Finite Group Databasebeta

← #28604106

Subgroups — #28604106

Order 15104.

1638 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C59⋊C8C211yesmaximal, characteristic, complemented
2C2×#16837398C211yesmaximal, characteristic, complemented
3C22×#14273648C211yesmaximal, characteristic, complemented
4#21427025C211yesmaximal, characteristic, complemented
5#21425029C211yesmaximal, characteristic, complemented
6#21424908C211yesmaximal, characteristic, complemented
7#21424525C211yesmaximal, characteristic, complemented
8#21424520C211yesmaximal, characteristic, complemented
9#21424419C211yesmaximal, characteristic, complemented
10#21424404C211yesmaximal, characteristic, complemented
11#21424106C211yesmaximal, characteristic, complemented
12#21424036C211yesmaximal, characteristic, complemented
13#21424027C211yesmaximal, characteristic, complemented
14C4×#14273648C211yesmaximal, characteristic, complemented
15C2×C59×#546C211yesmaximal, characteristic
16C23×C59⋊C8C2211yescharacteristic
17C23×C59⋊C8C2211yescharacteristic, complemented
18C2×#14273686C2211yescharacteristic, complemented
19C22×C4⋊Dic59C2211yescharacteristic
20D4×C59⋊C8—24no—
21C2×C4⋊(C59⋊C8)C2211yescharacteristic, complemented
22#16837398—24no—
23C2×#14273651C2211yescharacteristic, complemented
24C2×#14273651C2211yescharacteristic, complemented
25C2×#14273651C2211yescharacteristic, complemented
26C2×#14273651C2211yescharacteristic, complemented
27C2×#14273648—24no—
28C2×#14273648C2211yescharacteristic
29C2×#14273648C2211yescharacteristic
30C2×#14273648C2211yescharacteristic
31C2×#14273648C2211yescharacteristic
32C2×#14273648C2211yescharacteristic
33C2×#14273648C2211yescharacteristic
34C2×#14273648C2211yescharacteristic
35C2×#14273648C2211yescharacteristic
36C2×C22⋊(C59⋊C8)C2211yescharacteristic
37C2×C22⋊(C59⋊C8)C2211yescharacteristic, complemented
38C2×C4×C59⋊C8C2211yescharacteristic, complemented
39#16837295—21no—
40#16837288—21no—
41#16837282—21no—
42#16837268C2211yescharacteristic, complemented
43#16837262C2211yescharacteristic
44#16837262C2211yescharacteristic, complemented
45C4×C4⋊Dic59C2211yescharacteristic, complemented
46C22⋊C4×Dic59—21no—
47#16837164C2211yescharacteristic, complemented
48#16837164C2211yescharacteristic, complemented
49#16837164C2211yescharacteristic, complemented
50#16837164C2211yescharacteristic, complemented
51C22×#41×C59C2211yescharacteristic
52C23×D4×C59C2211yescharacteristic
53C59×#546—24no—
54C59×#546C418yescomplemented
55C2×#124×C59C2211yescharacteristic
56C2×#123×C59—21no—
57C2×C22⋊Q8×C59C2211yescharacteristic
58C2×#121×C59—21no—
59C2×#121×C59C2211yescharacteristic
60C2×#120×C59—21no—
61C2×C4×D4×C59C2211yescharacteristic
62C2×C4×D4×C59C2211yescharacteristic
63C22×C22⋊C4×C59—21no—
64C23×Dic59—21no—
65C22×C59⋊C8—22no—
66C22×C59⋊C8—22no—
67C22×C59⋊C8—22no—
68C22×C59⋊C8—22no—
69C22×C59⋊C8—41no—
70C22×C59⋊C8—41no—
71C22×C59⋊C8C2311yescharacteristic
72C22×C59⋊C8C2311yescharacteristic
73C22×C59⋊C8C2311yescharacteristic
74C22×C59⋊C8C2311yescharacteristic
75#14273686—22no—
76#14273686—41no—
77C2×C4⋊Dic59—22no—
78C2×C4⋊Dic59—21no—
79C2×C4⋊Dic59—41no—
80C2×C4⋊Dic59C2311yescharacteristic
81C2×C4⋊Dic59C2311yescharacteristic
82C2×C4⋊Dic59C2311yescharacteristic
83C2×C4⋊Dic59C2311yescharacteristic
84C2×C22⋊Dic59—21no—
85C2×C22⋊Dic59—21no—
86C2×C22⋊Dic59—21no—
87C2×C4×Dic59—21no—
88C2×C4×Dic59—21no—
89C4⋊(C59⋊C8)—22no—
90#14273651—22no—
91#14273651—22no—
92#14273651—41no—
93#14273651—41no—
94#14273648—22no—
95#14273648—22no—
96#14273648—22no—
97#14273648—22no—
98#14273648—22no—
99#14273648—41no—
100#14273648—41no—
101#14273648D414yescomplemented
102C22⋊(C59⋊C8)—22no—
103C22⋊(C59⋊C8)—22no—
104C4×C59⋊C8—22no—
105C59⋊#95—21no—
106C59⋊#95—21no—
107C59⋊#95—21no—
108C59⋊#95—21no—
109C59⋊#95—21no—
110C25×C59—21no—
111C2×#41×C59—22no—
112C2×#41×C59—22no—
113C2×#41×C59—22no—
114C2×#41×C59—41no—
115C2×#41×C59—41no—
116C2×#41×C59C2×C414yescomplemented
117C22×Q8×C59C2311yescharacteristic
118C22×D4×C59—22no—
119C22×D4×C59—22no—
120C22×D4×C59—21no—
121C22×D4×C59—21no—
122C22×D4×C59—21no—
123C22×D4×C59—22no—
124C22×D4×C59—41no—
125C22×D4×C59—41no—
126C22×D4×C59C2×C414yes—
127C22×D4×C59D411yescharacteristic
128C22×D4×C59C2311yescharacteristic
129C22×D4×C59C2311yescharacteristic
130C23×C4×C59—21no—
131C23×C4×C59—21no—
132C23×C4×C59C2311yescharacteristic
133C23×C4×C59C2311yescharacteristic
134#124×C59—22no—
135#124×C59C2×C414yescomplemented
136#123×C59—28no—
137C22⋊Q8×C59—22no—
138C22⋊Q8×C59C2×C414yes—
139#121×C59—22no—
140#121×C59—28no—
141#121×C59C2×C414yescomplemented
142#120×C59—28no—
143C4×D4×C59—22no—
144C4×D4×C59C2×C414yes—
145C4×D4×C59C2×C414yescomplemented
146C4×D4×C59D414yes—
147C2×C4⋊C4×C59—21no—
148C2×C4⋊C4×C59D411yescharacteristic
149C2×C4⋊C4×C59C2311yescharacteristic
150C2×C22⋊C4×C59—21no—
151C2×C22⋊C4×C59—21no—
152C2×C22⋊C4×C59—21no—
153C2×C22⋊C4×C59—21no—
154C2×C22⋊C4×C59—21no—
155C2×C22⋊C4×C59—28no—
156C2×C22⋊C4×C59D411yescharacteristic
157C2×C22⋊C4×C59D411yescharacteristic
158C2×C42×C59C2311yescharacteristic
159C24×C59—21no—
160C24×C59—21no—
161C24×C59—24no—
162C24×C59—42no—
163C24×C59—42no—
164C24×C59—42no—
165C24×C59—42no—
166C24×C59—81no—
167C24×C59—81no—
168C24×C59C2×D411yescharacteristic
169C24×C59C2×D411yescharacteristic
170#41×C59—28no—
171#41×C59—44no—
172#41×C59—44no—
173#41×C59—44no—
174C2×Q8×C59—21no—
175C2×Q8×C59—21no—
176C2×Q8×C59—21no—
177C2×Q8×C59—21no—
178C2×Q8×C59—21no—
179C2×Q8×C59C22×C412yes—
180C2×D4×C59—22no—
181C2×D4×C59—22no—
182C2×D4×C59—28no—
183C2×D4×C59—24no—
184C2×D4×C59—24no—
185C2×D4×C59—24no—
186C2×D4×C59—21no—
187C2×D4×C59—21no—
188C2×D4×C59—21no—
189C2×D4×C59—21no—
190C2×D4×C59—21no—
191C2×D4×C59—21no—
192C2×D4×C59—21no—
193C2×D4×C59—21no—
194C2×D4×C59—44no—
195C2×D4×C59—44no—
196C2×D4×C59—44no—
197C2×D4×C59—42no—
198C2×D4×C59—42no—
199C2×D4×C59—42no—
200C2×D4×C59—42no—
201C2×D4×C59—81no—
202C2×D4×C59—81no—
203C2×D4×C59C22⋊C414yes—
204C2×D4×C59C22×C412yes—
205C2×D4×C59C22×C412yes—
206C2×D4×C59C2×D412yes—
207C2×D4×C59#4112yes—
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—24no—
220C22×C4×C59—42no—
221C22×C4×C59—42no—
222C22×C4×C59—81no—
223C22×C4×C59—81no—
224C22×C4×C59C22×C412yes—
225C22×C4×C59C22×C412yes—
226C22×C4×C59C2×D411yescharacteristic
227C22×C4×C59C2×D411yescharacteristic
228C22×C4×C59C2×D411yescharacteristic
229C22×C4×C59C2×D411yescharacteristic
230C22×C4×C59C2×D412yes—
231C22×C4×C59C2×D412yes—
232C22×C4×C59C2411yescharacteristic
233C22×Dic59—21no—
234C22×Dic59—21no—
235C22×Dic59—21no—
236C22×Dic59—21no—
237C22×Dic59—42no—
238C22×Dic59—42no—
239C22×Dic59—81no—
240C4⋊C4×C59—24no—
241C4⋊C4×C59—21no—
242C4⋊C4×C59C22⋊C414yes—
243C4⋊C4×C59C22×C412yes—
244C22⋊C4×C59—24no—
245C22⋊C4×C59—24no—
246C22⋊C4×C59—24no—
247C22⋊C4×C59—24no—
248C22⋊C4×C59—24no—
249C22⋊C4×C59C22⋊C414yes—
250C22⋊C4×C59C22⋊C414yes—
251C42×C59C22×C412yes—
252C42×C59C2×D412yes—
253C22⋊Dic59—42no—
254C22⋊Dic59—42no—
255C22⋊Dic59—81no—
256C4⋊Dic59—21no—
257C4⋊Dic59—21no—
258C4⋊Dic59—21no—
259C4⋊Dic59—21no—
260C4⋊Dic59—21no—
261C4⋊Dic59—21no—
262C4⋊Dic59—21no—
263C4⋊Dic59—42no—
264C4⋊Dic59C2×D412yes—
265C4×Dic59—42no—
266C4×Dic59—81no—
267C2×C59⋊C8—21no—
268C2×C59⋊C8—21no—
269C2×C59⋊C8—21no—
270C2×C59⋊C8—21no—
271C2×C59⋊C8—21no—
272C2×C59⋊C8—21no—
273C2×C59⋊C8—21no—
274C2×C59⋊C8—21no—
275C2×C59⋊C8—21no—
276C2×C59⋊C8—21no—
277C2×C59⋊C8—21no—
278C2×C59⋊C8—44no—
279C2×C59⋊C8—44no—
280C2×C59⋊C8C2×D412yes—
281C23×C59—21no—
282C23×C59—21no—
283C23×C59—21no—
284C23×C59—21no—
285C23×C59—22no—
286C23×C59—21no—
287C23×C59—22no—
288C23×C59—21no—
289C23×C59—22no—
290C23×C59—21no—
291C23×C59—21no—
292C23×C59—21no—
293C23×C59—21no—
294C23×C59—22no—
295C23×C59—48no—
296C23×C59—41no—
297C23×C59—41no—
298C23×C59—41no—
299C23×C59—41no—
300C23×C59—41no—
301C23×C59—41no—
302C23×C59—41no—
303C23×C59—41no—
304C23×C59—41no—
305C23×C59—41no—
306C23×C59—48no—
307C23×C59—84no—
308C23×C59—84no—
309C23×C59—84no—
310C23×C59—84no—
311C23×C59—84no—
312C23×C59C2×C22⋊C412yes—
313C23×C59C2×C22⋊C412yes—
314C23×C59#13512yes—
315C23×C59#13512yes—
316C23×C59C22×D411yescharacteristic
317Q8×C59—22no—
318Q8×C59—22no—
319Q8×C59—41no—
320Q8×C59—41no—
321D4×C59—28no—
322D4×C59—22no—
323D4×C59—22no—
324D4×C59—22no—
325D4×C59—22no—
326D4×C59—22no—
327D4×C59—48no—
328D4×C59—48no—
329D4×C59—41no—
330D4×C59—41no—
331D4×C59—84no—
332D4×C59C4×D414yes—
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—22no—
342C2×C4×C59—22no—
343C2×C4×C59—22no—
344C2×C4×C59—22no—
345C2×C4×C59—22no—
346C2×C4×C59—22no—
347C2×C4×C59—22no—
348C2×C4×C59—22no—
349C2×C4×C59—22no—
350C2×C4×C59—22no—
351C2×C4×C59—48no—
352C2×C4×C59—41no—
353C2×C4×C59—41no—
354C2×C4×C59—41no—
355C2×C4×C59—41no—
356C2×C4×C59—84no—
357C2×C4×C59C2×C22⋊C412yes—
358C2×C4×C59C2×C22⋊C412yes—
359C2×C4×C59C2×C22⋊C412yes—
360C2×C4×C59C2×C22⋊C412yes—
361C2×C4×C59C23×C411yescharacteristic
362C2×C4×C59C22×D411yescharacteristic
363C2×C4×C59C22×D411yescharacteristic
364C2×C4×C59C2×#4111yescharacteristic
365C2×C4×C59H(5,𝔽2)11yescharacteristic
366C2×C4×C59H(5,𝔽2)11yescharacteristic
367C2×Dic59—22no—
368C2×Dic59—41no—
369C2×Dic59—41no—
370C2×Dic59—41no—
371C2×Dic59—41no—
372C2×Dic59—41no—
373C2×Dic59—41no—
374C2×Dic59—41no—
375C2×Dic59—41no—
376C2×Dic59—41no—
377C2×Dic59—41no—
378C2×Dic59—41no—
379C2×Dic59—84no—
380C59⋊C8—22no—
381C59⋊C8—41no—
382C59⋊C8—41no—
383C59⋊C8—41no—
384#22414—591nomaximal, Sylow
385C22×C59—22no—
386C22×C59—22no—
387C22×C59—22no—
388C22×C59—22no—
389C22×C59—22no—
390C22×C59—22no—
391C22×C59—22no—
392C22×C59—24no—
393C22×C59—22no—
394C22×C59—22no—
395C22×C59—42no—
396C22×C59—42no—
397C22×C59—41no—
398C22×C59—42no—
399C22×C59—41no—
400C22×C59—42no—
401C22×C59—41no—
402C22×C59—42no—
403C22×C59—41no—
404C22×C59—42no—
405C22×C59—42no—
406C22×C59—42no—
407C22×C59—42no—
408C22×C59—816no—
409C22×C59—81no—
410C22×C59—81no—
411C22×C59—81no—
412C22×C59—81no—
413C22×C59#41614yescomplemented
414C22×C59C22×C22⋊C411yescharacteristic
415C22×C59D4211yescharacteristic
416C22×C59#54611yescharacteristic
417C22×C59C2×#13511yescharacteristic
418C22×C59C2×#13511yescharacteristic
419C22×C59#57611yescharacteristic
420C22×C59#57711yescharacteristic
421C4×C59—22no—
422C4×C59—22no—
423C4×C59—22no—
424C4×C59—22no—
425C4×C59—42no—
426C4×C59—42no—
427C4×C59C2×C4×D411yescharacteristic
428C4×C59#51811yescharacteristic
429C4×C59D4211yescharacteristic
430C4×C59#54611yescharacteristic
431Dic59—42no—
432Dic59—81no—
433Dic59—81no—
434Dic59—81no—
435C2×#546D5911yescharacteristic
436C2×C8×D4—591no—
437C2×#416—591no—
438C22×#102—591no—
439#2352—591no—
440#1983—591no—
441#1958—591no—
442#1893—591no—
443#1892—591no—
444#1875—591no—
445#1872—591no—
446#1804—591no—
447#1788—591no—
448#1786—591no—
449C4×#102—591no—
450C2×C59—24no—
451C2×C59—42no—
452C2×C59—44no—
453C2×C59—82no—
454C2×C59D4×C22⋊C411yescharacteristic
455C2×C59C2×#41611yescharacteristic
456C2×C59#289711yescharacteristic
457C2×C59#328011yescharacteristic
458C2×C59#328211yescharacteristic
459C2×C59#329611yescharacteristic
460C2×C59#329711yescharacteristic
461C22×#41C2×D5911yescharacteristic
462C23×D4C2×D5911yescharacteristic
463C23×C8—591no—
464C23×C8—591no—
465#546—24no—
466#546Dic5918yescomplemented
467C2×#124C2×D5911yescharacteristic
468C2×#123—21no—
469C2×C22⋊Q8C2×D5911yescharacteristic
470C2×#121—21no—
471C2×#121C2×D5911yescharacteristic
472C2×#120—21no—
473C2×C4×D4C2×D5911yescharacteristic
474C2×C4×D4C2×D5911yescharacteristic
475C2×#117—591no—
476C22×C4⋊C4—591no—
477C22×C22⋊C4—21no—
478C8×D4—1184no—
479C2×C4⋊C8—591no—
480#416—1184no—
481C2×#103—591no—
482C2×#103—591no—
483C2×#103—591no—
484C2×#103—591no—
485C2×#102—591no—
486C2×#102—591no—
487C2×#102—591no—
488C2×#102—591no—
489C2×#102—591no—
490C2×#102—591no—
491C2×#102—591no—
492C2×#102—591no—
493C2×#102—1184no—
494C2×C22⋊C8—591no—
495C2×C22⋊C8—591no—
496C2×C4×C8—591no—
497#388—1181no—
498#387—1181no—
499#386—1181no—
500#382—591no—
501#380—591no—
502#380—591no—
503C4×C4⋊C4—591no—
504C4×C22⋊C4—1181no—
505#340—591no—
506#340—591no—
507#340—591no—
508#340—591no—
509C59#2241411yescharacteristic, complemented, Sylow
510C25—21no—
511C2×#41—22no—
512C2×#41—22no—
513C2×#41—22no—
514C2×#41—41no—
515C2×#41—41no—
516C2×#41C2×Dic5914yescomplemented
517C22×Q8C22×D5911yescharacteristic
518C22×D4—22no—
519C22×D4—22no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—22no—
524C22×D4—41no—
525C22×D4—41no—
526C22×D4C2×Dic5914yes—
527C22×D4C22⋊D5911yescharacteristic
528C22×D4C22×D5911yescharacteristic
529C22×D4C22×D5911yescharacteristic
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—1181no—
533C23×C4C22×D5911yescharacteristic
534C23×C4C22×D5911yescharacteristic
535C22×C8—591no—
536C22×C8—591no—
537C22×C8—591no—
538C22×C8—591no—
539C22×C8—1182no—
540C22×C8—1182no—
541C22×C8—1182no—
542C22×C8—1182no—
543C22×C8—2361no—
544C22×C8—2361no—
545#124—22no—
546#124C2×Dic5914yescomplemented
547#123—28no—
548C22⋊Q8—22no—
549C22⋊Q8C2×Dic5914yes—
550#121—22no—
551#121—28no—
552#121C2×Dic5914yescomplemented
553#120—28no—
554C4×D4—22no—
555C4×D4C2×Dic5914yes—
556C4×D4C2×Dic5914yescomplemented
557C4×D4C22⋊D5914yes—
558#117—1182no—
559#117—2361no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—591no—
562C2×C4⋊C4—591no—
563C2×C4⋊C4—591no—
564C2×C4⋊C4—591no—
565C2×C4⋊C4—1182no—
566C2×C4⋊C4—1181no—
567C2×C4⋊C4—2361no—
568C2×C4⋊C4C22⋊D5911yescharacteristic
569C2×C4⋊C4C22×D5911yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—28no—
576C2×C22⋊C4—1181no—
577C2×C22⋊C4—1181no—
578C2×C22⋊C4—1181no—
579C2×C22⋊C4C22⋊D5911yescharacteristic
580C2×C22⋊C4C22⋊D5911yescharacteristic
581C2×C42—1181no—
582C2×C42—1181no—
583C2×C42C22×D5911yescharacteristic
584C4⋊C8—1182no—
585#103—1182no—
586#103—1182no—
587#103—2361no—
588#103—2361no—
589#102—594no—
590#102—1182no—
591#102—1182no—
592#102—1182no—
593#102—1182no—
594#102—1182no—
595#102—2361no—
596#102—2361no—
597C22⋊C8—1182no—
598C22⋊C8—1182no—
599C4×C8—1182no—
600#95—1181no—
601#95—1181no—
602#95—1181no—
603#95—1181no—
604#95—1181no—
605C24—21no—
606C24—21no—
607C24—24no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—42no—
612C24—81no—
613C24—81no—
614C24C2×C22⋊D5911yescharacteristic
615C24C2×C22⋊D5911yescharacteristic
616#41—28no—
617#41—44no—
618#41—44no—
619#41—44no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8C22×Dic5912yes—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—28no—
629C2×D4—24no—
630C2×D4—24no—
631C2×D4—24no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—44no—
641C2×D4—44no—
642C2×D4—44no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—42no—
647C2×D4—81no—
648C2×D4—81no—
649C2×D4C22⋊Dic5914yes—
650C2×D4D4×D5912yes—
651C2×D4#1174568712yes—
652C2×D4C22×Dic5912yes—
653C2×D4C22×Dic5912yes—
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—21no—
663C22×C4—21no—
664C22×C4—24no—
665C22×C4—24no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4—81no—
669C22×C4—81no—
670C22×C4—1181no—
671C22×C4—1181no—
672C22×C4—1181no—
673C22×C4—1181no—
674C22×C4—4721no—
675C22×C4—2362no—
676C22×C4—2362no—
677C22×C4C22×Dic5912yes—
678C22×C4C22×Dic5912yes—
679C22×C4C2×C22⋊D5911yescharacteristic
680C22×C4C2×C22⋊D5911yescharacteristic
681C22×C4C2×C22⋊D5911yescharacteristic
682C22×C4C2×C22⋊D5911yescharacteristic
683C22×C4C2×C22⋊D5912yes—
684C22×C4C2×C22⋊D5912yes—
685C22×C4C23×D5911yescharacteristic
686C2×C8—592no—
687C2×C8—1181no—
688C2×C8—1181no—
689C2×C8—1181no—
690C2×C8—1181no—
691C2×C8—1181no—
692C2×C8—1181no—
693C2×C8—1181no—
694C2×C8—1181no—
695C2×C8—1181no—
696C2×C8—1181no—
697C2×C8—1181no—
698C2×C8—2364no—
699C2×C8—2364no—
700C4⋊C4—24no—
701C4⋊C4—21no—
702C4⋊C4—592no—
703C4⋊C4—1181no—
704C4⋊C4—1181no—
705C4⋊C4—1181no—
706C4⋊C4—1181no—
707C4⋊C4—1181no—
708C4⋊C4—1181no—
709C4⋊C4—1181no—
710C4⋊C4—2362no—
711C4⋊C4C22⋊Dic5914yes—
712C4⋊C4C22×Dic5912yes—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—24no—
716C22⋊C4—24no—
717C22⋊C4—24no—
718C22⋊C4—4721no—
719C22⋊C4—2362no—
720C22⋊C4—2362no—
721C22⋊C4C22⋊Dic5914yes—
722C22⋊C4C22⋊Dic5914yes—
723C42—4721no—
724C42—2362no—
725C42C22×Dic5912yes—
726C42C2×C22⋊D5912yes—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—22no—
737C23—21no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—48no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—48no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—84no—
754C23—84no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23C2×C22⋊Dic5912yes—
759C23C2×C22⋊Dic5912yes—
760C23#1427374712yes—
761C23#1427374712yes—
762C23C22×C22⋊D5911yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—41no—
766Q8—41no—
767D4—28no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—22no—
772D4—22no—
773D4—48no—
774D4—48no—
775D4—41no—
776D4—41no—
777D4—84no—
778D4D4×Dic5914yes—
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—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—48no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—84no—
803C2×C4—1182no—
804C2×C4—4724no—
805C2×C4—2361no—
806C2×C4—2361no—
807C2×C4—2361no—
808C2×C4—2361no—
809C2×C4—2361no—
810C2×C4—2361no—
811C2×C4—2361no—
812C2×C4—2361no—
813C2×C4—2361no—
814C2×C4—2361no—
815C2×C4—2361no—
816C2×C4C2×C22⋊Dic5912yes—
817C2×C4C2×C22⋊Dic5912yes—
818C2×C4C2×C22⋊Dic5912yes—
819C2×C4C2×C22⋊Dic5912yes—
820C2×C4C23×Dic5911yescharacteristic
821C2×C4C2×D4×D5911yescharacteristic
822C2×C4C22×C22⋊D5911yescharacteristic
823C2×C4C2×#1174568711yescharacteristic
824C2×C4#1427377211yescharacteristic
825C2×C4#1427377211yescharacteristic
826C8—1182no—
827C8—2361no—
828C8—2361no—
829C8—2361no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—24no—
840C22—42no—
841C22—41no—
842C22—42no—
843C22—41no—
844C22—42no—
845C22—42no—
846C22—41no—
847C22—42no—
848C22—41no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—816no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22#1683739814yescomplemented
859C22C22×C22⋊Dic5911yescharacteristic
860C22D4×C22⋊D5911yescharacteristic
861C22#1683804611yescharacteristic
862C22C2×#1427374711yescharacteristic
863C22C2×#1427374711yescharacteristic
864C22#1683820511yescharacteristic
865C22#1683821311yescharacteristic
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—42no—
871C4—42no—
872C4—4721no—
873C4—4721no—
874C4—4721no—
875C4—2362no—
876C4C2×D4×Dic5911yescharacteristic
877C4#1683787711yescharacteristic
878C4D4×C22⋊D5911yescharacteristic
879C4#1683804611yescharacteristic
880C2—24no—
881C2—42no—
882C2—44no—
883C2—82no—
884C2D4×C22⋊Dic5911yescharacteristic
885C2C2×#1683739811yescharacteristic
886C2#2143262211yescharacteristic
887C2#2143577711yescharacteristic
888C2#2143579911yescharacteristic
889C2#2143593111yescharacteristic
890C2#2143594611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
Fitting, prime radicalC2×C59×#546C2
socleC23×C59C22×D4
cosocleC22×C4×C59C24
hypercenterC2×#546D59
hypocenterC59#22414
LCSG ▷ C2×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×D4×C59⋊C8C2semidirect
2. C2×#16837398C2semidirect
3. C22×#14273648C2semidirect
4. #21427025C2semidirect
5. #21425029C2semidirect
6. #21424908C2semidirect
7. #21424525C2semidirect
8. #21424520C2semidirect
9. #21424419C2semidirect
10. #21424404C2semidirect
11. #21424106C2semidirect
12. #21424036C2semidirect
13. #21424027C2semidirect
14. C4×#14273648C2semidirect
17. C23×C59⋊C8C22semidirect
18. C2×#14273686C22semidirect
21. C2×C4⋊(C59⋊C8)C22semidirect
23. C2×#14273651C22semidirect
24. C2×#14273651C22semidirect
25. C2×#14273651C22semidirect
26. C2×#14273651C22semidirect
37. C2×C22⋊(C59⋊C8)C22semidirect
38. C2×C4×C59⋊C8C22semidirect
42. #16837268C22semidirect
44. #16837262C22semidirect
45. C4×C4⋊Dic59C22semidirect
47. #16837164C22semidirect
48. #16837164C22semidirect
49. #16837164C22semidirect
50. #16837164C22semidirect
54. C59×#546C4semidirect
101. #14273648D4semidirect
116. C2×#41×C59C2×C4semidirect
135. #124×C59C2×C4semidirect
141. #121×C59C2×C4semidirect
145. C4×D4×C59C2×C4semidirect
413. C22×C59#416semidirect
466. #546Dic59semidirect
509. C59#22414semidirect
516. C2×#41C2×Dic59semidirect
546. #124C2×Dic59semidirect
552. #121C2×Dic59semidirect
556. C4×D4C2×Dic59semidirect
858. C22#16837398semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C59⋊C82
C2×#168373982
C22×#142736482
#214270252
#214250292
#214249082
#214245252
#214245202
#214244192
#214244042
#214241062
#214240362
#214240272
C4×#142736482
C2×C59×#5462
#2241459