Finite Group Databasebeta

← D59×#3529 #29495576

Subgroups — D59×#3529 #29495576

Order 15104.

7418 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21438237C213yesmaximal, complemented
2#21438236C211yesmaximal, characteristic, complemented
3#21438235C216yesmaximal, complemented
4#21438234C216yesmaximal, complemented
5#21438233C216yesmaximal, complemented
6#21438232C213yesmaximal, complemented
7#21438231C216yesmaximal, complemented
8#563×D59C213yesmaximal, complemented
9#562×D59C216yesmaximal, complemented
10H(3,𝔽4)×D59C211yesmaximal, characteristic, complemented
11#560×D59C216yesmaximal, complemented
12#532×D59C213yesmaximal, complemented
13#529×D59C216yesmaximal, complemented
14#525×D59C216yesmaximal, complemented
15C59×#3529C211yesmaximal, characteristic, complemented
16C2×#41×D59C2213yes—
17C2×#41×D59C2211yescharacteristic, complemented
18C23×C4×D59C2212yescomplemented
19#16838156C2216yescomplemented
20#16838155C2216yescomplemented
21#16838154C22112yescomplemented
22#16838153C22112yescomplemented
23#16838152C2213yescomplemented
24#16838151C2216yescomplemented
25#16838150C2216yescomplemented
26#16838149C22112yescomplemented
27#16838149C22112yescomplemented
28#16838148C22112yescomplemented
29#16838148C22112yescomplemented
30#16838147C22112yescomplemented
31#16838147C22112yescomplemented
32#16838146C2216yescomplemented
33#16838146C2216yescomplemented
34#16838145C2216yescomplemented
35#16838144C2213yescomplemented
36#16838144C2216yescomplemented
37#16838143C22112yescomplemented
38#16838142C2216yescomplemented
39#16838142C22112yescomplemented
40#16838141C2216yescomplemented
41#16838141C22112yescomplemented
42#16838140C22112yescomplemented
43#16838140C22112yescomplemented
44#16838140C22112yescomplemented
45#16838139C2216yescomplemented
46#16837953C2213yescomplemented
47#16837952C2213yescomplemented
48#16837951C2213yescomplemented
49#16837951C2213yescomplemented
50#16837950C2213yescomplemented
51#16837949C22112yescomplemented
52#16837948C2213yescomplemented
53#16837948C2213yescomplemented
54#16837947C22112yescomplemented
55C4⋊Q8×D59C2213yescomplemented
56#127×D59C2213yes—
57#16837939C2216yescomplemented
58#16837938C2216yescomplemented
59#16837937C2216yescomplemented
60#16837936C2216yescomplemented
61#16837935C22112yescomplemented
62#16837934C2216yescomplemented
63#16837933C2216yescomplemented
64#16837932C22112yescomplemented
65#16837931C2216yescomplemented
66#16837930C22112yescomplemented
67#16837929C22112yescomplemented
68#126×D59C22112yescomplemented
69#125×D59C2216yescomplemented
70#124×D59C2216yes—
71#124×D59C2213yes—
72#124×D59C2213yescomplemented
73#16837915C22112yescomplemented
74#16837914C2216yescomplemented
75#16837913C2216yescomplemented
76#16837912C22112yescomplemented
77#16837911C22112yescomplemented
78#16837911C22112yescomplemented
79#16837910C2216yescomplemented
80#16837910C2216yescomplemented
81#16837909C2216yescomplemented
82#16837908C2216yescomplemented
83#16837908C2216yescomplemented
84#123×D59C2216yes—
85#123×D59C22112yescomplemented
86#123×D59C2216yescomplemented
87C22⋊Q8×D59C2216yescomplemented
88C22⋊Q8×D59C22112yescomplemented
89#121×D59C2216yes—
90#121×D59C22112yes—
91#121×D59C22112yescomplemented
92#120×D59C2216yes—
93#120×D59C2216yescomplemented
94C4×Q8×D59C2212yescomplemented
95C4×D4×D59C2216yes—
96C4×D4×D59C22112yescomplemented
97#117×D59C2216yescomplemented
98C2×C42×D59C2213yescomplemented
99C59×#563C2213yescomplemented
100C59×#562C2216yescomplemented
101C59×H(3,𝔽4)C2211yescharacteristic, complemented
102C59×#560C2216yescomplemented
103C59×#532C2213yescomplemented
104C59×#529C2216yescomplemented
105C59×#525C2216yescomplemented
106C24×D59C2312yes—
107C2×#11745689C2313yes—
108C2×#11745689C2311yescharacteristic, complemented
109C2×#11745685C2313yes—
110C2×#11745685C2316yes—
111C2×#11745685C2313yescomplemented
112C2×#11745687C2313yes—
113C2×#11745687C2316yes—
114C2×#11745687C2313yescomplemented
115#41×D59—412no—
116#41×D59—44no—
117C2×Q8×D59C2313yes—
118C2×Q8×D59C2312yes—
119C2×Q8×D59C2311yescharacteristic
120C2×D4×D59C2316yes—
121C2×D4×D59C2316yes—
122C2×D4×D59C23112yes—
123C2×D4×D59C2313yes—
124C2×D4×D59C2313yes—
125C23×Dic59C2312yescomplemented
126C22×C4×D59—48no—
127C22×C4×D59C2316yes—
128C22×C4×D59C2313yes—
129C22×C4×D59C2316yes—
130C22×C4×D59C2316yes—
131C22×C4×D59C2316yescomplemented
132C22×C4×D59C2316yescomplemented
133#14273727C2313yescomplemented
134#14273726C23112yescomplemented
135#14273725C2313yescomplemented
136#14273725C2313yescomplemented
137#14273724C2313yes—
138#14273723C23112yes—
139#14273723C2313yes—
140#14273723C2313yes—
141#14273722C23112yescomplemented
142#14273722C23112yescomplemented
143#14273722C23112yescomplemented
144#14273721C23112yescomplemented
145#14273720C23112yescomplemented
146#14273720C23112yescomplemented
147#14273720C23112yescomplemented
148#14273719C2316yescomplemented
149#14273718C2316yescomplemented
150#14273718C2316yescomplemented
151#14273717C23112yescomplemented
152#14273717C23112yescomplemented
153#14273716C2316yes—
154#14273716C2313yes—
155#14273716C2313yescomplemented
156#14273715C2316yes—
157#14273715C2313yes—
158#14273715C2313yescomplemented
159#14273714C2316yes—
160#14273714C2313yes—
161#14273714C2313yescomplemented
162#14273713C23112yes—
163#14273713C23112yes—
164#14273713C23112yes—
165#14273713C23112yescomplemented
166#14273712C23112yes—
167#14273712C23112yescomplemented
168#14273712C23112yescomplemented
169#14273712C23112yescomplemented
170#14273711C2316yes—
171#14273711C2316yescomplemented
172#14273711C23112yescomplemented
173#14273710C2316yes—
174#14273710C2316yescomplemented
175#14273710C23112yescomplemented
176#14273709C23112yes—
177#14273709C23112yescomplemented
178#14273709C23112yescomplemented
179#14273709C23112yescomplemented
180#14273708C2316yes—
181#14273708C2316yescomplemented
182#14273708C23112yescomplemented
183#14273707C2316yescomplemented
184#14273707C23112yescomplemented
185#14273706C2316yescomplemented
186#14273706C23112yescomplemented
187#14273705C23112yescomplemented
188#14273705C23112yescomplemented
189#14273705C23112yescomplemented
190#14273704C23112yescomplemented
191#14273704C23112yescomplemented
192#14273704C23112yescomplemented
193#14273703C2316yescomplemented
194#14273703C23112yescomplemented
195#14273702C23112yes—
196#14273702C2316yes—
197#14273702C23112yescomplemented
198#14273701C23112yes—
199#14273701C2316yes—
200#14273701C23112yescomplemented
201#14273700C23112yes—
202#14273700C23112yes—
203#14273700C23112yes—
204#14273700C23112yescomplemented
205#14273700C23112yescomplemented
206#14273699C23112yes—
207#14273699C23112yes—
208#14273699C23112yes—
209#14273699C23112yescomplemented
210#14273699C23112yescomplemented
211#14273698C23112yes—
212#14273698C2316yes—
213#14273698C23112yescomplemented
214#14273697C2316yes—
215#14273697C23112yes—
216#14273697C2316yescomplemented
217#14273697C23112yescomplemented
218#14273696C2316yes—
219#14273696C2316yescomplemented
220#14273695C2316yes—
221#14273695C23112yes—
222#14273695C2316yescomplemented
223#14273695C23112yescomplemented
224Q8×Dic59C2312yescomplemented
225C4×Dic118C2316yescomplemented
226#14273692C2316yescomplemented
227C4×D236C2316yes—
228C4×D236C23112yescomplemented
229D4×Dic59C2316yes—
230D4×Dic59C23112yescomplemented
231#14273689C2316yes—
232#14273689C23112yescomplemented
233C4×C22⋊D59C23112yes—
234C4×C22⋊D59C23112yescomplemented
235C4×C22⋊D59C23112yescomplemented
236(C22⋊D59)⋊C4C23112yes—
237(C22⋊D59)⋊C4C23112yescomplemented
238(C22⋊D59)⋊C4C23112yescomplemented
239#14273686C2316yescomplemented
240#14273685C23112yescomplemented
241#14273684C23112yescomplemented
242#14273683C2316yescomplemented
243#14273683C2316yescomplemented
244C4⋊C4×D59C23112yes—
245C4⋊C4×D59C2316yes—
246C4⋊C4×D59C23112yes—
247C4⋊C4×D59C2316yes—
248C22⋊C4×D59C2316yes—
249C22⋊C4×D59C23112yes—
250C22⋊C4×D59C23112yes—
251C22⋊C4×D59C23112yes—
252C22⋊C4×D59C2316yes—
253C2×C4×Dic59C2316yescomplemented
254C2×C4×Dic59C2313yescomplemented
255C42×D59C2313yes—
256C42×D59C2313yes—
257C42×D59C2316yes—
258C42×D59C2316yescomplemented
259C42×D59C2313yescomplemented
260C42×D59C2313yescomplemented
261C2×#41×C59C2313yes—
262C2×#41×C59C2311yescharacteristic, complemented
263C23×C4×C59C2312yescomplemented
264C4⋊Q8×C59C2313yescomplemented
265#127×C59C2313yes—
266#126×C59C23112yescomplemented
267#125×C59C2316yescomplemented
268#124×C59C2316yes—
269#124×C59C2313yes—
270#124×C59C2313yescomplemented
271#123×C59C2316yes—
272#123×C59C2316yescomplemented
273#123×C59C23112yescomplemented
274C22⋊Q8×C59C2316yescomplemented
275C22⋊Q8×C59C23112yescomplemented
276#121×C59C23112yes—
277#121×C59C2316yes—
278#121×C59C23112yescomplemented
279#120×C59C2316yes—
280#120×C59C2316yescomplemented
281C4×Q8×C59C2312yescomplemented
282C4×D4×C59C2316yes—
283C4×D4×C59C23112yescomplemented
284#117×C59C2316yescomplemented
285C2×C42×C59C2313yescomplemented
286C24×C59C2412yes—
287C23×D59—44no—
288C23×D59—48no—
289C23×D59C2416yes—
290C23×D59C2413yes—
291C23×D59C2416yes—
292#41×C59—46no—
293#41×C59—42no—
294C2×Q8×C59C2412yes—
295C2×Q8×C59C2413yes—
296C2×Q8×C59C2411yescharacteristic
297C2×D4×C59C2416yes—
298C2×D4×C59C24112yes—
299C2×D4×C59C2413yes—
300C2×D4×C59C2416yes—
301C2×D4×C59C2413yes—
302C22×C4×C59—44no—
303C22×C4×C59C2413yes—
304C22×C4×C59C2416yes—
305C22×C4×C59C2416yes—
306C22×C4×C59C2416yes—
307C2×C22⋊D59C24112yes—
308C2×C22⋊D59C24112yes—
309C2×C22⋊D59C24112yes—
310C2×C22⋊D59C2416yes—
311C2×C22⋊D59C2416yes—
312C2×C22⋊D59C2416yes—
313C2×C22⋊D59C2416yes—
314C22×Dic59—44no—
315C22×Dic59C2413yes—
316C22×Dic59C2416yes—
317C22×Dic59C2416yes—
318C22×Dic59C2416yes—
319#11745689—46no—
320#11745689—42no—
321Q8×D59—44no—
322Q8×D59—46no—
323Q8×D59—42no—
324#11745687—412no—
325#11745687—46no—
326#11745687—46no—
327D4×D59—424no—
328D4×D59—412no—
329D4×D59—412no—
330D4×D59—46no—
331D4×D59—46no—
332#11745685—46no—
333#11745685—412no—
334#11745685—46no—
335C2×D236C2416yes—
336C2×D236C24112yes—
337C2×D236C2413yes—
338C2×D236C2416yes—
339C2×D236C2413yes—
340C2×C4×D59—224no—
341C2×C4×D59—212no—
342C2×C4×D59—412no—
343C2×C4×D59—412no—
344C2×C4×D59—412no—
345C2×C4×D59—412no—
346C2×C4×D59C2416yes—
347C2×C4×D59C2416yes—
348C2×C4×D59C2413yes—
349C2×C4×D59C2413yes—
350C2×C4×D59C2413yes—
351C2×C4×D59C2416yes—
352C2×C4×D59C2416yes—
353C2×C4×D59C2416yes—
354C2×C4×D59C2416yes—
355C2×C4×D59C2416yes—
356C2×C4×D59C24112yes—
357C2×C4×D59C2411yescharacteristic
358C2×Dic118C2416yes—
359C2×Dic118C2413yes—
360C2×Dic118C2416yes—
361C2×Dic118C2413yes—
362C4⋊C4×C59C24112yes—
363C4⋊C4×C59C2416yes—
364C4⋊C4×C59C24112yes—
365C4⋊C4×C59C2416yes—
366C22⋊C4×C59C2416yes—
367C22⋊C4×C59C2416yes—
368C22⋊C4×C59C24112yes—
369C22⋊C4×C59C24112yes—
370C22⋊C4×C59C24112yes—
371C42×C59C2416yes—
372C42×C59C2413yes—
373C42×C59C2413yes—
374C22⋊Dic59C2416yes—
375C22⋊Dic59C2416yes—
376C22⋊Dic59C24112yes—
377C22⋊Dic59C24112yes—
378C22⋊Dic59C24112yes—
379(C2×D59)⋊C4C24112yes—
380(C2×D59)⋊C4C24112yes—
381(C2×D59)⋊C4C24112yes—
382(C2×D59)⋊C4C24112yes—
383(C2×D59)⋊C4C24112yes—
384(C2×D59)⋊C4C24112yes—
385(C2×D59)⋊C4C24112yes—
386(C2×D59)⋊C4C24112yes—
387C4⋊Dic59C24112yes—
388C4⋊Dic59C2416yes—
389C4⋊Dic59C24112yes—
390C4⋊Dic59C2416yes—
391Dic59⋊C4C24112yes—
392Dic59⋊C4C24112yes—
393Dic59⋊C4C24112yes—
394Dic59⋊C4C24112yes—
395Dic59⋊C4C24112yes—
396Dic59⋊C4C24112yes—
397C4×Dic59C2416yes—
398C4×Dic59C2416yes—
399C4×Dic59C2416yes—
400C4×Dic59C2416yes—
401C4×Dic59C2413yes—
402C4×Dic59C2413yes—
403C4×Dic59C2416yes—
404C23×C59—42no—
405C23×C59—44no—
406C23×C59C2516yes—
407C23×C59C2513yes—
408C22×D59—212no—
409C22×D59—26no—
410C22×D59—212no—
411C22×D59—224no—
412C22×D59—46no—
413C22×D59—412no—
414C22×D59—432no—
415C22×D59C2516yes—
416C22×D59C2513yes—
417C22×D59C2511yescharacteristic
418Q8×C59—41no—
419Q8×C59—43no—
420Q8×C59—42no—
421D4×C59—43no—
422D4×C59—43no—
423D4×C59—46no—
424D4×C59—46no—
425D4×C59—412no—
426C2×C4×C59—212no—
427C2×C4×C59—26no—
428C2×C4×C59—46no—
429C2×C4×C59—46no—
430C2×C4×C59C2516yes—
431C2×C4×C59C2513yes—
432C2×C4×C59C2516yes—
433C2×C4×C59C2516yes—
434C2×C4×C59C2511yescharacteristic
435C22⋊D59—46no—
436C22⋊D59—46no—
437C22⋊D59—46no—
438C22⋊D59—46no—
439C22⋊D59—412no—
440C22⋊D59—412no—
441C22⋊D59—412no—
442C2×Dic59—212no—
443C2×Dic59—26no—
444C2×Dic59—46no—
445C2×Dic59—46no—
446C2×Dic59C2516yes—
447C2×Dic59C2516yes—
448C2×Dic59C2513yes—
449C2×Dic59C2516yes—
450C2×Dic59C2511yescharacteristic
451D236—43no—
452D236—43no—
453D236—46no—
454D236—46no—
455D236—412no—
456C4×D59—212no—
457C4×D59—26no—
458C4×D59—212no—
459C4×D59—212no—
460C4×D59—212no—
461C4×D59—26no—
462C4×D59—212no—
463C4×D59—26no—
464C4×D59—412no—
465C4×D59—46no—
466C4×D59—46no—
467C4×D59H(5,𝔽2)14yes—
468Dic118—43no—
469Dic118—46no—
470Dic118—43no—
471Dic118—46no—
472C2×#3529—591nomaximal, Sylow
473C22×C59—26no—
474C22×C59—23no—
475C22×C59—26no—
476C22×C59—212no—
477C22×C59—48no—
478C22×C59C2611yescharacteristic
479C2×D59—26no—
480C2×D59—23no—
481C2×D59—26no—
482C2×D59—212no—
483C2×D59—424no—
484C2×D59—412no—
485C2×D59—424no—
486C2×D59C2×H(5,𝔽2)12yes—
487C2×D59#58514yes—
488C4×C59—23no—
489C4×C59—26no—
490C4×C59—26no—
491C4×C59—26no—
492C4×C59C2×H(5,𝔽2)12yes—
493Dic59—23no—
494Dic59—26no—
495Dic59—26no—
496Dic59—26no—
497Dic59C2×H(5,𝔽2)12yes—
498#3529—593no—
499#3529—596no—
500#3529—591no—
501#3529—596no—
502#3529—593no—
503#3529—596no—
504#3529—596no—
505#3529D5911yescharacteristic, direct product factor
506C2×#563—593no—
507C2×#562—596no—
508C2×H(3,𝔽4)—591no—
509C2×#560—596no—
510C2×#532—593no—
511C2×#529—596no—
512C2×#525—596no—
513C2×C59—46no—
514C2×C59—43no—
515C2×C59C22×H(5,𝔽2)11yescharacteristic
516C2×C59C2×#58512yes—
517D59—43no—
518D59—46no—
519D59#352914yesdirect product factor
520C22×#41—593no—
521C22×#41—591no—
522C24×C4—592no—
523#563—596no—
524#563—5912no—
525#563—596no—
526#563—593no—
527#563—596no—
528#563—5912no—
529#563C2×D5913yescomplemented
530#562—596no—
531#562—596no—
532#562—596no—
533#562—5912no—
534#562—5912no—
535#562—5912no—
536#562—5912no—
537#562—5912no—
538#562—5912no—
539#562C2×D5916yescomplemented
540H(3,𝔽4)—596no—
541H(3,𝔽4)—593no—
542H(3,𝔽4)—596no—
543H(3,𝔽4)C2×D5911yescharacteristic, complemented
544#560—596no—
545#560—5912no—
546#560—596no—
547#560—5912no—
548#560—5912no—
549#560—5912no—
550#560—5912no—
551#560—596no—
552#560—5912no—
553#560C2×D5916yescomplemented
554#532—593no—
555#532—593no—
556#532—593no—
557#532—593no—
558#532—593no—
559#532—593no—
560#532—5912no—
561#532—5912no—
562#532—593no—
563#532C2×D5913yescomplemented
564C2×C4⋊Q8—593no—
565C2×#127—593no—
566#529—5912no—
567#529—596no—
568#529—596no—
569#529—5912no—
570#529—596no—
571#529—596no—
572#529—596no—
573#529—596no—
574#529—5912no—
575#529—5912no—
576#529—596no—
577#529C2×D5916yescomplemented
578C2×#126—5912no—
579C2×#125—596no—
580C2×#124—596no—
581C2×#124—593no—
582C2×#124—593no—
583#525—596no—
584#525—596no—
585#525—596no—
586#525—596no—
587#525—5912no—
588#525—5912no—
589#525—596no—
590#525—596no—
591#525—5912no—
592#525—5912no—
593#525—596no—
594#525C2×D5916yescomplemented
595C2×#123—596no—
596C2×#123—596no—
597C2×#123—5912no—
598C2×C22⋊Q8—5912no—
599C2×C22⋊Q8—596no—
600C2×#121—5912no—
601C2×#121—596no—
602C2×#121—5912no—
603C2×#120—596no—
604C2×#120—596no—
605C2×C4×Q8—592no—
606C2×C4×D4—596no—
607C2×C4×D4—5912no—
608C2×#117—596no—
609C22×C42—593no—
610C59C2×#352911yescharacteristic, complemented, Sylow
611C25—592no—
612C2×#41—593no—
613C2×#41—591no—
614C2×#41—596no—
615C2×#41—593no—
616C2×#41—593no—
617C2×#41—596no—
618C2×#41—593no—
619C2×#41—593no—
620C2×#41—23612no—
621C2×#41—2364no—
622C2×#41C22×D5913yes—
623C2×#41C22×D5911yescharacteristic, complemented
624C22×Q8—592no—
625C22×Q8—593no—
626C22×Q8—591no—
627C22×D4—596no—
628C22×D4—5912no—
629C22×D4—593no—
630C22×D4—596no—
631C22×D4—593no—
632C23×C4—592no—
633C23×C4—596no—
634C23×C4—593no—
635C23×C4—596no—
636C23×C4—596no—
637C23×C4—596no—
638C23×C4—596no—
639C23×C4—2368no—
640C23×C4C22×D5912yescomplemented
641C4⋊Q8—593no—
642C4⋊Q8—593no—
643C4⋊Q8—5912no—
644C4⋊Q8—593no—
645C4⋊Q8C22×D5913yescomplemented
646#127—593no—
647#127—593no—
648#127—5912no—
649#127—593no—
650#127C22×D5913yes—
651#126—5912no—
652#126—5912no—
653#126—5912no—
654#126—5912no—
655#126—5912no—
656#126—5912no—
657#126—5912no—
658#126C22×D59112yescomplemented
659#125—5912no—
660#125—5912no—
661#125—596no—
662#125—596no—
663#125—596no—
664#125C22×D5916yescomplemented
665#124—596no—
666#124—593no—
667#124—593no—
668#124—596no—
669#124—593no—
670#124—593no—
671#124—5912no—
672#124—5912no—
673#124—5912no—
674#124—5912no—
675#124—596no—
676#124—593no—
677#124—593no—
678#124C22×D5916yes—
679#124C22×D5913yes—
680#124C22×D5913yescomplemented
681#123—596no—
682#123—596no—
683#123—5912no—
684#123—596no—
685#123—596no—
686#123—5912no—
687#123—5912no—
688#123—5912no—
689#123—5912no—
690#123—5912no—
691#123—5912no—
692#123—596no—
693#123—5912no—
694#123—596no—
695#123—5912no—
696#123—5912no—
697#123—5912no—
698#123C22×D5916yes—
699#123C22×D5916yescomplemented
700#123C22×D59112yescomplemented
701C22⋊Q8—5912no—
702C22⋊Q8—596no—
703C22⋊Q8—5912no—
704C22⋊Q8—596no—
705C22⋊Q8—5912no—
706C22⋊Q8—5912no—
707C22⋊Q8—5912no—
708C22⋊Q8—5912no—
709C22⋊Q8—596no—
710C22⋊Q8—5912no—
711C22⋊Q8—5912no—
712C22⋊Q8—5912no—
713C22⋊Q8C22×D59112yescomplemented
714C22⋊Q8C22×D5916yescomplemented
715#121—5912no—
716#121—5912no—
717#121—5912no—
718#121—596no—
719#121—5912no—
720#121—5912no—
721#121—5912no—
722#121—5912no—
723#121—5912no—
724#121—596no—
725#121—5912no—
726#121—5912no—
727#121—596no—
728#121—5912no—
729#121—5912no—
730#121—5912no—
731#121—5912no—
732#121—5912no—
733#121—5912no—
734#121C22×D59112yes—
735#121C22×D5916yes—
736#121C22×D59112yescomplemented
737#120—596no—
738#120—596no—
739#120—596no—
740#120—5912no—
741#120—596no—
742#120—5912no—
743#120—5912no—
744#120—596no—
745#120—5912no—
746#120—596no—
747#120C22×D5916yes—
748#120C22×D5916yescomplemented
749C4×Q8—592no—
750C4×Q8—596no—
751C4×Q8—596no—
752C4×Q8C22×D5912yescomplemented
753C4×D4—596no—
754C4×D4—5912no—
755C4×D4—5912no—
756C4×D4—5912no—
757C4×D4—5912no—
758C4×D4—596no—
759C4×D4—5912no—
760C4×D4—5912no—
761C4×D4—5912no—
762C4×D4—5912no—
763C4×D4—596no—
764C4×D4—5912no—
765C4×D4C22×D5916yes—
766C4×D4C22×D59112yescomplemented
767#117—596no—
768#117—5912no—
769#117—596no—
770#117—596no—
771#117—5912no—
772#117C22×D5916yescomplemented
773C2×C4⋊C4—5912no—
774C2×C4⋊C4—5912no—
775C2×C4⋊C4—596no—
776C2×C4⋊C4—596no—
777C2×C22⋊C4—596no—
778C2×C22⋊C4—596no—
779C2×C22⋊C4—5912no—
780C2×C22⋊C4—5912no—
781C2×C22⋊C4—5912no—
782C2×C42—596no—
783C2×C42—593no—
784C2×C42—596no—
785C2×C42—593no—
786C2×C42—593no—
787C2×C42—593no—
788C2×C42—593no—
789C2×C42—596no—
790C2×C42C22×D5913yescomplemented
791C24—596no—
792C24—593no—
793C24—596no—
794C24—2364no—
795C24—2368no—
796C24C23×D5912yes—
797#41—46no—
798#41—42no—
799#41—23612no—
800#41—2366no—
801#41—2366no—
802#41—23612no—
803#41—2366no—
804#41—2366no—
805#41—2366no—
806#41—2362no—
807C2×Q8—596no—
808C2×Q8—596no—
809C2×Q8—593no—
810C2×Q8—593no—
811C2×Q8—2366no—
812C2×Q8—2362no—
813C2×Q8—2364no—
814C2×Q8C23×D5912yes—
815C2×Q8C23×D5913yes—
816C2×Q8C23×D5911yescharacteristic
817C2×D4—5912no—
818C2×D4—5912no—
819C2×D4—5912no—
820C2×D4—596no—
821C2×D4—596no—
822C2×D4—596no—
823C2×D4—596no—
824C2×D4—596no—
825C2×D4—5912no—
826C2×D4—593no—
827C2×D4—596no—
828C2×D4—593no—
829C2×D4—23612no—
830C2×D4—2366no—
831C2×D4—2366no—
832C2×D4—23624no—
833C2×D4—23612no—
834C2×D4C23×D5916yes—
835C2×D4C23×D59112yes—
836C2×D4C23×D5913yes—
837C2×D4C23×D5916yes—
838C2×D4C23×D5913yes—
839C22×C4—44no—
840C22×C4—591no—
841C22×C4—593no—
842C22×C4—596no—
843C22×C4—596no—
844C22×C4—596no—
845C22×C4—596no—
846C22×C4—596no—
847C22×C4—593no—
848C22×C4—593no—
849C22×C4—596no—
850C22×C4—596no—
851C22×C4—593no—
852C22×C4—596no—
853C22×C4—596no—
854C22×C4—596no—
855C22×C4—5912no—
856C22×C4—11824no—
857C22×C4—11812no—
858C22×C4—23612no—
859C22×C4—23612no—
860C22×C4—23612no—
861C22×C4—23612no—
862C22×C4—2364no—
863C22×C4C23×D5913yes—
864C22×C4C23×D5916yes—
865C22×C4C23×D5916yes—
866C22×C4C23×D5916yes—
867C4⋊C4—5912no—
868C4⋊C4—5912no—
869C4⋊C4—5912no—
870C4⋊C4—5912no—
871C4⋊C4—5912no—
872C4⋊C4—5912no—
873C4⋊C4—5912no—
874C4⋊C4—596no—
875C4⋊C4—5912no—
876C4⋊C4—596no—
877C4⋊C4C23×D59112yes—
878C4⋊C4C23×D5916yes—
879C4⋊C4C23×D59112yes—
880C4⋊C4C23×D5916yes—
881C22⋊C4—596no—
882C22⋊C4—596no—
883C22⋊C4—5912no—
884C22⋊C4—5912no—
885C22⋊C4—5912no—
886C22⋊C4—5912no—
887C22⋊C4—5912no—
888C22⋊C4—5912no—
889C22⋊C4—5912no—
890C22⋊C4—5912no—
891C22⋊C4—5912no—
892C22⋊C4—5912no—
893C22⋊C4—5912no—
894C22⋊C4C23×D5916yes—
895C22⋊C4C23×D5916yes—
896C22⋊C4C23×D59112yes—
897C22⋊C4C23×D59112yes—
898C22⋊C4C23×D59112yes—
899C42—596no—
900C42—596no—
901C42—593no—
902C42—596no—
903C42—593no—
904C42—596no—
905C42—596no—
906C42C23×D5913yes—
907C42C23×D5913yes—
908C42C23×D5916yes—
909C23—42no—
910C23—44no—
911C23—591no—
912C23—596no—
913C23—593no—
914C23—11812no—
915C23—1186no—
916C23—11812no—
917C23—11824no—
918C23—2366no—
919C23—23612no—
920C23—23632no—
921C23C24×D5916yes—
922C23C24×D5913yes—
923Q8—42no—
924Q8—43no—
925Q8—41no—
926Q8—2366no—
927Q8—2366no—
928Q8—2363no—
929Q8—2363no—
930D4—412no—
931D4—46no—
932D4—46no—
933D4—43no—
934D4—43no—
935D4—23612no—
936D4—2366no—
937D4—2366no—
938D4—2363no—
939D4—2363no—
940D4—23612no—
941D4—23612no—
942D4—23612no—
943D4—2366no—
944D4—2366no—
945D4—2366no—
946D4—2366no—
947C2×C4—212no—
948C2×C4—26no—
949C2×C4—46no—
950C2×C4—46no—
951C2×C4—591no—
952C2×C4—594no—
953C2×C4—596no—
954C2×C4—596no—
955C2×C4—593no—
956C2×C4—596no—
957C2×C4—11812no—
958C2×C4—1186no—
959C2×C4—11812no—
960C2×C4—1186no—
961C2×C4—11812no—
962C2×C4—11812no—
963C2×C4—11812no—
964C2×C4—1186no—
965C2×C4—11812no—
966C2×C4—1186no—
967C2×C4—2366no—
968C2×C4—2366no—
969C2×C4—23612no—
970C2×C4—2366no—
971C2×C4—2366no—
972C2×C4C24×D5916yes—
973C2×C4C24×D5916yes—
974C2×C4C24×D5913yes—
975C2×C4C24×D5916yes—
976C2×C4C24×D5911yescharacteristic
977C22—26no—
978C22—23no—
979C22—26no—
980C22—212no—
981C22—48no—
982C22—592no—
983C22—594no—
984C22—1186no—
985C22—1183no—
986C22—1186no—
987C22—11812no—
988C22—23624no—
989C22—23612no—
990C22—23624no—
991C22C25×D5911yescharacteristic
992C4—26no—
993C4—23no—
994C4—26no—
995C4—26no—
996C4—592no—
997C4—1186no—
998C4—1183no—
999C4—1186no—
1000C4—1186no—
1001C4H(5,𝔽2)×D5912yes—
1002C2—46no—
1003C2—43no—
1004C2—594no—
1005C2—2366no—
1006C2—2363no—
1007C2C2×H(5,𝔽2)×D5911yescharacteristic
1008C2#585×D5912yes—
subgroupG/H
centerC2×C4C24×D59
commutator, socle, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC59×#3529C2
hypercenter#3529D59
hypocenterC59C2×#3529
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ #3529

Complements

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

NH ≅ G/Ntype
1. #21438237C2semidirect
2. #21438236C2semidirect
3. #21438235C2semidirect
4. #21438234C2semidirect
5. #21438233C2semidirect
6. #21438232C2semidirect
7. #21438231C2semidirect
8. #563×D59C2semidirect
9. #562×D59C2semidirect
10. H(3,𝔽4)×D59C2semidirect
11. #560×D59C2semidirect
12. #532×D59C2semidirect
13. #529×D59C2semidirect
14. #525×D59C2semidirect
15. C59×#3529C2semidirect
17. C2×#41×D59C22semidirect
18. C23×C4×D59C22semidirect
19. #16838156C22semidirect
20. #16838155C22semidirect
21. #16838154C22semidirect
22. #16838153C22semidirect
23. #16838152C22semidirect
24. #16838151C22semidirect
25. #16838150C22semidirect
26. #16838149C22semidirect
27. #16838149C22semidirect
28. #16838148C22semidirect
29. #16838148C22semidirect
30. #16838147C22semidirect
31. #16838147C22semidirect
32. #16838146C22semidirect
33. #16838146C22semidirect
34. #16838145C22semidirect
35. #16838144C22semidirect
36. #16838144C22semidirect
37. #16838143C22semidirect
38. #16838142C22semidirect
39. #16838142C22semidirect
40. #16838141C22semidirect
41. #16838141C22semidirect
42. #16838140C22semidirect
43. #16838140C22semidirect
44. #16838140C22semidirect
45. #16838139C22semidirect
46. #16837953C22semidirect
47. #16837952C22semidirect
48. #16837951C22semidirect
49. #16837951C22semidirect
50. #16837950C22semidirect
51. #16837949C22semidirect
52. #16837948C22semidirect
53. #16837948C22semidirect
54. #16837947C22semidirect
55. C4⋊Q8×D59C22semidirect
57. #16837939C22semidirect
58. #16837938C22semidirect
59. #16837937C22semidirect
60. #16837936C22semidirect
61. #16837935C22semidirect
62. #16837934C22semidirect
63. #16837933C22semidirect
64. #16837932C22semidirect
65. #16837931C22semidirect
66. #16837930C22semidirect
67. #16837929C22semidirect
68. #126×D59C22semidirect
69. #125×D59C22semidirect
72. #124×D59C22semidirect
73. #16837915C22semidirect
74. #16837914C22semidirect
75. #16837913C22semidirect
76. #16837912C22semidirect
77. #16837911C22semidirect
78. #16837911C22semidirect
79. #16837910C22semidirect
80. #16837910C22semidirect
81. #16837909C22semidirect
82. #16837908C22semidirect
83. #16837908C22semidirect
85. #123×D59C22semidirect
86. #123×D59C22semidirect
87. C22⋊Q8×D59C22semidirect
88. C22⋊Q8×D59C22semidirect
91. #121×D59C22semidirect
93. #120×D59C22semidirect
94. C4×Q8×D59C22semidirect
96. C4×D4×D59C22semidirect
97. #117×D59C22semidirect
98. C2×C42×D59C22semidirect
99. C59×#563C22semidirect
100. C59×#562C22semidirect
101. C59×H(3,𝔽4)C22semidirect
102. C59×#560C22semidirect
103. C59×#532C22semidirect
104. C59×#529C22semidirect
105. C59×#525C22semidirect
108. C2×#11745689C23semidirect
111. C2×#11745685C23semidirect
114. C2×#11745687C23semidirect
125. C23×Dic59C23semidirect
131. C22×C4×D59C23semidirect
132. C22×C4×D59C23semidirect
133. #14273727C23semidirect
134. #14273726C23semidirect
135. #14273725C23semidirect
136. #14273725C23semidirect
141. #14273722C23semidirect
142. #14273722C23semidirect
143. #14273722C23semidirect
144. #14273721C23semidirect
145. #14273720C23semidirect
146. #14273720C23semidirect
147. #14273720C23semidirect
148. #14273719C23semidirect
149. #14273718C23semidirect
150. #14273718C23semidirect
151. #14273717C23semidirect
152. #14273717C23semidirect
155. #14273716C23semidirect
158. #14273715C23semidirect
161. #14273714C23semidirect
165. #14273713C23semidirect
167. #14273712C23semidirect
168. #14273712C23semidirect
169. #14273712C23semidirect
171. #14273711C23semidirect
172. #14273711C23semidirect
174. #14273710C23semidirect
175. #14273710C23semidirect
177. #14273709C23semidirect
178. #14273709C23semidirect
179. #14273709C23semidirect
181. #14273708C23semidirect
182. #14273708C23semidirect
183. #14273707C23semidirect
184. #14273707C23semidirect
185. #14273706C23semidirect
186. #14273706C23semidirect
187. #14273705C23semidirect
188. #14273705C23semidirect
189. #14273705C23semidirect
190. #14273704C23semidirect
191. #14273704C23semidirect
192. #14273704C23semidirect
193. #14273703C23semidirect
194. #14273703C23semidirect
197. #14273702C23semidirect
200. #14273701C23semidirect
204. #14273700C23semidirect
205. #14273700C23semidirect
209. #14273699C23semidirect
210. #14273699C23semidirect
213. #14273698C23semidirect
216. #14273697C23semidirect
217. #14273697C23semidirect
219. #14273696C23semidirect
222. #14273695C23semidirect
223. #14273695C23semidirect
224. Q8×Dic59C23semidirect
225. C4×Dic118C23semidirect
226. #14273692C23semidirect
228. C4×D236C23semidirect
230. D4×Dic59C23semidirect
232. #14273689C23semidirect
234. C4×C22⋊D59C23semidirect
235. C4×C22⋊D59C23semidirect
237. (C22⋊D59)⋊C4C23semidirect
238. (C22⋊D59)⋊C4C23semidirect
239. #14273686C23semidirect
240. #14273685C23semidirect
241. #14273684C23semidirect
242. #14273683C23semidirect
243. #14273683C23semidirect
253. C2×C4×Dic59C23semidirect
254. C2×C4×Dic59C23semidirect
258. C42×D59C23semidirect
259. C42×D59C23semidirect
260. C42×D59C23semidirect
262. C2×#41×C59C23semidirect
263. C23×C4×C59C23semidirect
264. C4⋊Q8×C59C23semidirect
266. #126×C59C23semidirect
267. #125×C59C23semidirect
270. #124×C59C23semidirect
272. #123×C59C23semidirect
273. #123×C59C23semidirect
274. C22⋊Q8×C59C23semidirect
275. C22⋊Q8×C59C23semidirect
278. #121×C59C23semidirect
280. #120×C59C23semidirect
281. C4×Q8×C59C23semidirect
283. C4×D4×C59C23semidirect
284. #117×C59C23semidirect
285. C2×C42×C59C23semidirect
505. #3529D59direct (N × H)
519. D59#3529direct (N × H)
529. #563C2×D59semidirect
539. #562C2×D59semidirect
543. H(3,𝔽4)C2×D59semidirect
553. #560C2×D59semidirect
563. #532C2×D59semidirect
577. #529C2×D59semidirect
594. #525C2×D59semidirect
610. C59C2×#3529semidirect
623. C2×#41C22×D59semidirect
640. C23×C4C22×D59semidirect
645. C4⋊Q8C22×D59semidirect
658. #126C22×D59semidirect
664. #125C22×D59semidirect
680. #124C22×D59semidirect
699. #123C22×D59semidirect
700. #123C22×D59semidirect
713. C22⋊Q8C22×D59semidirect
714. C22⋊Q8C22×D59semidirect
736. #121C22×D59semidirect
748. #120C22×D59semidirect
752. C4×Q8C22×D59semidirect
766. C4×D4C22×D59semidirect
772. #117C22×D59semidirect
790. C2×C42C22×D59semidirect

Maximal subgroups

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

subgroupindex
#214382372
#214382362
#214382352
#214382342
#214382332
#214382322
#214382312
#563×D592
#562×D592
H(3,𝔽4)×D592
#560×D592
#532×D592
#529×D592
#525×D592
C59×#35292
C2×#352959