Finite Group Databasebeta

← #28516919

Subgroups — #28516919

Order 15104.

1874 conjugacy classes of subgroups.

The subgroup lattice has 1152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837296C211yesmaximal, characteristic, complemented
2C2×#16837282C211yesmaximal, characteristic
3#21422357C211yesmaximal, characteristic, complemented
4#21422356C211yesmaximal, characteristic, complemented
5#21422354C211yesmaximal, characteristic, complemented
6#21422343C211yesmaximal, characteristic, complemented
7#21422339C211yesmaximal, characteristic, complemented
8#21422337C211yesmaximal, characteristic
9#21422333C211yesmaximal, characteristic, complemented
10#21422320C211yesmaximal, characteristic, complemented
11#21422319C211yesmaximal, characteristic, complemented
12#21422319C211yesmaximal, characteristic, complemented
13#21422318C211yesmaximal, characteristic, complemented
14#21422318C211yesmaximal, characteristic, complemented
15C2×C59×#386C211yesmaximal, characteristic
16C24×Dic59C2211yescharacteristic
17C22×Dic59⋊C4C2211yescharacteristic
18C22×C22⋊Dic59C2211yescharacteristic
19C22×C22⋊Dic59C2211yescharacteristic
20C22×C22⋊Dic59C2211yescharacteristic
21C22×C22⋊Dic59C2211yescharacteristic
22C22×C22⋊Dic59C2211yescharacteristic
23C22×C22⋊Dic59C2211yescharacteristic
24C22×C22⋊Dic59C2211yescharacteristic
25C22×C4×Dic59C2211yescharacteristic
26#16837296—24no—
27#16837282C418yescomplemented
28C2×C59⋊#95C2211yescharacteristic
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
45C2×C59⋊#95C2211yescharacteristic
46C23×D4×C59C2211yescharacteristic
47C24×C4×C59C2211yescharacteristic
48C22×C22⋊C4×C59C2211yescharacteristic
49C22×C22⋊C4×C59C2211yescharacteristic
50C22×C22⋊C4×C59C2211yescharacteristic
51C59×#386—24no—
52C2×#95×C59C2211yescharacteristic
53C2×#95×C59C2211yescharacteristic
54C23×Dic59—41no—
55C23×Dic59—41no—
56C23×Dic59—41no—
57C23×Dic59—41no—
58C23×Dic59—41no—
59C23×Dic59—41no—
60C23×Dic59C2×C414yescomplemented
61C23×Dic59C2311yescharacteristic
62C23×Dic59C2311yescharacteristic
63C23×Dic59C2311yescharacteristic
64C23×Dic59C2311yescharacteristic
65C23×Dic59C2311yescharacteristic
66C23×Dic59C2311yescharacteristic
67C23×Dic59C2311yescharacteristic
68C23×Dic59C2311yescharacteristic
69C2×Dic59⋊C4—22no—
70C2×Dic59⋊C4—41no—
71C2×Dic59⋊C4—41no—
72C2×C22⋊Dic59—22no—
73C2×C22⋊Dic59—22no—
74C2×C22⋊Dic59—22no—
75C2×C22⋊Dic59—22no—
76C2×C22⋊Dic59—22no—
77C2×C22⋊Dic59—22no—
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⋊Dic59—41no—
87C2×C22⋊Dic59—41no—
88C2×C22⋊Dic59—41no—
89C2×C22⋊Dic59—41no—
90C2×C22⋊Dic59C2×C414yes—
91C2×C22⋊Dic59C2×C414yes—
92C2×C22⋊Dic59C2×C414yescomplemented
93C2×C4×Dic59—22no—
94C2×C4×Dic59—22no—
95C2×C4×Dic59—41no—
96C59⋊#95—22no—
97C59⋊#95—22no—
98C59⋊#95—22no—
99C59⋊#95—41no—
100C59⋊#95—41no—
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⋊#95—41no—
110C59⋊#95—41no—
111C59⋊#95—41no—
112C59⋊#95C2×C414yescomplemented
113C59⋊#95C2×C414yescomplemented
114C25×C59C2311yescharacteristic
115C25×C59C2311yescharacteristic
116C22×D4×C59—22no—
117C22×D4×C59—22no—
118C22×D4×C59—22no—
119C22×D4×C59—22no—
120C22×D4×C59—41no—
121C22×D4×C59—41no—
122C22×D4×C59C2×C414yes—
123C23×C4×C59—22no—
124C23×C4×C59—22no—
125C23×C4×C59—22no—
126C23×C4×C59—41no—
127C23×C4×C59—41no—
128C23×C4×C59—41no—
129C23×C4×C59—41no—
130C23×C4×C59C2311yescharacteristic
131C23×C4×C59C2311yescharacteristic
132C23×C4×C59C2311yescharacteristic
133C23×C4×C59C2311yescharacteristic
134C23×C4×C59C2311yescharacteristic
135C2×C22⋊C4×C59—22no—
136C2×C22⋊C4×C59—22no—
137C2×C22⋊C4×C59—22no—
138C2×C22⋊C4×C59—22no—
139C2×C22⋊C4×C59—41no—
140C2×C22⋊C4×C59—41no—
141C2×C22⋊C4×C59—41no—
142C2×C22⋊C4×C59—41no—
143C2×C22⋊C4×C59D414yes—
144#95×C59—22no—
145#95×C59—22no—
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×C59—21no—
161C24×C59—21no—
162C24×C59—21no—
163C24×C59—21no—
164C24×C59—21no—
165C24×C59—21no—
166C24×C59—21no—
167C24×C59—21no—
168C24×C59—21no—
169C24×C59—21no—
170C24×C59C22×C412yes—
171C24×C59C22×C412yes—
172C24×C59C2×D412yes—
173C24×C59#4112yes—
174C24×C59#4112yes—
175C24×C59#4112yes—
176C24×C59C2411yescharacteristic
177C2×D4×C59—28no—
178C2×D4×C59—28no—
179C2×D4×C59—44no—
180C2×D4×C59—44no—
181C2×D4×C59—44no—
182C2×D4×C59—44no—
183C2×D4×C59—44no—
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×C59—21no—
214C22×C4×C59—21no—
215C22×C4×C59—44no—
216C22×C4×C59—44no—
217C22×C4×C59—44no—
218C22×C4×C59—44no—
219C22×C4×C59—44no—
220C22×C4×C59—44no—
221C22×C4×C59—44no—
222C22×C4×C59C22×C412yes—
223C22×C4×C59C2×D412yes—
224C22×C4×C59C2×D412yes—
225C22×C4×C59#4112yes—
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×Dic59—21no—
269C22×Dic59—21no—
270C22×Dic59—21no—
271C22×Dic59—21no—
272C22×Dic59—21no—
273C22×Dic59—21no—
274C22×Dic59—21no—
275C22×Dic59—21no—
276C22×Dic59—21no—
277C22×Dic59—44no—
278C22×Dic59—44no—
279C22×Dic59—44no—
280C22×Dic59—44no—
281C22×Dic59—44no—
282C22×Dic59—44no—
283C22×Dic59—44no—
284C22×Dic59C22×C412yes—
285C22×Dic59C22×C412yes—
286C22×Dic59C22×C412yes—
287C22×Dic59C22×C412yes—
288C22×Dic59#4112yes—
289C22⋊C4×C59—44no—
290C22⋊C4×C59—44no—
291C22⋊C4×C59—44no—
292C22⋊Dic59—28no—
293C22⋊Dic59—44no—
294C22⋊Dic59—44no—
295C22⋊Dic59—44no—
296C22⋊Dic59—44no—
297C22⋊Dic59—44no—
298C22⋊Dic59—44no—
299Dic59⋊C4—44no—
300C4×Dic59—44no—
301C23×C59—22no—
302C23×C59—22no—
303C23×C59—22no—
304C23×C59—22no—
305C23×C59—22no—
306C23×C59—22no—
307C23×C59—22no—
308C23×C59—22no—
309C23×C59—22no—
310C23×C59—22no—
311C23×C59—22no—
312C23×C59—22no—
313C23×C59—22no—
314C23×C59—22no—
315C23×C59—22no—
316C23×C59—22no—
317C23×C59—22no—
318C23×C59—22no—
319C23×C59—22no—
320C23×C59—22no—
321C23×C59—22no—
322C23×C59—22no—
323C23×C59—22no—
324C23×C59—22no—
325C23×C59—22no—
326C23×C59—22no—
327C23×C59—22no—
328C23×C59—22no—
329C23×C59—22no—
330C23×C59—22no—
331C23×C59—22no—
332C23×C59—22no—
333C23×C59—22no—
334C23×C59—22no—
335C23×C59—22no—
336C23×C59—22no—
337C23×C59—41no—
338C23×C59—41no—
339C23×C59—41no—
340C23×C59—41no—
341C23×C59—41no—
342C23×C59—41no—
343C23×C59—41no—
344C23×C59—41no—
345C23×C59—41no—
346C23×C59—41no—
347C23×C59—41no—
348C23×C59—41no—
349C23×C59—41no—
350C23×C59—41no—
351C23×C59—41no—
352C23×C59—41no—
353C23×C59—41no—
354C23×C59—41no—
355C23×C59—41no—
356C23×C59—41no—
357C23×C59—41no—
358C23×C59—41no—
359C23×C59—41no—
360C23×C59—41no—
361C23×C59—41no—
362C23×C59—41no—
363C23×C59—41no—
364C23×C59—41no—
365C23×C59—41no—
366C23×C59—41no—
367C23×C59—41no—
368C23×C59—41no—
369C23×C59#11714yes—
370C23×C59C4×D414yes—
371C23×C59C23×C411yescharacteristic
372C23×C59C22×D411yescharacteristic
373C23×C59C2×#4111yescharacteristic
374C23×C59C2×#4111yescharacteristic
375C23×C59C2×#4111yescharacteristic
376C23×C59C2×#4111yescharacteristic
377C23×C59C2×#4111yescharacteristic
378C23×C59H(5,𝔽2)11yescharacteristic
379C23×C59H(5,𝔽2)11yescharacteristic
380C23×C59H(5,𝔽2)11yescharacteristic
381C23×C59H(5,𝔽2)11yescharacteristic
382C23×C59H(5,𝔽2)11yescharacteristic
383C23×C59H(5,𝔽2)11yescharacteristic
384C23×C59H(5,𝔽2)11yescharacteristic
385C23×C592−1+411yescharacteristic
386D4×C59—416no—
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—22no—
394C2×C4×C59—22no—
395C2×C4×C59—22no—
396C2×C4×C59—22no—
397C2×C4×C59—22no—
398C2×C4×C59—22no—
399C2×C4×C59—416no—
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×C59—41no—
420C2×C4×C59—41no—
421C2×C4×C59—41no—
422C2×C4×C59—41no—
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—416no—
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—41no—
470C2×Dic59—41no—
471C2×Dic59—41no—
472C2×Dic59—41no—
473C2×Dic59—41no—
474C2×Dic59—41no—
475C2×Dic59—41no—
476C2×Dic59—41no—
477C2×Dic59—41no—
478C2×Dic59—41no—
479C2×Dic59—41no—
480#14427—591nomaximal, Sylow
481C22×C59—24no—
482C22×C59—24no—
483C22×C59—24no—
484C22×C59—24no—
485C22×C59—24no—
486C22×C59—24no—
487C22×C59—42no—
488C22×C59—42no—
489C22×C59—42no—
490C22×C59—42no—
491C22×C59—42no—
492C22×C59—42no—
493C22×C59—42no—
494C22×C59—42no—
495C22×C59—42no—
496C22×C59—42no—
497C22×C59—42no—
498C22×C59—42no—
499C22×C59—42no—
500C22×C59—42no—
501C22×C59—42no—
502C22×C59—42no—
503C22×C59—42no—
504C22×C59—42no—
505C22×C59—42no—
506C22×C59—42no—
507C22×C59—42no—
508C22×C59—42no—
509C22×C59—42no—
510C22×C59—42no—
511C22×C59C2×#11711yescharacteristic
512C22×C59C2×C4×D411yescharacteristic
513C22×C59C4×#4111yescharacteristic
514C22×C59#51811yescharacteristic
515C22×C59#51811yescharacteristic
516C22×C59#51811yescharacteristic
517C22×C59#52011yescharacteristic
518C22×C59#53411yescharacteristic
519C22×C59#53711yescharacteristic
520C22×C59#53811yescharacteristic
521C22×C59#53811yescharacteristic
522C22×C59#53811yescharacteristic
523C22×C59#53811yescharacteristic
524C22×C59#53911yescharacteristic
525C22×C59#53911yescharacteristic
526C22×C59#53911yescharacteristic
527C22×C59#53911yescharacteristic
528C22×C59#54011yescharacteristic
529C22×C59#54211yescharacteristic
530C22×C59#54611yescharacteristic
531C22×C59#54611yescharacteristic
532C22×C59#54611yescharacteristic
533C22×C59#54611yescharacteristic
534C22×C59#55111yescharacteristic
535C22×C59#55111yescharacteristic
536C22×C59#55111yescharacteristic
537C22×C59#55111yescharacteristic
538C22×C59#55311yescharacteristic
539C22×C59#55311yescharacteristic
540C22×C59#55311yescharacteristic
541C22×C59#55311yescharacteristic
542C22×C59#56011yescharacteristic
543C22×C59#56011yescharacteristic
544C22×C59#56011yescharacteristic
545C22×C59H(3,𝔽4)11yescharacteristic
546C4×C59—42no—
547C4×C59—42no—
548C4×C59—42no—
549C4×C59—42no—
550C4×C59—81no—
551Dic59—42no—
552Dic59—42no—
553Dic59—42no—
554Dic59—42no—
555Dic59—42no—
556Dic59—81no—
557Dic59—81no—
558Dic59—81no—
559C2×#388—591no—
560C2×#386—591no—
561C2×#386D5911yescharacteristic
562#1443—591no—
563#1443—591no—
564#1442—591no—
565#1440—591no—
566#1439—591no—
567#1438—591no—
568#1437—591no—
569#1434—591no—
570C22⋊#95—591no—
571C22⋊#95—591no—
572C22⋊#95—591no—
573C22⋊#95—591no—
574C2×C59—44no—
575C2×C59—44no—
576C2×C59#231811yescharacteristic
577C2×C59#232511yescharacteristic
578C2×C59#233511yescharacteristic
579C2×C59#234211yescharacteristic
580C2×C59#235311yescharacteristic
581C2×C59#236411yescharacteristic
582C2×C59#237511yescharacteristic
583C2×C59#268411yescharacteristic
584C2×C59#268811yescharacteristic
585C2×C59#269111yescharacteristic
586C2×C59#269311yescharacteristic
587C2×C59#274611yescharacteristic
588C2×C59#274911yescharacteristic
589C2×C59#277811yescharacteristic
590C2×C59#278211yescharacteristic
591C23×D4C2×D5911yescharacteristic
592C24×C4—591no—
593C24×C4C2×D5911yescharacteristic
594C22×C4⋊C4—591no—
595C22×C22⋊C4—591no—
596C22×C22⋊C4—591no—
597C22×C22⋊C4—591no—
598C22×C22⋊C4—591no—
599C22×C22⋊C4—591no—
600C22×C22⋊C4—591no—
601C22×C22⋊C4—591no—
602C22×C22⋊C4C2×D5911yescharacteristic
603C22×C22⋊C4C2×D5911yescharacteristic
604C22×C22⋊C4C2×D5911yescharacteristic
605C22×C42—591no—
606#388—1184no—
607#386—24no—
608#386—598no—
609C2×#95—591no—
610C2×#95—591no—
611C2×#95—591no—
612C2×#95—591no—
613C2×#95—591no—
614C2×#95—591no—
615C2×#95—591no—
616C2×#95—591no—
617C2×#95—591no—
618C2×#95—591no—
619C2×#95—591no—
620C2×#95—591no—
621C2×#95—591no—
622C2×#95—591no—
623C2×#95—591no—
624C2×#95—591no—
625C2×#95—591no—
626C2×#95—591no—
627C2×#95C2×D5911yescharacteristic
628C2×#95C2×D5911yescharacteristic
629C59#1442711yescharacteristic, complemented, Sylow
630C25C22×D5911yescharacteristic
631C25C22×D5911yescharacteristic
632C22×D4—22no—
633C22×D4—22no—
634C22×D4—22no—
635C22×D4—22no—
636C22×D4—41no—
637C22×D4—41no—
638C22×D4C4×D5914yes—
639C23×C4—22no—
640C23×C4—22no—
641C23×C4—22no—
642C23×C4—41no—
643C23×C4—41no—
644C23×C4—41no—
645C23×C4—41no—
646C23×C4—591no—
647C23×C4—591no—
648C23×C4—591no—
649C23×C4—591no—
650C23×C4—591no—
651C23×C4—594no—
652C23×C4—591no—
653C23×C4—591no—
654C23×C4—591no—
655C23×C4—2361no—
656C23×C4—2361no—
657C23×C4—2361no—
658C23×C4—2361no—
659C23×C4—2361no—
660C23×C4—2361no—
661C23×C4C22×D5911yescharacteristic
662C23×C4C22×D5911yescharacteristic
663C23×C4C22×D5911yescharacteristic
664C23×C4C22×D5911yescharacteristic
665C23×C4C22×D5911yescharacteristic
666C2×C4⋊C4—1182no—
667C2×C4⋊C4—2361no—
668C2×C4⋊C4—2361no—
669C2×C22⋊C4—22no—
670C2×C22⋊C4—22no—
671C2×C22⋊C4—22no—
672C2×C22⋊C4—22no—
673C2×C22⋊C4—41no—
674C2×C22⋊C4—41no—
675C2×C22⋊C4—41no—
676C2×C22⋊C4—41no—
677C2×C22⋊C4—594no—
678C2×C22⋊C4—594no—
679C2×C22⋊C4—594no—
680C2×C22⋊C4—1182no—
681C2×C22⋊C4—1182no—
682C2×C22⋊C4—1182no—
683C2×C22⋊C4—1182no—
684C2×C22⋊C4—1182no—
685C2×C22⋊C4—1182no—
686C2×C22⋊C4—1182no—
687C2×C22⋊C4—1182no—
688C2×C22⋊C4—2361no—
689C2×C22⋊C4—2361no—
690C2×C22⋊C4—2361no—
691C2×C22⋊C4—2361no—
692C2×C22⋊C4—2361no—
693C2×C22⋊C4—2361no—
694C2×C22⋊C4—2361no—
695C2×C22⋊C4—2361no—
696C2×C22⋊C4—2361no—
697C2×C22⋊C4—2361no—
698C2×C22⋊C4C22⋊D5914yes—
699C2×C42—1182no—
700C2×C42—1182no—
701C2×C42—2361no—
702#95—22no—
703#95—22no—
704#95—594no—
705#95—594no—
706#95—1182no—
707#95—1182no—
708#95—1182no—
709#95—2361no—
710#95—2361no—
711#95—2361no—
712#95—2361no—
713#95—2361no—
714#95—2361no—
715#95—2361no—
716#95—2361no—
717#95—2361no—
718#95—2361no—
719#95—2361no—
720#95—2361no—
721#95—2361no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—21no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24C2×C4×D5912yes—
747C24C2×C4×D5912yes—
748C24#1174568512yes—
749C24#1174568712yes—
750C24#1174568712yes—
751C24C2×C22⋊D5912yes—
752C24C23×D5911yescharacteristic
753C2×D4—28no—
754C2×D4—28no—
755C2×D4—44no—
756C2×D4—44no—
757C2×D4—44no—
758C2×D4—44no—
759C2×D4—44no—
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—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—44no—
792C22×C4—44no—
793C22×C4—44no—
794C22×C4—44no—
795C22×C4—44no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4—592no—
799C22×C4—592no—
800C22×C4—592no—
801C22×C4—592no—
802C22×C4—592no—
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×C4—1181no—
836C22×C4—1181no—
837C22×C4—1181no—
838C22×C4—1181no—
839C22×C4—1181no—
840C22×C4—1181no—
841C22×C4—1181no—
842C22×C4—1181no—
843C22×C4—1181no—
844C22×C4—1181no—
845C22×C4—1181no—
846C22×C4—1181no—
847C22×C4—1181no—
848C22×C4—1181no—
849C22×C4—1181no—
850C22×C4—1181no—
851C22×C4—1181no—
852C22×C4—1181no—
853C22×C4—1181no—
854C22×C4—2364no—
855C22×C4—2364no—
856C22×C4—2364no—
857C22×C4—2364no—
858C22×C4—2364no—
859C22×C4—2364no—
860C22×C4—2364no—
861C22×C4C2×C4×D5912yes—
862C22×C4#1174568712yes—
863C22×C4C2×C22⋊D5912yes—
864C22×C4C2×C22⋊D5912yes—
865C4⋊C4—2364no—
866C22⋊C4—44no—
867C22⋊C4—44no—
868C22⋊C4—44no—
869C22⋊C4—1188no—
870C22⋊C4—2364no—
871C22⋊C4—2364no—
872C22⋊C4—2364no—
873C22⋊C4—2364no—
874C22⋊C4—2364no—
875C22⋊C4—2364no—
876C42—2364no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23#1427368314yes—
946C23C4×C22⋊D5914yes—
947C23C22×C4×D5911yescharacteristic
948C23C22×C22⋊D5911yescharacteristic
949C23#41×D5911yescharacteristic
950C23C2×#1174568711yescharacteristic
951C23C2×#1174568711yescharacteristic
952C23C2×#1174568711yescharacteristic
953C23C2×#1174568511yescharacteristic
954C23#1427377211yescharacteristic
955C23#1427377211yescharacteristic
956C23#1427377211yescharacteristic
957C23#1427377211yescharacteristic
958C23#1427377211yescharacteristic
959C23#1427377311yescharacteristic
960C23#1427377311yescharacteristic
961C23#1427377411yescharacteristic
962D4—416no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—416no—
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—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—1182no—
1000C2×C4—1182no—
1001C2×C4—1182no—
1002C2×C4—1182no—
1003C2×C4—1182no—
1004C2×C4—1182no—
1005C2×C4—1182no—
1006C2×C4—1182no—
1007C2×C4—1182no—
1008C2×C4—1182no—
1009C2×C4—1182no—
1010C2×C4—1182no—
1011C2×C4—1182no—
1012C2×C4—1182no—
1013C2×C4—1182no—
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—23616no—
1036C2×C4—2361no—
1037C2×C4—2361no—
1038C2×C4—2361no—
1039C2×C4—2361no—
1040C2×C4—2361no—
1041C2×C4—2361no—
1042C2×C4—2361no—
1043C2×C4—2361no—
1044C2×C4—2361no—
1045C2×C4—2361no—
1046C2×C4—2361no—
1047C2×C4—2361no—
1048C2×C4—2361no—
1049C2×C4—2361no—
1050C2×C4—2361no—
1051C2×C4—2361no—
1052C2×C4—2361no—
1053C2×C4—2361no—
1054C2×C4—2361no—
1055C2×C4—2361no—
1056C22—24no—
1057C22—24no—
1058C22—24no—
1059C22—24no—
1060C22—24no—
1061C22—24no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22C2×#1427368311yescharacteristic
1087C22C2×C4×C22⋊D5911yescharacteristic
1088C22C4×#1174568711yescharacteristic
1089C22#1683787411yescharacteristic
1090C22#1683787411yescharacteristic
1091C22#1683787511yescharacteristic
1092C22#1683788111yescharacteristic
1093C22#1683796111yescharacteristic
1094C22#1683798011yescharacteristic
1095C22#1683798511yescharacteristic
1096C22#1683798711yescharacteristic
1097C22#1683798711yescharacteristic
1098C22#1683798911yescharacteristic
1099C22#1683799411yescharacteristic
1100C22#1683799511yescharacteristic
1101C22#1683799611yescharacteristic
1102C22#1683799711yescharacteristic
1103C22#1683800211yescharacteristic
1104C22#1683801911yescharacteristic
1105C22#1683804011yescharacteristic
1106C22#1683804611yescharacteristic
1107C22#1683804611yescharacteristic
1108C22#1683804611yescharacteristic
1109C22#1683807511yescharacteristic
1110C22#1683807811yescharacteristic
1111C22#1683807811yescharacteristic
1112C22#1683808311yescharacteristic
1113C22#1683809511yescharacteristic
1114C22#1683809811yescharacteristic
1115C22#1683810111yescharacteristic
1116C22#1683810411yescharacteristic
1117C22#1683814011yescharacteristic
1118C22#1683814011yescharacteristic
1119C22#1683814211yescharacteristic
1120C22#1683814511yescharacteristic
1121C4—42no—
1122C4—42no—
1123C4—42no—
1124C4—42no—
1125C4—81no—
1126C4—4721no—
1127C4—4721no—
1128C4—4721no—
1129C4—2362no—
1130C4—2362no—
1131C4—2362no—
1132C4—2362no—
1133C4—2362no—
1134C2—44no—
1135C2—44no—
1136C2#2142672211yescharacteristic
1137C2#2142679411yescharacteristic
1138C2#2142688711yescharacteristic
1139C2#2142694111yescharacteristic
1140C2#2142703411yescharacteristic
1141C2#2142714111yescharacteristic
1142C2#2142723411yescharacteristic
1143C2#2143047411yescharacteristic
1144C2#2143052611yescharacteristic
1145C2#2143057311yescharacteristic
1146C2#2143060111yescharacteristic
1147C2#2143128411yescharacteristic
1148C2#2143131911yescharacteristic
1149C2#2143171411yescharacteristic
1150C2#2143176911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC2×C59×#386C2
socle, cosocleC24×C59C24
prime radicalC23×D4×C59C22
hypercenterC2×#386D59
hypocenterC59#14427
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C2×#16837296C2semidirect
3. #21422357C2semidirect
4. #21422356C2semidirect
5. #21422354C2semidirect
6. #21422343C2semidirect
7. #21422339C2semidirect
9. #21422333C2semidirect
10. #21422320C2semidirect
11. #21422319C2semidirect
12. #21422319C2semidirect
13. #21422318C2semidirect
14. #21422318C2semidirect
27. #16837282C4semidirect
60. C23×Dic59C2×C4semidirect
92. C2×C22⋊Dic59C2×C4semidirect
112. C59⋊#95C2×C4semidirect
113. C59⋊#95C2×C4semidirect
629. C59#14427semidirect

Maximal subgroups

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

subgroupindex
C2×#168372962
C2×#168372822
#214223572
#214223562
#214223542
#214223432
#214223392
#214223372
#214223332
#214223202
#214223192
#214223182
C2×C59×#3862
#1442759