Finite Group Databasebeta

← #29459798

Subgroups — #29459798

Order 15104.

2254 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21437765C212yesmaximal, complemented
2#21435008C212yesmaximal, complemented
3#21434961C212yesmaximal, complemented
4#21434950C214yesmaximal, complemented
5#21434938C212yesmaximal, complemented
6#21434912C214yesmaximal, complemented
7#21434896C212yesmaximal, complemented
8#21434087C212yesmaximal, complemented
9#21434055C212yesmaximal, complemented
10#21433715C212yesmaximal, complemented
11#21433705C211yesmaximal, characteristic, complemented
12C2×#16837655C211yesmaximal, characteristic, complemented
13#21433403C212yesmaximal, complemented
14#21433366C212yesmaximal, complemented
15C59×#2879C211yesmaximal, characteristic, complemented
16C2×#14273773C2212yescomplemented
17C2×#14273755C2212yescomplemented
18C2×#14273749C2211yescharacteristic, complemented
19C22×D472C2211yescharacteristic, complemented
20#16838071—22no—
21#16838063—22no—
22#16838040—24no—
23#16838040—22no—
24D4×C22⋊D59—24no—
25D4×C22⋊D59—22no—
26#16837980C2212yes—
27#16837980C2214yescomplemented
28#16837966C2212yes—
29#16837966C2214yescomplemented
30#16837913C2214yescomplemented
31#16837913C2212yescomplemented
32C2×#14273701C2214yescomplemented
33C2×#14273701C2212yescomplemented
34#16837885C2212yescomplemented
35#16837744C2214yescomplemented
36#16837733C2214yescomplemented
37#16837727C2214yescomplemented
38#16837727C2214yescomplemented
39#16837727C2214yescomplemented
40#16837721C2214yescomplemented
41#16837721C2214yescomplemented
42#16837716C2214yescomplemented
43#16837660C2211yescharacteristic, complemented
44#16837660C2211yescharacteristic, complemented
45#16837655C2211yescharacteristic, complemented
46#16837655C2214yescomplemented
47#16837655C2212yescomplemented
48#16837655C2212yescomplemented
49#16837655C2212yescomplemented
50#16837655C2211yescharacteristic, complemented
51#16837655C2212yescomplemented
52#16837648C2212yescomplemented
53#16837648C2214yescomplemented
54#16837648C2212yescomplemented
55#16837638C2214yescomplemented
56#16837631C2214yescomplemented
57#16837566C2214yescomplemented
58#16837555C2214yescomplemented
59#16837549C2214yescomplemented
60#16837549C2214yescomplemented
61#16837549C2214yescomplemented
62#16837538C2214yescomplemented
63#16837538C2214yescomplemented
64#16837538C2214yescomplemented
65#16837444C2212yescomplemented
66#16837440C2211yescharacteristic, complemented
67C2×#14273659C2211yescharacteristic, complemented
68#16837408C2212yescomplemented
69#16837404C2212yescomplemented
70#16837399C2212yescomplemented
71C2×#14273649C2212yescomplemented
72C22×#41×C59C2211yescharacteristic
73C22×M16×C59C2211yescharacteristic, complemented
74C22×M16×C59C2211yescharacteristic, complemented
75C59×#408C2212yescomplemented
76C59×#408C2212yescomplemented
77C59×#408C2212yescomplemented
78C59×#408C2212yescomplemented
79C59×#407C2212yescomplemented
80C59×#407C2212yescomplemented
81#14273773—44no—
82#14273773—44no—
83C2×#11745689—22no—
84C2×#11745685C2312yes—
85C2×#11745685C2314yes—
86C22×D236C2312yes—
87C22×D236C2314yes—
88C22×C22⋊D59—22no—
89C22×C22⋊D59—24no—
90C2×D4×D59—24no—
91C2×D4×D59—22no—
92#14273755—44no—
93#14273749—42no—
94C2×Dic236C2311yescharacteristic
95C2×#11745660C2312yes—
96C2×#11745660C2314yes—
97C2×D472—42no—
98C2×D472C2314yes—
99C2×D472C2312yes—
100C2×D472C2312yes—
101C2×D472C2311yescharacteristic
102#14273723—22no—
103#14273723—24no—
104#14273716—22no—
105#14273716—24no—
106#14273710—22no—
107#14273710—24no—
108#14273706C2312yes—
109#14273706C2312yes—
110#14273706C2314yes—
111#14273703—22no—
112#14273703—24no—
113#14273701—22no—
114#14273701—24no—
115#14273701—22no—
116#14273701—24no—
117#14273701C2312yes—
118#14273701C2314yes—
119#14273701C2312yes—
120#14273701C2314yes—
121#14273701C2314yes—
122#14273701C2314yes—
123#14273701C2314yes—
124#14273699—24no—
125#14273699—24no—
126#14273699—24no—
127#14273698—22no—
128#14273698—24no—
129#14273696—22no—
130#14273696—24no—
131#14273695—24no—
132#14273695—24no—
133#14273695—24no—
134Q8×Dic59—22no—
135D4×Dic59—24no—
136D4×Dic59—22no—
137C4×C22⋊D59—22no—
138C4×C22⋊D59—24no—
139C4×C22⋊D59—22no—
140C4×C22⋊D59—24no—
141#14273686C2312yes—
142#14273686C2314yes—
143C2×C4⋊Dic59C2312yes—
144C2×C4⋊Dic59C2314yes—
145C2×(C2×D59)⋊C4—22no—
146C2×(C2×D59)⋊C4—24no—
147#14273661C2314yes—
148#14273661C2312yes—
149#14273659C2312yes—
150#14273659C2312yes—
151#14273659C2311yescharacteristic
152#14273659C2311yescharacteristic
153#14273659C2314yes—
154#14273652C2312yes—
155#14273652C2312yes—
156#14273652C2314yes—
157#14273649C2314yes—
158#14273649C2314yes—
159#14273649C2314yes—
160#14273649C2314yes—
161#14273649C2312yes—
162#14273649C2312yes—
163#14273649C2314yes—
164C2×#41×C59—42no—
165C2×#41×C59—42no—
166C2×#41×C59D412yes—
167C2×#41×C59D412yes—
168C2×#41×C59C2312yes—
169C2×#41×C59C2312yes—
170C22×Q8×C59D411yescharacteristic
171C22×D4×C59D411yescharacteristic
172C22×D4×C59D412yes—
173C23×C4×C59C2311yescharacteristic
174C23×C4×C59C2312yes—
175C2×M16×C59—42no—
176C2×M16×C59—42no—
177C2×M16×C59C2312yes—
178C2×M16×C59C2311yescharacteristic
179C2×M16×C59C2312yes—
180C2×M16×C59C2311yescharacteristic
181C2×M16×C59C2311yescharacteristic
182C2×M16×C59C2311yescharacteristic
183C22×C8×C59C2311yescharacteristic
184C22×C8×C59C2311yescharacteristic
185C22×C8×C59C2312yes—
186C22⋊C8×C59C2314yes—
187C22⋊C8×C59C2314yes—
188C22⋊C8×C59C2314yes—
189C22⋊C8×C59C2314yes—
190C24×C59C2×D411yescharacteristic
191C24×C59C2×D412yes—
192C23×D59—24no—
193C23×D59—22no—
194#41×C59—24no—
195#41×C59—24no—
196#41×C59—42no—
197#41×C59—42no—
198#41×C59—44no—
199#41×C59—44no—
200C2×Q8×C59—42no—
201C2×Q8×C59C2×D412yes—
202C2×Q8×C59C2×D412yes—
203C2×D4×C59—42no—
204C2×D4×C59—44no—
205C2×D4×C59C2×D414yes—
206C2×D4×C59C2×D412yes—
207C2×D4×C59C2×D412yes—
208C2×D4×C59C2×D414yes—
209C22×C4×C59—22no—
210C22×C4×C59—22no—
211C22×C4×C59—42no—
212C22×C4×C59—42no—
213C22×C4×C59C2×D411yescharacteristic
214C22×C4×C59C2×D411yescharacteristic
215C22×C4×C59C2×D411yescharacteristic
216C22×C4×C59C2×D412yes—
217C22×C4×C59C2×D414yes—
218C22×C4×C59C2414yes—
219C22×C4×C59C2411yescharacteristic
220C22×C4×C59C2411yescharacteristic
221C22×C4×C59C2411yescharacteristic
222C2×C22⋊D59—22no—
223C2×C22⋊D59—24no—
224C2×C22⋊D59—24no—
225C2×C22⋊D59—22no—
226C2×C22⋊D59—24no—
227C2×C22⋊D59—22no—
228C2×C22⋊D59—24no—
229C2×C22⋊D59—24no—
230C2×C22⋊D59—24no—
231C2×C22⋊D59—84no—
232C2×C22⋊D59—88no—
233C22×Dic59—24no—
234C22×Dic59—22no—
235#11745689—48no—
236D4×D59—416no—
237D4×D59—48no—
238#11745685—24no—
239#11745685—24no—
240#11745685—44no—
241#11745685—44no—
242C2×D236—24no—
243C2×D236—24no—
244C2×D236—24no—
245C2×D236—22no—
246C2×D236—44no—
247C2×D236—44no—
248C2×D236C2414yes—
249C2×D236C2412yes—
250C2×C4×D59—24no—
251C2×C4×D59—22no—
252C2×Dic118C2412yes—
253M16×C59—24no—
254M16×C59—41no—
255M16×C59—41no—
256M16×C59—42no—
257M16×C59—41no—
258M16×C59—41no—
259C2×C8×C59—22no—
260C2×C8×C59—22no—
261C2×C8×C59—42no—
262C2×C8×C59C2411yescharacteristic
263C2×C8×C59C2411yescharacteristic
264C2×C8×C59C2414yes—
265C2×C8×C59C2411yescharacteristic
266C2×C8×C59C2411yescharacteristic
267C22⋊Dic59—24no—
268C22⋊Dic59—22no—
269C22⋊Dic59—22no—
270C22⋊Dic59—24no—
271C22⋊Dic59—22no—
272(C2×D59)⋊C4—24no—
273(C2×D59)⋊C4—22no—
274(C2×D59)⋊C4—24no—
275(C2×D59)⋊C4—24no—
276(C2×D59)⋊C4—24no—
277(C2×D59)⋊C4—24no—
278(C2×D59)⋊C4—22no—
279C4⋊Dic59—24no—
280C4⋊Dic59—22no—
281C4⋊Dic59C2414yes—
282C4⋊Dic59C2412yes—
283C4⋊Dic59C2412yes—
284Dic59⋊C4—22no—
285Dic59⋊C4—24no—
286Dic59⋊C4—22no—
287C4×Dic59—24no—
288C4×Dic59—22no—
289Dic236—41no—
290D472—42no—
291D472—42no—
292D472—41no—
293D472—44no—
294#11745660—42no—
295#11745660—44no—
296C23×C59—22no—
297C23×C59—42no—
298C23×C59—44no—
299C23×C59—42no—
300C23×C59C22×D414yes—
301C23×C59C22×D411yescharacteristic
302C23×C59C22×D411yescharacteristic
303C23×C59C22×D411yescharacteristic
304C22×D59—24no—
305C22×D59—22no—
306C22×D59—48no—
307C22×D59—44no—
308C22×D59—82no—
309C22×D59—84no—
310C22×D59—82no—
311C22×D59—84no—
312Q8×C59—24no—
313Q8×C59—42no—
314D4×C59—28no—
315D4×C59—24no—
316D4×C59—44no—
317D4×C59—42no—
318C2×C4×C59—22no—
319C2×C4×C59—22no—
320C2×C4×C59—22no—
321C2×C4×C59—21no—
322C2×C4×C59—21no—
323C2×C4×C59—21no—
324C2×C4×C59—21no—
325C2×C4×C59—24no—
326C2×C4×C59—24no—
327C2×C4×C59—42no—
328C2×C4×C59—44no—
329C2×C4×C59C22×D414yes—
330C2×C4×C59C22×D411yescharacteristic
331C2×C4×C59C22×D411yescharacteristic
332C2×C4×C59C22×D411yescharacteristic
333C2×C4×C59H(5,𝔽2)12yes—
334C2×C4×C59H(5,𝔽2)12yes—
335C2×C4×C59C2511yescharacteristic
336C22⋊D59—48no—
337C22⋊D59—48no—
338C22⋊D59—44no—
339C22⋊D59—44no—
340C22⋊D59—84no—
341C22⋊D59—82no—
342C22⋊D59—84no—
343C22⋊D59—84no—
344C22⋊D59—84no—
345C2×Dic59—22no—
346C2×Dic59—24no—
347C2×Dic59—22no—
348C2×Dic59—22no—
349C2×Dic59—82no—
350C2×Dic59—84no—
351D236—24no—
352D236—22no—
353D236—24no—
354D236—22no—
355D236—48no—
356D236—44no—
357C4×D59—48no—
358C4×D59—44no—
359Dic118—22no—
360Dic118—22no—
361C8×C59—21no—
362C8×C59—24no—
363C8×C59—21no—
364C8×C59—21no—
365C8×C59—21no—
366#60771—591nomaximal, Sylow
367C22×C59—22no—
368C22×C59—24no—
369C22×C59—22no—
370C22×C59—22no—
371C22×C59—24no—
372C22×C59—24no—
373C22×C59—21no—
374C22×C59—21no—
375C22×C59—82no—
376C22×C59—84no—
377C22×C59#53412yes—
378C22×C59C23×D411yescharacteristic
379C2×D59—44no—
380C2×D59—42no—
381C2×D59—44no—
382C2×D59—42no—
383C2×D59—44no—
384C2×D59—42no—
385C2×D59—164no—
386C2×D59—168no—
387C4×C59—24no—
388C4×C59—21no—
389C4×C59—21no—
390C4×C59#53412yes—
391C4×C59C2×H(5,𝔽2)11yescharacteristic
392C4×C59C2×H(5,𝔽2)11yescharacteristic
393Dic59—44no—
394Dic59—42no—
395Dic59—42no—
396Dic59—42no—
397#3488—592no—
398#3204—592no—
399#3199—592no—
400#3198—594no—
401#3197—592no—
402#3194—594no—
403#3192—592no—
404#3099—592no—
405#3096—592no—
406#3055—592no—
407#3054—591no—
408C2×#469—591no—
409#3012—592no—
410#3008—592no—
411#2879D5911yescharacteristic, complemented
412C2×C59—22no—
413C2×C59—44no—
414C2×C59—41no—
415C2×C59—41no—
416C2×C59C2×#53411yescharacteristic
417C2×C59#358512yes—
418D59—84no—
419D59—82no—
420C2×H(5,𝔽2)—592no—
421C22×#41C2×D5911yescharacteristic
422C2×AGL(1,ℤ/8)—592no—
423C2×#135—591no—
424C22×D8—591no—
425C22×M16C2×D5911yescharacteristic, complemented
426C22×M16C2×D5911yescharacteristic, complemented
427#550—1182no—
428#548—1182no—
429#546—1184no—
430#546—1182no—
431D42—1184no—
432D42—1182no—
433#537—592no—
434#537—594no—
435#535—592no—
436#535—594no—
437#525—594no—
438#525—592no—
439C2×#121—594no—
440C2×#121—592no—
441#520—592no—
442#485—594no—
443#483—594no—
444#482—594no—
445#482—594no—
446#482—594no—
447#481—594no—
448#481—594no—
449#480—594no—
450#470—591no—
451#470—591no—
452#469—591no—
453#469—594no—
454#469—592no—
455#469—592no—
456#469—592no—
457#469—591no—
458#469—592no—
459#468—592no—
460#468—594no—
461#468—592no—
462#466—594no—
463#465—594no—
464#452—594no—
465#450—594no—
466#449—594no—
467#449—594no—
468#449—594no—
469#447—594no—
470#447—594no—
471#447—594no—
472#428—592no—
473#427—591no—
474C2×#106—591no—
475#418—592no—
476#417—592no—
477#416—592no—
478C2×#102—592no—
479#408C2×D5912yescomplemented
480#408C2×D5912yescomplemented
481#408C2×D5912yescomplemented
482#408C2×D5912yescomplemented
483#407C2×D5912yescomplemented
484#407C2×D5912yescomplemented
485C59#6077111yescharacteristic, complemented, Sylow
486H(5,𝔽2)—2364no—
487H(5,𝔽2)—2364no—
488C2×#41—42no—
489C2×#41—42no—
490C2×#41—592no—
491C2×#41—594no—
492C2×#41—1182no—
493C2×#41D23612yes—
494C2×#41D23612yes—
495C2×#41C22×D5912yes—
496C2×#41C22×D5912yes—
497C22×Q8D23611yescharacteristic
498C22×D4—592no—
499C22×D4—594no—
500C22×D4—1182no—
501C22×D4—1184no—
502C22×D4—1184no—
503C22×D4—1182no—
504C22×D4D23611yescharacteristic
505C22×D4D23612yes—
506C23×C4C22×D5911yescharacteristic
507C23×C4C22×D5912yes—
508AGL(1,ℤ/8)—2364no—
509#135—2362no—
510C2×Q16—591no—
511C2×SD16—592no—
512C2×SD16—594no—
513C2×D8—592no—
514C2×D8—592no—
515C2×D8—591no—
516C2×D8—594no—
517C2×D8—2362no—
518C2×M16—42no—
519C2×M16—42no—
520C2×M16C22×D5912yes—
521C2×M16C22×D5911yescharacteristic
522C2×M16C22×D5912yes—
523C2×M16C22×D5911yescharacteristic
524C2×M16C22×D5911yescharacteristic
525C2×M16C22×D5911yescharacteristic
526C22×C8C22×D5911yescharacteristic
527C22×C8C22×D5911yescharacteristic
528C22×C8C22×D5912yes—
529#127—1182no—
530#127—1184no—
531#124—1182no—
532#124—1184no—
533#123—1182no—
534#123—1184no—
535C22⋊Q8—592no—
536C22⋊Q8—594no—
537C22⋊Q8—592no—
538C22⋊Q8—1182no—
539C22⋊Q8—1184no—
540#121—592no—
541#121—594no—
542#121—594no—
543#121—594no—
544#121—594no—
545#121—594no—
546#121—592no—
547#121—1184no—
548#121—1184no—
549#121—1184no—
550#121—1182no—
551#121—1184no—
552#121—1182no—
553#121—1184no—
554#121—1182no—
555#121—1184no—
556#120—1182no—
557#120—1184no—
558#120—1184no—
559#120—1184no—
560#120—1184no—
561C4×Q8—1182no—
562C4×D4—1184no—
563C4×D4—1182no—
564C4×D4—1182no—
565C4×D4—1184no—
566C4×D4—1182no—
567C4×D4—1184no—
568#117—592no—
569#117—594no—
570C2×C4⋊C4—592no—
571C2×C4⋊C4—594no—
572C2×C22⋊C4—1182no—
573C2×C22⋊C4—1184no—
574#107—592no—
575#107—594no—
576#106—592no—
577#106—592no—
578#106—591no—
579#106—591no—
580#106—594no—
581#103—592no—
582#103—592no—
583#103—594no—
584#102—594no—
585#102—594no—
586#102—592no—
587#102—592no—
588#102—594no—
589#102—594no—
590#102—594no—
591C22⋊C8C22×D5914yes—
592C22⋊C8C22×D5914yes—
593C22⋊C8C22×D5914yes—
594C22⋊C8C22×D5914yes—
595C24—1184no—
596C24—1182no—
597C24C2×D23611yescharacteristic
598C24C2×D23612yes—
599#41—24no—
600#41—24no—
601#41—42no—
602#41—42no—
603#41—44no—
604#41—44no—
605#41—1184no—
606#41—1184no—
607#41—2364no—
608#41—2364no—
609#41—2368no—
610C2×Q8—42no—
611C2×Q8—592no—
612C2×Q8C2×D23612yes—
613C2×Q8C2×D23612yes—
614C2×D4—42no—
615C2×D4—44no—
616C2×D4—594no—
617C2×D4—592no—
618C2×D4—1184no—
619C2×D4—1182no—
620C2×D4—1184no—
621C2×D4—1184no—
622C2×D4—1184no—
623C2×D4—1182no—
624C2×D4—1184no—
625C2×D4—1184no—
626C2×D4—1182no—
627C2×D4—1184no—
628C2×D4—1182no—
629C2×D4—1184no—
630C2×D4—1184no—
631C2×D4—4724no—
632C2×D4—4728no—
633C2×D4—2364no—
634C2×D4—2364no—
635C2×D4—23616no—
636C2×D4—2368no—
637C2×D4C2×D23614yes—
638C2×D4C2×D23612yes—
639C2×D4C2×D23612yes—
640C2×D4C2×D23614yes—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—42no—
644C22×C4—42no—
645C22×C4—1184no—
646C22×C4—1182no—
647C22×C4—1184no—
648C22×C4—1182no—
649C22×C4C2×D23611yescharacteristic
650C22×C4C2×D23611yescharacteristic
651C22×C4C2×D23611yescharacteristic
652C22×C4C2×D23614yes—
653C22×C4C2×D23612yes—
654C22×C4C23×D5914yes—
655C22×C4C23×D5911yescharacteristic
656C22×C4C23×D5911yescharacteristic
657C22×C4C23×D5911yescharacteristic
658Q16—2361no—
659SD16—2362no—
660SD16—2364no—
661D8—2362no—
662D8—2362no—
663D8—2361no—
664D8—2364no—
665M16—24no—
666M16—41no—
667M16—41no—
668M16—41no—
669M16—41no—
670M16—42no—
671C2×C8—22no—
672C2×C8—22no—
673C2×C8—42no—
674C2×C8C23×D5911yescharacteristic
675C2×C8C23×D5911yescharacteristic
676C2×C8C23×D5914yes—
677C2×C8C23×D5911yescharacteristic
678C2×C8C23×D5911yescharacteristic
679C4⋊C4—594no—
680C4⋊C4—592no—
681C4⋊C4—592no—
682C4⋊C4—1184no—
683C4⋊C4—1182no—
684C4⋊C4—1182no—
685C4⋊C4—1184no—
686C4⋊C4—1182no—
687C22⋊C4—1184no—
688C22⋊C4—1182no—
689C22⋊C4—1182no—
690C22⋊C4—1184no—
691C22⋊C4—1182no—
692C22⋊C4—1184no—
693C22⋊C4—1182no—
694C22⋊C4—1184no—
695C22⋊C4—1184no—
696C22⋊C4—1184no—
697C22⋊C4—1184no—
698C22⋊C4—1182no—
699C42—1184no—
700C42—1182no—
701C23—22no—
702C23—42no—
703C23—42no—
704C23—44no—
705C23—1184no—
706C23—1182no—
707C23—4722no—
708C23—4724no—
709C23—4722no—
710C23—4724no—
711C23—2368no—
712C23—2364no—
713C23C22×D23614yes—
714C23C22×D23611yescharacteristic
715C23C22×D23611yescharacteristic
716C23C22×D23611yescharacteristic
717Q8—24no—
718Q8—42no—
719Q8—1182no—
720Q8—1182no—
721D4—28no—
722D4—24no—
723D4—42no—
724D4—44no—
725D4—1184no—
726D4—1182no—
727D4—1184no—
728D4—1182no—
729D4—4724no—
730D4—4722no—
731D4—4724no—
732D4—4724no—
733D4—4724no—
734D4—2368no—
735D4—2368no—
736D4—2364no—
737D4—2368no—
738D4—2364no—
739D4—2364no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—42no—
750C2×C4—44no—
751C2×C4—1182no—
752C2×C4—1184no—
753C2×C4—1182no—
754C2×C4—1182no—
755C2×C4—4722no—
756C2×C4—4724no—
757C2×C4—2368no—
758C2×C4—2364no—
759C2×C4C22×D23614yes—
760C2×C4C22×D23611yescharacteristic
761C2×C4C22×D23611yescharacteristic
762C2×C4C22×D23611yescharacteristic
763C2×C4#1427377212yes—
764C2×C4#1427377212yes—
765C2×C4C24×D5911yescharacteristic
766C8—21no—
767C8—21no—
768C8—21no—
769C8—21no—
770C8—24no—
771C22—22no—
772C22—24no—
773C22—22no—
774C22—24no—
775C22—22no—
776C22—21no—
777C22—21no—
778C22—24no—
779C22—82no—
780C22—84no—
781C22—9444no—
782C22—9448no—
783C22—2364no—
784C22—2362no—
785C22—2364no—
786C22—2362no—
787C22—2364no—
788C22—2362no—
789C22#1683796412yes—
790C22C23×D23611yescharacteristic
791C4—21no—
792C4—21no—
793C4—24no—
794C4—2364no—
795C4—2362no—
796C4—2362no—
797C4—2362no—
798C4#1683796412yes—
799C4C2×#1427377211yescharacteristic
800C4C2×#1427377211yescharacteristic
801C2—22no—
802C2—41no—
803C2—44no—
804C2—41no—
805C2—4724no—
806C2—4722no—
807C2C2×#1683796411yescharacteristic
808C2#2143887712yes—
subgroupG/H
centerC22C23×D236
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC59×#2879C2
socleC22×C59C23×D4
hypercenter#2879D59
hypocenterC59#60771
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×#41 ◁ #2879

Complements

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

NH ≅ G/Ntype
1. #21437765C2semidirect
2. #21435008C2semidirect
3. #21434961C2semidirect
4. #21434950C2semidirect
5. #21434938C2semidirect
6. #21434912C2semidirect
7. #21434896C2semidirect
8. #21434087C2semidirect
9. #21434055C2semidirect
10. #21433715C2semidirect
11. #21433705C2semidirect
12. C2×#16837655C2semidirect
13. #21433403C2semidirect
14. #21433366C2semidirect
15. C59×#2879C2semidirect
16. C2×#14273773C22semidirect
17. C2×#14273755C22semidirect
18. C2×#14273749C22semidirect
19. C22×D472C22semidirect
27. #16837980C22semidirect
29. #16837966C22semidirect
30. #16837913C22semidirect
31. #16837913C22semidirect
32. C2×#14273701C22semidirect
33. C2×#14273701C22semidirect
34. #16837885C22semidirect
35. #16837744C22semidirect
36. #16837733C22semidirect
37. #16837727C22semidirect
38. #16837727C22semidirect
39. #16837727C22semidirect
40. #16837721C22semidirect
41. #16837721C22semidirect
42. #16837716C22semidirect
43. #16837660C22semidirect
44. #16837660C22semidirect
45. #16837655C22semidirect
46. #16837655C22semidirect
47. #16837655C22semidirect
48. #16837655C22semidirect
49. #16837655C22semidirect
50. #16837655C22semidirect
51. #16837655C22semidirect
52. #16837648C22semidirect
53. #16837648C22semidirect
54. #16837648C22semidirect
55. #16837638C22semidirect
56. #16837631C22semidirect
57. #16837566C22semidirect
58. #16837555C22semidirect
59. #16837549C22semidirect
60. #16837549C22semidirect
61. #16837549C22semidirect
62. #16837538C22semidirect
63. #16837538C22semidirect
64. #16837538C22semidirect
65. #16837444C22semidirect
66. #16837440C22semidirect
67. C2×#14273659C22semidirect
68. #16837408C22semidirect
69. #16837404C22semidirect
70. #16837399C22semidirect
71. C2×#14273649C22semidirect
73. C22×M16×C59C22semidirect
74. C22×M16×C59C22semidirect
75. C59×#408C22semidirect
76. C59×#408C22semidirect
77. C59×#408C22semidirect
78. C59×#408C22semidirect
79. C59×#407C22semidirect
80. C59×#407C22semidirect
411. #2879D59semidirect
425. C22×M16C2×D59semidirect
426. C22×M16C2×D59semidirect
479. #408C2×D59semidirect
480. #408C2×D59semidirect
481. #408C2×D59semidirect
482. #408C2×D59semidirect
483. #407C2×D59semidirect
484. #407C2×D59semidirect
485. C59#60771semidirect

Maximal subgroups

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

subgroupindex
#214377652
#214350082
#214349612
#214349502
#214349382
#214349122
#214348962
#214340872
#214340552
#214337152
#214337052
C2×#168376552
#214334032
#214333662
C59×#28792
#6077159