Finite Group Databasebeta

← #28511593

Subgroups — #28511593

Order 15104.

1962 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837283C211yesmaximal, characteristic, complemented
2C2×#16837276C211yesmaximal, characteristic
3C2×#16837259C211yesmaximal, characteristic
4C2×#16837249C211yesmaximal, characteristic
5C2×#95×D59C211yesmaximal, characteristic
6#21422365C211yesmaximal, characteristic, complemented
7#21422357C211yesmaximal, characteristic, complemented
8#21422350C211yesmaximal, characteristic, complemented
9#21422330C211yesmaximal, characteristic, complemented
10#21422330C211yesmaximal, characteristic, complemented
11#21422321C211yesmaximal, characteristic, complemented
12(C2×D59)⋊#95C211yesmaximal, characteristic
13(C2×D59)⋊#95C211yesmaximal, characteristic
14(C2×D59)⋊#95C211yesmaximal, characteristic
15C59×#1442C211yesmaximal, characteristic, complemented
16C23×C4×D59C2211yescharacteristic
17C23×C4×D59C2211yescharacteristic
18C23×C4×D59C2211yescharacteristic
19C22×C4⋊Dic59C2211yescharacteristic
20C22×C4⋊Dic59C2211yescharacteristic
21C22×Dic59⋊C4C2211yescharacteristic
22C22×(C2×D59)⋊C4C2211yescharacteristic
23C22×(C2×D59)⋊C4C2211yescharacteristic
24C22×(C2×D59)⋊C4C2211yescharacteristic
25C22×(C2×D59)⋊C4C2211yescharacteristic
26C22×C4×Dic59C2211yescharacteristic
27C22×C4×Dic59C2211yescharacteristic
28#16837283—24no—
29#16837276C418yescomplemented
30#16837259—24no—
31#16837249—24no—
32C2×C59⋊#95C2211yescharacteristic
33C2×C59⋊#95C2211yescharacteristic
34C2×C59⋊#95C2211yescharacteristic
35C2×C59⋊#95C2211yescharacteristic
36C2×C59⋊#95C2211yescharacteristic
37C2×C59⋊#95C2211yescharacteristic
38C2×C59⋊#95C2211yescharacteristic
39C2×C59⋊#95C2211yescharacteristic
40C2×C59⋊#95C2211yescharacteristic
41C2×C59⋊#95C2211yescharacteristic
42C2×C59⋊#95C2211yescharacteristic
43C2×C59⋊#95C2211yescharacteristic
44C2×C59⋊#95C2211yescharacteristic
45C2×C59⋊#95C2211yescharacteristic
46C2×C59⋊#95C2211yescharacteristic
47C2×C59⋊#95C2211yescharacteristic
48#95×D59—24no—
49C22×C4⋊C4×C59C2211yescharacteristic
50C2×#95×C59C2211yescharacteristic
51C2×#95×C59C2211yescharacteristic
52C2×#95×C59C2211yescharacteristic
53C2×#95×C59C2211yescharacteristic
54C2×#95×C59C2211yescharacteristic
55C2×#95×C59C2211yescharacteristic
56C24×D59C2311yescharacteristic
57C23×Dic59C2311yescharacteristic
58C23×Dic59C2311yescharacteristic
59C23×Dic59C2311yescharacteristic
60C23×Dic59C2311yescharacteristic
61C23×Dic59C2311yescharacteristic
62C23×Dic59C2311yescharacteristic
63C23×Dic59C2311yescharacteristic
64C22×C4×D59—22no—
65C22×C4×D59—22no—
66C22×C4×D59—22no—
67C22×C4×D59—22no—
68C22×C4×D59—22no—
69C22×C4×D59—22no—
70C22×C4×D59—22no—
71C22×C4×D59—22no—
72C22×C4×D59—22no—
73C22×C4×D59—22no—
74C22×C4×D59—22no—
75C22×C4×D59—22no—
76C22×C4×D59—22no—
77C22×C4×D59—41no—
78C22×C4×D59—41no—
79C22×C4×D59—41no—
80C22×C4×D59—41no—
81C22×C4×D59—41no—
82C22×C4×D59—41no—
83C22×C4×D59C2×C414yes—
84C22×C4×D59Q814yes—
85C2×C4⋊Dic59—22no—
86C2×C4⋊Dic59—22no—
87C2×C4⋊Dic59—41no—
88C2×C4⋊Dic59—41no—
89C2×C4⋊Dic59—41no—
90C2×C4⋊Dic59C2×C414yescomplemented
91C2×Dic59⋊C4—22no—
92C2×Dic59⋊C4—22no—
93C2×Dic59⋊C4C2×C414yescomplemented
94C2×(C2×D59)⋊C4—22no—
95C2×(C2×D59)⋊C4—22no—
96C2×(C2×D59)⋊C4—22no—
97C2×(C2×D59)⋊C4—22no—
98C2×(C2×D59)⋊C4—22no—
99C2×(C2×D59)⋊C4—22no—
100C2×(C2×D59)⋊C4—22no—
101C2×(C2×D59)⋊C4—22no—
102C2×(C2×D59)⋊C4—22no—
103C2×(C2×D59)⋊C4C2×C414yes—
104C2×(C2×D59)⋊C4C2×C414yes—
105C2×(C2×D59)⋊C4D414yes—
106C2×C4×Dic59—22no—
107C2×C4×Dic59—22no—
108C2×C4×Dic59—22no—
109C2×C4×Dic59—22no—
110C2×C4×Dic59—41no—
111C2×C4×Dic59—41no—
112C59⋊#95—22no—
113C59⋊#95—22no—
114C59⋊#95—22no—
115C59⋊#95—22no—
116C59⋊#95—22no—
117C59⋊#95—22no—
118C59⋊#95—22no—
119C59⋊#95—22no—
120C59⋊#95—22no—
121C59⋊#95—41no—
122C59⋊#95—41no—
123C59⋊#95—41no—
124C59⋊#95—41no—
125C59⋊#95—41no—
126C59⋊#95C2×C414yescomplemented
127C59⋊#95D414yes—
128C23×C4×C59C2311yescharacteristic
129C23×C4×C59C2311yescharacteristic
130C23×C4×C59C2311yescharacteristic
131C23×C4×C59C2311yescharacteristic
132C23×C4×C59C2311yescharacteristic
133C23×C4×C59C2311yescharacteristic
134C23×C4×C59C2311yescharacteristic
135C2×C4⋊C4×C59—22no—
136C2×C4⋊C4×C59—22no—
137C2×C4⋊C4×C59—41no—
138#95×C59—22no—
139#95×C59—22no—
140#95×C59—22no—
141#95×C59—22no—
142#95×C59—41no—
143#95×C59C2×C414yescomplemented
144C24×C59C2411yescharacteristic
145C23×D59—21no—
146C23×D59—21no—
147C23×D59—21no—
148C23×D59—21no—
149C23×D59—21no—
150C23×D59—21no—
151C23×D59—21no—
152C23×D59—21no—
153C23×D59C22×C412yes—
154C23×D59C2×D412yes—
155C23×D59C2×Q812yes—
156C23×D59#4112yes—
157C23×D59#4112yes—
158C23×D59#4112yes—
159C23×D59#4112yes—
160C22×C4×C59—21no—
161C22×C4×C59—21no—
162C22×C4×C59—21no—
163C22×C4×C59—21no—
164C22×C4×C59—21no—
165C22×C4×C59—21no—
166C22×C4×C59—21no—
167C22×C4×C59—21no—
168C22×C4×C59—21no—
169C22×C4×C59—21no—
170C22×C4×C59—21no—
171C22×C4×C59—21no—
172C22×C4×C59—21no—
173C22×C4×C59—21no—
174C22×C4×C59—21no—
175C22×C4×C59—21no—
176C22×C4×C59—21no—
177C22×C4×C59—21no—
178C22×C4×C59—21no—
179C22×C4×C59—21no—
180C22×C4×C59—21no—
181C22×C4×C59—21no—
182C22×C4×C59—21no—
183C22×C4×C59—21no—
184C22×C4×C59—21no—
185C22×C4×C59—21no—
186C22×C4×C59—21no—
187C22×C4×C59—21no—
188C22×C4×C59—21no—
189C22×C4×C59—21no—
190C22×C4×C59—21no—
191C22×C4×C59—21no—
192C22×C4×C59—21no—
193C22×C4×C59—21no—
194C22×C4×C59—21no—
195C22×C4×C59—21no—
196C22×C4×C59—21no—
197C22×C4×C59—21no—
198C22×C4×C59—21no—
199C22×C4×C59—21no—
200C22×C4×C59—21no—
201C22×C4×C59C22×C412yes—
202C22×C4×C59C22×C412yes—
203C22×C4×C59C22×C412yes—
204C22×C4×C59C2×D412yes—
205C22×C4×C59C2×D412yes—
206C22×C4×C59C2×Q812yes—
207C22×C4×C59#4112yes—
208C22×C4×C59#4112yes—
209C22×Dic59—21no—
210C22×Dic59—21no—
211C22×Dic59—21no—
212C22×Dic59—21no—
213C22×Dic59—21no—
214C22×Dic59—21no—
215C22×Dic59—21no—
216C22×Dic59—21no—
217C22×Dic59—21no—
218C22×Dic59—21no—
219C22×Dic59—21no—
220C22×Dic59—21no—
221C22×Dic59—21no—
222C22×Dic59—21no—
223C22×Dic59—21no—
224C22×Dic59—21no—
225C22×Dic59—21no—
226C22×Dic59—21no—
227C22×Dic59—21no—
228C22×Dic59—21no—
229C22×Dic59—21no—
230C22×Dic59—21no—
231C22×Dic59—21no—
232C22×Dic59—21no—
233C22×Dic59—21no—
234C22×Dic59—21no—
235C22×Dic59—21no—
236C22×Dic59—21no—
237C22×Dic59—21no—
238C22×Dic59—21no—
239C22×Dic59—21no—
240C22×Dic59—21no—
241C22×Dic59—21no—
242C22×Dic59—21no—
243C22×Dic59—21no—
244C22×Dic59—21no—
245C22×Dic59—21no—
246C22×Dic59—21no—
247C22×Dic59—21no—
248C22×Dic59—21no—
249C22×Dic59—21no—
250C22×Dic59C22×C412yes—
251C22×Dic59C22×C412yes—
252C22×Dic59C22×C412yes—
253C22×Dic59C2×D412yes—
254C22×Dic59C2×D412yes—
255C22×Dic59C2×D412yes—
256C22×Dic59C2×Q812yes—
257C22×Dic59#4112yes—
258C2×C4×D59—28no—
259C2×C4×D59—28no—
260C2×C4×D59—28no—
261C2×C4×D59—28no—
262C2×C4×D59—28no—
263C2×C4×D59—44no—
264C2×C4×D59—44no—
265C2×C4×D59—44no—
266C2×C4×D59—44no—
267C2×C4×D59—44no—
268C2×C4×D59—44no—
269C2×C4×D59—44no—
270C2×C4×D59—44no—
271C2×C4×D59—44no—
272C2×C4×D59—44no—
273C2×C4×D59—44no—
274C2×C4×D59—44no—
275C2×C4×D59—44no—
276C2×C4×D59—44no—
277C2×C4×D59—44no—
278C2×C4×D59—44no—
279C4⋊C4×C59—44no—
280(C2×D59)⋊C4—28no—
281(C2×D59)⋊C4—28no—
282(C2×D59)⋊C4—28no—
283(C2×D59)⋊C4—44no—
284C4⋊Dic59—44no—
285C4⋊Dic59—44no—
286Dic59⋊C4—28no—
287C4×Dic59—44no—
288C4×Dic59—44no—
289C23×C59C23×C411yescharacteristic
290C23×C59C22×D411yescharacteristic
291C23×C59C22×D411yescharacteristic
292C23×C59C22×Q811yescharacteristic
293C23×C59C2×#4111yescharacteristic
294C23×C59C2×#4111yescharacteristic
295C23×C59C2×#4111yescharacteristic
296C23×C59C2×#4111yescharacteristic
297C23×C59C2×#4111yescharacteristic
298C23×C59C2×#4111yescharacteristic
299C23×C59C2×#4111yescharacteristic
300C23×C59H(5,𝔽2)11yescharacteristic
301C23×C59H(5,𝔽2)11yescharacteristic
302C23×C59H(5,𝔽2)11yescharacteristic
303C23×C592−1+411yescharacteristic
304C22×D59—22no—
305C22×D59—22no—
306C22×D59—22no—
307C22×D59—22no—
308C22×D59—22no—
309C22×D59—22no—
310C22×D59—22no—
311C22×D59—22no—
312C22×D59—22no—
313C22×D59—22no—
314C22×D59—22no—
315C22×D59—22no—
316C22×D59—22no—
317C22×D59—22no—
318C22×D59—22no—
319C22×D59—22no—
320C22×D59—22no—
321C22×D59—22no—
322C22×D59—22no—
323C22×D59—22no—
324C22×D59—22no—
325C22×D59—22no—
326C22×D59—22no—
327C22×D59—22no—
328C22×D59—22no—
329C22×D59—22no—
330C22×D59—22no—
331C22×D59—22no—
332C22×D59#11714yes—
333C22×D59C4×D414yes—
334C22×D59C4×Q814yes—
335C22×D59C22⋊Q814yes—
336C22×D59#12314yes—
337C22×D59#12514yes—
338C22×D59#12614yes—
339C2×C4×C59—22no—
340C2×C4×C59—22no—
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—22no—
352C2×C4×C59—22no—
353C2×C4×C59—22no—
354C2×C4×C59—22no—
355C2×C4×C59—22no—
356C2×C4×C59—22no—
357C2×C4×C59—22no—
358C2×C4×C59—22no—
359C2×C4×C59—22no—
360C2×C4×C59—41no—
361C2×C4×C59—41no—
362C2×C4×C59—41no—
363C2×C4×C59—41no—
364C2×C4×C59—41no—
365C2×C4×C59—41no—
366C2×C4×C59—41no—
367C2×C4×C59—41no—
368C2×C4×C59—41no—
369C2×C4×C59—41no—
370C2×C4×C59—41no—
371C2×C4×C59—41no—
372C2×C4×C59—41no—
373C2×C4×C59—41no—
374C2×C4×C59—41no—
375C2×C4×C59—41no—
376C2×C4×C59—41no—
377C2×C4×C59—41no—
378C2×C4×C59—41no—
379C2×C4×C59—41no—
380C2×C4×C59—41no—
381C2×C4×C59—41no—
382C2×C4×C59—41no—
383C2×C4×C59—41no—
384C2×C4×C59—41no—
385C2×C4×C59—41no—
386C2×C4×C59—41no—
387C2×C4×C59C4×D414yes—
388C2×Dic59—22no—
389C2×Dic59—22no—
390C2×Dic59—22no—
391C2×Dic59—22no—
392C2×Dic59—22no—
393C2×Dic59—22no—
394C2×Dic59—22no—
395C2×Dic59—22no—
396C2×Dic59—22no—
397C2×Dic59—22no—
398C2×Dic59—22no—
399C2×Dic59—22no—
400C2×Dic59—22no—
401C2×Dic59—22no—
402C2×Dic59—22no—
403C2×Dic59—22no—
404C2×Dic59—22no—
405C2×Dic59—22no—
406C2×Dic59—22no—
407C2×Dic59—22no—
408C2×Dic59—22no—
409C2×Dic59—41no—
410C2×Dic59—41no—
411C2×Dic59—41no—
412C2×Dic59—41no—
413C2×Dic59—41no—
414C2×Dic59—41no—
415C2×Dic59—41no—
416C2×Dic59—41no—
417C2×Dic59—41no—
418C2×Dic59—41no—
419C2×Dic59—41no—
420C2×Dic59—41no—
421C2×Dic59—41no—
422C2×Dic59—41no—
423C2×Dic59—41no—
424C2×Dic59—41no—
425C2×Dic59—41no—
426C2×Dic59—41no—
427C2×Dic59—41no—
428C2×Dic59—41no—
429C2×Dic59—41no—
430C2×Dic59—41no—
431C2×Dic59—41no—
432C2×Dic59—41no—
433C2×Dic59—41no—
434C2×Dic59—41no—
435C2×Dic59—41no—
436C2×Dic59C22⋊Q814yes—
437C4×D59—416no—
438C4×D59—416no—
439C4×D59—416no—
440#13980—591nomaximal, Sylow
441C22×C59C2×#11711yescharacteristic
442C22×C59C2×C4×D411yescharacteristic
443C22×C59C2×C4×D411yescharacteristic
444C22×C59C2×C4×Q811yescharacteristic
445C22×C59C4×#4111yescharacteristic
446C22×C59#51811yescharacteristic
447C22×C59#52011yescharacteristic
448C22×C59C2×C22⋊Q811yescharacteristic
449C22×C59C2×C22⋊Q811yescharacteristic
450C22×C59C2×#12311yescharacteristic
451C22×C59#52511yescharacteristic
452C22×C59C2×#12511yescharacteristic
453C22×C59C2×#12611yescharacteristic
454C22×C59#52911yescharacteristic
455C22×C59#53311yescharacteristic
456C22×C59#53811yescharacteristic
457C22×C59#53911yescharacteristic
458C22×C59#54311yescharacteristic
459C22×C59#54411yescharacteristic
460C22×C59D4211yescharacteristic
461C22×C59#54611yescharacteristic
462C22×C59#54611yescharacteristic
463C22×C59#54611yescharacteristic
464C22×C59#54611yescharacteristic
465C22×C59#54711yescharacteristic
466C22×C59#54811yescharacteristic
467C22×C59#55111yescharacteristic
468C22×C59#55111yescharacteristic
469C22×C59#55111yescharacteristic
470C22×C59#55111yescharacteristic
471C22×C59#55211yescharacteristic
472C22×C59#55211yescharacteristic
473C22×C59#55311yescharacteristic
474C22×C59#55311yescharacteristic
475C22×C59#55311yescharacteristic
476C2×D59—24no—
477C2×D59—24no—
478C2×D59—24no—
479C2×D59—24no—
480C2×D59—24no—
481C2×D59—24no—
482C2×D59—24no—
483C2×D59—24no—
484C2×D59—24no—
485C2×D59—24no—
486C2×D59—24no—
487C2×D59—24no—
488C2×D59—24no—
489C2×D59—24no—
490C2×D59#38718yescomplemented
491C4×C59—24no—
492C4×C59—42no—
493C4×C59—42no—
494C4×C59—42no—
495C4×C59—42no—
496C4×C59—42no—
497C4×C59—81no—
498Dic59—24no—
499Dic59—42no—
500Dic59—42no—
501Dic59—42no—
502Dic59—42no—
503Dic59—42no—
504Dic59—81no—
505C2×#387—591no—
506C2×#385—591no—
507C2×#380—591no—
508C2×C4×C22⋊C4—591no—
509C22×#95—591no—
510#1445—591no—
511#1443—591no—
512#1442D5911yescharacteristic, complemented
513#1441—591no—
514#1436—591no—
515#1436—591no—
516#1434—591no—
517C22⋊#95—591no—
518C22⋊#95—591no—
519C22⋊#95—591no—
520C2×C59C2×#38711yescharacteristic
521C2×C59C4×C22⋊Q811yescharacteristic
522C2×C59#232911yescharacteristic
523C2×C59#235211yescharacteristic
524C2×C59#235311yescharacteristic
525C2×C59#235811yescharacteristic
526C2×C59#235911yescharacteristic
527C2×C59#243711yescharacteristic
528C2×C59#243811yescharacteristic
529C2×C59#244211yescharacteristic
530C2×C59#244311yescharacteristic
531C2×C59#244411yescharacteristic
532C2×C59#248011yescharacteristic
533C2×C59#249311yescharacteristic
534C2×C59#256911yescharacteristic
535D59—28no—
536C24×C4—591no—
537C24×C4—591no—
538C24×C4—591no—
539C22×C4⋊C4—591no—
540C22×C4⋊C4—591no—
541C22×C4⋊C4—591no—
542C22×C4⋊C4C2×D5911yescharacteristic
543C22×C22⋊C4—591no—
544C22×C22⋊C4—591no—
545C22×C22⋊C4—591no—
546C22×C22⋊C4—591no—
547C22×C42—591no—
548C22×C42—591no—
549#387—1184no—
550#385—598no—
551#380—1184no—
552C4×C22⋊C4—1184no—
553C2×#95—591no—
554C2×#95—591no—
555C2×#95—591no—
556C2×#95—591no—
557C2×#95—591no—
558C2×#95—591no—
559C2×#95—591no—
560C2×#95—591no—
561C2×#95—591no—
562C2×#95—591no—
563C2×#95—591no—
564C2×#95—591no—
565C2×#95—591no—
566C2×#95—591no—
567C2×#95—591no—
568C2×#95—591no—
569C2×#95—1184no—
570C2×#95C2×D5911yescharacteristic
571C2×#95C2×D5911yescharacteristic
572C2×#95C2×D5911yescharacteristic
573C2×#95C2×D5911yescharacteristic
574C2×#95C2×D5911yescharacteristic
575C2×#95C2×D5911yescharacteristic
576C59#1398011yescharacteristic, complemented, Sylow
577C25—591no—
578C23×C4—591no—
579C23×C4—591no—
580C23×C4—591no—
581C23×C4—591no—
582C23×C4—591no—
583C23×C4—591no—
584C23×C4—594no—
585C23×C4—594no—
586C23×C4—591no—
587C23×C4—1182no—
588C23×C4—1182no—
589C23×C4—1182no—
590C23×C4—1182no—
591C23×C4—1182no—
592C23×C4—1182no—
593C23×C4—1182no—
594C23×C4—1182no—
595C23×C4—1182no—
596C23×C4—1182no—
597C23×C4—1182no—
598C23×C4—1182no—
599C23×C4—1182no—
600C23×C4—2361no—
601C23×C4—2361no—
602C23×C4—2361no—
603C23×C4—2361no—
604C23×C4—2361no—
605C23×C4—2361no—
606C23×C4C22×D5911yescharacteristic
607C23×C4C22×D5911yescharacteristic
608C23×C4C22×D5911yescharacteristic
609C23×C4C22×D5911yescharacteristic
610C23×C4C22×D5911yescharacteristic
611C23×C4C22×D5911yescharacteristic
612C23×C4C22×D5911yescharacteristic
613C2×C4⋊C4—22no—
614C2×C4⋊C4—22no—
615C2×C4⋊C4—41no—
616C2×C4⋊C4—594no—
617C2×C4⋊C4—594no—
618C2×C4⋊C4—1182no—
619C2×C4⋊C4—1182no—
620C2×C4⋊C4—1182no—
621C2×C4⋊C4—1182no—
622C2×C4⋊C4—2361no—
623C2×C4⋊C4—2361no—
624C2×C4⋊C4—2361no—
625C2×C22⋊C4—594no—
626C2×C22⋊C4—594no—
627C2×C22⋊C4—594no—
628C2×C22⋊C4—1182no—
629C2×C22⋊C4—1182no—
630C2×C22⋊C4—1182no—
631C2×C22⋊C4—1182no—
632C2×C22⋊C4—1182no—
633C2×C22⋊C4—1182no—
634C2×C22⋊C4—1182no—
635C2×C22⋊C4—1182no—
636C2×C22⋊C4—1182no—
637C2×C42—1182no—
638C2×C42—1182no—
639C2×C42—1182no—
640C2×C42—1182no—
641C2×C42—2361no—
642C2×C42—2361no—
643#95—22no—
644#95—22no—
645#95—22no—
646#95—22no—
647#95—41no—
648#95—594no—
649#95—594no—
650#95—1182no—
651#95—1182no—
652#95—1182no—
653#95—1182no—
654#95—1182no—
655#95—1182no—
656#95—1182no—
657#95—1182no—
658#95—1182no—
659#95—2361no—
660#95—2361no—
661#95—2361no—
662#95—2361no—
663#95—2361no—
664#95C4×D5914yescomplemented
665C24—592no—
666C24—592no—
667C24—592no—
668C24—592no—
669C24—592no—
670C24—592no—
671C24—592no—
672C24—1181no—
673C24—1181no—
674C24—1181no—
675C24—1181no—
676C24—1181no—
677C24—1181no—
678C24—1181no—
679C24—1181no—
680C24C23×D5911yescharacteristic
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—592no—
723C22×C4—592no—
724C22×C4—592no—
725C22×C4—592no—
726C22×C4—592no—
727C22×C4—592no—
728C22×C4—592no—
729C22×C4—592no—
730C22×C4—1188no—
731C22×C4—1188no—
732C22×C4—1188no—
733C22×C4—1188no—
734C22×C4—1181no—
735C22×C4—1181no—
736C22×C4—1181no—
737C22×C4—1181no—
738C22×C4—1181no—
739C22×C4—1181no—
740C22×C4—1181no—
741C22×C4—1181no—
742C22×C4—1181no—
743C22×C4—1181no—
744C22×C4—1181no—
745C22×C4—1181no—
746C22×C4—1181no—
747C22×C4—1181no—
748C22×C4—1181no—
749C22×C4—1181no—
750C22×C4—1181no—
751C22×C4—1181no—
752C22×C4—1181no—
753C22×C4—1181no—
754C22×C4—1181no—
755C22×C4—1181no—
756C22×C4—1181no—
757C22×C4—1181no—
758C22×C4—1181no—
759C22×C4—1181no—
760C22×C4—1181no—
761C22×C4—1181no—
762C22×C4—1181no—
763C22×C4—1181no—
764C22×C4—1181no—
765C22×C4—1181no—
766C22×C4—1181no—
767C22×C4—1181no—
768C22×C4—1188no—
769C22×C4—1181no—
770C22×C4—1181no—
771C22×C4—1181no—
772C22×C4—1181no—
773C22×C4—1181no—
774C22×C4—1181no—
775C22×C4—1181no—
776C22×C4—2364no—
777C22×C4—2364no—
778C22×C4—2364no—
779C22×C4—2364no—
780C22×C4—2364no—
781C22×C4—2364no—
782C22×C4—2364no—
783C22×C4—2364no—
784C22×C4—2364no—
785C22×C4—2364no—
786C22×C4—2364no—
787C22×C4—2364no—
788C22×C4—2364no—
789C22×C4—2364no—
790C22×C4—2364no—
791C22×C4—2364no—
792C22×C4C2×C4×D5912yes—
793C22×C4C2×C4×D5912yes—
794C22×C4C2×C4×D5912yes—
795C22×C4D4×D5912yes—
796C22×C4D4×D5912yes—
797C22×C4#1174568712yes—
798C22×C4Q8×D5912yes—
799C22×C4#1174568912yes—
800C4⋊C4—44no—
801C4⋊C4—1188no—
802C4⋊C4—2364no—
803C4⋊C4—2364no—
804C22⋊C4—1188no—
805C22⋊C4—1188no—
806C22⋊C4—1188no—
807C22⋊C4—2364no—
808C42—2364no—
809C42—2364no—
810C23—594no—
811C23—594no—
812C23—594no—
813C23—594no—
814C23—594no—
815C23—594no—
816C23—594no—
817C23—1182no—
818C23—1182no—
819C23—1182no—
820C23—1182no—
821C23—1182no—
822C23—1182no—
823C23—1182no—
824C23—1182no—
825C23—1182no—
826C23—1182no—
827C23—1182no—
828C23—1182no—
829C23—1182no—
830C23—1182no—
831C23—1182no—
832C23—1182no—
833C23—1182no—
834C23—1182no—
835C23—1182no—
836C23—1182no—
837C23—1182no—
838C23—1182no—
839C23—1182no—
840C23—1182no—
841C23—1182no—
842C23—1182no—
843C23—1182no—
844C23—1182no—
845C23C22×C4×D5911yescharacteristic
846C23C2×D4×D5911yescharacteristic
847C23C2×D4×D5911yescharacteristic
848C23C2×Q8×D5911yescharacteristic
849C23#41×D5911yescharacteristic
850C23#41×D5911yescharacteristic
851C23#41×D5911yescharacteristic
852C23#41×D5911yescharacteristic
853C23#41×D5911yescharacteristic
854C23C2×#1174568711yescharacteristic
855C23C2×#1174568911yescharacteristic
856C23#1427377211yescharacteristic
857C23#1427377311yescharacteristic
858C23#1427377311yescharacteristic
859C23#1427377411yescharacteristic
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
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—594no—
909C2×C4—1182no—
910C2×C4—1182no—
911C2×C4—1182no—
912C2×C4—1182no—
913C2×C4—1182no—
914C2×C4—1182no—
915C2×C4—1182no—
916C2×C4—1182no—
917C2×C4—1182no—
918C2×C4—1182no—
919C2×C4—1182no—
920C2×C4—1182no—
921C2×C4—1182no—
922C2×C4—1182no—
923C2×C4—1182no—
924C2×C4—1182no—
925C2×C4—1182no—
926C2×C4—1182no—
927C2×C4—1182no—
928C2×C4—1182no—
929C2×C4—1182no—
930C2×C4—23616no—
931C2×C4—23616no—
932C2×C4—23616no—
933C2×C4—2361no—
934C2×C4—2361no—
935C2×C4—2361no—
936C2×C4—2361no—
937C2×C4—2361no—
938C2×C4—2361no—
939C2×C4—2361no—
940C2×C4—2361no—
941C2×C4—2361no—
942C2×C4—2361no—
943C2×C4—2361no—
944C2×C4—2361no—
945C2×C4—2361no—
946C2×C4—2361no—
947C2×C4—2361no—
948C2×C4—2361no—
949C2×C4—2361no—
950C2×C4—2361no—
951C2×C4—2361no—
952C2×C4—2361no—
953C2×C4—2361no—
954C2×C4—2361no—
955C2×C4—2361no—
956C2×C4—2361no—
957C2×C4—2361no—
958C2×C4—2361no—
959C2×C4—2361no—
960C2×C4#1427368914yes—
961C22—598no—
962C22—1184no—
963C22—1184no—
964C22—1184no—
965C22—1184no—
966C22—1184no—
967C22—1184no—
968C22—1184no—
969C22—1184no—
970C22—1184no—
971C22—1184no—
972C22—1184no—
973C22—1184no—
974C22—1184no—
975C22—1184no—
976C22#117×D5911yescharacteristic
977C22C4×D4×D5911yescharacteristic
978C22C2×#1427368911yescharacteristic
979C22C4×Q8×D5911yescharacteristic
980C22C4×#1174568711yescharacteristic
981C22#1683787411yescharacteristic
982C22#1683788211yescharacteristic
983C22C22⋊Q8×D5911yescharacteristic
984C22C22⋊Q8×D5911yescharacteristic
985C22#123×D5911yescharacteristic
986C22#1683791211yescharacteristic
987C22#125×D5911yescharacteristic
988C22#126×D5911yescharacteristic
989C22#1683793711yescharacteristic
990C22#1683795711yescharacteristic
991C22#1683799111yescharacteristic
992C22#1683799511yescharacteristic
993C22#1683802711yescharacteristic
994C22#1683803211yescharacteristic
995C22#1683803411yescharacteristic
996C22#1683804311yescharacteristic
997C22#1683804411yescharacteristic
998C22#1683804511yescharacteristic
999C22#1683804511yescharacteristic
1000C22#1683805211yescharacteristic
1001C22#1683806011yescharacteristic
1002C22#1683807511yescharacteristic
1003C22#1683807511yescharacteristic
1004C22#1683807911yescharacteristic
1005C22#1683808211yescharacteristic
1006C22#1683808811yescharacteristic
1007C22#1683809011yescharacteristic
1008C22#1683809911yescharacteristic
1009C22#1683810311yescharacteristic
1010C22#1683810511yescharacteristic
1011C4—24no—
1012C4—42no—
1013C4—42no—
1014C4—42no—
1015C4—42no—
1016C4—42no—
1017C4—81no—
1018C4—1184no—
1019C4—4721no—
1020C4—2362no—
1021C4—2362no—
1022C4—2362no—
1023C4—2362no—
1024C4—2362no—
1025C2—1188no—
1026C2#387×D5911yescharacteristic
1027C2#2142662611yescharacteristic
1028C2#2142682311yescharacteristic
1029C2#2142702211yescharacteristic
1030C2#2142703111yescharacteristic
1031C2#2142707211yescharacteristic
1032C2#2142708711yescharacteristic
1033C2#2142775611yescharacteristic
1034C2#2142777311yescharacteristic
1035C2#2142781311yescharacteristic
1036C2#2142782411yescharacteristic
1037C2#2142784711yescharacteristic
1038C2#2142834311yescharacteristic
1039C2#2142847411yescharacteristic
1040C2#2142931411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC59×#1442C2
socle, cosocleC24×C59C24
prime radicalC24×D59C23
hypercenter#1442D59
hypocenterC59#13980
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
1. C2×#16837283C2semidirect
6. #21422365C2semidirect
7. #21422357C2semidirect
8. #21422350C2semidirect
9. #21422330C2semidirect
10. #21422330C2semidirect
11. #21422321C2semidirect
15. C59×#1442C2semidirect
29. #16837276C4semidirect
90. C2×C4⋊Dic59C2×C4semidirect
93. C2×Dic59⋊C4C2×C4semidirect
126. C59⋊#95C2×C4semidirect
143. #95×C59C2×C4semidirect
490. C2×D59#387semidirect
512. #1442D59semidirect
576. C59#13980semidirect
664. #95C4×D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168372832
C2×#168372762
C2×#168372592
C2×#168372492
C2×#95×D592
#214223652
#214223572
#214223502
#214223302
#214223212
(C2×D59)⋊#952
C59×#14422
#1398059