Finite Group Databasebeta

← #28645168

Subgroups — #28645168

Order 15104.

1432 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
1C2×#16837756C211yesmaximal, characteristic, complemented
2C2×#16837702C211yesmaximal, characteristic, complemented
3#21429262C211yesmaximal, characteristic, complemented
4#21425296C211yesmaximal, characteristic, complemented
5#21425289C211yesmaximal, characteristic, complemented
6#21425282C211yesmaximal, characteristic, complemented
7#21425275C211yesmaximal, characteristic, complemented
8#21425029C211yesmaximal, characteristic, complemented
9#21424891C211yesmaximal, characteristic, complemented
10#21424036C211yesmaximal, characteristic, complemented
11#21424036C211yesmaximal, characteristic, complemented
12#21424027C211yesmaximal, characteristic, complemented
13#21424027C211yesmaximal, characteristic, complemented
14C4×#14273648C211yesmaximal, characteristic, complemented
15C2×C59×#546C211yesmaximal, characteristic
16C2×#14273719C2211yescharacteristic, complemented
17#16837756—24no—
18#16837702—24no—
19C2×#14273660C2211yescharacteristic, complemented
20C2×#14273658C2211yescharacteristic, complemented
21C2×C4⋊(C59⋊C8)C2211yescharacteristic, complemented
22C2×#14273651C2211yescharacteristic, complemented
23C2×#14273651C2211yescharacteristic, complemented
24C2×#14273651C2211yescharacteristic, complemented
25C2×#14273651C2211yescharacteristic, complemented
26C2×#14273648C2211yescharacteristic
27C2×#14273648C2211yescharacteristic
28C2×#14273648C2211yescharacteristic
29C2×#14273648C2211yescharacteristic
30C2×#14273648C2211yescharacteristic
31C2×#14273648C2211yescharacteristic
32C2×#14273648C2211yescharacteristic
33C2×#14273648C2211yescharacteristic
34C2×C22⋊(C59⋊C8)C2211yescharacteristic
35C2×C22⋊(C59⋊C8)C2211yescharacteristic
36C2×C22⋊(C59⋊C8)C2211yescharacteristic, complemented
37C2×C22⋊(C59⋊C8)C2211yescharacteristic, complemented
38C2×C4×C59⋊C8C2211yescharacteristic, complemented
39#16837340—21no—
40#16837316—21no—
41#16837296—21no—
42#16837296—21no—
43#16837262C2211yescharacteristic
44#16837262C2211yescharacteristic
45#16837262C2211yescharacteristic, complemented
46#16837262C2211yescharacteristic, complemented
47C4×C4⋊Dic59C2211yescharacteristic, complemented
48#16837164C2211yescharacteristic, complemented
49#16837164C2211yescharacteristic, complemented
50C22×#41×C59C2211yescharacteristic
51C23×D4×C59C2211yescharacteristic
52C59×#546—24no—
53C59×#546—24no—
54C2×#124×C59C2211yescharacteristic
55C2×#123×C59—21no—
56C2×C22⋊Q8×C59C2211yescharacteristic
57C2×#121×C59—21no—
58C2×#121×C59C2211yescharacteristic
59C2×#120×C59—21no—
60C2×C4×D4×C59C2211yescharacteristic
61C2×C4×D4×C59C2211yescharacteristic
62C22×C22⋊C4×C59—21no—
63C22×C59⋊C8C2311yescharacteristic
64C22×C59⋊C8C2311yescharacteristic
65C22×C59⋊C8C2311yescharacteristic
66C22×C59⋊C8C2311yescharacteristic
67#14273719—22no—
68#14273719—22no—
69C2×C4⋊Dic59C2311yescharacteristic
70C2×C4⋊Dic59C2311yescharacteristic
71C2×C4⋊Dic59C2311yescharacteristic
72C2×C4⋊Dic59C2311yescharacteristic
73C2×Dic59⋊C4—21no—
74C2×Dic59⋊C4—21no—
75C2×C22⋊Dic59—21no—
76C2×C22⋊Dic59—21no—
77C2×C22⋊Dic59—21no—
78C2×C22⋊Dic59—21no—
79C2×C4×Dic59—21no—
80#14273660—22no—
81#14273658—22no—
82C4⋊(C59⋊C8)—22no—
83#14273651—22no—
84#14273651—22no—
85#14273651—41no—
86#14273651—41no—
87#14273648—22no—
88#14273648—22no—
89#14273648—22no—
90#14273648—22no—
91#14273648—22no—
92#14273648—22no—
93#14273648—41no—
94#14273648—41no—
95C22⋊(C59⋊C8)—41no—
96C22⋊(C59⋊C8)—41no—
97C22⋊(C59⋊C8)—41no—
98C22⋊(C59⋊C8)—41no—
99C4×C59⋊C8—22no—
100C59⋊#95—21no—
101C59⋊#95—21no—
102C59⋊#95—21no—
103C59⋊#95—21no—
104C59⋊#95—21no—
105C25×C59—21no—
106C2×#41×C59—22no—
107C2×#41×C59—22no—
108C2×#41×C59—22no—
109C2×#41×C59—22no—
110C2×#41×C59—41no—
111C2×#41×C59—41no—
112C22×Q8×C59C2311yescharacteristic
113C22×D4×C59—21no—
114C22×D4×C59—21no—
115C22×D4×C59—22no—
116C22×D4×C59—22no—
117C22×D4×C59—22no—
118C22×D4×C59—22no—
119C22×D4×C59—21no—
120C22×D4×C59—41no—
121C22×D4×C59—41no—
122C22×D4×C59D411yescharacteristic
123C22×D4×C59C2311yescharacteristic
124C22×D4×C59C2311yescharacteristic
125C23×C4×C59—21no—
126C23×C4×C59—21no—
127C23×C4×C59C2311yescharacteristic
128C23×C4×C59C2311yescharacteristic
129#124×C59—22no—
130#124×C59D414yes—
131#123×C59—28no—
132C22⋊Q8×C59—22no—
133C22⋊Q8×C59—22no—
134#121×C59—28no—
135#121×C59—22no—
136#121×C59—22no—
137#120×C59—28no—
138C4×D4×C59—22no—
139C4×D4×C59—22no—
140C4×D4×C59—22no—
141C4×D4×C59D414yes—
142C2×C4⋊C4×C59—21no—
143C2×C4⋊C4×C59D411yescharacteristic
144C2×C4⋊C4×C59C2311yescharacteristic
145C2×C22⋊C4×C59—28no—
146C2×C22⋊C4×C59—21no—
147C2×C22⋊C4×C59—21no—
148C2×C22⋊C4×C59—21no—
149C2×C22⋊C4×C59—21no—
150C2×C22⋊C4×C59—21no—
151C2×C22⋊C4×C59D411yescharacteristic
152C2×C22⋊C4×C59D411yescharacteristic
153C2×C42×C59C2311yescharacteristic
154C24×C59—21no—
155C24×C59—24no—
156C24×C59—21no—
157C24×C59—42no—
158C24×C59—42no—
159C24×C59—42no—
160C24×C59—42no—
161C24×C59—81no—
162C24×C59—81no—
163C24×C59C2×D411yescharacteristic
164C24×C59C2×D411yescharacteristic
165#41×C59—44no—
166#41×C59—44no—
167#41×C59—44no—
168#41×C59—44no—
169C2×Q8×C59—21no—
170C2×Q8×C59—21no—
171C2×Q8×C59—21no—
172C2×Q8×C59—21no—
173C2×Q8×C59—21no—
174C2×Q8×C59C2×D412yes—
175C2×D4×C59—24no—
176C2×D4×C59—24no—
177C2×D4×C59—22no—
178C2×D4×C59—24no—
179C2×D4×C59—22no—
180C2×D4×C59—21no—
181C2×D4×C59—21no—
182C2×D4×C59—21no—
183C2×D4×C59—21no—
184C2×D4×C59—21no—
185C2×D4×C59—21no—
186C2×D4×C59—21no—
187C2×D4×C59—21no—
188C2×D4×C59—41no—
189C2×D4×C59—42no—
190C2×D4×C59—42no—
191C2×D4×C59—44no—
192C2×D4×C59—44no—
193C2×D4×C59—44no—
194C2×D4×C59—42no—
195C2×D4×C59—42no—
196C2×D4×C59—44no—
197C2×D4×C59—81no—
198C2×D4×C59—81no—
199C2×D4×C59C2×D412yes—
200C2×D4×C59C2×D412yes—
201C2×D4×C59#4112yes—
202C2×D4×C59#4112yes—
203C22×C4×C59—24no—
204C22×C4×C59—21no—
205C22×C4×C59—21no—
206C22×C4×C59—21no—
207C22×C4×C59—21no—
208C22×C4×C59—21no—
209C22×C4×C59—21no—
210C22×C4×C59—21no—
211C22×C4×C59—21no—
212C22×C4×C59—21no—
213C22×C4×C59—21no—
214C22×C4×C59—21no—
215C22×C4×C59—21no—
216C22×C4×C59—21no—
217C22×C4×C59—21no—
218C22×C4×C59—24no—
219C22×C4×C59—42no—
220C22×C4×C59—42no—
221C22×C4×C59—81no—
222C22×C4×C59—81no—
223C22×C4×C59C2×D411yescharacteristic
224C22×C4×C59C2×D411yescharacteristic
225C22×C4×C59C2×D411yescharacteristic
226C22×C4×C59C2×D411yescharacteristic
227C22×C4×C59C2411yescharacteristic
228C22×Dic59—21no—
229C22×Dic59—21no—
230C22×Dic59—21no—
231C22×Dic59—21no—
232C4⋊C4×C59—24no—
233C4⋊C4×C59—22no—
234C4⋊C4×C59—21no—
235C4⋊C4×C59C2×D412yes—
236C22⋊C4×C59—24no—
237C22⋊C4×C59—24no—
238C22⋊C4×C59—22no—
239C22⋊C4×C59—24no—
240C22⋊C4×C59—24no—
241C22⋊C4×C59—24no—
242C22⋊C4×C59—22no—
243C42×C59C2×D412yes—
244C42×C59C2×D412yes—
245C22⋊Dic59—42no—
246C22⋊Dic59—42no—
247C22⋊Dic59—81no—
248C22⋊Dic59—81no—
249C4⋊Dic59—21no—
250C4⋊Dic59—21no—
251C4⋊Dic59—21no—
252C4⋊Dic59—21no—
253C4⋊Dic59—21no—
254C4⋊Dic59—21no—
255C4⋊Dic59—21no—
256C4⋊Dic59—21no—
257Dic59⋊C4—42no—
258Dic59⋊C4—42no—
259C4×Dic59—81no—
260C2×C59⋊C8—21no—
261C2×C59⋊C8—21no—
262C2×C59⋊C8—21no—
263C2×C59⋊C8—21no—
264C2×C59⋊C8—21no—
265C2×C59⋊C8—21no—
266C2×C59⋊C8—21no—
267C2×C59⋊C8—21no—
268C2×C59⋊C8—21no—
269C2×C59⋊C8—21no—
270C2×C59⋊C8—21no—
271C2×C59⋊C8—21no—
272C23×C59—21no—
273C23×C59—22no—
274C23×C59—21no—
275C23×C59—21no—
276C23×C59—22no—
277C23×C59—22no—
278C23×C59—21no—
279C23×C59—21no—
280C23×C59—21no—
281C23×C59—22no—
282C23×C59—21no—
283C23×C59—21no—
284C23×C59—21no—
285C23×C59—21no—
286C23×C59—21no—
287C23×C59—21no—
288C23×C59—21no—
289C23×C59—48no—
290C23×C59—48no—
291C23×C59—41no—
292C23×C59—41no—
293C23×C59—41no—
294C23×C59—41no—
295C23×C59—41no—
296C23×C59—41no—
297C23×C59—41no—
298C23×C59—41no—
299C23×C59—41no—
300C23×C59—41no—
301C23×C59—84no—
302C23×C59—84no—
303C23×C59—84no—
304C23×C59—84no—
305C23×C59—84no—
306C23×C59#13512yes—
307C23×C59C22×D411yescharacteristic
308Q8×C59—22no—
309Q8×C59—22no—
310Q8×C59—41no—
311Q8×C59—41no—
312D4×C59—22no—
313D4×C59—22no—
314D4×C59—22no—
315D4×C59—22no—
316D4×C59—22no—
317D4×C59—44no—
318D4×C59—48no—
319D4×C59—48no—
320D4×C59—41no—
321D4×C59—41no—
322D4×C59—84no—
323D4×C59#12414yes—
324C2×C4×C59—21no—
325C2×C4×C59—21no—
326C2×C4×C59—21no—
327C2×C4×C59—21no—
328C2×C4×C59—22no—
329C2×C4×C59—21no—
330C2×C4×C59—22no—
331C2×C4×C59—21no—
332C2×C4×C59—21no—
333C2×C4×C59—21no—
334C2×C4×C59—21no—
335C2×C4×C59—21no—
336C2×C4×C59—48no—
337C2×C4×C59—41no—
338C2×C4×C59—41no—
339C2×C4×C59—41no—
340C2×C4×C59—41no—
341C2×C4×C59—41no—
342C2×C4×C59—41no—
343C2×C4×C59—41no—
344C2×C4×C59—41no—
345C2×C4×C59—41no—
346C2×C4×C59—41no—
347C2×C4×C59—41no—
348C2×C4×C59—41no—
349C2×C4×C59—84no—
350C2×C4×C59#12012yes—
351C2×C4×C59#12012yes—
352C2×C4×C59C22×D411yescharacteristic
353C2×C4×C59C22×D411yescharacteristic
354C2×C4×C59C2×#4111yescharacteristic
355C2×C4×C59C2×#4111yescharacteristic
356C2×C4×C59H(5,𝔽2)11yescharacteristic
357C2×C4×C59H(5,𝔽2)11yescharacteristic
358C2×Dic59—41no—
359C2×Dic59—41no—
360C2×Dic59—41no—
361C2×Dic59—41no—
362C2×Dic59—41no—
363C2×Dic59—41no—
364C2×Dic59—41no—
365C2×Dic59—41no—
366C2×Dic59—41no—
367C2×Dic59—41no—
368C2×Dic59—41no—
369C2×Dic59—41no—
370C59⋊C8—41no—
371C59⋊C8—41no—
372C59⋊C8—41no—
373C59⋊C8—41no—
374#25890—591nomaximal, Sylow
375C22×C59—24no—
376C22×C59—22no—
377C22×C59—22no—
378C22×C59—22no—
379C22×C59—41no—
380C22×C59—42no—
381C22×C59—42no—
382C22×C59—41no—
383C22×C59—42no—
384C22×C59—42no—
385C22×C59—41no—
386C22×C59—42no—
387C22×C59—41no—
388C22×C59—42no—
389C22×C59—41no—
390C22×C59—42no—
391C22×C59—41no—
392C22×C59—42no—
393C22×C59—41no—
394C22×C59—42no—
395C22×C59—41no—
396C22×C59—41no—
397C22×C59—41no—
398C22×C59—41no—
399C22×C59—816no—
400C22×C59—81no—
401C22×C59—81no—
402C22×C59—81no—
403C22×C59—81no—
404C22×C59C2×#12011yescharacteristic
405C22×C59#54611yescharacteristic
406C22×C59#54611yescharacteristic
407C22×C59C2×#13511yescharacteristic
408C22×C59#57511yescharacteristic
409C22×C59#57611yescharacteristic
410C22×C59#57711yescharacteristic
411C4×C59—22no—
412C4×C59—22no—
413C4×C59—41no—
414C4×C59—41no—
415C4×C59—42no—
416C4×C59—42no—
417C4×C59C2×#12411yescharacteristic
418C4×C59#53511yescharacteristic
419C4×C59#54611yescharacteristic
420C4×C59#54611yescharacteristic
421Dic59—81no—
422Dic59—81no—
423Dic59—81no—
424Dic59—81no—
425C2×#546D5911yescharacteristic
426C2×#488—591no—
427C2×#478—591no—
428#2562—591no—
429#2036—591no—
430#2035—591no—
431#2034—591no—
432#2033—591no—
433#1983—591no—
434#1954—591no—
435#1788—591no—
436#1788—591no—
437#1786—591no—
438#1786—591no—
439C4×#102—591no—
440C2×C59—42no—
441C2×C59—44no—
442C2×C59—81no—
443C2×C59—82no—
444C2×C59#243511yescharacteristic
445C2×C59#300211yescharacteristic
446C2×C59#301211yescharacteristic
447C2×C59#329611yescharacteristic
448C2×C59#329711yescharacteristic
449C2×C59#332211yescharacteristic
450C2×C59#332311yescharacteristic
451C22×#41C2×D5911yescharacteristic
452C23×D4C2×D5911yescharacteristic
453#546—24no—
454#546—24no—
455C2×#125—591no—
456C2×#124C2×D5911yescharacteristic
457C2×#123—21no—
458C2×C22⋊Q8C2×D5911yescharacteristic
459C2×#121—21no—
460C2×#121C2×D5911yescharacteristic
461C2×#120—21no—
462C2×C4×D4C2×D5911yescharacteristic
463C2×C4×D4C2×D5911yescharacteristic
464C22×C22⋊C4—21no—
465#488—1184no—
466#478—1184no—
467C2×#107—591no—
468C2×#106—591no—
469C2×C4⋊C8—591no—
470C2×#103—591no—
471C2×#103—591no—
472C2×#103—591no—
473C2×#103—591no—
474C2×#102—591no—
475C2×#102—591no—
476C2×#102—591no—
477C2×#102—591no—
478C2×#102—591no—
479C2×#102—591no—
480C2×#102—591no—
481C2×#102—591no—
482C2×C22⋊C8—591no—
483C2×C22⋊C8—591no—
484C2×C22⋊C8—591no—
485C2×C22⋊C8—591no—
486C2×C4×C8—591no—
487#400—1181no—
488#394—1181no—
489#388—1181no—
490#388—1181no—
491#380—591no—
492#380—591no—
493#380—591no—
494#380—591no—
495C4×C4⋊C4—591no—
496#340—591no—
497#340—591no—
498C59#2589011yescharacteristic, complemented, Sylow
499C25—21no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8C22×D5911yescharacteristic
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—22no—
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—22no—
513C22×D4—21no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4C22⋊D5911yescharacteristic
517C22×D4C22×D5911yescharacteristic
518C22×D4C22×D5911yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4C22×D5911yescharacteristic
522C23×C4C22×D5911yescharacteristic
523C22×C8—591no—
524C22×C8—591no—
525C22×C8—591no—
526C22×C8—591no—
527#125—1182no—
528#125—1182no—
529#124—22no—
530#124C22⋊D5914yes—
531#123—28no—
532C22⋊Q8—22no—
533C22⋊Q8—22no—
534#121—28no—
535#121—22no—
536#121—22no—
537#120—28no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4C22⋊D5914yes—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—591no—
544C2×C4⋊C4—591no—
545C2×C4⋊C4—591no—
546C2×C4⋊C4—591no—
547C2×C4⋊C4—1181no—
548C2×C4⋊C4—1181no—
549C2×C4⋊C4C22⋊D5911yescharacteristic
550C2×C4⋊C4C22×D5911yescharacteristic
551C2×C22⋊C4—28no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—1181no—
558C2×C22⋊C4—1181no—
559C2×C22⋊C4—1181no—
560C2×C22⋊C4—1181no—
561C2×C22⋊C4C22⋊D5911yescharacteristic
562C2×C22⋊C4C22⋊D5911yescharacteristic
563C2×C42—1181no—
564C2×C42C22×D5911yescharacteristic
565#107—1182no—
566#106—1182no—
567C4⋊C8—1182no—
568#103—1182no—
569#103—1182no—
570#103—2361no—
571#103—2361no—
572#102—1182no—
573#102—1182no—
574#102—1182no—
575#102—1182no—
576#102—1182no—
577#102—1182no—
578#102—2361no—
579#102—2361no—
580C22⋊C8—2361no—
581C22⋊C8—2361no—
582C22⋊C8—2361no—
583C22⋊C8—2361no—
584C4×C8—1182no—
585#95—1181no—
586#95—1181no—
587#95—1181no—
588#95—1181no—
589#95—1181no—
590C24—21no—
591C24—24no—
592C24—21no—
593C24—42no—
594C24—42no—
595C24—42no—
596C24—42no—
597C24—81no—
598C24—81no—
599C24C2×C22⋊D5911yescharacteristic
600C24C2×C22⋊D5911yescharacteristic
601#41—44no—
602#41—44no—
603#41—44no—
604#41—44no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8C2×C22⋊D5912yes—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—22no—
614C2×D4—24no—
615C2×D4—22no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—41no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—44no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—44no—
633C2×D4—81no—
634C2×D4—81no—
635C2×D4#1174568712yes—
636C2×D4#1174568712yes—
637C2×D4C2×C22⋊D5912yes—
638C2×D4C2×C22⋊D5912yes—
639C22×C4—24no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—24no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—81no—
658C22×C4—81no—
659C22×C4—1181no—
660C22×C4—1181no—
661C22×C4—1181no—
662C22×C4—1181no—
663C22×C4C2×C22⋊D5911yescharacteristic
664C22×C4C2×C22⋊D5911yescharacteristic
665C22×C4C2×C22⋊D5911yescharacteristic
666C22×C4C2×C22⋊D5911yescharacteristic
667C22×C4C23×D5911yescharacteristic
668C2×C8—1181no—
669C2×C8—1181no—
670C2×C8—1181no—
671C2×C8—1181no—
672C2×C8—1181no—
673C2×C8—1181no—
674C2×C8—1181no—
675C2×C8—1181no—
676C2×C8—1181no—
677C2×C8—1181no—
678C2×C8—1181no—
679C2×C8—1181no—
680C4⋊C4—24no—
681C4⋊C4—22no—
682C4⋊C4—21no—
683C4⋊C4—1181no—
684C4⋊C4—1181no—
685C4⋊C4—1181no—
686C4⋊C4—1181no—
687C4⋊C4—1181no—
688C4⋊C4—1181no—
689C4⋊C4—1181no—
690C4⋊C4—1181no—
691C4⋊C4—2362no—
692C4⋊C4—2362no—
693C4⋊C4C2×C22⋊D5912yes—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—22no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—22no—
701C22⋊C4—4721no—
702C22⋊C4—4721no—
703C22⋊C4—2362no—
704C22⋊C4—2362no—
705C42—4721no—
706C42C2×C22⋊D5912yes—
707C42C2×C22⋊D5912yes—
708C23—21no—
709C23—22no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—48no—
726C23—48no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—84no—
738C23—84no—
739C23—84no—
740C23—84no—
741C23—84no—
742C23#1427374712yes—
743C23C22×C22⋊D5911yescharacteristic
744Q8—22no—
745Q8—22no—
746Q8—41no—
747Q8—41no—
748D4—22no—
749D4—22no—
750D4—22no—
751D4—22no—
752D4—22no—
753D4—44no—
754D4—48no—
755D4—48no—
756D4—41no—
757D4—41no—
758D4—84no—
759D4#1427371414yes—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—48no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—84no—
786C2×C4—2361no—
787C2×C4—2361no—
788C2×C4—2361no—
789C2×C4—2361no—
790C2×C4—2361no—
791C2×C4—2361no—
792C2×C4—2361no—
793C2×C4—2361no—
794C2×C4—2361no—
795C2×C4—2361no—
796C2×C4—2361no—
797C2×C4—2361no—
798C2×C4#1427369612yes—
799C2×C4#1427369612yes—
800C2×C4C22×C22⋊D5911yescharacteristic
801C2×C4C22×C22⋊D5911yescharacteristic
802C2×C4C2×#1174568711yescharacteristic
803C2×C4C2×#1174568711yescharacteristic
804C2×C4#1427377211yescharacteristic
805C2×C4#1427377211yescharacteristic
806C8—2361no—
807C8—2361no—
808C8—2361no—
809C8—2361no—
810C22—22no—
811C22—24no—
812C22—22no—
813C22—22no—
814C22—42no—
815C22—41no—
816C22—42no—
817C22—42no—
818C22—41no—
819C22—41no—
820C22—42no—
821C22—41no—
822C22—42no—
823C22—42no—
824C22—41no—
825C22—41no—
826C22—42no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—42no—
834C22—816no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22C2×#1427369611yescharacteristic
840C22#1683804611yescharacteristic
841C22#1683804611yescharacteristic
842C22C2×#1427374711yescharacteristic
843C22#1683820011yescharacteristic
844C22#1683820511yescharacteristic
845C22#1683821311yescharacteristic
846C4—22no—
847C4—22no—
848C4—41no—
849C4—41no—
850C4—42no—
851C4—42no—
852C4—4721no—
853C4—4721no—
854C4—4721no—
855C4—4721no—
856C4C2×#1427371411yescharacteristic
857C4#1683796911yescharacteristic
858C4#1683804611yescharacteristic
859C4#1683804611yescharacteristic
860C2—42no—
861C2—44no—
862C2—81no—
863C2—82no—
864C2#2142774311yescharacteristic
865C2#2143331411yescharacteristic
866C2#2143340011yescharacteristic
867C2#2143593111yescharacteristic
868C2#2143594611yescharacteristic
869C2#2143629711yescharacteristic
870C2#2143631211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
Fitting, prime radicalC2×C59×#546C2
socleC23×C59C22×D4
hypercenterC2×#546D59
hypocenterC59#25890
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#16837756C2semidirect
2. C2×#16837702C2semidirect
3. #21429262C2semidirect
4. #21425296C2semidirect
5. #21425289C2semidirect
6. #21425282C2semidirect
7. #21425275C2semidirect
8. #21425029C2semidirect
9. #21424891C2semidirect
10. #21424036C2semidirect
11. #21424036C2semidirect
12. #21424027C2semidirect
13. #21424027C2semidirect
14. C4×#14273648C2semidirect
16. C2×#14273719C22semidirect
19. C2×#14273660C22semidirect
20. C2×#14273658C22semidirect
21. C2×C4⋊(C59⋊C8)C22semidirect
22. C2×#14273651C22semidirect
23. C2×#14273651C22semidirect
24. C2×#14273651C22semidirect
25. C2×#14273651C22semidirect
36. C2×C22⋊(C59⋊C8)C22semidirect
37. C2×C22⋊(C59⋊C8)C22semidirect
38. C2×C4×C59⋊C8C22semidirect
45. #16837262C22semidirect
46. #16837262C22semidirect
47. C4×C4⋊Dic59C22semidirect
48. #16837164C22semidirect
49. #16837164C22semidirect
498. C59#25890semidirect

Maximal subgroups

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

subgroupindex
C2×#168377562
C2×#168377022
#214292622
#214252962
#214252892
#214252822
#214252752
#214250292
#214248912
#214240362
#214240272
C4×#142736482
C2×C59×#5462
#2589059