Finite Group Databasebeta

← C59×#11057 #28423166

Subgroups — C59×#11057 #28423166

Order 15104.

910 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#421C211yesmaximal, characteristic
2C2×C59×#417C211yesmaximal, characteristic
3C2×C59×#410C211yesmaximal, characteristic
4C59×#2316C211yesmaximal, characteristic, complemented
5C2×C59×#344C211yesmaximal, characteristic, complemented
6C59×#1736C211yesmaximal, characteristic, complemented
7C2×C59×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
8C22×#41×C59C2211yescharacteristic
9C22×M16×C59C2211yescharacteristic
10C22×M16×C59C2211yescharacteristic
11C2×#117×C59C2211yescharacteristic
12C2×#117×C59C2211yescharacteristic
13C2×#117×C59C2211yescharacteristic
14C22×C4⋊C4×C59C2211yescharacteristic
15C59×#421—22no—
16C59×#421—22no—
17C2×#104×C59—22no—
18C59×#417—22no—
19C59×#417—22no—
20C2×#103×C59C412yescomplemented
21C2×#102×C59C412yescomplemented
22C59×#410—22no—
23C59×#410—22no—
24C2×#99×C59—22no—
25C59×#389—22no—
26C59×#389—22no—
27C59×#380—22no—
28C59×#344—22no—
29C59×#340—22no—
30C59×H(3,ℤ/4)—22no—
31C2×#41×C59—21no—
32C2×#41×C59—21no—
33C2×#41×C59—21no—
34C2×#41×C59—21no—
35C2×#41×C59—21no—
36C2×#41×C59—21no—
37C2×#41×C59—21no—
38C2×#41×C59—21no—
39C2×#41×C59—21no—
40C2×#41×C59—21no—
41C2×#41×C59D412yes—
42C2×#41×C59Q812yes—
43C22×Q8×C59C2×C411yescharacteristic
44C22×D4×C59—21no—
45C22×D4×C59C2×C411yescharacteristic
46C23×C4×C59—21no—
47C23×C4×C59—21no—
48C23×C4×C59C2311yescharacteristic
49C2×M16×C59—21no—
50C2×M16×C59—21no—
51C2×M16×C59—21no—
52C2×M16×C59—21no—
53C2×M16×C59—21no—
54C2×M16×C59—21no—
55C2×M16×C59—21no—
56C2×M16×C59—21no—
57C2×M16×C59—21no—
58C2×M16×C59—21no—
59C2×M16×C59—21no—
60C2×M16×C59D412yes—
61C22×C8×C59—21no—
62C22×C8×C59C2×C412yes—
63#117×C59—21no—
64#117×C59—21no—
65#117×C59—21no—
66#117×C59—21no—
67#117×C59—21no—
68#117×C59—21no—
69#117×C59—21no—
70#117×C59—21no—
71#117×C59—21no—
72#117×C59—21no—
73#117×C59—21no—
74#117×C59D412yes—
75C2×C4⋊C4×C59—21no—
76C2×C4⋊C4×C59—21no—
77C2×C4⋊C4×C59—21no—
78C2×C4⋊C4×C59—21no—
79C2×C4⋊C4×C59—21no—
80C2×C4⋊C4×C59—21no—
81C2×C4⋊C4×C59—24no—
82C2×C4⋊C4×C59C2×C412yes—
83C2×C4⋊C4×C59D412yes—
84C2×C4⋊C4×C59D412yes—
85C2×C22⋊C4×C59—21no—
86C2×C22⋊C4×C59—21no—
87C2×C22⋊C4×C59D412yes—
88C2×C42×C59—21no—
89C2×C42×C59—21no—
90C2×C42×C59D412yes—
91#104×C59—28no—
92#103×C59—24no—
93#102×C59—24no—
94#99×C59—28no—
95#95×C59—24no—
96C24×C59—21no—
97C24×C59C2×D411yescharacteristic
98#41×C59—22no—
99#41×C59—22no—
100#41×C59—22no—
101#41×C59—22no—
102#41×C59—22no—
103#41×C59—22no—
104#41×C59—22no—
105#41×C59—22no—
106#41×C59—41no—
107#41×C59—41no—
108#41×C59—41no—
109#41×C59—41no—
110#41×C59—41no—
111#41×C59—41no—
112#41×C59—41no—
113#41×C59—41no—
114C2×Q8×C59—21no—
115C2×Q8×C59—21no—
116C2×Q8×C59—21no—
117C2×Q8×C59—21no—
118C2×Q8×C59—21no—
119C2×Q8×C59C4⋊C412yescomplemented
120C2×D4×C59—22no—
121C2×D4×C59—22no—
122C2×D4×C59—21no—
123C2×D4×C59—21no—
124C2×D4×C59—21no—
125C2×D4×C59—21no—
126C2×D4×C59—21no—
127C2×D4×C59—41no—
128C2×D4×C59—41no—
129C2×D4×C59—41no—
130C2×D4×C59—41no—
131C2×D4×C59C4⋊C412yescomplemented
132C22×C4×C59—21no—
133C22×C4×C59—22no—
134C22×C4×C59—22no—
135C22×C4×C59—22no—
136C22×C4×C59—22no—
137C22×C4×C59—22no—
138C22×C4×C59—22no—
139C22×C4×C59—22no—
140C22×C4×C59—41no—
141C22×C4×C59—41no—
142C22×C4×C59—41no—
143C22×C4×C59—41no—
144C22×C4×C59—41no—
145C22×C4×C59—82no—
146C22×C4×C59C22×C411yescharacteristic
147C22×C4×C59C2×D411yescharacteristic
148C22×C4×C59C2×D411yescharacteristic
149C22×C4×C59C2×D411yescharacteristic
150C22×C4×C59C2×D411yescharacteristic
151C22×C4×C59C2×D411yescharacteristic
152C22×C4×C59C2×D411yescharacteristic
153C22×C4×C59C2×Q811yescharacteristic
154C22×C4×C59#4111yescharacteristic
155C22×C4×C59#4111yescharacteristic
156C22×C4×C59#4111yescharacteristic
157C22×C4×C59#4111yescharacteristic
158C22×C4×C59#4111yescharacteristic
159C22×C4×C59#4111yescharacteristic
160M16×C59—22no—
161M16×C59—22no—
162M16×C59—41no—
163M16×C59—41no—
164M16×C59—41no—
165M16×C59—41no—
166M16×C59—41no—
167M16×C59—41no—
168C2×C8×C59—22no—
169C2×C8×C59—22no—
170C2×C8×C59—22no—
171C2×C8×C59—22no—
172C2×C8×C59—41no—
173C2×C8×C59—41no—
174C4⋊C4×C59—22no—
175C4⋊C4×C59—22no—
176C4⋊C4×C59—22no—
177C4⋊C4×C59—22no—
178C4⋊C4×C59—41no—
179C4⋊C4×C59—41no—
180C4⋊C4×C59—41no—
181C4⋊C4×C59—41no—
182C4⋊C4×C59—41no—
183C4⋊C4×C59—84no—
184C4⋊C4×C59C22⋊C414yes—
185C22⋊C4×C59—22no—
186C22⋊C4×C59—22no—
187C22⋊C4×C59—22no—
188C22⋊C4×C59—41no—
189C22⋊C4×C59—41no—
190C22⋊C4×C59—41no—
191C42×C59—22no—
192C42×C59—22no—
193C42×C59—22no—
194C42×C59—41no—
195C42×C59—41no—
196C42×C59—41no—
197C23×C59—22no—
198C23×C59—41no—
199C23×C59—41no—
200C23×C59—41no—
201C23×C59—41no—
202C23×C59—81no—
203C23×C59—81no—
204C23×C59C4×D411yescharacteristic
205C23×C59#12011yescharacteristic
206C23×C59#12011yescharacteristic
207C23×C59#12111yescharacteristic
208C23×C59#12111yescharacteristic
209C23×C59C22⋊Q811yescharacteristic
210C23×C59#12411yescharacteristic
211Q8×C59—22no—
212Q8×C59—22no—
213Q8×C59—41no—
214Q8×C59—41no—
215D4×C59—22no—
216D4×C59—22no—
217D4×C59—42no—
218D4×C59—42no—
219D4×C59—42no—
220D4×C59—42no—
221D4×C59—41no—
222D4×C59—41no—
223C2×C4×C59—22no—
224C2×C4×C59—24no—
225C2×C4×C59—44no—
226C2×C4×C59—41no—
227C2×C4×C59—41no—
228C2×C4×C59—42no—
229C2×C4×C59—42no—
230C2×C4×C59—42no—
231C2×C4×C59—42no—
232C2×C4×C59—42no—
233C2×C4×C59—42no—
234C2×C4×C59—42no—
235C2×C4×C59—42no—
236C2×C4×C59—42no—
237C2×C4×C59—42no—
238C2×C4×C59—42no—
239C2×C4×C59—82no—
240C2×C4×C59—82no—
241C2×C4×C59—81no—
242C2×C4×C59—81no—
243C2×C4×C59C2×C22⋊C411yescharacteristic
244C2×C4×C59C2×C4⋊C411yescharacteristic
245C2×C4×C59#11711yescharacteristic
246C2×C4×C59C4×D411yescharacteristic
247C2×C4×C59C4×D411yescharacteristic
248C2×C4×C59C4×D411yescharacteristic
249C2×C4×C59#12011yescharacteristic
250C2×C4×C59#12111yescharacteristic
251C2×C4×C59#12111yescharacteristic
252C2×C4×C59#12111yescharacteristic
253C2×C4×C59#12111yescharacteristic
254C2×C4×C59#12111yescharacteristic
255C2×C4×C59#12111yescharacteristic
256C2×C4×C59C22⋊Q811yescharacteristic
257C2×C4×C59C22⋊Q811yescharacteristic
258C2×C4×C59C22⋊Q811yescharacteristic
259C2×C4×C59C22⋊Q811yescharacteristic
260C2×C4×C59C22⋊Q811yescharacteristic
261C2×C4×C59#12311yescharacteristic
262C2×C4×C59#12311yescharacteristic
263C2×C4×C59#12311yescharacteristic
264C2×C4×C59#12311yescharacteristic
265C2×C4×C59#12311yescharacteristic
266C2×C4×C59#12411yescharacteristic
267C2×C4×C59#12411yescharacteristic
268C2×C4×C59#12611yescharacteristic
269C2×C4×C59#12611yescharacteristic
270C2×C4×C59#12711yescharacteristic
271C8×C59—42no—
272C8×C59—42no—
273#11057C5911yesmaximal, characteristic, direct product factor, Sylow
274C22×C59—21no—
275C22×C59—21no—
276C22×C59—21no—
277C22×C59—21no—
278C22×C59—21no—
279C22×C59—21no—
280C22×C59—41no—
281C22×C59—41no—
282C22×C59—41no—
283C22×C59—41no—
284C22×C59—42no—
285C22×C59—82no—
286C22×C59—82no—
287C22×C59—81no—
288C22×C59—81no—
289C22×C59#38511yescharacteristic
290C22×C59#38611yescharacteristic
291C22×C59#38811yescharacteristic
292C22×C59#39211yescharacteristic
293C22×C59#39311yescharacteristic
294C22×C59#39411yescharacteristic
295C22×C59#39611yescharacteristic
296C4×C59—44no—
297C4×C59—42no—
298C4×C59—82no—
299C4×C59—82no—
300C4×C59—82no—
301C4×C59#38011yescharacteristic
302C4×C59#38511yescharacteristic
303C4×C59#38811yescharacteristic
304C4×C59#39011yescharacteristic
305C4×C59#39411yescharacteristic
306C4×C59#39611yescharacteristic
307C4×C59#39711yescharacteristic
308C4×C59#39911yescharacteristic
309C2×#421C2×C5911yescharacteristic
310C2×#417C2×C5911yescharacteristic
311C2×#410C2×C5911yescharacteristic
312#2316C2×C5911yescharacteristic, complemented
313C2×#344C2×C5911yescharacteristic, complemented
314#1736C2×C5911yescharacteristic, complemented
315C2×H(3,ℤ/4)C2×C5911yescharacteristic, complemented
316C2×C59—21no—
317C2×C59—21no—
318C2×C59—21no—
319C2×C59—21no—
320C2×C59—21no—
321C2×C59—21no—
322C2×C59—82no—
323C2×C59#143911yescharacteristic
324C2×C59#190411yescharacteristic
325C2×C59#190511yescharacteristic
326C22×#41C22×C5911yescharacteristic
327C22×M16C22×C5911yescharacteristic
328C22×M16C22×C5911yescharacteristic
329C2×#117C22×C5911yescharacteristic
330C2×#117C22×C5911yescharacteristic
331C2×#117C22×C5911yescharacteristic
332C22×C4⋊C4C22×C5911yescharacteristic
333#421—22no—
334#421—22no—
335C2×#104—22no—
336#417—22no—
337#417—22no—
338C2×#103C4×C5912yescomplemented
339C2×#102C4×C5912yescomplemented
340#410—22no—
341#410—22no—
342C2×#99—22no—
343#389—22no—
344#389—22no—
345#380—22no—
346#344—22no—
347#340—22no—
348H(3,ℤ/4)—22no—
349C59#1105711yescharacteristic, direct product factor, Sylow
350C2×#41—21no—
351C2×#41—21no—
352C2×#41—21no—
353C2×#41—21no—
354C2×#41—21no—
355C2×#41—21no—
356C2×#41—21no—
357C2×#41—21no—
358C2×#41—21no—
359C2×#41—21no—
360C2×#41D4×C5912yes—
361C2×#41Q8×C5912yes—
362C22×Q8C2×C4×C5911yescharacteristic
363C22×D4—21no—
364C22×D4C2×C4×C5911yescharacteristic
365C23×C4—21no—
366C23×C4—21no—
367C23×C4C23×C5911yescharacteristic
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—21no—
376C2×M16—21no—
377C2×M16—21no—
378C2×M16—21no—
379C2×M16D4×C5912yes—
380C22×C8—21no—
381C22×C8C2×C4×C5912yes—
382#117—21no—
383#117—21no—
384#117—21no—
385#117—21no—
386#117—21no—
387#117—21no—
388#117—21no—
389#117—21no—
390#117—21no—
391#117—21no—
392#117—21no—
393#117D4×C5912yes—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—24no—
401C2×C4⋊C4C2×C4×C5912yes—
402C2×C4⋊C4D4×C5912yes—
403C2×C4⋊C4D4×C5912yes—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4D4×C5912yes—
407C2×C42—21no—
408C2×C42—21no—
409C2×C42D4×C5912yes—
410#104—28no—
411#103—24no—
412#102—24no—
413#99—28no—
414#95—24no—
415C24—21no—
416C24C2×D4×C5911yescharacteristic
417#41—22no—
418#41—22no—
419#41—22no—
420#41—22no—
421#41—22no—
422#41—22no—
423#41—22no—
424#41—22no—
425#41—41no—
426#41—41no—
427#41—41no—
428#41—41no—
429#41—41no—
430#41—41no—
431#41—41no—
432#41—41no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8C4⋊C4×C5912yescomplemented
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—41no—
450C2×D4C4⋊C4×C5912yescomplemented
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—82no—
465C22×C4C22×C4×C5911yescharacteristic
466C22×C4C2×D4×C5911yescharacteristic
467C22×C4C2×D4×C5911yescharacteristic
468C22×C4C2×D4×C5911yescharacteristic
469C22×C4C2×D4×C5911yescharacteristic
470C22×C4C2×D4×C5911yescharacteristic
471C22×C4C2×D4×C5911yescharacteristic
472C22×C4C2×Q8×C5911yescharacteristic
473C22×C4#41×C5911yescharacteristic
474C22×C4#41×C5911yescharacteristic
475C22×C4#41×C5911yescharacteristic
476C22×C4#41×C5911yescharacteristic
477C22×C4#41×C5911yescharacteristic
478C22×C4#41×C5911yescharacteristic
479M16—22no—
480M16—22no—
481M16—41no—
482M16—41no—
483M16—41no—
484M16—41no—
485M16—41no—
486M16—41no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—41no—
492C2×C8—41no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4—84no—
503C4⋊C4C22⋊C4×C5914yes—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—41no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C42—22no—
511C42—22no—
512C42—22no—
513C42—41no—
514C42—41no—
515C42—41no—
516C23—22no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23—81no—
522C23—81no—
523C23C4×D4×C5911yescharacteristic
524C23#120×C5911yescharacteristic
525C23#120×C5911yescharacteristic
526C23#121×C5911yescharacteristic
527C23#121×C5911yescharacteristic
528C23C22⋊Q8×C5911yescharacteristic
529C23#124×C5911yescharacteristic
530Q8—22no—
531Q8—22no—
532Q8—41no—
533Q8—41no—
534D4—22no—
535D4—22no—
536D4—42no—
537D4—42no—
538D4—42no—
539D4—42no—
540D4—41no—
541D4—41no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—44no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—82no—
559C2×C4—82no—
560C2×C4—81no—
561C2×C4—81no—
562C2×C4C2×C22⋊C4×C5911yescharacteristic
563C2×C4C2×C4⋊C4×C5911yescharacteristic
564C2×C4#117×C5911yescharacteristic
565C2×C4C4×D4×C5911yescharacteristic
566C2×C4C4×D4×C5911yescharacteristic
567C2×C4C4×D4×C5911yescharacteristic
568C2×C4#120×C5911yescharacteristic
569C2×C4#121×C5911yescharacteristic
570C2×C4#121×C5911yescharacteristic
571C2×C4#121×C5911yescharacteristic
572C2×C4#121×C5911yescharacteristic
573C2×C4#121×C5911yescharacteristic
574C2×C4#121×C5911yescharacteristic
575C2×C4C22⋊Q8×C5911yescharacteristic
576C2×C4C22⋊Q8×C5911yescharacteristic
577C2×C4C22⋊Q8×C5911yescharacteristic
578C2×C4C22⋊Q8×C5911yescharacteristic
579C2×C4C22⋊Q8×C5911yescharacteristic
580C2×C4#123×C5911yescharacteristic
581C2×C4#123×C5911yescharacteristic
582C2×C4#123×C5911yescharacteristic
583C2×C4#123×C5911yescharacteristic
584C2×C4#123×C5911yescharacteristic
585C2×C4#124×C5911yescharacteristic
586C2×C4#124×C5911yescharacteristic
587C2×C4#126×C5911yescharacteristic
588C2×C4#126×C5911yescharacteristic
589C2×C4#127×C5911yescharacteristic
590C8—42no—
591C8—42no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—42no—
603C22—82no—
604C22—82no—
605C22—81no—
606C22—81no—
607C22C59×#38511yescharacteristic
608C22C59×#38611yescharacteristic
609C22C59×#38811yescharacteristic
610C22C59×#39211yescharacteristic
611C22C59×#39311yescharacteristic
612C22C59×#39411yescharacteristic
613C22C59×#39611yescharacteristic
614C4—44no—
615C4—42no—
616C4—82no—
617C4—82no—
618C4—82no—
619C4C59×#38011yescharacteristic
620C4C59×#38511yescharacteristic
621C4C59×#38811yescharacteristic
622C4C59×#39011yescharacteristic
623C4C59×#39411yescharacteristic
624C4C59×#39611yescharacteristic
625C4C59×#39711yescharacteristic
626C4C59×#39911yescharacteristic
627C2—21no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—21no—
633C2—82no—
634C2C59×#143911yescharacteristic
635C2C59×#190411yescharacteristic
636C2C59×#190511yescharacteristic
subgroupG/H
center, socleC22×C59#386
commutatorC22×C4C22×C4×C59
Frattini, cosocleC23×C4C23×C59
prime radicalC22×#41×C59C22
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
4. C59×#2316C2semidirect
5. C2×C59×#344C2semidirect
6. C59×#1736C2semidirect
7. C2×C59×H(3,ℤ/4)C2semidirect
20. C2×#103×C59C4semidirect
21. C2×#102×C59C4semidirect
119. C2×Q8×C59C4⋊C4semidirect
131. C2×D4×C59C4⋊C4semidirect
273. #11057C59direct (N × H)
312. #2316C2×C59semidirect
313. C2×#344C2×C59semidirect
314. #1736C2×C59semidirect
315. C2×H(3,ℤ/4)C2×C59semidirect
338. C2×#103C4×C59semidirect
339. C2×#102C4×C59semidirect
349. C59#11057direct (N × H)
438. C2×Q8C4⋊C4×C59semidirect
450. C2×D4C4⋊C4×C59semidirect

Maximal subgroups

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

subgroupindex
C2×C59×#4212
C2×C59×#4172
C2×C59×#4102
C59×#23162
C2×C59×#3442
C59×#17362
C2×C59×H(3,ℤ/4)2
#1105759