Finite Group Databasebeta

← C59×#24257 #28436366

Subgroups — C59×#24257 #28436366

Order 15104.

1650 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#546C211yesmaximal, characteristic, complemented
2C2×C59×#463C211yesmaximal, characteristic, complemented
3C2×C59×#449C211yesmaximal, characteristic, complemented
4C2×C59×#447C211yesmaximal, characteristic, complemented
5C2×C59×#442C211yesmaximal, characteristic, complemented
6C59×#2537C211yesmaximal, characteristic, complemented
7C59×#2035C211yesmaximal, characteristic, complemented
8C59×#2034C211yesmaximal, characteristic, complemented
9C59×#2000C211yesmaximal, characteristic, complemented
10C59×#1999C211yesmaximal, characteristic, complemented
11C59×#1959C211yesmaximal, characteristic, complemented
12C59×#1955C211yesmaximal, characteristic, complemented
13C59×#1802C211yesmaximal, characteristic, complemented
14C59×#1788C211yesmaximal, characteristic, complemented
15C59×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C59C2211yescharacteristic
17C23×D4×C59C2211yescharacteristic
18C22×SD16×C59C2211yescharacteristic, complemented
19C22×D8×C59C2211yescharacteristic
20C22×D8×C59C2211yescharacteristic
21C59×#546—24no—
22C59×#546—24no—
23C2×#124×C59C2211yescharacteristic
24C2×#123×C59—21no—
25C2×C22⋊Q8×C59C2211yescharacteristic
26C2×#121×C59—21no—
27C2×#121×C59—21no—
28C2×#121×C59C2211yescharacteristic
29C2×#121×C59C2211yescharacteristic
30C2×#121×C59C2211yescharacteristic, complemented
31C2×#120×C59—21no—
32C2×C4×D4×C59C2211yescharacteristic
33C2×C4×D4×C59C2211yescharacteristic
34C2×C4×D4×C59C2211yescharacteristic, complemented
35C22×C22⋊C4×C59—21no—
36C59×#463—24no—
37C59×#449—24no—
38C59×#447—24no—
39C59×#442—24no—
40C2×#106×C59C2211yescharacteristic, complemented
41C2×C4⋊C8×C59C2211yescharacteristic, complemented
42C2×#103×C59C2211yescharacteristic, complemented
43C2×#103×C59C2211yescharacteristic, complemented
44C2×#103×C59C2211yescharacteristic, complemented
45C2×#102×C59C2211yescharacteristic
46C2×#102×C59C2211yescharacteristic
47C2×#102×C59C2211yescharacteristic
48C2×#102×C59C2211yescharacteristic
49C2×#102×C59C2211yescharacteristic
50C2×#102×C59C2211yescharacteristic
51C2×#102×C59C2211yescharacteristic, complemented
52C2×C22⋊C8×C59C2211yescharacteristic
53C2×C22⋊C8×C59C2211yescharacteristic
54C2×C22⋊C8×C59C2211yescharacteristic, complemented
55C2×C22⋊C8×C59C2211yescharacteristic, complemented
56C2×#97×C59C2211yescharacteristic, complemented
57C59×#394—21no—
58C59×#394—21no—
59C59×#384C2211yescharacteristic, complemented
60C59×#380—21no—
61C59×#380C2211yescharacteristic
62C59×#380C2211yescharacteristic, complemented
63C59×#340C2211yescharacteristic, complemented
64C59×#340C2211yescharacteristic, complemented
65C25×C59—21no—
66C2×#41×C59—22no—
67C2×#41×C59—22no—
68C2×#41×C59—22no—
69C2×#41×C59—22no—
70C2×#41×C59—41no—
71C2×#41×C59—41no—
72C22×Q8×C59C2311yescharacteristic
73C22×D4×C59—21no—
74C22×D4×C59—21no—
75C22×D4×C59—22no—
76C22×D4×C59—22no—
77C22×D4×C59—22no—
78C22×D4×C59—22no—
79C22×D4×C59—21no—
80C22×D4×C59—21no—
81C22×D4×C59—21no—
82C22×D4×C59—41no—
83C22×D4×C59—41no—
84C22×D4×C59D411yescharacteristic
85C22×D4×C59C2311yescharacteristic
86C22×D4×C59C2311yescharacteristic
87C22×D4×C59C2311yescharacteristic
88C23×C4×C59—21no—
89C23×C4×C59—21no—
90C23×C4×C59—21no—
91C23×C4×C59C2311yescharacteristic
92C23×C4×C59C2311yescharacteristic
93C2×SD16×C59—22no—
94C2×SD16×C59—22no—
95C2×SD16×C59—41no—
96C2×D8×C59—22no—
97C2×D8×C59—22no—
98C2×D8×C59—22no—
99C2×D8×C59—22no—
100C2×D8×C59—41no—
101C2×D8×C59D414yescomplemented
102C22×C8×C59C2311yescharacteristic
103C22×C8×C59C2311yescharacteristic
104C22×C8×C59C2311yescharacteristic
105C22×C8×C59C2311yescharacteristic
106#124×C59—22no—
107#124×C59D414yescomplemented
108#123×C59—28no—
109C22⋊Q8×C59—22no—
110C22⋊Q8×C59—22no—
111#121×C59—28no—
112#121×C59—22no—
113#121×C59—22no—
114#121×C59—22no—
115#121×C59—22no—
116#121×C59—41no—
117#121×C59—41no—
118#121×C59—44no—
119#120×C59—28no—
120C4×D4×C59—22no—
121C4×D4×C59—22no—
122C4×D4×C59—22no—
123C4×D4×C59—22no—
124C4×D4×C59—22no—
125C4×D4×C59D414yescomplemented
126C2×C4⋊C4×C59—21no—
127C2×C4⋊C4×C59—21no—
128C2×C4⋊C4×C59—21no—
129C2×C4⋊C4×C59D411yescharacteristic
130C2×C4⋊C4×C59C2311yescharacteristic
131C2×C4⋊C4×C59C2311yescharacteristic
132C2×C4⋊C4×C59C2311yescharacteristic
133C2×C4⋊C4×C59C2311yescharacteristic
134C2×C22⋊C4×C59—28no—
135C2×C22⋊C4×C59—21no—
136C2×C22⋊C4×C59—21no—
137C2×C22⋊C4×C59—21no—
138C2×C22⋊C4×C59—21no—
139C2×C22⋊C4×C59—21no—
140C2×C22⋊C4×C59—21no—
141C2×C22⋊C4×C59—21no—
142C2×C22⋊C4×C59—21no—
143C2×C22⋊C4×C59—21no—
144C2×C22⋊C4×C59—21no—
145C2×C22⋊C4×C59D411yescharacteristic
146C2×C22⋊C4×C59D411yescharacteristic
147C2×C42×C59C2311yescharacteristic
148#106×C59—22no—
149C4⋊C8×C59—22no—
150#103×C59—22no—
151#103×C59—22no—
152#103×C59—41no—
153#102×C59—22no—
154#102×C59—22no—
155#102×C59—22no—
156#102×C59—22no—
157#102×C59—22no—
158#102×C59—22no—
159#102×C59—41no—
160C22⋊C8×C59—22no—
161C22⋊C8×C59—22no—
162C22⋊C8×C59—41no—
163C22⋊C8×C59—41no—
164#97×C59—22no—
165#95×C59—21no—
166#95×C59—21no—
167C24×C59—21no—
168C24×C59—24no—
169C24×C59—21no—
170C24×C59—21no—
171C24×C59—42no—
172C24×C59—42no—
173C24×C59—42no—
174C24×C59—42no—
175C24×C59—81no—
176C24×C59—81no—
177C24×C59C2×D411yescharacteristic
178C24×C59C2×D411yescharacteristic
179#41×C59—44no—
180#41×C59—44no—
181#41×C59—44no—
182#41×C59—44no—
183C2×Q8×C59—21no—
184C2×Q8×C59—21no—
185C2×Q8×C59—21no—
186C2×Q8×C59—21no—
187C2×Q8×C59—21no—
188C2×Q8×C59C2×D412yes—
189C2×D4×C59—24no—
190C2×D4×C59—24no—
191C2×D4×C59—22no—
192C2×D4×C59—24no—
193C2×D4×C59—22no—
194C2×D4×C59—21no—
195C2×D4×C59—21no—
196C2×D4×C59—21no—
197C2×D4×C59—21no—
198C2×D4×C59—21no—
199C2×D4×C59—21no—
200C2×D4×C59—21no—
201C2×D4×C59—21no—
202C2×D4×C59—21no—
203C2×D4×C59—21no—
204C2×D4×C59—21no—
205C2×D4×C59—21no—
206C2×D4×C59—21no—
207C2×D4×C59—41no—
208C2×D4×C59—42no—
209C2×D4×C59—42no—
210C2×D4×C59—44no—
211C2×D4×C59—44no—
212C2×D4×C59—44no—
213C2×D4×C59—42no—
214C2×D4×C59—42no—
215C2×D4×C59—44no—
216C2×D4×C59—42no—
217C2×D4×C59—42no—
218C2×D4×C59—42no—
219C2×D4×C59—42no—
220C2×D4×C59—81no—
221C2×D4×C59—81no—
222C2×D4×C59—81no—
223C2×D4×C59—81no—
224C2×D4×C59C2×D412yes—
225C2×D4×C59C2×D412yes—
226C2×D4×C59C2×D412yes—
227C2×D4×C59C2×D412yes—
228C2×D4×C59#4112yes—
229C22×C4×C59—24no—
230C22×C4×C59—21no—
231C22×C4×C59—21no—
232C22×C4×C59—21no—
233C22×C4×C59—21no—
234C22×C4×C59—21no—
235C22×C4×C59—21no—
236C22×C4×C59—21no—
237C22×C4×C59—21no—
238C22×C4×C59—21no—
239C22×C4×C59—21no—
240C22×C4×C59—21no—
241C22×C4×C59—21no—
242C22×C4×C59—21no—
243C22×C4×C59—21no—
244C22×C4×C59—24no—
245C22×C4×C59—21no—
246C22×C4×C59—21no—
247C22×C4×C59—21no—
248C22×C4×C59—42no—
249C22×C4×C59—42no—
250C22×C4×C59—42no—
251C22×C4×C59—42no—
252C22×C4×C59—42no—
253C22×C4×C59—81no—
254C22×C4×C59—81no—
255C22×C4×C59C2×D411yescharacteristic
256C22×C4×C59C2×D411yescharacteristic
257C22×C4×C59C2×D411yescharacteristic
258C22×C4×C59C2×D411yescharacteristic
259C22×C4×C59C2411yescharacteristic
260SD16×C59—44no—
261D8×C59—28no—
262D8×C59—44no—
263C2×C8×C59—21no—
264C2×C8×C59—21no—
265C2×C8×C59—21no—
266C2×C8×C59—21no—
267C2×C8×C59—21no—
268C2×C8×C59—21no—
269C2×C8×C59—21no—
270C2×C8×C59—21no—
271C2×C8×C59—21no—
272C2×C8×C59—21no—
273C2×C8×C59—21no—
274C2×C8×C59C2×D412yes—
275C4⋊C4×C59—24no—
276C4⋊C4×C59—22no—
277C4⋊C4×C59—21no—
278C4⋊C4×C59—21no—
279C4⋊C4×C59—21no—
280C4⋊C4×C59—21no—
281C4⋊C4×C59—21no—
282C4⋊C4×C59—21no—
283C4⋊C4×C59—21no—
284C4⋊C4×C59—42no—
285C4⋊C4×C59—81no—
286C4⋊C4×C59C2×D412yes—
287C22⋊C4×C59—24no—
288C22⋊C4×C59—24no—
289C22⋊C4×C59—22no—
290C22⋊C4×C59—24no—
291C22⋊C4×C59—24no—
292C22⋊C4×C59—24no—
293C22⋊C4×C59—22no—
294C22⋊C4×C59—42no—
295C22⋊C4×C59—42no—
296C22⋊C4×C59—42no—
297C22⋊C4×C59—42no—
298C22⋊C4×C59—42no—
299C42×C59C2×D412yes—
300C42×C59C2×D412yes—
301C23×C59—21no—
302C23×C59—22no—
303C23×C59—21no—
304C23×C59—22no—
305C23×C59—21no—
306C23×C59—22no—
307C23×C59—21no—
308C23×C59—21no—
309C23×C59—21no—
310C23×C59—22no—
311C23×C59—21no—
312C23×C59—22no—
313C23×C59—21no—
314C23×C59—21no—
315C23×C59—21no—
316C23×C59—21no—
317C23×C59—21no—
318C23×C59—21no—
319C23×C59—48no—
320C23×C59—48no—
321C23×C59—41no—
322C23×C59—41no—
323C23×C59—41no—
324C23×C59—41no—
325C23×C59—41no—
326C23×C59—41no—
327C23×C59—41no—
328C23×C59—41no—
329C23×C59—41no—
330C23×C59—41no—
331C23×C59—41no—
332C23×C59—41no—
333C23×C59—41no—
334C23×C59—41no—
335C23×C59—41no—
336C23×C59—41no—
337C23×C59—84no—
338C23×C59—84no—
339C23×C59—84no—
340C23×C59—84no—
341C23×C59—84no—
342C23×C59AGL(1,ℤ/8)12yes—
343C23×C59C22×D411yescharacteristic
344Q8×C59—22no—
345Q8×C59—22no—
346Q8×C59—41no—
347Q8×C59—41no—
348D4×C59—22no—
349D4×C59—22no—
350D4×C59—22no—
351D4×C59—22no—
352D4×C59—22no—
353D4×C59—22no—
354D4×C59—22no—
355D4×C59—44no—
356D4×C59—48no—
357D4×C59—48no—
358D4×C59—41no—
359D4×C59—41no—
360D4×C59—41no—
361D4×C59—41no—
362D4×C59—84no—
363D4×C59—84no—
364D4×C59—84no—
365D4×C59#12114yescomplemented
366C2×C4×C59—21no—
367C2×C4×C59—21no—
368C2×C4×C59—21no—
369C2×C4×C59—21no—
370C2×C4×C59—22no—
371C2×C4×C59—21no—
372C2×C4×C59—22no—
373C2×C4×C59—21no—
374C2×C4×C59—21no—
375C2×C4×C59—21no—
376C2×C4×C59—21no—
377C2×C4×C59—21no—
378C2×C4×C59—48no—
379C2×C4×C59—41no—
380C2×C4×C59—41no—
381C2×C4×C59—41no—
382C2×C4×C59—41no—
383C2×C4×C59—41no—
384C2×C4×C59—41no—
385C2×C4×C59—41no—
386C2×C4×C59—41no—
387C2×C4×C59—41no—
388C2×C4×C59—41no—
389C2×C4×C59—41no—
390C2×C4×C59—41no—
391C2×C4×C59—41no—
392C2×C4×C59—41no—
393C2×C4×C59—41no—
394C2×C4×C59—41no—
395C2×C4×C59—41no—
396C2×C4×C59—41no—
397C2×C4×C59—41no—
398C2×C4×C59—41no—
399C2×C4×C59—41no—
400C2×C4×C59—84no—
401C2×C4×C59—84no—
402C2×C4×C59#12012yes—
403C2×C4×C59#12012yes—
404C2×C4×C59C22×D411yescharacteristic
405C2×C4×C59C22×D411yescharacteristic
406C2×C4×C59C22×D411yescharacteristic
407C2×C4×C59C2×#4111yescharacteristic
408C2×C4×C59H(5,𝔽2)11yescharacteristic
409C2×C4×C59H(5,𝔽2)11yescharacteristic
410C8×C59—22no—
411C8×C59—41no—
412C8×C59—41no—
413C8×C59—41no—
414#24257C5911yesmaximal, characteristic, direct product factor, Sylow
415C22×C59—24no—
416C22×C59—22no—
417C22×C59—22no—
418C22×C59—22no—
419C22×C59—41no—
420C22×C59—42no—
421C22×C59—42no—
422C22×C59—41no—
423C22×C59—42no—
424C22×C59—42no—
425C22×C59—41no—
426C22×C59—42no—
427C22×C59—41no—
428C22×C59—42no—
429C22×C59—41no—
430C22×C59—42no—
431C22×C59—42no—
432C22×C59—41no—
433C22×C59—42no—
434C22×C59—41no—
435C22×C59—42no—
436C22×C59—41no—
437C22×C59—42no—
438C22×C59—41no—
439C22×C59—42no—
440C22×C59—41no—
441C22×C59—41no—
442C22×C59—816no—
443C22×C59—81no—
444C22×C59—81no—
445C22×C59—81no—
446C22×C59—81no—
447C22×C59—81no—
448C22×C59—81no—
449C22×C59—81no—
450C22×C59—81no—
451C22×C59C2×#12011yescharacteristic
452C22×C59D4211yescharacteristic
453C22×C59#54611yescharacteristic
454C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
455C22×C59#57511yescharacteristic
456C22×C59#57611yescharacteristic
457C22×C59#57711yescharacteristic
458C4×C59—22no—
459C4×C59—22no—
460C4×C59—41no—
461C4×C59—41no—
462C4×C59—42no—
463C4×C59—42no—
464C4×C59—81no—
465C4×C59—81no—
466C4×C59—81no—
467C4×C59C2×#12111yescharacteristic
468C4×C59#53511yescharacteristic
469C4×C59D4211yescharacteristic
470C4×C59#54611yescharacteristic
471C2×#546C2×C5911yescharacteristic, complemented
472C2×#463C2×C5911yescharacteristic, complemented
473C2×#449C2×C5911yescharacteristic, complemented
474C2×#447C2×C5911yescharacteristic, complemented
475C2×#442C2×C5911yescharacteristic, complemented
476#2537C2×C5911yescharacteristic, complemented
477#2035C2×C5911yescharacteristic, complemented
478#2034C2×C5911yescharacteristic, complemented
479#2000C2×C5911yescharacteristic, complemented
480#1999C2×C5911yescharacteristic, complemented
481#1959C2×C5911yescharacteristic, complemented
482#1955C2×C5911yescharacteristic, complemented
483#1802C2×C5911yescharacteristic, complemented
484#1788C2×C5911yescharacteristic, complemented
485#1786C2×C5911yescharacteristic, complemented
486C2×C59—42no—
487C2×C59—44no—
488C2×C59—81no—
489C2×C59—82no—
490C2×C59—82no—
491C2×C59#240811yescharacteristic
492C2×C59#300611yescharacteristic
493C2×C59#301211yescharacteristic
494C2×C59#326411yescharacteristic
495C2×C59#326711yescharacteristic
496C2×C59#330611yescharacteristic
497C2×C59#331911yescharacteristic
498C22×#41C22×C5911yescharacteristic
499C23×D4C22×C5911yescharacteristic
500C22×SD16C22×C5911yescharacteristic, complemented
501C22×D8C22×C5911yescharacteristic
502C22×D8C22×C5911yescharacteristic
503#546—24no—
504#546—24no—
505C2×#124C22×C5911yescharacteristic
506C2×#123—21no—
507C2×C22⋊Q8C22×C5911yescharacteristic
508C2×#121—21no—
509C2×#121—21no—
510C2×#121C22×C5911yescharacteristic
511C2×#121C22×C5911yescharacteristic
512C2×#121C22×C5911yescharacteristic, complemented
513C2×#120—21no—
514C2×C4×D4C22×C5911yescharacteristic
515C2×C4×D4C22×C5911yescharacteristic
516C2×C4×D4C22×C5911yescharacteristic, complemented
517C22×C22⋊C4—21no—
518#463—24no—
519#449—24no—
520#447—24no—
521#442—24no—
522C2×#106C22×C5911yescharacteristic, complemented
523C2×C4⋊C8C22×C5911yescharacteristic, complemented
524C2×#103C22×C5911yescharacteristic, complemented
525C2×#103C22×C5911yescharacteristic, complemented
526C2×#103C22×C5911yescharacteristic, complemented
527C2×#102C22×C5911yescharacteristic
528C2×#102C22×C5911yescharacteristic
529C2×#102C22×C5911yescharacteristic
530C2×#102C22×C5911yescharacteristic
531C2×#102C22×C5911yescharacteristic
532C2×#102C22×C5911yescharacteristic
533C2×#102C22×C5911yescharacteristic, complemented
534C2×C22⋊C8C22×C5911yescharacteristic
535C2×C22⋊C8C22×C5911yescharacteristic
536C2×C22⋊C8C22×C5911yescharacteristic, complemented
537C2×C22⋊C8C22×C5911yescharacteristic, complemented
538C2×#97C22×C5911yescharacteristic, complemented
539#394—21no—
540#394—21no—
541#384C22×C5911yescharacteristic, complemented
542#380—21no—
543#380C22×C5911yescharacteristic
544#380C22×C5911yescharacteristic, complemented
545#340C22×C5911yescharacteristic, complemented
546#340C22×C5911yescharacteristic, complemented
547C59#2425711yescharacteristic, direct product factor, Sylow
548C25—21no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—22no—
553C2×#41—41no—
554C2×#41—41no—
555C22×Q8C23×C5911yescharacteristic
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—22no—
559C22×D4—22no—
560C22×D4—22no—
561C22×D4—22no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—41no—
566C22×D4—41no—
567C22×D4D4×C5911yescharacteristic
568C22×D4C23×C5911yescharacteristic
569C22×D4C23×C5911yescharacteristic
570C22×D4C23×C5911yescharacteristic
571C23×C4—21no—
572C23×C4—21no—
573C23×C4—21no—
574C23×C4C23×C5911yescharacteristic
575C23×C4C23×C5911yescharacteristic
576C2×SD16—22no—
577C2×SD16—22no—
578C2×SD16—41no—
579C2×D8—22no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—22no—
583C2×D8—41no—
584C2×D8D4×C5914yescomplemented
585C22×C8C23×C5911yescharacteristic
586C22×C8C23×C5911yescharacteristic
587C22×C8C23×C5911yescharacteristic
588C22×C8C23×C5911yescharacteristic
589#124—22no—
590#124D4×C5914yescomplemented
591#123—28no—
592C22⋊Q8—22no—
593C22⋊Q8—22no—
594#121—28no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—41no—
600#121—41no—
601#121—44no—
602#120—28no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—22no—
608C4×D4D4×C5914yescomplemented
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4D4×C5911yescharacteristic
613C2×C4⋊C4C23×C5911yescharacteristic
614C2×C4⋊C4C23×C5911yescharacteristic
615C2×C4⋊C4C23×C5911yescharacteristic
616C2×C4⋊C4C23×C5911yescharacteristic
617C2×C22⋊C4—28no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4D4×C5911yescharacteristic
629C2×C22⋊C4D4×C5911yescharacteristic
630C2×C42C23×C5911yescharacteristic
631#106—22no—
632C4⋊C8—22no—
633#103—22no—
634#103—22no—
635#103—41no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—22no—
640#102—22no—
641#102—22no—
642#102—41no—
643C22⋊C8—22no—
644C22⋊C8—22no—
645C22⋊C8—41no—
646C22⋊C8—41no—
647#97—22no—
648#95—21no—
649#95—21no—
650C24—21no—
651C24—24no—
652C24—21no—
653C24—21no—
654C24—42no—
655C24—42no—
656C24—42no—
657C24—42no—
658C24—81no—
659C24—81no—
660C24C2×D4×C5911yescharacteristic
661C24C2×D4×C5911yescharacteristic
662#41—44no—
663#41—44no—
664#41—44no—
665#41—44no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8C2×D4×C5912yes—
672C2×D4—24no—
673C2×D4—24no—
674C2×D4—22no—
675C2×D4—24no—
676C2×D4—22no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—41no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—44no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—44no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—81no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4C2×D4×C5912yes—
708C2×D4C2×D4×C5912yes—
709C2×D4C2×D4×C5912yes—
710C2×D4C2×D4×C5912yes—
711C2×D4#41×C5912yes—
712C22×C4—24no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—24no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—42no—
735C22×C4—42no—
736C22×C4—81no—
737C22×C4—81no—
738C22×C4C2×D4×C5911yescharacteristic
739C22×C4C2×D4×C5911yescharacteristic
740C22×C4C2×D4×C5911yescharacteristic
741C22×C4C2×D4×C5911yescharacteristic
742C22×C4C24×C5911yescharacteristic
743SD16—44no—
744D8—28no—
745D8—44no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8C2×D4×C5912yes—
758C4⋊C4—24no—
759C4⋊C4—22no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—42no—
768C4⋊C4—81no—
769C4⋊C4C2×D4×C5912yes—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—22no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—24no—
776C22⋊C4—22no—
777C22⋊C4—42no—
778C22⋊C4—42no—
779C22⋊C4—42no—
780C22⋊C4—42no—
781C22⋊C4—42no—
782C42C2×D4×C5912yes—
783C42C2×D4×C5912yes—
784C23—21no—
785C23—22no—
786C23—21no—
787C23—22no—
788C23—21no—
789C23—22no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—22no—
794C23—21no—
795C23—22no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—48no—
803C23—48no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—84no—
821C23—84no—
822C23—84no—
823C23—84no—
824C23—84no—
825C23AGL(1,ℤ/8)×C5912yes—
826C23C22×D4×C5911yescharacteristic
827Q8—22no—
828Q8—22no—
829Q8—41no—
830Q8—41no—
831D4—22no—
832D4—22no—
833D4—22no—
834D4—22no—
835D4—22no—
836D4—22no—
837D4—22no—
838D4—44no—
839D4—48no—
840D4—48no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—84no—
846D4—84no—
847D4—84no—
848D4#121×C5914yescomplemented
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—21no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—48no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—84no—
884C2×C4—84no—
885C2×C4#120×C5912yes—
886C2×C4#120×C5912yes—
887C2×C4C22×D4×C5911yescharacteristic
888C2×C4C22×D4×C5911yescharacteristic
889C2×C4C22×D4×C5911yescharacteristic
890C2×C4C2×#41×C5911yescharacteristic
891C2×C4H(5,𝔽2)×C5911yescharacteristic
892C2×C4H(5,𝔽2)×C5911yescharacteristic
893C8—22no—
894C8—41no—
895C8—41no—
896C8—41no—
897C22—22no—
898C22—22no—
899C22—22no—
900C22—24no—
901C22—42no—
902C22—42no—
903C22—41no—
904C22—42no—
905C22—42no—
906C22—41no—
907C22—42no—
908C22—41no—
909C22—42no—
910C22—41no—
911C22—41no—
912C22—42no—
913C22—41no—
914C22—42no—
915C22—41no—
916C22—42no—
917C22—41no—
918C22—42no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—42no—
923C22—42no—
924C22—816no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22C2×#120×C5911yescharacteristic
934C22D42×C5911yescharacteristic
935C22C59×#54611yescharacteristic
936C22C2×AGL(1,ℤ/8)×C5911yescharacteristic
937C22C59×#57511yescharacteristic
938C22C59×#57611yescharacteristic
939C22C59×#57711yescharacteristic
940C4—22no—
941C4—22no—
942C4—42no—
943C4—41no—
944C4—41no—
945C4—42no—
946C4—81no—
947C4—81no—
948C4—81no—
949C4C2×#121×C5911yescharacteristic
950C4C59×#53511yescharacteristic
951C4D42×C5911yescharacteristic
952C4C59×#54611yescharacteristic
953C2—42no—
954C2—44no—
955C2—81no—
956C2—82no—
957C2—82no—
958C2C59×#240811yescharacteristic
959C2C59×#300611yescharacteristic
960C2C59×#301211yescharacteristic
961C2C59×#326411yescharacteristic
962C2C59×#326711yescharacteristic
963C2C59×#330611yescharacteristic
964C2C59×#331911yescharacteristic
subgroupG/H
center, socleC23×C59C22×D4
commutator, Frattini, cosocleC22×C4C24×C59
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
1. C2×C59×#546C2semidirect
2. C2×C59×#463C2semidirect
3. C2×C59×#449C2semidirect
4. C2×C59×#447C2semidirect
5. C2×C59×#442C2semidirect
6. C59×#2537C2semidirect
7. C59×#2035C2semidirect
8. C59×#2034C2semidirect
9. C59×#2000C2semidirect
10. C59×#1999C2semidirect
11. C59×#1959C2semidirect
12. C59×#1955C2semidirect
13. C59×#1802C2semidirect
14. C59×#1788C2semidirect
15. C59×#1786C2semidirect
18. C22×SD16×C59C22semidirect
30. C2×#121×C59C22semidirect
34. C2×C4×D4×C59C22semidirect
40. C2×#106×C59C22semidirect
41. C2×C4⋊C8×C59C22semidirect
42. C2×#103×C59C22semidirect
43. C2×#103×C59C22semidirect
44. C2×#103×C59C22semidirect
51. C2×#102×C59C22semidirect
54. C2×C22⋊C8×C59C22semidirect
55. C2×C22⋊C8×C59C22semidirect
56. C2×#97×C59C22semidirect
59. C59×#384C22semidirect
62. C59×#380C22semidirect
63. C59×#340C22semidirect
64. C59×#340C22semidirect
101. C2×D8×C59D4semidirect
107. #124×C59D4semidirect
125. C4×D4×C59D4semidirect
365. D4×C59#121semidirect
414. #24257C59direct (N × H)
471. C2×#546C2×C59semidirect
472. C2×#463C2×C59semidirect
473. C2×#449C2×C59semidirect
474. C2×#447C2×C59semidirect
475. C2×#442C2×C59semidirect
476. #2537C2×C59semidirect
477. #2035C2×C59semidirect
478. #2034C2×C59semidirect
479. #2000C2×C59semidirect
480. #1999C2×C59semidirect
481. #1959C2×C59semidirect
482. #1955C2×C59semidirect
483. #1802C2×C59semidirect
484. #1788C2×C59semidirect
485. #1786C2×C59semidirect
500. C22×SD16C22×C59semidirect
512. C2×#121C22×C59semidirect
516. C2×C4×D4C22×C59semidirect
522. C2×#106C22×C59semidirect
523. C2×C4⋊C8C22×C59semidirect
524. C2×#103C22×C59semidirect
525. C2×#103C22×C59semidirect
526. C2×#103C22×C59semidirect
533. C2×#102C22×C59semidirect
536. C2×C22⋊C8C22×C59semidirect
537. C2×C22⋊C8C22×C59semidirect
538. C2×#97C22×C59semidirect
541. #384C22×C59semidirect
544. #380C22×C59semidirect
545. #340C22×C59semidirect
546. #340C22×C59semidirect
547. C59#24257direct (N × H)
584. C2×D8D4×C59semidirect
590. #124D4×C59semidirect
608. C4×D4D4×C59semidirect
848. D4#121×C59semidirect

Maximal subgroups

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

subgroupindex
C2×C59×#5462
C2×C59×#4632
C2×C59×#4492
C2×C59×#4472
C2×C59×#4422
C59×#25372
C59×#20352
C59×#20342
C59×#20002
C59×#19992
C59×#19592
C59×#19552
C59×#18022
C59×#17882
C59×#17862
#2425759