Finite Group Databasebeta

← C59×#33347 #28445456

Subgroups — C59×#33347 #28445456

Order 15104.

1236 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3449C211yesmaximal, characteristic
2C2×C59×#413C211yesmaximal, characteristic, complemented
3C2×C59×#410C211yesmaximal, characteristic, complemented
4C59×#2123C212yesmaximal, complemented
5C59×#2122C212yesmaximal, complemented
6C59×#2121C214yesmaximal, complemented
7C59×#2120C214yesmaximal, complemented
8C22×#41×C59C411yescharacteristic, complemented
9C22×#41×C59C2211yescharacteristic
10C22×M16×C59—21no—
11C59×#537—21no—
12C59×#537—21no—
13C59×#536—21no—
14C59×#536C411yescharacteristic, complemented
15C59×#536C2211yescharacteristic
16C59×#535—21no—
17C59×#535C411yescharacteristic, complemented
18C59×#535C2211yescharacteristic
19C59×#534C412yescomplemented
20C59×#534C2212yes—
21C59×#532—21no—
22C59×#532—21no—
23C59×#525—21no—
24C59×#525—21no—
25C59×#525C412yescomplemented
26C59×#525C2212yes—
27C2×#117×C59—21no—
28C2×#117×C59C411yescharacteristic, complemented
29C59×#413—21no—
30C59×#413—21no—
31C59×#413C2212yes—
32C59×#413C2212yes—
33C2×#101×C59—21no—
34C2×#100×C59C2212yes—
35C59×#410—21no—
36C59×#410—21no—
37C59×#410C2212yes—
38C59×#410C2212yes—
39C2×#99×C59—21no—
40C2×#99×C59C2212yes—
41C59×#352C2218yescomplemented
42C59×AΣL(1,𝔽16)C2218yescomplemented
43C2×#41×C59—21no—
44C2×#41×C59—21no—
45C2×#41×C59—21no—
46C2×#41×C59—21no—
47C2×#41×C59—41no—
48C2×#41×C59—41no—
49C2×#41×C59—41no—
50C2×#41×C59—41no—
51C2×#41×C59—41no—
52C2×#41×C59—41no—
53C2×#41×C59—41no—
54C2×#41×C59—41no—
55C2×#41×C59C2×C411yescharacteristic
56C2×#41×C59C2×C411yescharacteristic
57C2×#41×C59D411yescharacteristic
58C2×#41×C59D411yescharacteristic
59C2×#41×C59D411yescharacteristic
60C2×#41×C59D411yescharacteristic
61C2×#41×C59C2311yescharacteristic
62C2×#41×C59C2311yescharacteristic
63C22×Q8×C59C2×C411yescharacteristic, complemented
64C22×Q8×C59D411yescharacteristic
65C22×D4×C59C2×C411yescharacteristic
66C22×D4×C59C2×C412yes—
67C22×D4×C59C2×C411yescharacteristic, complemented
68C22×D4×C59D411yescharacteristic
69C22×D4×C59C2311yescharacteristic
70C23×C4×C59C2×C411yescharacteristic
71C23×C4×C59C2×C412yescomplemented
72C23×C4×C59D411yescharacteristic
73C23×C4×C59D411yescharacteristic
74C2×M16×C59—22no—
75C2×M16×C59—22no—
76C2×M16×C59—22no—
77C2×M16×C59—41no—
78C2×M16×C59—41no—
79C2×M16×C59—41no—
80C22×C8×C59—41no—
81C4⋊Q8×C59—21no—
82C4⋊Q8×C59—21no—
83#127×C59—21no—
84#127×C59—21no—
85#124×C59—21no—
86#124×C59—21no—
87#124×C59—21no—
88#124×C59—21no—
89#123×C59—22no—
90#123×C59—22no—
91#123×C59C2×C412yes—
92#123×C59C2×C412yescomplemented
93#123×C59C2×C412yescomplemented
94#123×C59C2312yes—
95C22⋊Q8×C59—22no—
96C22⋊Q8×C59—22no—
97C22⋊Q8×C59—21no—
98C22⋊Q8×C59—21no—
99C22⋊Q8×C59—21no—
100C22⋊Q8×C59—21no—
101#121×C59—22no—
102#121×C59—22no—
103#121×C59—22no—
104#121×C59—22no—
105#121×C59—22no—
106#121×C59—22no—
107#121×C59—21no—
108#121×C59—21no—
109#121×C59—21no—
110#121×C59—21no—
111#120×C59—22no—
112#120×C59—22no—
113#120×C59C2×C412yes—
114#120×C59C2×C412yescomplemented
115#120×C59C2×C412yescomplemented
116#120×C59C2312yes—
117C4×D4×C59—22no—
118C4×D4×C59—22no—
119C4×D4×C59—22no—
120C4×D4×C59—22no—
121#117×C59—21no—
122#117×C59—21no—
123#117×C59—22no—
124#117×C59—22no—
125#117×C59—41no—
126#117×C59—41no—
127#117×C59C2×C412yescomplemented
128#117×C59C2×C411yescharacteristic, complemented
129#117×C59C2×C411yescharacteristic, complemented
130C2×C4⋊C4×C59—21no—
131C2×C4⋊C4×C59—41no—
132C2×C22⋊C4×C59—22no—
133C2×C22⋊C4×C59C2×C412yes—
134C2×C42×C59—21no—
135C2×C42×C59—41no—
136#101×C59—22no—
137#101×C59—22no—
138#100×C59—22no—
139#100×C59C2314yes—
140#99×C59—22no—
141#99×C59—22no—
142#99×C59—22no—
143#99×C59C2314yes—
144C24×C59C22⋊C411yescharacteristic
145C24×C59C22×C411yescharacteristic
146C24×C59C22×C412yes—
147C24×C59C2×D411yescharacteristic
148#41×C59—41no—
149#41×C59—41no—
150#41×C59—41no—
151#41×C59—41no—
152#41×C59—41no—
153#41×C59—41no—
154#41×C59—41no—
155#41×C59—41no—
156#41×C59—41no—
157#41×C59—41no—
158#41×C59—41no—
159#41×C59—41no—
160#41×C59—41no—
161#41×C59—41no—
162#41×C59—41no—
163#41×C59—41no—
164#41×C59—42no—
165#41×C59—42no—
166#41×C59—42no—
167#41×C59—42no—
168#41×C59—42no—
169#41×C59—42no—
170#41×C59—41no—
171#41×C59—41no—
172#41×C59—41no—
173#41×C59—41no—
174C2×Q8×C59—21no—
175C2×Q8×C59—21no—
176C2×Q8×C59—41no—
177C2×Q8×C59—41no—
178C2×Q8×C59—41no—
179C2×Q8×C59—41no—
180C2×Q8×C59C22⋊C411yescharacteristic
181C2×Q8×C59C22⋊C411yescharacteristic
182C2×Q8×C59C2×D411yescharacteristic
183C2×Q8×C59C2×D411yescharacteristic
184C2×D4×C59—22no—
185C2×D4×C59—22no—
186C2×D4×C59—22no—
187C2×D4×C59—22no—
188C2×D4×C59—22no—
189C2×D4×C59—22no—
190C2×D4×C59—21no—
191C2×D4×C59—21no—
192C2×D4×C59—41no—
193C2×D4×C59—41no—
194C2×D4×C59—41no—
195C2×D4×C59—41no—
196C2×D4×C59—41no—
197C2×D4×C59—41no—
198C2×D4×C59—41no—
199C2×D4×C59—41no—
200C2×D4×C59—42no—
201C2×D4×C59—42no—
202C2×D4×C59C22⋊C411yescharacteristic
203C2×D4×C59C22⋊C411yescharacteristic
204C2×D4×C59C22⋊C411yescharacteristic
205C2×D4×C59C22⋊C411yescharacteristic
206C2×D4×C59C22×C411yescharacteristic
207C2×D4×C59C22×C411yescharacteristic
208C2×D4×C59C22×C411yescharacteristic
209C2×D4×C59C2×D411yescharacteristic
210C2×D4×C59C2×D411yescharacteristic
211C2×D4×C59C2×D411yescharacteristic
212C2×D4×C59C2×D411yescharacteristic
213C2×D4×C59C2411yescharacteristic
214C22×C4×C59—21no—
215C22×C4×C59—21no—
216C22×C4×C59—21no—
217C22×C4×C59—21no—
218C22×C4×C59—21no—
219C22×C4×C59—21no—
220C22×C4×C59—21no—
221C22×C4×C59—21no—
222C22×C4×C59—21no—
223C22×C4×C59—21no—
224C22×C4×C59—21no—
225C22×C4×C59—21no—
226C22×C4×C59—22no—
227C22×C4×C59—22no—
228C22×C4×C59—22no—
229C22×C4×C59—42no—
230C22×C4×C59—42no—
231C22×C4×C59—42no—
232C22×C4×C59C22⋊C411yescharacteristic
233C22×C4×C59C22⋊C411yescharacteristic
234C22×C4×C59C22⋊C411yescharacteristic
235C22×C4×C59C22⋊C411yescharacteristic
236C22×C4×C59C22⋊C411yescharacteristic
237C22×C4×C59C22⋊C411yescharacteristic
238C22×C4×C59C22⋊C411yescharacteristic
239C22×C4×C59C22⋊C411yescharacteristic
240C22×C4×C59C22⋊C411yescharacteristic
241C22×C4×C59C22×C411yescharacteristic
242C22×C4×C59C22×C411yescharacteristic
243C22×C4×C59C22×C412yes—
244C22×C4×C59C2×D411yescharacteristic
245C22×C4×C59C2×D411yescharacteristic
246C22×C4×C59C2×D411yescharacteristic
247C22×C4×C59C2×D411yescharacteristic
248C22×C4×C59C2×D411yescharacteristic
249M16×C59—24no—
250M16×C59—42no—
251M16×C59—42no—
252M16×C59—42no—
253C2×C8×C59—42no—
254C2×C8×C59—42no—
255C2×C8×C59—42no—
256C4⋊C4×C59—22no—
257C4⋊C4×C59—21no—
258C4⋊C4×C59—21no—
259C4⋊C4×C59—22no—
260C4⋊C4×C59—22no—
261C4⋊C4×C59—22no—
262C4⋊C4×C59—22no—
263C4⋊C4×C59—42no—
264C4⋊C4×C59—42no—
265C22⋊C4×C59—22no—
266C22⋊C4×C59—22no—
267C22⋊C4×C59—22no—
268C22⋊C4×C59—22no—
269C22⋊C4×C59—22no—
270C22⋊C4×C59—22no—
271C22⋊C4×C59—22no—
272C22⋊C4×C59—22no—
273C22⋊C4×C59—22no—
274C22⋊C4×C59—24no—
275C22⋊C4×C59—42no—
276C22⋊C4×C59C22×C412yes—
277C22⋊C4×C59C22×C412yes—
278C42×C59—22no—
279C42×C59—21no—
280C42×C59—21no—
281C42×C59—42no—
282C42×C59—42no—
283C23×C59—21no—
284C23×C59—21no—
285C23×C59—21no—
286C23×C59—21no—
287C23×C59—21no—
288C23×C59—21no—
289C23×C59—22no—
290C23×C59—42no—
291C23×C59—81no—
292C23×C59—81no—
293C23×C59—81no—
294C23×C59—82no—
295C23×C59C2×C22⋊C411yescharacteristic
296C23×C59C2×C22⋊C411yescharacteristic
297C23×C59C2×C22⋊C411yescharacteristic
298C23×C59C2×C22⋊C411yescharacteristic
299C23×C59C2×C22⋊C411yescharacteristic
300C23×C59C23×C411yescharacteristic
301C23×C59C22×D411yescharacteristic
302Q8×C59—41no—
303Q8×C59—41no—
304Q8×C59—41no—
305Q8×C59—41no—
306Q8×C59—42no—
307Q8×C59—41no—
308Q8×C59—41no—
309D4×C59—41no—
310D4×C59—41no—
311D4×C59—41no—
312D4×C59—41no—
313D4×C59—41no—
314D4×C59—41no—
315D4×C59—41no—
316D4×C59—41no—
317D4×C59—41no—
318D4×C59—41no—
319D4×C59—41no—
320D4×C59—41no—
321D4×C59—42no—
322D4×C59—44no—
323D4×C59—42no—
324D4×C59—42no—
325D4×C59—41no—
326D4×C59—41no—
327D4×C59—82no—
328D4×C59—82no—
329D4×C59—82no—
330D4×C59—82no—
331C2×C4×C59—21no—
332C2×C4×C59—21no—
333C2×C4×C59—21no—
334C2×C4×C59—21no—
335C2×C4×C59—21no—
336C2×C4×C59—21no—
337C2×C4×C59—21no—
338C2×C4×C59—21no—
339C2×C4×C59—21no—
340C2×C4×C59—21no—
341C2×C4×C59—21no—
342C2×C4×C59—21no—
343C2×C4×C59—21no—
344C2×C4×C59—21no—
345C2×C4×C59—21no—
346C2×C4×C59—21no—
347C2×C4×C59—21no—
348C2×C4×C59—21no—
349C2×C4×C59—21no—
350C2×C4×C59—21no—
351C2×C4×C59—21no—
352C2×C4×C59—21no—
353C2×C4×C59—21no—
354C2×C4×C59—21no—
355C2×C4×C59—21no—
356C2×C4×C59—21no—
357C2×C4×C59—21no—
358C2×C4×C59—21no—
359C2×C4×C59—21no—
360C2×C4×C59—21no—
361C2×C4×C59—22no—
362C2×C4×C59—22no—
363C2×C4×C59—22no—
364C2×C4×C59—44no—
365C2×C4×C59—42no—
366C2×C4×C59—42no—
367C2×C4×C59—42no—
368C2×C4×C59—44no—
369C2×C4×C59—82no—
370C2×C4×C59—84no—
371C2×C4×C59#9911yescharacteristic
372C2×C4×C59#9911yescharacteristic
373C2×C4×C59#9911yescharacteristic
374C2×C4×C59#9911yescharacteristic
375C2×C4×C59C2×C22⋊C411yescharacteristic
376C2×C4×C59C2×C22⋊C411yescharacteristic
377C2×C4×C59C2×C22⋊C411yescharacteristic
378C2×C4×C59C2×C22⋊C411yescharacteristic
379C2×C4×C59C2×C22⋊C411yescharacteristic
380C2×C4×C59C2×C22⋊C411yescharacteristic
381C2×C4×C59C2×C22⋊C411yescharacteristic
382C2×C4×C59C22×D411yescharacteristic
383C8×C59—44no—
384#33347C5911yesmaximal, characteristic, direct product factor, Sylow
385C22×C59—21no—
386C22×C59—21no—
387C22×C59—21no—
388C22×C59—21no—
389C22×C59—21no—
390C22×C59—21no—
391C22×C59—41no—
392C22×C59—41no—
393C22×C59—41no—
394C22×C59—41no—
395C22×C59—41no—
396C22×C59—41no—
397C22×C59—41no—
398C22×C59—42no—
399C22×C59—42no—
400C22×C59—42no—
401C22×C59—42no—
402C22×C59—42no—
403C22×C59—81no—
404C22×C59—81no—
405C22×C59—81no—
406C22×C59—81no—
407C22×C59—84no—
408C22×C59C2×#9911yescharacteristic
409C22×C59C2×#9911yescharacteristic
410C22×C59C22×C22⋊C411yescharacteristic
411C4×C59—21no—
412C4×C59—21no—
413C4×C59—21no—
414C4×C59—21no—
415C4×C59—21no—
416C4×C59—21no—
417C4×C59—42no—
418C4×C59—42no—
419C4×C59—42no—
420C4×C59—84no—
421C4×C59C2×#9911yescharacteristic
422C4×C59C2×#9911yescharacteristic
423C4×C59C2×#9911yescharacteristic
424C4×C59C2×#9911yescharacteristic
425#3449C2×C5911yescharacteristic
426C2×#413C2×C5911yescharacteristic, complemented
427C2×#410C2×C5911yescharacteristic, complemented
428#2123C2×C5912yescomplemented
429#2122C2×C5912yescomplemented
430#2121C2×C5914yescomplemented
431#2120C2×C5914yescomplemented
432C2×C59—21no—
433C2×C59—21no—
434C2×C59—21no—
435C2×C59—41no—
436C2×C59—41no—
437C2×C59—41no—
438C2×C59—41no—
439C2×C59—41no—
440C2×C59—41no—
441C2×C59—82no—
442C2×C59C22×#9911yescharacteristic
443C22×#41C4×C5911yescharacteristic, complemented
444C22×#41C22×C5911yescharacteristic
445C22×M16—21no—
446#537—21no—
447#537—21no—
448#536—21no—
449#536C4×C5911yescharacteristic, complemented
450#536C22×C5911yescharacteristic
451#535—21no—
452#535C4×C5911yescharacteristic, complemented
453#535C22×C5911yescharacteristic
454#534C4×C5912yescomplemented
455#534C22×C5912yes—
456#532—21no—
457#532—21no—
458#525—21no—
459#525—21no—
460#525C4×C5912yescomplemented
461#525C22×C5912yes—
462C2×#117—21no—
463C2×#117C4×C5911yescharacteristic, complemented
464#413—21no—
465#413—21no—
466#413C22×C5912yes—
467#413C22×C5912yes—
468C2×#101—21no—
469C2×#100C22×C5912yes—
470#410—21no—
471#410—21no—
472#410C22×C5912yes—
473#410C22×C5912yes—
474C2×#99—21no—
475C2×#99C22×C5912yes—
476#352C22×C5918yescomplemented
477AΣL(1,𝔽16)C22×C5918yescomplemented
478C59#3334711yescharacteristic, direct product factor, Sylow
479C2×#41—21no—
480C2×#41—21no—
481C2×#41—21no—
482C2×#41—21no—
483C2×#41—41no—
484C2×#41—41no—
485C2×#41—41no—
486C2×#41—41no—
487C2×#41—41no—
488C2×#41—41no—
489C2×#41—41no—
490C2×#41—41no—
491C2×#41C2×C4×C5911yescharacteristic
492C2×#41C2×C4×C5911yescharacteristic
493C2×#41D4×C5911yescharacteristic
494C2×#41D4×C5911yescharacteristic
495C2×#41D4×C5911yescharacteristic
496C2×#41D4×C5911yescharacteristic
497C2×#41C23×C5911yescharacteristic
498C2×#41C23×C5911yescharacteristic
499C22×Q8C2×C4×C5911yescharacteristic, complemented
500C22×Q8D4×C5911yescharacteristic
501C22×D4C2×C4×C5911yescharacteristic
502C22×D4C2×C4×C5912yes—
503C22×D4C2×C4×C5911yescharacteristic, complemented
504C22×D4D4×C5911yescharacteristic
505C22×D4C23×C5911yescharacteristic
506C23×C4C2×C4×C5911yescharacteristic
507C23×C4C2×C4×C5912yescomplemented
508C23×C4D4×C5911yescharacteristic
509C23×C4D4×C5911yescharacteristic
510C2×M16—22no—
511C2×M16—22no—
512C2×M16—22no—
513C2×M16—41no—
514C2×M16—41no—
515C2×M16—41no—
516C22×C8—41no—
517C4⋊Q8—21no—
518C4⋊Q8—21no—
519#127—21no—
520#127—21no—
521#124—21no—
522#124—21no—
523#124—21no—
524#124—21no—
525#123—22no—
526#123—22no—
527#123C2×C4×C5912yes—
528#123C2×C4×C5912yescomplemented
529#123C2×C4×C5912yescomplemented
530#123C23×C5912yes—
531C22⋊Q8—22no—
532C22⋊Q8—22no—
533C22⋊Q8—21no—
534C22⋊Q8—21no—
535C22⋊Q8—21no—
536C22⋊Q8—21no—
537#121—22no—
538#121—22no—
539#121—22no—
540#121—22no—
541#121—22no—
542#121—22no—
543#121—21no—
544#121—21no—
545#121—21no—
546#121—21no—
547#120—22no—
548#120—22no—
549#120C2×C4×C5912yes—
550#120C2×C4×C5912yescomplemented
551#120C2×C4×C5912yescomplemented
552#120C23×C5912yes—
553C4×D4—22no—
554C4×D4—22no—
555C4×D4—22no—
556C4×D4—22no—
557#117—21no—
558#117—21no—
559#117—22no—
560#117—22no—
561#117—41no—
562#117—41no—
563#117C2×C4×C5912yescomplemented
564#117C2×C4×C5911yescharacteristic, complemented
565#117C2×C4×C5911yescharacteristic, complemented
566C2×C4⋊C4—21no—
567C2×C4⋊C4—41no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4C2×C4×C5912yes—
570C2×C42—21no—
571C2×C42—41no—
572#101—22no—
573#101—22no—
574#100—22no—
575#100C23×C5914yes—
576#99—22no—
577#99—22no—
578#99—22no—
579#99C23×C5914yes—
580C24C22⋊C4×C5911yescharacteristic
581C24C22×C4×C5911yescharacteristic
582C24C22×C4×C5912yes—
583C24C2×D4×C5911yescharacteristic
584#41—41no—
585#41—41no—
586#41—41no—
587#41—41no—
588#41—41no—
589#41—41no—
590#41—41no—
591#41—41no—
592#41—41no—
593#41—41no—
594#41—41no—
595#41—41no—
596#41—41no—
597#41—41no—
598#41—41no—
599#41—41no—
600#41—42no—
601#41—42no—
602#41—42no—
603#41—42no—
604#41—42no—
605#41—42no—
606#41—41no—
607#41—41no—
608#41—41no—
609#41—41no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—41no—
613C2×Q8—41no—
614C2×Q8—41no—
615C2×Q8—41no—
616C2×Q8C22⋊C4×C5911yescharacteristic
617C2×Q8C22⋊C4×C5911yescharacteristic
618C2×Q8C2×D4×C5911yescharacteristic
619C2×Q8C2×D4×C5911yescharacteristic
620C2×D4—22no—
621C2×D4—22no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—41no—
631C2×D4—41no—
632C2×D4—41no—
633C2×D4—41no—
634C2×D4—41no—
635C2×D4—41no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4C22⋊C4×C5911yescharacteristic
639C2×D4C22⋊C4×C5911yescharacteristic
640C2×D4C22⋊C4×C5911yescharacteristic
641C2×D4C22⋊C4×C5911yescharacteristic
642C2×D4C22×C4×C5911yescharacteristic
643C2×D4C22×C4×C5911yescharacteristic
644C2×D4C22×C4×C5911yescharacteristic
645C2×D4C2×D4×C5911yescharacteristic
646C2×D4C2×D4×C5911yescharacteristic
647C2×D4C2×D4×C5911yescharacteristic
648C2×D4C2×D4×C5911yescharacteristic
649C2×D4C24×C5911yescharacteristic
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4C22⋊C4×C5911yescharacteristic
669C22×C4C22⋊C4×C5911yescharacteristic
670C22×C4C22⋊C4×C5911yescharacteristic
671C22×C4C22⋊C4×C5911yescharacteristic
672C22×C4C22⋊C4×C5911yescharacteristic
673C22×C4C22⋊C4×C5911yescharacteristic
674C22×C4C22⋊C4×C5911yescharacteristic
675C22×C4C22⋊C4×C5911yescharacteristic
676C22×C4C22⋊C4×C5911yescharacteristic
677C22×C4C22×C4×C5911yescharacteristic
678C22×C4C22×C4×C5911yescharacteristic
679C22×C4C22×C4×C5912yes—
680C22×C4C2×D4×C5911yescharacteristic
681C22×C4C2×D4×C5911yescharacteristic
682C22×C4C2×D4×C5911yescharacteristic
683C22×C4C2×D4×C5911yescharacteristic
684C22×C4C2×D4×C5911yescharacteristic
685M16—24no—
686M16—42no—
687M16—42no—
688M16—42no—
689C2×C8—42no—
690C2×C8—42no—
691C2×C8—42no—
692C4⋊C4—22no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—22no—
696C4⋊C4—22no—
697C4⋊C4—22no—
698C4⋊C4—22no—
699C4⋊C4—42no—
700C4⋊C4—42no—
701C22⋊C4—22no—
702C22⋊C4—22no—
703C22⋊C4—22no—
704C22⋊C4—22no—
705C22⋊C4—22no—
706C22⋊C4—22no—
707C22⋊C4—22no—
708C22⋊C4—22no—
709C22⋊C4—22no—
710C22⋊C4—24no—
711C22⋊C4—42no—
712C22⋊C4C22×C4×C5912yes—
713C22⋊C4C22×C4×C5912yes—
714C42—22no—
715C42—21no—
716C42—21no—
717C42—42no—
718C42—42no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—22no—
726C23—42no—
727C23—81no—
728C23—81no—
729C23—81no—
730C23—82no—
731C23C2×C22⋊C4×C5911yescharacteristic
732C23C2×C22⋊C4×C5911yescharacteristic
733C23C2×C22⋊C4×C5911yescharacteristic
734C23C2×C22⋊C4×C5911yescharacteristic
735C23C2×C22⋊C4×C5911yescharacteristic
736C23C23×C4×C5911yescharacteristic
737C23C22×D4×C5911yescharacteristic
738Q8—41no—
739Q8—41no—
740Q8—41no—
741Q8—41no—
742Q8—42no—
743Q8—41no—
744Q8—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—41no—
756D4—41no—
757D4—42no—
758D4—44no—
759D4—42no—
760D4—42no—
761D4—41no—
762D4—41no—
763D4—82no—
764D4—82no—
765D4—82no—
766D4—82no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—44no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—44no—
805C2×C4—82no—
806C2×C4—84no—
807C2×C4#99×C5911yescharacteristic
808C2×C4#99×C5911yescharacteristic
809C2×C4#99×C5911yescharacteristic
810C2×C4#99×C5911yescharacteristic
811C2×C4C2×C22⋊C4×C5911yescharacteristic
812C2×C4C2×C22⋊C4×C5911yescharacteristic
813C2×C4C2×C22⋊C4×C5911yescharacteristic
814C2×C4C2×C22⋊C4×C5911yescharacteristic
815C2×C4C2×C22⋊C4×C5911yescharacteristic
816C2×C4C2×C22⋊C4×C5911yescharacteristic
817C2×C4C2×C22⋊C4×C5911yescharacteristic
818C2×C4C22×D4×C5911yescharacteristic
819C8—44no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—84no—
843C22C2×#99×C5911yescharacteristic
844C22C2×#99×C5911yescharacteristic
845C22C22×C22⋊C4×C5911yescharacteristic
846C4—21no—
847C4—21no—
848C4—21no—
849C4—21no—
850C4—21no—
851C4—21no—
852C4—42no—
853C4—42no—
854C4—42no—
855C4—84no—
856C4C2×#99×C5911yescharacteristic
857C4C2×#99×C5911yescharacteristic
858C4C2×#99×C5911yescharacteristic
859C4C2×#99×C5911yescharacteristic
860C2—21no—
861C2—21no—
862C2—21no—
863C2—41no—
864C2—41no—
865C2—41no—
866C2—41no—
867C2—41no—
868C2—41no—
869C2—82no—
870C2C22×#99×C5911yescharacteristic
subgroupG/H
centerC4×C59C2×#99
commutatorC23C23×C4×C59
Frattini, cosocleC2×D4C24×C59
socleC2×C59C22×#99
prime radicalC59×#3449C2
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C59 ◁ C22×C4×C59 ◁ C22×#41×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C59×#413C2semidirect
3. C2×C59×#410C2semidirect
4. C59×#2123C2semidirect
5. C59×#2122C2semidirect
6. C59×#2121C2semidirect
7. C59×#2120C2semidirect
8. C22×#41×C59C4semidirect
14. C59×#536C4semidirect
17. C59×#535C4semidirect
19. C59×#534C4semidirect
25. C59×#525C4semidirect
28. C2×#117×C59C4semidirect
41. C59×#352C22semidirect
42. C59×AΣL(1,𝔽16)C22semidirect
63. C22×Q8×C59C2×C4semidirect
67. C22×D4×C59C2×C4semidirect
71. C23×C4×C59C2×C4semidirect
92. #123×C59C2×C4semidirect
93. #123×C59C2×C4semidirect
114. #120×C59C2×C4semidirect
115. #120×C59C2×C4semidirect
127. #117×C59C2×C4semidirect
128. #117×C59C2×C4semidirect
129. #117×C59C2×C4semidirect
384. #33347C59direct (N × H)
426. C2×#413C2×C59semidirect
427. C2×#410C2×C59semidirect
428. #2123C2×C59semidirect
429. #2122C2×C59semidirect
430. #2121C2×C59semidirect
431. #2120C2×C59semidirect
443. C22×#41C4×C59semidirect
449. #536C4×C59semidirect
452. #535C4×C59semidirect
454. #534C4×C59semidirect
460. #525C4×C59semidirect
463. C2×#117C4×C59semidirect
476. #352C22×C59semidirect
477. AΣL(1,𝔽16)C22×C59semidirect
478. C59#33347direct (N × H)
499. C22×Q8C2×C4×C59semidirect
503. C22×D4C2×C4×C59semidirect
507. C23×C4C2×C4×C59semidirect
528. #123C2×C4×C59semidirect
529. #123C2×C4×C59semidirect
550. #120C2×C4×C59semidirect
551. #120C2×C4×C59semidirect
563. #117C2×C4×C59semidirect
564. #117C2×C4×C59semidirect
565. #117C2×C4×C59semidirect

Maximal subgroups

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

subgroupindex
C59×#34492
C2×C59×#4132
C2×C59×#4102
C59×#21232
C59×#21222
C59×#21212
C59×#21202
#3334759