Finite Group Databasebeta

← C59×#24089 #28436198

Subgroups — C59×#24089 #28436198

Order 15104.

1334 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#547C211yesmaximal, characteristic
2C2×C59×#481C211yesmaximal, characteristic, complemented
3C22×#106×C59C211yesmaximal, characteristic, complemented
4C59×#2487C211yesmaximal, characteristic, complemented
5C59×#2058C212yesmaximal, complemented
6C59×#2034C212yesmaximal, complemented
7C59×#1893C211yesmaximal, characteristic, complemented
8C59×#1869C211yesmaximal, characteristic, complemented
9C59×#1864C212yesmaximal, complemented
10C59×#1853C212yesmaximal, complemented
11C59×#1823C211yesmaximal, characteristic, complemented
12C22×#41×C59—21no—
13C23×C8×C59C2211yescharacteristic
14C59×#547—24no—
15C59×#547—24no—
16C2×C4⋊Q8×C59C2211yescharacteristic
17C2×#123×C59—21no—
18C2×#123×C59—21no—
19C2×C22⋊Q8×C59—21no—
20C2×#121×C59C2211yescharacteristic
21C2×#121×C59C2211yescharacteristic
22C2×C4×D4×C59C2211yescharacteristic
23C2×C4×D4×C59C2211yescharacteristic
24C22×C4⋊C4×C59C2211yescharacteristic
25C22×C4⋊C4×C59C2211yescharacteristic
26C22×C4⋊C4×C59C2211yescharacteristic
27C59×#481—24no—
28C2×#106×C59—24no—
29C2×#106×C59C2212yes—
30C2×#106×C59C2212yes—
31C2×#106×C59C2212yes—
32C2×#102×C59C2212yes—
33C2×#102×C59C2212yes—
34C2×C22⋊C8×C59C2212yes—
35C2×C22⋊C8×C59C2211yescharacteristic
36C59×#400—21no—
37C59×#399—21no—
38C59×#389C2212yes—
39C59×#386—21no—
40C59×#385—21no—
41C59×#380C2212yes—
42C59×#380C2211yescharacteristic
43C59×#340C2212yes—
44C59×#340C2212yes—
45C59×#340C2212yes—
46C59×#336C2212yes—
47C2×#41×C59—28no—
48C2×#41×C59—44no—
49C2×#41×C59—44no—
50C22×Q8×C59—21no—
51C22×D4×C59—21no—
52C22×D4×C59—21no—
53C22×D4×C59D411yescharacteristic
54C22×D4×C59C2311yescharacteristic
55C23×C4×C59—21no—
56C23×C4×C59—21no—
57C23×C4×C59—21no—
58C23×C4×C59—21no—
59C23×C4×C59C2311yescharacteristic
60C23×C4×C59C2311yescharacteristic
61C22×C8×C59—22no—
62C22×C8×C59—24no—
63C22×C8×C59C2312yes—
64C22×C8×C59C2312yes—
65C4⋊Q8×C59—22no—
66C4⋊Q8×C59—22no—
67#123×C59—28no—
68#123×C59—28no—
69C22⋊Q8×C59—28no—
70#121×C59—22no—
71#121×C59—22no—
72#121×C59—22no—
73#121×C59D414yes—
74C4×D4×C59—22no—
75C4×D4×C59—22no—
76C4×D4×C59—22no—
77C4×D4×C59—22no—
78C2×C4⋊C4×C59—21no—
79C2×C4⋊C4×C59—21no—
80C2×C4⋊C4×C59—22no—
81C2×C4⋊C4×C59—21no—
82C2×C4⋊C4×C59—22no—
83C2×C4⋊C4×C59—22no—
84C2×C4⋊C4×C59—22no—
85C2×C4⋊C4×C59—22no—
86C2×C4⋊C4×C59—21no—
87C2×C4⋊C4×C59—22no—
88C2×C4⋊C4×C59D411yescharacteristic
89C2×C4⋊C4×C59D414yes—
90C2×C4⋊C4×C59C2312yes—
91C2×C4⋊C4×C59C2312yes—
92C2×C4⋊C4×C59C2311yescharacteristic
93C2×C4⋊C4×C59C2311yescharacteristic
94C2×C4⋊C4×C59C2311yescharacteristic
95C2×C22⋊C4×C59—21no—
96C2×C22⋊C4×C59—21no—
97C2×C22⋊C4×C59—21no—
98C2×C22⋊C4×C59—21no—
99C2×C22⋊C4×C59—22no—
100C2×C22⋊C4×C59D411yescharacteristic
101C2×C22⋊C4×C59D411yescharacteristic
102C2×C42×C59C2311yescharacteristic
103#106×C59—24no—
104#106×C59—24no—
105#106×C59—24no—
106#102×C59—24no—
107#102×C59—24no—
108C22⋊C8×C59—22no—
109C22⋊C8×C59—24no—
110#95×C59—22no—
111#95×C59—21no—
112#95×C59—22no—
113C24×C59—21no—
114C24×C59C2×D411yescharacteristic
115C24×C59C2×D411yescharacteristic
116#41×C59—432no—
117C2×Q8×C59—24no—
118C2×Q8×C59—42no—
119C2×Q8×C59—42no—
120C2×D4×C59—22no—
121C2×D4×C59—22no—
122C2×D4×C59—24no—
123C2×D4×C59—24no—
124C2×D4×C59—21no—
125C2×D4×C59—22no—
126C2×D4×C59—22no—
127C2×D4×C59—42no—
128C2×D4×C59—42no—
129C2×D4×C59—42no—
130C2×D4×C59—42no—
131C2×D4×C59SD1614yes—
132C2×D4×C59C2×D412yes—
133C22×C4×C59—22no—
134C22×C4×C59—22no—
135C22×C4×C59—24no—
136C22×C4×C59—24no—
137C22×C4×C59—24no—
138C22×C4×C59—21no—
139C22×C4×C59—21no—
140C22×C4×C59—21no—
141C22×C4×C59—21no—
142C22×C4×C59—21no—
143C22×C4×C59—22no—
144C22×C4×C59—22no—
145C22×C4×C59—22no—
146C22×C4×C59—22no—
147C22×C4×C59—42no—
148C22×C4×C59—42no—
149C22×C4×C59—42no—
150C22×C4×C59—42no—
151C22×C4×C59—42no—
152C22×C4×C59—42no—
153C22×C4×C59—42no—
154C22×C4×C59—82no—
155C22×C4×C59C2×D411yescharacteristic
156C22×C4×C59C2×D411yescharacteristic
157C22×C4×C59C2×D411yescharacteristic
158C22×C4×C59C2×D412yes—
159C22×C4×C59C2×D412yes—
160C22×C4×C59C2×D411yescharacteristic
161C22×C4×C59C2411yescharacteristic
162C2×C8×C59—28no—
163C2×C8×C59—22no—
164C2×C8×C59—22no—
165C2×C8×C59—22no—
166C2×C8×C59—22no—
167C2×C8×C59—22no—
168C2×C8×C59#4114yescomplemented
169C4⋊C4×C59—24no—
170C4⋊C4×C59—24no—
171C4⋊C4×C59—24no—
172C4⋊C4×C59—22no—
173C4⋊C4×C59—21no—
174C4⋊C4×C59—21no—
175C4⋊C4×C59—21no—
176C4⋊C4×C59—22no—
177C4⋊C4×C59—22no—
178C4⋊C4×C59—22no—
179C4⋊C4×C59—22no—
180C4⋊C4×C59—42no—
181C4⋊C4×C59—82no—
182C4⋊C4×C59C2×D412yes—
183C4⋊C4×C59C2×D412yes—
184C4⋊C4×C59C2×D412yes—
185C22⋊C4×C59—24no—
186C22⋊C4×C59—24no—
187C22⋊C4×C59—22no—
188C22⋊C4×C59—24no—
189C22⋊C4×C59—22no—
190C22⋊C4×C59—42no—
191C22⋊C4×C59—82no—
192C42×C59—21no—
193C42×C59—21no—
194C23×C59—22no—
195C23×C59—22no—
196C23×C59—21no—
197C23×C59—22no—
198C23×C59—21no—
199C23×C59—22no—
200C23×C59—22no—
201C23×C59—42no—
202C23×C59—41no—
203C23×C59—41no—
204C23×C59—42no—
205C23×C59#12012yes—
206C23×C59C2×SD1612yes—
207C23×C59C2×SD1612yes—
208C23×C59AGL(1,ℤ/8)12yes—
209C23×C59C22×D411yescharacteristic
210Q8×C59—48no—
211D4×C59—28no—
212D4×C59—24no—
213D4×C59—48no—
214D4×C59—48no—
215D4×C59—41no—
216D4×C59—41no—
217C2×C4×C59—21no—
218C2×C4×C59—22no—
219C2×C4×C59—21no—
220C2×C4×C59—22no—
221C2×C4×C59—22no—
222C2×C4×C59—24no—
223C2×C4×C59—21no—
224C2×C4×C59—21no—
225C2×C4×C59—22no—
226C2×C4×C59—22no—
227C2×C4×C59—22no—
228C2×C4×C59—22no—
229C2×C4×C59—22no—
230C2×C4×C59—48no—
231C2×C4×C59—48no—
232C2×C4×C59—41no—
233C2×C4×C59—41no—
234C2×C4×C59—41no—
235C2×C4×C59—41no—
236C2×C4×C59—41no—
237C2×C4×C59—41no—
238C2×C4×C59—48no—
239C2×C4×C59—41no—
240C2×C4×C59—41no—
241C2×C4×C59—42no—
242C2×C4×C59—42no—
243C2×C4×C59—42no—
244C2×C4×C59—42no—
245C2×C4×C59—42no—
246C2×C4×C59—42no—
247C2×C4×C59—42no—
248C2×C4×C59—84no—
249C2×C4×C59#12012yes—
250C2×C4×C59C2×SD1612yes—
251C2×C4×C59C22×D411yescharacteristic
252C2×C4×C59C22×D411yescharacteristic
253C2×C4×C59C2×#4112yes—
254C2×C4×C592−1+412yes—
255C8×C59—24no—
256C8×C59—42no—
257#24089C5911yesmaximal, characteristic, direct product factor, Sylow
258C22×C59—24no—
259C22×C59—24no—
260C22×C59—22no—
261C22×C59—22no—
262C22×C59—24no—
263C22×C59—22no—
264C22×C59—42no—
265C22×C59—41no—
266C22×C59—41no—
267C22×C59—42no—
268C22×C59—42no—
269C22×C59—42no—
270C22×C59—82no—
271C22×C59—82no—
272C22×C59#45014yes—
273C22×C59C2×#12011yescharacteristic
274C22×C59#54712yes—
275C22×C59C22×SD1611yescharacteristic
276C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
277C22×C59#57712yes—
278C4×C59—22no—
279C4×C59—22no—
280C4×C59—41no—
281C4×C59—42no—
282C4×C59—42no—
283C4×C59—42no—
284C4×C59—41no—
285C4×C59—82no—
286C4×C59—82no—
287C4×C59#52511yescharacteristic
288C4×C59#53611yescharacteristic
289C4×C59#54712yes—
290C2×#547C2×C5911yescharacteristic
291C2×#481C2×C5911yescharacteristic, complemented
292C22×#106C2×C5911yescharacteristic, complemented
293#2487C2×C5911yescharacteristic, complemented
294#2058C2×C5912yescomplemented
295#2034C2×C5912yescomplemented
296#1893C2×C5911yescharacteristic, complemented
297#1869C2×C5911yescharacteristic, complemented
298#1864C2×C5912yescomplemented
299#1853C2×C5912yescomplemented
300#1823C2×C5911yescharacteristic, complemented
301C2×C59—24no—
302C2×C59—42no—
303C2×C59—82no—
304C2×C59#240611yescharacteristic
305C2×C59C2×#45011yescharacteristic
306C2×C59#301011yescharacteristic
307C2×C59#333512yes—
308C2×C59#334512yes—
309C22×#41—21no—
310C23×C8C22×C5911yescharacteristic
311#547—24no—
312#547—24no—
313C2×C4⋊Q8C22×C5911yescharacteristic
314C2×#123—21no—
315C2×#123—21no—
316C2×C22⋊Q8—21no—
317C2×#121C22×C5911yescharacteristic
318C2×#121C22×C5911yescharacteristic
319C2×C4×D4C22×C5911yescharacteristic
320C2×C4×D4C22×C5911yescharacteristic
321C22×C4⋊C4C22×C5911yescharacteristic
322C22×C4⋊C4C22×C5911yescharacteristic
323C22×C4⋊C4C22×C5911yescharacteristic
324#481—24no—
325C2×#106—24no—
326C2×#106C22×C5912yes—
327C2×#106C22×C5912yes—
328C2×#106C22×C5912yes—
329C2×#102C22×C5912yes—
330C2×#102C22×C5912yes—
331C2×C22⋊C8C22×C5911yescharacteristic
332C2×C22⋊C8C22×C5912yes—
333#400—21no—
334#399—21no—
335#389C22×C5912yes—
336#386—21no—
337#385—21no—
338#380C22×C5911yescharacteristic
339#380C22×C5912yes—
340#340C22×C5912yes—
341#340C22×C5912yes—
342#340C22×C5912yes—
343#336C22×C5912yes—
344C59#2408911yescharacteristic, direct product factor, Sylow
345C2×#41—28no—
346C2×#41—44no—
347C2×#41—44no—
348C22×Q8—21no—
349C22×D4—21no—
350C22×D4—21no—
351C22×D4D4×C5911yescharacteristic
352C22×D4C23×C5911yescharacteristic
353C23×C4—21no—
354C23×C4—21no—
355C23×C4—21no—
356C23×C4—21no—
357C23×C4C23×C5911yescharacteristic
358C23×C4C23×C5911yescharacteristic
359C22×C8—22no—
360C22×C8—24no—
361C22×C8C23×C5912yes—
362C22×C8C23×C5912yes—
363C4⋊Q8—22no—
364C4⋊Q8—22no—
365#123—28no—
366#123—28no—
367C22⋊Q8—28no—
368#121—22no—
369#121—22no—
370#121—22no—
371#121D4×C5914yes—
372C4×D4—22no—
373C4×D4—22no—
374C4×D4—22no—
375C4×D4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4D4×C5911yescharacteristic
387C2×C4⋊C4D4×C5914yes—
388C2×C4⋊C4C23×C5912yes—
389C2×C4⋊C4C23×C5912yes—
390C2×C4⋊C4C23×C5911yescharacteristic
391C2×C4⋊C4C23×C5911yescharacteristic
392C2×C4⋊C4C23×C5911yescharacteristic
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4D4×C5911yescharacteristic
399C2×C22⋊C4D4×C5911yescharacteristic
400C2×C42C23×C5911yescharacteristic
401#106—24no—
402#106—24no—
403#106—24no—
404#102—24no—
405#102—24no—
406C22⋊C8—22no—
407C22⋊C8—24no—
408#95—22no—
409#95—21no—
410#95—22no—
411C24—21no—
412C24C2×D4×C5911yescharacteristic
413C24C2×D4×C5911yescharacteristic
414#41—432no—
415C2×Q8—24no—
416C2×Q8—42no—
417C2×Q8—42no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—24no—
421C2×D4—24no—
422C2×D4—21no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—42no—
426C2×D4—42no—
427C2×D4—42no—
428C2×D4—42no—
429C2×D4SD16×C5914yes—
430C2×D4C2×D4×C5912yes—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—82no—
453C22×C4C2×D4×C5911yescharacteristic
454C22×C4C2×D4×C5911yescharacteristic
455C22×C4C2×D4×C5911yescharacteristic
456C22×C4C2×D4×C5912yes—
457C22×C4C2×D4×C5912yes—
458C22×C4C2×D4×C5911yescharacteristic
459C22×C4C24×C5911yescharacteristic
460C2×C8—28no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—22no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8#41×C5914yescomplemented
467C4⋊C4—24no—
468C4⋊C4—24no—
469C4⋊C4—24no—
470C4⋊C4—22no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—42no—
479C4⋊C4—82no—
480C4⋊C4C2×D4×C5912yes—
481C4⋊C4C2×D4×C5912yes—
482C4⋊C4C2×D4×C5912yes—
483C22⋊C4—24no—
484C22⋊C4—24no—
485C22⋊C4—22no—
486C22⋊C4—24no—
487C22⋊C4—22no—
488C22⋊C4—42no—
489C22⋊C4—82no—
490C42—21no—
491C42—21no—
492C23—22no—
493C23—22no—
494C23—21no—
495C23—22no—
496C23—21no—
497C23—22no—
498C23—22no—
499C23—42no—
500C23—41no—
501C23—41no—
502C23—42no—
503C23#120×C5912yes—
504C23C2×SD16×C5912yes—
505C23C2×SD16×C5912yes—
506C23AGL(1,ℤ/8)×C5912yes—
507C23C22×D4×C5911yescharacteristic
508Q8—48no—
509D4—28no—
510D4—24no—
511D4—48no—
512D4—48no—
513D4—41no—
514D4—41no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—24no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—48no—
529C2×C4—48no—
530C2×C4—48no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—84no—
547C2×C4#120×C5912yes—
548C2×C4C2×SD16×C5912yes—
549C2×C4C22×D4×C5911yescharacteristic
550C2×C4C22×D4×C5911yescharacteristic
551C2×C4C2×#41×C5912yes—
552C2×C42−1+4×C5912yes—
553C8—24no—
554C8—42no—
555C22—22no—
556C22—24no—
557C22—24no—
558C22—22no—
559C22—22no—
560C22—24no—
561C22—41no—
562C22—42no—
563C22—41no—
564C22—42no—
565C22—42no—
566C22—42no—
567C22—82no—
568C22—82no—
569C22C59×#45014yes—
570C22C2×#120×C5911yescharacteristic
571C22C59×#54712yes—
572C22C22×SD16×C5911yescharacteristic
573C22C2×AGL(1,ℤ/8)×C5911yescharacteristic
574C22C59×#57712yes—
575C4—22no—
576C4—22no—
577C4—42no—
578C4—42no—
579C4—42no—
580C4—41no—
581C4—41no—
582C4—82no—
583C4—82no—
584C4C59×#52511yescharacteristic
585C4C59×#53611yescharacteristic
586C4C59×#54712yes—
587C2—24no—
588C2—42no—
589C2—82no—
590C2C59×#240611yescharacteristic
591C2C2×C59×#45011yescharacteristic
592C2C59×#301011yescharacteristic
593C2C59×#333512yes—
594C2C59×#334512yes—
subgroupG/H
center, socleC23×C59C22×D4
commutator, Frattini, cosocleC22×C4C24×C59
prime radicalC2×C59×#547C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C59 ◁ C2×C4×D4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C59×#481C2semidirect
3. C22×#106×C59C2semidirect
4. C59×#2487C2semidirect
5. C59×#2058C2semidirect
6. C59×#2034C2semidirect
7. C59×#1893C2semidirect
8. C59×#1869C2semidirect
9. C59×#1864C2semidirect
10. C59×#1853C2semidirect
11. C59×#1823C2semidirect
168. C2×C8×C59#41semidirect
257. #24089C59direct (N × H)
291. C2×#481C2×C59semidirect
292. C22×#106C2×C59semidirect
293. #2487C2×C59semidirect
294. #2058C2×C59semidirect
295. #2034C2×C59semidirect
296. #1893C2×C59semidirect
297. #1869C2×C59semidirect
298. #1864C2×C59semidirect
299. #1853C2×C59semidirect
300. #1823C2×C59semidirect
344. C59#24089direct (N × H)
466. C2×C8#41×C59semidirect

Maximal subgroups

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

subgroupindex
C2×C59×#5472
C2×C59×#4812
C22×#106×C592
C59×#24872
C59×#20582
C59×#20342
C59×#18932
C59×#18692
C59×#18642
C59×#18532
C59×#18232
#2408959