Finite Group Databasebeta

← #28515254

Subgroups — #28515254

Order 15104.

1658 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837302C211yesmaximal, characteristic
2C2×#16837295C211yesmaximal, characteristic, complemented
3C2×#16837291C211yesmaximal, characteristic, complemented
4#21422350C211yesmaximal, characteristic, complemented
5#21422347C211yesmaximal, characteristic, complemented
6#21422344C211yesmaximal, characteristic, complemented
7#21422343C211yesmaximal, characteristic, complemented
8#21422342C211yesmaximal, characteristic, complemented
9#21422339C211yesmaximal, characteristic, complemented
10#21422335C211yesmaximal, characteristic
11#21422335C211yesmaximal, characteristic
12#21422334C211yesmaximal, characteristic, complemented
13#21422322C211yesmaximal, characteristic, complemented
14C4×C59⋊#95C211yesmaximal, characteristic, complemented
15C59×#1437C211yesmaximal, characteristic, complemented
16C23×C22⋊D59C2211yescharacteristic
17C22×C4⋊Dic59C2211yescharacteristic
18C22×Dic59⋊C4C2211yescharacteristic
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
28C22×(C2×D59)⋊C4C2211yescharacteristic
29C22×C4×Dic59C2211yescharacteristic
30C22×C4×Dic59C2211yescharacteristic
31#16837302C418yescomplemented
32#16837295—24no—
33#16837291—24no—
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×C22⋊C4×C59C2211yescharacteristic
48C22×C22⋊C4×C59C2211yescharacteristic
49C22×C22⋊C4×C59C2211yescharacteristic
50C22×C42×C59C2211yescharacteristic
51C2×#95×C59C2211yescharacteristic
52C2×#95×C59C2211yescharacteristic
53C2×#95×C59C2211yescharacteristic
54C24×D59C2311yescharacteristic
55C22×C22⋊D59—22no—
56C22×C22⋊D59—22no—
57C22×C22⋊D59—41no—
58C22×C22⋊D59—41no—
59C22×C22⋊D59—41no—
60C22×C22⋊D59—41no—
61C22×C22⋊D59C2×C414yes—
62C23×Dic59C2311yescharacteristic
63C23×Dic59C2311yescharacteristic
64C23×Dic59C2311yescharacteristic
65C23×Dic59C2311yescharacteristic
66C23×Dic59C2311yescharacteristic
67C23×Dic59C2311yescharacteristic
68C23×Dic59C2311yescharacteristic
69C2×C4⋊Dic59—22no—
70C2×C4⋊Dic59—41no—
71C2×C4⋊Dic59—41no—
72C2×Dic59⋊C4—22no—
73C2×Dic59⋊C4—41no—
74C2×Dic59⋊C4—41no—
75C2×Dic59⋊C4—41no—
76C2×Dic59⋊C4—41no—
77C2×Dic59⋊C4C2×C414yes—
78C2×C22⋊Dic59—22no—
79C2×C22⋊Dic59—22no—
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⋊Dic59C2×C414yes—
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)⋊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—
104C2×(C2×D59)⋊C4C2×C414yes—
105C2×C4×Dic59—41no—
106C2×C4×Dic59—41no—
107C2×C4×Dic59—41no—
108C2×C4×Dic59—41no—
109C2×C4×Dic59C2×C414yes—
110C2×C4×Dic59D414yescomplemented
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⋊#95—41no—
122C59⋊#95—41no—
123C59⋊#95—41no—
124C25×C59C2311yescharacteristic
125C23×C4×C59C2311yescharacteristic
126C23×C4×C59C2311yescharacteristic
127C23×C4×C59C2311yescharacteristic
128C23×C4×C59C2311yescharacteristic
129C23×C4×C59C2311yescharacteristic
130C23×C4×C59C2311yescharacteristic
131C2×C22⋊C4×C59—22no—
132C2×C22⋊C4×C59—22no—
133C2×C22⋊C4×C59—22no—
134C2×C22⋊C4×C59—22no—
135C2×C22⋊C4×C59—41no—
136C2×C22⋊C4×C59—41no—
137C2×C22⋊C4×C59—41no—
138C2×C22⋊C4×C59—41no—
139C2×C22⋊C4×C59C2×C414yes—
140C2×C42×C59—22no—
141C2×C42×C59—41no—
142C2×C42×C59—41no—
143#95×C59—22no—
144#95×C59—41no—
145#95×C59—41no—
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×C59—21no—
155C24×C59—21no—
156C24×C59—21no—
157C24×C59—21no—
158C24×C59—21no—
159C24×C59—21no—
160C24×C59C22×C412yes—
161C24×C59C2411yescharacteristic
162C23×D59—21no—
163C23×D59—21no—
164C23×D59—21no—
165C23×D59—21no—
166C23×D59—21no—
167C23×D59—21no—
168C23×D59—21no—
169C23×D59—21no—
170C23×D59—21no—
171C23×D59—21no—
172C23×D59—21no—
173C23×D59—21no—
174C23×D59—21no—
175C23×D59—21no—
176C23×D59C22×C412yes—
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×C59—21no—
212C22×C4×C59—21no—
213C22×C4×C59C22×C412yes—
214C22×C4×C59C22×C412yes—
215C22×C4×C59C2×D412yes—
216C22×C4×C59#4112yes—
217C22×C4×C59#4112yes—
218C22×C4×C59#4112yes—
219C2×C22⋊D59—28no—
220C2×C22⋊D59—44no—
221C2×C22⋊D59—44no—
222C2×C22⋊D59—44no—
223C2×C22⋊D59—44no—
224C2×C22⋊D59—44no—
225C2×C22⋊D59—44no—
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×Dic59—21no—
267C22×Dic59—21no—
268C22×Dic59C22×C412yes—
269C22×Dic59C22×C412yes—
270C22×Dic59C22×C412yes—
271C22×Dic59C2×D412yes—
272C22×Dic59C2×D412yes—
273C22×Dic59#4112yes—
274C22×Dic59#4112yes—
275C22⋊C4×C59—28no—
276C22⋊C4×C59—44no—
277C22⋊C4×C59—44no—
278C42×C59—44no—
279C22⋊Dic59—44no—
280C22⋊Dic59—44no—
281C22⋊Dic59—44no—
282(C2×D59)⋊C4—28no—
283(C2×D59)⋊C4—44no—
284(C2×D59)⋊C4—44no—
285(C2×D59)⋊C4—44no—
286(C2×D59)⋊C4—44no—
287(C2×D59)⋊C4—44no—
288C4⋊Dic59—44no—
289Dic59⋊C4—44no—
290Dic59⋊C4—44no—
291C4×Dic59—44no—
292C4×Dic59—44no—
293C23×C59—22no—
294C23×C59—22no—
295C23×C59—22no—
296C23×C59—22no—
297C23×C59—22no—
298C23×C59—22no—
299C23×C59—22no—
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×C59—41no—
325C23×C59—41no—
326C23×C59—41no—
327C23×C59—41no—
328C23×C59C23×C411yescharacteristic
329C23×C59C22×D411yescharacteristic
330C23×C59C2×#4111yescharacteristic
331C23×C59C2×#4111yescharacteristic
332C23×C59C2×#4111yescharacteristic
333C23×C59C2×#4111yescharacteristic
334C23×C59C2×#4111yescharacteristic
335C23×C59H(5,𝔽2)11yescharacteristic
336C23×C59H(5,𝔽2)11yescharacteristic
337C23×C59H(5,𝔽2)11yescharacteristic
338C23×C59H(5,𝔽2)11yescharacteristic
339C23×C59H(5,𝔽2)11yescharacteristic
340C23×C59H(5,𝔽2)11yescharacteristic
341C23×C59H(5,𝔽2)11yescharacteristic
342C23×C592−1+411yescharacteristic
343C22×D59—22no—
344C22×D59—22no—
345C22×D59—22no—
346C22×D59—22no—
347C22×D59—22no—
348C22×D59—22no—
349C22×D59—22no—
350C22×D59—41no—
351C22×D59—41no—
352C22×D59—41no—
353C22×D59—41no—
354C22×D59—41no—
355C22×D59—41no—
356C22×D59—41no—
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—41no—
374C22×D59—41no—
375C22×D59—41no—
376C22×D59—41no—
377C22×D59—41no—
378C2×C4×C59—22no—
379C2×C4×C59—22no—
380C2×C4×C59—22no—
381C2×C4×C59—22no—
382C2×C4×C59—22no—
383C2×C4×C59—22no—
384C2×C4×C59—22no—
385C2×C4×C59—22no—
386C2×C4×C59—22no—
387C2×C4×C59—22no—
388C2×C4×C59—22no—
389C2×C4×C59—22no—
390C2×C4×C59—22no—
391C2×C4×C59—22no—
392C2×C4×C59—22no—
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—
416C2×C4×C59—41no—
417C2×C4×C59—41no—
418C2×C4×C59—41no—
419C2×C4×C59C4×D414yes—
420C22⋊D59—416no—
421C2×Dic59—22no—
422C2×Dic59—22no—
423C2×Dic59—22no—
424C2×Dic59—22no—
425C2×Dic59—22no—
426C2×Dic59—22no—
427C2×Dic59—22no—
428C2×Dic59—22no—
429C2×Dic59—22no—
430C2×Dic59—22no—
431C2×Dic59—22no—
432C2×Dic59—22no—
433C2×Dic59—22no—
434C2×Dic59—22no—
435C2×Dic59—22no—
436C2×Dic59—22no—
437C2×Dic59—22no—
438C2×Dic59—22no—
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—
466C2×Dic59—41no—
467C2×Dic59—41no—
468C2×Dic59—41no—
469C2×Dic59#11714yes—
470#14278—591nomaximal, Sylow
471C22×C59—42no—
472C22×C59—42no—
473C22×C59—42no—
474C22×C59—42no—
475C22×C59—42no—
476C22×C59—42no—
477C22×C59—42no—
478C22×C59—81no—
479C22×C59—81no—
480C22×C59—81no—
481C22×C59—81no—
482C22×C59—81no—
483C22×C59—81no—
484C22×C59—81no—
485C22×C59—81no—
486C22×C59C2×#11711yescharacteristic
487C22×C59C2×C4×D411yescharacteristic
488C22×C59C4×#4111yescharacteristic
489C22×C59#51811yescharacteristic
490C22×C59#51811yescharacteristic
491C22×C59#51811yescharacteristic
492C22×C59#52011yescharacteristic
493C22×C59#52911yescharacteristic
494C22×C59#52911yescharacteristic
495C22×C59#53211yescharacteristic
496C22×C59#53211yescharacteristic
497C22×C59#53411yescharacteristic
498C22×C59#53511yescharacteristic
499C22×C59#53511yescharacteristic
500C22×C59#53711yescharacteristic
501C22×C59#53811yescharacteristic
502C22×C59#53811yescharacteristic
503C22×C59#53811yescharacteristic
504C22×C59#53811yescharacteristic
505C22×C59#53811yescharacteristic
506C22×C59#53811yescharacteristic
507C22×C59#53811yescharacteristic
508C22×C59#53811yescharacteristic
509C22×C59#53811yescharacteristic
510C22×C59#53911yescharacteristic
511C22×C59#54011yescharacteristic
512C22×C59#54011yescharacteristic
513C22×C59#54011yescharacteristic
514C22×C59#54011yescharacteristic
515C22×C59#54011yescharacteristic
516C22×C59#54011yescharacteristic
517C22×C59#54211yescharacteristic
518C22×C59#54211yescharacteristic
519C22×C59#54211yescharacteristic
520C22×C59#54211yescharacteristic
521C2×D59—42no—
522C2×D59—42no—
523C2×D59—42no—
524C2×D59—42no—
525C2×D59—42no—
526C2×D59—42no—
527C2×D59—42no—
528C2×D59—81no—
529C2×D59—81no—
530C2×D59—81no—
531C2×D59—81no—
532C2×D59—81no—
533C2×D59—81no—
534C2×D59—81no—
535C2×D59—81no—
536C4×C59—24no—
537C4×C59—42no—
538C4×C59—42no—
539C4×C59—42no—
540C4×C59—81no—
541C4×C59—81no—
542Dic59—24no—
543Dic59—42no—
544Dic59—42no—
545Dic59—42no—
546Dic59—42no—
547Dic59—81no—
548Dic59—81no—
549C2×#390—591no—
550C2×#388—591no—
551C2×#388—591no—
552#1441—591no—
553#1441—591no—
554#1440—591no—
555#1440—591no—
556#1439—591no—
557#1439—591no—
558#1438—591no—
559#1438—591no—
560#1437—591no—
561#1437D5911yescharacteristic, complemented
562#1434—591no—
563C4×#95—591no—
564C2×C59—82no—
565C2×C59#229311yescharacteristic
566C2×C59#231211yescharacteristic
567C2×C59#231911yescharacteristic
568C2×C59#232511yescharacteristic
569C2×C59#232811yescharacteristic
570C2×C59#233311yescharacteristic
571C2×C59#233711yescharacteristic
572C2×C59#264811yescharacteristic
573C2×C59#264811yescharacteristic
574C2×C59#265111yescharacteristic
575C2×C59#265111yescharacteristic
576C2×C59#266111yescharacteristic
577C2×C59#266111yescharacteristic
578C2×C59#266211yescharacteristic
579C2×C59#266211yescharacteristic
580D59—82no—
581C23×D4—591no—
582C22×C4⋊C4—591no—
583C22×C4⋊C4—591no—
584C22×C4⋊C4—591no—
585C22×C22⋊C4—591no—
586C22×C22⋊C4—591no—
587C22×C22⋊C4—591no—
588C22×C22⋊C4—591no—
589C22×C22⋊C4—591no—
590C22×C22⋊C4—591no—
591C22×C22⋊C4—591no—
592C22×C22⋊C4—591no—
593C22×C22⋊C4—591no—
594C22×C22⋊C4C2×D5911yescharacteristic
595C22×C22⋊C4C2×D5911yescharacteristic
596C22×C22⋊C4C2×D5911yescharacteristic
597C22×C42—591no—
598C22×C42—591no—
599C22×C42C2×D5911yescharacteristic
600#390—598no—
601#388—1184no—
602#388—1184no—
603C2×#95—591no—
604C2×#95—591no—
605C2×#95—591no—
606C2×#95—591no—
607C2×#95—591no—
608C2×#95—591no—
609C2×#95—591no—
610C2×#95—591no—
611C2×#95—591no—
612C2×#95—591no—
613C2×#95—591no—
614C2×#95—591no—
615C2×#95—591no—
616C2×#95C2×D5911yescharacteristic
617C2×#95C2×D5911yescharacteristic
618C2×#95C2×D5911yescharacteristic
619C59#1427811yescharacteristic, complemented, Sylow
620C25—591no—
621C25C22×D5911yescharacteristic
622C22×D4—594no—
623C22×D4—1182no—
624C22×D4—1182no—
625C22×D4—2361no—
626C22×D4—2361no—
627C22×D4—2361no—
628C22×D4—2361no—
629C23×C4—591no—
630C23×C4—591no—
631C23×C4—591no—
632C23×C4—591no—
633C23×C4—591no—
634C23×C4—591no—
635C23×C4—591no—
636C23×C4C22×D5911yescharacteristic
637C23×C4C22×D5911yescharacteristic
638C23×C4C22×D5911yescharacteristic
639C23×C4C22×D5911yescharacteristic
640C23×C4C22×D5911yescharacteristic
641C23×C4C22×D5911yescharacteristic
642C2×C4⋊C4—594no—
643C2×C4⋊C4—1182no—
644C2×C4⋊C4—1182no—
645C2×C4⋊C4—2361no—
646C2×C4⋊C4—2361no—
647C2×C4⋊C4—2361no—
648C2×C4⋊C4—2361no—
649C2×C4⋊C4—2361no—
650C2×C4⋊C4—2361no—
651C2×C22⋊C4—22no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—22no—
654C2×C22⋊C4—22no—
655C2×C22⋊C4—41no—
656C2×C22⋊C4—41no—
657C2×C22⋊C4—41no—
658C2×C22⋊C4—41no—
659C2×C22⋊C4—594no—
660C2×C22⋊C4—594no—
661C2×C22⋊C4—594no—
662C2×C22⋊C4—1182no—
663C2×C22⋊C4—1182no—
664C2×C22⋊C4—1182no—
665C2×C22⋊C4—1182no—
666C2×C22⋊C4—1182no—
667C2×C22⋊C4—1182no—
668C2×C22⋊C4—1182no—
669C2×C22⋊C4—1182no—
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⋊C4—2361no—
683C2×C22⋊C4—2361no—
684C2×C22⋊C4—2361no—
685C2×C22⋊C4—2361no—
686C2×C22⋊C4C4×D5914yes—
687C2×C42—22no—
688C2×C42—41no—
689C2×C42—41no—
690C2×C42—594no—
691C2×C42—594no—
692C2×C42—2361no—
693C2×C42—2361no—
694C2×C42—2361no—
695C2×C42—2361no—
696#95—22no—
697#95—41no—
698#95—41no—
699#95—1182no—
700#95—1182no—
701#95—1182no—
702#95—1182no—
703#95—1182no—
704#95—1182no—
705#95—1182no—
706#95—1182no—
707#95—1182no—
708#95—2361no—
709#95—2361no—
710#95—2361no—
711#95—2361no—
712C24—21no—
713C24—21no—
714C24—21no—
715C24—21no—
716C24—21no—
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—592no—
727C24—1181no—
728C24—1181no—
729C24—1181no—
730C24—1181no—
731C24—1181no—
732C24—1181no—
733C24—1181no—
734C24—1181no—
735C24—1181no—
736C24—1181no—
737C24—1181no—
738C24—1181no—
739C24—1181no—
740C24—1181no—
741C24C2×C4×D5912yes—
742C24C23×D5911yescharacteristic
743C2×D4—1188no—
744C2×D4—2364no—
745C2×D4—2364no—
746C2×D4—2364no—
747C2×D4—2364no—
748C2×D4—2364no—
749C2×D4—2364no—
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—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—592no—
787C22×C4—592no—
788C22×C4—592no—
789C22×C4—592no—
790C22×C4—592no—
791C22×C4—592no—
792C22×C4—592no—
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—1181no—
831C22×C4—1181no—
832C22×C4—1181no—
833C22×C4—1181no—
834C22×C4—1181no—
835C22×C4C2×C4×D5912yes—
836C22×C4C2×C4×D5912yes—
837C22×C4#1174568512yes—
838C22×C4#1174568512yes—
839C22×C4D4×D5912yes—
840C22×C4#1174568712yes—
841C4⋊C4—2364no—
842C4⋊C4—2364no—
843C4⋊C4—2364no—
844C22⋊C4—28no—
845C22⋊C4—44no—
846C22⋊C4—44no—
847C22⋊C4—1188no—
848C22⋊C4—2364no—
849C22⋊C4—2364no—
850C22⋊C4—2364no—
851C22⋊C4—2364no—
852C22⋊C4—2364no—
853C22⋊C4—2364no—
854C22⋊C4—2364no—
855C22⋊C4—2364no—
856C42—44no—
857C42—2364no—
858C42—2364no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
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—41no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—1182no—
895C23—1182no—
896C23—1182no—
897C23—1182no—
898C23—1182no—
899C23—1182no—
900C23—1182no—
901C23—2361no—
902C23—2361no—
903C23—2361no—
904C23—2361no—
905C23—2361no—
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—
922C23—2361no—
923C23—2361no—
924C23—2361no—
925C23—2361no—
926C23—2361no—
927C23—2361no—
928C23—2361no—
929C23C22×C4×D5911yescharacteristic
930C23C2×D4×D5911yescharacteristic
931C23#41×D5911yescharacteristic
932C23#41×D5911yescharacteristic
933C23C2×#1174568711yescharacteristic
934C23C2×#1174568511yescharacteristic
935C23C2×#1174568511yescharacteristic
936C23#1427377211yescharacteristic
937C23#1427377211yescharacteristic
938C23#1427377211yescharacteristic
939C23#1427377211yescharacteristic
940C23#1427377311yescharacteristic
941C23#1427377311yescharacteristic
942C23#1427377311yescharacteristic
943C23#1427377411yescharacteristic
944D4—23616no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
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—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—594no—
987C2×C4—1182no—
988C2×C4—1182no—
989C2×C4—1182no—
990C2×C4—1182no—
991C2×C4—1182no—
992C2×C4—1182no—
993C2×C4—1182no—
994C2×C4—1182no—
995C2×C4—1182no—
996C2×C4—1182no—
997C2×C4—1182no—
998C2×C4—1182no—
999C2×C4—1182no—
1000C2×C4—1182no—
1001C2×C4—1182no—
1002C2×C4—1182no—
1003C2×C4—1182no—
1004C2×C4—1182no—
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—
1030C2×C4—2361no—
1031C2×C4—2361no—
1032C2×C4—2361no—
1033C2×C4—2361no—
1034C2×C4—2361no—
1035C2×C4(C22⋊D59)⋊C414yes—
1036C22—42no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—42no—
1042C22—42no—
1043C22—81no—
1044C22—81no—
1045C22—81no—
1046C22—81no—
1047C22—81no—
1048C22—81no—
1049C22—81no—
1050C22—81no—
1051C22—4721no—
1052C22—4721no—
1053C22—4721no—
1054C22—4721no—
1055C22—4721no—
1056C22—4721no—
1057C22—4721no—
1058C22—4721no—
1059C22—2362no—
1060C22—2362no—
1061C22—2362no—
1062C22—2362no—
1063C22—2362no—
1064C22—2362no—
1065C22—2362no—
1066C22#117×D5911yescharacteristic
1067C22C2×(C22⋊D59)⋊C411yescharacteristic
1068C22C4×#1174568511yescharacteristic
1069C22#1683787411yescharacteristic
1070C22#1683787411yescharacteristic
1071C22#1683787411yescharacteristic
1072C22#1683788111yescharacteristic
1073C22#1683793211yescharacteristic
1074C22#1683793211yescharacteristic
1075C22#1683794911yescharacteristic
1076C22#1683794911yescharacteristic
1077C22#1683796011yescharacteristic
1078C22#1683796511yescharacteristic
1079C22#1683797011yescharacteristic
1080C22#1683797911yescharacteristic
1081C22#1683798411yescharacteristic
1082C22#1683798511yescharacteristic
1083C22#1683798511yescharacteristic
1084C22#1683798611yescharacteristic
1085C22#1683798711yescharacteristic
1086C22#1683798811yescharacteristic
1087C22#1683799011yescharacteristic
1088C22#1683799011yescharacteristic
1089C22#1683799111yescharacteristic
1090C22#1683799611yescharacteristic
1091C22#1683800211yescharacteristic
1092C22#1683800311yescharacteristic
1093C22#1683800411yescharacteristic
1094C22#1683800511yescharacteristic
1095C22#1683800511yescharacteristic
1096C22#1683800711yescharacteristic
1097C22#1683801611yescharacteristic
1098C22#1683801711yescharacteristic
1099C22#1683801811yescharacteristic
1100C22#1683802311yescharacteristic
1101C4—24no—
1102C4—42no—
1103C4—42no—
1104C4—42no—
1105C4—81no—
1106C4—81no—
1107C4—1184no—
1108C4—4721no—
1109C4—4721no—
1110C4—2362no—
1111C4—2362no—
1112C4—2362no—
1113C4—2362no—
1114C2—82no—
1115C2—4722no—
1116C2#2142655911yescharacteristic
1117C2#2142669011yescharacteristic
1118C2#2142673711yescharacteristic
1119C2#2142679711yescharacteristic
1120C2#2142682011yescharacteristic
1121C2#2142685611yescharacteristic
1122C2#2142690411yescharacteristic
1123C2#2143008411yescharacteristic
1124C2#2143008611yescharacteristic
1125C2#2143012911yescharacteristic
1126C2#2143013111yescharacteristic
1127C2#2143022611yescharacteristic
1128C2#2143022811yescharacteristic
1129C2#2143023711yescharacteristic
1130C2#2143023911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC59×#1437C2
socle, cosocleC24×C59C24
prime radicalC23×C22⋊D59C22
hypercenter#1437D59
hypocenterC59#14278
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. C2×#16837295C2semidirect
3. C2×#16837291C2semidirect
4. #21422350C2semidirect
5. #21422347C2semidirect
6. #21422344C2semidirect
7. #21422343C2semidirect
8. #21422342C2semidirect
9. #21422339C2semidirect
12. #21422334C2semidirect
13. #21422322C2semidirect
14. C4×C59⋊#95C2semidirect
15. C59×#1437C2semidirect
31. #16837302C4semidirect
110. C2×C4×Dic59D4semidirect
561. #1437D59semidirect
619. C59#14278semidirect

Maximal subgroups

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

subgroupindex
C2×#168373022
C2×#168372952
C2×#168372912
#214223502
#214223472
#214223442
#214223432
#214223422
#214223392
#214223352
#214223342
#214223222
C4×C59⋊#952
C59×#14372
#1427859