Finite Group Databasebeta

← #11909866

Subgroups — #11909866

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×#556C211yesmaximal, characteristic, complemented
2#10589830C211yesmaximal, characteristic, complemented
3#10589823C211yesmaximal, characteristic, complemented
4#10589810C214yesmaximal, complemented
5#10589803C214yesmaximal, complemented
6#10589782C212yesmaximal
7#10589773C212yesmaximal, complemented
8#10589734C212yesmaximal, complemented
9#10589727C212yesmaximal, complemented
10#10589680C212yesmaximal, complemented
11C4×Q8×D9C211yesmaximal, characteristic, complemented
12#10589671C212yesmaximal, complemented
13#10589669C211yesmaximal, characteristic, complemented
14#10589659C211yesmaximal, characteristic
15D4×Dic18C211yesmaximal, characteristic, complemented
16#10589631C212yesmaximal, complemented
17#10589618C212yesmaximal, complemented
18#86993—31nomaximal
19C2×Q8×D9C2211yescharacteristic
20C22×Dic18C2212yes—
21C9×C4⋊Q8C2211yescharacteristic
22C9×#126C2214yes—
23C9×#124C2212yes—
24C9×C22⋊Q8C2212yes—
25C4×Q8×C9C2211yescharacteristic
26C4×Q8×C9C2212yes—
27C4×D4×C9C2211yescharacteristic
28C9×#117C2212yes—
29#63508C2212yes—
30Q8×Dic9C2211yescharacteristic
31Q8×Dic9C2212yes—
32Q8×Dic9C2212yes—
33#63506C2212yes—
34#63506C2212yes—
35#63500C2211yescharacteristic
36#63498C2211yescharacteristic
37D4×Dic9C2212yes—
38C4×#611C2212yes—
39#63488C2212yes—
40#63486C2212yes—
41#63459C2212yes—
42#63459C2211yescharacteristic
43#63458C2214yes—
44#63454C2212yes—
45C4⋊C4×D9C2212yes—
46C4⋊C4×D9C2211yescharacteristic
47#63452C2214yes—
48#63452C2212yes—
49#63452C2212yes—
50#63452C2211yescharacteristic
51#63451C2214yes—
52#63451C2214yes—
53#63451C2214yes—
54#63450C2214yes—
55#63450C2212yes—
56#63449C2212yes—
57#63449C2212yes—
58#63449C2212yes—
59#63449C2211yescharacteristic
60#63449C2212yes—
61#63445C2214yes—
62#63445C2212yes—
63#611⋊C4C2214yes—
64#63441C2214yes—
65#63441C2214yes—
66#63441C2214yes—
67#63441C2212yes—
68#63440C2214yes—
69#63440C2214yes—
70#63439C2214yes—
71#63439C2214yes—
72#63434C2214yes—
73C42×D9C2212yes—
74C42×D9C2211yescharacteristic
75#63432C2212yes—
76#63432C2214yes—
77#63431C2211yescharacteristic
78C4×Dic18C2212yes—
79C4×Dic18C2212yes—
80C4×Dic18C2214yes—
81C4×Dic18C2214yes—
82C4×Dic18C2211yescharacteristic
83C4×Dic18C2211yescharacteristic
84C3×#556D311yescharacteristic
85#5728—31no—
86#5721—31no—
87#5708—34no—
88#5701—34no—
89#5680—32no—
90#5671—32no—
91#5632—32no—
92#5625—32no—
93#5578—32no—
94C4×D3×Q8—31no—
95#5569—32no—
96#5567—31no—
97#5557—31no—
98D4×Dic6—31no—
99#5529—32no—
100#5516—32no—
101C2×Q8×C9C2311yescharacteristic
102C2×Q8×C9C2312yes—
103C2×D4×C9C2311yescharacteristic
104C22×C4×C9C2312yes—
105C2×#611C2312yes—
106C22×Dic9C2314yes—
107Q8×D9—24no—
108C2×C4×D9C2311yescharacteristic
109C2×C4×D9C2311yescharacteristic
110C2×C4×D9C2312yes—
111C2×C4×D9C2312yes—
112C2×C4×D9C2311yescharacteristic
113C2×Dic18—28no—
114C2×Dic18C2311yescharacteristic
115C2×Dic18C2312yes—
116C2×Dic18C2314yes—
117C2×Dic18C2312yes—
118C2×Dic18C2311yescharacteristic
119C9×C4⋊C4C2311yescharacteristic
120C9×C4⋊C4C2312yes—
121C9×C4⋊C4C2311yescharacteristic
122C9×C4⋊C4C2314yes—
123C9×C4⋊C4C2312yes—
124C9×C4⋊C4C2312yes—
125C9×C22⋊C4C2314yes—
126C9×C22⋊C4C2312yes—
127C9×C22⋊C4C2314yes—
128C42×C9C2314yes—
129C42×C9C2311yescharacteristic
130C42×C9C2312yes—
131#3676C2312yes—
132#3676C2312yes—
133#3676C2312yes—
134#3676C2314yes—
135(C2×D9)⋊C4C2312yes—
136(C2×D9)⋊C4C2314yes—
137C4⋊Dic9C2312yes—
138C4⋊Dic9C2312yes—
139C4⋊Dic9C2312yes—
140C4⋊Dic9C2311yescharacteristic
141C4⋊Dic9C2312yes—
142C4⋊Dic9C2311yescharacteristic
143C4⋊Dic9C2314yes—
144C4⋊Dic9C2314yes—
145C4⋊Dic9C2312yes—
146Dic9⋊C4C2312yes—
147Dic9⋊C4C2314yes—
148Dic9⋊C4C2314yes—
149Dic9⋊C4C2314yes—
150Dic9⋊C4C2314yes—
151Dic9⋊C4C2314yes—
152Dic9⋊C4C2312yes—
153Dic9⋊C4C2314yes—
154Dic9⋊C4C2312yes—
155Dic9⋊C4C2312yes—
156Dic9⋊C4C2312yes—
157Dic9⋊C4C2314yes—
158C4×Dic9C2311yescharacteristic
159C4×Dic9C2312yes—
160C4×Dic9C2312yes—
161C4×Dic9C2311yescharacteristic
162C4×Dic9C2314yes—
163C4×Dic9C2314yes—
164C4×Dic9C2312yes—
165C4×Dic9C2312yes—
166C4×Dic9C2314yes—
167C4×Dic9C2311yescharacteristic
168#3523—91noSylow
169C2×D3×Q8—31no—
170C22×Dic6—32no—
171C3×C4⋊Q8C2×D311yescharacteristic
172C3×#126C2×D314yes—
173C3×#124C2×D312yes—
174C3×C22⋊Q8C2×D312yes—
175C3×C4×Q8C2×D311yescharacteristic
176C3×C4×Q8C2×D312yes—
177C3×C4×D4C2×D311yescharacteristic
178C3×#117C2×D312yes—
179#946—32no—
180Q8×Dic3—32no—
181Q8×Dic3—32no—
182Q8×Dic3—31no—
183#944—32no—
184#944—32no—
185#938—31no—
186#936—31no—
187D4×Dic3—32no—
188C4×#67—32no—
189#926—32no—
190#924—32no—
191#897—32no—
192#897—31no—
193#896—34no—
194#892—32no—
195D3×C4⋊C4—32no—
196D3×C4⋊C4—31no—
197#890—32no—
198#890—34no—
199#890—32no—
200#890—31no—
201#889—34no—
202#889—34no—
203#889—34no—
204#888—34no—
205#888—32no—
206#887—32no—
207#887—32no—
208#887—32no—
209#887—31no—
210#887—32no—
211#883—34no—
212#883—32no—
213#67⋊C4—34no—
214#879—34no—
215#879—34no—
216#879—34no—
217#879—32no—
218#878—34no—
219#878—34no—
220#877—34no—
221#877—34no—
222#872—34no—
223C42×D3—32no—
224C42×D3—31no—
225#870—32no—
226#870—34no—
227#869—31no—
228C4×Dic6—32no—
229C4×Dic6—32no—
230C4×Dic6—34no—
231C4×Dic6—34no—
232C4×Dic6—31no—
233C4×Dic6—31no—
234C23×C9C2412yes—
235C22×D9C2411yescharacteristic
236Q8×C9—22no—
237Q8×C9—24no—
238D4×C9—22no—
239C2×C4×C9—24no—
240C2×C4×C9C2412yes—
241C2×C4×C9C2414yes—
242C2×C4×C9C2411yescharacteristic
243C2×C4×C9C2412yes—
244C2×C4×C9C2412yes—
245C2×C4×C9C2411yescharacteristic
246C2×C4×C9C2411yescharacteristic
247#611—24no—
248C2×Dic9—28no—
249C2×Dic9C2411yescharacteristic
250C2×Dic9C2411yescharacteristic
251C2×Dic9C2412yes—
252C2×Dic9C2412yes—
253C2×Dic9C2412yes—
254C2×Dic9C2414yes—
255C2×Dic9C2411yescharacteristic
256C2×Dic9C2412yes—
257C4×D9—24no—
258C4×D9—22no—
259C4×D9—22no—
260C4×D9—22no—
261C4×D9—24no—
262Dic18—24no—
263Dic18—22no—
264Dic18—28no—
265Dic18—24no—
266Dic18#4114yes—
267#557—91no—
268#557—91no—
269#557—92no—
270#556—92no—
271#556D911yescharacteristic, complemented
272#552—94no—
273#552—92no—
274D4×Q8—92no—
275D4×Q8—91no—
276#541—94no—
277#541—92no—
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×D4C22×D311yescharacteristic
287C22×C3×C4C22×D312yes—
288C2×#67—32no—
289C22×Dic3—34no—
290D3×Q8—64no—
291C2×C4×D3—31no—
292C2×C4×D3—32no—
293C2×C4×D3—32no—
294C2×C4×D3—31no—
295C2×C4×D3—31no—
296C2×Dic6—31no—
297C2×Dic6—31no—
298C2×Dic6—34no—
299C2×Dic6—32no—
300C2×Dic6—32no—
301C2×Dic6—68no—
302C3×C4⋊C4C22×D311yescharacteristic
303C3×C4⋊C4C22×D312yes—
304C3×C4⋊C4C22×D312yes—
305C3×C4⋊C4C22×D311yescharacteristic
306C3×C4⋊C4C22×D314yes—
307C3×C4⋊C4C22×D312yes—
308C3×C22⋊C4C22×D314yes—
309C3×C22⋊C4C22×D312yes—
310C3×C22⋊C4C22×D314yes—
311C3×C42C22×D311yescharacteristic
312C3×C42C22×D312yes—
313C3×C42C22×D314yes—
314#217—32no—
315#217—32no—
316#217—32no—
317#217—34no—
318(C2×D3)⋊C4—32no—
319(C2×D3)⋊C4—34no—
320C4⋊Dic3—32no—
321C4⋊Dic3—32no—
322C4⋊Dic3—32no—
323C4⋊Dic3—31no—
324C4⋊Dic3—32no—
325C4⋊Dic3—31no—
326C4⋊Dic3—32no—
327C4⋊Dic3—34no—
328C4⋊Dic3—34no—
329Dic3⋊C4—32no—
330Dic3⋊C4—34no—
331Dic3⋊C4—32no—
332Dic3⋊C4—34no—
333Dic3⋊C4—34no—
334Dic3⋊C4—32no—
335Dic3⋊C4—34no—
336Dic3⋊C4—32no—
337Dic3⋊C4—32no—
338Dic3⋊C4—34no—
339Dic3⋊C4—34no—
340Dic3⋊C4—34no—
341C4×Dic3—32no—
342C4×Dic3—32no—
343C4×Dic3—31no—
344C4×Dic3—34no—
345C4×Dic3—34no—
346C4×Dic3—34no—
347C4×Dic3—32no—
348C4×Dic3—31no—
349C4×Dic3—32no—
350C4×Dic3—31no—
351C22×C9—22no—
352C22×C9—22no—
353C22×C9—22no—
354C22×C9C2511yescharacteristic
355C2×D9—21no—
356C2×D9—21no—
357C2×D92−1+412yes—
358C4×C9—22no—
359C4×C9—22no—
360C4×C9—22no—
361C4×C9—21no—
362C4×C9—24no—
363C4×C9C2×#4112yes—
364C4×C92−1+412yes—
365Dic9—21no—
366Dic9—24no—
367Dic9—22no—
368Dic9—21no—
369Dic9—21no—
370Dic9—22no—
371Dic9—22no—
372Dic9C2×#4114yes—
373C22×Q8—91no—
374C22×Q8—92no—
375C4⋊Q8—92no—
376C4⋊Q8—92no—
377C4⋊Q8—92no—
378C4⋊Q8—94no—
379C4⋊Q8—91no—
380C4⋊Q8C2×D911yescharacteristic
381#126—94no—
382#126—92no—
383#126—94no—
384#126—94no—
385#126C2×D914yes—
386#125—91no—
387#125—94no—
388#125—92no—
389#125—94no—
390#125—94no—
391#125—94no—
392#125—92no—
393#125—92no—
394#125—94no—
395#124—91no—
396#124C2×D912yes—
397#123—92no—
398#123—94no—
399C22⋊Q8—92no—
400C22⋊Q8—92no—
401C22⋊Q8—91no—
402C22⋊Q8—94no—
403C22⋊Q8—92no—
404C22⋊Q8—94no—
405C22⋊Q8—94no—
406C22⋊Q8C2×D912yes—
407#121—91no—
408C4×Q8—91no—
409C4×Q8—92no—
410C4×Q8—92no—
411C4×Q8—91no—
412C4×Q8—92no—
413C4×Q8—92no—
414C4×Q8—92no—
415C4×Q8—92no—
416C4×Q8—91no—
417C4×Q8—92no—
418C4×Q8—94no—
419C4×Q8—94no—
420C4×Q8—91no—
421C4×Q8—92no—
422C4×Q8C2×D911yescharacteristic
423C4×Q8C2×D912yes—
424C4×D4—92no—
425C4×D4—92no—
426C4×D4—94no—
427C4×D4C2×D911yescharacteristic
428#117—92no—
429#117—92no—
430#117—94no—
431#117—94no—
432#117—94no—
433#117C2×D912yes—
434C2×C4⋊C4—92no—
435C2×C4⋊C4—91no—
436C2×C42—92no—
437C2×C42—91no—
438C23×C3C23×D312yes—
439C22×D3—31no—
440C3×Q8—22no—
441C3×Q8—24no—
442C3×D4—22no—
443C2×C3×C4—24no—
444C2×C3×C4C23×D312yes—
445C2×C3×C4C23×D314yes—
446C2×C3×C4C23×D311yescharacteristic
447C2×C3×C4C23×D312yes—
448C2×C3×C4C23×D312yes—
449C2×C3×C4C23×D311yescharacteristic
450C2×C3×C4C23×D311yescharacteristic
451#67—64no—
452C2×Dic3—32no—
453C2×Dic3—31no—
454C2×Dic3—31no—
455C2×Dic3—32no—
456C2×Dic3—32no—
457C2×Dic3—32no—
458C2×Dic3—34no—
459C2×Dic3—31no—
460C2×Dic3—68no—
461C4×D3—64no—
462C4×D3—64no—
463C4×D3—62no—
464C4×D3—62no—
465C4×D3—62no—
466Dic6—34no—
467Dic6—68no—
468Dic6—64no—
469Dic6—64no—
470Dic6—62no—
471C2×C9—42no—
472C2×C9C22×#4111yescharacteristic
473C2×C9C2×2−1+411yescharacteristic
474C2×C9C2×2−1+411yescharacteristic
475D9—22no—
476C2×Q8—91no—
477C2×Q8—91no—
478C2×Q8—92no—
479C2×Q8—94no—
480C2×Q8—92no—
481C2×Q8—188no—
482C2×Q8—184no—
483C2×Q8C22×D912yes—
484C2×Q8C22×D911yescharacteristic
485C2×D4—92no—
486C2×D4C22×D911yescharacteristic
487C22×C4—94no—
488C22×C4—91no—
489C22×C4—91no—
490C22×C4—92no—
491C22×C4—92no—
492C22×C4—91no—
493C22×C4C22×D912yes—
494C4⋊C4—92no—
495C4⋊C4—92no—
496C4⋊C4—91no—
497C4⋊C4—92no—
498C4⋊C4—92no—
499C4⋊C4—94no—
500C4⋊C4—94no—
501C4⋊C4—92no—
502C4⋊C4—94no—
503C4⋊C4—92no—
504C4⋊C4—94no—
505C4⋊C4—92no—
506C4⋊C4—94no—
507C4⋊C4—92no—
508C4⋊C4—94no—
509C4⋊C4—92no—
510C4⋊C4—91no—
511C4⋊C4—94no—
512C4⋊C4—94no—
513C4⋊C4—92no—
514C4⋊C4—94no—
515C4⋊C4C22×D911yescharacteristic
516C4⋊C4C22×D912yes—
517C4⋊C4C22×D912yes—
518C4⋊C4C22×D912yes—
519C4⋊C4C22×D911yescharacteristic
520C4⋊C4C22×D914yes—
521C22⋊C4—92no—
522C22⋊C4—92no—
523C22⋊C4—94no—
524C22⋊C4—92no—
525C22⋊C4—92no—
526C22⋊C4—94no—
527C22⋊C4C22×D914yes—
528C22⋊C4C22×D914yes—
529C22⋊C4C22×D912yes—
530C42—92no—
531C42—91no—
532C42—92no—
533C42—91no—
534C42—92no—
535C42—91no—
536C42—94no—
537C42—94no—
538C42—94no—
539C42—92no—
540C42C22×D911yescharacteristic
541C42C22×D912yes—
542C42C22×D914yes—
543C22×C3—22no—
544C22×C3—22no—
545C22×C3—22no—
546C22×C3C24×D311yescharacteristic
547C2×D3—32no—
548C2×D3—61no—
549C2×D3—61no—
550C3×C4—22no—
551C3×C4—22no—
552C3×C4—24no—
553C3×C4—22no—
554C3×C4—21no—
555C3×C4D3×#4112yes—
556C3×C4#101012yes—
557Dic3—34no—
558Dic3—61no—
559Dic3—64no—
560Dic3—62no—
561Dic3—61no—
562Dic3—61no—
563Dic3—62no—
564Dic3—62no—
565C9#352311yescharacteristic, complemented, Sylow
566C23—91no—
567C23C23×D912yes—
568Q8—22no—
569Q8—24no—
570Q8—94no—
571Q8—188no—
572Q8—184no—
573Q8—184no—
574Q8—182no—
575D4—22no—
576D4—184no—
577C2×C4—24no—
578C2×C4—92no—
579C2×C4—91no—
580C2×C4—91no—
581C2×C4—92no—
582C2×C4—92no—
583C2×C4—92no—
584C2×C4—91no—
585C2×C4—94no—
586C2×C4—184no—
587C2×C4—184no—
588C2×C4—182no—
589C2×C4—188no—
590C2×C4—182no—
591C2×C4—182no—
592C2×C4C23×D912yes—
593C2×C4C23×D914yes—
594C2×C4C23×D911yescharacteristic
595C2×C4C23×D912yes—
596C2×C4C23×D912yes—
597C2×C4C23×D911yescharacteristic
598C2×C4C23×D911yescharacteristic
599C2×C3—42no—
600C2×C3C2×D3×#4111yescharacteristic
601C2×C3C2×#101011yescharacteristic
602C2×C3D3×2−1+411yescharacteristic
603D3—62no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—92no—
608C22—181no—
609C22—181no—
610C22C24×D911yescharacteristic
611C4—22no—
612C4—22no—
613C4—24no—
614C4—22no—
615C4—21no—
616C4—94no—
617C4—184no—
618C4—181no—
619C4—181no—
620C4—182no—
621C4—181no—
622C4—182no—
623C4—182no—
624C4#41×D912yes—
625C4#6371612yes—
626C3#8699311yescharacteristic
627C2—42no—
628C2—182no—
629C2C2×#41×D911yescharacteristic
630C2C2×#6371611yescharacteristic
631C2D9×2−1+411yescharacteristic
subgroupG/H
centerC22C24×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC9×#556C2
prime radical#63500C22
hypercenter#556D9
hypocenterC9#3523
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ #556

Complements

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

NH ≅ G/Ntype
1. C9×#556C2semidirect
2. #10589830C2semidirect
3. #10589823C2semidirect
4. #10589810C2semidirect
5. #10589803C2semidirect
7. #10589773C2semidirect
8. #10589734C2semidirect
9. #10589727C2semidirect
10. #10589680C2semidirect
11. C4×Q8×D9C2semidirect
12. #10589671C2semidirect
13. #10589669C2semidirect
15. D4×Dic18C2semidirect
16. #10589631C2semidirect
17. #10589618C2semidirect
271. #556D9semidirect
565. C9#3523semidirect

Maximal subgroups

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

subgroupindex
C9×#5562
#105898302
#105898232
#105898102
#105898032
#105897822
#105897732
#105897342
#105897272
#105896802
C4×Q8×D92
#105896712
#105896692
#105896592
D4×Dic182
#105896312
#105896182
#869933