Finite Group Databasebeta

← #28519934

Subgroups — #28519934

Order 15104.

2574 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C42×D59C211yesmaximal, characteristic
2C2×#16837301C211yesmaximal, characteristic, complemented
3C2×#16837300C211yesmaximal, characteristic, complemented
4C2×#16837276C212yesmaximal
5C2×#16837259C211yesmaximal, characteristic
6C2×#16837259C211yesmaximal, characteristic
7#21422331C212yesmaximal, complemented
8#21422330C212yesmaximal, complemented
9#21422325C211yesmaximal, characteristic, complemented
10(C2×D59)⋊#95C212yesmaximal
11C59×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×C4×D59C2211yescharacteristic
13C23×C4×D59C2211yescharacteristic
14C23×C4×D59C2211yescharacteristic
15C22×C4⋊Dic59C2211yescharacteristic
16C22×C4⋊Dic59C2212yes—
17C22×C4⋊Dic59C2211yescharacteristic
18C22×Dic59⋊C4C2212yes—
19C22×(C2×D59)⋊C4C2212yes—
20C22×(C2×D59)⋊C4C2212yes—
21C22×C4×Dic59C2211yescharacteristic
22C22×C4×Dic59C2211yescharacteristic
23C22×C4×Dic59C2211yescharacteristic
24C2×C42×D59—24no—
25C2×C42×D59—24no—
26C2×C42×D59—24no—
27#16837301—24no—
28#16837300—24no—
29#16837276—28no—
30#16837259—24no—
31#16837259C418yescomplemented
32C2×C59⋊#95C2212yes—
33C2×C59⋊#95C2212yes—
34C2×C59⋊#95C2212yes—
35C2×C59⋊#95C2212yes—
36C2×C59⋊#95C2212yes—
37C2×C59⋊#95C2212yes—
38C22×C4⋊C4×C59C2211yescharacteristic
39C22×C4⋊C4×C59C2211yescharacteristic
40C22×C42×C59C2211yescharacteristic
41C2×#95×C59C2212yes—
42C2×#95×C59C2212yes—
43C24×D59C2311yescharacteristic
44C23×Dic59C2312yes—
45C23×Dic59C2312yes—
46C23×Dic59C2311yescharacteristic
47C23×Dic59C2311yescharacteristic
48C23×Dic59C2311yescharacteristic
49C22×C4×D59—22no—
50C22×C4×D59—22no—
51C22×C4×D59—22no—
52C22×C4×D59—22no—
53C22×C4×D59—22no—
54C22×C4×D59—22no—
55C22×C4×D59—22no—
56C22×C4×D59—22no—
57C22×C4×D59—22no—
58C22×C4×D59—22no—
59C22×C4×D59—22no—
60C22×C4×D59—22no—
61C22×C4×D59—22no—
62C22×C4×D59—22no—
63C22×C4×D59—22no—
64C22×C4×D59—22no—
65C22×C4×D59C2×C414yes—
66C22×C4×D59D414yes—
67C22×C4×D59D414yes—
68C22×C4×D59Q814yes—
69C22×C4×D59Q814yes—
70C2×C4⋊Dic59—22no—
71C2×C4⋊Dic59—22no—
72C2×C4⋊Dic59—22no—
73C2×C4⋊Dic59—22no—
74C2×C4⋊Dic59—22no—
75C2×C4⋊Dic59—24no—
76C2×C4⋊Dic59—24no—
77C2×C4⋊Dic59—24no—
78C2×C4⋊Dic59C2×C414yescomplemented
79C2×Dic59⋊C4—24no—
80C2×Dic59⋊C4—24no—
81C2×Dic59⋊C4—24no—
82C2×(C2×D59)⋊C4—24no—
83C2×(C2×D59)⋊C4—24no—
84C2×(C2×D59)⋊C4—24no—
85C2×(C2×D59)⋊C4—24no—
86C2×(C2×D59)⋊C4—24no—
87C2×(C2×D59)⋊C4C2×C418yes—
88C2×C4×Dic59—22no—
89C2×C4×Dic59—22no—
90C2×C4×Dic59—22no—
91C2×C4×Dic59—22no—
92C2×C4×Dic59—22no—
93C2×C4×Dic59—22no—
94C2×C4×Dic59—22no—
95C2×C4×Dic59—22no—
96C2×C4×Dic59D414yes—
97C42×D59—232no—
98C59⋊#95—24no—
99C59⋊#95—24no—
100C59⋊#95—24no—
101C59⋊#95—24no—
102C59⋊#95—24no—
103C59⋊#95C2×C418yescomplemented
104C23×C4×C59C2312yes—
105C23×C4×C59C2312yes—
106C23×C4×C59C2311yescharacteristic
107C23×C4×C59C2311yescharacteristic
108C23×C4×C59C2311yescharacteristic
109C2×C4⋊C4×C59—22no—
110C2×C4⋊C4×C59—22no—
111C2×C4⋊C4×C59—22no—
112C2×C4⋊C4×C59—22no—
113C2×C4⋊C4×C59—22no—
114C2×C4⋊C4×C59C2×C414yescomplemented
115C2×C42×C59—22no—
116C2×C42×C59—22no—
117C2×C42×C59D414yes—
118#95×C59—24no—
119#95×C59—24no—
120C24×C59C2411yescharacteristic
121C23×D59—21no—
122C23×D59—21no—
123C23×D59—21no—
124C23×D59—21no—
125C23×D59—21no—
126C23×D59—21no—
127C23×D59—21no—
128C23×D59—21no—
129C23×D59C22×C412yes—
130C23×D59C2×D412yes—
131C23×D59C2×D412yes—
132C23×D59C2×Q812yes—
133C23×D59C2×Q812yes—
134C23×D59#4112yes—
135C23×D59#4112yes—
136C22×C4×C59—21no—
137C22×C4×C59—21no—
138C22×C4×C59—21no—
139C22×C4×C59—21no—
140C22×C4×C59—21no—
141C22×C4×C59—21no—
142C22×C4×C59—21no—
143C22×C4×C59—21no—
144C22×C4×C59—22no—
145C22×C4×C59—22no—
146C22×C4×C59—22no—
147C22×C4×C59—22no—
148C22×C4×C59—22no—
149C22×C4×C59—22no—
150C22×C4×C59—22no—
151C22×C4×C59—22no—
152C22×C4×C59—22no—
153C22×C4×C59—22no—
154C22×C4×C59—22no—
155C22×C4×C59—22no—
156C22×C4×C59—22no—
157C22×C4×C59C22×C414yes—
158C22×C4×C59C22×C412yes—
159C22×C4×C59C2×D412yes—
160C22×C4×C59C2×D412yes—
161C22×C4×C59C2×D412yes—
162C22×C4×C59C2×D412yes—
163C22×C4×C59C2×D412yes—
164C22×C4×C59C2×D412yes—
165C22×C4×C59C2×Q812yes—
166C22×C4×C59C2×Q812yes—
167C22×C4×C59#4112yes—
168C22×C4×C59#4112yes—
169C22×C4×C59#4112yes—
170C22×C4×C59#4112yes—
171C22×Dic59—21no—
172C22×Dic59—21no—
173C22×Dic59—21no—
174C22×Dic59—21no—
175C22×Dic59—21no—
176C22×Dic59—21no—
177C22×Dic59—21no—
178C22×Dic59—21no—
179C22×Dic59—21no—
180C22×Dic59—21no—
181C22×Dic59—21no—
182C22×Dic59—21no—
183C22×Dic59—22no—
184C22×Dic59—22no—
185C22×Dic59—22no—
186C22×Dic59—22no—
187C22×Dic59—22no—
188C22×Dic59—22no—
189C22×Dic59—22no—
190C22×Dic59—22no—
191C22×Dic59—22no—
192C22×Dic59—22no—
193C22×Dic59—22no—
194C22×Dic59—22no—
195C22×Dic59—22no—
196C22×Dic59C22×C414yes—
197C22×Dic59C22×C412yes—
198C22×Dic59C2×D412yes—
199C22×Dic59C2×D412yes—
200C22×Dic59C2×D412yes—
201C22×Dic59C2×D412yes—
202C22×Dic59C2×Q812yes—
203C22×Dic59C2×Q812yes—
204C22×Dic59#4112yes—
205C22×Dic59#4112yes—
206C2×C4×D59—28no—
207C2×C4×D59—28no—
208C2×C4×D59—28no—
209C2×C4×D59—28no—
210C2×C4×D59—28no—
211C2×C4×D59—28no—
212C2×C4×D59—28no—
213C2×C4×D59—28no—
214C2×C4×D59—28no—
215C2×C4×D59—28no—
216C2×C4×D59—28no—
217C2×C4×D59—28no—
218C2×C4×D59—28no—
219C2×C4×D59—28no—
220C2×C4×D59—28no—
221C2×C4×D59—28no—
222C2×C4×D59—28no—
223C2×C4×D59—28no—
224C2×C4×D59—28no—
225C2×C4×D59—28no—
226C2×C4×D59C4⋊C4116yescomplemented
227C4⋊C4×C59—28no—
228C4⋊C4×C59—44no—
229C42×C59—28no—
230(C2×D59)⋊C4—216no—
231(C2×D59)⋊C4—48no—
232C4⋊Dic59—28no—
233C4⋊Dic59—44no—
234C4⋊Dic59—48no—
235Dic59⋊C4—48no—
236C4×Dic59—28no—
237C4×Dic59—28no—
238C4×Dic59—28no—
239C23×C59C23×C411yescharacteristic
240C23×C59C22×D411yescharacteristic
241C23×C59C22×D411yescharacteristic
242C23×C59C22×D411yescharacteristic
243C23×C59C22×D411yescharacteristic
244C23×C59C22×Q811yescharacteristic
245C23×C59C22×Q811yescharacteristic
246C23×C59C2×#4111yescharacteristic
247C23×C59C2×#4111yescharacteristic
248C23×C59C2×#4111yescharacteristic
249C23×C59C2×#4111yescharacteristic
250C23×C59C2×#4111yescharacteristic
251C23×C59C2×#4111yescharacteristic
252C23×C59C2×#4111yescharacteristic
253C23×C59C2×#4111yescharacteristic
254C22×D59—22no—
255C22×D59—22no—
256C22×D59—22no—
257C22×D59—22no—
258C22×D59—22no—
259C22×D59—22no—
260C22×D59—22no—
261C22×D59—22no—
262C22×D59—22no—
263C22×D59—22no—
264C22×D59—22no—
265C22×D59—22no—
266C22×D59—22no—
267C22×D59—22no—
268C22×D59—22no—
269C22×D59—22no—
270C22×D59—22no—
271C22×D59—22no—
272C22×D59—22no—
273C22×D59—22no—
274C22×D59—22no—
275C22×D59—22no—
276C22×D59—22no—
277C22×D59—22no—
278C22×D59—22no—
279C22×D59—22no—
280C22×D59—22no—
281C22×D59—22no—
282C22×D59C2×C4⋊C414yes—
283C22×D59C4×D414yes—
284C22×D59C4×Q814yes—
285C22×D59#12114yes—
286C22×D59C22⋊Q814yes—
287C22×D59#12514yes—
288C22×D59C4⋊Q814yes—
289C2×C4×C59—22no—
290C2×C4×C59—22no—
291C2×C4×C59—22no—
292C2×C4×C59—22no—
293C2×C4×C59—22no—
294C2×C4×C59—22no—
295C2×C4×C59—22no—
296C2×C4×C59—22no—
297C2×C4×C59—22no—
298C2×C4×C59—22no—
299C2×C4×C59—22no—
300C2×C4×C59—22no—
301C2×C4×C59—24no—
302C2×C4×C59—24no—
303C2×C4×C59—24no—
304C2×C4×C59—42no—
305C2×C4×C59—42no—
306C2×C4×C59—42no—
307C2×C4×C59—42no—
308C2×C4×C59—42no—
309C2×C4×C59—42no—
310C2×C4×C59—42no—
311C2×C4×C59—42no—
312C2×C4×C59—42no—
313C2×C4×C59—42no—
314C2×C4×C59—42no—
315C2×C4×C59C2×C4⋊C414yes—
316C2×C4×C59C4×D414yes—
317C2×C4×C59C4×D414yes—
318C2×C4×C59#12014yes—
319C2×C4×C59#12114yes—
320C2×C4×C59C22⋊Q814yes—
321C2×C4×C59C22⋊Q814yes—
322C2×C4×C59C22⋊Q814yes—
323C2×C4×C59#12314yes—
324C2×Dic59—22no—
325C2×Dic59—22no—
326C2×Dic59—22no—
327C2×Dic59—22no—
328C2×Dic59—22no—
329C2×Dic59—22no—
330C2×Dic59—22no—
331C2×Dic59—22no—
332C2×Dic59—22no—
333C2×Dic59—22no—
334C2×Dic59—22no—
335C2×Dic59—22no—
336C2×Dic59—22no—
337C2×Dic59—22no—
338C2×Dic59—22no—
339C2×Dic59—22no—
340C2×Dic59—22no—
341C2×Dic59—22no—
342C2×Dic59—24no—
343C2×Dic59—24no—
344C2×Dic59—24no—
345C2×Dic59—42no—
346C2×Dic59—42no—
347C2×Dic59—42no—
348C2×Dic59—42no—
349C2×Dic59—42no—
350C2×Dic59—42no—
351C2×Dic59—42no—
352C2×Dic59—42no—
353C2×Dic59—42no—
354C2×Dic59—42no—
355C2×Dic59—42no—
356C2×Dic59C2×C4⋊C414yes—
357C2×Dic59#12114yes—
358C2×Dic59C22⋊Q814yes—
359C4×D59—232no—
360C4×D59—232no—
361C4×D59—232no—
362#14697—591nomaximal, Sylow
363C22×C59C22×C4⋊C411yescharacteristic
364C22×C59C2×C4×D411yescharacteristic
365C22×C59C2×C4×D411yescharacteristic
366C22×C59C2×C4×D411yescharacteristic
367C22×C59C2×C4×Q811yescharacteristic
368C22×C59C4×#4111yescharacteristic
369C22×C59C4×#4111yescharacteristic
370C22×C59C2×#12011yescharacteristic
371C22×C59C2×#12111yescharacteristic
372C22×C59C2×#12111yescharacteristic
373C22×C59C2×#12111yescharacteristic
374C22×C59C2×C22⋊Q811yescharacteristic
375C22×C59C2×C22⋊Q811yescharacteristic
376C22×C59C2×C22⋊Q811yescharacteristic
377C22×C59C2×C22⋊Q811yescharacteristic
378C22×C59C2×C22⋊Q811yescharacteristic
379C22×C59C2×#12311yescharacteristic
380C22×C59#52511yescharacteristic
381C22×C59#52511yescharacteristic
382C22×C59#52511yescharacteristic
383C22×C59#52511yescharacteristic
384C22×C59#52511yescharacteristic
385C22×C59#52511yescharacteristic
386C22×C59C2×#12511yescharacteristic
387C22×C59#52911yescharacteristic
388C22×C59#52911yescharacteristic
389C22×C59#52911yescharacteristic
390C22×C59#52911yescharacteristic
391C22×C59C2×C4⋊Q811yescharacteristic
392C22×C59#53211yescharacteristic
393C22×C59#53211yescharacteristic
394C22×C59#53311yescharacteristic
395C22×C59#53311yescharacteristic
396C22×C59#53311yescharacteristic
397C22×C59#53311yescharacteristic
398C2×D59—24no—
399C2×D59—24no—
400C2×D59—24no—
401C2×D59—24no—
402C2×D59—24no—
403C2×D59—24no—
404C2×D59—24no—
405C2×D59—24no—
406C2×D59—24no—
407C2×D59—24no—
408C2×D59—24no—
409C2×D59—24no—
410C2×D59—24no—
411C2×D59—24no—
412C2×D59#38918yescomplemented
413C4×C59—24no—
414C4×C59—24no—
415C4×C59—44no—
416C4×C59—82no—
417C4×C59#38518yescomplemented
418Dic59—24no—
419Dic59—24no—
420Dic59—24no—
421Dic59—44no—
422Dic59—82no—
423C23×C42—591no—
424C2×#389—591no—
425C2×#389—591no—
426C2×#385—592no—
427C2×#380—591no—
428C2×#380—591no—
429#1436—592no—
430#1436—592no—
431C4⋊#95—591no—
432C4⋊#95D5911yescharacteristic, complemented
433C22⋊#95—592no—
434C2×C59C2×#38511yescharacteristic
435C2×C59C2×#38911yescharacteristic
436C2×C59#229611yescharacteristic
437C2×C59C4×#12111yescharacteristic
438C2×C59C4×#12111yescharacteristic
439C2×C59C4×C22⋊Q811yescharacteristic
440C2×C59C4×C22⋊Q811yescharacteristic
441C2×C59#284711yescharacteristic
442C2×C59#284811yescharacteristic
443C2×C59#285111yescharacteristic
444C2×C59#285111yescharacteristic
445C2×C59#285411yescharacteristic
446C2×C59#285511yescharacteristic
447C2×C59#285711yescharacteristic
448C2×C59#285711yescharacteristic
449D59—28no—
450C24×C4—591no—
451C24×C4—591no—
452C24×C4—591no—
453C22×C4⋊C4—591no—
454C22×C4⋊C4—592no—
455C22×C4⋊C4—592no—
456C22×C4⋊C4—591no—
457C22×C4⋊C4C2×D5911yescharacteristic
458C22×C4⋊C4C2×D5911yescharacteristic
459C22×C22⋊C4—592no—
460C22×C22⋊C4—592no—
461C22×C42—591no—
462C22×C42—591no—
463C22×C42—591no—
464C22×C42—1184no—
465C22×C42—1184no—
466C22×C42—1184no—
467C22×C42C2×D5911yescharacteristic
468#389—1184no—
469#389—1184no—
470#385—1188no—
471#380—598no—
472#380—1184no—
473C2×#95—592no—
474C2×#95—592no—
475C2×#95—592no—
476C2×#95—592no—
477C2×#95—592no—
478C2×#95—592no—
479C2×#95C2×D5912yes—
480C2×#95C2×D5912yes—
481C59#1469711yescharacteristic, complemented, Sylow
482C25—591no—
483C23×C4—591no—
484C23×C4—591no—
485C23×C4—591no—
486C23×C4—594no—
487C23×C4—594no—
488C23×C4—594no—
489C23×C4—592no—
490C23×C4—594no—
491C23×C4—594no—
492C23×C4—592no—
493C23×C4—1182no—
494C23×C4—1182no—
495C23×C4—1182no—
496C23×C4—1182no—
497C23×C4—1182no—
498C23×C4—1182no—
499C23×C4—1182no—
500C23×C4—1182no—
501C23×C4—1182no—
502C23×C4—1182no—
503C23×C4—1182no—
504C23×C4—1182no—
505C23×C4—1182no—
506C23×C4—1182no—
507C23×C4—1182no—
508C23×C4—1182no—
509C23×C4C22×D5912yes—
510C23×C4C22×D5912yes—
511C23×C4C22×D5911yescharacteristic
512C23×C4C22×D5911yescharacteristic
513C23×C4C22×D5911yescharacteristic
514C2×C4⋊C4—22no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4—22no—
518C2×C4⋊C4—22no—
519C2×C4⋊C4—594no—
520C2×C4⋊C4—1182no—
521C2×C4⋊C4—1182no—
522C2×C4⋊C4—1184no—
523C2×C4⋊C4—1184no—
524C2×C4⋊C4—1184no—
525C2×C4⋊C4—1184no—
526C2×C4⋊C4—1182no—
527C2×C4⋊C4—1182no—
528C2×C4⋊C4—1184no—
529C2×C4⋊C4—1182no—
530C2×C4⋊C4—1184no—
531C2×C4⋊C4C4×D5914yescomplemented
532C2×C22⋊C4—598no—
533C2×C22⋊C4—1184no—
534C2×C22⋊C4—1184no—
535C2×C22⋊C4—1184no—
536C2×C22⋊C4—1184no—
537C2×C22⋊C4—1184no—
538C2×C42—22no—
539C2×C42—22no—
540C2×C42—594no—
541C2×C42—11832no—
542C2×C42—1182no—
543C2×C42—1182no—
544C2×C42—1182no—
545C2×C42—1182no—
546C2×C42—1182no—
547C2×C42—1182no—
548C2×C42—1182no—
549C2×C42—1182no—
550C2×C42D23614yes—
551#95—24no—
552#95—24no—
553#95—598no—
554#95—1184no—
555#95—1184no—
556#95—1184no—
557#95—1184no—
558#95—1184no—
559C24—592no—
560C24—592no—
561C24—592no—
562C24—592no—
563C24—592no—
564C24—592no—
565C24—592no—
566C24—1181no—
567C24—1181no—
568C24—1181no—
569C24—1181no—
570C24—1181no—
571C24—1181no—
572C24—1181no—
573C24—1181no—
574C24C23×D5911yescharacteristic
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—592no—
597C22×C4—592no—
598C22×C4—592no—
599C22×C4—592no—
600C22×C4—592no—
601C22×C4—592no—
602C22×C4—592no—
603C22×C4—592no—
604C22×C4—592no—
605C22×C4—5916no—
606C22×C4—594no—
607C22×C4—1188no—
608C22×C4—1188no—
609C22×C4—1188no—
610C22×C4—1188no—
611C22×C4—1188no—
612C22×C4—1188no—
613C22×C4—1188no—
614C22×C4—1188no—
615C22×C4—1188no—
616C22×C4—1188no—
617C22×C4—1188no—
618C22×C4—1188no—
619C22×C4—1181no—
620C22×C4—1181no—
621C22×C4—1181no—
622C22×C4—1181no—
623C22×C4—1181no—
624C22×C4—1181no—
625C22×C4—1181no—
626C22×C4—1181no—
627C22×C4—1181no—
628C22×C4—1181no—
629C22×C4—1181no—
630C22×C4—1181no—
631C22×C4—1188no—
632C22×C4—1188no—
633C22×C4—1188no—
634C22×C4—1188no—
635C22×C4—1188no—
636C22×C4—1188no—
637C22×C4—1188no—
638C22×C4—1188no—
639C22×C4—1182no—
640C22×C4—1182no—
641C22×C4—1182no—
642C22×C4—1182no—
643C22×C4—1182no—
644C22×C4—1182no—
645C22×C4—1182no—
646C22×C4—1182no—
647C22×C4—1182no—
648C22×C4—1182no—
649C22×C4—1182no—
650C22×C4—1182no—
651C22×C4—1182no—
652C22×C4C2×C4×D5914yes—
653C22×C4C2×C4×D5912yes—
654C22×C4C2×D23612yes—
655C22×C4C2×D23612yes—
656C22×C4C2×D23612yes—
657C22×C4#1174568512yes—
658C22×C4D4×D5912yes—
659C22×C4D4×D5912yes—
660C22×C4D4×D5912yes—
661C22×C4#1174568712yes—
662C22×C4#1174568712yes—
663C22×C4Q8×D5912yes—
664C22×C4Q8×D5912yes—
665C22×C4#1174568912yes—
666C4⋊C4—28no—
667C4⋊C4—44no—
668C4⋊C4—1188no—
669C4⋊C4—2368no—
670C4⋊C4—2364no—
671C4⋊C4—2368no—
672C22⋊C4—11816no—
673C22⋊C4—2368no—
674C42—28no—
675C42—1188no—
676C42—1188no—
677C42—1188no—
678C23—594no—
679C23—594no—
680C23—594no—
681C23—594no—
682C23—594no—
683C23—594no—
684C23—594no—
685C23—1182no—
686C23—1182no—
687C23—1182no—
688C23—1182no—
689C23—1182no—
690C23—1182no—
691C23—1182no—
692C23—1182no—
693C23—1182no—
694C23—1182no—
695C23—1182no—
696C23—1182no—
697C23—1182no—
698C23—1182no—
699C23—1182no—
700C23—1182no—
701C23—1182no—
702C23—1182no—
703C23—1182no—
704C23—1182no—
705C23—1182no—
706C23—1182no—
707C23—1182no—
708C23—1182no—
709C23—1182no—
710C23—1182no—
711C23—1182no—
712C23—1182no—
713C23C22×C4×D5911yescharacteristic
714C23C2×D4×D5911yescharacteristic
715C23C2×D4×D5911yescharacteristic
716C23C2×D4×D5911yescharacteristic
717C23C22×D23611yescharacteristic
718C23C2×Q8×D5911yescharacteristic
719C23C2×Q8×D5911yescharacteristic
720C23#41×D5911yescharacteristic
721C23#41×D5911yescharacteristic
722C23#41×D5911yescharacteristic
723C23#41×D5911yescharacteristic
724C23C2×#1174568711yescharacteristic
725C23C2×#1174568711yescharacteristic
726C23C2×#1174568511yescharacteristic
727C23C2×#1174568911yescharacteristic
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—594no—
755C2×C4—594no—
756C2×C4—594no—
757C2×C4—11832no—
758C2×C4—11832no—
759C2×C4—1182no—
760C2×C4—1182no—
761C2×C4—1182no—
762C2×C4—1182no—
763C2×C4—1182no—
764C2×C4—1182no—
765C2×C4—1182no—
766C2×C4—1182no—
767C2×C4—1182no—
768C2×C4—1182no—
769C2×C4—1182no—
770C2×C4—1182no—
771C2×C4—1182no—
772C2×C4—1182no—
773C2×C4—1182no—
774C2×C4—1182no—
775C2×C4—1182no—
776C2×C4—1182no—
777C2×C4—11832no—
778C2×C4—1184no—
779C2×C4—1184no—
780C2×C4—1184no—
781C2×C4—2362no—
782C2×C4—2362no—
783C2×C4—2362no—
784C2×C4—2362no—
785C2×C4—2362no—
786C2×C4—2362no—
787C2×C4—2362no—
788C2×C4—2362no—
789C2×C4—2362no—
790C2×C4—2362no—
791C2×C4—2362no—
792C2×C4C4⋊C4×D5914yes—
793C2×C4(C22⋊D59)⋊C414yes—
794C2×C4C4×D23614yes—
795C2×C4#1427369714yes—
796C2×C4#1427370214yes—
797C2×C4#1427370514yes—
798C2×C4#1427370714yes—
799C2×C4#1427370714yes—
800C2×C4#1427370914yes—
801C22—598no—
802C22—1184no—
803C22—1184no—
804C22—1184no—
805C22—1184no—
806C22—1184no—
807C22—1184no—
808C22—1184no—
809C22—1184no—
810C22—1184no—
811C22—1184no—
812C22—1184no—
813C22—1184no—
814C22—1184no—
815C22—1184no—
816C22C2×C4⋊C4×D5911yescharacteristic
817C22C4×D4×D5911yescharacteristic
818C22C2×(C22⋊D59)⋊C411yescharacteristic
819C22C2×C4×D23611yescharacteristic
820C22C4×Q8×D5911yescharacteristic
821C22C4×#1174568711yescharacteristic
822C22C4×#1174568911yescharacteristic
823C22C2×#1427369711yescharacteristic
824C22#121×D5911yescharacteristic
825C22#121×D5911yescharacteristic
826C22C2×#1427370211yescharacteristic
827C22C22⋊Q8×D5911yescharacteristic
828C22C22⋊Q8×D5911yescharacteristic
829C22C2×#1427370511yescharacteristic
830C22C2×#1427370711yescharacteristic
831C22C2×#1427370711yescharacteristic
832C22C2×#1427370911yescharacteristic
833C22#1683791211yescharacteristic
834C22#1683791211yescharacteristic
835C22#1683791411yescharacteristic
836C22#1683791411yescharacteristic
837C22#1683791511yescharacteristic
838C22#1683791511yescharacteristic
839C22#125×D5911yescharacteristic
840C22#1683793111yescharacteristic
841C22#1683793111yescharacteristic
842C22#1683793411yescharacteristic
843C22#1683793911yescharacteristic
844C22C4⋊Q8×D5911yescharacteristic
845C22#1683794911yescharacteristic
846C22#1683795011yescharacteristic
847C22#1683795611yescharacteristic
848C22#1683795711yescharacteristic
849C22#1683795711yescharacteristic
850C22#1683795811yescharacteristic
851C4—24no—
852C4—24no—
853C4—44no—
854C4—82no—
855C4—1184no—
856C4—1184no—
857C4—1184no—
858C4—4722no—
859C4—2364no—
860C4#1683727618yescomplemented
861C2—1188no—
862C2C2×#1683727611yescharacteristic
863C2#389×D5911yescharacteristic
864C2#2142657711yescharacteristic
865C2C4×#1427370211yescharacteristic
866C2#2142661211yescharacteristic
867C2C4×#1427370711yescharacteristic
868C2#2142663411yescharacteristic
869C2#2143237911yescharacteristic
870C2#2143238411yescharacteristic
871C2#2143240511yescharacteristic
872C2#2143240711yescharacteristic
873C2#2143242611yescharacteristic
874C2#2143243711yescharacteristic
875C2#2143244711yescharacteristic
876C2#2143244911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC59×C4⋊#95C2
socle, cosocleC24×C59C24
prime radicalC24×D59C23
hypercenterC4⋊#95D59
hypocenterC59#14697
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#16837301C2semidirect
3. C2×#16837300C2semidirect
7. #21422331C2semidirect
8. #21422330C2semidirect
9. #21422325C2semidirect
11. C59×C4⋊#95C2semidirect
31. #16837259C4semidirect
78. C2×C4⋊Dic59C2×C4semidirect
103. C59⋊#95C2×C4semidirect
114. C2×C4⋊C4×C59C2×C4semidirect
226. C2×C4×D59C4⋊C4semidirect
412. C2×D59#389semidirect
417. C4×C59#385semidirect
432. C4⋊#95D59semidirect
481. C59#14697semidirect
531. C2×C4⋊C4C4×D59semidirect
860. C4#16837276semidirect

Maximal subgroups

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

subgroupindex
C22×C42×D592
C2×#168373012
C2×#168373002
C2×#168372762
C2×#168372592
#214223312
#214223302
#214223252
(C2×D59)⋊#952
C59×C4⋊#952
#1469759