Finite Group Databasebeta

← #28519747

Subgroups — #28519747

Order 15104.

1602 conjugacy classes of subgroups.

The subgroup lattice has 1126 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837278C211yesmaximal, characteristic
2#21422357C211yesmaximal, characteristic, complemented
3#21422356C211yesmaximal, characteristic, complemented
4#21422354C211yesmaximal, characteristic, complemented
5#21422352C211yesmaximal, characteristic, complemented
6#21422343C211yesmaximal, characteristic, complemented
7#21422342C211yesmaximal, characteristic, complemented
8#21422341C211yesmaximal, characteristic, complemented
9#21422340C211yesmaximal, characteristic, complemented
10#21422339C211yesmaximal, characteristic, complemented
11#21422335C211yesmaximal, characteristic
12#21422335C211yesmaximal, characteristic
13(C2×D59)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D59)⋊#95C211yesmaximal, characteristic, complemented
15C59×#1440C211yesmaximal, characteristic, complemented
16C23×C22⋊D59C2211yescharacteristic
17C23×C4×D59C2211yescharacteristic
18C22×C4⋊Dic59C2211yescharacteristic
19C22×Dic59⋊C4C2211yescharacteristic
20C22×C22⋊Dic59C2211yescharacteristic
21C22×C22⋊Dic59C2211yescharacteristic
22C22×C22⋊Dic59C2211yescharacteristic
23C22×(C2×D59)⋊C4C2211yescharacteristic
24C22×(C2×D59)⋊C4C2211yescharacteristic
25C22×(C2×D59)⋊C4C2211yescharacteristic
26C22×(C2×D59)⋊C4C2211yescharacteristic
27C22×(C2×D59)⋊C4C2211yescharacteristic
28#16837278C418yescomplemented
29C2×C59⋊#95C2211yescharacteristic
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
45C22×C22⋊C4×C59C2211yescharacteristic
46C22×C22⋊C4×C59C2211yescharacteristic
47C22×C22⋊C4×C59C2211yescharacteristic
48C2×#95×C59C2211yescharacteristic
49C2×#95×C59C2211yescharacteristic
50C2×#95×C59C2211yescharacteristic
51C2×#95×C59C2211yescharacteristic
52C24×D59C2311yescharacteristic
53C22×C22⋊D59—22no—
54C22×C22⋊D59—22no—
55C22×C22⋊D59—41no—
56C22×C22⋊D59—41no—
57C22×C22⋊D59—41no—
58C22×C22⋊D59—41no—
59C22×C22⋊D59C2×C414yes—
60C23×Dic59C2311yescharacteristic
61C23×Dic59C2311yescharacteristic
62C23×Dic59C2311yescharacteristic
63C23×Dic59C2311yescharacteristic
64C23×Dic59C2311yescharacteristic
65C23×Dic59C2311yescharacteristic
66C23×Dic59C2311yescharacteristic
67C22×C4×D59—41no—
68C22×C4×D59—41no—
69C22×C4×D59—41no—
70C22×C4×D59—41no—
71C22×C4×D59—41no—
72C22×C4×D59—41no—
73C22×C4×D59C2×C414yes—
74C2×C4⋊Dic59—41no—
75C2×C4⋊Dic59—41no—
76C2×C4⋊Dic59—41no—
77C2×Dic59⋊C4—41no—
78C2×Dic59⋊C4—41no—
79C2×Dic59⋊C4—41no—
80C2×C22⋊Dic59—41no—
81C2×C22⋊Dic59—41no—
82C2×C22⋊Dic59—41no—
83C2×C22⋊Dic59—41no—
84C2×C22⋊Dic59—41no—
85C2×C22⋊Dic59—41no—
86C2×C22⋊Dic59—41no—
87C2×C22⋊Dic59—41no—
88C2×C22⋊Dic59C2×C414yes—
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)⋊C4—41no—
96C2×(C2×D59)⋊C4—41no—
97C2×(C2×D59)⋊C4—41no—
98C2×(C2×D59)⋊C4—41no—
99C2×(C2×D59)⋊C4—41no—
100C2×(C2×D59)⋊C4—41no—
101C2×(C2×D59)⋊C4—41no—
102C2×(C2×D59)⋊C4—41no—
103C2×(C2×D59)⋊C4C2×C414yes—
104C59⋊#95—41no—
105C59⋊#95—41no—
106C59⋊#95—41no—
107C59⋊#95—41no—
108C59⋊#95—41no—
109C59⋊#95—41no—
110C59⋊#95—41no—
111C59⋊#95—41no—
112C59⋊#95—41no—
113C59⋊#95—41no—
114C59⋊#95—41no—
115C59⋊#95—41no—
116C59⋊#95—41no—
117C59⋊#95—41no—
118C59⋊#95C2×C414yes—
119C59⋊#95C2×C414yes—
120C25×C59C2311yescharacteristic
121C23×C4×C59C2311yescharacteristic
122C23×C4×C59C2311yescharacteristic
123C23×C4×C59C2311yescharacteristic
124C23×C4×C59C2311yescharacteristic
125C23×C4×C59C2311yescharacteristic
126C23×C4×C59C2311yescharacteristic
127C2×C22⋊C4×C59—41no—
128C2×C22⋊C4×C59—41no—
129C2×C22⋊C4×C59—41no—
130C2×C22⋊C4×C59—41no—
131C2×C22⋊C4×C59—41no—
132C2×C22⋊C4×C59—41no—
133C2×C22⋊C4×C59—41no—
134C2×C22⋊C4×C59—41no—
135C2×C22⋊C4×C59C2×C414yes—
136#95×C59—41no—
137#95×C59—41no—
138#95×C59—41no—
139#95×C59—41no—
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×C59—21no—
149C24×C59—21no—
150C24×C59—21no—
151C24×C59—21no—
152C24×C59—21no—
153C24×C59—21no—
154C24×C59C22×C412yes—
155C24×C59C2411yescharacteristic
156C23×D59—21no—
157C23×D59—21no—
158C23×D59—21no—
159C23×D59—21no—
160C23×D59—21no—
161C23×D59—21no—
162C23×D59—21no—
163C23×D59—21no—
164C23×D59—21no—
165C23×D59—21no—
166C23×D59—21no—
167C23×D59—21no—
168C23×D59C22×C412yes—
169C23×D59#4112yes—
170C23×D59#4112yes—
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×C59—21no—
202C22×C4×C59—21no—
203C22×C4×C59—21no—
204C22×C4×C59—21no—
205C22×C4×C59—21no—
206C22×C4×C59—21no—
207C22×C4×C59—21no—
208C22×C4×C59—21no—
209C22×C4×C59—21no—
210C22×C4×C59—21no—
211C22×C4×C59C22×C412yes—
212C22×C4×C59C22×C412yes—
213C2×C22⋊D59—28no—
214C2×C22⋊D59—44no—
215C2×C22⋊D59—44no—
216C2×C22⋊D59—44no—
217C2×C22⋊D59—44no—
218C2×C22⋊D59—44no—
219C2×C22⋊D59—44no—
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×Dic59—21no—
254C22×Dic59—21no—
255C22×Dic59—21no—
256C22×Dic59—21no—
257C22×Dic59—21no—
258C22×Dic59—21no—
259C22×Dic59—21no—
260C22×Dic59—21no—
261C22×Dic59—21no—
262C22×Dic59—21no—
263C22×Dic59—21no—
264C22×Dic59—21no—
265C22×Dic59—21no—
266C22×Dic59C22×C412yes—
267C22×Dic59C22×C412yes—
268C22×Dic59C22×C412yes—
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—
276C22⋊C4×C59—44no—
277C22⋊C4×C59—44no—
278C22⋊C4×C59—44no—
279C22⋊Dic59—44no—
280C22⋊Dic59—44no—
281C22⋊Dic59—44no—
282(C2×D59)⋊C4—44no—
283(C2×D59)⋊C4—44no—
284(C2×D59)⋊C4—44no—
285(C2×D59)⋊C4—44no—
286(C2×D59)⋊C4—44no—
287C4⋊Dic59—44no—
288Dic59⋊C4—44no—
289C23×C59—22no—
290C23×C59—22no—
291C23×C59—22no—
292C23×C59—22no—
293C23×C59—22no—
294C23×C59—22no—
295C23×C59—22no—
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—41no—
307C23×C59—41no—
308C23×C59—41no—
309C23×C59—41no—
310C23×C59—41no—
311C23×C59—41no—
312C23×C59—41no—
313C23×C59—41no—
314C23×C59—41no—
315C23×C59—41no—
316C23×C59—41no—
317C23×C59—41no—
318C23×C59—41no—
319C23×C59—41no—
320C23×C59—41no—
321C23×C59—41no—
322C23×C59—41no—
323C23×C59—41no—
324C23×C59C23×C411yescharacteristic
325C23×C59C2×#4111yescharacteristic
326C23×C59C2×#4111yescharacteristic
327C23×C59H(5,𝔽2)11yescharacteristic
328C23×C59H(5,𝔽2)11yescharacteristic
329C23×C59H(5,𝔽2)11yescharacteristic
330C23×C59H(5,𝔽2)11yescharacteristic
331C23×C59H(5,𝔽2)11yescharacteristic
332C23×C59H(5,𝔽2)11yescharacteristic
333C23×C59H(5,𝔽2)11yescharacteristic
334C23×C59H(5,𝔽2)11yescharacteristic
335C23×C59H(5,𝔽2)11yescharacteristic
336C23×C59H(5,𝔽2)11yescharacteristic
337C23×C592−1+411yescharacteristic
338C23×C592−1+411yescharacteristic
339C22×D59—22no—
340C22×D59—22no—
341C22×D59—22no—
342C22×D59—22no—
343C22×D59—22no—
344C22×D59—22no—
345C22×D59—22no—
346C22×D59—22no—
347C22×D59—22no—
348C22×D59—22no—
349C22×D59—22no—
350C22×D59—22no—
351C22×D59—22no—
352C22×D59—22no—
353C22×D59—22no—
354C22×D59—22no—
355C22×D59—22no—
356C22×D59—22no—
357C22×D59—41no—
358C22×D59—41no—
359C22×D59—41no—
360C22×D59—41no—
361C22×D59—41no—
362C22×D59—41no—
363C22×D59—41no—
364C22×D59—41no—
365C22×D59—41no—
366C22×D59—41no—
367C22×D59—41no—
368C22×D59—41no—
369C22×D59—41no—
370C22×D59—41no—
371C22×D59—41no—
372C22×D59—41no—
373C22×D59#11714yes—
374C2×C4×C59—22no—
375C2×C4×C59—22no—
376C2×C4×C59—22no—
377C2×C4×C59—22no—
378C2×C4×C59—22no—
379C2×C4×C59—22no—
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×C59—41no—
388C2×C4×C59—41no—
389C2×C4×C59—41no—
390C2×C4×C59—41no—
391C2×C4×C59—41no—
392C2×C4×C59—41no—
393C2×C4×C59—41no—
394C2×C4×C59—41no—
395C2×C4×C59—41no—
396C2×C4×C59—41no—
397C2×C4×C59—41no—
398C2×C4×C59—41no—
399C2×C4×C59—41no—
400C2×C4×C59—41no—
401C2×C4×C59—41no—
402C2×C4×C59—41no—
403C2×C4×C59—41no—
404C2×C4×C59—41no—
405C2×C4×C59—41no—
406C2×C4×C59—41no—
407C2×C4×C59—41no—
408C2×C4×C59—41no—
409C2×C4×C59—41no—
410C2×C4×C59—41no—
411C2×C4×C59—41no—
412C2×C4×C59—41no—
413C2×C4×C59—41no—
414C2×C4×C59—41no—
415C2×C4×C59—41no—
416C22⋊D59—416no—
417C2×Dic59—22no—
418C2×Dic59—22no—
419C2×Dic59—22no—
420C2×Dic59—22no—
421C2×Dic59—22no—
422C2×Dic59—22no—
423C2×Dic59—22no—
424C2×Dic59—22no—
425C2×Dic59—22no—
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×Dic59—41no—
437C2×Dic59—41no—
438C2×Dic59—41no—
439C2×Dic59—41no—
440C2×Dic59—41no—
441C2×Dic59—41no—
442C2×Dic59—41no—
443C2×Dic59—41no—
444C2×Dic59—41no—
445C2×Dic59—41no—
446C2×Dic59—41no—
447C2×Dic59—41no—
448C2×Dic59—41no—
449C2×Dic59—41no—
450C2×Dic59—41no—
451C2×Dic59—41no—
452C2×Dic59—41no—
453C2×Dic59—41no—
454C2×Dic59—41no—
455C2×Dic59—41no—
456C2×Dic59—41no—
457C2×Dic59—41no—
458C2×Dic59—41no—
459C2×Dic59—41no—
460C2×Dic59—41no—
461C2×Dic59—41no—
462C2×Dic59—41no—
463C2×Dic59—41no—
464C2×Dic59—41no—
465C2×Dic59—41no—
466C4×D59—416no—
467#14666—591nomaximal, Sylow
468C22×C59—42no—
469C22×C59—42no—
470C22×C59—42no—
471C22×C59—42no—
472C22×C59—42no—
473C22×C59—42no—
474C22×C59—42no—
475C22×C59—81no—
476C22×C59—81no—
477C22×C59—81no—
478C22×C59—81no—
479C22×C59—81no—
480C22×C59—81no—
481C22×C59—81no—
482C22×C59—81no—
483C22×C59C2×#11711yescharacteristic
484C22×C59#51811yescharacteristic
485C22×C59#51811yescharacteristic
486C22×C59#51811yescharacteristic
487C22×C59#51811yescharacteristic
488C22×C59#52011yescharacteristic
489C22×C59#52011yescharacteristic
490C22×C59#53811yescharacteristic
491C22×C59#53811yescharacteristic
492C22×C59#53811yescharacteristic
493C22×C59#53811yescharacteristic
494C22×C59#53811yescharacteristic
495C22×C59#53811yescharacteristic
496C22×C59#53811yescharacteristic
497C22×C59#53811yescharacteristic
498C22×C59#53911yescharacteristic
499C22×C59#53911yescharacteristic
500C22×C59#53911yescharacteristic
501C22×C59#53911yescharacteristic
502C22×C59#56011yescharacteristic
503C22×C59#56011yescharacteristic
504C22×C59#56011yescharacteristic
505C22×C59#56011yescharacteristic
506C22×C59#56011yescharacteristic
507C22×C59#56011yescharacteristic
508C22×C59#56011yescharacteristic
509C22×C59#56011yescharacteristic
510C22×C59H(3,𝔽4)11yescharacteristic
511C22×C59#56211yescharacteristic
512C22×C59#56211yescharacteristic
513C22×C59#56211yescharacteristic
514C22×C59#56211yescharacteristic
515C22×C59#56211yescharacteristic
516C22×C59#56211yescharacteristic
517C22×C59#56311yescharacteristic
518C2×D59—24no—
519C2×D59—24no—
520C2×D59—24no—
521C2×D59—42no—
522C2×D59—42no—
523C2×D59—42no—
524C2×D59—42no—
525C2×D59—42no—
526C2×D59—42no—
527C2×D59—42no—
528C2×D59—42no—
529C2×D59—42no—
530C2×D59—42no—
531C2×D59—42no—
532C2×D59—42no—
533C4×C59—42no—
534C4×C59—42no—
535C4×C59—81no—
536C4×C59—81no—
537C4×C59—81no—
538C4×C59—81no—
539Dic59—42no—
540Dic59—42no—
541Dic59—42no—
542Dic59—81no—
543Dic59—81no—
544Dic59—81no—
545Dic59—81no—
546C2×#386—591no—
547#1443—591no—
548#1443—591no—
549#1442—591no—
550#1442—591no—
551#1440—591no—
552#1440D5911yescharacteristic, complemented
553#1439—591no—
554#1439—591no—
555#1439—591no—
556#1439—591no—
557#1438—591no—
558#1438—591no—
559C22⋊#95—591no—
560C22⋊#95—591no—
561C2×C59—82no—
562C2×C59#231211yescharacteristic
563C2×C59#231811yescharacteristic
564C2×C59#231811yescharacteristic
565C2×C59#237511yescharacteristic
566C2×C59#237611yescharacteristic
567C2×C59#237711yescharacteristic
568C2×C59#237711yescharacteristic
569C2×C59#282411yescharacteristic
570C2×C59#282411yescharacteristic
571C2×C59#282511yescharacteristic
572C2×C59#282511yescharacteristic
573C2×C59#282611yescharacteristic
574C2×C59#282611yescharacteristic
575C2×C59#282711yescharacteristic
576C2×C59#282711yescharacteristic
577D59—44no—
578C23×D4—591no—
579C24×C4—591no—
580C22×C4⋊C4—591no—
581C22×C4⋊C4—591no—
582C22×C22⋊C4—591no—
583C22×C22⋊C4—591no—
584C22×C22⋊C4—591no—
585C22×C22⋊C4—591no—
586C22×C22⋊C4—591no—
587C22×C22⋊C4—591no—
588C22×C22⋊C4—591no—
589C22×C22⋊C4—591no—
590C22×C22⋊C4C2×D5911yescharacteristic
591C22×C22⋊C4C2×D5911yescharacteristic
592C22×C22⋊C4C2×D5911yescharacteristic
593#386—598no—
594C2×#95—591no—
595C2×#95—591no—
596C2×#95—591no—
597C2×#95—591no—
598C2×#95—591no—
599C2×#95—591no—
600C2×#95—591no—
601C2×#95—591no—
602C2×#95—591no—
603C2×#95—591no—
604C2×#95—591no—
605C2×#95—591no—
606C2×#95—591no—
607C2×#95—591no—
608C2×#95—591no—
609C2×#95—591no—
610C2×#95C2×D5911yescharacteristic
611C2×#95C2×D5911yescharacteristic
612C2×#95C2×D5911yescharacteristic
613C2×#95C2×D5911yescharacteristic
614C59#1466611yescharacteristic, complemented, Sylow
615C25—591no—
616C25C22×D5911yescharacteristic
617C22×D4—594no—
618C22×D4—1182no—
619C22×D4—1182no—
620C22×D4—2361no—
621C22×D4—2361no—
622C22×D4—2361no—
623C22×D4—2361no—
624C23×C4—591no—
625C23×C4—591no—
626C23×C4—591no—
627C23×C4—594no—
628C23×C4—591no—
629C23×C4—591no—
630C23×C4—591no—
631C23×C4—591no—
632C23×C4—2361no—
633C23×C4—2361no—
634C23×C4—2361no—
635C23×C4—2361no—
636C23×C4—2361no—
637C23×C4—2361no—
638C23×C4C22×D5911yescharacteristic
639C23×C4C22×D5911yescharacteristic
640C23×C4C22×D5911yescharacteristic
641C23×C4C22×D5911yescharacteristic
642C23×C4C22×D5911yescharacteristic
643C23×C4C22×D5911yescharacteristic
644C2×C4⋊C4—2361no—
645C2×C4⋊C4—2361no—
646C2×C4⋊C4—2361no—
647C2×C4⋊C4—2361no—
648C2×C4⋊C4—2361no—
649C2×C4⋊C4—2361no—
650C2×C22⋊C4—41no—
651C2×C22⋊C4—41no—
652C2×C22⋊C4—41no—
653C2×C22⋊C4—41no—
654C2×C22⋊C4—41no—
655C2×C22⋊C4—41no—
656C2×C22⋊C4—41no—
657C2×C22⋊C4—41no—
658C2×C22⋊C4—594no—
659C2×C22⋊C4—594no—
660C2×C22⋊C4—1182no—
661C2×C22⋊C4—1182no—
662C2×C22⋊C4—1182no—
663C2×C22⋊C4—1182no—
664C2×C22⋊C4—2361no—
665C2×C22⋊C4—2361no—
666C2×C22⋊C4—2361no—
667C2×C22⋊C4—2361no—
668C2×C22⋊C4—2361no—
669C2×C22⋊C4—2361no—
670C2×C22⋊C4—2361no—
671C2×C22⋊C4—2361no—
672C2×C22⋊C4—2361no—
673C2×C22⋊C4—2361no—
674C2×C22⋊C4—2361no—
675C2×C22⋊C4—2361no—
676C2×C22⋊C4—2361no—
677C2×C22⋊C4—2361no—
678C2×C22⋊C4—2361no—
679C2×C22⋊C4—2361no—
680C2×C22⋊C4—2361no—
681C2×C22⋊C4—2361no—
682C2×C22⋊C4C4×D5914yes—
683#95—41no—
684#95—41no—
685#95—41no—
686#95—41no—
687#95—594no—
688#95—594no—
689#95—2361no—
690#95—2361no—
691#95—2361no—
692#95—2361no—
693#95—2361no—
694#95—2361no—
695#95—2361no—
696#95—2361no—
697#95—2361no—
698#95—2361no—
699#95—2361no—
700#95—2361no—
701#95—2361no—
702#95—2361no—
703C24—21no—
704C24—21no—
705C24—21no—
706C24—21no—
707C24—21no—
708C24—21no—
709C24—21no—
710C24—21no—
711C24—21no—
712C24—21no—
713C24—21no—
714C24—21no—
715C24—21no—
716C24—21no—
717C24—592no—
718C24—592no—
719C24—592no—
720C24—1181no—
721C24—1181no—
722C24—1181no—
723C24—1181no—
724C24—1181no—
725C24—1181no—
726C24—1181no—
727C24—1181no—
728C24—1181no—
729C24—1181no—
730C24—1181no—
731C24—1181no—
732C24C2×C4×D5912yes—
733C24C23×D5911yescharacteristic
734C2×D4—1188no—
735C2×D4—2364no—
736C2×D4—2364no—
737C2×D4—2364no—
738C2×D4—2364no—
739C2×D4—2364no—
740C2×D4—2364no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—592no—
782C22×C4—592no—
783C22×C4—592no—
784C22×C4—1181no—
785C22×C4—1181no—
786C22×C4—1181no—
787C22×C4—1181no—
788C22×C4—1181no—
789C22×C4—1181no—
790C22×C4—1181no—
791C22×C4—1181no—
792C22×C4—1181no—
793C22×C4—1181no—
794C22×C4—1181no—
795C22×C4—1181no—
796C22×C4—1181no—
797C22×C4—1181no—
798C22×C4—1181no—
799C22×C4—1181no—
800C22×C4—1181no—
801C22×C4—1181no—
802C22×C4—1181no—
803C22×C4—1181no—
804C22×C4—1181no—
805C22×C4—1181no—
806C22×C4—1181no—
807C22×C4—1181no—
808C22×C4—1181no—
809C22×C4—1181no—
810C22×C4—1181no—
811C22×C4—1181no—
812C22×C4—1181no—
813C22×C4—1181no—
814C22×C4—1181no—
815C22×C4—1181no—
816C22×C4—1181no—
817C22×C4—1181no—
818C22×C4—1181no—
819C22×C4—1181no—
820C22×C4—1181no—
821C22×C4—1181no—
822C22×C4—1181no—
823C22×C4—1181no—
824C22×C4—1181no—
825C22×C4—1181no—
826C22×C4—1181no—
827C22×C4—1181no—
828C22×C4—1181no—
829C22×C4—1181no—
830C22×C4—2364no—
831C22×C4—2364no—
832C22×C4—2364no—
833C22×C4—2364no—
834C22×C4—2364no—
835C22×C4—2364no—
836C22×C4—2364no—
837C22×C4C2×C4×D5912yes—
838C22×C4C2×C4×D5912yes—
839C4⋊C4—2364no—
840C4⋊C4—2364no—
841C22⋊C4—44no—
842C22⋊C4—44no—
843C22⋊C4—44no—
844C22⋊C4—2364no—
845C22⋊C4—2364no—
846C22⋊C4—2364no—
847C22⋊C4—2364no—
848C22⋊C4—2364no—
849C22⋊C4—2364no—
850C22⋊C4—2364no—
851C22⋊C4—2364no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—41no—
879C23—41no—
880C23—41no—
881C23—41no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—594no—
888C23—1182no—
889C23—1182no—
890C23—1182no—
891C23—1182no—
892C23—1182no—
893C23—1182no—
894C23—1182no—
895C23—1182no—
896C23—1182no—
897C23—1182no—
898C23—1182no—
899C23—1182no—
900C23—1182no—
901C23—1182no—
902C23—1182no—
903C23—1182no—
904C23—1182no—
905C23—1182no—
906C23—2361no—
907C23—2361no—
908C23—2361no—
909C23—2361no—
910C23—2361no—
911C23—2361no—
912C23—2361no—
913C23—2361no—
914C23—2361no—
915C23—2361no—
916C23—2361no—
917C23—2361no—
918C23—2361no—
919C23—2361no—
920C23—2361no—
921C23—2361no—
922C23C22×C4×D5911yescharacteristic
923C23#41×D5911yescharacteristic
924C23#41×D5911yescharacteristic
925C23#1427377211yescharacteristic
926C23#1427377211yescharacteristic
927C23#1427377211yescharacteristic
928C23#1427377211yescharacteristic
929C23#1427377211yescharacteristic
930C23#1427377211yescharacteristic
931C23#1427377311yescharacteristic
932C23#1427377311yescharacteristic
933C23#1427377311yescharacteristic
934C23#1427377311yescharacteristic
935C23#1427377411yescharacteristic
936C23#1427377411yescharacteristic
937D4—23616no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—1182no—
981C2×C4—1182no—
982C2×C4—1182no—
983C2×C4—1182no—
984C2×C4—1182no—
985C2×C4—1182no—
986C2×C4—1182no—
987C2×C4—1182no—
988C2×C4—1182no—
989C2×C4—23616no—
990C2×C4—2361no—
991C2×C4—2361no—
992C2×C4—2361no—
993C2×C4—2361no—
994C2×C4—2361no—
995C2×C4—2361no—
996C2×C4—2361no—
997C2×C4—2361no—
998C2×C4—2361no—
999C2×C4—2361no—
1000C2×C4—2361no—
1001C2×C4—2361no—
1002C2×C4—2361no—
1003C2×C4—2361no—
1004C2×C4—2361no—
1005C2×C4—2361no—
1006C2×C4—2361no—
1007C2×C4—2361no—
1008C2×C4—2361no—
1009C2×C4—2361no—
1010C2×C4—2361no—
1011C2×C4—2361no—
1012C2×C4—2361no—
1013C2×C4—2361no—
1014C2×C4—2361no—
1015C2×C4—2361no—
1016C2×C4—2361no—
1017C2×C4—2361no—
1018C2×C4—2361no—
1019C2×C4—2361no—
1020C2×C4—2361no—
1021C2×C4—2361no—
1022C2×C4—2361no—
1023C2×C4—2361no—
1024C2×C4—2361no—
1025C2×C4—2361no—
1026C2×C4—2361no—
1027C2×C4—2361no—
1028C2×C4—2361no—
1029C2×C4—2361no—
1030C22—42no—
1031C22—42no—
1032C22—42no—
1033C22—42no—
1034C22—42no—
1035C22—42no—
1036C22—42no—
1037C22—81no—
1038C22—81no—
1039C22—81no—
1040C22—81no—
1041C22—81no—
1042C22—81no—
1043C22—81no—
1044C22—81no—
1045C22—1184no—
1046C22—1184no—
1047C22—1184no—
1048C22—2362no—
1049C22—2362no—
1050C22—2362no—
1051C22—2362no—
1052C22—2362no—
1053C22—2362no—
1054C22—2362no—
1055C22—2362no—
1056C22—2362no—
1057C22—2362no—
1058C22—2362no—
1059C22—2362no—
1060C22#117×D5911yescharacteristic
1061C22#1683787411yescharacteristic
1062C22#1683787411yescharacteristic
1063C22#1683787411yescharacteristic
1064C22#1683787511yescharacteristic
1065C22#1683788111yescharacteristic
1066C22#1683788211yescharacteristic
1067C22#1683798411yescharacteristic
1068C22#1683798411yescharacteristic
1069C22#1683798611yescharacteristic
1070C22#1683798611yescharacteristic
1071C22#1683798811yescharacteristic
1072C22#1683798811yescharacteristic
1073C22#1683798811yescharacteristic
1074C22#1683799111yescharacteristic
1075C22#1683799311yescharacteristic
1076C22#1683799511yescharacteristic
1077C22#1683799511yescharacteristic
1078C22#1683799511yescharacteristic
1079C22#1683814011yescharacteristic
1080C22#1683814011yescharacteristic
1081C22#1683814011yescharacteristic
1082C22#1683814011yescharacteristic
1083C22#1683814111yescharacteristic
1084C22#1683814211yescharacteristic
1085C22#1683814211yescharacteristic
1086C22#1683814311yescharacteristic
1087C22#1683814511yescharacteristic
1088C22#1683814611yescharacteristic
1089C22#1683814611yescharacteristic
1090C22#1683814711yescharacteristic
1091C22#1683814711yescharacteristic
1092C22#1683814911yescharacteristic
1093C22#1683814911yescharacteristic
1094C22#1683815411yescharacteristic
1095C4—42no—
1096C4—42no—
1097C4—81no—
1098C4—81no—
1099C4—81no—
1100C4—81no—
1101C4—4721no—
1102C4—4721no—
1103C4—4721no—
1104C4—4721no—
1105C4—2362no—
1106C4—2362no—
1107C4—2362no—
1108C2—82no—
1109C2—2364no—
1110C2#2142669011yescharacteristic
1111C2#2142672511yescharacteristic
1112C2#2142672611yescharacteristic
1113C2#2142723411yescharacteristic
1114C2#2142723811yescharacteristic
1115C2#2142724811yescharacteristic
1116C2#2142724911yescharacteristic
1117C2#2143217211yescharacteristic
1118C2#2143217211yescharacteristic
1119C2#2143218111yescharacteristic
1120C2#2143218611yescharacteristic
1121C2#2143218811yescharacteristic
1122C2#2143219211yescharacteristic
1123C2#2143220111yescharacteristic
1124C2#2143220911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC59×#1440C2
socle, cosocleC24×C59C24
prime radicalC23×C22⋊D59C22
hypercenter#1440D59
hypocenterC59#14666
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
2. #21422357C2semidirect
3. #21422356C2semidirect
4. #21422354C2semidirect
5. #21422352C2semidirect
6. #21422343C2semidirect
7. #21422342C2semidirect
8. #21422341C2semidirect
9. #21422340C2semidirect
10. #21422339C2semidirect
13. (C2×D59)⋊#95C2semidirect
14. (C2×D59)⋊#95C2semidirect
15. C59×#1440C2semidirect
28. #16837278C4semidirect
552. #1440D59semidirect
614. C59#14666semidirect

Maximal subgroups

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

subgroupindex
C2×#168372782
#214223572
#214223562
#214223542
#214223522
#214223432
#214223422
#214223412
#214223402
#214223392
#214223352
(C2×D59)⋊#952
C59×#14402
#1466659