Finite Group Databasebeta

← #28604283

Subgroups — #28604283

Order 15104.

1606 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838048C211yesmaximal, characteristic
2C2×#16837480C211yesmaximal, characteristic, complemented
3C2×#16837401C211yesmaximal, characteristic, complemented
4C2×#16837406C211yesmaximal, characteristic, complemented
5#21425028C211yesmaximal, characteristic, complemented
6#21424905C211yesmaximal, characteristic, complemented
7#21424532C211yesmaximal, characteristic, complemented
8#21424527C211yesmaximal, characteristic, complemented
9#21424413C211yesmaximal, characteristic, complemented
10#21424408C211yesmaximal, characteristic, complemented
11#21424103C211yesmaximal, characteristic, complemented
12#21424034C211yesmaximal, characteristic, complemented
13#21424026C211yesmaximal, characteristic, complemented
14C4×#14273647C211yesmaximal, characteristic, complemented
15C59×#2352C211yesmaximal, characteristic, complemented
16C22×#11745685C2211yescharacteristic
17C23×D236C2211yescharacteristic
18C22×#11745664C2211yescharacteristic
19C22×#11745664C2211yescharacteristic, complemented
20#16838048—24no—
21#16838048C418yescomplemented
22C2×#14273715C2211yescharacteristic
23C2×#14273712—21no—
24C2×#14273706C2211yescharacteristic
25C2×#14273701C2211yescharacteristic
26C2×#14273700—21no—
27C2×#14273695—21no—
28C2×C4×D236C2211yescharacteristic
29C2×C22⋊C4×D59—21no—
30#16837480—24no—
31C2×C4⋊(C59⋊C8)C2211yescharacteristic, complemented
32#16837406—24no—
33#16837401—24no—
34C2×#14273650C2211yescharacteristic, complemented
35C2×#14273650C2211yescharacteristic, complemented
36C2×#14273650C2211yescharacteristic, complemented
37C2×#14273650C2211yescharacteristic, complemented
38C2×#14273647C2211yescharacteristic
39C2×#14273647C2211yescharacteristic
40C2×#14273647C2211yescharacteristic
41C2×#14273647C2211yescharacteristic
42C2×#14273647C2211yescharacteristic
43C2×#14273647C2211yescharacteristic
44C2×#14273647C2211yescharacteristic
45C2×#14273647C2211yescharacteristic
46C2×C22⋊(C59⋊C8)C2211yescharacteristic
47C2×C22⋊(C59⋊C8)C2211yescharacteristic, complemented
48C2×C4×C59⋊C8C2211yescharacteristic, complemented
49#16837164C2211yescharacteristic, complemented
50#16837164C2211yescharacteristic, complemented
51#16837164C2211yescharacteristic, complemented
52#16837164C2211yescharacteristic, complemented
53C2×C4×D4×C59C2211yescharacteristic
54C2×#117×C59C2211yescharacteristic
55C22×C4⋊C4×C59C2211yescharacteristic, complemented
56C59×#388—21no—
57C59×#387—21no—
58C59×#386—21no—
59C59×#382C2211yescharacteristic, complemented
60C59×#380C2211yescharacteristic
61C59×#380C2211yescharacteristic, complemented
62C4×C4⋊C4×C59C2211yescharacteristic, complemented
63C4×C22⋊C4×C59—21no—
64C24×D59—21no—
65C2×#11745685—22no—
66C2×#11745685—22no—
67C2×#11745685—22no—
68C2×#11745685—41no—
69C2×#11745685—41no—
70C2×#11745685C2×C414yes—
71C22×Dic118C2311yescharacteristic
72C22×D236—22no—
73C22×D236—22no—
74C22×D236—21no—
75C22×D236—22no—
76C22×D236—41no—
77C22×D236—41no—
78C22×D236C2×C414yescomplemented
79C22×D236C2311yescharacteristic
80C22×D236C2311yescharacteristic
81C22×C22⋊D59—21no—
82C22×C22⋊D59—21no—
83C22×C4×D59—21no—
84C22×C4×D59—21no—
85C2×#11745664—22no—
86C2×#11745664—22no—
87C2×#11745664—22no—
88C2×#11745664—22no—
89C2×#11745664—41no—
90C2×#11745664—41no—
91C22×C59⋊C8C2311yescharacteristic
92C22×C59⋊C8C2311yescharacteristic
93C22×C59⋊C8C2311yescharacteristic
94C22×C59⋊C8C2311yescharacteristic
95#14273715—22no—
96#14273715C2×C414yescomplemented
97#14273712—28no—
98#14273706—22no—
99#14273706C2×C414yescomplemented
100#14273701—22no—
101#14273701C2×C414yes—
102#14273700—28no—
103#14273695—28no—
104C4×D236—22no—
105C4×D236C2×C414yescomplemented
106C2×C4⋊Dic59C2311yescharacteristic
107C2×Dic59⋊C4—21no—
108C2×C22⋊Dic59—21no—
109C2×(C2×D59)⋊C4—21no—
110C2×(C2×D59)⋊C4—21no—
111C2×(C2×D59)⋊C4—21no—
112C2×(C2×D59)⋊C4—21no—
113C22⋊C4×D59—28no—
114C4⋊(C59⋊C8)—22no—
115#14273650—22no—
116#14273650—22no—
117#14273650—41no—
118#14273650—41no—
119#14273647—22no—
120#14273647—22no—
121#14273647—22no—
122#14273647—22no—
123#14273647—22no—
124#14273647—41no—
125#14273647—41no—
126#14273647D414yescomplemented
127C22⋊(C59⋊C8)—22no—
128C22⋊(C59⋊C8)—22no—
129C4×C59⋊C8—22no—
130C22×D4×C59D411yescharacteristic
131C23×C4×C59—21no—
132C23×C4×C59C2311yescharacteristic
133C23×C4×C59C2311yescharacteristic
134C4×D4×C59C2×C414yes—
135C4×D4×C59D414yes—
136#117×C59—22no—
137#117×C59—41no—
138C2×C4⋊C4×C59—22no—
139C2×C4⋊C4×C59—21no—
140C2×C4⋊C4×C59—41no—
141C2×C4⋊C4×C59D411yescharacteristic
142C2×C4⋊C4×C59C2311yescharacteristic
143C2×C4⋊C4×C59C2311yescharacteristic
144C2×C4⋊C4×C59C2311yescharacteristic
145C2×C4⋊C4×C59C2311yescharacteristic
146C2×C22⋊C4×C59—21no—
147C2×C22⋊C4×C59—21no—
148C2×C22⋊C4×C59—21no—
149C2×C22⋊C4×C59D411yescharacteristic
150C2×C22⋊C4×C59D411yescharacteristic
151C2×C42×C59—21no—
152C2×C42×C59—21no—
153C2×C42×C59C2311yescharacteristic
154#95×C59—21no—
155#95×C59—21no—
156#95×C59—21no—
157#95×C59—21no—
158#95×C59—21no—
159C24×C59C2×D411yescharacteristic
160C24×C59C2×D411yescharacteristic
161C23×D59—21no—
162C23×D59—21no—
163C23×D59—24no—
164C23×D59—42no—
165C23×D59—42no—
166C23×D59—42no—
167C23×D59—42no—
168C23×D59—81no—
169C23×D59—81no—
170C2×D4×C59—41no—
171C2×D4×C59—41no—
172C2×D4×C59C22⋊C414yes—
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—42no—
186C22×C4×C59—42no—
187C22×C4×C59—81no—
188C22×C4×C59C22×C412yes—
189C22×C4×C59C22×C412yes—
190C22×C4×C59C2×D411yescharacteristic
191C22×C4×C59C2×D411yescharacteristic
192C22×C4×C59C2×D411yescharacteristic
193C22×C4×C59C2×D411yescharacteristic
194C22×C4×C59C2×D412yes—
195C22×C4×C59C2×D412yes—
196C22×C4×C59C2411yescharacteristic
197C2×C22⋊D59—24no—
198C2×C22⋊D59—24no—
199C2×C22⋊D59—42no—
200C2×C22⋊D59—42no—
201C2×C22⋊D59—81no—
202C2×C22⋊D59—81no—
203C22×Dic59—21no—
204C22×Dic59—21no—
205#11745685—28no—
206#11745685—44no—
207#11745685—44no—
208#11745685—44no—
209C2×D236—21no—
210C2×D236—21no—
211C2×D236—21no—
212C2×D236—21no—
213C2×D236—21no—
214C2×D236—21no—
215C2×D236—21no—
216C2×D236—28no—
217C2×D236—24no—
218C2×D236—21no—
219C2×D236—44no—
220C2×D236—44no—
221C2×D236—44no—
222C2×D236—42no—
223C2×D236—42no—
224C2×D236C22×C412yes—
225C2×D236C22×C412yes—
226C2×D236C2×D412yes—
227C2×D236#4112yes—
228C2×C4×D59—24no—
229C2×C4×D59—24no—
230C2×C4×D59—42no—
231C2×C4×D59—42no—
232C2×C4×D59—81no—
233C2×C4×D59—81no—
234C2×Dic118—21no—
235C2×Dic118—21no—
236C2×Dic118—21no—
237C2×Dic118—21no—
238C2×Dic118—21no—
239C2×Dic118C22×C412yes—
240C4⋊C4×C59—21no—
241C4⋊C4×C59—21no—
242C4⋊C4×C59—21no—
243C4⋊C4×C59—21no—
244C4⋊C4×C59—21no—
245C4⋊C4×C59—21no—
246C4⋊C4×C59—21no—
247C4⋊C4×C59—42no—
248C4⋊C4×C59C22⋊C414yes—
249C4⋊C4×C59C2×D412yes—
250C22⋊C4×C59—42no—
251C22⋊C4×C59—42no—
252C22⋊C4×C59—81no—
253C22⋊C4×C59C22⋊C414yes—
254C22⋊C4×C59C22⋊C414yes—
255C42×C59—42no—
256C42×C59—81no—
257C42×C59C22×C412yes—
258C42×C59C2×D412yes—
259C22⋊Dic59—24no—
260(C2×D59)⋊C4—24no—
261(C2×D59)⋊C4—24no—
262(C2×D59)⋊C4—24no—
263(C2×D59)⋊C4—24no—
264C4⋊Dic59—21no—
265C4⋊Dic59C22×C412yes—
266Dic59⋊C4—24no—
267#11745664—44no—
268#11745664—44no—
269C2×C59⋊C8—21no—
270C2×C59⋊C8—21no—
271C2×C59⋊C8—21no—
272C2×C59⋊C8—21no—
273C2×C59⋊C8—21no—
274C2×C59⋊C8—21no—
275C2×C59⋊C8—21no—
276C2×C59⋊C8—21no—
277C2×C59⋊C8—21no—
278C2×C59⋊C8—21no—
279C2×C59⋊C8—21no—
280C2×C59⋊C8C2×D412yes—
281C23×C59—21no—
282C23×C59—21no—
283C23×C59—21no—
284C23×C59—21no—
285C23×C59—21no—
286C23×C59—21no—
287C23×C59—21no—
288C23×C59—21no—
289C23×C59—21no—
290C23×C59—21no—
291C23×C59—21no—
292C23×C59—21no—
293C23×C59C2×C22⋊C412yes—
294C23×C59C2×C22⋊C412yes—
295C23×C59C22×D411yescharacteristic
296C22×D59—22no—
297C22×D59—22no—
298C22×D59—22no—
299C22×D59—22no—
300C22×D59—48no—
301C22×D59—41no—
302C22×D59—41no—
303C22×D59—41no—
304C22×D59—41no—
305C22×D59—48no—
306C22×D59—41no—
307C22×D59—41no—
308C22×D59—41no—
309C22×D59—41no—
310C22×D59—41no—
311C22×D59—41no—
312C22×D59—84no—
313C22×D59—84no—
314C22×D59—84no—
315C22×D59—84no—
316C22×D59—84no—
317D4×C59—44no—
318C2×C4×C59—21no—
319C2×C4×C59—21no—
320C2×C4×C59—21no—
321C2×C4×C59—21no—
322C2×C4×C59—21no—
323C2×C4×C59—21no—
324C2×C4×C59—21no—
325C2×C4×C59—21no—
326C2×C4×C59—22no—
327C2×C4×C59—22no—
328C2×C4×C59—22no—
329C2×C4×C59—22no—
330C2×C4×C59—22no—
331C2×C4×C59—22no—
332C2×C4×C59—22no—
333C2×C4×C59—22no—
334C2×C4×C59—22no—
335C2×C4×C59—41no—
336C2×C4×C59—41no—
337C2×C4×C59—41no—
338C2×C4×C59—41no—
339C2×C4×C59—41no—
340C2×C4×C59—41no—
341C2×C4×C59—41no—
342C2×C4×C59—41no—
343C2×C4×C59—41no—
344C2×C4×C59—41no—
345C2×C4×C59—41no—
346C2×C4×C59—84no—
347C2×C4×C59C2×C22⋊C412yes—
348C2×C4×C59C2×C22⋊C412yes—
349C2×C4×C59C2×C22⋊C412yes—
350C2×C4×C59C2×C22⋊C412yes—
351C2×C4×C59C23×C411yescharacteristic
352C2×C4×C59C22×D411yescharacteristic
353C2×C4×C59C22×D411yescharacteristic
354C2×C4×C59C2×#4111yescharacteristic
355C2×C4×C59H(5,𝔽2)11yescharacteristic
356C2×C4×C59H(5,𝔽2)11yescharacteristic
357C22⋊D59—48no—
358C22⋊D59—84no—
359C2×Dic59—22no—
360C2×Dic59—22no—
361C2×Dic59—41no—
362C2×Dic59—41no—
363C2×Dic59—41no—
364C2×Dic59—41no—
365D236—22no—
366D236—22no—
367D236—22no—
368D236—22no—
369D236—22no—
370D236—48no—
371D236—41no—
372D236—41no—
373D236C4×D414yes—
374C4×D59—48no—
375C4×D59—84no—
376Dic118—22no—
377Dic118—22no—
378Dic118—41no—
379Dic118—41no—
380C59⋊C8—22no—
381C59⋊C8—41no—
382C59⋊C8—41no—
383C59⋊C8—41no—
384#22427—591nomaximal, Sylow
385C22×C59—22no—
386C22×C59—22no—
387C22×C59—22no—
388C22×C59—22no—
389C22×C59—22no—
390C22×C59—22no—
391C22×C59—41no—
392C22×C59—41no—
393C22×C59—41no—
394C22×C59—41no—
395C22×C59—41no—
396C22×C59—41no—
397C22×C59—41no—
398C22×C59—41no—
399C22×C59C22×C22⋊C411yescharacteristic
400C22×C59D4211yescharacteristic
401C22×C59#54611yescharacteristic
402C22×C59#57511yescharacteristic
403C22×C59#57511yescharacteristic
404C22×C59#57611yescharacteristic
405C22×C59#57711yescharacteristic
406C2×D59—24no—
407C2×D59—42no—
408C2×D59—42no—
409C2×D59—42no—
410C2×D59—42no—
411C2×D59—42no—
412C2×D59—42no—
413C2×D59—42no—
414C2×D59—42no—
415C2×D59—42no—
416C2×D59—816no—
417C2×D59—81no—
418C2×D59—81no—
419C2×D59—81no—
420C2×D59—81no—
421C4×C59—22no—
422C4×C59—22no—
423C4×C59—22no—
424C4×C59—22no—
425C4×C59—42no—
426C4×C59—81no—
427C4×C59—81no—
428C4×C59—81no—
429C4×C59C2×C4×D411yescharacteristic
430C4×C59#51811yescharacteristic
431C4×C59D4211yescharacteristic
432C4×C59#54611yescharacteristic
433Dic59—42no—
434Dic59—42no—
435C2×#546—591no—
436C2×#436—591no—
437C2×#417—591no—
438C2×#418—591no—
439#2352D5911yescharacteristic, complemented
440#1983—591no—
441#1958—591no—
442#1895—591no—
443#1894—591no—
444#1874—591no—
445#1873—591no—
446#1804—591no—
447#1788—591no—
448#1786—591no—
449C4×#102—591no—
450C2×C59—42no—
451C2×C59—42no—
452C2×C59D4×C22⋊C411yescharacteristic
453C2×C59#289611yescharacteristic
454C2×C59#289711yescharacteristic
455C2×C59#327311yescharacteristic
456C2×C59#327511yescharacteristic
457C2×C59#332211yescharacteristic
458C2×C59#332311yescharacteristic
459D59—44no—
460D59—82no—
461C22×#41—591no—
462C23×D4—591no—
463C22×M16—591no—
464C22×M16—591no—
465#546—598no—
466#546—1184no—
467C2×#124—591no—
468C2×#123—1181no—
469C2×C22⋊Q8—591no—
470C2×#121—591no—
471C2×#121—1181no—
472C2×#120—1181no—
473C2×C4×D4—591no—
474C2×C4×D4C2×D5911yescharacteristic
475C2×#117C2×D5911yescharacteristic
476C22×C4⋊C4C2×D5911yescharacteristic, complemented
477C22×C22⋊C4—1181no—
478#436—1184no—
479C2×C4⋊C8—591no—
480#418—1184no—
481#417—1184no—
482C2×#103—591no—
483C2×#103—591no—
484C2×#103—591no—
485C2×#103—591no—
486C2×#102—591no—
487C2×#102—591no—
488C2×#102—591no—
489C2×#102—591no—
490C2×#102—591no—
491C2×#102—591no—
492C2×#102—591no—
493C2×#102—591no—
494C2×C22⋊C8—591no—
495C2×C22⋊C8—591no—
496C2×C4×C8—591no—
497#388—21no—
498#387—21no—
499#386—21no—
500#382C2×D5911yescharacteristic, complemented
501#380C2×D5911yescharacteristic
502#380C2×D5911yescharacteristic, complemented
503C4×C4⋊C4C2×D5911yescharacteristic, complemented
504C4×C22⋊C4—21no—
505#340—591no—
506#340—591no—
507#340—591no—
508#340—591no—
509C59#2242711yescharacteristic, complemented, Sylow
510C25—1181no—
511C2×#41—594no—
512C2×#41—1182no—
513C2×#41—1182no—
514C2×#41—1182no—
515C2×#41—2361no—
516C2×#41—2361no—
517C22×Q8—591no—
518C22×D4—594no—
519C22×D4—591no—
520C22×D4—591no—
521C22×D4—1182no—
522C22×D4—1182no—
523C22×D4—1181no—
524C22×D4—1181no—
525C22×D4—1182no—
526C22×D4—1181no—
527C22×D4—2361no—
528C22×D4—2361no—
529C22×D4C22⋊D5911yescharacteristic
530C23×C4—21no—
531C23×C4—1181no—
532C23×C4—1181no—
533C23×C4C22×D5911yescharacteristic
534C23×C4C22×D5911yescharacteristic
535C2×M16—1182no—
536C2×M16—1182no—
537C2×M16—1182no—
538C2×M16—1182no—
539C2×M16—2361no—
540C2×M16—2361no—
541C22×C8—591no—
542C22×C8—591no—
543C22×C8—591no—
544C22×C8—591no—
545#124—594no—
546#124—1182no—
547#123—1188no—
548C22⋊Q8—594no—
549C22⋊Q8—1182no—
550#121—594no—
551#121—1182no—
552#121—1188no—
553#120—1188no—
554C4×D4—594no—
555C4×D4—1182no—
556C4×D4C4×D5914yes—
557C4×D4D23614yes—
558#117—22no—
559#117—41no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—41no—
563C2×C4⋊C4—591no—
564C2×C4⋊C4—1181no—
565C2×C4⋊C4C22⋊D5911yescharacteristic
566C2×C4⋊C4C22×D5911yescharacteristic
567C2×C4⋊C4C22×D5911yescharacteristic
568C2×C4⋊C4C22×D5911yescharacteristic
569C2×C4⋊C4C22×D5911yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—1181no—
574C2×C22⋊C4—1181no—
575C2×C22⋊C4—1181no—
576C2×C22⋊C4—1181no—
577C2×C22⋊C4—1181no—
578C2×C22⋊C4—1188no—
579C2×C22⋊C4C22⋊D5911yescharacteristic
580C2×C22⋊C4C22⋊D5911yescharacteristic
581C2×C42—21no—
582C2×C42—21no—
583C2×C42C22×D5911yescharacteristic
584C4⋊C8—1182no—
585#103—1182no—
586#103—1182no—
587#103—2361no—
588#103—2361no—
589#102—594no—
590#102—1182no—
591#102—1182no—
592#102—1182no—
593#102—1182no—
594#102—1182no—
595#102—2361no—
596#102—2361no—
597C22⋊C8—1182no—
598C22⋊C8—1182no—
599C4×C8—1182no—
600#95—21no—
601#95—21no—
602#95—21no—
603#95—21no—
604#95—21no—
605C24—1181no—
606C24—1184no—
607C24—1181no—
608C24—4721no—
609C24—4721no—
610C24—2362no—
611C24—2362no—
612C24—2362no—
613C24—2362no—
614C24C2×C22⋊D5911yescharacteristic
615C24C2×C22⋊D5911yescharacteristic
616#41—1188no—
617#41—2364no—
618#41—2364no—
619#41—2364no—
620C2×Q8—592no—
621C2×Q8—1181no—
622C2×Q8—1181no—
623C2×Q8—1181no—
624C2×Q8—1181no—
625C2×Q8—1181no—
626C2×D4—41no—
627C2×D4—41no—
628C2×D4—592no—
629C2×D4—592no—
630C2×D4—592no—
631C2×D4—592no—
632C2×D4—1188no—
633C2×D4—1184no—
634C2×D4—1184no—
635C2×D4—1184no—
636C2×D4—1181no—
637C2×D4—1181no—
638C2×D4—1181no—
639C2×D4—1181no—
640C2×D4—1181no—
641C2×D4—1181no—
642C2×D4—1181no—
643C2×D4—1181no—
644C2×D4—4721no—
645C2×D4—4721no—
646C2×D4—2364no—
647C2×D4—2364no—
648C2×D4—2364no—
649C2×D4—2362no—
650C2×D4—2362no—
651C2×D4—2362no—
652C2×D4—2362no—
653C2×D4(C2×D59)⋊C414yes—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4—81no—
669C22×C4—1181no—
670C22×C4—1181no—
671C22×C4—1184no—
672C22×C4—1184no—
673C22×C4—4721no—
674C22×C4—4721no—
675C22×C4—2362no—
676C22×C4—2362no—
677C22×C4C2×C4×D5912yes—
678C22×C4C2×C4×D5912yes—
679C22×C4C2×D23612yes—
680C22×C4C2×D23612yes—
681C22×C4C2×C22⋊D5911yescharacteristic
682C22×C4C2×C22⋊D5911yescharacteristic
683C22×C4C2×C22⋊D5911yescharacteristic
684C22×C4C2×C22⋊D5911yescharacteristic
685C22×C4C23×D5911yescharacteristic
686M16—2364no—
687M16—2364no—
688C2×C8—592no—
689C2×C8—1181no—
690C2×C8—1181no—
691C2×C8—1181no—
692C2×C8—1181no—
693C2×C8—1181no—
694C2×C8—1181no—
695C2×C8—1181no—
696C2×C8—1181no—
697C2×C8—1181no—
698C2×C8—1181no—
699C2×C8—1181no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—42no—
708C4⋊C4—592no—
709C4⋊C4—1184no—
710C4⋊C4—1181no—
711C4⋊C4(C2×D59)⋊C414yes—
712C4⋊C4D4×D5912yes—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—81no—
716C22⋊C4—1184no—
717C22⋊C4—1184no—
718C22⋊C4—1184no—
719C22⋊C4—1184no—
720C22⋊C4—1184no—
721C22⋊C4(C2×D59)⋊C414yes—
722C22⋊C4(C2×D59)⋊C414yes—
723C42—42no—
724C42—81no—
725C42C2×C4×D5912yes—
726C42C2×D23612yes—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—1182no—
740C23—1182no—
741C23—1182no—
742C23—1182no—
743C23—4724no—
744C23—4724no—
745C23—4724no—
746C23—4724no—
747C23—4724no—
748C23—2368no—
749C23—2368no—
750C23—2361no—
751C23—2361no—
752C23—2361no—
753C23—2361no—
754C23—2361no—
755C23—2361no—
756C23—2361no—
757C23—2361no—
758C23—2361no—
759C23—2361no—
760C23C2×(C2×D59)⋊C412yes—
761C23C2×(C2×D59)⋊C412yes—
762C23C22×C22⋊D5911yescharacteristic
763Q8—1182no—
764Q8—1182no—
765Q8—2361no—
766Q8—2361no—
767D4—44no—
768D4—594no—
769D4—1182no—
770D4—1182no—
771D4—1182no—
772D4—1182no—
773D4—1182no—
774D4—4724no—
775D4—2368no—
776D4—2368no—
777D4—2361no—
778D4—2361no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—84no—
808C2×C4—1182no—
809C2×C4—1182no—
810C2×C4—4724no—
811C2×C4—2368no—
812C2×C4—2361no—
813C2×C4—2361no—
814C2×C4—2361no—
815C2×C4—2361no—
816C2×C4C2×(C2×D59)⋊C412yes—
817C2×C4C2×(C2×D59)⋊C412yes—
818C2×C4C2×(C2×D59)⋊C412yes—
819C2×C4C2×(C2×D59)⋊C412yes—
820C2×C4C22×C4×D5911yescharacteristic
821C2×C4C2×D4×D5911yescharacteristic
822C2×C4C22×D23611yescharacteristic
823C2×C4#41×D5911yescharacteristic
824C2×C4#1427377211yescharacteristic
825C2×C4#1427377311yescharacteristic
826C8—1182no—
827C8—2361no—
828C8—2361no—
829C8—2361no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—1184no—
845C22—47216no—
846C22—4721no—
847C22—4721no—
848C22—4721no—
849C22—4721no—
850C22—2362no—
851C22—2362no—
852C22—2362no—
853C22—2362no—
854C22—2362no—
855C22—2362no—
856C22—2362no—
857C22—2362no—
858C22—2362no—
859C22C22×(C2×D59)⋊C411yescharacteristic
860C22D4×C22⋊D5911yescharacteristic
861C22#1683804011yescharacteristic
862C22#1683820011yescharacteristic
863C22#1683820011yescharacteristic
864C22#1683820511yescharacteristic
865C22#1683821011yescharacteristic
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—42no—
871C4—81no—
872C4—81no—
873C4—81no—
874C4—2362no—
875C4—2362no—
876C4C4×D4×D5911yescharacteristic
877C4#1683787411yescharacteristic
878C4D4×D23611yescharacteristic
879C4#1683804711yescharacteristic
880C2—42no—
881C2—42no—
882C2—4722no—
883C2—2364no—
884C2D4×(C2×D59)⋊C411yescharacteristic
885C2#2143261311yescharacteristic
886C2#2143261911yescharacteristic
887C2#2143570311yescharacteristic
888C2#2143572811yescharacteristic
889C2#2143629111yescharacteristic
890C2#2143630611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2352C2
socleC23×C59C22×D4
prime radicalC2×#16838048C2
cosocleC22×C4×C59C24
hypercenter#2352D59
hypocenterC59#22427
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. C2×#16837480C2semidirect
3. C2×#16837401C2semidirect
4. C2×#16837406C2semidirect
5. #21425028C2semidirect
6. #21424905C2semidirect
7. #21424532C2semidirect
8. #21424527C2semidirect
9. #21424413C2semidirect
10. #21424408C2semidirect
11. #21424103C2semidirect
12. #21424034C2semidirect
13. #21424026C2semidirect
14. C4×#14273647C2semidirect
15. C59×#2352C2semidirect
19. C22×#11745664C22semidirect
21. #16838048C4semidirect
31. C2×C4⋊(C59⋊C8)C22semidirect
34. C2×#14273650C22semidirect
35. C2×#14273650C22semidirect
36. C2×#14273650C22semidirect
37. C2×#14273650C22semidirect
47. C2×C22⋊(C59⋊C8)C22semidirect
48. C2×C4×C59⋊C8C22semidirect
49. #16837164C22semidirect
50. #16837164C22semidirect
51. #16837164C22semidirect
52. #16837164C22semidirect
55. C22×C4⋊C4×C59C22semidirect
59. C59×#382C22semidirect
61. C59×#380C22semidirect
62. C4×C4⋊C4×C59C22semidirect
78. C22×D236C2×C4semidirect
96. #14273715C2×C4semidirect
99. #14273706C2×C4semidirect
105. C4×D236C2×C4semidirect
126. #14273647D4semidirect
439. #2352D59semidirect
476. C22×C4⋊C4C2×D59semidirect
500. #382C2×D59semidirect
502. #380C2×D59semidirect
503. C4×C4⋊C4C2×D59semidirect
509. C59#22427semidirect

Maximal subgroups

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

subgroupindex
C2×#168380482
C2×#168374802
C2×#168374012
C2×#168374062
#214250282
#214249052
#214245322
#214245272
#214244132
#214244082
#214241032
#214240342
#214240262
C4×#142736472
C59×#23522
#2242759