Finite Group Databasebeta

← #28520303

Subgroups — #28520303

Order 15104.

1938 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837335C211yesmaximal, characteristic, complemented
2C2×#16837277C211yesmaximal, characteristic
3C2×#16837274C211yesmaximal, characteristic
4C2×#16837274C211yesmaximal, characteristic
5C22×C59⋊#95C211yesmaximal, characteristic
6#21422362C211yesmaximal, characteristic, complemented
7#21422359C211yesmaximal, characteristic, complemented
8#21422355C211yesmaximal, characteristic, complemented
9#21422354C211yesmaximal, characteristic, complemented
10#21422350C211yesmaximal, characteristic, complemented
11#21422349C211yesmaximal, characteristic, complemented
12#21422348C211yesmaximal, characteristic, complemented
13#21422319C211yesmaximal, characteristic
14#21422318C211yesmaximal, characteristic
15C2×C59×#380C211yesmaximal, characteristic
16C24×Dic59C2211yescharacteristic
17C24×Dic59C2211yescharacteristic
18C22×C4⋊Dic59C2211yescharacteristic
19C22×C4⋊Dic59C2211yescharacteristic
20C22×Dic59⋊C4C2211yescharacteristic
21C22×Dic59⋊C4C2211yescharacteristic
22C22×Dic59⋊C4C2211yescharacteristic
23C22×Dic59⋊C4C2211yescharacteristic
24C22×C22⋊Dic59C2211yescharacteristic
25C22×C22⋊Dic59C2211yescharacteristic
26#16837335—24no—
27#16837277—24no—
28#16837274—24no—
29#16837274—24no—
30C2×C59⋊#95—24no—
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
46C2×C59⋊#95C2211yescharacteristic
47C2×C59⋊#95C2211yescharacteristic
48C2×C59⋊#95C2211yescharacteristic
49C24×C4×C59C2211yescharacteristic
50C22×C4⋊C4×C59C2211yescharacteristic
51C22×C4⋊C4×C59C2211yescharacteristic
52C22×C22⋊C4×C59C2211yescharacteristic
53C22×C22⋊C4×C59C2211yescharacteristic
54C59×#380—24no—
55C2×#95×C59C2211yescharacteristic
56C2×#95×C59C2211yescharacteristic
57C23×Dic59—22no—
58C23×Dic59—22no—
59C23×Dic59—22no—
60C23×Dic59—22no—
61C23×Dic59—22no—
62C23×Dic59—22no—
63C23×Dic59—22no—
64C23×Dic59—22no—
65C23×Dic59—22no—
66C23×Dic59—22no—
67C23×Dic59—41no—
68C23×Dic59—41no—
69C23×Dic59—41no—
70C23×Dic59—41no—
71C23×Dic59C2311yescharacteristic
72C23×Dic59C2311yescharacteristic
73C23×Dic59C2311yescharacteristic
74C23×Dic59C2311yescharacteristic
75C23×Dic59C2311yescharacteristic
76C23×Dic59C2311yescharacteristic
77C23×Dic59C2311yescharacteristic
78C23×Dic59C2311yescharacteristic
79C2×C4⋊Dic59—22no—
80C2×C4⋊Dic59—22no—
81C2×C4⋊Dic59—22no—
82C2×C4⋊Dic59—22no—
83C2×C4⋊Dic59—41no—
84C2×C4⋊Dic59—41no—
85C2×Dic59⋊C4—22no—
86C2×Dic59⋊C4—22no—
87C2×Dic59⋊C4—22no—
88C2×Dic59⋊C4—22no—
89C2×Dic59⋊C4—22no—
90C2×Dic59⋊C4—22no—
91C2×Dic59⋊C4—22no—
92C2×Dic59⋊C4—22no—
93C2×Dic59⋊C4—41no—
94C2×Dic59⋊C4—41no—
95C2×Dic59⋊C4—41no—
96C2×Dic59⋊C4—41no—
97C2×C22⋊Dic59—22no—
98C2×C22⋊Dic59—22no—
99C2×C22⋊Dic59—22no—
100C2×C22⋊Dic59—22no—
101C2×C22⋊Dic59D414yes—
102C2×C22⋊Dic59Q814yes—
103C59⋊#95—22no—
104C59⋊#95—22no—
105C59⋊#95—22no—
106C59⋊#95—22no—
107C59⋊#95—22no—
108C59⋊#95—22no—
109C59⋊#95—22no—
110C59⋊#95—22no—
111C59⋊#95—22no—
112C59⋊#95—22no—
113C59⋊#95—22no—
114C59⋊#95—22no—
115C59⋊#95—22no—
116C59⋊#95—41no—
117C59⋊#95—41no—
118C59⋊#95—41no—
119C59⋊#95—41no—
120C59⋊#95D414yes—
121C25×C59C2311yescharacteristic
122C23×C4×C59—22no—
123C23×C4×C59—22no—
124C23×C4×C59—22no—
125C23×C4×C59—22no—
126C23×C4×C59—41no—
127C23×C4×C59—41no—
128C23×C4×C59Q814yes—
129C23×C4×C59C2311yescharacteristic
130C23×C4×C59C2311yescharacteristic
131C23×C4×C59C2311yescharacteristic
132C23×C4×C59C2311yescharacteristic
133C23×C4×C59C2311yescharacteristic
134C23×C4×C59C2311yescharacteristic
135C2×C4⋊C4×C59—22no—
136C2×C4⋊C4×C59—22no—
137C2×C4⋊C4×C59—22no—
138C2×C4⋊C4×C59—22no—
139C2×C4⋊C4×C59—41no—
140C2×C4⋊C4×C59—41no—
141C2×C22⋊C4×C59—22no—
142C2×C22⋊C4×C59—22no—
143C2×C22⋊C4×C59—22no—
144C2×C22⋊C4×C59—22no—
145C2×C22⋊C4×C59—22no—
146C2×C22⋊C4×C59D414yes—
147#95×C59—22no—
148#95×C59—22no—
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×C59C2×D412yes—
158C24×C59C2×D412yes—
159C24×C59C2×Q812yes—
160C24×C59C2×Q812yes—
161C24×C59#4112yes—
162C24×C59#4112yes—
163C24×C59#4112yes—
164C24×C59C2411yescharacteristic
165C22×C4×C59—21no—
166C22×C4×C59—21no—
167C22×C4×C59—21no—
168C22×C4×C59—21no—
169C22×C4×C59—28no—
170C22×C4×C59—21no—
171C22×C4×C59—21no—
172C22×C4×C59—21no—
173C22×C4×C59—21no—
174C22×C4×C59—21no—
175C22×C4×C59—21no—
176C22×C4×C59—21no—
177C22×C4×C59—21no—
178C22×C4×C59—21no—
179C22×C4×C59—21no—
180C22×C4×C59—21no—
181C22×C4×C59—21no—
182C22×C4×C59—21no—
183C22×C4×C59—21no—
184C22×C4×C59—21no—
185C22×C4×C59—21no—
186C22×C4×C59—21no—
187C22×C4×C59—21no—
188C22×C4×C59—28no—
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—44no—
204C22×C4×C59—44no—
205C22×C4×C59—44no—
206C22×C4×C59—44no—
207C22×C4×C59—44no—
208C22×C4×C59C2×D412yes—
209C22×C4×C59C2×D412yes—
210C22×C4×C59C2×D412yes—
211C22×C4×C59C2×Q812yes—
212C22×C4×C59C2×Q812yes—
213C22×C4×C59#4112yes—
214C22×Dic59—28no—
215C22×Dic59—28no—
216C22×Dic59—21no—
217C22×Dic59—21no—
218C22×Dic59—21no—
219C22×Dic59—21no—
220C22×Dic59—21no—
221C22×Dic59—21no—
222C22×Dic59—21no—
223C22×Dic59—21no—
224C22×Dic59—21no—
225C22×Dic59—21no—
226C22×Dic59—21no—
227C22×Dic59—21no—
228C22×Dic59—21no—
229C22×Dic59—21no—
230C22×Dic59—21no—
231C22×Dic59—21no—
232C22×Dic59—21no—
233C22×Dic59—21no—
234C22×Dic59—21no—
235C22×Dic59—21no—
236C22×Dic59—21no—
237C22×Dic59—21no—
238C22×Dic59—21no—
239C22×Dic59—21no—
240C22×Dic59—21no—
241C22×Dic59—21no—
242C22×Dic59—21no—
243C22×Dic59—21no—
244C22×Dic59—21no—
245C22×Dic59—21no—
246C22×Dic59—21no—
247C22×Dic59—21no—
248C22×Dic59—21no—
249C22×Dic59—21no—
250C22×Dic59—21no—
251C22×Dic59—21no—
252C22×Dic59—21no—
253C22×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—44no—
265C22×Dic59—44no—
266C22×Dic59—44no—
267C22×Dic59—44no—
268C22×Dic59—44no—
269C22×Dic59—44no—
270C22×Dic59—44no—
271C22×Dic59—44no—
272C22×Dic59—44no—
273C22×Dic59—44no—
274C22×Dic59—44no—
275C22×Dic59—44no—
276C22×Dic59C2×D412yes—
277C22×Dic59C2×D412yes—
278C22×Dic59C2×D412yes—
279C22×Dic59C2×D412yes—
280C22×Dic59C2×Q812yes—
281C22×Dic59C2×Q812yes—
282C22×Dic59#4112yes—
283C22×Dic59#4112yes—
284C4⋊C4×C59—44no—
285C4⋊C4×C59—44no—
286C22⋊C4×C59—28no—
287C22⋊C4×C59—44no—
288C22⋊Dic59—28no—
289C22⋊Dic59—28no—
290C4⋊Dic59—44no—
291C4⋊Dic59—44no—
292Dic59⋊C4—44no—
293Dic59⋊C4—44no—
294Dic59⋊C4—44no—
295Dic59⋊C4—44no—
296C23×C59—22no—
297C23×C59—22no—
298C23×C59—22no—
299C23×C59—22no—
300C23×C59—22no—
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#12114yes—
325C23×C59C22⋊Q814yes—
326C23×C59C22⋊Q814yes—
327C23×C59#12314yes—
328C23×C59#12514yes—
329C23×C59#12514yes—
330C23×C59C4⋊Q814yes—
331C23×C59C22×D411yescharacteristic
332C23×C59C22×D411yescharacteristic
333C23×C59C22×D411yescharacteristic
334C23×C59C22×Q811yescharacteristic
335C23×C59C22×Q811yescharacteristic
336C23×C59C2×#4111yescharacteristic
337C23×C59C2×#4111yescharacteristic
338C23×C59C2×#4111yescharacteristic
339C23×C59C2×#4111yescharacteristic
340C23×C59C2×#4111yescharacteristic
341C23×C59C2×#4111yescharacteristic
342C23×C59H(5,𝔽2)11yescharacteristic
343C23×C59H(5,𝔽2)11yescharacteristic
344C23×C59H(5,𝔽2)11yescharacteristic
345C23×C592−1+411yescharacteristic
346C2×C4×C59—22no—
347C2×C4×C59—22no—
348C2×C4×C59—22no—
349C2×C4×C59—22no—
350C2×C4×C59—22no—
351C2×C4×C59—22no—
352C2×C4×C59—22no—
353C2×C4×C59—22no—
354C2×C4×C59—22no—
355C2×C4×C59—22no—
356C2×C4×C59—22no—
357C2×C4×C59—22no—
358C2×C4×C59—22no—
359C2×C4×C59—22no—
360C2×C4×C59—22no—
361C2×C4×C59—416no—
362C2×C4×C59—41no—
363C2×C4×C59—41no—
364C2×C4×C59—41no—
365C2×C4×C59—41no—
366C2×C4×C59—41no—
367C2×C4×C59—41no—
368C2×C4×C59—41no—
369C2×C4×C59—41no—
370C2×C4×C59—41no—
371C2×C4×C59—41no—
372C2×C4×C59—41no—
373C2×C4×C59—41no—
374C2×C4×C59—41no—
375C2×C4×C59—41no—
376C2×C4×C59—41no—
377C2×C4×C59—41no—
378C2×C4×C59—41no—
379C2×C4×C59—41no—
380C2×C4×C59—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×C59C22⋊Q814yes—
389C2×Dic59—22no—
390C2×Dic59—22no—
391C2×Dic59—22no—
392C2×Dic59—22no—
393C2×Dic59—22no—
394C2×Dic59—22no—
395C2×Dic59—22no—
396C2×Dic59—22no—
397C2×Dic59—22no—
398C2×Dic59—22no—
399C2×Dic59—22no—
400C2×Dic59—22no—
401C2×Dic59—22no—
402C2×Dic59—22no—
403C2×Dic59—22no—
404C2×Dic59—22no—
405C2×Dic59—22no—
406C2×Dic59—22no—
407C2×Dic59—22no—
408C2×Dic59—22no—
409C2×Dic59—22no—
410C2×Dic59—22no—
411C2×Dic59—22no—
412C2×Dic59—22no—
413C2×Dic59—416no—
414C2×Dic59—416no—
415C2×Dic59—41no—
416C2×Dic59—41no—
417C2×Dic59—41no—
418C2×Dic59—41no—
419C2×Dic59—41no—
420C2×Dic59—41no—
421C2×Dic59—41no—
422C2×Dic59—41no—
423C2×Dic59—41no—
424C2×Dic59—41no—
425C2×Dic59—41no—
426C2×Dic59—41no—
427C2×Dic59—41no—
428C2×Dic59—41no—
429C2×Dic59—41no—
430C2×Dic59—41no—
431C2×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—
447#14736—591nomaximal, Sylow
448C22×C59—24no—
449C22×C59—24no—
450C22×C59—24no—
451C22×C59—24no—
452C22×C59—24no—
453C22×C59—24no—
454C22×C59—24no—
455C22×C59—24no—
456C22×C59—24no—
457C22×C59—24no—
458C22×C59—24no—
459C22×C59—24no—
460C22×C59—24no—
461C22×C59—24no—
462C22×C59#39818yescomplemented
463C22×C59C2×#12111yescharacteristic
464C22×C59C2×C22⋊Q811yescharacteristic
465C22×C59C2×C22⋊Q811yescharacteristic
466C22×C59C2×C22⋊Q811yescharacteristic
467C22×C59C2×#12311yescharacteristic
468C22×C59#52511yescharacteristic
469C22×C59#52511yescharacteristic
470C22×C59C2×#12511yescharacteristic
471C22×C59C2×#12511yescharacteristic
472C22×C59#52911yescharacteristic
473C22×C59#52911yescharacteristic
474C22×C59C2×C4⋊Q811yescharacteristic
475C22×C59#53311yescharacteristic
476C22×C59#53811yescharacteristic
477C22×C59#53811yescharacteristic
478C22×C59#53911yescharacteristic
479C22×C59#53911yescharacteristic
480C22×C59#54311yescharacteristic
481C22×C59#54411yescharacteristic
482C22×C59D4211yescharacteristic
483C22×C59D4211yescharacteristic
484C22×C59#54611yescharacteristic
485C22×C59#54611yescharacteristic
486C22×C59#54611yescharacteristic
487C22×C59#54611yescharacteristic
488C22×C59#54611yescharacteristic
489C22×C59#54711yescharacteristic
490C22×C59#54711yescharacteristic
491C22×C59D4×Q811yescharacteristic
492C22×C59#55111yescharacteristic
493C22×C59#55111yescharacteristic
494C22×C59#55211yescharacteristic
495C22×C59#55411yescharacteristic
496C22×C59#55411yescharacteristic
497C22×C59#55411yescharacteristic
498C4×C59—24no—
499C4×C59—42no—
500C4×C59—42no—
501C4×C59—42no—
502C4×C59—81no—
503C4×C59—81no—
504Dic59—42no—
505Dic59—42no—
506Dic59—42no—
507Dic59—42no—
508Dic59—42no—
509Dic59—42no—
510Dic59—42no—
511Dic59—42no—
512C2×#398—591no—
513C2×#385—591no—
514C2×#385—591no—
515C2×#385—591no—
516C2×#380D5911yescharacteristic
517C22×#95—591no—
518#1445—591no—
519#1444—591no—
520#1442—591no—
521#1442—591no—
522#1441—591no—
523#1441—591no—
524#1441—591no—
525C22⋊#95—591no—
526C22⋊#95—591no—
527C2×C59—28no—
528C2×C59C2×#39811yescharacteristic
529C2×C59#241811yescharacteristic
530C2×C59#241911yescharacteristic
531C2×C59#242411yescharacteristic
532C2×C59#242511yescharacteristic
533C2×C59#243711yescharacteristic
534C2×C59#243811yescharacteristic
535C2×C59#244011yescharacteristic
536C2×C59#244911yescharacteristic
537C2×C59#245011yescharacteristic
538C2×C59#247311yescharacteristic
539C2×C59#250511yescharacteristic
540C2×C59#254911yescharacteristic
541C2×C59#264611yescharacteristic
542C2×C59#285111yescharacteristic
543C24×C4—591no—
544C24×C4—591no—
545C24×C4C2×D5911yescharacteristic
546C22×C4⋊C4—591no—
547C22×C4⋊C4—591no—
548C22×C4⋊C4—591no—
549C22×C4⋊C4—591no—
550C22×C4⋊C4—591no—
551C22×C4⋊C4—591no—
552C22×C4⋊C4C2×D5911yescharacteristic
553C22×C4⋊C4C2×D5911yescharacteristic
554C22×C22⋊C4—591no—
555C22×C22⋊C4—591no—
556C22×C22⋊C4C2×D5911yescharacteristic
557C22×C22⋊C4C2×D5911yescharacteristic
558#398—1184no—
559#385—1184no—
560#385—1184no—
561#385—1184no—
562#380—24no—
563C2×#95—591no—
564C2×#95—591no—
565C2×#95—591no—
566C2×#95—591no—
567C2×#95—591no—
568C2×#95—591no—
569C2×#95—591no—
570C2×#95—591no—
571C2×#95—591no—
572C2×#95—591no—
573C2×#95—591no—
574C2×#95—591no—
575C2×#95—591no—
576C2×#95—591no—
577C2×#95—591no—
578C2×#95—591no—
579C2×#95—591no—
580C2×#95—591no—
581C2×#95—1184no—
582C2×#95C2×D5911yescharacteristic
583C2×#95C2×D5911yescharacteristic
584C59#1473611yescharacteristic, complemented, Sylow
585C25C22×D5911yescharacteristic
586C23×C4—22no—
587C23×C4—22no—
588C23×C4—22no—
589C23×C4—22no—
590C23×C4—41no—
591C23×C4—41no—
592C23×C4—591no—
593C23×C4—591no—
594C23×C4—591no—
595C23×C4—591no—
596C23×C4—591no—
597C23×C4—591no—
598C23×C4—591no—
599C23×C4—591no—
600C23×C4—1182no—
601C23×C4—1182no—
602C23×C4—1182no—
603C23×C4—1182no—
604C23×C4—1182no—
605C23×C4—1182no—
606C23×C4—1182no—
607C23×C4—1182no—
608C23×C4—1182no—
609C23×C4—1182no—
610C23×C4—2361no—
611C23×C4—2361no—
612C23×C4—2361no—
613C23×C4—2361no—
614C23×C4Dic11814yes—
615C23×C4C22×D5911yescharacteristic
616C23×C4C22×D5911yescharacteristic
617C23×C4C22×D5911yescharacteristic
618C23×C4C22×D5911yescharacteristic
619C23×C4C22×D5911yescharacteristic
620C23×C4C22×D5911yescharacteristic
621C2×C4⋊C4—22no—
622C2×C4⋊C4—22no—
623C2×C4⋊C4—22no—
624C2×C4⋊C4—22no—
625C2×C4⋊C4—41no—
626C2×C4⋊C4—41no—
627C2×C4⋊C4—1182no—
628C2×C4⋊C4—1182no—
629C2×C4⋊C4—1182no—
630C2×C4⋊C4—1182no—
631C2×C4⋊C4—1182no—
632C2×C4⋊C4—1182no—
633C2×C4⋊C4—1182no—
634C2×C4⋊C4—1182no—
635C2×C4⋊C4—1182no—
636C2×C4⋊C4—1182no—
637C2×C4⋊C4—1182no—
638C2×C4⋊C4—1182no—
639C2×C4⋊C4—2361no—
640C2×C4⋊C4—2361no—
641C2×C4⋊C4—2361no—
642C2×C4⋊C4—2361no—
643C2×C4⋊C4—2361no—
644C2×C4⋊C4—2361no—
645C2×C22⋊C4—22no—
646C2×C22⋊C4—22no—
647C2×C22⋊C4—22no—
648C2×C22⋊C4—22no—
649C2×C22⋊C4—22no—
650C2×C22⋊C4—594no—
651C2×C22⋊C4—594no—
652C2×C22⋊C4—1182no—
653C2×C22⋊C4—1182no—
654C2×C22⋊C4—1182no—
655C2×C22⋊C4—1182no—
656C2×C22⋊C4C22⋊D5914yes—
657#95—22no—
658#95—22no—
659#95—594no—
660#95—1182no—
661#95—1182no—
662#95—1182no—
663#95—1182no—
664#95—1182no—
665#95—1182no—
666#95—1182no—
667#95—1182no—
668#95—1182no—
669#95—1182no—
670#95—1182no—
671#95—1182no—
672#95—1182no—
673#95—2361no—
674#95—2361no—
675#95—2361no—
676#95—2361no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24—21no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24C2×Dic11812yes—
686C24#1174568512yes—
687C24D4×D5912yes—
688C24#1174568712yes—
689C24Q8×D5912yes—
690C24#1174568912yes—
691C24C2×C22⋊D5912yes—
692C24C23×D5911yescharacteristic
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—28no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—28no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—44no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4—44no—
735C22×C4—44no—
736C22×C4—592no—
737C22×C4—592no—
738C22×C4—592no—
739C22×C4—592no—
740C22×C4—592no—
741C22×C4—592no—
742C22×C4—592no—
743C22×C4—592no—
744C22×C4—1188no—
745C22×C4—1188no—
746C22×C4—1181no—
747C22×C4—1181no—
748C22×C4—1181no—
749C22×C4—1181no—
750C22×C4—1181no—
751C22×C4—1181no—
752C22×C4—1181no—
753C22×C4—1181no—
754C22×C4—1181no—
755C22×C4—1181no—
756C22×C4—1181no—
757C22×C4—1181no—
758C22×C4—1181no—
759C22×C4—1181no—
760C22×C4—1181no—
761C22×C4—1181no—
762C22×C4—1181no—
763C22×C4—1181no—
764C22×C4—1181no—
765C22×C4—1181no—
766C22×C4—1181no—
767C22×C4—1181no—
768C22×C4—1181no—
769C22×C4—1181no—
770C22×C4—1181no—
771C22×C4—1181no—
772C22×C4—1181no—
773C22×C4—1181no—
774C22×C4—1181no—
775C22×C4—1181no—
776C22×C4—1181no—
777C22×C4—1181no—
778C22×C4—1181no—
779C22×C4—1181no—
780C22×C4—1181no—
781C22×C4—1181no—
782C22×C4—1181no—
783C22×C4—1181no—
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—2364no—
795C22×C4—2364no—
796C22×C4—2364no—
797C22×C4—2364no—
798C22×C4—2364no—
799C22×C4—2364no—
800C22×C4—2364no—
801C22×C4—2364no—
802C22×C4—2364no—
803C22×C4—2364no—
804C22×C4—2364no—
805C22×C4—2364no—
806C22×C4C2×Dic11812yes—
807C22×C4C2×Dic11812yes—
808C22×C4D4×D5912yes—
809C22×C4#1174568712yes—
810C22×C4C2×C22⋊D5912yes—
811C22×C4C2×C22⋊D5912yes—
812C4⋊C4—44no—
813C4⋊C4—44no—
814C4⋊C4—2364no—
815C4⋊C4—2364no—
816C4⋊C4—2364no—
817C4⋊C4—2364no—
818C4⋊C4—2364no—
819C4⋊C4—2364no—
820C22⋊C4—28no—
821C22⋊C4—44no—
822C22⋊C4—1188no—
823C22⋊C4—1188no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23#1427369914yes—
853C23#1427370314yes—
854C23#1427370614yes—
855C23#1427371214yes—
856C23#1427371714yes—
857C23#1427371814yes—
858C23#1427372614yes—
859C23C2×D4×D5911yescharacteristic
860C23C2×D4×D5911yescharacteristic
861C23C22×C22⋊D5911yescharacteristic
862C23C2×Q8×D5911yescharacteristic
863C23C22×Dic11811yescharacteristic
864C23#41×D5911yescharacteristic
865C23#41×D5911yescharacteristic
866C23C2×#1174568711yescharacteristic
867C23C2×#1174568711yescharacteristic
868C23C2×#1174568511yescharacteristic
869C23C2×#1174568911yescharacteristic
870C23#1427377211yescharacteristic
871C23#1427377211yescharacteristic
872C23#1427377311yescharacteristic
873C23#1427377411yescharacteristic
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—416no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—1182no—
917C2×C4—1182no—
918C2×C4—1182no—
919C2×C4—1182no—
920C2×C4—1182no—
921C2×C4—1182no—
922C2×C4—1182no—
923C2×C4—1182no—
924C2×C4—1182no—
925C2×C4—1182no—
926C2×C4—1182no—
927C2×C4—1182no—
928C2×C4—1182no—
929C2×C4—1182no—
930C2×C4—1182no—
931C2×C4—1182no—
932C2×C4—1182no—
933C2×C4—1182no—
934C2×C4—1182no—
935C2×C4—1182no—
936C2×C4—1182no—
937C2×C4—1182no—
938C2×C4—1182no—
939C2×C4—1182no—
940C2×C4—23616no—
941C2×C4—23616no—
942C2×C4—2361no—
943C2×C4—2361no—
944C2×C4—2361no—
945C2×C4—2361no—
946C2×C4—2361no—
947C2×C4—2361no—
948C2×C4—2361no—
949C2×C4—2361no—
950C2×C4—2361no—
951C2×C4—2361no—
952C2×C4—2361no—
953C2×C4—2361no—
954C2×C4—2361no—
955C2×C4—2361no—
956C2×C4—2361no—
957C2×C4—2361no—
958C2×C4—2361no—
959C2×C4—2361no—
960C2×C4—2361no—
961C2×C4—2361no—
962C2×C4—2361no—
963C2×C4—2361no—
964C2×C4—2361no—
965C2×C4—2361no—
966C2×C4—2361no—
967C2×C4—2361no—
968C2×C4—2361no—
969C2×C4—2361no—
970C2×C4—2361no—
971C2×C4—2361no—
972C2×C4—2361no—
973C2×C4—2361no—
974C2×C4#1427370414yes—
975C22—24no—
976C22—24no—
977C22—24no—
978C22—24no—
979C22—24no—
980C22—24no—
981C22—24no—
982C22—24no—
983C22—24no—
984C22—24no—
985C22—24no—
986C22—24no—
987C22—24no—
988C22—24no—
989C22#1683733518yescomplemented
990C22C2×#1427369911yescharacteristic
991C22C2×#1427370311yescharacteristic
992C22C2×#1427370411yescharacteristic
993C22C2×#1427370611yescharacteristic
994C22C2×#1427371211yescharacteristic
995C22#1683791211yescharacteristic
996C22#1683791511yescharacteristic
997C22C2×#1427371711yescharacteristic
998C22C2×#1427371811yescharacteristic
999C22#1683793311yescharacteristic
1000C22#1683793811yescharacteristic
1001C22C2×#1427372611yescharacteristic
1002C22#1683795511yescharacteristic
1003C22#1683798911yescharacteristic
1004C22#1683799211yescharacteristic
1005C22#1683799711yescharacteristic
1006C22#1683800111yescharacteristic
1007C22#1683802811yescharacteristic
1008C22#1683803011yescharacteristic
1009C22D4×C22⋊D5911yescharacteristic
1010C22#1683803611yescharacteristic
1011C22#1683804011yescharacteristic
1012C22#1683804111yescharacteristic
1013C22#1683804111yescharacteristic
1014C22#1683804211yescharacteristic
1015C22#1683804611yescharacteristic
1016C22#1683805111yescharacteristic
1017C22#1683805211yescharacteristic
1018C22#1683806511yescharacteristic
1019C22#1683807611yescharacteristic
1020C22#1683807811yescharacteristic
1021C22#1683808511yescharacteristic
1022C22#1683810611yescharacteristic
1023C22#1683810611yescharacteristic
1024C22#1683811011yescharacteristic
1025C4—24no—
1026C4—42no—
1027C4—42no—
1028C4—42no—
1029C4—81no—
1030C4—81no—
1031C4—2362no—
1032C4—2362no—
1033C4—2362no—
1034C4—2362no—
1035C4—2362no—
1036C4—2362no—
1037C4—2362no—
1038C4—2362no—
1039C2—28no—
1040C2C2×#1683733511yescharacteristic
1041C2#2142756411yescharacteristic
1042C2#2142757911yescharacteristic
1043C2#2142763811yescharacteristic
1044C2#2142765311yescharacteristic
1045C2#2142775711yescharacteristic
1046C2#2142776611yescharacteristic
1047C2#2142779911yescharacteristic
1048C2#2142790111yescharacteristic
1049C2#2142791611yescharacteristic
1050C2#2142824211yescharacteristic
1051C2#2142859311yescharacteristic
1052C2#2142910811yescharacteristic
1053C2#2143006911yescharacteristic
1054C2#2143240411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutator, socle, cosocleC24×C59C24
FittingC2×C59×#380C2
prime radicalC25×C59C23
hypercenterC2×#380D59
hypocenterC59#14736
LCSG ▷ C24×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C2×#16837335C2semidirect
6. #21422362C2semidirect
7. #21422359C2semidirect
8. #21422355C2semidirect
9. #21422354C2semidirect
10. #21422350C2semidirect
11. #21422349C2semidirect
12. #21422348C2semidirect
462. C22×C59#398semidirect
584. C59#14736semidirect
989. C22#16837335semidirect

Maximal subgroups

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

subgroupindex
C2×#168373352
C2×#168372772
C2×#168372742
C22×C59⋊#952
#214223622
#214223592
#214223552
#214223542
#214223502
#214223492
#214223482
#214223192
#214223182
C2×C59×#3802
#1473659