Finite Group Databasebeta

← #29468632

Subgroups — #29468632

Order 15104.

1870 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21437897C211yesmaximal, characteristic, complemented
2#21436843C214yesmaximal, complemented
3#21436810C212yesmaximal, complemented
4#21436799C212yesmaximal, complemented
5#21436752C214yesmaximal, complemented
6#21436741C212yesmaximal, complemented
7#21436727C212yesmaximal, complemented
8#21434450C212yesmaximal, complemented
9#21434418C211yesmaximal, characteristic, complemented
10#21433947C212yesmaximal, complemented
11#21433893C211yesmaximal, characteristic, complemented
12#21433595C212yesmaximal, complemented
13#21433556C211yesmaximal, characteristic, complemented
14#21433031C211yesmaximal, characteristic, complemented
15#21432924C212yesmaximal, complemented
16C2×C4×#11745669C211yesmaximal, characteristic, complemented
17C59×#3506C211yesmaximal, characteristic, complemented
18C2×#14273752C2212yes—
19C22×#11745669C2211yescharacteristic
20#16838113—21no—
21#16838112C2212yescomplemented
22#16838112C2214yescomplemented
23#16838108—22no—
24Q8×D236C2212yescomplemented
25#16838067—21no—
26#16838030C2212yes—
27#16838027—22no—
28#16837959C2211yescharacteristic
29C22⋊Q8×D59—22no—
30#16837876C2212yes—
31C2×C4×D236C2211yescharacteristic
32#16837766C2214yescomplemented
33#16837761C2214yescomplemented
34#16837756C2212yescomplemented
35#16837756C2212yescomplemented
36#16837756C2214yescomplemented
37#16837752C2211yescharacteristic, complemented
38#16837752C2211yescharacteristic, complemented
39#16837748C2211yescharacteristic, complemented
40#16837748C2211yescharacteristic, complemented
41#16837748C2214yescomplemented
42#16837709C2214yescomplemented
43#16837702C2214yescomplemented
44#16837702C2214yescomplemented
45#16837697C2214yescomplemented
46#16837692C2212yescomplemented
47#16837682C2212yescomplemented
48#16837682C2214yescomplemented
49#16837614C2214yes—
50#16837614C2214yes—
51#16837614C2214yescomplemented
52#16837604C2212yescomplemented
53#16837594C2214yes—
54#16837594C2214yes—
55#16837594C2212yescomplemented
56#16837533C2212yescomplemented
57#16837533C2212yescomplemented
58Q8×C59⋊C8C2212yescomplemented
59Q8×C59⋊C8C2212yescomplemented
60#16837512C2214yescomplemented
61#16837500C2214yescomplemented
62C4×#11745671C2214yescomplemented
63C4×#11745669C2212yes—
64C4×#11745669C2212yes—
65C4×#11745669C2212yes—
66C4×#11745669C2212yes—
67C4×#11745669C2214yescomplemented
68#16837442C2212yes—
69C2×#14273660C2211yescharacteristic
70#16837429C2212yes—
71#16837426C2211yescharacteristic
72#16837407C2212yes—
73#16837403C2212yes—
74#16837398C2212yes—
75#16837398C2212yes—
76C2×#14273648C2211yescharacteristic
77C2×#14273647C2211yescharacteristic
78#16837358C2212yes—
79C2×C4×C59⋊C8C2211yescharacteristic
80C59×#559C2214yescomplemented
81C59×#556C2212yescomplemented
82C59×#555—21no—
83C59×#553—22no—
84C59×#550C2212yescomplemented
85C59×#547—21no—
86C59×#538—22no—
87C59×#535C2212yes—
88C59×#533C2211yescharacteristic
89C59×#532C2211yescharacteristic
90C59×#525—22no—
91C59×#520C2212yes—
92C2×C4×D4×C59C2211yescharacteristic
93C2×Q8×D59—22no—
94C22×D236C2311yescharacteristic
95C22×C4×D59—21no—
96#14273752—28no—
97C2×#11745671C2314yes—
98C2×#11745669—24no—
99C2×#11745669C2312yes—
100C2×#11745669C2312yes—
101C2×#11745669C2314yes—
102C2×#11745664C2312yes—
103C22×C59⋊C8C2311yescharacteristic
104C22×C59⋊C8C2311yescharacteristic
105#14273727C2311yescharacteristic
106#14273727C2314yes—
107#14273727C2311yescharacteristic
108#14273726—22no—
109#14273719C2312yes—
110#14273719C2314yes—
111#14273718—22no—
112#14273707—22no—
113#14273707—24no—
114#14273706—21no—
115#14273706—21no—
116#14273705—24no—
117#14273705—24no—
118#14273705—24no—
119#14273704—24no—
120#14273703—22no—
121#14273703—24no—
122C4×Dic118—21no—
123C4×Dic118—21no—
124C4×D236—21no—
125C4×D236—21no—
126C4×D236C2312yes—
127C4×D236C2312yes—
128C4×D236C2314yes—
129C4×D236C2314yes—
130#14273689—22no—
131#14273689—22no—
132#14273686C2312yes—
133C2×C4⋊Dic59C2311yescharacteristic
134C4⋊C4×D59—24no—
135C4⋊C4×D59—22no—
136C2×(C2×D59)⋊C4—21no—
137C22⋊C4×D59—24no—
138#14273660C2312yes—
139#14273660C2314yes—
140#14273660C2312yes—
141#14273658C2314yes—
142C4⋊(C59⋊C8)C2312yes—
143C4⋊(C59⋊C8)C2312yes—
144C4⋊(C59⋊C8)C2314yes—
145C4⋊(C59⋊C8)C2314yes—
146#14273651C2312yes—
147#14273651C2312yes—
148#14273651C2312yes—
149#14273651C2312yes—
150#14273651C2314yes—
151#14273648C2312yes—
152#14273648C2312yes—
153#14273648C2312yes—
154#14273648C2312yes—
155#14273648C2312yes—
156#14273648C2312yes—
157#14273648C2314yes—
158#14273648C2314yes—
159#14273648C2314yes—
160#14273647C2312yes—
161#14273647C2312yes—
162#14273638C2314yes—
163C4×C59⋊C8C2311yescharacteristic
164C4×C59⋊C8C2311yescharacteristic
165C4×C59⋊C8C2311yescharacteristic
166C4×C59⋊C8C2311yescharacteristic
167C4×C59⋊C8C2314yes—
168C2×#41×C59—22no—
169C2×#41×C59C2312yes—
170C22×D4×C59C2311yescharacteristic
171C23×C4×C59—21no—
172C4⋊Q8×C59D411yescharacteristic
173C4⋊Q8×C59D411yescharacteristic
174C4⋊Q8×C59C2311yescharacteristic
175#127×C59C2311yescharacteristic
176#127×C59C2314yes—
177#126×C59—24no—
178#125×C59D412yes—
179#124×C59—24no—
180#124×C59C2312yes—
181#124×C59C2314yes—
182#123×C59—24no—
183#123×C59—24no—
184C22⋊Q8×C59—22no—
185C22⋊Q8×C59D412yes—
186C22⋊Q8×C59D412yes—
187#121×C59—21no—
188#121×C59—21no—
189#121×C59—22no—
190#121×C59—22no—
191#121×C59—22no—
192#121×C59—24no—
193#120×C59—24no—
194C4×Q8×C59C2314yes—
195C4×Q8×C59C2312yes—
196C4×Q8×C59C2312yes—
197C4×D4×C59—24no—
198C4×D4×C59—24no—
199C4×D4×C59—21no—
200C4×D4×C59—21no—
201C4×D4×C59—21no—
202C4×D4×C59—21no—
203C4×D4×C59C2312yes—
204C4×D4×C59C2314yes—
205C4×D4×C59C2312yes—
206#117×C59—22no—
207#117×C59—22no—
208#117×C59C2312yes—
209C2×C4⋊C4×C59—22no—
210C2×C4⋊C4×C59C2311yescharacteristic
211C2×C22⋊C4×C59—21no—
212C2×C42×C59C2311yescharacteristic
213C24×C59—21no—
214C23×D59—21no—
215#41×C59—24no—
216#41×C59—24no—
217#41×C59—84no—
218C2×Q8×C59C2×D412yes—
219C2×Q8×C59C2×D412yes—
220C2×Q8×C59C2412yes—
221C2×D4×C59—22no—
222C2×D4×C59—21no—
223C2×D4×C59—21no—
224C2×D4×C59—24no—
225C2×D4×C59—21no—
226C2×D4×C59—24no—
227C2×D4×C59—22no—
228C2×D4×C59—22no—
229C2×D4×C59C2412yes—
230C2×D4×C59C2412yes—
231C22×C4×C59—21no—
232C22×C4×C59—22no—
233C22×C4×C59—22no—
234C22×C4×C59—24no—
235C22×C4×C59—22no—
236C22×C4×C59—82no—
237C22×C4×C59C2×D411yescharacteristic
238C22×C4×C59C2×D411yescharacteristic
239C22×C4×C59C2411yescharacteristic
240C22×Dic59—21no—
241Q8×D59—84no—
242C2×D236—21no—
243C2×D236—22no—
244C2×D236#4114yescomplemented
245C2×D236C2412yes—
246C2×C4×D59—22no—
247C2×C4×D59—24no—
248C2×C4×D59—24no—
249C2×C4×D59—22no—
250C2×C4×D59—82no—
251C2×Dic118—21no—
252C2×Dic118—21no—
253C2×Dic118—24no—
254C4⋊C4×C59—21no—
255C4⋊C4×C59—24no—
256C4⋊C4×C59—21no—
257C4⋊C4×C59—21no—
258C4⋊C4×C59C2×D412yes—
259C4⋊C4×C59C2×D412yes—
260C4⋊C4×C59C2×D412yes—
261C4⋊C4×C59C2×D414yes—
262C4⋊C4×C59C2×D414yes—
263C4⋊C4×C59C2×D412yes—
264C4⋊C4×C59C2412yes—
265C22⋊C4×C59—22no—
266C22⋊C4×C59—22no—
267C22⋊C4×C59—24no—
268C22⋊C4×C59—24no—
269C22⋊C4×C59—22no—
270C22⋊C4×C59—24no—
271C22⋊C4×C59—22no—
272C22⋊C4×C59C2×D414yes—
273C42×C59—24no—
274C42×C59C2×D411yescharacteristic
275C42×C59C2×D411yescharacteristic
276C42×C59C2411yescharacteristic
277C42×C59C2411yescharacteristic
278C42×C59C2414yes—
279C22⋊Dic59—22no—
280#11745671—28no—
281#11745669—24no—
282#11745669—24no—
283#11745669—28no—
284(C2×D59)⋊C4—24no—
285(C2×D59)⋊C4—24no—
286(C2×D59)⋊C4—22no—
287(C2×D59)⋊C4—22no—
288C4⋊Dic59—21no—
289C4⋊Dic59—24no—
290C4⋊Dic59—21no—
291C4⋊Dic59—21no—
292C4⋊Dic59C2412yes—
293C4⋊Dic59C2412yes—
294C4⋊Dic59C2412yes—
295Dic59⋊C4—22no—
296Dic59⋊C4—24no—
297Dic59⋊C4—24no—
298Dic59⋊C4—22no—
299C4×Dic59—22no—
300#11745664—24no—
301C2×C59⋊C8—22no—
302C2×C59⋊C8—22no—
303C2×C59⋊C8C2411yescharacteristic
304C2×C59⋊C8C2411yescharacteristic
305C2×C59⋊C8C2411yescharacteristic
306C2×C59⋊C8C2411yescharacteristic
307C2×C59⋊C8C2414yes—
308C23×C59—22no—
309C23×C59—22no—
310C23×C59—42no—
311C23×C59—81no—
312C23×C59—81no—
313C23×C59C22×D411yescharacteristic
314C22×D59—22no—
315C22×D59—24no—
316C22×D59—81no—
317C22×D59—81no—
318Q8×C59—24no—
319Q8×C59—22no—
320Q8×C59—22no—
321Q8×C59—42no—
322D4×C59—22no—
323D4×C59—22no—
324D4×C59—22no—
325D4×C59—22no—
326D4×C59—44no—
327D4×C59—42no—
328D4×C59—42no—
329D4×C59—81no—
330D4×C59—84no—
331D4×C59—84no—
332C2×C4×C59—22no—
333C2×C4×C59—22no—
334C2×C4×C59—22no—
335C2×C4×C59—41no—
336C2×C4×C59—44no—
337C2×C4×C59—44no—
338C2×C4×C59—82no—
339C2×C4×C59—84no—
340C2×C4×C59—81no—
341C2×C4×C59C22×D411yescharacteristic
342C2×C4×C59C22×D411yescharacteristic
343C2×C4×C59C22×D414yes—
344C2×C4×C59C22×D414yes—
345C2×C4×C59C22×D411yescharacteristic
346C2×C4×C59C22×D411yescharacteristic
347C2×C4×C59C22×D411yescharacteristic
348C2×C4×C59C2×#4112yes—
349C2×C4×C592−1+412yes—
350C2×C4×C59C2511yescharacteristic
351C2×Dic59—22no—
352C2×Dic59—22no—
353C2×Dic59—22no—
354C2×Dic59—81no—
355D236—24no—
356D236—22no—
357D236C2×#4114yes—
358C4×D59—44no—
359C4×D59—84no—
360C4×D59—82no—
361C4×D59—84no—
362Dic118—42no—
363Dic118—81no—
364Dic118—84no—
365C59⋊C8—21no—
366C59⋊C8—21no—
367C59⋊C8—24no—
368C59⋊C8—21no—
369C59⋊C8—21no—
370#61325—591nomaximal, Sylow
371C22×C59—21no—
372C22×C59—21no—
373C22×C59—42no—
374C22×C59—42no—
375C22×C59—42no—
376C22×C59—42no—
377C22×C59—42no—
378C22×C59—42no—
379C22×C59—84no—
380C22×C59#54812yes—
381C22×C59C23×D411yescharacteristic
382C2×D59—24no—
383C2×D59—42no—
384C2×D59—42no—
385C2×D59—84no—
386C4×C59—21no—
387C4×C59—24no—
388C4×C59—21no—
389C4×C59—24no—
390C4×C59—21no—
391C4×C59—42no—
392C4×C59—42no—
393C4×C59#54812yes—
394C4×C59#57612yes—
395C4×C59C22×#4111yescharacteristic
396C4×C59C2×2−1+411yescharacteristic
397Dic59—42no—
398Dic59—42no—
399Dic59—42no—
400#3506D5911yescharacteristic, complemented
401#3501—591no—
402#3370—594no—
403#3367—592no—
404#3366—592no—
405#3361—594no—
406#3360—592no—
407#3358—592no—
408#3136—592no—
409#3131—591no—
410#3083—592no—
411#3077—591no—
412#3041—592no—
413#3036—591no—
414#2960—591no—
415#2946—592no—
416C2×C4×D8—591no—
417C2×C59—22no—
418C2×C59—82no—
419C2×C59—82no—
420C2×C59C2×#54811yescharacteristic
421C2×C59C2×#57611yescharacteristic
422C2×C59#358411yescharacteristic
423D59—44no—
424C2×AGL(1,ℤ/8)—592no—
425C22×D8—591no—
426#559C2×D5914yescomplemented
427#556C2×D5912yescomplemented
428#555—21no—
429#554—592no—
430#554—594no—
431#554—1181no—
432#554—1182no—
433#553—22no—
434#550C2×D5912yescomplemented
435D4×Q8—592no—
436D4×Q8—1181no—
437#547—21no—
438#544—592no—
439#543—1182no—
440#538—22no—
441#535C2×D5912yes—
442#533—591no—
443#533C2×D5911yescharacteristic
444#532C2×D5911yescharacteristic
445#525—22no—
446C2×C22⋊Q8—1182no—
447#520C2×D5912yes—
448#518—592no—
449C2×C4×D4—591no—
450C2×C4×D4C2×D5911yescharacteristic
451#490—594no—
452#489—594no—
453#488—594no—
454#488—592no—
455#488—592no—
456#487—591no—
457#487—591no—
458#486—591no—
459#486—594no—
460#486—591no—
461#479—594no—
462#478—594no—
463#478—594no—
464#477—594no—
465#476—592no—
466#474—592no—
467#474—594no—
468#463—594no—
469#463—594no—
470#463—594no—
471#461—592no—
472#459—592no—
473#459—594no—
474#459—594no—
475#446—592no—
476#446—592no—
477C8×Q8—592no—
478C8×Q8—592no—
479#442—594no—
480#440—594no—
481C4×SD16—594no—
482C4×D8—592no—
483C4×D8—594no—
484C4×D8—592no—
485C4×D8—592no—
486C4×D8—592no—
487#428—592no—
488C2×#107—591no—
489#424—592no—
490#423—591no—
491#418—592no—
492#417—592no—
493#416—592no—
494#416—592no—
495C2×#102—591no—
496C2×#102—591no—
497#405—592no—
498C2×C4×C8—591no—
499C59#6132511yescharacteristic, complemented, Sylow
500C2×#41—22no—
501C2×#41C22×D5912yes—
502C22×Q8—1182no—
503C22×D4—591no—
504C22×D4C22×D5911yescharacteristic
505C23×C4—21no—
506C23×C4—1181no—
507AGL(1,ℤ/8)—1188no—
508C2×SD16—594no—
509C2×D8—592no—
510C2×D8—592no—
511C2×D8—594no—
512C2×D8—1184no—
513C2×M16—592no—
514C22×C8—591no—
515C22×C8—591no—
516C4⋊Q8—591no—
517C4⋊Q8—591no—
518C4⋊Q8—594no—
519C4⋊Q8—1182no—
520C4⋊Q8C22⋊D5911yescharacteristic
521C4⋊Q8C22⋊D5911yescharacteristic
522C4⋊Q8C22×D5911yescharacteristic
523#127C22×D5911yescharacteristic
524#127C22×D5914yes—
525#126—24no—
526#125—592no—
527#125—594no—
528#125—1182no—
529#125C22⋊D5912yes—
530#124—24no—
531#124C22×D5912yes—
532#124C22×D5914yes—
533#123—24no—
534#123—24no—
535C22⋊Q8—22no—
536C22⋊Q8—1182no—
537C22⋊Q8—1184no—
538C22⋊Q8—1181no—
539C22⋊Q8—1181no—
540C22⋊Q8—1182no—
541C22⋊Q8—1184no—
542C22⋊Q8—1184no—
543C22⋊Q8—1184no—
544C22⋊Q8—1184no—
545C22⋊Q8—1184no—
546C22⋊Q8C22⋊D5912yes—
547C22⋊Q8C22⋊D5912yes—
548#121—21no—
549#121—21no—
550#121—22no—
551#121—22no—
552#121—22no—
553#121—24no—
554#120—24no—
555C4×Q8—1181no—
556C4×Q8—1181no—
557C4×Q8C22×D5914yes—
558C4×Q8C22×D5912yes—
559C4×Q8C22×D5912yes—
560C4×D4—24no—
561C4×D4—24no—
562C4×D4—21no—
563C4×D4—21no—
564C4×D4—21no—
565C4×D4—21no—
566C4×D4—592no—
567C4×D4—592no—
568C4×D4—594no—
569C4×D4—594no—
570C4×D4—1182no—
571C4×D4—1182no—
572C4×D4—1181no—
573C4×D4—1181no—
574C4×D4C22×D5912yes—
575C4×D4C22×D5912yes—
576C4×D4C22×D5914yes—
577#117—22no—
578#117—22no—
579#117—592no—
580#117C22×D5912yes—
581C2×C4⋊C4—22no—
582C2×C4⋊C4—591no—
583C2×C4⋊C4—1184no—
584C2×C4⋊C4—1182no—
585C2×C4⋊C4C22×D5911yescharacteristic
586C2×C22⋊C4—21no—
587C2×C22⋊C4—1181no—
588C2×C22⋊C4—1184no—
589C2×C42C22×D5911yescharacteristic
590#107—592no—
591#107—592no—
592#107—594no—
593#106—594no—
594C4⋊C8—592no—
595C4⋊C8—592no—
596C4⋊C8—594no—
597C4⋊C8—594no—
598#103—592no—
599#103—592no—
600#103—592no—
601#103—592no—
602#103—594no—
603#102—592no—
604#102—592no—
605#102—592no—
606#102—592no—
607#102—592no—
608#102—592no—
609#102—594no—
610#102—594no—
611#102—594no—
612#102—592no—
613#102—592no—
614#97—594no—
615C4×C8—591no—
616C4×C8—591no—
617C4×C8—591no—
618C4×C8—591no—
619C4×C8—594no—
620C24—21no—
621C24—1181no—
622#41—24no—
623#41—24no—
624#41—84no—
625C2×Q8—1181no—
626C2×Q8—1184no—
627C2×Q8—1181no—
628C2×Q8—4724no—
629C2×Q8C2×C22⋊D5912yes—
630C2×Q8C2×C22⋊D5912yes—
631C2×Q8C23×D5912yes—
632C2×D4—22no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—24no—
636C2×D4—21no—
637C2×D4—24no—
638C2×D4—22no—
639C2×D4—22no—
640C2×D4—594no—
641C2×D4—592no—
642C2×D4—1181no—
643C2×D4—1182no—
644C2×D4C23×D5912yes—
645C2×D4C23×D5912yes—
646C22×C4—21no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—24no—
650C22×C4—22no—
651C22×C4—82no—
652C22×C4—1181no—
653C22×C4—1184no—
654C22×C4—1184no—
655C22×C4—1182no—
656C22×C4—1182no—
657C22×C4—4722no—
658C22×C4C2×C22⋊D5911yescharacteristic
659C22×C4C2×C22⋊D5911yescharacteristic
660C22×C4C23×D5911yescharacteristic
661SD16—1188no—
662D8—1184no—
663D8—1184no—
664D8—1188no—
665M16—1184no—
666C2×C8—591no—
667C2×C8—591no—
668C2×C8—591no—
669C2×C8—591no—
670C2×C8—594no—
671C2×C8—1182no—
672C2×C8—1182no—
673C4⋊C4—21no—
674C4⋊C4—24no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—592no—
678C4⋊C4—592no—
679C4⋊C4—592no—
680C4⋊C4—1181no—
681C4⋊C4—1182no—
682C4⋊C4—1181no—
683C4⋊C4—1184no—
684C4⋊C4—1184no—
685C4⋊C4—1184no—
686C4⋊C4—1182no—
687C4⋊C4—1181no—
688C4⋊C4C2×C22⋊D5912yes—
689C4⋊C4C2×C22⋊D5912yes—
690C4⋊C4C2×C22⋊D5914yes—
691C4⋊C4C2×C22⋊D5912yes—
692C4⋊C4C2×C22⋊D5914yes—
693C4⋊C4C2×C22⋊D5912yes—
694C4⋊C4C23×D5912yes—
695C22⋊C4—22no—
696C22⋊C4—22no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—22no—
700C22⋊C4—24no—
701C22⋊C4—22no—
702C22⋊C4—1182no—
703C22⋊C4—1184no—
704C22⋊C4—1184no—
705C22⋊C4—1182no—
706C22⋊C4—1182no—
707C22⋊C4C2×C22⋊D5914yes—
708C42—24no—
709C42—1182no—
710C42C2×C22⋊D5911yescharacteristic
711C42C2×C22⋊D5911yescharacteristic
712C42C23×D5911yescharacteristic
713C42C23×D5911yescharacteristic
714C42C23×D5914yes—
715C23—22no—
716C23—22no—
717C23—42no—
718C23—81no—
719C23—81no—
720C23—1184no—
721C23—1182no—
722C23—4721no—
723C23—4721no—
724C23C22×C22⋊D5911yescharacteristic
725Q8—24no—
726Q8—22no—
727Q8—22no—
728Q8—42no—
729Q8—4721no—
730Q8—4724no—
731Q8—2362no—
732D4—22no—
733D4—22no—
734D4—22no—
735D4—22no—
736D4—44no—
737D4—42no—
738D4—42no—
739D4—81no—
740D4—84no—
741D4—84no—
742D4—594no—
743D4—1182no—
744D4—1184no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—41no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—82no—
752C2×C4—84no—
753C2×C4—81no—
754C2×C4—1182no—
755C2×C4—1182no—
756C2×C4—1182no—
757C2×C4—4724no—
758C2×C4—4722no—
759C2×C4—4724no—
760C2×C4—4721no—
761C2×C4—2364no—
762C2×C4C22×C22⋊D5914yes—
763C2×C4C22×C22⋊D5911yescharacteristic
764C2×C4C22×C22⋊D5911yescharacteristic
765C2×C4C22×C22⋊D5911yescharacteristic
766C2×C4C22×C22⋊D5914yes—
767C2×C4C22×C22⋊D5911yescharacteristic
768C2×C4C22×C22⋊D5911yescharacteristic
769C2×C4#41×D5912yes—
770C2×C4#1427377412yes—
771C2×C4C24×D5911yescharacteristic
772C8—1181no—
773C8—1181no—
774C8—1184no—
775C8—1181no—
776C8—1181no—
777C22—21no—
778C22—21no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—84no—
786C22—1184no—
787C22—4724no—
788C22—2362no—
789C22—2362no—
790C22#1683805912yes—
791C22C23×C22⋊D5911yescharacteristic
792C4—21no—
793C4—24no—
794C4—21no—
795C4—21no—
796C4—24no—
797C4—42no—
798C4—42no—
799C4—2362no—
800C4—2362no—
801C4—2362no—
802C4#1683805912yes—
803C4#1683820512yes—
804C4C2×#41×D5911yescharacteristic
805C4C2×#1427377411yescharacteristic
806C2—22no—
807C2—82no—
808C2—82no—
809C2—2364no—
810C2C2×#1683805911yescharacteristic
811C2C2×#1683820511yescharacteristic
812C2#2143886711yescharacteristic
subgroupG/H
centerC22C23×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC59×#3506C2
socleC22×C59C23×D4
hypercenter#3506D59
hypocenterC59#61325
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ #533 ◁ #3506

Complements

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

NH ≅ G/Ntype
1. #21437897C2semidirect
2. #21436843C2semidirect
3. #21436810C2semidirect
4. #21436799C2semidirect
5. #21436752C2semidirect
6. #21436741C2semidirect
7. #21436727C2semidirect
8. #21434450C2semidirect
9. #21434418C2semidirect
10. #21433947C2semidirect
11. #21433893C2semidirect
12. #21433595C2semidirect
13. #21433556C2semidirect
14. #21433031C2semidirect
15. #21432924C2semidirect
16. C2×C4×#11745669C2semidirect
17. C59×#3506C2semidirect
21. #16838112C22semidirect
22. #16838112C22semidirect
24. Q8×D236C22semidirect
32. #16837766C22semidirect
33. #16837761C22semidirect
34. #16837756C22semidirect
35. #16837756C22semidirect
36. #16837756C22semidirect
37. #16837752C22semidirect
38. #16837752C22semidirect
39. #16837748C22semidirect
40. #16837748C22semidirect
41. #16837748C22semidirect
42. #16837709C22semidirect
43. #16837702C22semidirect
44. #16837702C22semidirect
45. #16837697C22semidirect
46. #16837692C22semidirect
47. #16837682C22semidirect
48. #16837682C22semidirect
51. #16837614C22semidirect
52. #16837604C22semidirect
55. #16837594C22semidirect
56. #16837533C22semidirect
57. #16837533C22semidirect
58. Q8×C59⋊C8C22semidirect
59. Q8×C59⋊C8C22semidirect
60. #16837512C22semidirect
61. #16837500C22semidirect
62. C4×#11745671C22semidirect
67. C4×#11745669C22semidirect
80. C59×#559C22semidirect
81. C59×#556C22semidirect
84. C59×#550C22semidirect
244. C2×D236#41semidirect
400. #3506D59semidirect
426. #559C2×D59semidirect
427. #556C2×D59semidirect
434. #550C2×D59semidirect
499. C59#61325semidirect

Maximal subgroups

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

subgroupindex
#214378972
#214368432
#214368102
#214367992
#214367522
#214367412
#214367272
#214344502
#214344182
#214339472
#214338932
#214335952
#214335562
#214330312
#214329242
C2×C4×#117456692
C59×#35062
#6132559