Finite Group Databasebeta

← C59×#24083 #28436192

Subgroups — C59×#24083 #28436192

Order 15104.

1074 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3494C211yesmaximal, characteristic
2C59×#3092C211yesmaximal, characteristic, complemented
3C2×C59×#428C211yesmaximal, characteristic, complemented
4C59×#2504C211yesmaximal, characteristic, complemented
5C59×#2061C212yesmaximal, complemented
6C59×#2037C212yesmaximal, complemented
7C59×#1900C211yesmaximal, characteristic, complemented
8C59×#1871C211yesmaximal, characteristic, complemented
9C59×#1860C212yesmaximal, complemented
10C59×#1856C212yesmaximal, complemented
11C59×#1826C211yesmaximal, characteristic, complemented
12C22×M16×C59C2211yescharacteristic
13C59×#555—21no—
14C59×#553—21no—
15C59×#553—21no—
16C59×#551—22no—
17C59×#547—21no—
18C59×#546—22no—
19C59×#544C2211yescharacteristic
20C59×#542—21no—
21C59×#540—21no—
22C59×#535C2211yescharacteristic
23C59×#532—21no—
24C59×#529—21no—
25C59×#525C2211yescharacteristic
26C2×#121×C59C2211yescharacteristic
27C59×#520C2211yescharacteristic
28C59×#518C2211yescharacteristic
29C2×#117×C59C2211yescharacteristic
30C22×C4⋊C4×C59C2211yescharacteristic
31C59×#484—21no—
32C59×#483—21no—
33C59×#481—21no—
34C59×#480—21no—
35C59×#428—21no—
36C59×#428—21no—
37C59×#428C2212yes—
38C59×#428C2212yes—
39C59×#428C2212yes—
40C2×#107×C59—21no—
41C2×#106×C59—21no—
42C2×#104×C59C2212yes—
43C59×#417C2212yes—
44C2×#100×C59C2212yes—
45C59×#407C2211yescharacteristic
46C59×#397—22no—
47C59×#390C2212yes—
48C59×#386—22no—
49C59×#382C2212yes—
50C4×C22⋊C4×C59C2211yescharacteristic
51C59×#343C2212yes—
52C59×#339C2212yes—
53C59×#339C2212yes—
54C59×#339C2212yes—
55C2×#41×C59—22no—
56C2×#41×C59C2311yescharacteristic
57C22×D4×C59D412yes—
58C22×D4×C59C2311yescharacteristic
59C23×C4×C59—21no—
60C23×C4×C59C2311yescharacteristic
61C2×M16×C59—21no—
62C2×M16×C59—24no—
63C2×M16×C59C2312yes—
64C2×M16×C59C2312yes—
65C22×C8×C59—21no—
66C4⋊Q8×C59—21no—
67C4⋊Q8×C59—21no—
68#127×C59—21no—
69#126×C59—22no—
70#126×C59—22no—
71#125×C59—21no—
72#125×C59—21no—
73#124×C59—22no—
74#124×C59—22no—
75#124×C59—21no—
76#123×C59—22no—
77#123×C59—22no—
78#123×C59—22no—
79#123×C59—22no—
80#123×C59—21no—
81C22⋊Q8×C59—22no—
82C22⋊Q8×C59—22no—
83C22⋊Q8×C59D411yescharacteristic
84C22⋊Q8×C59D411yescharacteristic
85#121×C59—22no—
86#121×C59—22no—
87#121×C59—22no—
88#121×C59—21no—
89#121×C59—21no—
90#121×C59—21no—
91#121×C59—21no—
92#121×C59—21no—
93#121×C59—21no—
94#121×C59D411yescharacteristic
95#121×C59D411yescharacteristic
96#120×C59—21no—
97#120×C59—22no—
98C4×Q8×C59—21no—
99C4×D4×C59—22no—
100C4×D4×C59—22no—
101C4×D4×C59—21no—
102C4×D4×C59—22no—
103C4×D4×C59—21no—
104C4×D4×C59—21no—
105C4×D4×C59—21no—
106C4×D4×C59—21no—
107C4×D4×C59—21no—
108C4×D4×C59—21no—
109#117×C59—22no—
110#117×C59—21no—
111#117×C59—21no—
112#117×C59—21no—
113#117×C59D411yescharacteristic
114#117×C59D411yescharacteristic
115#117×C59C2311yescharacteristic
116#117×C59C2311yescharacteristic
117#117×C59C2311yescharacteristic
118C2×C4⋊C4×C59—21no—
119C2×C4⋊C4×C59—21no—
120C2×C4⋊C4×C59—21no—
121C2×C4⋊C4×C59—21no—
122C2×C4⋊C4×C59—21no—
123C2×C4⋊C4×C59—21no—
124C2×C4⋊C4×C59D411yescharacteristic
125C2×C4⋊C4×C59D411yescharacteristic
126C2×C4⋊C4×C59C2312yes—
127C2×C4⋊C4×C59C2311yescharacteristic
128C2×C22⋊C4×C59—21no—
129C2×C22⋊C4×C59—22no—
130C2×C22⋊C4×C59—21no—
131C2×C22⋊C4×C59—24no—
132C2×C22⋊C4×C59D412yes—
133C2×C42×C59—21no—
134C2×C42×C59C2312yes—
135#107×C59—22no—
136#107×C59—22no—
137#107×C59—22no—
138#106×C59—22no—
139#106×C59—22no—
140#106×C59—22no—
141#104×C59—24no—
142#103×C59—22no—
143#102×C59—22no—
144#100×C59—24no—
145C22⋊C8×C59—21no—
146C22⋊C8×C59—21no—
147#95×C59—21no—
148#95×C59—24no—
149C24×C59C2×D411yescharacteristic
150C24×C59C2×D412yes—
151#41×C59—22no—
152#41×C59—22no—
153#41×C59—84no—
154C2×Q8×C59—22no—
155C2×Q8×C59C2×D411yescharacteristic
156C2×D4×C59—21no—
157C2×D4×C59—22no—
158C2×D4×C59—21no—
159C2×D4×C59—22no—
160C2×D4×C59—22no—
161C2×D4×C59—21no—
162C2×D4×C59—22no—
163C2×D4×C59—21no—
164C2×D4×C59—21no—
165C2×D4×C59—22no—
166C2×D4×C59—22no—
167C2×D4×C59—44no—
168C2×D4×C59C2×D411yescharacteristic
169C22×C4×C59—22no—
170C22×C4×C59—22no—
171C22×C4×C59—21no—
172C22×C4×C59—22no—
173C22×C4×C59—22no—
174C22×C4×C59—22no—
175C22×C4×C59—21no—
176C22×C4×C59—21no—
177C22×C4×C59—22no—
178C22×C4×C59—22no—
179C22×C4×C59—41no—
180C22×C4×C59—41no—
181C22×C4×C59—82no—
182C22×C4×C59C2×D411yescharacteristic
183C22×C4×C59C2×D411yescharacteristic
184C22×C4×C59C2×D411yescharacteristic
185C22×C4×C59C2×D411yescharacteristic
186C22×C4×C59C2×D411yescharacteristic
187C22×C4×C59C2×D412yes—
188C22×C4×C59C2411yescharacteristic
189M16×C59—24no—
190M16×C59—22no—
191M16×C59—22no—
192M16×C59—22no—
193M16×C59#4114yescomplemented
194C2×C8×C59—24no—
195C2×C8×C59—22no—
196C2×C8×C59—22no—
197C4⋊C4×C59—22no—
198C4⋊C4×C59—22no—
199C4⋊C4×C59—22no—
200C4⋊C4×C59—22no—
201C4⋊C4×C59—21no—
202C4⋊C4×C59—21no—
203C4⋊C4×C59—21no—
204C4⋊C4×C59—21no—
205C4⋊C4×C59—21no—
206C4⋊C4×C59—21no—
207C4⋊C4×C59—22no—
208C4⋊C4×C59—22no—
209C4⋊C4×C59—41no—
210C4⋊C4×C59—41no—
211C4⋊C4×C59C2×D411yescharacteristic
212C4⋊C4×C59C2×D411yescharacteristic
213C4⋊C4×C59C2×D411yescharacteristic
214C4⋊C4×C59C2×D411yescharacteristic
215C4⋊C4×C59C2×D411yescharacteristic
216C4⋊C4×C59C2×D411yescharacteristic
217C22⋊C4×C59—22no—
218C22⋊C4×C59—22no—
219C22⋊C4×C59—22no—
220C22⋊C4×C59—22no—
221C22⋊C4×C59—22no—
222C22⋊C4×C59—21no—
223C22⋊C4×C59—21no—
224C22⋊C4×C59—21no—
225C22⋊C4×C59—21no—
226C22⋊C4×C59—21no—
227C22⋊C4×C59—21no—
228C22⋊C4×C59—21no—
229C22⋊C4×C59—22no—
230C22⋊C4×C59—22no—
231C22⋊C4×C59—21no—
232C22⋊C4×C59—21no—
233C22⋊C4×C59—42no—
234C22⋊C4×C59—84no—
235C42×C59—22no—
236C42×C59—21no—
237C42×C59—21no—
238C42×C59—21no—
239C42×C59—21no—
240C42×C59—21no—
241C42×C59—22no—
242C42×C59—22no—
243C23×C59—22no—
244C23×C59—22no—
245C23×C59—22no—
246C23×C59—21no—
247C23×C59—24no—
248C23×C59—41no—
249C23×C59—42no—
250C23×C59—42no—
251C23×C59#12011yescharacteristic
252C23×C59#12011yescharacteristic
253C23×C59C22×D411yescharacteristic
254Q8×C59—22no—
255Q8×C59—82no—
256D4×C59—22no—
257D4×C59—42no—
258D4×C59—44no—
259D4×C59—42no—
260D4×C59—41no—
261D4×C59—41no—
262D4×C59—42no—
263D4×C59—81no—
264D4×C59—82no—
265D4×C59—82no—
266D4×C59—82no—
267C2×C4×C59—22no—
268C2×C4×C59—21no—
269C2×C4×C59—21no—
270C2×C4×C59—21no—
271C2×C4×C59—21no—
272C2×C4×C59—22no—
273C2×C4×C59—22no—
274C2×C4×C59—21no—
275C2×C4×C59—21no—
276C2×C4×C59—21no—
277C2×C4×C59—21no—
278C2×C4×C59—21no—
279C2×C4×C59—21no—
280C2×C4×C59—21no—
281C2×C4×C59—22no—
282C2×C4×C59—42no—
283C2×C4×C59—41no—
284C2×C4×C59—41no—
285C2×C4×C59—42no—
286C2×C4×C59—42no—
287C2×C4×C59—42no—
288C2×C4×C59—44no—
289C2×C4×C59—42no—
290C2×C4×C59—42no—
291C2×C4×C59—81no—
292C2×C4×C59—82no—
293C2×C4×C59—82no—
294C2×C4×C59—82no—
295C2×C4×C59—82no—
296C2×C4×C59—82no—
297C2×C4×C59#12011yescharacteristic
298C2×C4×C59#12011yescharacteristic
299C2×C4×C59C22×D411yescharacteristic
300C2×C4×C59C22×D411yescharacteristic
301C2×C4×C59C2×#4112yes—
302C2×C4×C592−1+412yes—
303C8×C59—24no—
304C8×C59—42no—
305#24083C5911yesmaximal, characteristic, direct product factor, Sylow
306C22×C59—21no—
307C22×C59—21no—
308C22×C59—21no—
309C22×C59—21no—
310C22×C59—21no—
311C22×C59—21no—
312C22×C59—21no—
313C22×C59—44no—
314C22×C59—41no—
315C22×C59—42no—
316C22×C59—41no—
317C22×C59—42no—
318C22×C59—42no—
319C22×C59—41no—
320C22×C59—84no—
321C22×C59#45512yes—
322C22×C59C2×#12011yescharacteristic
323C22×C59#54712yes—
324C4×C59—21no—
325C4×C59—21no—
326C4×C59—41no—
327C4×C59—41no—
328C4×C59—41no—
329C4×C59—42no—
330C4×C59—41no—
331C4×C59—41no—
332C4×C59—41no—
333C4×C59—41no—
334C4×C59—82no—
335C4×C59—82no—
336C4×C59#52511yescharacteristic
337C4×C59#53611yescharacteristic
338C4×C59#54712yes—
339#3494C2×C5911yescharacteristic
340#3092C2×C5911yescharacteristic, complemented
341C2×#428C2×C5911yescharacteristic, complemented
342#2504C2×C5911yescharacteristic, complemented
343#2061C2×C5912yescomplemented
344#2037C2×C5912yescomplemented
345#1900C2×C5911yescharacteristic, complemented
346#1871C2×C5911yescharacteristic, complemented
347#1860C2×C5912yescomplemented
348#1856C2×C5912yescomplemented
349#1826C2×C5911yescharacteristic, complemented
350C2×C59—22no—
351C2×C59—22no—
352C2×C59—41no—
353C2×C59—81no—
354C2×C59—82no—
355C2×C59#240611yescharacteristic
356C2×C59C2×#45511yescharacteristic
357C2×C59#302111yescharacteristic
358C22×M16C22×C5911yescharacteristic
359#555—21no—
360#553—21no—
361#553—21no—
362#551—22no—
363#547—21no—
364#546—22no—
365#544C22×C5911yescharacteristic
366#542—21no—
367#540—21no—
368#535C22×C5911yescharacteristic
369#532—21no—
370#529—21no—
371#525C22×C5911yescharacteristic
372C2×#121C22×C5911yescharacteristic
373#520C22×C5911yescharacteristic
374#518C22×C5911yescharacteristic
375C2×#117C22×C5911yescharacteristic
376C22×C4⋊C4C22×C5911yescharacteristic
377#484—21no—
378#483—21no—
379#481—21no—
380#480—21no—
381#428—21no—
382#428—21no—
383#428C22×C5912yes—
384#428C22×C5912yes—
385#428C22×C5912yes—
386C2×#107—21no—
387C2×#106—21no—
388C2×#104C22×C5912yes—
389#417C22×C5912yes—
390C2×#100C22×C5912yes—
391#407C22×C5911yescharacteristic
392#397—22no—
393#390C22×C5912yes—
394#386—22no—
395#382C22×C5912yes—
396C4×C22⋊C4C22×C5911yescharacteristic
397#343C22×C5912yes—
398#339C22×C5912yes—
399#339C22×C5912yes—
400#339C22×C5912yes—
401C59#2408311yescharacteristic, direct product factor, Sylow
402C2×#41—22no—
403C2×#41C23×C5911yescharacteristic
404C22×D4D4×C5912yes—
405C22×D4C23×C5911yescharacteristic
406C23×C4—21no—
407C23×C4C23×C5911yescharacteristic
408C2×M16—21no—
409C2×M16—24no—
410C2×M16C23×C5912yes—
411C2×M16C23×C5912yes—
412C22×C8—21no—
413C4⋊Q8—21no—
414C4⋊Q8—21no—
415#127—21no—
416#126—22no—
417#126—22no—
418#125—21no—
419#125—21no—
420#124—22no—
421#124—22no—
422#124—21no—
423#123—22no—
424#123—22no—
425#123—22no—
426#123—22no—
427#123—21no—
428C22⋊Q8—22no—
429C22⋊Q8—22no—
430C22⋊Q8D4×C5911yescharacteristic
431C22⋊Q8D4×C5911yescharacteristic
432#121—22no—
433#121—22no—
434#121—22no—
435#121—21no—
436#121—21no—
437#121—21no—
438#121—21no—
439#121—21no—
440#121—21no—
441#121D4×C5911yescharacteristic
442#121D4×C5911yescharacteristic
443#120—21no—
444#120—22no—
445C4×Q8—21no—
446C4×D4—22no—
447C4×D4—22no—
448C4×D4—21no—
449C4×D4—22no—
450C4×D4—21no—
451C4×D4—21no—
452C4×D4—21no—
453C4×D4—21no—
454C4×D4—21no—
455C4×D4—21no—
456#117—22no—
457#117—21no—
458#117—21no—
459#117—21no—
460#117D4×C5911yescharacteristic
461#117D4×C5911yescharacteristic
462#117C23×C5911yescharacteristic
463#117C23×C5911yescharacteristic
464#117C23×C5911yescharacteristic
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4D4×C5911yescharacteristic
472C2×C4⋊C4D4×C5911yescharacteristic
473C2×C4⋊C4C23×C5912yes—
474C2×C4⋊C4C23×C5911yescharacteristic
475C2×C22⋊C4—21no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4D4×C5912yes—
480C2×C42—21no—
481C2×C42C23×C5912yes—
482#107—22no—
483#107—22no—
484#107—22no—
485#106—22no—
486#106—22no—
487#106—22no—
488#104—24no—
489#103—22no—
490#102—22no—
491#100—24no—
492C22⋊C8—21no—
493C22⋊C8—21no—
494#95—21no—
495#95—24no—
496C24C2×D4×C5911yescharacteristic
497C24C2×D4×C5912yes—
498#41—22no—
499#41—22no—
500#41—84no—
501C2×Q8—22no—
502C2×Q8C2×D4×C5911yescharacteristic
503C2×D4—21no—
504C2×D4—22no—
505C2×D4—21no—
506C2×D4—22no—
507C2×D4—22no—
508C2×D4—21no—
509C2×D4—22no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—44no—
515C2×D4C2×D4×C5911yescharacteristic
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—82no—
529C22×C4C2×D4×C5911yescharacteristic
530C22×C4C2×D4×C5911yescharacteristic
531C22×C4C2×D4×C5911yescharacteristic
532C22×C4C2×D4×C5911yescharacteristic
533C22×C4C2×D4×C5911yescharacteristic
534C22×C4C2×D4×C5912yes—
535C22×C4C24×C5911yescharacteristic
536M16—24no—
537M16—22no—
538M16—22no—
539M16—22no—
540M16#41×C5914yescomplemented
541C2×C8—24no—
542C2×C8—22no—
543C2×C8—22no—
544C4⋊C4—22no—
545C4⋊C4—22no—
546C4⋊C4—22no—
547C4⋊C4—22no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—41no—
557C4⋊C4—41no—
558C4⋊C4C2×D4×C5911yescharacteristic
559C4⋊C4C2×D4×C5911yescharacteristic
560C4⋊C4C2×D4×C5911yescharacteristic
561C4⋊C4C2×D4×C5911yescharacteristic
562C4⋊C4C2×D4×C5911yescharacteristic
563C4⋊C4C2×D4×C5911yescharacteristic
564C22⋊C4—22no—
565C22⋊C4—22no—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C22⋊C4—22no—
569C22⋊C4—21no—
570C22⋊C4—21no—
571C22⋊C4—21no—
572C22⋊C4—21no—
573C22⋊C4—21no—
574C22⋊C4—21no—
575C22⋊C4—21no—
576C22⋊C4—22no—
577C22⋊C4—22no—
578C22⋊C4—21no—
579C22⋊C4—21no—
580C22⋊C4—42no—
581C22⋊C4—84no—
582C42—22no—
583C42—21no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—22no—
589C42—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—21no—
594C23—24no—
595C23—41no—
596C23—42no—
597C23—42no—
598C23#120×C5911yescharacteristic
599C23#120×C5911yescharacteristic
600C23C22×D4×C5911yescharacteristic
601Q8—22no—
602Q8—82no—
603D4—22no—
604D4—44no—
605D4—42no—
606D4—42no—
607D4—41no—
608D4—41no—
609D4—42no—
610D4—81no—
611D4—82no—
612D4—82no—
613D4—82no—
614C2×C4—22no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—42no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—44no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—81no—
639C2×C4—82no—
640C2×C4—82no—
641C2×C4—82no—
642C2×C4—82no—
643C2×C4—82no—
644C2×C4#120×C5911yescharacteristic
645C2×C4#120×C5911yescharacteristic
646C2×C4C22×D4×C5911yescharacteristic
647C2×C4C22×D4×C5911yescharacteristic
648C2×C4C2×#41×C5912yes—
649C2×C42−1+4×C5912yes—
650C8—24no—
651C8—42no—
652C22—21no—
653C22—21no—
654C22—21no—
655C22—21no—
656C22—21no—
657C22—21no—
658C22—21no—
659C22—44no—
660C22—41no—
661C22—42no—
662C22—42no—
663C22—41no—
664C22—41no—
665C22—42no—
666C22—84no—
667C22C59×#45512yes—
668C22C2×#120×C5911yescharacteristic
669C22C59×#54712yes—
670C4—21no—
671C4—21no—
672C4—41no—
673C4—41no—
674C4—42no—
675C4—41no—
676C4—41no—
677C4—41no—
678C4—41no—
679C4—41no—
680C4—82no—
681C4—82no—
682C4C59×#52511yescharacteristic
683C4C59×#53611yescharacteristic
684C4C59×#54712yes—
685C2—22no—
686C2—22no—
687C2—41no—
688C2—82no—
689C2—81no—
690C2C59×#240611yescharacteristic
691C2C2×C59×#45511yescharacteristic
692C2C59×#302111yescharacteristic
subgroupG/H
center, socleC22×C59C2×#120
commutator, Frattini, cosocleC22×C4C24×C59
prime radicalC59×#3494C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C59 ◁ C23×C4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C59×#3092C2semidirect
3. C2×C59×#428C2semidirect
4. C59×#2504C2semidirect
5. C59×#2061C2semidirect
6. C59×#2037C2semidirect
7. C59×#1900C2semidirect
8. C59×#1871C2semidirect
9. C59×#1860C2semidirect
10. C59×#1856C2semidirect
11. C59×#1826C2semidirect
193. M16×C59#41semidirect
305. #24083C59direct (N × H)
340. #3092C2×C59semidirect
341. C2×#428C2×C59semidirect
342. #2504C2×C59semidirect
343. #2061C2×C59semidirect
344. #2037C2×C59semidirect
345. #1900C2×C59semidirect
346. #1871C2×C59semidirect
347. #1860C2×C59semidirect
348. #1856C2×C59semidirect
349. #1826C2×C59semidirect
401. C59#24083direct (N × H)
540. M16#41×C59semidirect

Maximal subgroups

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

subgroupindex
C59×#34942
C59×#30922
C2×C59×#4282
C59×#25042
C59×#20612
C59×#20372
C59×#19002
C59×#18712
C59×#18602
C59×#18562
C59×#18262
#2408359