Finite Group Databasebeta

← #11901962

Subgroups — #11901962

Order 1152.

1740 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#534C211yesmaximal, characteristic, complemented
2#10589906C212yesmaximal, complemented
3C2×D4×Dic9C212yesmaximal, complemented
4#10589767C214yesmaximal, complemented
5#10589751C214yesmaximal, complemented
6#10589719C212yesmaximal, complemented
7#10589708C212yesmaximal, complemented
8#10589704C212yesmaximal, complemented
9#10589702C212yesmaximal, complemented
10#10589695C214yesmaximal, complemented
11#10589688C214yesmaximal, complemented
12C2×#611⋊C4C211yesmaximal, characteristic, complemented
13#10589585C211yesmaximal, characteristic, complemented
14#86295—31nomaximal
15C22×D4×C9C2212yes—
16C22×#611C2211yescharacteristic
17C23×Dic9C2211yescharacteristic
18C23×Dic9C2212yescomplemented
19C2×#3699C2212yescomplemented
20C22×C4×D9C2211yescharacteristic, complemented
21C9×#123C2214yescomplemented
22C9×#121C2212yes—
23C9×#121C2212yes—
24C9×#120C2214yescomplemented
25C2×C9×C22⋊C4C2211yescharacteristic
26#63515C2214yescomplemented
27C2×#3676C2212yes—
28C2×#3676C2212yescomplemented
29#63501C2214yes—
30#63501C2214yes—
31#63501C2214yescomplemented
32#63500C2212yescomplemented
33#63499C2214yescomplemented
34#63498C2212yescomplemented
35#63497C2214yescomplemented
36#63497C2214yescomplemented
37D4×Dic9C2214yescomplemented
38D4×Dic9C2212yescomplemented
39D4×Dic9C2214yescomplemented
40D4×Dic9C2214yescomplemented
41D4×Dic9C2214yescomplemented
42#63491C2214yescomplemented
43C2×(C2×D9)⋊C4C2211yescharacteristic, complemented
44C2×C4⋊Dic9C2212yescomplemented
45#63486C2212yescomplemented
46#63486C2212yescomplemented
47C2×Dic9⋊C4C2211yescharacteristic, complemented
48C2×C4×Dic9C2211yescharacteristic, complemented
49C2×C4×Dic9C2212yescomplemented
50#63460C2214yescomplemented
51#63459C2212yescomplemented
52#63454C2212yescomplemented
53#63452C2212yescomplemented
54#63451C2214yescomplemented
55#63449C2212yescomplemented
56#63448C2214yescomplemented
57#63447C2214yescomplemented
58#63445C2214yescomplemented
59#611⋊C4C2214yescomplemented
60#611⋊C4C2214yescomplemented
61#611⋊C4C2214yescomplemented
62#63441C2214yescomplemented
63#63441C2214yescomplemented
64#63440C2214yescomplemented
65#63440C2214yescomplemented
66#63440C2214yescomplemented
67#63439C2214yescomplemented
68C3×#534D311yescharacteristic
69#5804—32no—
70C2×D4×Dic3—32no—
71#5665—34no—
72#5649—34no—
73#5617—32no—
74#5606—32no—
75#5602—32no—
76#5600—32no—
77#5593—34no—
78#5586—34no—
79C2×#67⋊C4—31no—
80#5483—31no—
81C24×C9C2312yes—
82C24×C9C2311yescharacteristic
83C23×D9C2311yescharacteristic
84C2×D4×C9—28no—
85C2×D4×C9C2314yes—
86C2×D4×C9C2314yes—
87C2×D4×C9C2312yes—
88C2×D4×C9C2312yes—
89C22×C4×C9C2312yes—
90C22×C4×C9C2311yescharacteristic
91C22×C4×C9C2311yescharacteristic
92C2×#611—24no—
93C2×#611C2314yes—
94C2×#611C2314yes—
95C2×#611C2314yes—
96C22×Dic9—42no—
97C22×Dic9—44no—
98C22×Dic9C2311yescharacteristic
99C22×Dic9C2314yes—
100C22×Dic9C2312yes—
101C22×Dic9C2311yescharacteristic
102C22×Dic9C2311yescharacteristic
103C22×Dic9C2314yes—
104C22×Dic9C2312yes—
105C22×Dic9C2312yes—
106C22×Dic9C2312yes—
107#3699—44no—
108C2×C4×D9—42no—
109C2×C4×D9C2312yes—
110C2×C4×D9C2312yes—
111C2×Dic18C2312yes—
112C2×Dic18C2312yes—
113C9×C4⋊C4C2312yes—
114C9×C4⋊C4C2312yes—
115C9×C22⋊C4C2314yes—
116C9×C22⋊C4C2314yes—
117C9×C22⋊C4C2314yes—
118#3676C2314yes—
119#3676C2314yes—
120#3676C2314yes—
121#3676C2314yes—
122#3676C2314yes—
123#3676C2314yes—
124(C2×D9)⋊C4C2314yes—
125(C2×D9)⋊C4C2314yes—
126(C2×D9)⋊C4C2314yes—
127C4⋊Dic9C2314yes—
128C4⋊Dic9C2314yes—
129C4⋊Dic9C2312yes—
130C4⋊Dic9C2312yes—
131Dic9⋊C4C2314yes—
132Dic9⋊C4C2314yes—
133Dic9⋊C4C2314yes—
134Dic9⋊C4C2314yes—
135Dic9⋊C4C2314yes—
136C4×Dic9C2314yes—
137C4×Dic9C2314yes—
138C4×Dic9C2312yes—
139C4×Dic9C2312yes—
140#3459—91noSylow
141C22×C3×D4C2×D312yes—
142C22×#67—31no—
143C23×Dic3—31no—
144C23×Dic3—32no—
145C2×#237—32no—
146C22×C4×D3—31no—
147C3×#123C2×D314yes—
148C3×#121C2×D312yes—
149C3×#121C2×D312yes—
150C3×#120C2×D314yes—
151C2×C3×C22⋊C4C2×D311yescharacteristic
152#953—34no—
153C2×#217—32no—
154C2×#217—32no—
155#939—34no—
156#939—34no—
157#939—34no—
158#938—32no—
159#937—34no—
160#936—32no—
161#935—34no—
162#935—34no—
163D4×Dic3—34no—
164D4×Dic3—34no—
165D4×Dic3—34no—
166D4×Dic3—34no—
167D4×Dic3—32no—
168#929—34no—
169C2×(C2×D3)⋊C4—31no—
170C2×C4⋊Dic3—32no—
171#924—32no—
172#924—32no—
173C2×Dic3⋊C4—31no—
174C2×C4×Dic3—32no—
175C2×C4×Dic3—31no—
176#898—34no—
177#897—32no—
178#892—32no—
179#890—32no—
180#889—34no—
181#887—32no—
182#886—34no—
183#885—34no—
184#883—34no—
185#67⋊C4—34no—
186#67⋊C4—34no—
187#67⋊C4—34no—
188#879—34no—
189#879—34no—
190#878—34no—
191#878—34no—
192#878—34no—
193#877—34no—
194C23×C9—24no—
195C23×C9—41no—
196C23×C9—42no—
197C23×C9—41no—
198C23×C9—42no—
199C23×C9#4114yescomplemented
200C23×C9C2414yes—
201C23×C9C2411yescharacteristic
202C23×C9C2412yes—
203C22×D9—22no—
204C22×D9—41no—
205C22×D9—41no—
206C22×D9C2412yes—
207D4×C9—28no—
208D4×C9—28no—
209D4×C9—42no—
210D4×C9—42no—
211C2×C4×C9—24no—
212C2×C4×C9—41no—
213C2×C4×C9—41no—
214C2×C4×C9C2414yes—
215C2×C4×C9C2412yes—
216C2×C4×C9C2412yes—
217#611—28no—
218#611—44no—
219#611—44no—
220C2×Dic9—22no—
221C2×Dic9—22no—
222C2×Dic9—28no—
223C2×Dic9—24no—
224C2×Dic9—42no—
225C2×Dic9—44no—
226C2×Dic9—42no—
227C2×Dic9—41no—
228C2×Dic9—42no—
229C2×Dic9C2412yes—
230C2×Dic9C2414yes—
231C2×Dic9C2412yes—
232C2×Dic9C2411yescharacteristic
233C2×Dic9C2414yes—
234C2×Dic9C2411yescharacteristic
235C4×D9—24no—
236C4×D9—42no—
237Dic18—42no—
238Dic18—42no—
239#543—91no—
240#539—94no—
241#539—92no—
242#538—92no—
243#538—94no—
244#534—92no—
245#534D911yescharacteristic, complemented
246#529—94no—
247#529—92no—
248#525—92no—
249#525—94no—
250C2×C4×D4—92no—
251C2×C4×D4—91no—
252C24×C3C22×D312yes—
253C24×C3C22×D311yescharacteristic
254C23×D3—31no—
255C2×C3×D4—28no—
256C2×C3×D4C22×D314yes—
257C2×C3×D4C22×D314yes—
258C2×C3×D4C22×D312yes—
259C2×C3×D4C22×D312yes—
260C22×C3×C4C22×D312yes—
261C22×C3×C4C22×D311yescharacteristic
262C22×C3×C4C22×D311yescharacteristic
263C2×#67—34no—
264C2×#67—34no—
265C2×#67—34no—
266C2×#67—64no—
267C22×Dic3—34no—
268C22×Dic3—32no—
269C22×Dic3—31no—
270C22×Dic3—31no—
271C22×Dic3—32no—
272C22×Dic3—32no—
273C22×Dic3—34no—
274C22×Dic3—32no—
275C22×Dic3—31no—
276C22×Dic3—122no—
277C22×Dic3—124no—
278#237—124no—
279C2×C4×D3—32no—
280C2×C4×D3—32no—
281C2×C4×D3—122no—
282C2×Dic6—32no—
283C2×Dic6—32no—
284C3×C4⋊C4C22×D312yes—
285C3×C4⋊C4C22×D312yes—
286C3×C22⋊C4C22×D314yes—
287C3×C22⋊C4C22×D314yes—
288C3×C22⋊C4C22×D314yes—
289#217—34no—
290#217—34no—
291#217—34no—
292#217—34no—
293#217—34no—
294#217—34no—
295(C2×D3)⋊C4—34no—
296(C2×D3)⋊C4—34no—
297(C2×D3)⋊C4—34no—
298C4⋊Dic3—32no—
299C4⋊Dic3—32no—
300C4⋊Dic3—34no—
301C4⋊Dic3—34no—
302Dic3⋊C4—34no—
303Dic3⋊C4—34no—
304Dic3⋊C4—34no—
305Dic3⋊C4—34no—
306Dic3⋊C4—34no—
307C4×Dic3—32no—
308C4×Dic3—34no—
309C4×Dic3—32no—
310C4×Dic3—34no—
311C22×C9—22no—
312C22×C9—21no—
313C22×C9—22no—
314C22×C9—21no—
315C22×C9—24no—
316C22×C9—24no—
317C22×C9—24no—
318C22×C9—44no—
319C22×C9—48no—
320C22×C9C2×#4112yes—
321C22×C9C2×#4114yes—
322C22×C9C2511yescharacteristic
323C2×D9—22no—
324C2×D9—22no—
325C2×D9—22no—
326C2×D9—44no—
327C4×C9—24no—
328C4×C9—22no—
329C4×C9—22no—
330Dic9—22no—
331Dic9—24no—
332Dic9—21no—
333Dic9—22no—
334Dic9—24no—
335Dic9H(5,𝔽2)12yes—
336C2×#41—92no—
337C22×D4—91no—
338C22×D4C2×D912yes—
339C23×C4—91no—
340C23×C4—92no—
341C23×C4—91no—
342#126—94no—
343#126—94no—
344#126—94no—
345#125—94no—
346#125—92no—
347#124—92no—
348#124—94no—
349#123—94no—
350#123—94no—
351#123—94no—
352#123—94no—
353#123—94no—
354#123C2×D914yescomplemented
355C22⋊Q8—92no—
356C22⋊Q8—92no—
357C22⋊Q8—92no—
358C22⋊Q8—94no—
359C22⋊Q8—94no—
360C22⋊Q8—94no—
361#121—94no—
362#121—92no—
363#121—94no—
364#121—94no—
365#121C2×D912yes—
366#121C2×D912yes—
367#120—94no—
368#120—94no—
369#120C2×D914yescomplemented
370C4×Q8—92no—
371C4×D4—94no—
372C4×D4—94no—
373C4×D4—94no—
374C4×D4—94no—
375C4×D4—92no—
376C4×D4—94no—
377C4×D4—94no—
378C4×D4—94no—
379#117—92no—
380#117—94no—
381C2×C4⋊C4—91no—
382C2×C4⋊C4—92no—
383C2×C22⋊C4—92no—
384C2×C22⋊C4—92no—
385C2×C22⋊C4—91no—
386C2×C22⋊C4C2×D911yescharacteristic
387C2×C42—91no—
388C2×C42—92no—
389C23×C3—24no—
390C23×C3—41no—
391C23×C3—42no—
392C23×C3—41no—
393C23×C3—42no—
394C23×C3#23714yes—
395C23×C3C23×D314yes—
396C23×C3C23×D311yescharacteristic
397C23×C3C23×D312yes—
398C22×D3—32no—
399C22×D3—62no—
400C22×D3—121no—
401C22×D3—121no—
402C3×D4—28no—
403C3×D4—28no—
404C3×D4—42no—
405C3×D4—42no—
406C2×C3×C4—24no—
407C2×C3×C4—41no—
408C2×C3×C4—41no—
409C2×C3×C4C23×D314yes—
410C2×C3×C4C23×D312yes—
411C2×C3×C4C23×D312yes—
412#67—68no—
413#67—124no—
414#67—124no—
415C2×Dic3—31no—
416C2×Dic3—32no—
417C2×Dic3—34no—
418C2×Dic3—32no—
419C2×Dic3—31no—
420C2×Dic3—34no—
421C2×Dic3—62no—
422C2×Dic3—68no—
423C2×Dic3—64no—
424C2×Dic3—62no—
425C2×Dic3—122no—
426C2×Dic3—122no—
427C2×Dic3—124no—
428C2×Dic3—122no—
429C2×Dic3—121no—
430C4×D3—64no—
431C4×D3—122no—
432Dic6—122no—
433Dic6—122no—
434C2×C9—22no—
435C2×C9—24no—
436C2×C9—44no—
437C2×C9C22×#4111yescharacteristic
438C2×C9C2×H(5,𝔽2)11yescharacteristic
439C2×C9#58511yescharacteristic
440D9—42no—
441C24—91no—
442C24C22×D912yes—
443C24C22×D911yescharacteristic
444#41—364no—
445C2×Q8—92no—
446C2×Q8—92no—
447C2×D4—28no—
448C2×D4—94no—
449C2×D4—94no—
450C2×D4—94no—
451C2×D4—184no—
452C2×D4C22×D914yes—
453C2×D4C22×D914yes—
454C2×D4C22×D912yes—
455C2×D4C22×D912yes—
456C22×C4—91no—
457C22×C4—91no—
458C22×C4—92no—
459C22×C4—94no—
460C22×C4—92no—
461C22×C4—91no—
462C22×C4—92no—
463C22×C4—92no—
464C22×C4—94no—
465C22×C4—92no—
466C22×C4—92no—
467C22×C4—362no—
468C22×C4—362no—
469C22×C4—364no—
470C22×C4C22×D912yes—
471C22×C4C22×D911yescharacteristic
472C22×C4C22×D911yescharacteristic
473C4⋊C4—94no—
474C4⋊C4—94no—
475C4⋊C4—94no—
476C4⋊C4—94no—
477C4⋊C4—92no—
478C4⋊C4—94no—
479C4⋊C4—94no—
480C4⋊C4—92no—
481C4⋊C4—94no—
482C4⋊C4C22×D912yes—
483C4⋊C4C22×D912yes—
484C22⋊C4—94no—
485C22⋊C4—94no—
486C22⋊C4—94no—
487C22⋊C4—94no—
488C22⋊C4—94no—
489C22⋊C4—94no—
490C22⋊C4—94no—
491C22⋊C4—94no—
492C22⋊C4—94no—
493C22⋊C4C22×D914yes—
494C22⋊C4C22×D914yes—
495C22⋊C4C22×D914yes—
496C42—94no—
497C42—92no—
498C42—94no—
499C42—92no—
500C22×C3—22no—
501C22×C3—21no—
502C22×C3—22no—
503C22×C3—21no—
504C22×C3—24no—
505C22×C3—24no—
506C22×C3—24no—
507C22×C3—44no—
508C22×C3—48no—
509C22×C3C2×#23712yes—
510C22×C3C2×#23714yes—
511C22×C3C24×D311yescharacteristic
512C2×D3—62no—
513C2×D3—62no—
514C2×D3—62no—
515C2×D3—124no—
516C3×C4—24no—
517C3×C4—22no—
518C3×C4—22no—
519Dic3—32no—
520Dic3—62no—
521Dic3—64no—
522Dic3—61no—
523Dic3—62no—
524Dic3—64no—
525C9#345911yescharacteristic, complemented, Sylow
526C23—24no—
527C23—41no—
528C23—42no—
529C23—41no—
530C23—42no—
531C23—92no—
532C23—182no—
533C23—361no—
534C23—361no—
535C23#369914yescomplemented
536C23C23×D914yes—
537C23C23×D911yescharacteristic
538C23C23×D912yes—
539Q8—362no—
540Q8—362no—
541D4—28no—
542D4—28no—
543D4—42no—
544D4—42no—
545D4—188no—
546D4—364no—
547D4—364no—
548C2×C4—24no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—91no—
552C2×C4—94no—
553C2×C4—92no—
554C2×C4—91no—
555C2×C4—92no—
556C2×C4—94no—
557C2×C4—184no—
558C2×C4—182no—
559C2×C4—184no—
560C2×C4—188no—
561C2×C4—182no—
562C2×C4—362no—
563C2×C4—361no—
564C2×C4—362no—
565C2×C4—364no—
566C2×C4—362no—
567C2×C4—362no—
568C2×C4C23×D912yes—
569C2×C4C23×D914yes—
570C2×C4C23×D912yes—
571C2×C3—22no—
572C2×C3—24no—
573C2×C3—44no—
574C2×C3C22×#23711yescharacteristic
575C2×C3D3×H(5,𝔽2)11yescharacteristic
576C2×C3#596611yescharacteristic
577D3—122no—
578C22—21no—
579C22—22no—
580C22—21no—
581C22—22no—
582C22—24no—
583C22—24no—
584C22—24no—
585C22—44no—
586C22—48no—
587C22—182no—
588C22—182no—
589C22—182no—
590C22—364no—
591C22C2×#369914yes—
592C22C2×#369912yes—
593C22C24×D911yescharacteristic
594C4—24no—
595C4—22no—
596C4—22no—
597C4—92no—
598C4—182no—
599C4—181no—
600C4—182no—
601C4—184no—
602C4—184no—
603C3#8629511yescharacteristic
604C2—24no—
605C2—22no—
606C2—44no—
607C2—362no—
608C2C22×#369911yescharacteristic
609C2D9×H(5,𝔽2)11yescharacteristic
610C2#1059314111yescharacteristic
subgroupG/H
centerC22C24×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC9×#534C2
hypercenter#534D9
hypocenterC9#3459
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ #534

Complements

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

NH ≅ G/Ntype
1. C9×#534C2semidirect
2. #10589906C2semidirect
3. C2×D4×Dic9C2semidirect
4. #10589767C2semidirect
5. #10589751C2semidirect
6. #10589719C2semidirect
7. #10589708C2semidirect
8. #10589704C2semidirect
9. #10589702C2semidirect
10. #10589695C2semidirect
11. #10589688C2semidirect
12. C2×#611⋊C4C2semidirect
13. #10589585C2semidirect
18. C23×Dic9C22semidirect
19. C2×#3699C22semidirect
20. C22×C4×D9C22semidirect
21. C9×#123C22semidirect
24. C9×#120C22semidirect
26. #63515C22semidirect
28. C2×#3676C22semidirect
31. #63501C22semidirect
32. #63500C22semidirect
33. #63499C22semidirect
34. #63498C22semidirect
35. #63497C22semidirect
36. #63497C22semidirect
37. D4×Dic9C22semidirect
38. D4×Dic9C22semidirect
39. D4×Dic9C22semidirect
40. D4×Dic9C22semidirect
41. D4×Dic9C22semidirect
42. #63491C22semidirect
43. C2×(C2×D9)⋊C4C22semidirect
44. C2×C4⋊Dic9C22semidirect
45. #63486C22semidirect
46. #63486C22semidirect
47. C2×Dic9⋊C4C22semidirect
48. C2×C4×Dic9C22semidirect
49. C2×C4×Dic9C22semidirect
50. #63460C22semidirect
51. #63459C22semidirect
52. #63454C22semidirect
53. #63452C22semidirect
54. #63451C22semidirect
55. #63449C22semidirect
56. #63448C22semidirect
57. #63447C22semidirect
58. #63445C22semidirect
59. #611⋊C4C22semidirect
60. #611⋊C4C22semidirect
61. #611⋊C4C22semidirect
62. #63441C22semidirect
63. #63441C22semidirect
64. #63440C22semidirect
65. #63440C22semidirect
66. #63440C22semidirect
67. #63439C22semidirect
199. C23×C9#41semidirect
245. #534D9semidirect
354. #123C2×D9semidirect
369. #120C2×D9semidirect
525. C9#3459semidirect
535. C23#3699semidirect

Maximal subgroups

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

subgroupindex
C9×#5342
#105899062
C2×D4×Dic92
#105897672
#105897512
#105897192
#105897082
#105897042
#105897022
#105896952
#105896882
C2×#611⋊C42
#105895852
#862953