Finite Group Databasebeta

← #28516753

Subgroups — #28516753

Order 15104.

1398 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837296C211yesmaximal, characteristic
2C2×#16837295C211yesmaximal, characteristic
3C2×#16837267C211yesmaximal, characteristic, complemented
4#21422363C211yesmaximal, characteristic, complemented
5#21422354C211yesmaximal, characteristic, complemented
6#21422343C211yesmaximal, characteristic
7#21422341C211yesmaximal, characteristic
8#21422339C211yesmaximal, characteristic
9#21422333C211yesmaximal, characteristic
10#21422330C211yesmaximal, characteristic, complemented
11#21422330C211yesmaximal, characteristic, complemented
12#21422328C211yesmaximal, characteristic, complemented
13#21422327C211yesmaximal, characteristic, complemented
14Dic59⋊#95C211yesmaximal, characteristic, complemented
15C59×#1439C211yesmaximal, characteristic
16C22×C4⋊Dic59C2211yescharacteristic
17C22×C4⋊Dic59C2211yescharacteristic
18C22×Dic59⋊C4C2211yescharacteristic
19C22×Dic59⋊C4C2211yescharacteristic
20C22×C22⋊Dic59C2211yescharacteristic
21C22×C22⋊Dic59C2211yescharacteristic
22C22×C22⋊Dic59C2211yescharacteristic
23C22×C22⋊Dic59C2211yescharacteristic
24C22×C4×Dic59C2211yescharacteristic
25C22×C4×Dic59C2211yescharacteristic
26C22×C4×Dic59C2211yescharacteristic
27#16837296—24no—
28#16837295C418yescomplemented
29#16837267—24no—
30C2×C59⋊#95C2211yescharacteristic
31C2×C59⋊#95C2211yescharacteristic
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
47C22×C4⋊C4×C59C2211yescharacteristic
48C22×C22⋊C4×C59C2211yescharacteristic
49C22×C22⋊C4×C59C2211yescharacteristic
50C22×C22⋊C4×C59C2211yescharacteristic
51C2×#95×C59C2211yescharacteristic
52C2×#95×C59C2211yescharacteristic
53C2×#95×C59C2211yescharacteristic
54C23×Dic59C2311yescharacteristic
55C23×Dic59C2311yescharacteristic
56C23×Dic59C2311yescharacteristic
57C23×Dic59C2311yescharacteristic
58C23×Dic59C2311yescharacteristic
59C23×Dic59C2311yescharacteristic
60C23×Dic59C2311yescharacteristic
61C23×Dic59C2311yescharacteristic
62C2×C4⋊Dic59—22no—
63C2×C4⋊Dic59—22no—
64C2×C4⋊Dic59—41no—
65C2×C4⋊Dic59—41no—
66C2×C4⋊Dic59—41no—
67C2×C4⋊Dic59C2×C414yes—
68C2×Dic59⋊C4—22no—
69C2×Dic59⋊C4—22no—
70C2×Dic59⋊C4—22no—
71C2×Dic59⋊C4—22no—
72C2×Dic59⋊C4—41no—
73C2×Dic59⋊C4—41no—
74C2×C22⋊Dic59—22no—
75C2×C22⋊Dic59—22no—
76C2×C22⋊Dic59—22no—
77C2×C22⋊Dic59—22no—
78C2×C22⋊Dic59—41no—
79C2×C22⋊Dic59—41no—
80C2×C22⋊Dic59—41no—
81C2×C22⋊Dic59—41no—
82C2×C22⋊Dic59—41no—
83C2×C22⋊Dic59—41no—
84C2×C22⋊Dic59C2×C414yes—
85C2×C22⋊Dic59C2×C414yes—
86C2×C4×Dic59—22no—
87C2×C4×Dic59—22no—
88C2×C4×Dic59—22no—
89C2×C4×Dic59—41no—
90C2×C4×Dic59—41no—
91C2×C4×Dic59—41no—
92C2×C4×Dic59—41no—
93C2×C4×Dic59—41no—
94C2×C4×Dic59C2×C414yes—
95C59⋊#95—22no—
96C59⋊#95—22no—
97C59⋊#95—22no—
98C59⋊#95—22no—
99C59⋊#95—22no—
100C59⋊#95—22no—
101C59⋊#95—41no—
102C59⋊#95—41no—
103C59⋊#95—41no—
104C59⋊#95—41no—
105C59⋊#95—41no—
106C59⋊#95—41no—
107C59⋊#95—41no—
108C59⋊#95—41no—
109C59⋊#95C2×C414yes—
110C59⋊#95C2×C414yes—
111C59⋊#95D414yes—
112C25×C59C2311yescharacteristic
113C23×C4×C59C2311yescharacteristic
114C23×C4×C59C2311yescharacteristic
115C23×C4×C59C2311yescharacteristic
116C23×C4×C59C2311yescharacteristic
117C23×C4×C59C2311yescharacteristic
118C23×C4×C59C2311yescharacteristic
119C2×C4⋊C4×C59—22no—
120C2×C4⋊C4×C59—22no—
121C2×C4⋊C4×C59—41no—
122C2×C22⋊C4×C59—22no—
123C2×C22⋊C4×C59—22no—
124C2×C22⋊C4×C59—22no—
125C2×C22⋊C4×C59—22no—
126C2×C22⋊C4×C59—41no—
127C2×C22⋊C4×C59—41no—
128C2×C22⋊C4×C59—41no—
129C2×C22⋊C4×C59—41no—
130C2×C22⋊C4×C59C2×C414yes—
131#95×C59—22no—
132#95×C59—22no—
133#95×C59—41no—
134C24×C59—21no—
135C24×C59—21no—
136C24×C59—21no—
137C24×C59—21no—
138C24×C59—21no—
139C24×C59—21no—
140C24×C59—21no—
141C24×C59—21no—
142C24×C59—21no—
143C24×C59—21no—
144C24×C59—21no—
145C24×C59—21no—
146C24×C59—21no—
147C24×C59—21no—
148C24×C59C22×C412yes—
149C24×C59C2411yescharacteristic
150C22×C4×C59—21no—
151C22×C4×C59—21no—
152C22×C4×C59—21no—
153C22×C4×C59—21no—
154C22×C4×C59—21no—
155C22×C4×C59—21no—
156C22×C4×C59—21no—
157C22×C4×C59—21no—
158C22×C4×C59—21no—
159C22×C4×C59—21no—
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×C59C22×C412yes—
187C22×C4×C59C22×C412yes—
188C22×C4×C59C2×D412yes—
189C22×C4×C59#4112yes—
190C22×C4×C59#4112yes—
191C22×C4×C59#4112yes—
192C22×Dic59—21no—
193C22×Dic59—21no—
194C22×Dic59—21no—
195C22×Dic59—21no—
196C22×Dic59—21no—
197C22×Dic59—21no—
198C22×Dic59—21no—
199C22×Dic59—21no—
200C22×Dic59—21no—
201C22×Dic59—21no—
202C22×Dic59—21no—
203C22×Dic59—21no—
204C22×Dic59—21no—
205C22×Dic59—21no—
206C22×Dic59—21no—
207C22×Dic59—21no—
208C22×Dic59—21no—
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×Dic59C22×C412yes—
241C22×Dic59C22×C412yes—
242C22×Dic59C22×C412yes—
243C22×Dic59C22×C412yes—
244C22×Dic59C2×D412yes—
245C22×Dic59C2×D412yes—
246C22×Dic59#4112yes—
247C22×Dic59#4112yes—
248C4⋊C4×C59—44no—
249C22⋊C4×C59—28no—
250C22⋊C4×C59—44no—
251C22⋊C4×C59—44no—
252C22⋊Dic59—28no—
253C22⋊Dic59—44no—
254C22⋊Dic59—44no—
255C22⋊Dic59—44no—
256C4⋊Dic59—44no—
257C4⋊Dic59—44no—
258Dic59⋊C4—44no—
259Dic59⋊C4—44no—
260C4×Dic59—28no—
261C4×Dic59—44no—
262C4×Dic59—44no—
263C23×C59—22no—
264C23×C59—22no—
265C23×C59—22no—
266C23×C59—22no—
267C23×C59—22no—
268C23×C59—22no—
269C23×C59—22no—
270C23×C59—41no—
271C23×C59—41no—
272C23×C59—41no—
273C23×C59—41no—
274C23×C59—41no—
275C23×C59—41no—
276C23×C59—41no—
277C23×C59—41no—
278C23×C59—41no—
279C23×C59—41no—
280C23×C59—41no—
281C23×C59—41no—
282C23×C59—41no—
283C23×C59—41no—
284C23×C59—41no—
285C23×C59—41no—
286C23×C59—41no—
287C23×C59—41no—
288C23×C59—41no—
289C23×C59—41no—
290C23×C59—41no—
291C23×C59—41no—
292C23×C59—41no—
293C23×C59—41no—
294C23×C59—41no—
295C23×C59—41no—
296C23×C59—41no—
297C23×C59—41no—
298C23×C59C23×C411yescharacteristic
299C23×C59C22×D411yescharacteristic
300C23×C59C2×#4111yescharacteristic
301C23×C59C2×#4111yescharacteristic
302C23×C59C2×#4111yescharacteristic
303C23×C59C2×#4111yescharacteristic
304C23×C59C2×#4111yescharacteristic
305C23×C59H(5,𝔽2)11yescharacteristic
306C23×C59H(5,𝔽2)11yescharacteristic
307C23×C59H(5,𝔽2)11yescharacteristic
308C23×C59H(5,𝔽2)11yescharacteristic
309C23×C59H(5,𝔽2)11yescharacteristic
310C23×C592−1+411yescharacteristic
311C23×C592−1+411yescharacteristic
312C23×C592−1+411yescharacteristic
313C2×C4×C59—22no—
314C2×C4×C59—22no—
315C2×C4×C59—22no—
316C2×C4×C59—22no—
317C2×C4×C59—22no—
318C2×C4×C59—22no—
319C2×C4×C59—22no—
320C2×C4×C59—22no—
321C2×C4×C59—22no—
322C2×C4×C59—22no—
323C2×C4×C59—22no—
324C2×C4×C59—22no—
325C2×C4×C59—22no—
326C2×C4×C59—22no—
327C2×C4×C59—22no—
328C2×C4×C59—41no—
329C2×C4×C59—41no—
330C2×C4×C59—41no—
331C2×C4×C59—41no—
332C2×C4×C59—41no—
333C2×C4×C59—41no—
334C2×C4×C59—41no—
335C2×C4×C59—41no—
336C2×C4×C59—41no—
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—41no—
350C2×C4×C59—41no—
351C2×C4×C59—41no—
352C2×C4×C59—41no—
353C2×C4×C59—41no—
354C2×C4×C59#11714yes—
355C2×Dic59—22no—
356C2×Dic59—22no—
357C2×Dic59—22no—
358C2×Dic59—22no—
359C2×Dic59—22no—
360C2×Dic59—22no—
361C2×Dic59—22no—
362C2×Dic59—22no—
363C2×Dic59—22no—
364C2×Dic59—22no—
365C2×Dic59—22no—
366C2×Dic59—22no—
367C2×Dic59—22no—
368C2×Dic59—22no—
369C2×Dic59—22no—
370C2×Dic59—22no—
371C2×Dic59—22no—
372C2×Dic59—22no—
373C2×Dic59—22no—
374C2×Dic59—22no—
375C2×Dic59—22no—
376C2×Dic59—41no—
377C2×Dic59—41no—
378C2×Dic59—41no—
379C2×Dic59—41no—
380C2×Dic59—41no—
381C2×Dic59—41no—
382C2×Dic59—41no—
383C2×Dic59—41no—
384C2×Dic59—41no—
385C2×Dic59—41no—
386C2×Dic59—41no—
387C2×Dic59—41no—
388C2×Dic59—41no—
389C2×Dic59—41no—
390C2×Dic59—41no—
391C2×Dic59—41no—
392C2×Dic59—41no—
393C2×Dic59—41no—
394C2×Dic59—41no—
395C2×Dic59—41no—
396C2×Dic59—41no—
397C2×Dic59—41no—
398C2×Dic59—41no—
399C2×Dic59—41no—
400C2×Dic59—41no—
401C2×Dic59—41no—
402C2×Dic59—41no—
403C2×Dic59—41no—
404C2×Dic59—41no—
405C2×Dic59—41no—
406C2×Dic59—41no—
407C2×Dic59—41no—
408C2×Dic59—41no—
409C2×Dic59—41no—
410C2×Dic59C4×D414yes—
411#14412—591nomaximal, Sylow
412C22×C59—42no—
413C22×C59—42no—
414C22×C59—42no—
415C22×C59—42no—
416C22×C59—42no—
417C22×C59—42no—
418C22×C59—42no—
419C22×C59—81no—
420C22×C59—81no—
421C22×C59—81no—
422C22×C59—81no—
423C22×C59—81no—
424C22×C59—81no—
425C22×C59—81no—
426C22×C59—81no—
427C22×C59C2×#11711yescharacteristic
428C22×C59C2×C4×D411yescharacteristic
429C22×C59C4×#4111yescharacteristic
430C22×C59#51811yescharacteristic
431C22×C59#52011yescharacteristic
432C22×C59#52011yescharacteristic
433C22×C59#52011yescharacteristic
434C22×C59#53511yescharacteristic
435C22×C59#53711yescharacteristic
436C22×C59#53811yescharacteristic
437C22×C59#53911yescharacteristic
438C22×C59#54011yescharacteristic
439C22×C59#54011yescharacteristic
440C22×C59#54111yescharacteristic
441C22×C59#54111yescharacteristic
442C22×C59#54211yescharacteristic
443C22×C59#54211yescharacteristic
444C22×C59#54211yescharacteristic
445C22×C59#54211yescharacteristic
446C22×C59#54611yescharacteristic
447C22×C59#54611yescharacteristic
448C22×C59#54711yescharacteristic
449C22×C59#54811yescharacteristic
450C22×C59#55111yescharacteristic
451C22×C59#55211yescharacteristic
452C22×C59#55211yescharacteristic
453C22×C59#55311yescharacteristic
454C22×C59#55311yescharacteristic
455C22×C59#55311yescharacteristic
456C22×C59#55911yescharacteristic
457C22×C59#55911yescharacteristic
458C22×C59H(3,𝔽4)11yescharacteristic
459C22×C59#56211yescharacteristic
460C22×C59#56211yescharacteristic
461C22×C59#56311yescharacteristic
462C4×C59—24no—
463C4×C59—42no—
464C4×C59—42no—
465C4×C59—42no—
466C4×C59—81no—
467C4×C59—81no—
468Dic59—24no—
469Dic59—42no—
470Dic59—42no—
471Dic59—42no—
472Dic59—42no—
473Dic59—42no—
474Dic59—81no—
475Dic59—81no—
476C2×#388—591no—
477C2×#388—591no—
478C2×#382—591no—
479#1445—591no—
480#1442—591no—
481#1440—591no—
482#1439—591no—
483#1439—591no—
484#1439D5911yescharacteristic
485#1437—591no—
486#1436—591no—
487#1436—591no—
488#1436—591no—
489#1436—591no—
490C4⋊#95—591no—
491C2×C59—82no—
492C2×C59#231411yescharacteristic
493C2×C59#232411yescharacteristic
494C2×C59#233411yescharacteristic
495C2×C59#235211yescharacteristic
496C2×C59#235711yescharacteristic
497C2×C59#235911yescharacteristic
498C2×C59#237911yescharacteristic
499C2×C59#271011yescharacteristic
500C2×C59#271111yescharacteristic
501C2×C59#271211yescharacteristic
502C2×C59#272511yescharacteristic
503C2×C59#275311yescharacteristic
504C2×C59#275411yescharacteristic
505C2×C59#277211yescharacteristic
506C2×C59#277311yescharacteristic
507C22×C4⋊C4—591no—
508C22×C4⋊C4—591no—
509C22×C4⋊C4—591no—
510C22×C4⋊C4—591no—
511C22×C4⋊C4C2×D5911yescharacteristic
512C22×C22⋊C4—591no—
513C22×C22⋊C4—591no—
514C22×C22⋊C4—591no—
515C22×C22⋊C4—591no—
516C22×C22⋊C4C2×D5911yescharacteristic
517C22×C22⋊C4C2×D5911yescharacteristic
518C22×C22⋊C4C2×D5911yescharacteristic
519C22×C42—591no—
520C22×C42—591no—
521C22×C42—591no—
522#388—598no—
523#388—1184no—
524#382—1184no—
525C2×#95—591no—
526C2×#95—591no—
527C2×#95—591no—
528C2×#95—591no—
529C2×#95—591no—
530C2×#95—591no—
531C2×#95—591no—
532C2×#95—591no—
533C2×#95—591no—
534C2×#95—591no—
535C2×#95—591no—
536C2×#95—591no—
537C2×#95—591no—
538C2×#95—591no—
539C2×#95—591no—
540C2×#95—591no—
541C2×#95—591no—
542C2×#95C2×D5911yescharacteristic
543C2×#95C2×D5911yescharacteristic
544C2×#95C2×D5911yescharacteristic
545C59#1441211yescharacteristic, complemented, Sylow
546C25C22×D5911yescharacteristic
547C23×C4—591no—
548C23×C4—591no—
549C23×C4—591no—
550C23×C4—591no—
551C23×C4—591no—
552C23×C4—591no—
553C23×C4—591no—
554C23×C4—591no—
555C23×C4C22×D5911yescharacteristic
556C23×C4C22×D5911yescharacteristic
557C23×C4C22×D5911yescharacteristic
558C23×C4C22×D5911yescharacteristic
559C23×C4C22×D5911yescharacteristic
560C23×C4C22×D5911yescharacteristic
561C2×C4⋊C4—22no—
562C2×C4⋊C4—22no—
563C2×C4⋊C4—41no—
564C2×C4⋊C4—594no—
565C2×C4⋊C4—1182no—
566C2×C4⋊C4—1182no—
567C2×C4⋊C4—1182no—
568C2×C4⋊C4—1182no—
569C2×C4⋊C4—1182no—
570C2×C4⋊C4—1182no—
571C2×C4⋊C4—2361no—
572C2×C4⋊C4—2361no—
573C2×C4⋊C4—2361no—
574C2×C4⋊C4—2361no—
575C2×C4⋊C4—2361no—
576C2×C22⋊C4—22no—
577C2×C22⋊C4—22no—
578C2×C22⋊C4—22no—
579C2×C22⋊C4—22no—
580C2×C22⋊C4—41no—
581C2×C22⋊C4—41no—
582C2×C22⋊C4—41no—
583C2×C22⋊C4—41no—
584C2×C22⋊C4—594no—
585C2×C22⋊C4—594no—
586C2×C22⋊C4—1182no—
587C2×C22⋊C4—1182no—
588C2×C22⋊C4—1182no—
589C2×C22⋊C4—1182no—
590C2×C22⋊C4—2361no—
591C2×C22⋊C4—2361no—
592C2×C22⋊C4—2361no—
593C2×C22⋊C4—2361no—
594C2×C22⋊C4—2361no—
595C2×C22⋊C4—2361no—
596C2×C22⋊C4C4×D5914yes—
597C2×C42—594no—
598C2×C42—1182no—
599C2×C42—1182no—
600C2×C42—1182no—
601C2×C42—2361no—
602C2×C42—2361no—
603C2×C42—2361no—
604C2×C42—2361no—
605C2×C42—2361no—
606#95—22no—
607#95—22no—
608#95—41no—
609#95—594no—
610#95—594no—
611#95—594no—
612#95—1182no—
613#95—1182no—
614#95—1182no—
615#95—1182no—
616#95—1182no—
617#95—1182no—
618#95—2361no—
619#95—2361no—
620#95—2361no—
621#95—2361no—
622#95—2361no—
623#95—2361no—
624#95—2361no—
625#95—2361no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24C2×C4×D5912yes—
641C24C23×D5911yescharacteristic
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—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—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—592no—
679C22×C4—592no—
680C22×C4—592no—
681C22×C4—592no—
682C22×C4—592no—
683C22×C4—592no—
684C22×C4—592no—
685C22×C4—592no—
686C22×C4—1181no—
687C22×C4—1181no—
688C22×C4—1181no—
689C22×C4—1181no—
690C22×C4—1181no—
691C22×C4—1181no—
692C22×C4—1181no—
693C22×C4—1181no—
694C22×C4—1181no—
695C22×C4—1181no—
696C22×C4—1181no—
697C22×C4—1181no—
698C22×C4—1181no—
699C22×C4—1181no—
700C22×C4—1181no—
701C22×C4—1181no—
702C22×C4—1181no—
703C22×C4—1181no—
704C22×C4—1181no—
705C22×C4—1181no—
706C22×C4—1181no—
707C22×C4—1181no—
708C22×C4—1181no—
709C22×C4—1181no—
710C22×C4—1181no—
711C22×C4—1181no—
712C22×C4—1181no—
713C22×C4—1181no—
714C22×C4—1181no—
715C22×C4—1181no—
716C22×C4—1181no—
717C22×C4—1181no—
718C22×C4—1181no—
719C22×C4—1181no—
720C22×C4—1181no—
721C22×C4—1181no—
722C22×C4—1181no—
723C22×C4—1181no—
724C22×C4—1181no—
725C22×C4—1181no—
726C22×C4—1181no—
727C22×C4—1181no—
728C22×C4—1181no—
729C22×C4—1181no—
730C22×C4—1181no—
731C22×C4—1181no—
732C22×C4—1181no—
733C22×C4—1181no—
734C22×C4C2×C4×D5912yes—
735C22×C4C2×C4×D5912yes—
736C22×C4D4×D5912yes—
737C22×C4#1174568712yes—
738C22×C4#1174568712yes—
739C22×C4#1174568712yes—
740C4⋊C4—44no—
741C4⋊C4—2364no—
742C4⋊C4—2364no—
743C4⋊C4—2364no—
744C4⋊C4—2364no—
745C22⋊C4—28no—
746C22⋊C4—44no—
747C22⋊C4—44no—
748C22⋊C4—1188no—
749C22⋊C4—2364no—
750C22⋊C4—2364no—
751C22⋊C4—2364no—
752C42—1188no—
753C42—2364no—
754C42—2364no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23C22×C4×D5911yescharacteristic
791C23C2×D4×D5911yescharacteristic
792C23#41×D5911yescharacteristic
793C23#41×D5911yescharacteristic
794C23C2×#1174568711yescharacteristic
795C23C2×#1174568711yescharacteristic
796C23C2×#1174568711yescharacteristic
797C23#1427377211yescharacteristic
798C23#1427377211yescharacteristic
799C23#1427377211yescharacteristic
800C23#1427377311yescharacteristic
801C23#1427377311yescharacteristic
802C23#1427377411yescharacteristic
803C23#1427377411yescharacteristic
804C23#1427377511yescharacteristic
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—594no—
847C2×C4—1182no—
848C2×C4—1182no—
849C2×C4—1182no—
850C2×C4—1182no—
851C2×C4—1182no—
852C2×C4—1182no—
853C2×C4—1182no—
854C2×C4—1182no—
855C2×C4—1182no—
856C2×C4—1182no—
857C2×C4—1182no—
858C2×C4—1182no—
859C2×C4—1182no—
860C2×C4—1182no—
861C2×C4—1182no—
862C2×C4—1182no—
863C2×C4—1182no—
864C2×C4—1182no—
865C2×C4—1182no—
866C2×C4—1182no—
867C2×C4—1182no—
868C2×C4—2361no—
869C2×C4—2361no—
870C2×C4—2361no—
871C2×C4—2361no—
872C2×C4—2361no—
873C2×C4—2361no—
874C2×C4—2361no—
875C2×C4—2361no—
876C2×C4—2361no—
877C2×C4—2361no—
878C2×C4—2361no—
879C2×C4—2361no—
880C2×C4—2361no—
881C2×C4—2361no—
882C2×C4—2361no—
883C2×C4—2361no—
884C2×C4—2361no—
885C2×C4—2361no—
886C2×C4—2361no—
887C2×C4—2361no—
888C2×C4—2361no—
889C2×C4—2361no—
890C2×C4—2361no—
891C2×C4—2361no—
892C2×C4—2361no—
893C2×C4—2361no—
894C2×C4—2361no—
895C2×C4—2361no—
896C2×C4—2361no—
897C2×C4—2361no—
898C2×C4—2361no—
899C2×C4—2361no—
900C2×C4—2361no—
901C2×C4—2361no—
902C2×C4#1427368314yes—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22C2×#1427368311yescharacteristic
919C22C4×D4×D5911yescharacteristic
920C22C4×#1174568711yescharacteristic
921C22#1683787411yescharacteristic
922C22#1683788111yescharacteristic
923C22#1683788211yescharacteristic
924C22#1683788311yescharacteristic
925C22#1683797011yescharacteristic
926C22#1683797911yescharacteristic
927C22#1683798611yescharacteristic
928C22#1683799611yescharacteristic
929C22#1683800411yescharacteristic
930C22#1683800511yescharacteristic
931C22#1683800911yescharacteristic
932C22#1683801211yescharacteristic
933C22#1683801811yescharacteristic
934C22#1683801911yescharacteristic
935C22#1683801911yescharacteristic
936C22#1683802511yescharacteristic
937C22#1683803911yescharacteristic
938C22#1683803911yescharacteristic
939C22#1683805411yescharacteristic
940C22#1683805811yescharacteristic
941C22#1683808011yescharacteristic
942C22#1683808611yescharacteristic
943C22#1683808911yescharacteristic
944C22#1683809511yescharacteristic
945C22#1683809911yescharacteristic
946C22#1683810411yescharacteristic
947C22#1683813411yescharacteristic
948C22#1683813811yescharacteristic
949C22#1683814511yescharacteristic
950C22#1683814811yescharacteristic
951C22#1683814911yescharacteristic
952C22#1683815311yescharacteristic
953C4—24no—
954C4—42no—
955C4—42no—
956C4—42no—
957C4—81no—
958C4—81no—
959C4—1184no—
960C4—4721no—
961C4—4721no—
962C4—2362no—
963C4—2362no—
964C4—2362no—
965C4—2362no—
966C4—2362no—
967C2—82no—
968C2#2142670311yescharacteristic
969C2#2142678411yescharacteristic
970C2#2142687811yescharacteristic
971C2#2142702311yescharacteristic
972C2#2142706811yescharacteristic
973C2#2142709111yescharacteristic
974C2#2142726911yescharacteristic
975C2#2143083111yescharacteristic
976C2#2143084611yescharacteristic
977C2#2143086111yescharacteristic
978C2#2143102911yescharacteristic
979C2#2143137811yescharacteristic
980C2#2143139311yescharacteristic
981C2#2143162911yescharacteristic
982C2#2143164411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC59×#1439C2
socle, cosocleC24×C59C24
prime radicalC25×C59C23
hypercenter#1439D59
hypocenterC59#14412
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
3. C2×#16837267C2semidirect
4. #21422363C2semidirect
5. #21422354C2semidirect
10. #21422330C2semidirect
11. #21422330C2semidirect
12. #21422328C2semidirect
13. #21422327C2semidirect
14. Dic59⋊#95C2semidirect
28. #16837295C4semidirect
545. C59#14412semidirect

Maximal subgroups

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

subgroupindex
C2×#168372962
C2×#168372952
C2×#168372672
#214223632
#214223542
#214223432
#214223412
#214223392
#214223332
#214223302
#214223282
#214223272
Dic59⋊#952
C59×#14392
#1441259