Finite Group Databasebeta

← #28511845

Subgroups — #28511845

Order 15104.

2278 conjugacy classes of subgroups.

The subgroup lattice has 1194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837294C211yesmaximal, characteristic, complemented
2C2×#16837281C211yesmaximal, characteristic
3C2×#16837281C211yesmaximal, characteristic
4C2×#16837281C211yesmaximal, characteristic
5C2×#16837262C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊Dic59C211yesmaximal, characteristic, complemented
7#21422356C211yesmaximal, characteristic, complemented
8#21422352C211yesmaximal, characteristic, complemented
9#21422344C211yesmaximal, characteristic, complemented
10#21422342C211yesmaximal, characteristic, complemented
11#21422332C211yesmaximal, characteristic, complemented
12#21422330C211yesmaximal, characteristic, complemented
13#21422320C211yesmaximal, characteristic, complemented
14#21422319C211yesmaximal, characteristic, complemented
15C22×#95×C59C211yesmaximal, characteristic, complemented
16C23×C22⋊D59C2211yescharacteristic
17C22×C4⋊Dic59C2211yescharacteristic
18C22×C4⋊Dic59C2211yescharacteristic
19C22×C22⋊Dic59C2211yescharacteristic
20C22×C22⋊Dic59C2211yescharacteristic
21C22×C22⋊Dic59C2211yescharacteristic
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
30#16837294—24no—
31#16837281—24no—
32#16837281—24no—
33#16837281C418yescomplemented
34#16837262—24no—
35C4×C22⋊Dic59—24no—
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
50C24×C4×C59C2211yescharacteristic
51C24×C4×C59C2211yescharacteristic
52C24×C4×C59C2211yescharacteristic
53C2×#95×C59—24no—
54C2×#95×C59C2211yescharacteristic
55C2×#95×C59C2211yescharacteristic
56C2×#95×C59C2211yescharacteristic
57C2×#95×C59C2211yescharacteristic
58C24×D59C2311yescharacteristic
59C22×C22⋊D59—22no—
60C22×C22⋊D59—22no—
61C22×C22⋊D59—22no—
62C22×C22⋊D59—22no—
63C22×C22⋊D59—22no—
64C22×C22⋊D59—22no—
65C22×C22⋊D59C2×C414yes—
66C23×Dic59C2311yescharacteristic
67C23×Dic59C2311yescharacteristic
68C23×Dic59C2311yescharacteristic
69C23×Dic59C2311yescharacteristic
70C23×Dic59C2311yescharacteristic
71C23×Dic59C2311yescharacteristic
72C23×Dic59C2311yescharacteristic
73C2×C4⋊Dic59—22no—
74C2×C4⋊Dic59—22no—
75C2×C4⋊Dic59—22no—
76C2×C4⋊Dic59—22no—
77C2×C4⋊Dic59—41no—
78C2×C4⋊Dic59—41no—
79C2×C22⋊Dic59—22no—
80C2×C22⋊Dic59—22no—
81C2×C22⋊Dic59—22no—
82C2×C22⋊Dic59—22no—
83C2×C22⋊Dic59—22no—
84C2×C22⋊Dic59—22no—
85C2×C22⋊Dic59—22no—
86C2×C22⋊Dic59C2×C414yes—
87C2×C22⋊Dic59D414yes—
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—22no—
94C2×(C2×D59)⋊C4—22no—
95C2×(C2×D59)⋊C4—22no—
96C2×(C2×D59)⋊C4—22no—
97C2×(C2×D59)⋊C4—22no—
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)⋊C4—41no—
104C2×(C2×D59)⋊C4C2×C414yescomplemented
105C2×(C2×D59)⋊C4C2×C414yescomplemented
106C2×C4×Dic59—22no—
107C2×C4×Dic59—22no—
108C2×C4×Dic59—22no—
109C2×C4×Dic59—22no—
110C2×C4×Dic59—41no—
111C2×C4×Dic59—41no—
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—22no—
121C59⋊#95—22no—
122C59⋊#95—41no—
123C59⋊#95—41no—
124C59⋊#95C2×C414yescomplemented
125C59⋊#95C2×C414yescomplemented
126C25×C59C2311yescharacteristic
127C23×C4×C59—22no—
128C23×C4×C59—22no—
129C23×C4×C59—22no—
130C23×C4×C59—22no—
131C23×C4×C59—22no—
132C23×C4×C59—22no—
133C23×C4×C59—22no—
134C23×C4×C59—22no—
135C23×C4×C59—22no—
136C23×C4×C59—22no—
137C23×C4×C59—22no—
138C23×C4×C59—22no—
139C23×C4×C59—22no—
140C23×C4×C59—41no—
141C23×C4×C59—41no—
142C23×C4×C59—41no—
143C23×C4×C59—41no—
144C23×C4×C59—41no—
145C23×C4×C59—41no—
146C23×C4×C59C2×C414yes—
147C23×C4×C59D414yes—
148C23×C4×C59C2311yescharacteristic
149C23×C4×C59C2311yescharacteristic
150C23×C4×C59C2311yescharacteristic
151C23×C4×C59C2311yescharacteristic
152C23×C4×C59C2311yescharacteristic
153C23×C4×C59C2311yescharacteristic
154#95×C59—22no—
155#95×C59—22no—
156#95×C59—22no—
157#95×C59D414yescomplemented
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×C59C22×C412yes—
167C24×C59C2×D412yes—
168C24×C59C2×D412yes—
169C24×C59#4112yes—
170C24×C59#4112yes—
171C24×C59#4112yes—
172C24×C59#4112yes—
173C24×C59C2411yescharacteristic
174C23×D59—21no—
175C23×D59—21no—
176C23×D59—21no—
177C23×D59—21no—
178C23×D59—21no—
179C23×D59—21no—
180C23×D59—21no—
181C23×D59—21no—
182C23×D59—21no—
183C23×D59—21no—
184C23×D59—21no—
185C23×D59—21no—
186C23×D59—21no—
187C23×D59—21no—
188C23×D59C22×C412yes—
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—28no—
198C22×C4×C59—28no—
199C22×C4×C59—28no—
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—21no—
216C22×C4×C59—21no—
217C22×C4×C59—21no—
218C22×C4×C59—21no—
219C22×C4×C59—21no—
220C22×C4×C59—21no—
221C22×C4×C59—21no—
222C22×C4×C59—21no—
223C22×C4×C59—21no—
224C22×C4×C59—28no—
225C22×C4×C59—28no—
226C22×C4×C59—44no—
227C22×C4×C59—44no—
228C22×C4×C59—44no—
229C22×C4×C59—44no—
230C22×C4×C59—44no—
231C22×C4×C59—44no—
232C22×C4×C59—44no—
233C22×C4×C59—44no—
234C22×C4×C59—44no—
235C22×C4×C59—44no—
236C22×C4×C59—44no—
237C22×C4×C59—44no—
238C22×C4×C59—44no—
239C22×C4×C59—44no—
240C22×C4×C59—44no—
241C22×C4×C59—44no—
242C22×C4×C59C22×C412yes—
243C22×C4×C59C22×C412yes—
244C22×C4×C59C2×D412yes—
245C22×C4×C59C2×D412yes—
246C22×C4×C59C2×D412yes—
247C22×C4×C59C2×D412yes—
248C22×C4×C59C2×D412yes—
249C22×C4×C59#4112yes—
250C22×C4×C59#4112yes—
251C22×C4×C59#4112yes—
252C2×C22⋊D59—28no—
253C2×C22⋊D59—28no—
254C2×C22⋊D59—28no—
255C2×C22⋊D59—44no—
256C2×C22⋊D59—44no—
257C2×C22⋊D59—44no—
258C2×C22⋊D59—44no—
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—21no—
278C22×Dic59—21no—
279C22×Dic59—21no—
280C22×Dic59—21no—
281C22×Dic59—21no—
282C22×Dic59—21no—
283C22×Dic59—21no—
284C22×Dic59—21no—
285C22×Dic59—21no—
286C22×Dic59—21no—
287C22×Dic59—21no—
288C22×Dic59—21no—
289C22×Dic59—21no—
290C22×Dic59—21no—
291C22×Dic59—21no—
292C22×Dic59—21no—
293C22×Dic59—21no—
294C22×Dic59—21no—
295C22×Dic59—21no—
296C22×Dic59—21no—
297C22×Dic59—21no—
298C22×Dic59—21no—
299C22×Dic59—21no—
300C22×Dic59—21no—
301C22×Dic59—21no—
302C22×Dic59—21no—
303C22×Dic59C22×C412yes—
304C22×Dic59C22×C412yes—
305C22×Dic59C22×C412yes—
306C22×Dic59C2×D412yes—
307C22×Dic59C2×D412yes—
308C22⋊Dic59—28no—
309C22⋊Dic59—28no—
310C22⋊Dic59—44no—
311(C2×D59)⋊C4—28no—
312(C2×D59)⋊C4—44no—
313(C2×D59)⋊C4—44no—
314(C2×D59)⋊C4—44no—
315(C2×D59)⋊C4—44no—
316(C2×D59)⋊C4—44no—
317C4⋊Dic59—44no—
318C4⋊Dic59—44no—
319C4×Dic59—44no—
320C4×Dic59—44no—
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—22no—
338C23×C59—22no—
339C23×C59—22no—
340C23×C59—22no—
341C23×C59—22no—
342C23×C59—22no—
343C23×C59—22no—
344C23×C59—22no—
345C23×C59—22no—
346C23×C59—22no—
347C23×C59—22no—
348C23×C59—22no—
349C23×C59#11714yes—
350C23×C59C4×D414yes—
351C23×C59C4×D414yes—
352C23×C59#12114yes—
353C23×C59#12314yes—
354C23×C59#12414yes—
355C23×C59#12614yes—
356C23×C59C23×C411yescharacteristic
357C23×C59C22×D411yescharacteristic
358C23×C59C22×D411yescharacteristic
359C23×C59C22×D411yescharacteristic
360C23×C59C2×#4111yescharacteristic
361C23×C59C2×#4111yescharacteristic
362C23×C59C2×#4111yescharacteristic
363C23×C59C2×#4111yescharacteristic
364C23×C59C2×#4111yescharacteristic
365C23×C59C2×#4111yescharacteristic
366C23×C59C2×#4111yescharacteristic
367C23×C59H(5,𝔽2)11yescharacteristic
368C23×C59H(5,𝔽2)11yescharacteristic
369C23×C59H(5,𝔽2)11yescharacteristic
370C23×C592−1+411yescharacteristic
371C22×D59—22no—
372C22×D59—22no—
373C22×D59—22no—
374C22×D59—22no—
375C22×D59—22no—
376C22×D59—22no—
377C22×D59—22no—
378C22×D59—41no—
379C22×D59—41no—
380C22×D59—41no—
381C22×D59—41no—
382C22×D59—41no—
383C22×D59—41no—
384C22×D59—41no—
385C22×D59—41no—
386C22×D59—41no—
387C22×D59—41no—
388C22×D59—41no—
389C22×D59—41no—
390C22×D59—41no—
391C22×D59—41no—
392C22×D59—41no—
393C22×D59—41no—
394C22×D59—41no—
395C22×D59—41no—
396C22×D59—41no—
397C22×D59—41no—
398C22×D59—41no—
399C22×D59—41no—
400C22×D59—41no—
401C22×D59—41no—
402C22×D59—41no—
403C22×D59—41no—
404C22×D59—41no—
405C22×D59—41no—
406C2×C4×C59—22no—
407C2×C4×C59—22no—
408C2×C4×C59—22no—
409C2×C4×C59—22no—
410C2×C4×C59—22no—
411C2×C4×C59—22no—
412C2×C4×C59—22no—
413C2×C4×C59—22no—
414C2×C4×C59—22no—
415C2×C4×C59—22no—
416C2×C4×C59—22no—
417C2×C4×C59—22no—
418C2×C4×C59—22no—
419C2×C4×C59—22no—
420C2×C4×C59—22no—
421C2×C4×C59—22no—
422C2×C4×C59—22no—
423C2×C4×C59—22no—
424C2×C4×C59—22no—
425C2×C4×C59—22no—
426C2×C4×C59—22no—
427C2×C4×C59—22no—
428C2×C4×C59—22no—
429C2×C4×C59—22no—
430C2×C4×C59—416no—
431C2×C4×C59—416no—
432C2×C4×C59—416no—
433C2×C4×C59—41no—
434C2×C4×C59—41no—
435C2×C4×C59—41no—
436C2×C4×C59—41no—
437C2×C4×C59—41no—
438C2×C4×C59—41no—
439C2×C4×C59—41no—
440C2×C4×C59—41no—
441C2×C4×C59—41no—
442C2×C4×C59—41no—
443C2×C4×C59—41no—
444C2×C4×C59—41no—
445C2×C4×C59—41no—
446C2×C4×C59—41no—
447C2×C4×C59—41no—
448C2×C4×C59—41no—
449C2×C4×C59C4×D414yes—
450C2×C4×C59#12114yes—
451C22⋊D59—416no—
452C2×Dic59—22no—
453C2×Dic59—22no—
454C2×Dic59—22no—
455C2×Dic59—22no—
456C2×Dic59—22no—
457C2×Dic59—22no—
458C2×Dic59—22no—
459C2×Dic59—22no—
460C2×Dic59—22no—
461C2×Dic59—22no—
462C2×Dic59—22no—
463C2×Dic59—22no—
464C2×Dic59—22no—
465C2×Dic59—22no—
466C2×Dic59—22no—
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—
480C2×Dic59—41no—
481C2×Dic59—41no—
482C2×Dic59—41no—
483C2×Dic59—41no—
484C2×Dic59—41no—
485C2×Dic59—41no—
486C2×Dic59—41no—
487C2×Dic59—41no—
488C2×Dic59—41no—
489C2×Dic59—41no—
490C2×Dic59—41no—
491C2×Dic59—41no—
492C2×Dic59—41no—
493C2×Dic59—41no—
494C2×Dic59—41no—
495C2×Dic59—41no—
496C2×Dic59—41no—
497C2×Dic59—41no—
498C2×Dic59—41no—
499C2×Dic59—41no—
500C2×Dic59—41no—
501#13999—591nomaximal, Sylow
502C22×C59—24no—
503C22×C59—24no—
504C22×C59—24no—
505C22×C59—24no—
506C22×C59—24no—
507C22×C59—24no—
508C22×C59—24no—
509C22×C59—24no—
510C22×C59—24no—
511C22×C59—24no—
512C22×C59—24no—
513C22×C59—24no—
514C22×C59—24no—
515C22×C59—24no—
516C22×C59#38818yescomplemented
517C22×C59C2×#11711yescharacteristic
518C22×C59C2×C4×D411yescharacteristic
519C22×C59C2×C4×D411yescharacteristic
520C22×C59C2×C4×D411yescharacteristic
521C22×C59C4×#4111yescharacteristic
522C22×C59#51811yescharacteristic
523C22×C59#52011yescharacteristic
524C22×C59C2×#12111yescharacteristic
525C22×C59C2×#12111yescharacteristic
526C22×C59C2×#12311yescharacteristic
527C22×C59#52511yescharacteristic
528C22×C59C2×#12411yescharacteristic
529C22×C59C2×#12611yescharacteristic
530C22×C59#52911yescharacteristic
531C22×C59#53211yescharacteristic
532C22×C59#53411yescharacteristic
533C22×C59#53711yescharacteristic
534C22×C59#53811yescharacteristic
535C22×C59#53911yescharacteristic
536C22×C59D4211yescharacteristic
537C22×C59#54611yescharacteristic
538C22×C59#54611yescharacteristic
539C22×C59#54611yescharacteristic
540C22×C59#54611yescharacteristic
541C22×C59#54711yescharacteristic
542C22×C59#54811yescharacteristic
543C22×C59#55111yescharacteristic
544C22×C59#55111yescharacteristic
545C22×C59#55111yescharacteristic
546C22×C59#55111yescharacteristic
547C22×C59#55211yescharacteristic
548C22×C59#55211yescharacteristic
549C22×C59#55311yescharacteristic
550C22×C59#55311yescharacteristic
551C22×C59#55311yescharacteristic
552C2×D59—42no—
553C2×D59—42no—
554C2×D59—42no—
555C2×D59—42no—
556C2×D59—42no—
557C2×D59—42no—
558C2×D59—42no—
559C2×D59—81no—
560C2×D59—81no—
561C2×D59—81no—
562C2×D59—81no—
563C2×D59—81no—
564C2×D59—81no—
565C2×D59—81no—
566C2×D59—81no—
567C4×C59—24no—
568C4×C59—24no—
569C4×C59—42no—
570C4×C59—42no—
571C4×C59—42no—
572C4×C59—42no—
573Dic59—42no—
574Dic59—42no—
575Dic59—42no—
576Dic59—42no—
577Dic59—42no—
578Dic59—81no—
579Dic59—81no—
580C2×#388—591no—
581C2×#386—591no—
582C2×#386—591no—
583C2×#386—591no—
584C2×#380—591no—
585C2×C4×C22⋊C4—591no—
586C22×#95D5911yescharacteristic, complemented
587#1443—591no—
588#1442—591no—
589#1440—591no—
590#1439—591no—
591#1437—591no—
592#1436—591no—
593#1434—591no—
594C22⋊#95—591no—
595C2×C59—28no—
596C2×C59C2×#38811yescharacteristic
597C2×C59C4×#12111yescharacteristic
598C2×C59#232511yescharacteristic
599C2×C59#235211yescharacteristic
600C2×C59#235311yescharacteristic
601C2×C59#235811yescharacteristic
602C2×C59#235911yescharacteristic
603C2×C59#241211yescharacteristic
604C2×C59#241611yescharacteristic
605C2×C59#247211yescharacteristic
606C2×C59#248111yescharacteristic
607C2×C59#248811yescharacteristic
608C2×C59#249811yescharacteristic
609C2×C59#251011yescharacteristic
610C2×C59#254311yescharacteristic
611D59—82no—
612C23×D4—591no—
613C24×C4C2×D5911yescharacteristic
614C24×C4C2×D5911yescharacteristic
615C24×C4C2×D5911yescharacteristic
616C22×C4⋊C4—591no—
617C22×C4⋊C4—591no—
618C22×C22⋊C4—591no—
619C22×C22⋊C4—591no—
620C22×C22⋊C4—591no—
621C22×C22⋊C4—591no—
622C22×C22⋊C4—591no—
623C22×C22⋊C4—591no—
624C22×C22⋊C4—591no—
625C22×C22⋊C4—591no—
626C22×C22⋊C4—591no—
627C22×C42—591no—
628C22×C42—591no—
629#388—1184no—
630#386—598no—
631#386—1184no—
632#386—1184no—
633#380—1184no—
634C4×C22⋊C4—1184no—
635C2×#95—24no—
636C2×#95—591no—
637C2×#95—591no—
638C2×#95—591no—
639C2×#95—591no—
640C2×#95—591no—
641C2×#95—591no—
642C2×#95—591no—
643C2×#95—591no—
644C2×#95—591no—
645C2×#95—591no—
646C2×#95—591no—
647C2×#95—591no—
648C2×#95—591no—
649C2×#95—591no—
650C2×#95C2×D5911yescharacteristic
651C2×#95C2×D5911yescharacteristic
652C2×#95C2×D5911yescharacteristic
653C2×#95C2×D5911yescharacteristic
654C59#1399911yescharacteristic, complemented, Sylow
655C25—591no—
656C25C22×D5911yescharacteristic
657C22×D4—594no—
658C22×D4—1182no—
659C22×D4—1182no—
660C22×D4—1182no—
661C22×D4—1182no—
662C22×D4—1182no—
663C22×D4—1182no—
664C23×C4—22no—
665C23×C4—22no—
666C23×C4—22no—
667C23×C4—22no—
668C23×C4—22no—
669C23×C4—22no—
670C23×C4—22no—
671C23×C4—22no—
672C23×C4—22no—
673C23×C4—22no—
674C23×C4—22no—
675C23×C4—22no—
676C23×C4—22no—
677C23×C4—41no—
678C23×C4—41no—
679C23×C4—41no—
680C23×C4—41no—
681C23×C4—41no—
682C23×C4—41no—
683C23×C4—591no—
684C23×C4—591no—
685C23×C4—591no—
686C23×C4—591no—
687C23×C4—591no—
688C23×C4—591no—
689C23×C4—591no—
690C23×C4C4×D5914yes—
691C23×C4D23614yes—
692C23×C4C22×D5911yescharacteristic
693C23×C4C22×D5911yescharacteristic
694C23×C4C22×D5911yescharacteristic
695C23×C4C22×D5911yescharacteristic
696C23×C4C22×D5911yescharacteristic
697C23×C4C22×D5911yescharacteristic
698C2×C4⋊C4—1182no—
699C2×C4⋊C4—1182no—
700C2×C4⋊C4—1182no—
701C2×C4⋊C4—1182no—
702C2×C4⋊C4—2361no—
703C2×C4⋊C4—2361no—
704C2×C22⋊C4—594no—
705C2×C22⋊C4—594no—
706C2×C22⋊C4—594no—
707C2×C22⋊C4—594no—
708C2×C22⋊C4—1182no—
709C2×C22⋊C4—1182no—
710C2×C22⋊C4—1182no—
711C2×C22⋊C4—1182no—
712C2×C22⋊C4—1182no—
713C2×C22⋊C4—1182no—
714C2×C22⋊C4—1182no—
715C2×C22⋊C4—1182no—
716C2×C22⋊C4—1182no—
717C2×C22⋊C4—1182no—
718C2×C22⋊C4—1182no—
719C2×C22⋊C4—1182no—
720C2×C22⋊C4—1182no—
721C2×C22⋊C4—1182no—
722C2×C22⋊C4—1182no—
723C2×C22⋊C4—1182no—
724C2×C22⋊C4—1182no—
725C2×C22⋊C4—2361no—
726C2×C22⋊C4—2361no—
727C2×C22⋊C4—2361no—
728C2×C22⋊C4—2361no—
729C2×C22⋊C4—2361no—
730C2×C22⋊C4—2361no—
731C2×C42—1182no—
732C2×C42—1182no—
733C2×C42—1182no—
734C2×C42—1182no—
735C2×C42—2361no—
736C2×C42—2361no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—594no—
741#95—594no—
742#95—1182no—
743#95—1182no—
744#95—1182no—
745#95—1182no—
746#95—1182no—
747#95—1182no—
748#95—1182no—
749#95—1182no—
750#95—1182no—
751#95—1182no—
752#95—2361no—
753#95—2361no—
754#95C22⋊D5914yescomplemented
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—592no—
764C24—1181no—
765C24—1181no—
766C24—1181no—
767C24—1181no—
768C24—1181no—
769C24—1181no—
770C24—1181no—
771C24—1181no—
772C24—1181no—
773C24—1181no—
774C24—1181no—
775C24—1181no—
776C24—1181no—
777C24—1181no—
778C24C2×C4×D5912yes—
779C24C2×D23612yes—
780C24#1174568512yes—
781C24D4×D5912yes—
782C24#1174568712yes—
783C24#1174568712yes—
784C24#1174568912yes—
785C24C23×D5911yescharacteristic
786C2×D4—1188no—
787C2×D4—1188no—
788C2×D4—1188no—
789C2×D4—2364no—
790C2×D4—2364no—
791C2×D4—2364no—
792C2×D4—2364no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—28no—
802C22×C4—28no—
803C22×C4—28no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—28no—
829C22×C4—28no—
830C22×C4—44no—
831C22×C4—44no—
832C22×C4—44no—
833C22×C4—44no—
834C22×C4—44no—
835C22×C4—44no—
836C22×C4—44no—
837C22×C4—44no—
838C22×C4—44no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4—44no—
843C22×C4—44no—
844C22×C4—44no—
845C22×C4—44no—
846C22×C4—592no—
847C22×C4—592no—
848C22×C4—592no—
849C22×C4—592no—
850C22×C4—592no—
851C22×C4—1181no—
852C22×C4—1181no—
853C22×C4—1181no—
854C22×C4—1181no—
855C22×C4—1181no—
856C22×C4—1181no—
857C22×C4—1181no—
858C22×C4—1181no—
859C22×C4—1181no—
860C22×C4—1181no—
861C22×C4—1181no—
862C22×C4—1181no—
863C22×C4—1181no—
864C22×C4—1181no—
865C22×C4—1181no—
866C22×C4—1181no—
867C22×C4—1181no—
868C22×C4—1181no—
869C22×C4—1181no—
870C22×C4—1181no—
871C22×C4—1181no—
872C22×C4—1181no—
873C22×C4—1181no—
874C22×C4—1181no—
875C22×C4—1181no—
876C22×C4—1181no—
877C22×C4—1181no—
878C22×C4—1181no—
879C22×C4—1181no—
880C22×C4—1181no—
881C22×C4—1181no—
882C22×C4—1181no—
883C22×C4—1181no—
884C22×C4—1181no—
885C22×C4—1181no—
886C22×C4—1181no—
887C22×C4—1181no—
888C22×C4—1181no—
889C22×C4—1181no—
890C22×C4—1181no—
891C22×C4—1181no—
892C22×C4—1181no—
893C22×C4—1181no—
894C22×C4—1181no—
895C22×C4C2×C4×D5912yes—
896C22×C4C2×C4×D5912yes—
897C22×C4C2×D23612yes—
898C22×C4C2×D23612yes—
899C22×C4#1174568512yes—
900C22×C4#1174568512yes—
901C22×C4#1174568512yes—
902C22×C4C2×C22⋊D5912yes—
903C22×C4C2×C22⋊D5912yes—
904C22×C4C2×C22⋊D5912yes—
905C4⋊C4—2364no—
906C4⋊C4—2364no—
907C22⋊C4—1188no—
908C22⋊C4—1188no—
909C22⋊C4—1188no—
910C22⋊C4—2364no—
911C22⋊C4—2364no—
912C22⋊C4—2364no—
913C22⋊C4—2364no—
914C22⋊C4—2364no—
915C22⋊C4—2364no—
916C42—2364no—
917C42—2364no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—1182no—
947C23—1182no—
948C23—1182no—
949C23—1182no—
950C23—1182no—
951C23—1182no—
952C23—1182no—
953C23—2361no—
954C23—2361no—
955C23—2361no—
956C23—2361no—
957C23—2361no—
958C23—2361no—
959C23—2361no—
960C23—2361no—
961C23—2361no—
962C23—2361no—
963C23—2361no—
964C23—2361no—
965C23—2361no—
966C23—2361no—
967C23—2361no—
968C23—2361no—
969C23—2361no—
970C23—2361no—
971C23—2361no—
972C23—2361no—
973C23—2361no—
974C23—2361no—
975C23—2361no—
976C23—2361no—
977C23—2361no—
978C23—2361no—
979C23—2361no—
980C23—2361no—
981C23#1427368514yes—
982C23(C22⋊D59)⋊C414yes—
983C23C4×D23614yes—
984C23#1427370214yes—
985C23#1427371114yes—
986C23#1427371314yes—
987C23#1427372214yes—
988C23C22×C4×D5911yescharacteristic
989C23C2×D4×D5911yescharacteristic
990C23C22×C22⋊D5911yescharacteristic
991C23C22×D23611yescharacteristic
992C23C2×#1174568711yescharacteristic
993C23C2×#1174568711yescharacteristic
994C23C2×#1174568511yescharacteristic
995C23C2×#1174568511yescharacteristic
996C23C2×#1174568511yescharacteristic
997C23C2×#1174568511yescharacteristic
998C23C2×#1174568911yescharacteristic
999C23#1427377211yescharacteristic
1000C23#1427377211yescharacteristic
1001C23#1427377211yescharacteristic
1002C23#1427377511yescharacteristic
1003D4—23616no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—416no—
1029C2×C4—416no—
1030C2×C4—416no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—1182no—
1048C2×C4—1182no—
1049C2×C4—1182no—
1050C2×C4—1182no—
1051C2×C4—1182no—
1052C2×C4—1182no—
1053C2×C4—1182no—
1054C2×C4—1182no—
1055C2×C4—1182no—
1056C2×C4—1182no—
1057C2×C4—1182no—
1058C2×C4—1182no—
1059C2×C4—1182no—
1060C2×C4—1182no—
1061C2×C4—1182no—
1062C2×C4—2361no—
1063C2×C4—2361no—
1064C2×C4—2361no—
1065C2×C4—2361no—
1066C2×C4—2361no—
1067C2×C4—2361no—
1068C2×C4—2361no—
1069C2×C4—2361no—
1070C2×C4—2361no—
1071C2×C4—2361no—
1072C2×C4—2361no—
1073C2×C4—2361no—
1074C2×C4—2361no—
1075C2×C4—2361no—
1076C2×C4—2361no—
1077C2×C4—2361no—
1078C2×C4—2361no—
1079C2×C4—2361no—
1080C2×C4—2361no—
1081C2×C4—2361no—
1082C2×C4—2361no—
1083C2×C4—2361no—
1084C2×C4—2361no—
1085C2×C4—2361no—
1086C2×C4—2361no—
1087C2×C4—2361no—
1088C2×C4—2361no—
1089C2×C4—2361no—
1090C2×C4—2361no—
1091C2×C4—2361no—
1092C2×C4—2361no—
1093C2×C4—2361no—
1094C2×C4—2361no—
1095C2×C4—2361no—
1096C2×C4C4×C22⋊D5914yes—
1097C2×C4#1427370114yes—
1098C22—24no—
1099C22—24no—
1100C22—24no—
1101C22—24no—
1102C22—24no—
1103C22—24no—
1104C22—24no—
1105C22—24no—
1106C22—24no—
1107C22—24no—
1108C22—24no—
1109C22—24no—
1110C22—24no—
1111C22—24no—
1112C22—4721no—
1113C22—4721no—
1114C22—4721no—
1115C22—4721no—
1116C22—4721no—
1117C22—4721no—
1118C22—4721no—
1119C22—4721no—
1120C22—2362no—
1121C22—2362no—
1122C22—2362no—
1123C22—2362no—
1124C22—2362no—
1125C22—2362no—
1126C22—2362no—
1127C22#1683729418yescomplemented
1128C22C2×#1427368511yescharacteristic
1129C22C2×(C22⋊D59)⋊C411yescharacteristic
1130C22C2×C4×C22⋊D5911yescharacteristic
1131C22C2×C4×D23611yescharacteristic
1132C22C4×#1174568511yescharacteristic
1133C22#1683787511yescharacteristic
1134C22#1683788311yescharacteristic
1135C22C2×#1427370111yescharacteristic
1136C22C2×#1427370211yescharacteristic
1137C22C2×#1427371111yescharacteristic
1138C22#1683791311yescharacteristic
1139C22C2×#1427371311yescharacteristic
1140C22C2×#1427372211yescharacteristic
1141C22#1683793611yescharacteristic
1142C22#1683795211yescharacteristic
1143C22#1683796411yescharacteristic
1144C22#1683798311yescharacteristic
1145C22#1683799011yescharacteristic
1146C22#1683799911yescharacteristic
1147C22D4×C22⋊D5911yescharacteristic
1148C22#1683804211yescharacteristic
1149C22#1683804211yescharacteristic
1150C22#1683804611yescharacteristic
1151C22#1683804611yescharacteristic
1152C22#1683805311yescharacteristic
1153C22#1683806311yescharacteristic
1154C22#1683807811yescharacteristic
1155C22#1683807811yescharacteristic
1156C22#1683807811yescharacteristic
1157C22#1683807811yescharacteristic
1158C22#1683808711yescharacteristic
1159C22#1683808711yescharacteristic
1160C22#1683810011yescharacteristic
1161C22#1683810011yescharacteristic
1162C22#1683810011yescharacteristic
1163C4—24no—
1164C4—24no—
1165C4—42no—
1166C4—42no—
1167C4—42no—
1168C4—42no—
1169C4—4721no—
1170C4—4721no—
1171C4—2362no—
1172C4—2362no—
1173C4—2362no—
1174C4—2362no—
1175C4—2362no—
1176C2—28no—
1177C2—4722no—
1178C2C2×#1683729411yescharacteristic
1179C2C4×#1427370111yescharacteristic
1180C2#2142679911yescharacteristic
1181C2#2142702111yescharacteristic
1182C2#2142703211yescharacteristic
1183C2#2142707511yescharacteristic
1184C2#2142708411yescharacteristic
1185C2#2142748611yescharacteristic
1186C2#2142753011yescharacteristic
1187C2#2142821611yescharacteristic
1188C2#2142835111yescharacteristic
1189C2#2142842211yescharacteristic
1190C2#2142854011yescharacteristic
1191C2#2142865611yescharacteristic
1192C2#2142905611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC22×#95×C59C2
socle, cosocleC24×C59C24
prime radicalC23×C22⋊D59C22
hypercenterC22×#95D59
hypocenterC59#13999
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
1. C2×#16837294C2semidirect
5. C2×#16837262C2semidirect
6. C2×C4×C22⋊Dic59C2semidirect
7. #21422356C2semidirect
8. #21422352C2semidirect
9. #21422344C2semidirect
10. #21422342C2semidirect
11. #21422332C2semidirect
12. #21422330C2semidirect
13. #21422320C2semidirect
14. #21422319C2semidirect
15. C22×#95×C59C2semidirect
33. #16837281C4semidirect
104. C2×(C2×D59)⋊C4C2×C4semidirect
105. C2×(C2×D59)⋊C4C2×C4semidirect
124. C59⋊#95C2×C4semidirect
125. C59⋊#95C2×C4semidirect
157. #95×C59D4semidirect
516. C22×C59#388semidirect
586. C22×#95D59semidirect
654. C59#13999semidirect
754. #95C22⋊D59semidirect
1127. C22#16837294semidirect

Maximal subgroups

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

subgroupindex
C2×#168372942
C2×#168372812
C2×#168372622
C2×C4×C22⋊Dic592
#214223562
#214223522
#214223442
#214223422
#214223322
#214223302
#214223202
#214223192
C22×#95×C592
#1399959