Finite Group Databasebeta

← #11909860

Subgroups — #11909860

Order 1152.

1488 conjugacy classes of subgroups.

The subgroup lattice has 633 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#557C211yesmaximal, characteristic, complemented
2#10589833C212yesmaximal, complemented
3#10589830C211yesmaximal, characteristic, complemented
4#10589829C212yesmaximal, complemented
5#10589829C211yesmaximal, characteristic, complemented
6#10589798C214yesmaximal, complemented
7#10589795C214yesmaximal, complemented
8#10589793C212yesmaximal
9#10589787C212yesmaximal, complemented
10#10589686C211yesmaximal, characteristic, complemented
11#10589683C212yesmaximal, complemented
12#10589682C211yesmaximal, characteristic
13#10589680C212yesmaximal, complemented
14#10589674C212yesmaximal, complemented
15C4×Q8×D9C211yesmaximal, characteristic, complemented
16#10589670C212yesmaximal, complemented
17#10589669C211yesmaximal, characteristic, complemented
18#87025—31nomaximal
19C2×Q8×D9C2211yescharacteristic
20C2×Q8×D9C2212yes—
21C9×C4⋊Q8C2211yescharacteristic
22C9×C4⋊Q8C2212yes—
23C9×#125C2212yes—
24C9×#125C2214yes—
25C4×Q8×C9C2211yescharacteristic
26C4×Q8×C9C2212yes—
27C4×Q8×C9C2211yescharacteristic
28C4×Q8×C9C2212yes—
29#63509C2211yescharacteristic
30#63508C2212yes—
31#63508C2212yes—
32#63508C2212yes—
33#63508C2211yescharacteristic
34Q8×Dic9C2212yes—
35Q8×Dic9C2211yescharacteristic
36#63506C2212yes—
37#63460C2214yes—
38#63460C2214yes—
39#63460C2214yes—
40#63460C2212yes—
41#63459C2212yes—
42#63458C2214yes—
43#63458C2214yes—
44#63458C2214yes—
45#63457C2211yescharacteristic
46#63456C2214yes—
47#63456C2212yes—
48#63455C2214yes—
49#63455C2212yes—
50#63454C2214yes—
51#63454C2212yes—
52#63454C2212yes—
53C4⋊C4×D9C2212yes—
54C4⋊C4×D9C2211yescharacteristic
55#63452C2211yescharacteristic
56#63452C2212yes—
57#63451C2214yes—
58#63451C2214yes—
59#63451C2214yes—
60#63451C2214yes—
61#63450C2214yes—
62#63450C2212yes—
63#63449C2212yes—
64#63449C2214yes—
65#63449C2212yes—
66#63449C2212yes—
67#63449C2211yescharacteristic
68#63438C2214yes—
69#63437C2212yes—
70C4×D36C2212yes—
71C4×D36C2211yescharacteristic
72#63434C2214yes—
73#63434C2214yes—
74#63434C2212yes—
75C42×D9C2212yes—
76C42×D9C2211yescharacteristic
77#63432C2212yes—
78#63431C2211yescharacteristic
79C4×Dic18C2212yes—
80C4×Dic18C2212yes—
81C4×Dic18C2214yes—
82C4×Dic18C2211yescharacteristic
83C4×Dic18C2212yes—
84C3×#557D311yescharacteristic
85#5731—32no—
86#5728—31no—
87#5727—31no—
88#5727—32no—
89#5696—34no—
90#5693—34no—
91#5691—32no—
92#5685—32no—
93#5584—31no—
94#5581—32no—
95#5580—31no—
96#5578—32no—
97#5572—32no—
98C4×D3×Q8—31no—
99#5568—32no—
100#5567—31no—
101C2×Q8×C9C2311yescharacteristic
102C2×Q8×C9C2312yes—
103C2×Q8×C9C2311yescharacteristic
104Q8×D9—24no—
105Q8×D9—28no—
106C2×D36C2311yescharacteristic
107C2×D36C2312yes—
108C2×C4×D9C2311yescharacteristic
109C2×C4×D9C2312yes—
110C2×C4×D9C2311yescharacteristic
111C2×C4×D9C2312yes—
112C2×C4×D9C2311yescharacteristic
113C2×C4×D9C2312yes—
114C2×C4×D9C2314yes—
115C2×Dic18C2312yes—
116C2×Dic18C2312yes—
117C2×Dic18C2314yes—
118C2×Dic18C2311yescharacteristic
119C9×C4⋊C4C2311yescharacteristic
120C9×C4⋊C4C2311yescharacteristic
121C9×C4⋊C4C2314yes—
122C9×C4⋊C4C2312yes—
123C9×C4⋊C4C2312yes—
124C9×C4⋊C4C2312yes—
125C9×C4⋊C4C2314yes—
126C9×C4⋊C4C2314yes—
127C9×C4⋊C4C2312yes—
128C42×C9C2312yes—
129C42×C9C2314yes—
130C42×C9C2311yescharacteristic
131C42×C9C2312yes—
132(C2×D9)⋊C4C2312yes—
133(C2×D9)⋊C4C2314yes—
134(C2×D9)⋊C4C2314yes—
135(C2×D9)⋊C4C2314yes—
136(C2×D9)⋊C4C2312yes—
137(C2×D9)⋊C4C2312yes—
138(C2×D9)⋊C4C2314yes—
139(C2×D9)⋊C4C2312yes—
140(C2×D9)⋊C4C2312yes—
141C4⋊Dic9C2312yes—
142C4⋊Dic9C2311yescharacteristic
143C4⋊Dic9C2312yes—
144C4⋊Dic9C2314yes—
145C4⋊Dic9C2311yescharacteristic
146C4⋊Dic9C2312yes—
147C4⋊Dic9C2312yes—
148Dic9⋊C4C2314yes—
149Dic9⋊C4C2314yes—
150Dic9⋊C4C2312yes—
151Dic9⋊C4C2314yes—
152Dic9⋊C4C2314yes—
153Dic9⋊C4C2314yes—
154Dic9⋊C4C2312yes—
155Dic9⋊C4C2312yes—
156Dic9⋊C4C2312yes—
157Dic9⋊C4C2314yes—
158Dic9⋊C4C2312yes—
159C4×Dic9C2312yes—
160C4×Dic9C2311yescharacteristic
161C4×Dic9C2312yes—
162C4×Dic9C2314yes—
163C4×Dic9C2311yescharacteristic
164C4×Dic9C2312yes—
165C4×Dic9C2314yes—
166C4×Dic9C2314yes—
167C4×Dic9C2311yescharacteristic
168#3523—91noSylow
169C2×D3×Q8—31no—
170C2×D3×Q8—32no—
171C3×C4⋊Q8C2×D311yescharacteristic
172C3×C4⋊Q8C2×D312yes—
173C3×#125C2×D312yes—
174C3×#125C2×D314yes—
175C3×C4×Q8C2×D311yescharacteristic
176C3×C4×Q8C2×D312yes—
177C3×C4×Q8C2×D311yescharacteristic
178C3×C4×Q8C2×D312yes—
179#947—31no—
180#946—32no—
181#946—32no—
182#946—32no—
183#946—31no—
184Q8×Dic3—32no—
185Q8×Dic3—31no—
186#944—32no—
187#898—34no—
188#898—34no—
189#898—34no—
190#898—32no—
191#897—32no—
192#896—34no—
193#896—34no—
194#896—34no—
195#895—31no—
196#894—34no—
197#894—32no—
198#893—34no—
199#893—32no—
200#892—34no—
201#892—32no—
202#892—32no—
203D3×C4⋊C4—32no—
204D3×C4⋊C4—31no—
205#890—31no—
206#890—32no—
207#889—34no—
208#889—34no—
209#889—34no—
210#889—34no—
211#888—34no—
212#888—32no—
213#887—32no—
214#887—34no—
215#887—32no—
216#887—32no—
217#887—31no—
218#876—34no—
219#875—32no—
220C4×D12—32no—
221C4×D12—31no—
222#872—34no—
223#872—34no—
224#872—32no—
225C42×D3—32no—
226C42×D3—31no—
227#870—32no—
228#869—31no—
229C4×Dic6—32no—
230C4×Dic6—32no—
231C4×Dic6—34no—
232C4×Dic6—31no—
233C4×Dic6—32no—
234C22×D9C2412yes—
235C22×D9C2411yescharacteristic
236Q8×C9—22no—
237Q8×C9—24no—
238Q8×C9—22no—
239C2×C4×C9C2412yes—
240C2×C4×C9C2412yes—
241C2×C4×C9C2411yescharacteristic
242C2×C4×C9C2412yes—
243C2×C4×C9C2414yes—
244C2×C4×C9C2412yes—
245C2×C4×C9C2411yescharacteristic
246C2×C4×C9C2411yescharacteristic
247C2×Dic9C2411yescharacteristic
248C2×Dic9C2411yescharacteristic
249C2×Dic9C2414yes—
250C2×Dic9C2412yes—
251C2×Dic9C2411yescharacteristic
252C2×Dic9C2412yes—
253C2×Dic9C2412yes—
254D36—24no—
255D36—22no—
256C4×D9—24no—
257C4×D9—22no—
258C4×D9—22no—
259C4×D9—24no—
260C4×D9—22no—
261C4×D9—24no—
262C4×D9—28no—
263Dic18—24no—
264Dic18—24no—
265Dic18—28no—
266Dic18#4114yes—
267#557—92no—
268#557—91no—
269#557D911yescharacteristic, complemented
270#556—92no—
271#556—91no—
272#552—94no—
273#552—92no—
274D4×Q8—92no—
275D4×Q8—91no—
276#541—92no—
277#541—94no—
278#533—91no—
279#533—92no—
280#529—92no—
281#529—91no—
282#519—92no—
283C2×C4×Q8—91no—
284C2×C3×Q8C22×D311yescharacteristic
285C2×C3×Q8C22×D312yes—
286C2×C3×Q8C22×D311yescharacteristic
287D3×Q8—64no—
288D3×Q8—68no—
289C2×D12—31no—
290C2×D12—32no—
291C2×C4×D3—31no—
292C2×C4×D3—32no—
293C2×C4×D3—31no—
294C2×C4×D3—31no—
295C2×C4×D3—32no—
296C2×C4×D3—32no—
297C2×C4×D3—34no—
298C2×Dic6—31no—
299C2×Dic6—32no—
300C2×Dic6—32no—
301C2×Dic6—34no—
302C3×C4⋊C4C22×D311yescharacteristic
303C3×C4⋊C4C22×D312yes—
304C3×C4⋊C4C22×D314yes—
305C3×C4⋊C4C22×D311yescharacteristic
306C3×C4⋊C4C22×D312yes—
307C3×C4⋊C4C22×D314yes—
308C3×C4⋊C4C22×D312yes—
309C3×C4⋊C4C22×D314yes—
310C3×C4⋊C4C22×D312yes—
311C3×C42C22×D312yes—
312C3×C42C22×D311yescharacteristic
313C3×C42C22×D312yes—
314C3×C42C22×D314yes—
315(C2×D3)⋊C4—32no—
316(C2×D3)⋊C4—32no—
317(C2×D3)⋊C4—34no—
318(C2×D3)⋊C4—32no—
319(C2×D3)⋊C4—34no—
320(C2×D3)⋊C4—32no—
321(C2×D3)⋊C4—32no—
322(C2×D3)⋊C4—34no—
323(C2×D3)⋊C4—34no—
324C4⋊Dic3—31no—
325C4⋊Dic3—32no—
326C4⋊Dic3—31no—
327C4⋊Dic3—32no—
328C4⋊Dic3—34no—
329C4⋊Dic3—32no—
330C4⋊Dic3—32no—
331Dic3⋊C4—32no—
332Dic3⋊C4—34no—
333Dic3⋊C4—32no—
334Dic3⋊C4—32no—
335Dic3⋊C4—32no—
336Dic3⋊C4—34no—
337Dic3⋊C4—34no—
338Dic3⋊C4—34no—
339Dic3⋊C4—32no—
340Dic3⋊C4—34no—
341Dic3⋊C4—34no—
342C4×Dic3—31no—
343C4×Dic3—32no—
344C4×Dic3—32no—
345C4×Dic3—34no—
346C4×Dic3—34no—
347C4×Dic3—31no—
348C4×Dic3—31no—
349C4×Dic3—32no—
350C4×Dic3—34no—
351C22×C9C2511yescharacteristic
352C2×D9—21no—
353C2×D9—21no—
354C2×D9—22no—
355C2×D9—22no—
356C2×D9—22no—
357C2×D92−1+412yes—
358C4×C9—22no—
359C4×C9—24no—
360C4×C9—22no—
361C4×C9—21no—
362C4×C9—22no—
363C4×C9—22no—
364C4×C9C2×#4112yes—
365C4×C92−1+412yes—
366Dic9—21no—
367Dic9—22no—
368Dic9—24no—
369Dic9—21no—
370Dic9—21no—
371Dic9—22no—
372Dic9C2×#4114yes—
373C22×Q8—91no—
374C22×Q8—92no—
375C4⋊Q8—92no—
376C4⋊Q8—92no—
377C4⋊Q8—94no—
378C4⋊Q8—91no—
379C4⋊Q8C2×D911yescharacteristic
380C4⋊Q8C2×D912yes—
381#126—92no—
382#126—94no—
383#126—94no—
384#126—94no—
385#126—94no—
386#125—91no—
387#125—94no—
388#125—92no—
389#125—94no—
390#125—94no—
391#125—94no—
392#125—92no—
393#125C2×D912yes—
394#125C2×D914yes—
395#124—91no—
396#124—92no—
397#123—92no—
398#123—94no—
399C22⋊Q8—91no—
400C22⋊Q8—92no—
401C22⋊Q8—92no—
402C22⋊Q8—92no—
403C22⋊Q8—92no—
404C22⋊Q8—94no—
405C22⋊Q8—94no—
406C22⋊Q8—94no—
407#121—91no—
408C4×Q8—91no—
409C4×Q8—92no—
410C4×Q8—91no—
411C4×Q8—92no—
412C4×Q8—94no—
413C4×Q8—92no—
414C4×Q8—92no—
415C4×Q8—91no—
416C4×Q8—92no—
417C4×Q8—94no—
418C4×Q8—92no—
419C4×Q8—92no—
420C4×Q8C2×D911yescharacteristic
421C4×Q8C2×D912yes—
422C4×Q8C2×D911yescharacteristic
423C4×Q8C2×D912yes—
424C4×D4—94no—
425C4×D4—92no—
426C4×D4—92no—
427C4×D4—91no—
428#117—94no—
429#117—92no—
430#117—92no—
431#117—92no—
432#117—94no—
433#117—94no—
434C2×C4⋊C4—92no—
435C2×C4⋊C4—91no—
436C2×C42—92no—
437C2×C42—91no—
438C22×D3—31no—
439C22×D3—32no—
440C3×Q8—22no—
441C3×Q8—22no—
442C3×Q8—24no—
443C2×C3×C4C23×D312yes—
444C2×C3×C4C23×D312yes—
445C2×C3×C4C23×D311yescharacteristic
446C2×C3×C4C23×D312yes—
447C2×C3×C4C23×D314yes—
448C2×C3×C4C23×D312yes—
449C2×C3×C4C23×D311yescharacteristic
450C2×C3×C4C23×D311yescharacteristic
451C2×Dic3—32no—
452C2×Dic3—31no—
453C2×Dic3—31no—
454C2×Dic3—34no—
455C2×Dic3—32no—
456C2×Dic3—31no—
457C2×Dic3—32no—
458D12—64no—
459D12—62no—
460C4×D3—64no—
461C4×D3—68no—
462C4×D3—64no—
463C4×D3—62no—
464C4×D3—62no—
465C4×D3—62no—
466C4×D3—64no—
467Dic6—34no—
468Dic6—64no—
469Dic6—68no—
470Dic6—64no—
471C2×C9C22×#4111yescharacteristic
472C2×C9C2×2−1+411yescharacteristic
473C2×C9C2×2−1+411yescharacteristic
474D9—22no—
475D9—42no—
476C2×Q8—91no—
477C2×Q8—92no—
478C2×Q8—92no—
479C2×Q8—94no—
480C2×Q8—184no—
481C2×Q8—188no—
482C2×Q8C22×D911yescharacteristic
483C2×Q8C22×D912yes—
484C2×Q8C22×D911yescharacteristic
485C2×D4—92no—
486C2×D4—91no—
487C22×C4—91no—
488C22×C4—91no—
489C22×C4—92no—
490C22×C4—92no—
491C22×C4—91no—
492C22×C4—94no—
493C22×C4—92no—
494C4⋊C4—92no—
495C4⋊C4—92no—
496C4⋊C4—91no—
497C4⋊C4—92no—
498C4⋊C4—92no—
499C4⋊C4—94no—
500C4⋊C4—92no—
501C4⋊C4—92no—
502C4⋊C4—94no—
503C4⋊C4—92no—
504C4⋊C4—94no—
505C4⋊C4—94no—
506C4⋊C4—92no—
507C4⋊C4—91no—
508C4⋊C4—92no—
509C4⋊C4—94no—
510C4⋊C4—94no—
511C4⋊C4—94no—
512C4⋊C4C22×D911yescharacteristic
513C4⋊C4C22×D912yes—
514C4⋊C4C22×D914yes—
515C4⋊C4C22×D912yes—
516C4⋊C4C22×D912yes—
517C4⋊C4C22×D914yes—
518C4⋊C4C22×D911yescharacteristic
519C4⋊C4C22×D914yes—
520C4⋊C4C22×D912yes—
521C22⋊C4—92no—
522C22⋊C4—92no—
523C22⋊C4—94no—
524C22⋊C4—94no—
525C22⋊C4—92no—
526C22⋊C4—94no—
527C22⋊C4—92no—
528C22⋊C4—94no—
529C22⋊C4—92no—
530C42—92no—
531C42—91no—
532C42—92no—
533C42—91no—
534C42—92no—
535C42—91no—
536C42—94no—
537C42—94no—
538C42—94no—
539C42C22×D911yescharacteristic
540C42C22×D912yes—
541C42C22×D914yes—
542C42C22×D912yes—
543C22×C3C24×D311yescharacteristic
544C2×D3—32no—
545C2×D3—61no—
546C2×D3—61no—
547C2×D3—62no—
548C2×D3—62no—
549C2×D3—62no—
550C3×C4—22no—
551C3×C4—22no—
552C3×C4—24no—
553C3×C4—22no—
554C3×C4—21no—
555C3×C4—22no—
556C3×C4#100712yes—
557C3×C4D3×#4112yes—
558Dic3—34no—
559Dic3—64no—
560Dic3—61no—
561Dic3—61no—
562Dic3—62no—
563Dic3—61no—
564Dic3—62no—
565C9#352311yescharacteristic, complemented, Sylow
566C23—91no—
567C23—92no—
568Q8—22no—
569Q8—22no—
570Q8—24no—
571Q8—94no—
572Q8—184no—
573Q8—188no—
574Q8—184no—
575D4—184no—
576D4—182no—
577C2×C4—92no—
578C2×C4—91no—
579C2×C4—91no—
580C2×C4—94no—
581C2×C4—92no—
582C2×C4—91no—
583C2×C4—92no—
584C2×C4—184no—
585C2×C4—188no—
586C2×C4—184no—
587C2×C4—182no—
588C2×C4—182no—
589C2×C4—182no—
590C2×C4—184no—
591C2×C4C23×D912yes—
592C2×C4C23×D912yes—
593C2×C4C23×D911yescharacteristic
594C2×C4C23×D912yes—
595C2×C4C23×D914yes—
596C2×C4C23×D912yes—
597C2×C4C23×D911yescharacteristic
598C2×C4C23×D911yescharacteristic
599C2×C3C2×#100711yescharacteristic
600C2×C3C2×D3×#4111yescharacteristic
601C2×C3D3×2−1+411yescharacteristic
602D3—62no—
603D3—122no—
604C22—92no—
605C22—181no—
606C22—181no—
607C22—182no—
608C22—182no—
609C22—182no—
610C22C24×D911yescharacteristic
611C4—22no—
612C4—22no—
613C4—24no—
614C4—22no—
615C4—21no—
616C4—22no—
617C4—94no—
618C4—181no—
619C4—184no—
620C4—181no—
621C4—182no—
622C4—181no—
623C4—182no—
624C4#6371312yes—
625C4#41×D912yes—
626C3#8702511yescharacteristic
627C2—182no—
628C2—362no—
629C2C2×#6371311yescharacteristic
630C2C2×#41×D911yescharacteristic
631C2D9×2−1+411yescharacteristic
subgroupG/H
centerC22C24×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC9×#557C2
prime radical#63457C22
hypercenter#557D9
hypocenterC9#3523
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ #557

Complements

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

NH ≅ G/Ntype
1. C9×#557C2semidirect
2. #10589833C2semidirect
3. #10589830C2semidirect
4. #10589829C2semidirect
5. #10589829C2semidirect
6. #10589798C2semidirect
7. #10589795C2semidirect
9. #10589787C2semidirect
10. #10589686C2semidirect
11. #10589683C2semidirect
13. #10589680C2semidirect
14. #10589674C2semidirect
15. C4×Q8×D9C2semidirect
16. #10589670C2semidirect
17. #10589669C2semidirect
269. #557D9semidirect
565. C9#3523semidirect

Maximal subgroups

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

subgroupindex
C9×#5572
#105898332
#105898302
#105898292
#105897982
#105897952
#105897932
#105897872
#105896862
#105896832
#105896822
#105896802
#105896742
C4×Q8×D92
#105896702
#105896692
#870253