Finite Group Databasebeta

← #28512779

Subgroups — #28512779

Order 15104.

1946 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273685C211yesmaximal, characteristic
2C2×#16837292C211yesmaximal, characteristic
3C2×#16837283C211yesmaximal, characteristic, complemented
4C2×#16837273C211yesmaximal, characteristic
5#21422352C211yesmaximal, characteristic, complemented
6#21422349C211yesmaximal, characteristic, complemented
7#21422344C211yesmaximal, characteristic
8#21422338C211yesmaximal, characteristic
9#21422334C211yesmaximal, characteristic
10#21422328C211yesmaximal, characteristic, complemented
11#21422328C211yesmaximal, characteristic, complemented
12#21422327C211yesmaximal, characteristic, complemented
13(C2×D59)⋊#95C211yesmaximal, characteristic
14C4×C59⋊#95C211yesmaximal, characteristic, complemented
15C2×C59×#389C211yesmaximal, characteristic, complemented
16C23×C4×D59C2211yescharacteristic
17C2×#14273685—24no—
18C2×#14273685—24no—
19C2×#14273685—24no—
20C22×C4⋊Dic59C2211yescharacteristic
21C22×Dic59⋊C4C2211yescharacteristic
22C22×(C2×D59)⋊C4C2211yescharacteristic
23C22×(C2×D59)⋊C4C2211yescharacteristic
24C22×(C2×D59)⋊C4C2211yescharacteristic
25C22×(C2×D59)⋊C4C2211yescharacteristic
26C22×(C2×D59)⋊C4C2211yescharacteristic
27C22×(C2×D59)⋊C4C2211yescharacteristic
28C22×C4×Dic59C2211yescharacteristic
29C22×C4×Dic59C2211yescharacteristic
30C22×C4×Dic59C2211yescharacteristic
31#16837292—24no—
32#16837283—24no—
33#16837273C418yescomplemented
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
48C2×C59⋊#95C2211yescharacteristic
49C2×C59⋊#95C2211yescharacteristic
50C22×C4⋊C4×C59C2211yescharacteristic
51C22×C4⋊C4×C59C2211yescharacteristic
52C22×C4⋊C4×C59C2211yescharacteristic
53C22×C4⋊C4×C59C2211yescharacteristic
54C22×C42×C59C2211yescharacteristic
55C59×#389—24no—
56C2×#95×C59C2211yescharacteristic
57C2×#95×C59C2211yescharacteristic
58C24×D59C2311yescharacteristic
59C23×Dic59C2311yescharacteristic
60C23×Dic59C2311yescharacteristic
61C23×Dic59C2311yescharacteristic
62C23×Dic59C2311yescharacteristic
63C23×Dic59C2311yescharacteristic
64C23×Dic59C2311yescharacteristic
65C23×Dic59C2311yescharacteristic
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×D59C2×C414yes—
73#14273685—232no—
74C2×C4⋊Dic59—22no—
75C2×C4⋊Dic59—22no—
76C2×C4⋊Dic59—22no—
77C2×Dic59⋊C4—22no—
78C2×Dic59⋊C4—22no—
79C2×Dic59⋊C4C2×C414yes—
80C2×(C2×D59)⋊C4—22no—
81C2×(C2×D59)⋊C4—22no—
82C2×(C2×D59)⋊C4—22no—
83C2×(C2×D59)⋊C4—22no—
84C2×(C2×D59)⋊C4—22no—
85C2×(C2×D59)⋊C4—22no—
86C2×(C2×D59)⋊C4—22no—
87C2×(C2×D59)⋊C4—22no—
88C2×(C2×D59)⋊C4—22no—
89C2×(C2×D59)⋊C4—22no—
90C2×(C2×D59)⋊C4—22no—
91C2×(C2×D59)⋊C4—22no—
92C2×(C2×D59)⋊C4—22no—
93C2×(C2×D59)⋊C4—41no—
94C2×(C2×D59)⋊C4—41no—
95C2×(C2×D59)⋊C4C2×C414yes—
96C2×(C2×D59)⋊C4C2×C414yes—
97C2×(C2×D59)⋊C4D414yes—
98C2×C4×Dic59—22no—
99C2×C4×Dic59—22no—
100C2×C4×Dic59—22no—
101C2×C4×Dic59—22no—
102C2×C4×Dic59—22no—
103C2×C4×Dic59—22no—
104C2×C4×Dic59—22no—
105C2×C4×Dic59—41no—
106C2×C4×Dic59D414yes—
107C59⋊#95—22no—
108C59⋊#95—22no—
109C59⋊#95—22no—
110C59⋊#95—22no—
111C59⋊#95—22no—
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—41no—
121C59⋊#95C2×C414yes—
122C59⋊#95C2×C414yes—
123C23×C4×C59C2311yescharacteristic
124C23×C4×C59C2311yescharacteristic
125C23×C4×C59C2311yescharacteristic
126C23×C4×C59C2311yescharacteristic
127C23×C4×C59C2311yescharacteristic
128C23×C4×C59C2311yescharacteristic
129C23×C4×C59C2311yescharacteristic
130C2×C4⋊C4×C59—22no—
131C2×C4⋊C4×C59—22no—
132C2×C4⋊C4×C59—22no—
133C2×C4⋊C4×C59—22no—
134C2×C4⋊C4×C59—22no—
135C2×C4⋊C4×C59—22no—
136C2×C4⋊C4×C59—22no—
137C2×C4⋊C4×C59—22no—
138C2×C4⋊C4×C59—22no—
139C2×C4⋊C4×C59—41no—
140C2×C4⋊C4×C59C2×C414yes—
141C2×C4⋊C4×C59D414yes—
142C2×C42×C59—22no—
143C2×C42×C59—22no—
144C2×C42×C59—41no—
145#95×C59—22no—
146#95×C59—22no—
147C24×C59C2411yescharacteristic
148C23×D59—21no—
149C23×D59—21no—
150C23×D59—21no—
151C23×D59—21no—
152C23×D59—21no—
153C23×D59—21no—
154C23×D59—21no—
155C23×D59—21no—
156C23×D59—21no—
157C23×D59—21no—
158C23×D59—21no—
159C23×D59—21no—
160C23×D59C22×C412yes—
161C23×D59C2×D412yes—
162C23×D59#4112yes—
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×C59C22×C412yes—
201C22×C4×C59C22×C412yes—
202C22×C4×C59C22×C412yes—
203C22×C4×C59C2×D412yes—
204C22×C4×C59C2×D412yes—
205C22×C4×C59C2×D412yes—
206C22×C4×C59C2×D412yes—
207C22×C4×C59C2×D412yes—
208C22×C4×C59#4112yes—
209C22×C4×C59#4112yes—
210C22×C4×C59#4112yes—
211C22×C4×C59#4112yes—
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×Dic59—21no—
251C22×Dic59—21no—
252C22×Dic59—21no—
253C22×Dic59C22×C412yes—
254C22×Dic59C22×C412yes—
255C22×Dic59C22×C412yes—
256C22×Dic59C2×D412yes—
257C22×Dic59C2×D412yes—
258C22×Dic59C2×D412yes—
259C22×Dic59#4112yes—
260C22×Dic59#4112yes—
261C2×C4×D59—28no—
262C2×C4×D59—28no—
263C2×C4×D59—28no—
264C2×C4×D59—28no—
265C2×C4×D59—28no—
266C2×C4×D59—28no—
267C2×C4×D59—28no—
268C4⋊C4×C59—28no—
269C4⋊C4×C59—28no—
270C4⋊C4×C59—44no—
271C4⋊C4×C59—44no—
272C42×C59—44no—
273(C2×D59)⋊C4—28no—
274(C2×D59)⋊C4—28no—
275(C2×D59)⋊C4—28no—
276(C2×D59)⋊C4—28no—
277(C2×D59)⋊C4—44no—
278(C2×D59)⋊C4—44no—
279C4⋊Dic59—28no—
280Dic59⋊C4—28no—
281C4×Dic59—28no—
282C4×Dic59—28no—
283C4×Dic59—44no—
284C23×C59C23×C411yescharacteristic
285C23×C59C22×D411yescharacteristic
286C23×C59C22×D411yescharacteristic
287C23×C59C22×D411yescharacteristic
288C23×C59C2×#4111yescharacteristic
289C23×C59C2×#4111yescharacteristic
290C23×C59C2×#4111yescharacteristic
291C23×C59C2×#4111yescharacteristic
292C23×C59C2×#4111yescharacteristic
293C23×C59C2×#4111yescharacteristic
294C23×C59C2×#4111yescharacteristic
295C23×C59H(5,𝔽2)11yescharacteristic
296C23×C592−1+411yescharacteristic
297C23×C592−1+411yescharacteristic
298C23×C592−1+411yescharacteristic
299C22×D59—22no—
300C22×D59—22no—
301C22×D59—22no—
302C22×D59—22no—
303C22×D59—22no—
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—41no—
318C22×D59—41no—
319C22×D59—41no—
320C22×D59—41no—
321C22×D59—41no—
322C22×D59—41no—
323C22×D59—41no—
324C22×D59—41no—
325C22×D59—41no—
326C22×D59—41no—
327C22×D59—41no—
328C22×D59—41no—
329C22×D59—41no—
330C22×D59—41no—
331C22×D59—41no—
332C22×D59—41no—
333C22×D59C4×D414yes—
334C2×C4×C59—22no—
335C2×C4×C59—22no—
336C2×C4×C59—22no—
337C2×C4×C59—22no—
338C2×C4×C59—22no—
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—22no—
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#11714yescomplemented
381C2×C4×C59C4×D414yes—
382C2×C4×C59#12014yes—
383C2×Dic59—22no—
384C2×Dic59—22no—
385C2×Dic59—22no—
386C2×Dic59—22no—
387C2×Dic59—22no—
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—41no—
405C2×Dic59—41no—
406C2×Dic59—41no—
407C2×Dic59—41no—
408C2×Dic59—41no—
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×Dic59C4×D414yes—
432C4×D59—232no—
433#14072—591nomaximal, Sylow
434C22×C59C2×#11711yescharacteristic
435C22×C59C2×C4×D411yescharacteristic
436C22×C59C2×C4×D411yescharacteristic
437C22×C59C2×C4×D411yescharacteristic
438C22×C59C4×#4111yescharacteristic
439C22×C59#51911yescharacteristic
440C22×C59#52011yescharacteristic
441C22×C59C2×#12011yescharacteristic
442C22×C59#52511yescharacteristic
443C22×C59#52511yescharacteristic
444C22×C59#52511yescharacteristic
445C22×C59#52911yescharacteristic
446C22×C59#52911yescharacteristic
447C22×C59#53211yescharacteristic
448C22×C59#53211yescharacteristic
449C22×C59#53611yescharacteristic
450C22×C59#53711yescharacteristic
451C22×C59#54111yescharacteristic
452C22×C59#54211yescharacteristic
453C22×C59#54611yescharacteristic
454C22×C59#54611yescharacteristic
455C22×C59#54711yescharacteristic
456C22×C59#54711yescharacteristic
457C22×C59#54711yescharacteristic
458C22×C59#54711yescharacteristic
459C22×C59#54811yescharacteristic
460C22×C59#54811yescharacteristic
461C22×C59#55111yescharacteristic
462C22×C59#55211yescharacteristic
463C22×C59#55211yescharacteristic
464C22×C59#55211yescharacteristic
465C22×C59#55211yescharacteristic
466C22×C59#55211yescharacteristic
467C22×C59#55311yescharacteristic
468C22×C59#55611yescharacteristic
469C2×D59—24no—
470C2×D59—24no—
471C2×D59—24no—
472C2×D59—42no—
473C2×D59—42no—
474C2×D59—42no—
475C2×D59—42no—
476C2×D59—42no—
477C2×D59—42no—
478C2×D59—42no—
479C2×D59—42no—
480C2×D59—42no—
481C2×D59—42no—
482C2×D59—42no—
483C2×D59—42no—
484C4×C59—24no—
485C4×C59—24no—
486C4×C59—24no—
487C4×C59—42no—
488C4×C59—42no—
489C4×C59—42no—
490C4×C59—81no—
491Dic59—24no—
492Dic59—42no—
493Dic59—42no—
494Dic59—42no—
495Dic59—42no—
496Dic59—42no—
497Dic59—81no—
498C22×#117—591no—
499C2×#389D5911yescharacteristic, complemented
500C2×#388—591no—
501C2×#387—591no—
502C2×#385—591no—
503#1442—591no—
504#1441—591no—
505#1440—591no—
506#1439—591no—
507#1437—591no—
508#1436—591no—
509#1436—591no—
510#1436—591no—
511C22⋊#95—591no—
512C4×#95—591no—
513C2×C59#229311yescharacteristic
514C2×C59C4×#12011yescharacteristic
515C2×C59#232311yescharacteristic
516C2×C59#234411yescharacteristic
517C2×C59#235211yescharacteristic
518C2×C59#235911yescharacteristic
519C2×C59#236211yescharacteristic
520C2×C59#243011yescharacteristic
521C2×C59#243211yescharacteristic
522C2×C59#247011yescharacteristic
523C2×C59#247511yescharacteristic
524C2×C59#247711yescharacteristic
525C2×C59#247811yescharacteristic
526C2×C59#260111yescharacteristic
527C2×C59#261111yescharacteristic
528D59—44no—
529C24×C4—591no—
530C2×#117—1184no—
531C2×#117—1184no—
532C2×#117—1184no—
533C22×C4⋊C4—591no—
534C22×C4⋊C4—591no—
535C22×C4⋊C4C2×D5911yescharacteristic
536C22×C4⋊C4C2×D5911yescharacteristic
537C22×C4⋊C4C2×D5911yescharacteristic
538C22×C4⋊C4C2×D5911yescharacteristic
539C22×C22⋊C4—591no—
540C22×C22⋊C4—591no—
541C22×C22⋊C4—591no—
542C22×C22⋊C4—591no—
543C22×C22⋊C4—591no—
544C22×C22⋊C4—591no—
545C22×C42—591no—
546C22×C42—591no—
547C22×C42—591no—
548C22×C42C2×D5911yescharacteristic
549#389—24no—
550#388—1184no—
551#387—1184no—
552#385—598no—
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×#95C2×D5911yescharacteristic
570C2×#95C2×D5911yescharacteristic
571C59#1407211yescharacteristic, complemented, Sylow
572C25—591no—
573C23×C4—591no—
574C23×C4—591no—
575C23×C4—591no—
576C23×C4—591no—
577C23×C4—591no—
578C23×C4—591no—
579C23×C4—594no—
580C23×C4—591no—
581C23×C4—1182no—
582C23×C4—1182no—
583C23×C4—1182no—
584C23×C4—1182no—
585C23×C4—1182no—
586C23×C4—1182no—
587C23×C4C22×D5911yescharacteristic
588C23×C4C22×D5911yescharacteristic
589C23×C4C22×D5911yescharacteristic
590C23×C4C22×D5911yescharacteristic
591C23×C4C22×D5911yescharacteristic
592C23×C4C22×D5911yescharacteristic
593C23×C4C22×D5911yescharacteristic
594#117—11832no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—41no—
605C2×C4⋊C4—594no—
606C2×C4⋊C4—1182no—
607C2×C4⋊C4—1182no—
608C2×C4⋊C4—1182no—
609C2×C4⋊C4—1182no—
610C2×C4⋊C4—1182no—
611C2×C4⋊C4C4×D5914yes—
612C2×C4⋊C4C22⋊D5914yes—
613C2×C22⋊C4—594no—
614C2×C22⋊C4—594no—
615C2×C22⋊C4—594no—
616C2×C22⋊C4—1182no—
617C2×C22⋊C4—1182no—
618C2×C22⋊C4—1182no—
619C2×C22⋊C4—1182no—
620C2×C22⋊C4—1182no—
621C2×C22⋊C4—1182no—
622C2×C22⋊C4—1182no—
623C2×C22⋊C4—1182no—
624C2×C22⋊C4—1182no—
625C2×C22⋊C4—1182no—
626C2×C22⋊C4—1182no—
627C2×C22⋊C4—1182no—
628C2×C22⋊C4—1182no—
629C2×C22⋊C4—2361no—
630C2×C22⋊C4—2361no—
631C2×C42—22no—
632C2×C42—22no—
633C2×C42—41no—
634C2×C42—594no—
635C2×C42—1182no—
636C2×C42—1182no—
637C2×C42—1182no—
638C2×C42—1182no—
639C2×C42—1182no—
640C2×C42—1182no—
641C2×C42—1182no—
642C2×C42—2361no—
643#95—22no—
644#95—22no—
645#95—594no—
646#95—594no—
647#95—1182no—
648#95—1182no—
649#95—1182no—
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—1182no—
660#95—2361no—
661C24—592no—
662C24—592no—
663C24—592no—
664C24—1181no—
665C24—1181no—
666C24—1181no—
667C24—1181no—
668C24—1181no—
669C24—1181no—
670C24—1181no—
671C24—1181no—
672C24—1181no—
673C24—1181no—
674C24—1181no—
675C24—1181no—
676C24C23×D5911yescharacteristic
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
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—592no—
715C22×C4—592no—
716C22×C4—592no—
717C22×C4—592no—
718C22×C4—592no—
719C22×C4—592no—
720C22×C4—592no—
721C22×C4—592no—
722C22×C4—1188no—
723C22×C4—1188no—
724C22×C4—1188no—
725C22×C4—1188no—
726C22×C4—1188no—
727C22×C4—1188no—
728C22×C4—1181no—
729C22×C4—1181no—
730C22×C4—1181no—
731C22×C4—1181no—
732C22×C4—1188no—
733C22×C4—1181no—
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—1181no—
769C22×C4—1181no—
770C22×C4C2×C4×D5912yes—
771C22×C4C2×C4×D5912yes—
772C22×C4C2×C4×D5912yes—
773C22×C4#1174568512yes—
774C22×C4D4×D5912yes—
775C22×C4D4×D5912yes—
776C22×C4#1174568712yes—
777C22×C4#1174568912yes—
778C22×C4#1174568912yes—
779C22×C4C2×C22⋊D5912yes—
780C22×C4C2×C22⋊D5912yes—
781C22×C4C2×C22⋊D5912yes—
782C4⋊C4—28no—
783C4⋊C4—28no—
784C4⋊C4—44no—
785C4⋊C4—44no—
786C4⋊C4—1188no—
787C4⋊C4—1188no—
788C22⋊C4—1188no—
789C22⋊C4—1188no—
790C22⋊C4—1188no—
791C22⋊C4—1188no—
792C22⋊C4—2364no—
793C22⋊C4—2364no—
794C42—44no—
795C42—1188no—
796C42—1188no—
797C42—2364no—
798C23—594no—
799C23—1182no—
800C23—1182no—
801C23—1182no—
802C23—1182no—
803C23—1182no—
804C23—1182no—
805C23—1182no—
806C23—1182no—
807C23—1182no—
808C23—1182no—
809C23—1182no—
810C23—1182no—
811C23—1182no—
812C23—1182no—
813C23—1182no—
814C23—1182no—
815C23—1182no—
816C23—1182no—
817C23—2361no—
818C23—2361no—
819C23—2361no—
820C23—2361no—
821C23—2361no—
822C23—2361no—
823C23—2361no—
824C23—2361no—
825C23—2361no—
826C23—2361no—
827C23—2361no—
828C23—2361no—
829C23—2361no—
830C23—2361no—
831C23—2361no—
832C23—2361no—
833C23C22×C4×D5911yescharacteristic
834C23C2×D4×D5911yescharacteristic
835C23C2×D4×D5911yescharacteristic
836C23C22×C22⋊D5911yescharacteristic
837C23#41×D5911yescharacteristic
838C23#41×D5911yescharacteristic
839C23#41×D5911yescharacteristic
840C23C2×#1174568711yescharacteristic
841C23C2×#1174568511yescharacteristic
842C23C2×#1174568911yescharacteristic
843C23C2×#1174568911yescharacteristic
844C23#1427377211yescharacteristic
845C23#1427377411yescharacteristic
846C23#1427377511yescharacteristic
847C23#1427377511yescharacteristic
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
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—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
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—594no—
895C2×C4—11832no—
896C2×C4—1182no—
897C2×C4—1182no—
898C2×C4—1182no—
899C2×C4—1182no—
900C2×C4—1182no—
901C2×C4—1182no—
902C2×C4—1182no—
903C2×C4—1182no—
904C2×C4—1182no—
905C2×C4—1182no—
906C2×C4—1182no—
907C2×C4—1182no—
908C2×C4—1182no—
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—2361no—
918C2×C4—2361no—
919C2×C4—2361no—
920C2×C4—2361no—
921C2×C4—2361no—
922C2×C4—2361no—
923C2×C4—2361no—
924C2×C4—2361no—
925C2×C4—2361no—
926C2×C4—2361no—
927C2×C4—2361no—
928C2×C4—2361no—
929C2×C4—2361no—
930C2×C4—2361no—
931C2×C4—2361no—
932C2×C4—2361no—
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#1427368514yescomplemented
945C2×C4C4×C22⋊D5914yes—
946C2×C4#1427369514yes—
947C22—1184no—
948C22—1184no—
949C22—1184no—
950C22—2362no—
951C22—2362no—
952C22—2362no—
953C22—2362no—
954C22—2362no—
955C22—2362no—
956C22—2362no—
957C22—2362no—
958C22—2362no—
959C22—2362no—
960C22—2362no—
961C22—2362no—
962C22C2×#1427368511yescharacteristic
963C22C4×D4×D5911yescharacteristic
964C22C4×D4×D5911yescharacteristic
965C22C2×C4×C22⋊D5911yescharacteristic
966C22C4×#1174568911yescharacteristic
967C22#1683787811yescharacteristic
968C22#1683788311yescharacteristic
969C22C2×#1427369511yescharacteristic
970C22#1683790911yescharacteristic
971C22#1683791111yescharacteristic
972C22#1683791111yescharacteristic
973C22#1683793711yescharacteristic
974C22#1683793811yescharacteristic
975C22#1683794711yescharacteristic
976C22#1683795311yescharacteristic
977C22#1683797711yescharacteristic
978C22#1683797911yescharacteristic
979C22#1683801111yescharacteristic
980C22#1683802211yescharacteristic
981C22#1683804111yescharacteristic
982C22#1683804611yescharacteristic
983C22#1683805111yescharacteristic
984C22#1683805211yescharacteristic
985C22#1683805511yescharacteristic
986C22#1683805511yescharacteristic
987C22#1683806311yescharacteristic
988C22#1683806311yescharacteristic
989C22#1683807911yescharacteristic
990C22#1683808411yescharacteristic
991C22#1683808611yescharacteristic
992C22#1683808711yescharacteristic
993C22#1683809011yescharacteristic
994C22#1683809311yescharacteristic
995C22#1683810011yescharacteristic
996C22#1683812511yescharacteristic
997C4—24no—
998C4—24no—
999C4—24no—
1000C4—42no—
1001C4—42no—
1002C4—42no—
1003C4—81no—
1004C4—1184no—
1005C4—4721no—
1006C4—2362no—
1007C4—2362no—
1008C4—2362no—
1009C4—2362no—
1010C4—2362no—
1011C2—2364no—
1012C2#2142655411yescharacteristic
1013C2C4×#1427369511yescharacteristic
1014C2#2142677311yescharacteristic
1015C2#2142696411yescharacteristic
1016C2#2142702111yescharacteristic
1017C2#2142708311yescharacteristic
1018C2#2142711911yescharacteristic
1019C2#2142770211yescharacteristic
1020C2#2142772111yescharacteristic
1021C2#2142819811yescharacteristic
1022C2#2142826311yescharacteristic
1023C2#2142829311yescharacteristic
1024C2#2142831811yescharacteristic
1025C2#2142969211yescharacteristic
1026C2#2142979311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC2×C59×#389C2
socle, cosocleC24×C59C24
prime radicalC24×D59C23
hypercenterC2×#389D59
hypocenterC59#14072
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
3. C2×#16837283C2semidirect
5. #21422352C2semidirect
6. #21422349C2semidirect
10. #21422328C2semidirect
11. #21422328C2semidirect
12. #21422327C2semidirect
14. C4×C59⋊#95C2semidirect
15. C2×C59×#389C2semidirect
33. #16837273C4semidirect
380. C2×C4×C59#117semidirect
499. C2×#389D59semidirect
571. C59#14072semidirect
944. C2×C4#14273685semidirect

Maximal subgroups

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

subgroupindex
C22×#142736852
C2×#168372922
C2×#168372832
C2×#168372732
#214223522
#214223492
#214223442
#214223382
#214223342
#214223282
#214223272
(C2×D59)⋊#952
C4×C59⋊#952
C2×C59×#3892
#1407259