Finite Group Databasebeta

← #28557579

Subgroups — #28557579

Order 15104.

926 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21438007C211yesmaximal, characteristic
2#21433221C211yesmaximal, characteristic, complemented
3#21422827C211yesmaximal, characteristic, complemented
4#21422816C211yesmaximal, characteristic, complemented
5#21422812C211yesmaximal, characteristic, complemented
6#21422804C211yesmaximal, characteristic, complemented
7#21422802C211yesmaximal, characteristic, complemented
8#21422792C211yesmaximal, characteristic, complemented
9#21422789C211yesmaximal, characteristic, complemented
10#21422787C211yesmaximal, characteristic, complemented
11#21422771C211yesmaximal, characteristic, complemented
12#21422754C211yesmaximal, characteristic, complemented
13#21422743C211yesmaximal, characteristic, complemented
14C2×#16837147C211yesmaximal, characteristic, complemented
15C59×#2990C211yesmaximal, characteristic, complemented
16#16838125—21no—
17#16838117—21no—
18#16838112—21no—
19#16838098—21no—
20#16838098—21no—
21#16838061—21no—
22#16838061—21no—
23#16838057—21no—
24#16838023C412yes—
25#16838023C412yes—
26#16837980C412yes—
27#16837959C2211yescharacteristic
28#16837959C2211yescharacteristic
29#16837952C2211yescharacteristic
30#16837952C2211yescharacteristic
31#16837952C2211yescharacteristic
32C2×#14273727C2211yescharacteristic
33#16837882C412yes—
34#16837533—21no—
35#16837474—21no—
36#16837474—21no—
37D4×C59⋊C8—21no—
38#16837459C2211yescharacteristic
39#16837459C2211yescharacteristic
40#16837455C2211yescharacteristic
41#16837426C2211yescharacteristic
42C2×C4⋊(C59⋊C8)C2211yescharacteristic
43C2×C4⋊(C59⋊C8)C2211yescharacteristic
44#16837150C2211yescharacteristic
45#16837150C2211yescharacteristic
46#16837150C2211yescharacteristic
47#16837150C2211yescharacteristic
48#16837147C2211yescharacteristic
49#16837147C2211yescharacteristic
50#16837147C2211yescharacteristic
51#16837147C2211yescharacteristic
52#16837147C2211yescharacteristic
53#16837147C2211yescharacteristic
54#16837147C2211yescharacteristic
55#16837147C2211yescharacteristic
56#16837145C2211yescharacteristic
57#16837145C2211yescharacteristic
58#16837145C2211yescharacteristic
59#16837145C2211yescharacteristic
60C4×#41×C59C2211yescharacteristic
61C59×#446—21no—
62C59×#435—21no—
63C59×#435—21no—
64C8×D4×C59—21no—
65C59×#432C2211yescharacteristic
66C59×#432C2211yescharacteristic
67C59×#431C2211yescharacteristic
68C59×#423C2211yescharacteristic
69C2×C4⋊C8×C59C2211yescharacteristic
70C2×C4⋊C8×C59C2211yescharacteristic
71C2×#11745685—21no—
72C2×#11745685—21no—
73C2×#11745685C2×C412yes—
74C22×Dic118—21no—
75C2×#11745664—21no—
76C22×C59⋊C8—21no—
77C22×C59⋊C8—21no—
78#14273727—21no—
79#14273727—21no—
80#14273727C2×C412yes—
81#14273727C2311yescharacteristic
82#14273727C2311yescharacteristic
83#14273727C2311yescharacteristic
84#14273724C2311yescharacteristic
85#14273722—22no—
86#14273722—22no—
87#14273719—21no—
88#14273719—21no—
89#14273715—21no—
90#14273715—21no—
91#14273715C2×C412yes—
92#14273713—22no—
93#14273713—22no—
94#14273709—22no—
95#14273709—22no—
96#14273706—21no—
97#14273706—21no—
98#14273706C2×C412yes—
99#14273706C2×C412yes—
100#14273705—22no—
101#14273705—22no—
102#14273703—22no—
103#14273701—21no—
104#14273701—21no—
105#14273701—21no—
106#14273701—21no—
107#14273701C2×C412yes—
108#14273701C2×C412yes—
109#14273699—22no—
110#14273699—22no—
111#14273698—22no—
112C4×Dic118—21no—
113C4×Dic118—21no—
114C4×Dic118C2×C412yes—
115C4×Dic118C2×C412yes—
116C4×D236—21no—
117C4×D236—21no—
118C4×D236—21no—
119C4×D236—21no—
120C4×D236C2×C412yes—
121C4×D236C2×C412yes—
122(C22⋊D59)⋊C4—22no—
123(C22⋊D59)⋊C4—22no—
124#14273686—21no—
125#14273686—21no—
126#14273685—22no—
127C2×C4⋊Dic59—21no—
128C2×C4⋊Dic59C2×C412yes—
129C4⋊C4×D59—22no—
130C4⋊(C59⋊C8)—21no—
131C4⋊(C59⋊C8)—21no—
132C4⋊(C59⋊C8)—21no—
133C4⋊(C59⋊C8)C2311yescharacteristic
134C4⋊(C59⋊C8)C2311yescharacteristic
135C4⋊(C59⋊C8)C2311yescharacteristic
136C4⋊(C59⋊C8)C2311yescharacteristic
137C22⋊(C59⋊C8)—21no—
138C22⋊(C59⋊C8)—21no—
139C22⋊(C59⋊C8)—21no—
140#14273638—21no—
141#14273638—21no—
142C4×C59⋊C8—21no—
143C2×#41×C59C2×C411yescharacteristic
144C2×M16×C59—21no—
145C22×C8×C59—21no—
146C22×C8×C59—21no—
147C4×Q8×C59D411yescharacteristic
148C4×Q8×C59D411yescharacteristic
149C4×D4×C59D411yescharacteristic
150C4×D4×C59D411yescharacteristic
151C4×D4×C59D411yescharacteristic
152C4×D4×C59D411yescharacteristic
153C4×D4×C59D411yescharacteristic
154C4×D4×C59D411yescharacteristic
155#117×C59C2×C411yescharacteristic
156#117×C59C2×C411yescharacteristic
157#117×C59C2×C411yescharacteristic
158C2×C42×C59C2311yescharacteristic
159C2×C42×C59C2311yescharacteristic
160C2×C42×C59C2311yescharacteristic
161C4⋊C8×C59—21no—
162C4⋊C8×C59—21no—
163C4⋊C8×C59—21no—
164C4⋊C8×C59C2311yescharacteristic
165C4⋊C8×C59C2311yescharacteristic
166C4⋊C8×C59C2311yescharacteristic
167C4⋊C8×C59C2311yescharacteristic
168C22⋊C8×C59—21no—
169C22⋊C8×C59—21no—
170C22⋊C8×C59—21no—
171#97×C59—21no—
172#97×C59—21no—
173C4×C8×C59—21no—
174#41×C59—42no—
175C2×Q8×C59C22⋊C411yescharacteristic
176C2×D4×C59C22⋊C411yescharacteristic
177C2×D4×C59C22⋊C411yescharacteristic
178C2×D4×C59C22⋊C411yescharacteristic
179C22×C4×C59C22×C411yescharacteristic
180C22×C4×C59C22×C411yescharacteristic
181C22×C4×C59C22×C411yescharacteristic
182C22×C4×C59C2×D411yescharacteristic
183C22×C4×C59C2×D411yescharacteristic
184C22×C4×C59C2×D411yescharacteristic
185C22×C4×C59C2×D411yescharacteristic
186C22×C4×C59C2×D411yescharacteristic
187C22×C4×C59C2×D411yescharacteristic
188C2×C22⋊D59—22no—
189C2×C22⋊D59—22no—
190C2×C22⋊D59—22no—
191C22×Dic59—22no—
192#11745685—44no—
193#11745685—81no—
194#11745685—81no—
195#11745685—81no—
196#11745685—81no—
197C2×D236—21no—
198C2×D236—21no—
199C2×D236C22×C412yes—
200C2×C4×D59—22no—
201C2×C4×D59—22no—
202C2×C4×D59—22no—
203C2×Dic118—21no—
204C2×Dic118—21no—
205C2×Dic118—22no—
206C2×Dic118—81no—
207C2×Dic118—81no—
208C2×Dic118C22×C412yes—
209M16×C59—81no—
210C2×C8×C59—21no—
211C2×C8×C59—21no—
212C2×C8×C59—21no—
213C2×C8×C59—21no—
214C2×C8×C59—81no—
215C2×C8×C59—81no—
216C4⋊C4×C59C22⋊C411yescharacteristic
217C4⋊C4×C59C22⋊C411yescharacteristic
218C4⋊C4×C59C22⋊C411yescharacteristic
219C4⋊C4×C59C22⋊C411yescharacteristic
220C4⋊C4×C59C22⋊C411yescharacteristic
221C4⋊C4×C59C22⋊C411yescharacteristic
222C22⋊C4×C59C22⋊C411yescharacteristic
223C22⋊C4×C59C22⋊C411yescharacteristic
224C22⋊C4×C59C22⋊C411yescharacteristic
225C22⋊C4×C59C22⋊C411yescharacteristic
226C22⋊C4×C59C22⋊C411yescharacteristic
227C22⋊C4×C59C22⋊C411yescharacteristic
228C42×C59C22×C411yescharacteristic
229C42×C59C22×C411yescharacteristic
230C42×C59C22×C411yescharacteristic
231C42×C59C2×D411yescharacteristic
232C42×C59C2×D411yescharacteristic
233C42×C59C2×D411yescharacteristic
234C42×C59C2×D411yescharacteristic
235C42×C59C2×D411yescharacteristic
236C42×C59C2×D411yescharacteristic
237C42×C59C2411yescharacteristic
238C22⋊Dic59—22no—
239C22⋊Dic59—22no—
240(C2×D59)⋊C4—22no—
241(C2×D59)⋊C4—22no—
242(C2×D59)⋊C4—22no—
243(C2×D59)⋊C4—22no—
244(C2×D59)⋊C4—22no—
245(C2×D59)⋊C4—22no—
246C4⋊Dic59—22no—
247C4⋊Dic59—22no—
248C4⋊Dic59—21no—
249C4⋊Dic59—21no—
250C4⋊Dic59—21no—
251C4⋊Dic59—21no—
252C4⋊Dic59C22×C412yes—
253C4⋊Dic59C22×C412yes—
254Dic59⋊C4—22no—
255Dic59⋊C4—22no—
256Dic59⋊C4—22no—
257Dic59⋊C4—22no—
258C4×Dic59—22no—
259C4×Dic59—22no—
260#11745664—81no—
261C2×C59⋊C8—21no—
262C2×C59⋊C8—21no—
263C2×C59⋊C8—21no—
264C2×C59⋊C8—21no—
265C2×C59⋊C8—81no—
266C2×C59⋊C8—81no—
267C23×C59C2×C22⋊C411yescharacteristic
268C23×C59C2×C22⋊C411yescharacteristic
269C23×C59C2×C22⋊C411yescharacteristic
270C22×D59—22no—
271Q8×C59—41no—
272D4×C59—22no—
273D4×C59—22no—
274D4×C59—41no—
275C2×C4×C59—22no—
276C2×C4×C59—21no—
277C2×C4×C59—21no—
278C2×C4×C59—21no—
279C2×C4×C59—21no—
280C2×C4×C59—21no—
281C2×C4×C59—21no—
282C2×C4×C59—21no—
283C2×C4×C59—21no—
284C2×C4×C59—21no—
285C2×C4×C59—21no—
286C2×C4×C59—21no—
287C2×C4×C59—21no—
288C2×C4×C59—41no—
289C2×C4×C59—41no—
290C2×C4×C59C2×C22⋊C411yescharacteristic
291C2×C4×C59C2×C22⋊C411yescharacteristic
292C2×C4×C59C2×C22⋊C411yescharacteristic
293C2×C4×C59C2×C22⋊C411yescharacteristic
294C2×C4×C59C2×C22⋊C411yescharacteristic
295C2×C4×C59C2×C22⋊C411yescharacteristic
296C2×C4×C59C2×C22⋊C411yescharacteristic
297C2×C4×C59C2×C22⋊C411yescharacteristic
298C2×C4×C59C2×C22⋊C411yescharacteristic
299C2×C4×C59C23×C411yescharacteristic
300C2×C4×C59C22×D411yescharacteristic
301C2×C4×C59C22×D411yescharacteristic
302C22⋊D59—44no—
303C22⋊D59—82no—
304C22⋊D59—82no—
305C2×Dic59—22no—
306C2×Dic59—22no—
307C2×Dic59—22no—
308C2×Dic59—82no—
309D236—42no—
310D236—41no—
311D236—41no—
312D236—41no—
313D236—41no—
314C4×D59—44no—
315C4×D59—82no—
316C4×D59—82no—
317Dic118—41no—
318Dic118—41no—
319Dic118—41no—
320Dic118—41no—
321Dic118—42no—
322Dic118—82no—
323C8×C59—41no—
324C8×C59—41no—
325C8×C59—41no—
326C8×C59—41no—
327C59⋊C8—41no—
328C59⋊C8—41no—
329C59⋊C8—41no—
330C59⋊C8—41no—
331#17775—591nomaximal, Sylow
332C22×C59—21no—
333C22×C59—21no—
334C22×C59—21no—
335C22×C59—21no—
336C22×C59—21no—
337C22×C59—21no—
338C22×C59—21no—
339C22×C59—21no—
340C22×C59#41312yes—
341C22×C59C22×C22⋊C411yescharacteristic
342C2×D59—42no—
343C2×D59—42no—
344C2×D59—42no—
345C4×C59—21no—
346C4×C59—21no—
347C4×C59—21no—
348C4×C59—21no—
349C4×C59—21no—
350C4×C59—21no—
351C4×C59—21no—
352C4×C59—21no—
353C4×C59—21no—
354C4×C59—21no—
355C4×C59#57611yescharacteristic
356C4×C59#57711yescharacteristic
357C4×C59#57711yescharacteristic
358C4×C59#57811yescharacteristic
359Dic59—42no—
360Dic59—42no—
361Dic59—42no—
362#3511—591no—
363#2990—591no—
364#2990D5911yescharacteristic, complemented
365#1559—591no—
366#1557—591no—
367#1556—591no—
368#1554—591no—
369#1553—591no—
370#1551—591no—
371#1551—591no—
372#1550—591no—
373#1547—591no—
374#1542—591no—
375#1540—591no—
376C2×#332—591no—
377C2×C59—22no—
378C2×C59—41no—
379C2×C59—41no—
380C2×C59C2×#41311yescharacteristic
381C2×C59#289711yescharacteristic
382C2×C59#289811yescharacteristic
383D59—82no—
384#556—1181no—
385#555—1181no—
386#554—1181no—
387#553—1181no—
388#553—1181no—
389#548—1181no—
390#548—1181no—
391#547—1181no—
392#542—592no—
393#542—592no—
394#537—592no—
395#533—591no—
396#533—591no—
397#532—591no—
398#532—591no—
399#532—591no—
400C2×C4⋊Q8—591no—
401#520—592no—
402C4×#41C2×D5911yescharacteristic
403#446—21no—
404#446—1181no—
405#435—21no—
406#435—21no—
407#435—1181no—
408#435—1181no—
409C8×D4—21no—
410C8×D4—1181no—
411#432—591no—
412#432—591no—
413#432C2×D5911yescharacteristic
414#432C2×D5911yescharacteristic
415#431—591no—
416#431C2×D5911yescharacteristic
417#423—591no—
418#423C2×D5911yescharacteristic
419C2×C4⋊C8—591no—
420C2×C4⋊C8—591no—
421C2×C4⋊C8C2×D5911yescharacteristic
422C2×C4⋊C8C2×D5911yescharacteristic
423#333—591no—
424#333—591no—
425#333—591no—
426#333—591no—
427#332—591no—
428#332—591no—
429#332—591no—
430#332—591no—
431#332—591no—
432#332—591no—
433#332—591no—
434#332—591no—
435#331—591no—
436#331—591no—
437#331—591no—
438#331—591no—
439C59#1777511yescharacteristic, complemented, Sylow
440C2×#41—592no—
441C2×#41—1181no—
442C2×#41—1181no—
443C2×#41C4×D5911yescharacteristic
444C22×Q8—1181no—
445C2×M16—21no—
446C2×M16—1181no—
447C22×C8—21no—
448C22×C8—21no—
449C22×C8—1181no—
450C22×C8—1181no—
451C4⋊Q8—592no—
452C4⋊Q8—591no—
453C4⋊Q8—591no—
454C4⋊Q8—591no—
455C4⋊Q8—1181no—
456C4⋊Q8—1181no—
457#127—591no—
458#126—1182no—
459#126—1182no—
460#125—1181no—
461#125—1181no—
462#124—592no—
463#124—1182no—
464#124—1182no—
465#124—1181no—
466#124—1181no—
467#123—1182no—
468#123—1182no—
469C22⋊Q8—592no—
470C22⋊Q8—592no—
471C22⋊Q8—1182no—
472C22⋊Q8—1181no—
473C22⋊Q8—1181no—
474C22⋊Q8—1182no—
475C22⋊Q8—1182no—
476#121—592no—
477#121—592no—
478#121—1182no—
479#121—1182no—
480#121—1182no—
481#121—1181no—
482#121—1181no—
483#121—1181no—
484#121—1181no—
485C4×Q8—592no—
486C4×Q8—592no—
487C4×Q8—1181no—
488C4×Q8—1181no—
489C4×Q8D23611yescharacteristic
490C4×Q8C22⋊D5911yescharacteristic
491C4×D4—592no—
492C4×D4—592no—
493C4×D4—1182no—
494C4×D4—1182no—
495C4×D4—1181no—
496C4×D4—1181no—
497C4×D4—1181no—
498C4×D4—1181no—
499C4×D4D23611yescharacteristic
500C4×D4D23611yescharacteristic
501C4×D4D23611yescharacteristic
502C4×D4C22⋊D5911yescharacteristic
503C4×D4C22⋊D5911yescharacteristic
504C4×D4C22⋊D5911yescharacteristic
505#117—1181no—
506#117—1181no—
507#117—1182no—
508#117C4×D5911yescharacteristic
509#117C4×D5911yescharacteristic
510#117C4×D5911yescharacteristic
511C2×C4⋊C4—592no—
512C2×C4⋊C4—1181no—
513C2×C4⋊C4—1182no—
514C2×C42C22×D5911yescharacteristic
515C2×C42C22×D5911yescharacteristic
516C2×C42C22×D5911yescharacteristic
517C4⋊C8—21no—
518C4⋊C8—21no—
519C4⋊C8—21no—
520C4⋊C8—591no—
521C4⋊C8—591no—
522C4⋊C8—591no—
523C4⋊C8—591no—
524C4⋊C8—1181no—
525C4⋊C8—1181no—
526C4⋊C8—1181no—
527C4⋊C8C22×D5911yescharacteristic
528C4⋊C8C22×D5911yescharacteristic
529C4⋊C8C22×D5911yescharacteristic
530C4⋊C8C22×D5911yescharacteristic
531C22⋊C8—21no—
532C22⋊C8—21no—
533C22⋊C8—21no—
534C22⋊C8—1181no—
535C22⋊C8—1181no—
536C22⋊C8—1181no—
537#97—21no—
538#97—21no—
539#97—1181no—
540#97—1181no—
541C4×C8—21no—
542C4×C8—1181no—
543#41—42no—
544#41—4721no—
545#41—4721no—
546#41—4721no—
547#41—4721no—
548#41—2364no—
549C2×Q8—592no—
550C2×Q8—1182no—
551C2×Q8—1181no—
552C2×Q8—1181no—
553C2×Q8—4721no—
554C2×Q8—4721no—
555C2×Q8(C2×D59)⋊C411yescharacteristic
556C2×D4—592no—
557C2×D4—1182no—
558C2×D4—1182no—
559C2×D4—1182no—
560C2×D4—1181no—
561C2×D4—1181no—
562C2×D4(C2×D59)⋊C411yescharacteristic
563C2×D4(C2×D59)⋊C411yescharacteristic
564C2×D4(C2×D59)⋊C411yescharacteristic
565C22×C4—1182no—
566C22×C4—1182no—
567C22×C4—1182no—
568C22×C4—1182no—
569C22×C4C2×C4×D5911yescharacteristic
570C22×C4C2×C4×D5911yescharacteristic
571C22×C4C2×C4×D5911yescharacteristic
572C22×C4C2×D23611yescharacteristic
573C22×C4C2×D23611yescharacteristic
574C22×C4C2×D23611yescharacteristic
575C22×C4C2×C22⋊D5911yescharacteristic
576C22×C4C2×C22⋊D5911yescharacteristic
577C22×C4C2×C22⋊D5911yescharacteristic
578M16—81no—
579M16—4721no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—81no—
585C2×C8—81no—
586C2×C8—1181no—
587C2×C8—1181no—
588C2×C8—1181no—
589C2×C8—1181no—
590C2×C8—4721no—
591C2×C8—4721no—
592C4⋊C4—592no—
593C4⋊C4—592no—
594C4⋊C4—1182no—
595C4⋊C4—1182no—
596C4⋊C4—1182no—
597C4⋊C4—1182no—
598C4⋊C4—1182no—
599C4⋊C4—1182no—
600C4⋊C4—1181no—
601C4⋊C4—1181no—
602C4⋊C4—1181no—
603C4⋊C4—1181no—
604C4⋊C4(C2×D59)⋊C411yescharacteristic
605C4⋊C4(C2×D59)⋊C411yescharacteristic
606C4⋊C4(C2×D59)⋊C411yescharacteristic
607C4⋊C4(C2×D59)⋊C411yescharacteristic
608C4⋊C4(C2×D59)⋊C411yescharacteristic
609C4⋊C4(C2×D59)⋊C411yescharacteristic
610C22⋊C4—1182no—
611C22⋊C4—1182no—
612C22⋊C4—1182no—
613C22⋊C4—1182no—
614C22⋊C4—1182no—
615C22⋊C4—1182no—
616C22⋊C4—1182no—
617C22⋊C4—1182no—
618C22⋊C4(C2×D59)⋊C411yescharacteristic
619C22⋊C4(C2×D59)⋊C411yescharacteristic
620C22⋊C4(C2×D59)⋊C411yescharacteristic
621C22⋊C4(C2×D59)⋊C411yescharacteristic
622C22⋊C4(C2×D59)⋊C411yescharacteristic
623C22⋊C4(C2×D59)⋊C411yescharacteristic
624C42—1182no—
625C42—1182no—
626C42C2×C4×D5911yescharacteristic
627C42C2×C4×D5911yescharacteristic
628C42C2×C4×D5911yescharacteristic
629C42C2×D23611yescharacteristic
630C42C2×D23611yescharacteristic
631C42C2×D23611yescharacteristic
632C42C2×C22⋊D5911yescharacteristic
633C42C2×C22⋊D5911yescharacteristic
634C42C2×C22⋊D5911yescharacteristic
635C42C23×D5911yescharacteristic
636C23—1182no—
637C23C2×(C2×D59)⋊C411yescharacteristic
638C23C2×(C2×D59)⋊C411yescharacteristic
639C23C2×(C2×D59)⋊C411yescharacteristic
640Q8—41no—
641Q8—4722no—
642Q8—2362no—
643Q8—2361no—
644Q8—2361no—
645Q8—2361no—
646Q8—2361no—
647D4—22no—
648D4—22no—
649D4—41no—
650D4—4722no—
651D4—4722no—
652D4—2362no—
653D4—2364no—
654D4—2361no—
655D4—2361no—
656D4—2361no—
657D4—2361no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—1182no—
674C2×C4—1182no—
675C2×C4—1182no—
676C2×C4—4722no—
677C2×C4—4722no—
678C2×C4—4722no—
679C2×C4—2364no—
680C2×C4C2×(C2×D59)⋊C411yescharacteristic
681C2×C4C2×(C2×D59)⋊C411yescharacteristic
682C2×C4C2×(C2×D59)⋊C411yescharacteristic
683C2×C4C2×(C2×D59)⋊C411yescharacteristic
684C2×C4C2×(C2×D59)⋊C411yescharacteristic
685C2×C4C2×(C2×D59)⋊C411yescharacteristic
686C2×C4C2×(C2×D59)⋊C411yescharacteristic
687C2×C4C2×(C2×D59)⋊C411yescharacteristic
688C2×C4C2×(C2×D59)⋊C411yescharacteristic
689C2×C4C22×C4×D5911yescharacteristic
690C2×C4C22×C22⋊D5911yescharacteristic
691C2×C4C22×D23611yescharacteristic
692C8—41no—
693C8—41no—
694C8—41no—
695C8—41no—
696C8—2361no—
697C8—2361no—
698C8—2361no—
699C8—2361no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—21no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—21no—
708C22—2362no—
709C22—2362no—
710C22—2362no—
711C22#1683738412yes—
712C22C22×(C2×D59)⋊C411yescharacteristic
713C4—21no—
714C4—21no—
715C4—21no—
716C4—21no—
717C4—21no—
718C4—21no—
719C4—21no—
720C4—21no—
721C4—21no—
722C4—21no—
723C4—2362no—
724C4—2362no—
725C4—2362no—
726C4#1683820711yescharacteristic
727C4#1683821311yescharacteristic
728C4#1683821411yescharacteristic
729C4#1683821711yescharacteristic
730C2—22no—
731C2—41no—
732C2—41no—
733C2—4722no—
734C2C2×#1683738411yescharacteristic
735C2#2143262311yescharacteristic
736C2#2143262611yescharacteristic
subgroupG/H
centerC22C22×(C2×D59)⋊C4
commutatorC2×C4×C59C23×C4
FrattiniC42C23×D59
FittingC59×#2990C2
socleC22×C59C22×C22⋊C4
prime radical#21438007C2
cosocleC42×C59C24
hypercenter#2990D59
hypocenterC59#17775
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2990

Complements

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

NH ≅ G/Ntype
2. #21433221C2semidirect
3. #21422827C2semidirect
4. #21422816C2semidirect
5. #21422812C2semidirect
6. #21422804C2semidirect
7. #21422802C2semidirect
8. #21422792C2semidirect
9. #21422789C2semidirect
10. #21422787C2semidirect
11. #21422771C2semidirect
12. #21422754C2semidirect
13. #21422743C2semidirect
14. C2×#16837147C2semidirect
15. C59×#2990C2semidirect
364. #2990D59semidirect
439. C59#17775semidirect

Maximal subgroups

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

subgroupindex
#214380072
#214332212
#214228272
#214228162
#214228122
#214228042
#214228022
#214227922
#214227892
#214227872
#214227712
#214227542
#214227432
C2×#168371472
C59×#29902
#1777559