Finite Group Databasebeta

← C59×#24448 #28436557

Subgroups — C59×#24448 #28436557

Order 15104.

1888 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C59C211yesmaximal, characteristic
2C2×C59×#468C211yesmaximal, characteristic, complemented
3C2×C59×#450C211yesmaximal, characteristic, complemented
4C2×C59×#450C211yesmaximal, characteristic, complemented
5C2×C59×#418C211yesmaximal, characteristic, complemented
6C59×#2415C211yesmaximal, characteristic, complemented
7C59×#2041C211yesmaximal, characteristic, complemented
8C59×#2033C211yesmaximal, characteristic, complemented
9C59×#2014C211yesmaximal, characteristic, complemented
10C59×#2000C211yesmaximal, characteristic, complemented
11C59×#1877C211yesmaximal, characteristic, complemented
12C59×#1875C211yesmaximal, characteristic, complemented
13C59×#1870C211yesmaximal, characteristic, complemented
14C59×#1862C211yesmaximal, characteristic, complemented
15C59×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C59—21no—
17C23×D4×C59C2211yescharacteristic
18C23×D4×C59C2211yescharacteristic
19C22×SD16×C59C2211yescharacteristic
20C22×SD16×C59C2211yescharacteristic, complemented
21C22×SD16×C59C2211yescharacteristic, complemented
22C22×M16×C59C2211yescharacteristic, complemented
23D42×C59—24no—
24D42×C59—24no—
25C2×#127×C59C2211yescharacteristic
26C2×C22⋊Q8×C59C2211yescharacteristic, complemented
27C2×C22⋊Q8×C59C2211yescharacteristic, complemented
28C2×#121×C59—21no—
29C2×#121×C59C2211yescharacteristic
30C2×#121×C59C2211yescharacteristic
31C2×#120×C59—21no—
32C2×#120×C59—21no—
33C2×C4×D4×C59C2211yescharacteristic
34C2×C4×D4×C59C2211yescharacteristic
35C2×#117×C59C2211yescharacteristic, complemented
36C59×#468—24no—
37C59×#450—24no—
38C59×#450—24no—
39C2×#107×C59C2211yescharacteristic, complemented
40C59×#418—24no—
41C2×#103×C59C2211yescharacteristic, complemented
42C2×#102×C59C2211yescharacteristic
43C2×#102×C59C2211yescharacteristic
44C2×#102×C59C2211yescharacteristic
45C2×#102×C59C2211yescharacteristic, complemented
46C2×#102×C59C2211yescharacteristic, complemented
47C2×#102×C59C2211yescharacteristic, complemented
48C2×#102×C59C2211yescharacteristic, complemented
49C2×#102×C59C2211yescharacteristic, complemented
50C2×#102×C59C2211yescharacteristic, complemented
51C2×C22⋊C8×C59C2211yescharacteristic, complemented
52C2×C22⋊C8×C59C2211yescharacteristic, complemented
53C2×C22⋊C8×C59C2211yescharacteristic, complemented
54C59×#397—21no—
55C59×#394—21no—
56C59×#391C2211yescharacteristic, complemented
57C59×#389—21no—
58C59×#389C2211yescharacteristic, complemented
59C59×#388—21no—
60C59×#380C2211yescharacteristic, complemented
61C59×#340C2211yescharacteristic, complemented
62C59×#340C2211yescharacteristic, complemented
63C59×#336C2211yescharacteristic, complemented
64C59×#336C2211yescharacteristic, complemented
65C25×C59—21no—
66C25×C59—21no—
67C22×Q8×C59C2311yescharacteristic
68C22×D4×C59—22no—
69C22×D4×C59—22no—
70C22×D4×C59—28no—
71C22×D4×C59—21no—
72C22×D4×C59—21no—
73C22×D4×C59—22no—
74C22×D4×C59—22no—
75C22×D4×C59—22no—
76C22×D4×C59—22no—
77C22×D4×C59—21no—
78C22×D4×C59—21no—
79C22×D4×C59—21no—
80C22×D4×C59—22no—
81C22×D4×C59—21no—
82C22×D4×C59—41no—
83C22×D4×C59—41no—
84C22×D4×C59—41no—
85C22×D4×C59—41no—
86C22×D4×C59—44no—
87C22×D4×C59—44no—
88C22×D4×C59D411yescharacteristic
89C22×D4×C59D414yes—
90C22×D4×C59C2311yescharacteristic
91C22×D4×C59C2311yescharacteristic
92C22×D4×C59C2311yescharacteristic
93C23×C4×C59—21no—
94C23×C4×C59C2311yescharacteristic
95C23×C4×C59C2311yescharacteristic
96C2×SD16×C59—22no—
97C2×SD16×C59—22no—
98C2×SD16×C59—22no—
99C2×SD16×C59—22no—
100C2×SD16×C59—22no—
101C2×SD16×C59—22no—
102C2×SD16×C59—41no—
103C2×SD16×C59—41no—
104C2×SD16×C59—41no—
105C2×M16×C59—22no—
106C2×M16×C59—22no—
107C2×M16×C59—41no—
108C22×C8×C59C2311yescharacteristic
109C22×C8×C59C2311yescharacteristic
110C22×C8×C59C2311yescharacteristic
111C22×C8×C59C2311yescharacteristic
112#127×C59—22no—
113#127×C59—22no—
114C22⋊Q8×C59—22no—
115C22⋊Q8×C59—22no—
116C22⋊Q8×C59—22no—
117C22⋊Q8×C59—41no—
118#121×C59—28no—
119#121×C59—22no—
120#121×C59—22no—
121#121×C59—22no—
122#121×C59D414yes—
123#120×C59—28no—
124#120×C59—28no—
125C4×D4×C59—22no—
126C4×D4×C59—22no—
127C4×D4×C59—22no—
128C4×D4×C59—22no—
129#117×C59—22no—
130#117×C59—41no—
131C2×C4⋊C4×C59—21no—
132C2×C4⋊C4×C59—21no—
133C2×C4⋊C4×C59—21no—
134C2×C4⋊C4×C59D411yescharacteristic
135C2×C4⋊C4×C59C2311yescharacteristic
136C2×C4⋊C4×C59C2311yescharacteristic
137C2×C4⋊C4×C59C2311yescharacteristic
138C2×C4⋊C4×C59C2311yescharacteristic
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×C59—21no—
146C2×C22⋊C4×C59D411yescharacteristic
147C2×C22⋊C4×C59D411yescharacteristic
148C2×C42×C59—21no—
149C2×C42×C59C2311yescharacteristic
150#107×C59—22no—
151#103×C59—22no—
152#102×C59—22no—
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—
160#102×C59D414yescomplemented
161C22⋊C8×C59—22no—
162C22⋊C8×C59—22no—
163C22⋊C8×C59—41no—
164#95×C59—21no—
165#95×C59—21no—
166#95×C59—21no—
167#95×C59—21no—
168C24×C59—21no—
169C24×C59—24no—
170C24×C59—21no—
171C24×C59—21no—
172C24×C59—24no—
173C24×C59—42no—
174C24×C59—42no—
175C24×C59—42no—
176C24×C59—42no—
177C24×C59—42no—
178C24×C59—42no—
179C24×C59—42no—
180C24×C59—42no—
181C24×C59—81no—
182C24×C59—81no—
183C24×C59—81no—
184C24×C59—81no—
185C24×C59C2×D411yescharacteristic
186C24×C59C2×D411yescharacteristic
187C2×Q8×C59—21no—
188C2×Q8×C59—21no—
189C2×Q8×C59—21no—
190C2×Q8×C59—21no—
191C2×Q8×C59—21no—
192C2×Q8×C59—21no—
193C2×D4×C59—22no—
194C2×D4×C59—22no—
195C2×D4×C59—28no—
196C2×D4×C59—24no—
197C2×D4×C59—24no—
198C2×D4×C59—24no—
199C2×D4×C59—24no—
200C2×D4×C59—24no—
201C2×D4×C59—24no—
202C2×D4×C59—22no—
203C2×D4×C59—21no—
204C2×D4×C59—21no—
205C2×D4×C59—21no—
206C2×D4×C59—21no—
207C2×D4×C59—21no—
208C2×D4×C59—21no—
209C2×D4×C59—21no—
210C2×D4×C59—21no—
211C2×D4×C59—21no—
212C2×D4×C59—21no—
213C2×D4×C59—21no—
214C2×D4×C59—21no—
215C2×D4×C59—21no—
216C2×D4×C59—44no—
217C2×D4×C59—44no—
218C2×D4×C59—44no—
219C2×D4×C59—42no—
220C2×D4×C59—42no—
221C2×D4×C59—42no—
222C2×D4×C59—42no—
223C2×D4×C59—42no—
224C2×D4×C59—44no—
225C2×D4×C59—44no—
226C2×D4×C59—432no—
227C2×D4×C59—44no—
228C2×D4×C59—42no—
229C2×D4×C59—42no—
230C2×D4×C59—42no—
231C2×D4×C59—42no—
232C2×D4×C59—44no—
233C2×D4×C59—42no—
234C2×D4×C59—81no—
235C2×D4×C59—81no—
236C2×D4×C59C2×D412yes—
237C2×D4×C59C2×D412yes—
238C2×D4×C59C2×D412yes—
239C2×D4×C59C2×D412yes—
240C2×D4×C59#4112yes—
241C22×C4×C59—21no—
242C22×C4×C59—21no—
243C22×C4×C59—21no—
244C22×C4×C59—21no—
245C22×C4×C59—24no—
246C22×C4×C59—21no—
247C22×C4×C59—21no—
248C22×C4×C59—21no—
249C22×C4×C59—21no—
250C22×C4×C59—21no—
251C22×C4×C59—21no—
252C22×C4×C59—21no—
253C22×C4×C59—21no—
254C22×C4×C59—21no—
255C22×C4×C59—21no—
256C22×C4×C59—21no—
257C22×C4×C59—42no—
258C22×C4×C59—42no—
259C22×C4×C59C2×D411yescharacteristic
260C22×C4×C59C2×D411yescharacteristic
261C22×C4×C59C2×D411yescharacteristic
262C22×C4×C59C2×D412yes—
263C22×C4×C59C2×D412yes—
264C22×C4×C59C2×D411yescharacteristic
265C22×C4×C59C2411yescharacteristic
266SD16×C59—44no—
267SD16×C59—44no—
268SD16×C59—44no—
269M16×C59—44no—
270C2×C8×C59—21no—
271C2×C8×C59—21no—
272C2×C8×C59—21no—
273C2×C8×C59—21no—
274C2×C8×C59—21no—
275C2×C8×C59—21no—
276C2×C8×C59—21no—
277C2×C8×C59—21no—
278C2×C8×C59—21no—
279C2×C8×C59—21no—
280C2×C8×C59—21no—
281C2×C8×C59C2×D412yescomplemented
282C4⋊C4×C59—22no—
283C4⋊C4×C59—21no—
284C4⋊C4×C59—21no—
285C4⋊C4×C59—21no—
286C4⋊C4×C59—21no—
287C4⋊C4×C59—21no—
288C4⋊C4×C59—21no—
289C4⋊C4×C59—42no—
290C4⋊C4×C59—42no—
291C4⋊C4×C59—42no—
292C4⋊C4×C59C2×D412yes—
293C4⋊C4×C59C2×D412yescomplemented
294C22⋊C4×C59—24no—
295C22⋊C4×C59—24no—
296C22⋊C4×C59—22no—
297C22⋊C4×C59—24no—
298C22⋊C4×C59—22no—
299C22⋊C4×C59—42no—
300C22⋊C4×C59—42no—
301C22⋊C4×C59—42no—
302C22⋊C4×C59—42no—
303C42×C59—21no—
304C42×C59—21no—
305C42×C59—42no—
306C23×C59—21no—
307C23×C59—22no—
308C23×C59—21no—
309C23×C59—21no—
310C23×C59—22no—
311C23×C59—21no—
312C23×C59—21no—
313C23×C59—22no—
314C23×C59—21no—
315C23×C59—21no—
316C23×C59—21no—
317C23×C59—21no—
318C23×C59—21no—
319C23×C59—21no—
320C23×C59—21no—
321C23×C59—22no—
322C23×C59—22no—
323C23×C59—48no—
324C23×C59—48no—
325C23×C59—48no—
326C23×C59—48no—
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—41no—
338C23×C59—41no—
339C23×C59—41no—
340C23×C59—41no—
341C23×C59—41no—
342C23×C59—41no—
343C23×C59—84no—
344C23×C59—84no—
345C23×C59—84no—
346C23×C59—84no—
347C23×C59—84no—
348C23×C59—84no—
349C23×C59—84no—
350C23×C59—84no—
351C23×C59—84no—
352C23×C59—84no—
353C23×C59#12012yes—
354C23×C59AGL(1,ℤ/8)12yes—
355C23×C59C22×D411yescharacteristic
356Q8×C59—41no—
357Q8×C59—41no—
358Q8×C59—41no—
359Q8×C59—41no—
360D4×C59—28no—
361D4×C59—22no—
362D4×C59—22no—
363D4×C59—22no—
364D4×C59—22no—
365D4×C59—22no—
366D4×C59—22no—
367D4×C59—22no—
368D4×C59—48no—
369D4×C59—48no—
370D4×C59—48no—
371D4×C59—48no—
372D4×C59—48no—
373D4×C59—41no—
374D4×C59—41no—
375D4×C59—41no—
376D4×C59—41no—
377D4×C59—84no—
378D4×C59#12114yes—
379C2×C4×C59—21no—
380C2×C4×C59—21no—
381C2×C4×C59—21no—
382C2×C4×C59—21no—
383C2×C4×C59—22no—
384C2×C4×C59—22no—
385C2×C4×C59—22no—
386C2×C4×C59—22no—
387C2×C4×C59—21no—
388C2×C4×C59—21no—
389C2×C4×C59—22no—
390C2×C4×C59—22no—
391C2×C4×C59—21no—
392C2×C4×C59—21no—
393C2×C4×C59—21no—
394C2×C4×C59—21no—
395C2×C4×C59—48no—
396C2×C4×C59—41no—
397C2×C4×C59—41no—
398C2×C4×C59—41no—
399C2×C4×C59—41no—
400C2×C4×C59—41no—
401C2×C4×C59—41no—
402C2×C4×C59—41no—
403C2×C4×C59—41no—
404C2×C4×C59—41no—
405C2×C4×C59—41no—
406C2×C4×C59—41no—
407C2×C4×C59—41no—
408C2×C4×C59—41no—
409C2×C4×C59—41no—
410C2×C4×C59—41no—
411C2×C4×C59—41no—
412C2×C4×C59—41no—
413C2×C4×C59#12012yes—
414C2×C4×C59AGL(1,ℤ/8)12yes—
415C2×C4×C59C22×D411yescharacteristic
416C2×C4×C59C22×D411yescharacteristic
417C2×C4×C59C22×D411yescharacteristic
418C2×C4×C59C2×#4111yescharacteristic
419C2×C4×C59H(5,𝔽2)11yescharacteristic
420C2×C4×C59H(5,𝔽2)11yescharacteristic
421C8×C59—22no—
422C8×C59—41no—
423C8×C59—41no—
424C8×C59—41no—
425#24448C5911yesmaximal, characteristic, direct product factor, Sylow
426C22×C59—22no—
427C22×C59—24no—
428C22×C59—22no—
429C22×C59—22no—
430C22×C59—22no—
431C22×C59—22no—
432C22×C59—22no—
433C22×C59—41no—
434C22×C59—42no—
435C22×C59—41no—
436C22×C59—42no—
437C22×C59—41no—
438C22×C59—42no—
439C22×C59—41no—
440C22×C59—41no—
441C22×C59—42no—
442C22×C59—41no—
443C22×C59—42no—
444C22×C59—41no—
445C22×C59—41no—
446C22×C59—42no—
447C22×C59—42no—
448C22×C59—42no—
449C22×C59—42no—
450C22×C59—42no—
451C22×C59—42no—
452C22×C59—42no—
453C22×C59—816no—
454C22×C59—816no—
455C22×C59—81no—
456C22×C59—81no—
457C22×C59—81no—
458C22×C59—81no—
459C22×C59—81no—
460C22×C59—81no—
461C22×C59—81no—
462C22×C59—81no—
463C22×C59C2×#12011yescharacteristic
464C22×C59D4211yescharacteristic
465C22×C59#54611yescharacteristic
466C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
467C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
468C22×C59#57711yescharacteristic
469C22×C59#57711yescharacteristic
470C4×C59—22no—
471C4×C59—22no—
472C4×C59—41no—
473C4×C59—42no—
474C4×C59—41no—
475C4×C59—42no—
476C4×C59—81no—
477C4×C59—81no—
478C4×C59—81no—
479C4×C59C2×#12111yescharacteristic
480C4×C59#53411yescharacteristic
481C4×C59D4211yescharacteristic
482C4×C59#54611yescharacteristic
483C2×D42C2×C5911yescharacteristic
484C2×#468C2×C5911yescharacteristic, complemented
485C2×#450C2×C5911yescharacteristic, complemented
486C2×#450C2×C5911yescharacteristic, complemented
487C2×#418C2×C5911yescharacteristic, complemented
488#2415C2×C5911yescharacteristic, complemented
489#2041C2×C5911yescharacteristic, complemented
490#2033C2×C5911yescharacteristic, complemented
491#2014C2×C5911yescharacteristic, complemented
492#2000C2×C5911yescharacteristic, complemented
493#1877C2×C5911yescharacteristic, complemented
494#1875C2×C5911yescharacteristic, complemented
495#1870C2×C5911yescharacteristic, complemented
496#1862C2×C5911yescharacteristic, complemented
497#1786C2×C5911yescharacteristic, complemented
498C2×C59—42no—
499C2×C59—42no—
500C2×C59—44no—
501C2×C59—82no—
502C2×C59—82no—
503C2×C59#241011yescharacteristic
504C2×C59#300311yescharacteristic
505C2×C59#300911yescharacteristic
506C2×C59#326511yescharacteristic
507C2×C59#327211yescharacteristic
508C2×C59#331011yescharacteristic
509C2×C59#332411yescharacteristic
510C23×D4—21no—
511C23×D4C22×C5911yescharacteristic
512C23×D4C22×C5911yescharacteristic
513C22×SD16C22×C5911yescharacteristic
514C22×SD16C22×C5911yescharacteristic, complemented
515C22×SD16C22×C5911yescharacteristic, complemented
516C22×M16C22×C5911yescharacteristic, complemented
517D42—24no—
518D42—24no—
519C2×#127C22×C5911yescharacteristic
520C2×C22⋊Q8C22×C5911yescharacteristic, complemented
521C2×C22⋊Q8C22×C5911yescharacteristic, complemented
522C2×#121—21no—
523C2×#121C22×C5911yescharacteristic
524C2×#121C22×C5911yescharacteristic
525C2×#120—21no—
526C2×#120—21no—
527C2×C4×D4C22×C5911yescharacteristic
528C2×C4×D4C22×C5911yescharacteristic
529C2×#117C22×C5911yescharacteristic, complemented
530#468—24no—
531#450—24no—
532#450—24no—
533C2×#107C22×C5911yescharacteristic, complemented
534#418—24no—
535C2×#103C22×C5911yescharacteristic, complemented
536C2×#102C22×C5911yescharacteristic
537C2×#102C22×C5911yescharacteristic
538C2×#102C22×C5911yescharacteristic
539C2×#102C22×C5911yescharacteristic, complemented
540C2×#102C22×C5911yescharacteristic, complemented
541C2×#102C22×C5911yescharacteristic, complemented
542C2×#102C22×C5911yescharacteristic, complemented
543C2×#102C22×C5911yescharacteristic, complemented
544C2×#102C22×C5911yescharacteristic, complemented
545C2×C22⋊C8C22×C5911yescharacteristic, complemented
546C2×C22⋊C8C22×C5911yescharacteristic, complemented
547C2×C22⋊C8C22×C5911yescharacteristic, complemented
548#397—21no—
549#394—21no—
550#391C22×C5911yescharacteristic, complemented
551#389—21no—
552#389C22×C5911yescharacteristic, complemented
553#388—21no—
554#380C22×C5911yescharacteristic, complemented
555#340C22×C5911yescharacteristic, complemented
556#340C22×C5911yescharacteristic, complemented
557#336C22×C5911yescharacteristic, complemented
558#336C22×C5911yescharacteristic, complemented
559C59#2444811yescharacteristic, direct product factor, Sylow
560C25—21no—
561C25—21no—
562C22×Q8C23×C5911yescharacteristic
563C22×D4—22no—
564C22×D4—22no—
565C22×D4—28no—
566C22×D4—21no—
567C22×D4—21no—
568C22×D4—22no—
569C22×D4—22no—
570C22×D4—22no—
571C22×D4—22no—
572C22×D4—21no—
573C22×D4—21no—
574C22×D4—21no—
575C22×D4—22no—
576C22×D4—21no—
577C22×D4—41no—
578C22×D4—41no—
579C22×D4—41no—
580C22×D4—41no—
581C22×D4—44no—
582C22×D4—44no—
583C22×D4D4×C5911yescharacteristic
584C22×D4D4×C5914yes—
585C22×D4C23×C5911yescharacteristic
586C22×D4C23×C5911yescharacteristic
587C22×D4C23×C5911yescharacteristic
588C23×C4—21no—
589C23×C4C23×C5911yescharacteristic
590C23×C4C23×C5911yescharacteristic
591C2×SD16—22no—
592C2×SD16—22no—
593C2×SD16—22no—
594C2×SD16—22no—
595C2×SD16—22no—
596C2×SD16—22no—
597C2×SD16—41no—
598C2×SD16—41no—
599C2×SD16—41no—
600C2×M16—22no—
601C2×M16—22no—
602C2×M16—41no—
603C22×C8C23×C5911yescharacteristic
604C22×C8C23×C5911yescharacteristic
605C22×C8C23×C5911yescharacteristic
606C22×C8C23×C5911yescharacteristic
607#127—22no—
608#127—22no—
609C22⋊Q8—22no—
610C22⋊Q8—22no—
611C22⋊Q8—22no—
612C22⋊Q8—41no—
613#121—28no—
614#121—22no—
615#121—22no—
616#121—22no—
617#121D4×C5914yes—
618#120—28no—
619#120—28no—
620C4×D4—22no—
621C4×D4—22no—
622C4×D4—22no—
623C4×D4—22no—
624#117—22no—
625#117—41no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4D4×C5911yescharacteristic
630C2×C4⋊C4C23×C5911yescharacteristic
631C2×C4⋊C4C23×C5911yescharacteristic
632C2×C4⋊C4C23×C5911yescharacteristic
633C2×C4⋊C4C23×C5911yescharacteristic
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4D4×C5911yescharacteristic
642C2×C22⋊C4D4×C5911yescharacteristic
643C2×C42—21no—
644C2×C42C23×C5911yescharacteristic
645#107—22no—
646#103—22no—
647#102—22no—
648#102—22no—
649#102—22no—
650#102—22no—
651#102—22no—
652#102—22no—
653#102—22no—
654#102—41no—
655#102D4×C5914yescomplemented
656C22⋊C8—22no—
657C22⋊C8—22no—
658C22⋊C8—41no—
659#95—21no—
660#95—21no—
661#95—21no—
662#95—21no—
663C24—21no—
664C24—24no—
665C24—21no—
666C24—21no—
667C24—24no—
668C24—42no—
669C24—42no—
670C24—42no—
671C24—42no—
672C24—42no—
673C24—42no—
674C24—42no—
675C24—42no—
676C24—81no—
677C24—81no—
678C24—81no—
679C24—81no—
680C24C2×D4×C5911yescharacteristic
681C24C2×D4×C5911yescharacteristic
682C2×Q8—21no—
683C2×Q8—21no—
684C2×Q8—21no—
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×D4—22no—
689C2×D4—22no—
690C2×D4—28no—
691C2×D4—24no—
692C2×D4—24no—
693C2×D4—24no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—22no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—44no—
712C2×D4—44no—
713C2×D4—44no—
714C2×D4—42no—
715C2×D4—42no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—44no—
720C2×D4—44no—
721C2×D4—432no—
722C2×D4—44no—
723C2×D4—42no—
724C2×D4—42no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—44no—
728C2×D4—42no—
729C2×D4—81no—
730C2×D4—81no—
731C2×D4C2×D4×C5912yes—
732C2×D4C2×D4×C5912yes—
733C2×D4C2×D4×C5912yes—
734C2×D4C2×D4×C5912yes—
735C2×D4#41×C5912yes—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—24no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—42no—
753C22×C4—42no—
754C22×C4C2×D4×C5911yescharacteristic
755C22×C4C2×D4×C5911yescharacteristic
756C22×C4C2×D4×C5911yescharacteristic
757C22×C4C2×D4×C5912yes—
758C22×C4C2×D4×C5912yes—
759C22×C4C2×D4×C5911yescharacteristic
760C22×C4C24×C5911yescharacteristic
761SD16—44no—
762SD16—44no—
763SD16—44no—
764M16—44no—
765C2×C8—21no—
766C2×C8—21no—
767C2×C8—21no—
768C2×C8—21no—
769C2×C8—21no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8C2×D4×C5912yescomplemented
777C4⋊C4—22no—
778C4⋊C4—21no—
779C4⋊C4—21no—
780C4⋊C4—21no—
781C4⋊C4—21no—
782C4⋊C4—21no—
783C4⋊C4—21no—
784C4⋊C4—42no—
785C4⋊C4—42no—
786C4⋊C4—42no—
787C4⋊C4C2×D4×C5912yes—
788C4⋊C4C2×D4×C5912yescomplemented
789C22⋊C4—24no—
790C22⋊C4—24no—
791C22⋊C4—22no—
792C22⋊C4—24no—
793C22⋊C4—22no—
794C22⋊C4—42no—
795C22⋊C4—42no—
796C22⋊C4—42no—
797C22⋊C4—42no—
798C42—21no—
799C42—21no—
800C42—42no—
801C23—21no—
802C23—22no—
803C23—21no—
804C23—21no—
805C23—22no—
806C23—21no—
807C23—21no—
808C23—22no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—22no—
817C23—22no—
818C23—48no—
819C23—48no—
820C23—48no—
821C23—48no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—84no—
839C23—84no—
840C23—84no—
841C23—84no—
842C23—84no—
843C23—84no—
844C23—84no—
845C23—84no—
846C23—84no—
847C23—84no—
848C23#120×C5912yes—
849C23AGL(1,ℤ/8)×C5912yes—
850C23C22×D4×C5911yescharacteristic
851Q8—41no—
852Q8—41no—
853Q8—41no—
854Q8—41no—
855D4—28no—
856D4—22no—
857D4—22no—
858D4—22no—
859D4—22no—
860D4—22no—
861D4—22no—
862D4—22no—
863D4—48no—
864D4—48no—
865D4—48no—
866D4—48no—
867D4—48no—
868D4—41no—
869D4—41no—
870D4—41no—
871D4—41no—
872D4—84no—
873D4#121×C5914yes—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—21no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—21no—
890C2×C4—48no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4#120×C5912yes—
909C2×C4AGL(1,ℤ/8)×C5912yes—
910C2×C4C22×D4×C5911yescharacteristic
911C2×C4C22×D4×C5911yescharacteristic
912C2×C4C22×D4×C5911yescharacteristic
913C2×C4C2×#41×C5911yescharacteristic
914C2×C4H(5,𝔽2)×C5911yescharacteristic
915C2×C4H(5,𝔽2)×C5911yescharacteristic
916C8—22no—
917C8—41no—
918C8—41no—
919C8—41no—
920C22—22no—
921C22—22no—
922C22—22no—
923C22—22no—
924C22—22no—
925C22—22no—
926C22—24no—
927C22—42no—
928C22—41no—
929C22—42no—
930C22—41no—
931C22—42no—
932C22—41no—
933C22—41no—
934C22—42no—
935C22—41no—
936C22—42no—
937C22—41no—
938C22—41no—
939C22—42no—
940C22—41no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—816no—
948C22—816no—
949C22—81no—
950C22—81no—
951C22—81no—
952C22—81no—
953C22—81no—
954C22—81no—
955C22—81no—
956C22—81no—
957C22C2×#120×C5911yescharacteristic
958C22D42×C5911yescharacteristic
959C22C59×#54611yescharacteristic
960C22C2×AGL(1,ℤ/8)×C5911yescharacteristic
961C22C2×AGL(1,ℤ/8)×C5911yescharacteristic
962C22C59×#57711yescharacteristic
963C22C59×#57711yescharacteristic
964C4—22no—
965C4—22no—
966C4—42no—
967C4—41no—
968C4—42no—
969C4—41no—
970C4—81no—
971C4—81no—
972C4—81no—
973C4C2×#121×C5911yescharacteristic
974C4C59×#53411yescharacteristic
975C4D42×C5911yescharacteristic
976C4C59×#54611yescharacteristic
977C2—42no—
978C2—42no—
979C2—44no—
980C2—82no—
981C2—82no—
982C2C59×#241011yescharacteristic
983C2C59×#300311yescharacteristic
984C2C59×#300911yescharacteristic
985C2C59×#326511yescharacteristic
986C2C59×#327211yescharacteristic
987C2C59×#331011yescharacteristic
988C2C59×#332411yescharacteristic
subgroupG/H
center, socleC23×C59C22×D4
commutator, Frattini, cosocleC22×C4C24×C59
prime radicalC2×D42×C59C2
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×#468C2semidirect
3. C2×C59×#450C2semidirect
4. C2×C59×#450C2semidirect
5. C2×C59×#418C2semidirect
6. C59×#2415C2semidirect
7. C59×#2041C2semidirect
8. C59×#2033C2semidirect
9. C59×#2014C2semidirect
10. C59×#2000C2semidirect
11. C59×#1877C2semidirect
12. C59×#1875C2semidirect
13. C59×#1870C2semidirect
14. C59×#1862C2semidirect
15. C59×#1786C2semidirect
20. C22×SD16×C59C22semidirect
21. C22×SD16×C59C22semidirect
22. C22×M16×C59C22semidirect
26. C2×C22⋊Q8×C59C22semidirect
27. C2×C22⋊Q8×C59C22semidirect
35. C2×#117×C59C22semidirect
39. C2×#107×C59C22semidirect
41. C2×#103×C59C22semidirect
45. C2×#102×C59C22semidirect
46. C2×#102×C59C22semidirect
47. C2×#102×C59C22semidirect
48. C2×#102×C59C22semidirect
49. C2×#102×C59C22semidirect
50. C2×#102×C59C22semidirect
51. C2×C22⋊C8×C59C22semidirect
52. C2×C22⋊C8×C59C22semidirect
53. C2×C22⋊C8×C59C22semidirect
56. C59×#391C22semidirect
58. C59×#389C22semidirect
60. C59×#380C22semidirect
61. C59×#340C22semidirect
62. C59×#340C22semidirect
63. C59×#336C22semidirect
64. C59×#336C22semidirect
160. #102×C59D4semidirect
281. C2×C8×C59C2×D4semidirect
293. C4⋊C4×C59C2×D4semidirect
425. #24448C59direct (N × H)
484. C2×#468C2×C59semidirect
485. C2×#450C2×C59semidirect
486. C2×#450C2×C59semidirect
487. C2×#418C2×C59semidirect
488. #2415C2×C59semidirect
489. #2041C2×C59semidirect
490. #2033C2×C59semidirect
491. #2014C2×C59semidirect
492. #2000C2×C59semidirect
493. #1877C2×C59semidirect
494. #1875C2×C59semidirect
495. #1870C2×C59semidirect
496. #1862C2×C59semidirect
497. #1786C2×C59semidirect
514. C22×SD16C22×C59semidirect
515. C22×SD16C22×C59semidirect
516. C22×M16C22×C59semidirect
520. C2×C22⋊Q8C22×C59semidirect
521. C2×C22⋊Q8C22×C59semidirect
529. C2×#117C22×C59semidirect
533. C2×#107C22×C59semidirect
535. C2×#103C22×C59semidirect
539. C2×#102C22×C59semidirect
540. C2×#102C22×C59semidirect
541. C2×#102C22×C59semidirect
542. C2×#102C22×C59semidirect
543. C2×#102C22×C59semidirect
544. C2×#102C22×C59semidirect
545. C2×C22⋊C8C22×C59semidirect
546. C2×C22⋊C8C22×C59semidirect
547. C2×C22⋊C8C22×C59semidirect
550. #391C22×C59semidirect
552. #389C22×C59semidirect
554. #380C22×C59semidirect
555. #340C22×C59semidirect
556. #340C22×C59semidirect
557. #336C22×C59semidirect
558. #336C22×C59semidirect
559. C59#24448direct (N × H)
655. #102D4×C59semidirect
776. C2×C8C2×D4×C59semidirect
788. C4⋊C4C2×D4×C59semidirect

Maximal subgroups

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

subgroupindex
C2×D42×C592
C2×C59×#4682
C2×C59×#4502
C2×C59×#4182
C59×#24152
C59×#20412
C59×#20332
C59×#20142
C59×#20002
C59×#18772
C59×#18752
C59×#18702
C59×#18622
C59×#17862
#2444859