Finite Group Databasebeta

← #28640913

Subgroups — #28640913

Order 15104.

1164 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837641C211yesmaximal, characteristic, complemented
2C2×#16837629C211yesmaximal, characteristic
3#21432435C211yesmaximal, characteristic, complemented
4#21425431C211yesmaximal, characteristic, complemented
5#21425332C211yesmaximal, characteristic, complemented
6#21425244C211yesmaximal, characteristic, complemented
7#21425190C211yesmaximal, characteristic, complemented
8#21424525C211yesmaximal, characteristic
9#21424520C211yesmaximal, characteristic, complemented
10#21424437C211yesmaximal, characteristic, complemented
11#21424430C211yesmaximal, characteristic, complemented
12#21424364C211yesmaximal, characteristic, complemented
13#21424343C211yesmaximal, characteristic, complemented
14C2×#16837157C211yesmaximal, characteristic, complemented
15C2×C59×#529C211yesmaximal, characteristic
16C22×#11745672C2211yescharacteristic
17C22×#11745670C2211yescharacteristic
18C23×C59⋊C8C2211yescharacteristic
19C23×C59⋊C8C2211yescharacteristic
20C2×#14273706C2211yescharacteristic
21#16837641—24no—
22#16837629—24no—
23C2×#14273660C2211yescharacteristic
24C2×#14273658C2211yescharacteristic
25C2×#14273651C2211yescharacteristic
26C2×#14273651C2211yescharacteristic
27C2×#14273651C2211yescharacteristic
28C2×#14273650C2211yescharacteristic
29C2×#14273650C2211yescharacteristic
30C2×#14273648C2211yescharacteristic
31C2×#14273648C2211yescharacteristic
32C2×#14273648C2211yescharacteristic
33#16837308C2211yescharacteristic
34#16837308C2211yescharacteristic
35#16837300C2211yescharacteristic
36#16837300C2211yescharacteristic
37#16837286—21no—
38#16837286—21no—
39#16837275—21no—
40#16837265—21no—
41#16837262C2211yescharacteristic
42#16837164C2211yescharacteristic
43#16837164C2211yescharacteristic
44#16837164C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837157C2211yescharacteristic
47#16837157C2211yescharacteristic
48#16837157C2211yescharacteristic
49#16837157C2211yescharacteristic
50C59×#529—24no—
51C59×#529—24no—
52C2×#126×C59—21no—
53C2×#125×C59C2211yescharacteristic
54C2×#124×C59C2211yescharacteristic
55C2×#123×C59—21no—
56C2×C22⋊Q8×C59C2211yescharacteristic
57C2×#121×C59C2211yescharacteristic
58C2×C4×Q8×C59C2211yescharacteristic
59C2×C4×D4×C59—21no—
60C2×C4×D4×C59C2211yescharacteristic
61C2×#117×C59—21no—
62C22×C42×C59C2211yescharacteristic
63C22×Dic118C2311yescharacteristic
64C2×#11745672—22no—
65C2×#11745672—22no—
66C2×#11745672—41no—
67C2×#11745670—22no—
68C2×#11745670—22no—
69C2×#11745670—41no—
70C22×C59⋊C8—22no—
71C22×C59⋊C8—22no—
72C22×C59⋊C8—22no—
73C22×C59⋊C8—22no—
74C22×C59⋊C8—41no—
75C22×C59⋊C8—41no—
76C22×C59⋊C8C2311yescharacteristic
77C22×C59⋊C8C2311yescharacteristic
78C22×C59⋊C8C2311yescharacteristic
79C22×C59⋊C8C2311yescharacteristic
80#14273706—22no—
81#14273706—22no—
82C2×C4⋊Dic59C2311yescharacteristic
83C2×C4⋊Dic59C2311yescharacteristic
84C2×C4⋊Dic59C2311yescharacteristic
85C2×Dic59⋊C4—21no—
86C2×Dic59⋊C4—21no—
87C2×Dic59⋊C4—21no—
88C2×C22⋊Dic59—21no—
89C2×C22⋊Dic59—21no—
90#14273660—22no—
91#14273658—22no—
92#14273651—22no—
93#14273651—22no—
94#14273651—41no—
95#14273650—22no—
96#14273650—22no—
97#14273648—22no—
98#14273648—22no—
99#14273648—41no—
100C59⋊#95—21no—
101C59⋊#95—21no—
102C59⋊#95—21no—
103C59⋊#95—21no—
104C59⋊#95—21no—
105C59⋊#95—21no—
106C59⋊#95—21no—
107C22×Q8×C59C2311yescharacteristic
108C22×D4×C59—21no—
109C22×D4×C59C2311yescharacteristic
110C23×C4×C59—21no—
111C23×C4×C59D411yescharacteristic
112C23×C4×C59D411yescharacteristic
113C23×C4×C59C2311yescharacteristic
114#126×C59—28no—
115#125×C59—22no—
116#125×C59—22no—
117#124×C59—22no—
118#124×C59—22no—
119#123×C59—28no—
120C22⋊Q8×C59—22no—
121C22⋊Q8×C59D414yes—
122#121×C59—22no—
123#121×C59D414yes—
124C4×Q8×C59—22no—
125C4×Q8×C59—22no—
126C4×D4×C59—28no—
127C4×D4×C59—22no—
128C4×D4×C59—22no—
129#117×C59—28no—
130C2×C4⋊C4×C59—21no—
131C2×C4⋊C4×C59—21no—
132C2×C4⋊C4×C59—21no—
133C2×C4⋊C4×C59—21no—
134C2×C4⋊C4×C59C2311yescharacteristic
135C2×C4⋊C4×C59C2311yescharacteristic
136C2×C22⋊C4×C59—21no—
137C2×C22⋊C4×C59—21no—
138C2×C22⋊C4×C59—21no—
139C2×C22⋊C4×C59—21no—
140C2×C22⋊C4×C59—21no—
141C2×C42×C59—22no—
142C2×C42×C59—22no—
143C2×C42×C59—21no—
144C2×C42×C59D411yescharacteristic
145C2×C42×C59D411yescharacteristic
146C2×C42×C59C2311yescharacteristic
147C2×C42×C59C2311yescharacteristic
148C24×C59—21no—
149C24×C59C2×D411yescharacteristic
150C2×Q8×C59—21no—
151C2×Q8×C59—21no—
152C2×Q8×C59—21no—
153C2×Q8×C59—21no—
154C2×Q8×C59—21no—
155C2×Q8×C59C2×D412yes—
156C2×D4×C59—24no—
157C2×D4×C59—21no—
158C2×D4×C59—21no—
159C2×D4×C59—21no—
160C2×D4×C59—21no—
161C2×D4×C59—21no—
162C2×D4×C59—42no—
163C2×D4×C59—42no—
164C2×D4×C59C2×D412yes—
165C22×C4×C59—21no—
166C22×C4×C59—21no—
167C22×C4×C59—21no—
168C22×C4×C59—21no—
169C22×C4×C59—24no—
170C22×C4×C59—22no—
171C22×C4×C59—22no—
172C22×C4×C59—22no—
173C22×C4×C59—22no—
174C22×C4×C59—21no—
175C22×C4×C59—21no—
176C22×C4×C59—21no—
177C22×C4×C59—22no—
178C22×C4×C59—41no—
179C22×C4×C59—42no—
180C22×C4×C59—42no—
181C22×C4×C59C2×D411yescharacteristic
182C22×C4×C59C2×D411yescharacteristic
183C22×C4×C59C2×D411yescharacteristic
184C22×C4×C59C2×D411yescharacteristic
185C22×C4×C59C2×D412yes—
186C22×C4×C59C2×D412yes—
187C22×C4×C59C2×D411yescharacteristic
188C22×C4×C59C2411yescharacteristic
189C22×Dic59—21no—
190C22×Dic59—21no—
191C22×Dic59—21no—
192C22×Dic59—21no—
193C2×Dic118—21no—
194C2×Dic118—21no—
195C2×Dic118—21no—
196C2×Dic118—21no—
197C2×Dic118—21no—
198C2×Dic118—21no—
199C4⋊C4×C59—24no—
200C4⋊C4×C59—24no—
201C4⋊C4×C59—24no—
202C4⋊C4×C59—24no—
203C4⋊C4×C59—21no—
204C4⋊C4×C59—21no—
205C4⋊C4×C59C2×D412yes—
206C4⋊C4×C59C2×D412yes—
207C22⋊C4×C59—24no—
208C22⋊C4×C59—24no—
209C22⋊C4×C59—24no—
210C22⋊C4×C59—24no—
211C22⋊C4×C59—24no—
212C42×C59—24no—
213C42×C59—22no—
214C42×C59—22no—
215C42×C59—21no—
216C42×C59—21no—
217C42×C59—21no—
218C42×C59—21no—
219C22⋊Dic59—42no—
220C22⋊Dic59—42no—
221#11745672—44no—
222#11745670—44no—
223C4⋊Dic59—21no—
224C4⋊Dic59—21no—
225C4⋊Dic59—21no—
226C4⋊Dic59—21no—
227C4⋊Dic59—21no—
228C4⋊Dic59—21no—
229Dic59⋊C4—42no—
230Dic59⋊C4—42no—
231Dic59⋊C4—42no—
232C2×C59⋊C8—21no—
233C2×C59⋊C8—21no—
234C2×C59⋊C8—21no—
235C2×C59⋊C8—21no—
236C2×C59⋊C8—21no—
237C2×C59⋊C8—21no—
238C2×C59⋊C8—21no—
239C2×C59⋊C8—21no—
240C2×C59⋊C8—21no—
241C2×C59⋊C8—21no—
242C2×C59⋊C8—44no—
243C2×C59⋊C8—44no—
244C2×C59⋊C8#4112yes—
245C2×C59⋊C8#4112yes—
246C23×C59—21no—
247C23×C59—21no—
248C23×C59—21no—
249C23×C59—21no—
250C23×C59—22no—
251C23×C59—41no—
252C23×C59—41no—
253C23×C59—41no—
254C23×C59—41no—
255C23×C59—41no—
256C23×C59—41no—
257C23×C59#12012yes—
258C23×C59#13512yes—
259C23×C59#13712yes—
260C23×C59C22×D411yescharacteristic
261Q8×C59—22no—
262Q8×C59—22no—
263Q8×C59—41no—
264Q8×C59—41no—
265D4×C59—22no—
266D4×C59—22no—
267D4×C59—48no—
268D4×C59—41no—
269D4×C59—41no—
270C2×C4×C59—21no—
271C2×C4×C59—21no—
272C2×C4×C59—21no—
273C2×C4×C59—21no—
274C2×C4×C59—22no—
275C2×C4×C59—22no—
276C2×C4×C59—22no—
277C2×C4×C59—22no—
278C2×C4×C59—21no—
279C2×C4×C59—21no—
280C2×C4×C59—21no—
281C2×C4×C59—22no—
282C2×C4×C59—22no—
283C2×C4×C59—22no—
284C2×C4×C59—21no—
285C2×C4×C59—21no—
286C2×C4×C59—21no—
287C2×C4×C59—21no—
288C2×C4×C59—21no—
289C2×C4×C59—21no—
290C2×C4×C59—44no—
291C2×C4×C59—48no—
292C2×C4×C59—41no—
293C2×C4×C59—41no—
294C2×C4×C59—41no—
295C2×C4×C59—41no—
296C2×C4×C59—41no—
297C2×C4×C59—41no—
298C2×C4×C59—44no—
299C2×C4×C59#12012yes—
300C2×C4×C59#13512yes—
301C2×C4×C59C22×D411yescharacteristic
302C2×C4×C59C22×D411yescharacteristic
303C2×C4×C59C2×#4111yescharacteristic
304C2×C4×C59C2×#4111yescharacteristic
305C2×C4×C59H(5,𝔽2)11yescharacteristic
306C2×C4×C592−1+411yescharacteristic
307C2×Dic59—41no—
308C2×Dic59—41no—
309C2×Dic59—41no—
310C2×Dic59—41no—
311C2×Dic59—41no—
312C2×Dic59—41no—
313C2×Dic59—41no—
314C2×Dic59—41no—
315C2×Dic59—41no—
316C2×Dic59—41no—
317C2×Dic59—41no—
318C2×Dic59—41no—
319Dic118—41no—
320Dic118—41no—
321Dic118—41no—
322Dic118—41no—
323C59⋊C8—22no—
324C59⋊C8—22no—
325C59⋊C8—41no—
326C59⋊C8—41no—
327#25499—591nomaximal, Sylow
328C22×C59—22no—
329C22×C59—22no—
330C22×C59—22no—
331C22×C59—22no—
332C22×C59—22no—
333C22×C59—22no—
334C22×C59—42no—
335C22×C59—42no—
336C22×C59—42no—
337C22×C59—81no—
338C22×C59—81no—
339C22×C59—81no—
340C22×C59—81no—
341C22×C59#45214yes—
342C22×C59C2×#12011yescharacteristic
343C22×C59#53211yescharacteristic
344C22×C59#53711yescharacteristic
345C22×C59C2×#13511yescharacteristic
346C22×C59C2×#13511yescharacteristic
347C22×C59C2×#13711yescharacteristic
348C22×C59#57511yescharacteristic
349C4×C59—22no—
350C4×C59—22no—
351C4×C59—42no—
352C4×C59—41no—
353C4×C59—41no—
354C4×C59—42no—
355C4×C59—41no—
356C4×C59—42no—
357C4×C59#54611yescharacteristic
358C4×C59#54611yescharacteristic
359C4×C59#54711yescharacteristic
360C4×C59#54711yescharacteristic
361Dic59—81no—
362Dic59—81no—
363Dic59—81no—
364Dic59—81no—
365C2×#529D5911yescharacteristic
366C2×#467—591no—
367C2×#465—591no—
368#2855—591no—
369#2059—591no—
370#2042—591no—
371#2026—591no—
372#2015—591no—
373#1893—591no—
374#1892—591no—
375#1878—591no—
376#1877—591no—
377#1865—591no—
378#1862—591no—
379C2×#336—591no—
380C2×C59—24no—
381C2×C59—82no—
382C2×C59#243011yescharacteristic
383C2×C59C2×#45211yescharacteristic
384C2×C59#300211yescharacteristic
385C2×C59#316811yescharacteristic
386C2×C59#318111yescharacteristic
387C2×C59#324811yescharacteristic
388C2×C59#325011yescharacteristic
389C22×Q16—591no—
390C22×SD16—591no—
391C23×C8—591no—
392C23×C8—591no—
393#529—24no—
394#529—24no—
395C2×#126—21no—
396C2×#125C2×D5911yescharacteristic
397C2×#124C2×D5911yescharacteristic
398C2×#123—21no—
399C2×C22⋊Q8—591no—
400C2×C22⋊Q8C2×D5911yescharacteristic
401C2×#121C2×D5911yescharacteristic
402C2×C4×Q8C2×D5911yescharacteristic
403C2×C4×D4—21no—
404C2×C4×D4C2×D5911yescharacteristic
405C2×#117—21no—
406C22×C42C2×D5911yescharacteristic
407#467—1184no—
408#465—1184no—
409C2×#107—591no—
410C2×#106—591no—
411C2×#103—591no—
412C2×#103—591no—
413C2×#103—591no—
414C2×#103—591no—
415C2×#103—591no—
416C2×#102—591no—
417C2×#102—591no—
418C2×#102—591no—
419#391—591no—
420#391—591no—
421#389—591no—
422#389—591no—
423#387—1181no—
424#387—1181no—
425#385—1181no—
426#381—1181no—
427#380—591no—
428#340—591no—
429#340—591no—
430#340—591no—
431#340—591no—
432#336—591no—
433#336—591no—
434#336—591no—
435#336—591no—
436C59#2549911yescharacteristic, complemented, Sylow
437C22×Q8—591no—
438C22×Q8C22×D5911yescharacteristic
439C22×D4—21no—
440C22×D4C22×D5911yescharacteristic
441C23×C4—21no—
442C23×C4C22⋊D5911yescharacteristic
443C23×C4C22⋊D5911yescharacteristic
444C23×C4C22×D5911yescharacteristic
445C2×Q16—1182no—
446C2×Q16—1182no—
447C2×Q16—2361no—
448C2×SD16—1182no—
449C2×SD16—1182no—
450C2×SD16—2361no—
451C22×C8—591no—
452C22×C8—591no—
453C22×C8—591no—
454C22×C8—591no—
455C22×C8—1182no—
456C22×C8—1182no—
457C22×C8—1182no—
458C22×C8—1182no—
459C22×C8—2361no—
460C22×C8—2361no—
461#126—28no—
462#125—22no—
463#125—22no—
464#124—22no—
465#124—22no—
466#123—28no—
467C22⋊Q8—22no—
468C22⋊Q8—1182no—
469C22⋊Q8—1182no—
470C22⋊Q8C22⋊D5914yes—
471#121—22no—
472#121C22⋊D5914yes—
473C4×Q8—22no—
474C4×Q8—22no—
475C4×D4—28no—
476C4×D4—22no—
477C4×D4—22no—
478#117—28no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—591no—
484C2×C4⋊C4—591no—
485C2×C4⋊C4—591no—
486C2×C4⋊C4—1181no—
487C2×C4⋊C4—1181no—
488C2×C4⋊C4—1181no—
489C2×C4⋊C4C22×D5911yescharacteristic
490C2×C4⋊C4C22×D5911yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—1181no—
497C2×C22⋊C4—1181no—
498C2×C42—21no—
499C2×C42—22no—
500C2×C42—22no—
501C2×C42C22⋊D5911yescharacteristic
502C2×C42C22⋊D5911yescharacteristic
503C2×C42C22×D5911yescharacteristic
504C2×C42C22×D5911yescharacteristic
505#107—1182no—
506#106—1182no—
507#103—1182no—
508#103—1182no—
509#103—1182no—
510#103—1182no—
511#103—2361no—
512#102—1182no—
513#102—1182no—
514#102—2361no—
515#95—1181no—
516#95—1181no—
517#95—1181no—
518#95—1181no—
519#95—1181no—
520#95—1181no—
521#95—1181no—
522C24—21no—
523C24C2×C22⋊D5911yescharacteristic
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—1181no—
530C2×Q8—1181no—
531C2×Q8—1181no—
532C2×Q8—1181no—
533C2×Q8—1181no—
534C2×Q8—1181no—
535C2×Q8C2×C22⋊D5912yes—
536C2×D4—24no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4C2×C22⋊D5912yes—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—24no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—41no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—1181no—
562C22×C4—1181no—
563C22×C4—1181no—
564C22×C4—1181no—
565C22×C4C2×C22⋊D5911yescharacteristic
566C22×C4C2×C22⋊D5911yescharacteristic
567C22×C4C2×C22⋊D5911yescharacteristic
568C22×C4C2×C22⋊D5911yescharacteristic
569C22×C4C2×C22⋊D5912yes—
570C22×C4C2×C22⋊D5912yes—
571C22×C4C2×C22⋊D5911yescharacteristic
572C22×C4C23×D5911yescharacteristic
573Q16—2364no—
574SD16—2364no—
575C2×C8—592no—
576C2×C8—592no—
577C2×C8—1181no—
578C2×C8—1181no—
579C2×C8—1181no—
580C2×C8—1181no—
581C2×C8—1181no—
582C2×C8—1181no—
583C2×C8—1181no—
584C2×C8—1181no—
585C2×C8—1181no—
586C2×C8—1181no—
587C2×C8—2364no—
588C2×C8—2364no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—1181no—
596C4⋊C4—1181no—
597C4⋊C4—1181no—
598C4⋊C4—1181no—
599C4⋊C4—1181no—
600C4⋊C4—1181no—
601C4⋊C4—2362no—
602C4⋊C4—2362no—
603C4⋊C4—2362no—
604C4⋊C4C2×C22⋊D5912yes—
605C4⋊C4C2×C22⋊D5912yes—
606C22⋊C4—24no—
607C22⋊C4—24no—
608C22⋊C4—24no—
609C22⋊C4—24no—
610C22⋊C4—24no—
611C22⋊C4—2362no—
612C22⋊C4—2362no—
613C42—24no—
614C42—22no—
615C42—22no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—22no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23#1427369612yes—
632C23#1427374712yes—
633C23#1427375712yes—
634C23C22×C22⋊D5911yescharacteristic
635Q8—22no—
636Q8—22no—
637Q8—41no—
638Q8—41no—
639Q8—2361no—
640Q8—2361no—
641Q8—2361no—
642Q8—2361no—
643D4—22no—
644D4—22no—
645D4—48no—
646D4—41no—
647D4—41no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—44no—
669C2×C4—48no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—44no—
677C2×C4—2361no—
678C2×C4—2361no—
679C2×C4—2361no—
680C2×C4—2361no—
681C2×C4—2361no—
682C2×C4—2361no—
683C2×C4—2361no—
684C2×C4—2361no—
685C2×C4—2361no—
686C2×C4—2361no—
687C2×C4—2361no—
688C2×C4—2361no—
689C2×C4#1427369612yes—
690C2×C4#1427374712yes—
691C2×C4C22×C22⋊D5911yescharacteristic
692C2×C4C22×C22⋊D5911yescharacteristic
693C2×C4#41×D5911yescharacteristic
694C2×C4#41×D5911yescharacteristic
695C2×C4#1427377311yescharacteristic
696C2×C4#1427377411yescharacteristic
697C8—1182no—
698C8—1182no—
699C8—2361no—
700C8—2361no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22#1683756414yes—
715C22C2×#1427369611yescharacteristic
716C22#1683794811yescharacteristic
717C22#1683798011yescharacteristic
718C22C2×#1427374711yescharacteristic
719C22C2×#1427374711yescharacteristic
720C22C2×#1427375711yescharacteristic
721C22#1683820011yescharacteristic
722C4—22no—
723C4—22no—
724C4—41no—
725C4—41no—
726C4—42no—
727C4—41no—
728C4—42no—
729C4—42no—
730C4—4721no—
731C4—4721no—
732C4—4721no—
733C4—4721no—
734C4#1683804011yescharacteristic
735C4#1683804011yescharacteristic
736C4#1683805111yescharacteristic
737C4#1683805111yescharacteristic
738C2—24no—
739C2—82no—
740C2#2142770011yescharacteristic
741C2C2×#1683756411yescharacteristic
742C2#2143331411yescharacteristic
743C2#2143466011yescharacteristic
744C2#2143480611yescharacteristic
745C2#2143543311yescharacteristic
746C2#2143544311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC2×C59×#529C2
socleC23×C59C22×D4
prime radicalC2×#121×C59C22
hypercenterC2×#529D59
hypocenterC59#25499
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×#16837641C2semidirect
3. #21432435C2semidirect
4. #21425431C2semidirect
5. #21425332C2semidirect
6. #21425244C2semidirect
7. #21425190C2semidirect
9. #21424520C2semidirect
10. #21424437C2semidirect
11. #21424430C2semidirect
12. #21424364C2semidirect
13. #21424343C2semidirect
14. C2×#16837157C2semidirect
436. C59#25499semidirect

Maximal subgroups

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

subgroupindex
C2×#168376412
C2×#168376292
#214324352
#214254312
#214253322
#214252442
#214251902
#214245252
#214245202
#214244372
#214244302
#214243642
#214243432
C2×#168371572
C2×C59×#5292
#2549959