3—62no—
371C4×D3—61no—
372C4×D3—61no—
373C4×D3—122no—
374C4×D3—122no—
375C4×D3—122no—
376Dic6—61no—
377Dic6—61no—
378Dic6—122no—
379C3×C8—21no—
380C3×C8—21no—
381C3⋊C8—61no—
382C3⋊C8—61no—
383C2×C9—42no—
384C2×C9#52511yescharacteristic
385C2×C9C2×AGL(1,ℤ/8)11yescharacteristic
386C2×C9C2×#13711yescharacteristic
387D9—22no—
388D9—42no—
389C24—181no—
390C2×Q8—91no—
391C2×Q8—181no—
392C2×Q8C22×D911yescharacteristic
393C2×D4—91no—
394C2×D4—181no—
395C2×D4—182no—
396C2×D4—182no—
397C2×D4C22×D911yescharacteristic
398C22×C4—21no—
399C22×C4—91no—
400C22×C4—91no—
401C22×C4—91no—
402C22×C4—181no—
403C22×C4—181no—
404C22×C4—181no—
405C22×C4—181no—
406C22×C4—364no—
407SD16—22no—
408SD16—182no—
409SD16—182no—
410SD16—182no—
411C2×C8—91no—
412C2×C8—91no—
413C2×C8C22×D911yescharacteristic
414C2×C8C22×D911yescharacteristic
415C4⋊C4—21no—
416C4⋊C4—91no—
417C4⋊C4—91no—
418C4⋊C4—181no—
419C4⋊C4—181no—
420C4⋊C4—181no—
421C4⋊C4—181no—
422C4⋊C4—181no—
423C4⋊C4—181no—
424C4⋊C4—181no—
425C4⋊C4C22×D911yescharacteristic
426C4⋊C4C22×D911yescharacteristic
427C22⋊C4—21no—
428C22⋊C4—181no—
429C22⋊C4—181no—
430C22⋊C4—181no—
431C22⋊C4—181no—
432C22⋊C4—181no—
433C42—21no—
434C42—91no—
435C42—91no—
436C42—91no—
437C42—181no—
438C42C22×D911yescharacteristic
439C22×C3—22no—
440C22×C3—41no—
441C22×C3—41no—
442C22×C3C2×D3×D411yescharacteristic
443C2×D3—32no—
444C2×D3—61no—
445C2×D3—61no—
446C2×D3—62no—
447C2×D3—128no—
448C2×D3—121no—
449C2×D3—121no—
450C3×C4—21no—
451C3×C4—21no—
452C3×C4—41no—
453C3×C4—41no—
454C3×C4—41no—
455C3×C4C2×#23511yescharacteristic
456C3×C4D3×#4111yescharacteristic
457Dic3—32no—
458Dic3—61no—
459Dic3—61no—
460Dic3—121no—
461Dic3—121no—
462Dic3—121no—
463C9#311011yescharacteristic, complemented, Sylow
464C23—21no—
465C23—91no—
466C23—184no—
467C23—181no—
468C23—362no—
469C23—362no—
470Q8—21no—
471Q8—21no—
472Q8—181no—
473Q8—181no—
474Q8—362no—
475D4—21no—
476D4—92no—
477D4—184no—
478D4—181no—
479D4#369712yes—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—42no—
484C2×C4—91no—
485C2×C4—91no—
486C2×C4—91no—
487C2×C4—182no—
488C2×C4—182no—
489C2×C4—181no—
490C2×C4—181no—
491C2×C4—181no—
492C2×C4—181no—
493C2×C4—181no—
494C2×C4—362no—
495C2×C4—362no—
496C2×C4—362no—
497C2×C4—362no—
498C2×C4D4×D911yescharacteristic
499C2×C4D4×D911yescharacteristic
500C2×C4C23×D911yescharacteristic
501C8—21no—
502C8—21no—
503C8—181no—
504C8—181no—
505C2×C3—42no—
506C2×C3#554711yescharacteristic
507C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
508C2×C3D3×#13711yescharacteristic
509D3—62no—
510D3—122no—
511C22—22no—
512C22—41no—
513C22—41no—
514C22—92no—
515C22—181no—
516C22—181no—
517C22—182no—
518C22—368no—
519C22—361no—
520C22—361no—
521C22C2×D4×D911yescharacteristic
522C4—21no—
523C4—21no—
524C4—41no—
525C4—41no—
526C4—41no—
527C4—92no—
528C4—181no—
529C4—181no—
530C4—361no—
531C4—361no—
532C4—361no—
533C4C2×#369711yescharacteristic
534C4#41×D911yescharacteristic
535C3#7977911yescharacteristic
536C2—42no—
537C2—182no—
538C2—362no—
539C2#1058964911yescharacteristic
540C2D9×AGL(1,ℤ/8)11yescharacteristic
541C2D9×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#440C2
socleC22×C3C2×D3×D4
prime radicalC2×D4×D9C22
hypercenter#440D9
hypocenterC9#3110
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #10589680C2semidirect
3. C9×#440C2semidirect
5. #10588842C2semidirect
6. #10588709C2semidirect
7. #10588694C2semidirect
8. #10588570C2semidirect
9. #10588564C2semidirect
10. #10588498C2semidirect
11. #10588491C2semidirect
13. #10588439C2semidirect
14. #10588391C2semidirect
15. #10588386C2semidirect
20. C4×Q8×C9C22semidirect
23. #63506C22semidirect
34. #63450C22semidirect
41. C4×Dic18C22semidirect
42. C9×#107C22semidirect
43. C9×#103C22semidirect
45. C9×#97C22semidirect
46. #63395C22semidirect
51. #63378C22semidirect
52. #63376C22semidirect
53. Dic9⋊C8C22semidirect
54. Dic9⋊C8C22semidirect
56. #63368C22semidirect
57. #63366C22semidirect
58. #63366C22semidirect
59. #63362C22semidirect
223. #440D9semidirect
313. C4×Q8C2×D9semidirect
327. #107C2×D9semidirect
333. #103C2×D9semidirect
341. #97C2×D9semidirect
463. C9#3110semidirect

Maximal subgroups

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

subgroupindex
#105896802
C4×D4×D92
C9×#4402
#105888492
#105888422
#105887092
#105886942
#105885702
#105885642
#105884982
#105884912
#105884562
#105884392
#105883912
#105883862
#797793