Finite Group Databasebeta

← #11901737

Subgroups — #11901737

Order 1152.

1560 conjugacy classes of subgroups.

The subgroup lattice has 609 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C9×#41C211yesmaximal, characteristic, complemented
2#10589934C211yesmaximal, characteristic, complemented
3#10589930C211yesmaximal, characteristic, complemented
4#10589685C212yesmaximal, complemented
5#10589684C212yesmaximal, complemented
6#10589666C214yesmaximal, complemented
7#10589664C212yesmaximal, complemented
8#10589663C212yesmaximal, complemented
9#10589662C214yesmaximal, complemented
10#10589630C214yesmaximal, complemented
11#10589626C211yesmaximal, characteristic, complemented
12#10589619C211yesmaximal, characteristic, complemented
13#10589581C214yesmaximal, complemented
14C4×#3697C211yesmaximal, characteristic, complemented
15C2×#63434C211yesmaximal, characteristic, complemented
16#85837—31nomaximal
17C2×C9×#41C2211yescharacteristic
18C2×#3697C2211yescharacteristic
19C22×C4×D9C2211yescharacteristic
20C4×Q8×C9C2212yescomplemented
21C4×D4×C9C2214yes—
22C4×D4×C9C2212yescomplemented
23C9×#117C2211yescharacteristic
24C9×#117C2212yescomplemented
25C2×C42×C9C2211yescharacteristic
26C2×C42×C9C2212yescomplemented
27#63509C2211yescharacteristic, complemented
28#63508C2212yes—
29#63506C2211yescharacteristic, complemented
30#63502C2211yescharacteristic, complemented
31#63501C2214yes—
32#63500C2212yes—
33#63499C2212yes—
34#63498C2211yescharacteristic, complemented
35#63497C2212yes—
36#63492C2214yes—
37#63491C2214yes—
38#63491C2214yescomplemented
39C4×#611C2214yes—
40C4×#611C2214yes—
41C4×#611C2214yescomplemented
42C2×(C2×D9)⋊C4C2212yes—
43#63488C2211yescharacteristic
44#63486C2214yescomplemented
45C2×Dic9⋊C4C2212yes—
46C2×C4×Dic9C2211yescharacteristic
47#63460C2214yes—
48#63459C2212yes—
49#63458C2214yescomplemented
50#63457C2212yes—
51#63456C2214yes—
52#63452C2212yescomplemented
53#63451C2214yescomplemented
54#63450C2212yescomplemented
55#63448C2212yes—
56#63447C2214yes—
57#63446C2214yes—
58#63445C2214yescomplemented
59#63444C2212yes—
60#63441C2214yescomplemented
61#63440C2214yes—
62#63438C2214yes—
63#63438C2214yescomplemented
64#63437C2214yes—
65C4×D36C2214yes—
66C4×D36C2212yescomplemented
67#63434C2212yes—
68#63434C2212yes—
69#63434C2212yes—
70#63434C2212yes—
71#63434C2212yescomplemented
72C42×D9C2212yescomplemented
73#63432C2214yescomplemented
74C4×Dic18C2212yescomplemented
75C4×Dic18C2214yescomplemented
76C3×C4×#41D311yescharacteristic
77#5832—31no—
78#5828—31no—
79#5583—32no—
80#5582—32no—
81#5564—34no—
82#5562—32no—
83#5561—32no—
84#5560—34no—
85#5528—34no—
86#5524—31no—
87#5517—31no—
88#5479—34no—
89C4×#235—31no—
90C2×#872—31no—
91C23×D9C2311yescharacteristic
92C9×#41—24no—
93C2×Q8×C9C2311yescharacteristic
94C2×D4×C9C2312yes—
95C2×D4×C9C2311yescharacteristic
96C22×C4×C9C2312yes—
97C22×C4×C9C2312yes—
98C22×C4×C9C2314yes—
99C22×C4×C9C2311yescharacteristic
100C2×#611C2312yes—
101C2×#611C2314yes—
102C2×#611C2314yes—
103C22×Dic9C2311yescharacteristic
104C22×Dic9C2312yes—
105#3697—24no—
106C2×D36C2311yescharacteristic
107C2×D36C2314yes—
108C2×C4×D9—24no—
109C2×C4×D9C2312yes—
110C2×C4×D9C2312yes—
111C2×C4×D9C2312yes—
112C2×C4×D9C2314yes—
113C2×Dic18C2311yescharacteristic
114C2×Dic18C2314yes—
115C9×C4⋊C4C2312yes—
116C9×C4⋊C4C2314yes—
117C9×C22⋊C4C2312yes—
118C9×C22⋊C4C2314yes—
119C42×C9C2311yescharacteristic
120C42×C9C2311yescharacteristic
121C42×C9C2312yes—
122C42×C9C2312yes—
123C42×C9C2314yes—
124#3676C2312yes—
125#3676C2314yes—
126#3676C2314yes—
127(C2×D9)⋊C4C2312yes—
128(C2×D9)⋊C4C2312yes—
129(C2×D9)⋊C4C2312yes—
130(C2×D9)⋊C4C2312yes—
131(C2×D9)⋊C4C2314yes—
132(C2×D9)⋊C4C2314yes—
133(C2×D9)⋊C4C2314yes—
134(C2×D9)⋊C4C2314yes—
135(C2×D9)⋊C4C2314yes—
136C4⋊Dic9C2312yes—
137C4⋊Dic9C2314yes—
138C4⋊Dic9C2314yes—
139Dic9⋊C4C2314yes—
140Dic9⋊C4C2314yes—
141Dic9⋊C4C2314yes—
142Dic9⋊C4C2314yes—
143Dic9⋊C4C2312yes—
144Dic9⋊C4C2314yes—
145Dic9⋊C4C2312yes—
146Dic9⋊C4C2312yes—
147Dic9⋊C4C2312yes—
148C4×Dic9C2312yes—
149C4×Dic9C2314yes—
150C4×Dic9C2312yes—
151C4×Dic9C2311yescharacteristic
152C4×Dic9C2311yescharacteristic
153#3455—91noSylow
154C2×C3×#41C2×D311yescharacteristic
155C2×#235—31no—
156C22×C4×D3—31no—
157C3×C4×Q8C2×D312yes—
158C3×C4×D4C2×D314yes—
159C3×C4×D4C2×D312yes—
160C3×#117C2×D311yescharacteristic
161C3×#117C2×D312yes—
162C2×C3×C42C2×D311yescharacteristic
163C2×C3×C42C2×D312yes—
164#947—31no—
165#946—32no—
166#944—31no—
167#940—31no—
168#939—34no—
169#938—32no—
170#937—32no—
171#936—31no—
172#935—32no—
173#930—34no—
174#929—34no—
175#929—34no—
176C4×#67—34no—
177C4×#67—34no—
178C4×#67—34no—
179C2×(C2×D3)⋊C4—32no—
180#926—31no—
181#924—34no—
182C2×Dic3⋊C4—32no—
183C2×C4×Dic3—31no—
184#898—34no—
185#897—32no—
186#896—34no—
187#895—32no—
188#894—34no—
189#890—32no—
190#889—34no—
191#888—32no—
192#886—32no—
193#885—34no—
194#884—34no—
195#883—34no—
196#882—32no—
197#879—34no—
198#878—34no—
199#876—34no—
200#876—34no—
201#875—34no—
202C4×D12—32no—
203C4×D12—34no—
204#872—32no—
205#872—32no—
206#872—32no—
207#872—32no—
208#872—32no—
209C42×D3—32no—
210#870—34no—
211C4×Dic6—32no—
212C4×Dic6—34no—
213C23×C9C2412yes—
214C23×C9C2411yescharacteristic
215C22×D9—22no—
216C22×D9—42no—
217C22×D9C2412yes—
218C22×D9C2412yes—
219Q8×C9—22no—
220D4×C9—24no—
221D4×C9—22no—
222C2×C4×C9—24no—
223C2×C4×C9—44no—
224C2×C4×C9—42no—
225C2×C4×C9#4114yes—
226C2×C4×C9C2412yes—
227C2×C4×C9C2412yes—
228C2×C4×C9C2412yes—
229C2×C4×C9C2414yes—
230C2×C4×C9C2411yescharacteristic
231C2×C4×C9C2411yescharacteristic
232#611—24no—
233#611—44no—
234#611—44no—
235C2×Dic9—22no—
236C2×Dic9—42no—
237C2×Dic9C2412yes—
238C2×Dic9C2412yes—
239C2×Dic9C2414yes—
240C2×Dic9C2412yes—
241C2×Dic9C2412yes—
242D36—22no—
243D36—44no—
244C4×D9—24no—
245C4×D9—24no—
246C4×D9—24no—
247C4×D9—44no—
248Dic18—22no—
249Dic18—44no—
250#542—92no—
251#542—92no—
252#541—92no—
253#540—92no—
254#539—94no—
255#538—94no—
256#533—91no—
257#532—91no—
258#529—94no—
259#529—94no—
260#525—91no—
261#525—91no—
262C4×#41—91no—
263C4×#41D911yescharacteristic, complemented
264C2×#117—91no—
265C23×D3—31no—
266C3×#41—24no—
267C2×C3×Q8C22×D311yescharacteristic
268C2×C3×D4C22×D312yes—
269C2×C3×D4C22×D311yescharacteristic
270C22×C3×C4C22×D312yes—
271C22×C3×C4C22×D312yes—
272C22×C3×C4C22×D314yes—
273C22×C3×C4C22×D311yescharacteristic
274C2×#67—32no—
275C2×#67—34no—
276C2×#67—34no—
277C22×Dic3—31no—
278C22×Dic3—32no—
279#235—64no—
280C2×D12—31no—
281C2×D12—34no—
282C2×C4×D3—32no—
283C2×C4×D3—32no—
284C2×C4×D3—32no—
285C2×C4×D3—34no—
286C2×C4×D3—64no—
287C2×Dic6—31no—
288C2×Dic6—34no—
289C3×C4⋊C4C22×D312yes—
290C3×C4⋊C4C22×D314yes—
291C3×C22⋊C4C22×D312yes—
292C3×C22⋊C4C22×D314yes—
293C3×C42C22×D312yes—
294C3×C42C22×D312yes—
295C3×C42C22×D314yes—
296C3×C42C22×D311yescharacteristic
297C3×C42C22×D311yescharacteristic
298#217—32no—
299#217—34no—
300#217—34no—
301(C2×D3)⋊C4—32no—
302(C2×D3)⋊C4—32no—
303(C2×D3)⋊C4—32no—
304(C2×D3)⋊C4—32no—
305(C2×D3)⋊C4—34no—
306(C2×D3)⋊C4—34no—
307(C2×D3)⋊C4—34no—
308(C2×D3)⋊C4—34no—
309(C2×D3)⋊C4—34no—
310C4⋊Dic3—34no—
311C4⋊Dic3—32no—
312C4⋊Dic3—34no—
313Dic3⋊C4—34no—
314Dic3⋊C4—34no—
315Dic3⋊C4—34no—
316Dic3⋊C4—32no—
317Dic3⋊C4—34no—
318Dic3⋊C4—34no—
319Dic3⋊C4—32no—
320Dic3⋊C4—32no—
321Dic3⋊C4—32no—
322C4×Dic3—32no—
323C4×Dic3—32no—
324C4×Dic3—34no—
325C4×Dic3—31no—
326C4×Dic3—31no—
327C22×C9—22no—
328C22×C9—22no—
329C22×C9—24no—
330C22×C9C2×#4112yes—
331C22×C9C2511yescharacteristic
332C2×D9—22no—
333C2×D9—22no—
334C2×D9—24no—
335C2×D9—22no—
336C2×D9—22no—
337C2×D9—44no—
338C4×C9—22no—
339C4×C9—24no—
340C4×C9—22no—
341C4×C9—22no—
342C4×C9C2×#4112yes—
343C4×C9C2×#4112yes—
344Dic9—22no—
345Dic9—22no—
346Dic9—22no—
347Dic9—24no—
348Dic9—22no—
349C2×#41—91no—
350C2×#41C2×D911yescharacteristic
351C23×C4—91no—
352C4⋊Q8—91no—
353C4⋊Q8—92no—
354#127—91no—
355#126—94no—
356#126—94no—
357#126—94no—
358#126—94no—
359#125—94no—
360#125—92no—
361#125—94no—
362#124—91no—
363#124—91no—
364#124—94no—
365#124—94no—
366#123—92no—
367#123—94no—
368#123—94no—
369#123—94no—
370#123—92no—
371#123—94no—
372C22⋊Q8—92no—
373C22⋊Q8—94no—
374C22⋊Q8—92no—
375C22⋊Q8—94no—
376C22⋊Q8—94no—
377#121—92no—
378#121—94no—
379#121—94no—
380#121—92no—
381#121—94no—
382#120—92no—
383#120—92no—
384C4×Q8—92no—
385C4×Q8—94no—
386C4×Q8C2×D912yescomplemented
387C4×D4—94no—
388C4×D4—94no—
389C4×D4—94no—
390C4×D4—92no—
391C4×D4—94no—
392C4×D4C2×D914yes—
393C4×D4C2×D912yescomplemented
394#117—91no—
395#117—92no—
396#117—92no—
397#117—92no—
398#117—92no—
399#117—92no—
400#117C2×D911yescharacteristic
401#117C2×D912yescomplemented
402C2×C4⋊C4—92no—
403C2×C22⋊C4—92no—
404C2×C42—91no—
405C2×C42—92no—
406C2×C42C2×D911yescharacteristic
407C2×C42C2×D912yescomplemented
408C23×C3C23×D312yes—
409C23×C3C23×D311yescharacteristic
410C22×D3—32no—
411C22×D3—32no—
412C22×D3—62no—
413C22×D3—122no—
414C3×Q8—22no—
415C3×D4—24no—
416C3×D4—22no—
417C2×C3×C4—24no—
418C2×C3×C4—44no—
419C2×C3×C4—42no—
420C2×C3×C4#23514yes—
421C2×C3×C4C23×D312yes—
422C2×C3×C4C23×D312yes—
423C2×C3×C4C23×D312yes—
424C2×C3×C4C23×D314yes—
425C2×C3×C4C23×D311yescharacteristic
426C2×C3×C4C23×D311yescharacteristic
427#67—64no—
428#67—124no—
429#67—124no—
430C2×Dic3—32no—
431C2×Dic3—32no—
432C2×Dic3—34no—
433C2×Dic3—32no—
434C2×Dic3—32no—
435C2×Dic3—62no—
436C2×Dic3—122no—
437D12—62no—
438D12—124no—
439C4×D3—64no—
440C4×D3—64no—
441C4×D3—64no—
442C4×D3—124no—
443Dic6—62no—
444Dic6—124no—
445C2×C9—22no—
446C2×C9—42no—
447C2×C9C22×#4111yescharacteristic
448C2×C9#58512yes—
449D9—42no—
450D9—42no—
451C24—91no—
452#41—24no—
453#41—184no—
454C2×Q8—91no—
455C2×Q8—94no—
456C2×Q8C22×D911yescharacteristic
457C2×D4—92no—
458C2×D4—94no—
459C2×D4—94no—
460C2×D4—91no—
461C2×D4—94no—
462C2×D4C22×D912yes—
463C2×D4C22×D911yescharacteristic
464C22×C4—91no—
465C22×C4—92no—
466C22×C4—92no—
467C22×C4—92no—
468C22×C4—92no—
469C22×C4—94no—
470C22×C4—184no—
471C22×C4C22×D912yes—
472C22×C4C22×D912yes—
473C22×C4C22×D914yes—
474C22×C4C22×D911yescharacteristic
475C4⋊C4—92no—
476C4⋊C4—92no—
477C4⋊C4—92no—
478C4⋊C4—92no—
479C4⋊C4—92no—
480C4⋊C4—94no—
481C4⋊C4—94no—
482C4⋊C4—94no—
483C4⋊C4—94no—
484C4⋊C4—94no—
485C4⋊C4—94no—
486C4⋊C4—94no—
487C4⋊C4C22×D912yes—
488C4⋊C4C22×D914yes—
489C22⋊C4—92no—
490C22⋊C4—94no—
491C22⋊C4—94no—
492C22⋊C4—92no—
493C22⋊C4—92no—
494C22⋊C4—92no—
495C22⋊C4—92no—
496C22⋊C4—94no—
497C22⋊C4—94no—
498C22⋊C4—94no—
499C22⋊C4—94no—
500C22⋊C4—94no—
501C22⋊C4C22×D912yes—
502C22⋊C4C22×D914yes—
503C42—91no—
504C42—91no—
505C42—94no—
506C42—92no—
507C42—92no—
508C42C22×D912yes—
509C42C22×D914yes—
510C42C22×D911yescharacteristic
511C42C22×D911yescharacteristic
512C42C22×D912yes—
513C22×C3—22no—
514C22×C3—22no—
515C22×C3—24no—
516C22×C3C2×#23512yes—
517C22×C3C24×D311yescharacteristic
518C2×D3—62no—
519C2×D3—62no—
520C2×D3—64no—
521C2×D3—62no—
522C2×D3—62no—
523C2×D3—124no—
524C3×C4—22no—
525C3×C4—24no—
526C3×C4—22no—
527C3×C4—22no—
528C3×C4C2×#23512yes—
529C3×C4C2×#23512yes—
530Dic3—62no—
531Dic3—62no—
532Dic3—62no—
533Dic3—64no—
534Dic3—62no—
535C9#345511yescharacteristic, complemented, Sylow
536C23—92no—
537C23—92no—
538C23—182no—
539C23—362no—
540C23C23×D912yes—
541C23C23×D911yescharacteristic
542Q8—22no—
543Q8—182no—
544Q8—364no—
545D4—24no—
546D4—22no—
547D4—184no—
548D4—182no—
549D4—364no—
550D4—364no—
551D4—364no—
552C2×C4—24no—
553C2×C4—42no—
554C2×C4—44no—
555C2×C4—92no—
556C2×C4—92no—
557C2×C4—94no—
558C2×C4—92no—
559C2×C4—92no—
560C2×C4—182no—
561C2×C4—184no—
562C2×C4—184no—
563C2×C4—184no—
564C2×C4—364no—
565C2×C4—362no—
566C2×C4#369714yes—
567C2×C4C23×D912yes—
568C2×C4C23×D912yes—
569C2×C4C23×D912yes—
570C2×C4C23×D914yes—
571C2×C4C23×D911yescharacteristic
572C2×C4C23×D911yescharacteristic
573C2×C3—22no—
574C2×C3—42no—
575C2×C3C22×#23511yescharacteristic
576C2×C3#596412yes—
577D3—122no—
578D3—122no—
579C22—22no—
580C22—22no—
581C22—24no—
582C22—182no—
583C22—182no—
584C22—184no—
585C22—182no—
586C22—182no—
587C22—364no—
588C22C2×#369712yes—
589C22C24×D911yescharacteristic
590C4—22no—
591C4—22no—
592C4—22no—
593C4—24no—
594C4—182no—
595C4—182no—
596C4—182no—
597C4—184no—
598C4—182no—
599C4C2×#369712yes—
600C4C2×#369712yes—
601C3#8583711yescharacteristic
602C2—22no—
603C2—42no—
604C2—362no—
605C2—362no—
606C2C22×#369711yescharacteristic
607C2#1059313912yes—
subgroupG/H
centerC2×C4C23×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC4×C9×#41C2
hypercenterC4×#41D9
hypocenterC9#3455
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C2×C4 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. C4×C9×#41C2semidirect
2. #10589934C2semidirect
3. #10589930C2semidirect
4. #10589685C2semidirect
5. #10589684C2semidirect
6. #10589666C2semidirect
7. #10589664C2semidirect
8. #10589663C2semidirect
9. #10589662C2semidirect
10. #10589630C2semidirect
11. #10589626C2semidirect
12. #10589619C2semidirect
13. #10589581C2semidirect
14. C4×#3697C2semidirect
15. C2×#63434C2semidirect
20. C4×Q8×C9C22semidirect
22. C4×D4×C9C22semidirect
24. C9×#117C22semidirect
26. C2×C42×C9C22semidirect
27. #63509C22semidirect
29. #63506C22semidirect
30. #63502C22semidirect
34. #63498C22semidirect
38. #63491C22semidirect
41. C4×#611C22semidirect
44. #63486C22semidirect
49. #63458C22semidirect
52. #63452C22semidirect
53. #63451C22semidirect
54. #63450C22semidirect
58. #63445C22semidirect
60. #63441C22semidirect
63. #63438C22semidirect
66. C4×D36C22semidirect
71. #63434C22semidirect
72. C42×D9C22semidirect
73. #63432C22semidirect
74. C4×Dic18C22semidirect
75. C4×Dic18C22semidirect
263. C4×#41D9semidirect
386. C4×Q8C2×D9semidirect
393. C4×D4C2×D9semidirect
401. #117C2×D9semidirect
407. C2×C42C2×D9semidirect
535. C9#3455semidirect

Maximal subgroups

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

subgroupindex
C4×C9×#412
#105899342
#105899302
#105896852
#105896842
#105896662
#105896642
#105896632
#105896622
#105896302
#105896262
#105896192
#105895812
C4×#36972
C2×#634342
#858373