Finite Group Databasebeta

← #11860713

Subgroups — #11860713

Order 1152.

738 conjugacy classes of subgroups.

The subgroup lattice has 549 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D9C211yesmaximal, characteristic
2#10589674C211yesmaximal, characteristic, complemented
3#10589647C211yesmaximal, characteristic
4C4×C9×SD16C211yesmaximal, characteristic, complemented
5SD16×Dic9C211yesmaximal, characteristic, complemented
6#10588709C211yesmaximal, characteristic, complemented
7#10588694C211yesmaximal, characteristic, complemented
8#10588540C211yesmaximal, characteristic, complemented
9#10588532C211yesmaximal, characteristic, complemented
10#10588497C211yesmaximal, characteristic, complemented
11#10588482C211yesmaximal, characteristic, complemented
12#10588450C211yesmaximal, characteristic
13#10588437C211yesmaximal, characteristic, complemented
14C4×#3664C211yesmaximal, characteristic, complemented
15#10588371C211yesmaximal, characteristic, complemented
16#79649—31nomaximal
17C2×Q8×D9C2211yescharacteristic
18C2×D4×D9C2211yescharacteristic
19C2×C9×SD16C2211yescharacteristic
20C4×Q8×C9C2211yescharacteristic, complemented
21C4×D4×C9C2211yescharacteristic
22Q8×Dic9C2211yescharacteristic, complemented
23C2×#3675C2211yescharacteristic
24D4×Dic9C2211yescharacteristic
25C2×#3672C2211yescharacteristic
26C4×#611—21no—
27C2×(C2×D9)⋊C4—21no—
28SD16×D9C418yescomplemented
29C2×#3664C2211yescharacteristic
30C2×#3663C2211yescharacteristic
31C2×C8×D9C2211yescharacteristic
32#63455C2211yescharacteristic
33#63454—21no—
34#63454C2211yescharacteristic
35#63454C2211yescharacteristic
36#63449—21no—
37#63449C2211yescharacteristic, complemented
38#611⋊C4—21no—
39C22⋊C4×D9—21no—
40C4×D36C2211yescharacteristic
41#63434—21no—
42#63434C2211yescharacteristic
43C4×Dic18—21no—
44C4×Dic18C2211yescharacteristic, complemented
45C9×#106C2211yescharacteristic, complemented
46C9×#103C2211yescharacteristic, complemented
47C9×#102C2211yescharacteristic
48C4×C8×C9C2211yescharacteristic, complemented
49#63395C2211yescharacteristic, complemented
50#63392C2211yescharacteristic
51#63380C2211yescharacteristic
52#63377C2211yescharacteristic, complemented
53#63376C2211yescharacteristic, complemented
54#63375C2211yescharacteristic, complemented
55C8×Dic9C2211yescharacteristic, complemented
56#63369C2211yescharacteristic
57#63368C2211yescharacteristic, complemented
58#63366C2211yescharacteristic, complemented
59#63366C2211yescharacteristic, complemented
60#63362C2211yescharacteristic, complemented
61C2×D3×SD16—31no—
62#5572—31no—
63#5545—31no—
64C3×C4×SD16D311yescharacteristic
65Dic3×SD16—31no—
66#5026—31no—
67#5018—31no—
68#4860—31no—
69#4852—31no—
70#4817—31no—
71#4802—31no—
72#4770—31no—
73#4757—31no—
74C4×#204—31no—
75#4689—31no—
76C23×D9—21no—
77C2×Q8×C9C2311yescharacteristic
78C2×D4×C9C2311yescharacteristic
79C22×C4×C9—21no—
80C2×#611—21no—
81C22×Dic9—21no—
82Q8×D9—22no—
83Q8×D9C2×C414yescomplemented
84D4×D9—22no—
85D4×D9C2×C414yes—
86C2×D36C2311yescharacteristic
87C2×C4×D9—21no—
88C2×C4×D9—21no—
89C2×C4×D9—21no—
90C2×C4×D9C2311yescharacteristic
91C2×Dic18—21no—
92C2×Dic18C2311yescharacteristic
93C9×SD16C2×C414yescomplemented
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#3675C2×C414yescomplemented
104#3672C2×C414yescomplemented
105(C2×D9)⋊C4—21no—
106(C2×D9)⋊C4—21no—
107(C2×D9)⋊C4—21no—
108(C2×D9)⋊C4—21no—
109(C2×D9)⋊C4D411yescharacteristic
110(C2×D9)⋊C4D411yescharacteristic
111C4⋊Dic9—21no—
112C4⋊Dic9C2311yescharacteristic
113C4⋊Dic9C2311yescharacteristic
114Dic9⋊C4—21no—
115Dic9⋊C4—21no—
116Dic9⋊C4D411yescharacteristic
117Dic9⋊C4D411yescharacteristic
118C4×Dic9—21no—
119C4×Dic9—21no—
120C4×Dic9—21no—
121C4×Dic9—21no—
122C4×Dic9—21no—
123C4×Dic9C2311yescharacteristic
124C2×C9⋊C8C2311yescharacteristic
125C2×C9⋊C8C2311yescharacteristic
126#3664C2×C414yescomplemented
127#3663—22no—
128C8×D9C2×C414yescomplemented
129#2949—91noSylow
130C2×D3×Q8—31no—
131C2×D3×D4—31no—
132C2×C3×SD16C2×D311yescharacteristic
133C3×C4×Q8C2×D311yescharacteristic
134C3×C4×D4C2×D311yescharacteristic
135Q8×Dic3—31no—
136C2×#215—31no—
137D4×Dic3—31no—
138C2×#214—31no—
139C4×#67—61no—
140C2×(C2×D3)⋊C4—61no—
141D3×SD16—38no—
142C2×#204—31no—
143C2×ΓL(1,𝔽25)—31no—
144C2×D3×C8—31no—
145#893—31no—
146#892—31no—
147#892—31no—
148#892—61no—
149#887—31no—
150#887—61no—
151#67⋊C4—61no—
152D3×C22⋊C4—61no—
153C4×D12—31no—
154#872—31no—
155#872—61no—
156C4×Dic6—31no—
157C4×Dic6—61no—
158C3×#106C2×D311yescharacteristic
159C3×#103C2×D311yescharacteristic
160C3×#102C2×D311yescharacteristic
161C3×C4×C8C2×D311yescharacteristic
162#835—31no—
163#832—31no—
164#821—31no—
165#817—31no—
166#816—31no—
167#815—31no—
168C8×Dic3—31no—
169#810—31no—
170#809—31no—
171#807—31no—
172#807—31no—
173#803—31no—
174C23×C9—21no—
175C22×D9—21no—
176C22×D9—24no—
177C22×D9—81no—
178C22×D9—81no—
179C22×D9C2×D411yescharacteristic
180Q8×C9—21no—
181Q8×C9C22×C412yes—
182D4×C9—21no—
183D4×C9C22×C412yes—
184C2×C4×C9—21no—
185C2×C4×C9—21no—
186C2×C4×C9—21no—
187C2×C4×C9—81no—
188C2×C4×C9C2×D411yescharacteristic
189C2×C4×C9C2×D411yescharacteristic
190C2×C4×C9C2411yescharacteristic
191#611—24no—
192C2×Dic9—21no—
193C2×Dic9—21no—
194C2×Dic9—21no—
195C2×Dic9—81no—
196C2×Dic9C2×D411yescharacteristic
197C2×Dic9C2×D411yescharacteristic
198C2×Dic9C2×D411yescharacteristic
199D36—21no—
200D36C22×C412yes—
201C4×D9—24no—
202C4×D9—81no—
203C4×D9—81no—
204C4×D9C22×C412yes—
205C4×D9#4112yes—
206Dic18—21no—
207Dic18—24no—
208Dic18C22×C412yes—
209C8×C9—21no—
210C8×C9C22×C412yes—
211C9⋊C8—21no—
212C9⋊C8C22×C412yes—
213C22×SD16—91no—
214#519—91no—
215#518—91no—
216#440—91no—
217#440—91no—
218#440—91no—
219#440—91no—
220C4×SD16—91no—
221C4×SD16—91no—
222C4×SD16—91no—
223C4×SD16D911yescharacteristic, complemented
224#427—91no—
225#419—91no—
226#418—91no—
227#405—91no—
228C23×D3—61no—
229C2×C3×Q8C22×D311yescharacteristic
230C2×C3×D4C22×D311yescharacteristic
231C22×C3×C4—21no—
232C2×#67—61no—
233C22×Dic3—61no—
234D3×Q8—34no—
235D3×Q8—62no—
236D3×D4—34no—
237D3×D4—62no—
238C2×D12—31no—
239C2×C4×D3—31no—
240C2×C4×D3—61no—
241C2×C4×D3—61no—
242C2×C4×D3—61no—
243C2×Dic6—31no—
244C2×Dic6—61no—
245C3×SD16C4×D314yes—
246C2×C3×C8C22×D311yescharacteristic
247C2×C3×C8C22×D311yescharacteristic
248C3×C4⋊C4—21no—
249C3×C4⋊C4C22×D311yescharacteristic
250C3×C4⋊C4C22×D311yescharacteristic
251C3×C22⋊C4—21no—
252C3×C42—21no—
253C3×C42C22×D311yescharacteristic
254#217—61no—
255#215—34no—
256#214—34no—
257(C2×D3)⋊C4—31no—
258(C2×D3)⋊C4—31no—
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—61no—
266Dic3⋊C4—31no—
267Dic3⋊C4—31no—
268Dic3⋊C4—61no—
269Dic3⋊C4—61no—
270C4×Dic3—31no—
271C4×Dic3—61no—
272C4×Dic3—61no—
273C4×Dic3—61no—
274C4×Dic3—61no—
275C4×Dic3—61no—
276C2×C3⋊C8—31no—
277C2×C3⋊C8—31no—
278#204—34no—
279ΓL(1,𝔽25)—62no—
280D3×C8—34no—
281C22×C9—22no—
282C22×C9—41no—
283C22×C9—41no—
284C22×C9C22×D411yescharacteristic
285C2×D9—21no—
286C2×D9—21no—
287C2×D9—22no—
288C2×D9—41no—
289C2×D9—41no—
290C2×D9—84no—
291C2×D9C4×D412yes—
292C4×C9—22no—
293C4×C9—21no—
294C4×C9—21no—
295C4×C9—41no—
296C4×C9—41no—
297C4×C9C23×C411yescharacteristic
298C4×C9C2×#4111yescharacteristic
299Dic9—22no—
300Dic9—21no—
301Dic9—21no—
302Dic9—41no—
303Dic9—41no—
304Dic9C4×D412yes—
305C22×Q8—91no—
306C22×D4—91no—
307C2×SD16—91no—
308C2×SD16—91no—
309C2×SD16—98no—
310C2×SD16—91no—
311C2×SD16C2×D911yescharacteristic
312C2×M16—91no—
313C22×C8—91no—
314C4×Q8—91no—
315C4×Q8—91no—
316C4×Q8—91no—
317C4×Q8—181no—
318C4×Q8—181no—
319C4×Q8C2×D911yescharacteristic, complemented
320C4×D4—91no—
321C4×D4—91no—
322C4×D4—91no—
323C4×D4—181no—
324C4×D4—181no—
325C4×D4C2×D911yescharacteristic
326#117—91no—
327#117—91no—
328#117—91no—
329#117—181no—
330#117—181no—
331C2×C22⋊C4—181no—
332C2×C22⋊C4—181no—
333#107—91no—
334#107—91no—
335#106—91no—
336#106C2×D911yescharacteristic, complemented
337#103—91no—
338#103—91no—
339#103—91no—
340#103C2×D911yescharacteristic, complemented
341#102—91no—
342#102—91no—
343#102—91no—
344#102C2×D911yescharacteristic
345#97—91no—
346#97—91no—
347C4×C8—91no—
348C4×C8C2×D911yescharacteristic, complemented
349C23×C3—21no—
350C22×D3—31no—
351C22×D3—64no—
352C22×D3—61no—
353C22×D3—241no—
354C22×D3—241no—
355C3×Q8—21no—
356C3×Q8C2×C4×D312yes—
357C3×D4—21no—
358C3×D4C2×C4×D312yes—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—81no—
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4D3×D411yescharacteristic
365C2×C3×C4C23×D311yescharacteristic
366#67—64no—
367C2×Dic3—31no—
368C2×Dic3—31no—
369C2×Dic3—31no—
370C2×Dic3—61no—
371C2×Dic3—61no—
372C2×Dic3—61no—
373C2×Dic3—241no—
374D12—32no—
375D12—61no—
376C4×D3—32no—
377C4×D3—32no—
378C4×D3—64no—
379C4×D3—241no—
380C4×D3—241no—
381Dic6—32no—
382Dic6—64no—
383Dic6—61no—
384C3×C8—21no—
385C3×C8C2×C4×D312yes—
386C3⋊C8—32no—
387C3⋊C8—61no—
388C2×C9—42no—
389C2×C9C2×C4×D411yescharacteristic
390C2×C9#57711yescharacteristic
391C2×C9#57711yescharacteristic
392D9—22no—
393D9—42no—
394C24—181no—
395C2×Q8—94no—
396C2×Q8—91no—
397C2×Q8—181no—
398C2×Q8—182no—
399C2×Q8C22×D911yescharacteristic
400C2×D4—94no—
401C2×D4—91no—
402C2×D4—182no—
403C2×D4—181no—
404C2×D4C22×D911yescharacteristic
405C22×C4—21no—
406C22×C4—91no—
407C22×C4—181no—
408C22×C4—181no—
409C22×C4—181no—
410C22×C4—181no—
411SD16—94no—
412SD16—94no—
413SD16—94no—
414SD16C4×D914yescomplemented
415M16—182no—
416C2×C8—91no—
417C2×C8—94no—
418C2×C8—91no—
419C2×C8C22×D911yescharacteristic
420C2×C8C22×D911yescharacteristic
421C4⋊C4—21no—
422C4⋊C4—91no—
423C4⋊C4—91no—
424C4⋊C4—91no—
425C4⋊C4—91no—
426C4⋊C4—181no—
427C4⋊C4—181no—
428C4⋊C4—181no—
429C4⋊C4C22×D911yescharacteristic
430C4⋊C4C22×D911yescharacteristic
431C22⋊C4—21no—
432C22⋊C4—91no—
433C22⋊C4—91no—
434C22⋊C4—181no—
435C22⋊C4—181no—
436C22⋊C4—181no—
437C22⋊C4—181no—
438C22⋊C4—181no—
439C42—21no—
440C42—91no—
441C42—181no—
442C42—181no—
443C42—181no—
444C42—181no—
445C42—181no—
446C42C22×D911yescharacteristic
447C22×C3—22no—
448C22×C3—41no—
449C22×C3—41no—
450C22×C3C2×D3×D411yescharacteristic
451C2×D3—32no—
452C2×D3—61no—
453C2×D3—61no—
454C2×D3—62no—
455C2×D3—121no—
456C2×D3—121no—
457C2×D3—244no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—22no—
461C3×C4—41no—
462C3×C4—41no—
463C3×C4C22×C4×D311yescharacteristic
464C3×C4D3×#4111yescharacteristic
465Dic3—32no—
466Dic3—61no—
467Dic3—61no—
468Dic3—62no—
469Dic3—121no—
470Dic3—121no—
471C9#294911yescharacteristic, complemented, Sylow
472C23—21no—
473C23—91no—
474C23—184no—
475C23—181no—
476C23—721no—
477C23—721no—
478Q8—21no—
479Q8—92no—
480Q8—184no—
481Q8—181no—
482Q8C2×C4×D912yes—
483D4—21no—
484D4—92no—
485D4—184no—
486D4—181no—
487D4C2×C4×D912yes—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—81no—
492C2×C4—91no—
493C2×C4—92no—
494C2×C4—92no—
495C2×C4—91no—
496C2×C4—91no—
497C2×C4—184no—
498C2×C4—181no—
499C2×C4—181no—
500C2×C4—181no—
501C2×C4—721no—
502C2×C4—721no—
503C2×C4—721no—
504C2×C4D4×D911yescharacteristic
505C2×C4D4×D911yescharacteristic
506C2×C4C23×D911yescharacteristic
507C8—21no—
508C8—92no—
509C8—181no—
510C8C2×C4×D912yes—
511C2×C3—42no—
512C2×C3C4×D3×D411yescharacteristic
513C2×C3#576211yescharacteristic
514C2×C3#577011yescharacteristic
515D3—62no—
516D3—122no—
517C22—22no—
518C22—41no—
519C22—41no—
520C22—92no—
521C22—181no—
522C22—181no—
523C22—182no—
524C22—361no—
525C22—361no—
526C22—724no—
527C22C2×D4×D911yescharacteristic
528C4—21no—
529C4—21no—
530C4—22no—
531C4—41no—
532C4—41no—
533C4—92no—
534C4—181no—
535C4—181no—
536C4—182no—
537C4—361no—
538C4—361no—
539C4C22×C4×D911yescharacteristic
540C4#41×D911yescharacteristic
541C3#7964911yescharacteristic
542C2—42no—
543C2—182no—
544C2—362no—
545C2C4×D4×D911yescharacteristic
546C2#1058986411yescharacteristic
547C2#1058987211yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutatorC4×C9C23×C4
FrattiniC2×C3×C4C23×D3
FittingC4×C9×SD16C2
socleC22×C3C2×D3×D4
prime radicalC2×D4×D9C22
cosocleC2×C4×C9C24
hypercenterC4×SD16D9
hypocenterC9#2949
LCSG ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. #10589674C2semidirect
4. C4×C9×SD16C2semidirect
5. SD16×Dic9C2semidirect
6. #10588709C2semidirect
7. #10588694C2semidirect
8. #10588540C2semidirect
9. #10588532C2semidirect
10. #10588497C2semidirect
11. #10588482C2semidirect
13. #10588437C2semidirect
14. C4×#3664C2semidirect
15. #10588371C2semidirect
20. C4×Q8×C9C22semidirect
22. Q8×Dic9C22semidirect
28. SD16×D9C4semidirect
37. #63449C22semidirect
44. C4×Dic18C22semidirect
45. C9×#106C22semidirect
46. C9×#103C22semidirect
48. C4×C8×C9C22semidirect
49. #63395C22semidirect
52. #63377C22semidirect
53. #63376C22semidirect
54. #63375C22semidirect
55. C8×Dic9C22semidirect
57. #63368C22semidirect
58. #63366C22semidirect
59. #63366C22semidirect
60. #63362C22semidirect
83. Q8×D9C2×C4semidirect
93. C9×SD16C2×C4semidirect
103. #3675C2×C4semidirect
104. #3672C2×C4semidirect
126. #3664C2×C4semidirect
128. C8×D9C2×C4semidirect
223. C4×SD16D9semidirect
319. C4×Q8C2×D9semidirect
336. #106C2×D9semidirect
340. #103C2×D9semidirect
348. C4×C8C2×D9semidirect
414. SD16C4×D9semidirect
471. C9#2949semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D92
#105896742
#105896472
C4×C9×SD162
SD16×Dic92
#105887092
#105886942
#105885402
#105885322
#105884972
#105884822
#105884502
#105884372
C4×#36642
#105883712
#796493