Finite Group Databasebeta

← #29473713

Subgroups — #29473713

Order 15104.

2258 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21437935C211yesmaximal, characteristic, complemented
2#21436312C214yesmaximal, complemented
3#21436297C214yesmaximal, complemented
4#21435723C214yesmaximal, complemented
5#21435703C214yesmaximal, complemented
6#21435061C212yesmaximal, complemented
7#21434926C212yesmaximal, complemented
8#21434902C211yesmaximal, characteristic, complemented
9#21434893C211yesmaximal, characteristic, complemented
10#21434143C212yesmaximal, complemented
11#21433356C211yesmaximal, characteristic, complemented
12#21433348C211yesmaximal, characteristic, complemented
13#21433323C212yesmaximal, complemented
14#21433137C211yesmaximal, characteristic, complemented
15C2×C59×#546C211yesmaximal, characteristic, complemented
16C2×#14273757C2212yescomplemented
17C2×#14273753C2214yescomplemented
18C2×#14273752C2212yescomplemented
19#16838101—22no—
20#16838098C2212yescomplemented
21#16838092C2212yescomplemented
22#16838081—22no—
23#16838061C2212yescomplemented
24#16838048C2212yescomplemented
25#16837999—21no—
26#16837990—21no—
27#16837961—21no—
28#16837936C2212yescomplemented
29#16837913C2212yes—
30C2×#14273706C2211yescharacteristic, complemented
31C2×#14273701C2211yescharacteristic, complemented
32#16837875—21no—
33#16837784C2214yescomplemented
34#16837756C2214yescomplemented
35#16837740C2214yescomplemented
36#16837737C2212yescomplemented
37#16837720C2212yescomplemented
38#16837718C2212yescomplemented
39#16837713C2212yescomplemented
40#16837702C2214yescomplemented
41#16837658C2214yescomplemented
42#16837653C2214yescomplemented
43#16837650C2214yescomplemented
44#16837646C2214yescomplemented
45#16837621C2214yescomplemented
46#16837617C2214yescomplemented
47#16837614C2214yescomplemented
48#16837564C2214yescomplemented
49#16837562C2214yescomplemented
50#16837558C2212yescomplemented
51#16837553C2212yescomplemented
52#16837553C2212yescomplemented
53#16837553C2214yescomplemented
54#16837547C2214yescomplemented
55#16837541C2212yescomplemented
56#16837540C2212yescomplemented
57#16837536C2212yes—
58#16837536C2212yes—
59#16837536C2214yescomplemented
60#16837535C2212yescomplemented
61C4×#11745670C2214yescomplemented
62C4×#11745669C2214yescomplemented
63#16837480C2214yescomplemented
64#16837480C2214yescomplemented
65#16837455C2212yescomplemented
66#16837407C2214yescomplemented
67#16837403C2212yescomplemented
68#16837403C2212yescomplemented
69#16837366C2212yescomplemented
70#16837366C2211yescharacteristic, complemented
71#16837366C2211yescharacteristic, complemented
72C22×#41×C59C2211yescharacteristic
73C23×D4×C59C2211yescharacteristic, complemented
74C59×#546—22no—
75C59×#546—22no—
76C59×#546C2214yes—
77C59×#546C2214yescomplemented
78C2×#124×C59C2211yescharacteristic, complemented
79C2×#123×C59—21no—
80C2×C22⋊Q8×C59C2211yescharacteristic, complemented
81C2×#121×C59—21no—
82C2×#121×C59C2211yescharacteristic
83C2×#120×C59—21no—
84C2×C4×D4×C59C2211yescharacteristic
85C2×C4×D4×C59C2211yescharacteristic, complemented
86C22×C22⋊C4×C59—21no—
87C2×#11745685C2312yes—
88C22×Dic118C2311yescharacteristic, complemented
89C22×D236C2311yescharacteristic, complemented
90C22×C22⋊D59—21no—
91#14273757—44no—
92#14273753—48no—
93#14273752—44no—
94C2×#11745672C2314yescomplemented
95C2×#11745670C2314yes—
96C2×#11745670C2314yes—
97C2×#11745671C2314yescomplemented
98C2×#11745669C2314yes—
99C2×#11745669C2314yes—
100C2×#11745664C2314yes—
101C2×#11745664C2312yescomplemented
102C2×#11745664C2312yescomplemented
103#14273722—22no—
104#14273721—22no—
105#14273720—22no—
106#14273719C2312yescomplemented
107#14273717—22no—
108#14273715C2312yescomplemented
109#14273713—22no—
110#14273712—22no—
111#14273710—22no—
112#14273710—22no—
113#14273709—22no—
114#14273708—22no—
115#14273706—21no—
116#14273706—21no—
117#14273706C2312yes—
118#14273706C2312yes—
119#14273706C2312yescomplemented
120#14273705—22no—
121#14273701—21no—
122#14273701—21no—
123#14273701C2312yes—
124#14273701C2312yes—
125#14273701C2312yescomplemented
126#14273700—22no—
127#14273699—22no—
128#14273699—22no—
129#14273696—22no—
130#14273695—22no—
131C4×Dic118C2312yescomplemented
132C4×D236C2312yescomplemented
133C4×C22⋊D59—22no—
134C4×C22⋊D59—22no—
135C4×C22⋊D59—22no—
136(C22⋊D59)⋊C4—22no—
137(C22⋊D59)⋊C4—22no—
138#14273686C2312yes—
139#14273684—22no—
140#14273683—22no—
141C2×C4⋊Dic59C2311yescharacteristic, complemented
142C2×C4⋊Dic59C2311yescharacteristic, complemented
143C2×Dic59⋊C4—21no—
144C2×C22⋊Dic59—21no—
145C2×(C2×D59)⋊C4—21no—
146C22⋊C4×D59—22no—
147#14273660C2314yescomplemented
148#14273658C2314yescomplemented
149C4⋊(C59⋊C8)C2314yescomplemented
150#14273651C2314yescomplemented
151#14273651C2314yescomplemented
152#14273650C2314yescomplemented
153#14273648C2314yes—
154#14273648C2314yes—
155#14273648C2314yes—
156#14273648C2314yes—
157#14273647C2314yescomplemented
158C22⋊(C59⋊C8)C2312yes—
159C22⋊(C59⋊C8)C2312yes—
160C22⋊(C59⋊C8)C2314yes—
161C22⋊(C59⋊C8)C2312yescomplemented
162C22⋊(C59⋊C8)C2312yescomplemented
163C4×C59⋊C8C2314yescomplemented
164C25×C59—21no—
165C2×#41×C59—21no—
166C2×#41×C59—21no—
167C2×#41×C59—44no—
168C2×#41×C59C2312yes—
169C2×#41×C59C2312yes—
170C22×Q8×C59C2311yescharacteristic
171C22×D4×C59—21no—
172C22×D4×C59—21no—
173C22×D4×C59—21no—
174C22×D4×C59—22no—
175C22×D4×C59—44no—
176C22×D4×C59D411yescharacteristic
177C22×D4×C59C2311yescharacteristic
178C22×D4×C59C2314yes—
179C22×D4×C59C2311yescharacteristic
180C23×C4×C59—21no—
181C23×C4×C59—21no—
182C23×C4×C59C2311yescharacteristic
183C23×C4×C59C2311yescharacteristic
184#124×C59—22no—
185#124×C59C2314yes—
186#123×C59—24no—
187#123×C59—24no—
188C22⋊Q8×C59—22no—
189C22⋊Q8×C59C2314yes—
190#121×C59—21no—
191#121×C59—21no—
192#121×C59—24no—
193#121×C59—24no—
194#121×C59C2312yes—
195#121×C59C2312yes—
196#120×C59—24no—
197#120×C59—24no—
198C4×D4×C59—22no—
199C4×D4×C59D412yes—
200C4×D4×C59D412yes—
201C4×D4×C59C2314yes—
202C4×D4×C59C2312yes—
203C4×D4×C59C2312yes—
204C2×C4⋊C4×C59—21no—
205C2×C4⋊C4×C59D411yescharacteristic
206C2×C4⋊C4×C59C2311yescharacteristic
207C2×C22⋊C4×C59—21no—
208C2×C22⋊C4×C59—21no—
209C2×C22⋊C4×C59—21no—
210C2×C22⋊C4×C59—21no—
211C2×C22⋊C4×C59—21no—
212C2×C22⋊C4×C59—24no—
213C2×C22⋊C4×C59—24no—
214C2×C22⋊C4×C59D411yescharacteristic
215C2×C22⋊C4×C59D411yescharacteristic
216C2×C42×C59C2311yescharacteristic
217C24×C59—21no—
218C24×C59—21no—
219C24×C59—24no—
220C24×C59—44no—
221C24×C59—44no—
222C24×C59—82no—
223C24×C59C2×D411yescharacteristic
224C24×C59C2×D411yescharacteristic
225C23×D59—21no—
226#41×C59—24no—
227#41×C59—24no—
228#41×C59—42no—
229#41×C59—42no—
230#41×C59—44no—
231#41×C59—44no—
232C2×Q8×C59—21no—
233C2×Q8×C59—42no—
234C2×Q8×C59C2412yes—
235C2×D4×C59—24no—
236C2×D4×C59—28no—
237C2×D4×C59—22no—
238C2×D4×C59—22no—
239C2×D4×C59—22no—
240C2×D4×C59—22no—
241C2×D4×C59—21no—
242C2×D4×C59—24no—
243C2×D4×C59—21no—
244C2×D4×C59—44no—
245C2×D4×C59—42no—
246C2×D4×C59—42no—
247C2×D4×C59—48no—
248C2×D4×C59—44no—
249C2×D4×C59—44no—
250C2×D4×C59—82no—
251C2×D4×C59C2×D412yes—
252C2×D4×C59C2×D412yes—
253C2×D4×C59C2412yes—
254C2×D4×C59C2412yes—
255C22×C4×C59—21no—
256C22×C4×C59—21no—
257C22×C4×C59—22no—
258C22×C4×C59—22no—
259C22×C4×C59—24no—
260C22×C4×C59—42no—
261C22×C4×C59—42no—
262C22×C4×C59—44no—
263C22×C4×C59—82no—
264C22×C4×C59C2×D411yescharacteristic
265C22×C4×C59C2×D411yescharacteristic
266C22×C4×C59C2×D411yescharacteristic
267C22×C4×C59C2×D411yescharacteristic
268C22×C4×C59C2×D411yescharacteristic
269C22×C4×C59C2×D411yescharacteristic
270C22×C4×C59C2×D412yes—
271C22×C4×C59C2411yescharacteristic
272C22×C4×C59C2411yescharacteristic
273C22×C4×C59C2411yescharacteristic
274C22×C4×C59C2412yes—
275C2×C22⋊D59—22no—
276C2×C22⋊D59—22no—
277C2×C22⋊D59—22no—
278C2×C22⋊D59—22no—
279C2×C22⋊D59—44no—
280C22×Dic59—21no—
281C22×Dic59—21no—
282C22×Dic59—21no—
283#11745685—44no—
284C2×D236—21no—
285C2×D236—42no—
286C2×D236C2412yes—
287C2×C4×D59—22no—
288C2×C4×D59—22no—
289C2×Dic118—21no—
290C2×Dic118—42no—
291C2×Dic118C2412yes—
292C4⋊C4×C59—24no—
293C4⋊C4×C59—21no—
294C4⋊C4×C59C2×D412yes—
295C4⋊C4×C59C2×D412yes—
296C4⋊C4×C59C2412yes—
297C22⋊C4×C59—24no—
298C22⋊C4×C59—24no—
299C22⋊C4×C59—22no—
300C22⋊C4×C59—22no—
301C22⋊C4×C59—24no—
302C22⋊C4×C59—24no—
303C22⋊C4×C59C2×D412yes—
304C22⋊C4×C59C2×D412yes—
305C22⋊C4×C59C2×D412yes—
306C22⋊C4×C59C2×D412yes—
307C42×C59C2×D412yes—
308C42×C59C2412yes—
309C22⋊Dic59—22no—
310C22⋊Dic59—22no—
311C22⋊Dic59—22no—
312C22⋊Dic59—22no—
313#11745672—44no—
314#11745671—44no—
315#11745670—28no—
316#11745670—44no—
317#11745669—28no—
318#11745669—44no—
319(C2×D59)⋊C4—22no—
320(C2×D59)⋊C4—22no—
321(C2×D59)⋊C4—22no—
322(C2×D59)⋊C4—22no—
323(C2×D59)⋊C4—22no—
324(C2×D59)⋊C4—22no—
325C4⋊Dic59—21no—
326C4⋊Dic59—21no—
327C4⋊Dic59C2412yes—
328C4⋊Dic59C2412yes—
329Dic59⋊C4—22no—
330Dic59⋊C4—22no—
331Dic59⋊C4—22no—
332Dic59⋊C4—22no—
333Dic59⋊C4—22no—
334Dic59⋊C4—22no—
335C4×Dic59—22no—
336C4×Dic59—22no—
337#11745664—44no—
338#11745664—42no—
339#11745664—42no—
340C2×C59⋊C8C2414yes—
341C2×C59⋊C8C2414yes—
342C23×C59—24no—
343C23×C59—22no—
344C23×C59—22no—
345C23×C59—22no—
346C23×C59—22no—
347C23×C59—41no—
348C23×C59—41no—
349C23×C59—41no—
350C23×C59—41no—
351C23×C59—48no—
352C23×C59—42no—
353C23×C59—42no—
354C23×C59—42no—
355C23×C59—48no—
356C23×C59—42no—
357C23×C59—42no—
358C23×C59—84no—
359C23×C59—816no—
360C23×C59C22×D412yes—
361C23×C59C22×D411yescharacteristic
362C23×C59C22×D411yescharacteristic
363C23×C59C22×D411yescharacteristic
364C22×D59—22no—
365C22×D59—42no—
366C22×D59—81no—
367C22×D59—81no—
368Q8×C59—22no—
369Q8×C59—22no—
370Q8×C59—42no—
371D4×C59—24no—
372D4×C59—22no—
373D4×C59—24no—
374D4×C59—42no—
375D4×C59—42no—
376D4×C59—48no—
377D4×C59—42no—
378D4×C59—44no—
379D4×C59—44no—
380D4×C59—82no—
381D4×C59—82no—
382D4×C59H(5,𝔽2)14yes—
383C2×C4×C59—22no—
384C2×C4×C59—22no—
385C2×C4×C59—22no—
386C2×C4×C59—24no—
387C2×C4×C59—22no—
388C2×C4×C59—22no—
389C2×C4×C59—22no—
390C2×C4×C59—41no—
391C2×C4×C59—41no—
392C2×C4×C59—42no—
393C2×C4×C59—41no—
394C2×C4×C59—41no—
395C2×C4×C59—41no—
396C2×C4×C59—44no—
397C2×C4×C59—44no—
398C2×C4×C59—42no—
399C2×C4×C59—42no—
400C2×C4×C59—84no—
401C2×C4×C59C22×D412yes—
402C2×C4×C59C22×D412yes—
403C2×C4×C59C22×D411yescharacteristic
404C2×C4×C59C22×D411yescharacteristic
405C2×C4×C59C22×D412yes—
406C2×C4×C59C22×D411yescharacteristic
407C2×C4×C59C2511yescharacteristic
408C22⋊D59—44no—
409C22⋊D59—44no—
410C22⋊D59—82no—
411C22⋊D59—82no—
412C2×Dic59—22no—
413C2×Dic59—22no—
414C2×Dic59—22no—
415C2×Dic59—42no—
416C2×Dic59—81no—
417C2×Dic59—81no—
418D236—24no—
419D236—81no—
420C4×D59—82no—
421C4×D59—82no—
422Dic118—24no—
423Dic118—81no—
424C59⋊C8—24no—
425C59⋊C8—24no—
426#61581—591nomaximal, Sylow
427C22×C59—21no—
428C22×C59—21no—
429C22×C59—21no—
430C22×C59—22no—
431C22×C59—21no—
432C22×C59—21no—
433C22×C59—22no—
434C22×C59—21no—
435C22×C59—24no—
436C22×C59—21no—
437C22×C59—21no—
438C22×C59—22no—
439C22×C59—48no—
440C22×C59—44no—
441C22×C59—42no—
442C22×C59—42no—
443C22×C59—42no—
444C22×C59—42no—
445C22×C59—42no—
446C22×C59—82no—
447C22×C59—84no—
448C22×C59—816no—
449C22×C59#57512yes—
450C22×C59C23×D411yescharacteristic
451C2×D59—42no—
452C2×D59—42no—
453C2×D59—42no—
454C2×D59—162no—
455C4×C59—22no—
456C4×C59—21no—
457C4×C59—22no—
458C4×C59—21no—
459C4×C59—21no—
460C4×C59—22no—
461C4×C59—42no—
462C4×C59—42no—
463C4×C59C2×H(5,𝔽2)12yes—
464Dic59—42no—
465Dic59—42no—
466Dic59—42no—
467#3505—591no—
468C2×#546D5911yescharacteristic, complemented
469#3323—594no—
470#3322—594no—
471#3275—594no—
472#3273—594no—
473#3211—592no—
474#3196—592no—
475#3193—591no—
476#3192—591no—
477#3105—592no—
478#3007—591no—
479#3006—591no—
480#3003—592no—
481#2975—591no—
482C2×C59—22no—
483C2×C59—41no—
484C2×C59—42no—
485C2×C59—41no—
486C2×C59—44no—
487C2×C59—82no—
488C2×C59#348411yescharacteristic
489C2×C59C2×#57511yescharacteristic
490C2×C59#358511yescharacteristic
491D59—82no—
492C22×#41C2×D5911yescharacteristic
493C23×D4C2×D5911yescharacteristic, complemented
494C2×#137—592no—
495C2×AGL(1,ℤ/8)—592no—
496C2×AGL(1,ℤ/8)—594no—
497#553—592no—
498#553—1182no—
499#552—592no—
500#551—1182no—
501#548—592no—
502#546—22no—
503#546—22no—
504#546—592no—
505#546C2×D5914yes—
506#546C2×D5914yescomplemented
507#539—1181no—
508#538—1181no—
509#534—1181no—
510#529—592no—
511C2×#124C2×D5911yescharacteristic, complemented
512#525—592no—
513C2×#123—21no—
514C2×C22⋊Q8—591no—
515C2×C22⋊Q8C2×D5911yescharacteristic, complemented
516C2×#121—21no—
517C2×#121—591no—
518C2×#121C2×D5911yescharacteristic
519C2×#120—21no—
520#518—1181no—
521C2×C4×D4C2×D5911yescharacteristic
522C2×C4×D4C2×D5911yescharacteristic, complemented
523C22×C22⋊C4—21no—
524#495—594no—
525#488—594no—
526#485—594no—
527#484—592no—
528#481—592no—
529#481—592no—
530#480—592no—
531#478—594no—
532#470—594no—
533#469—594no—
534#468—594no—
535#468—594no—
536#464—594no—
537#463—594no—
538#463—594no—
539#452—594no—
540#452—594no—
541#451—592no—
542#450—592no—
543#450—592no—
544#450—594no—
545#449—594no—
546#448—592no—
547#448—592no—
548#447—592no—
549#447—592no—
550#447—594no—
551#447—592no—
552C4×SD16—594no—
553C4×D8—594no—
554#436—594no—
555#436—594no—
556#431—592no—
557#418—594no—
558#417—592no—
559#417—592no—
560#407—591no—
561#407—591no—
562#407—592no—
563C59#6158111yescharacteristic, complemented, Sylow
564C25—21no—
565C2×#41—21no—
566C2×#41—21no—
567C2×#41—44no—
568C2×#41—592no—
569C2×#41C22×D5912yes—
570C2×#41C22×D5912yes—
571C22×Q8—591no—
572C22×Q8C22×D5911yescharacteristic
573C22×D4—21no—
574C22×D4—21no—
575C22×D4—21no—
576C22×D4—22no—
577C22×D4—44no—
578C22×D4—591no—
579C22×D4—1181no—
580C22×D4C22⋊D5911yescharacteristic
581C22×D4C22×D5911yescharacteristic
582C22×D4C22×D5914yes—
583C22×D4C22×D5911yescharacteristic
584C23×C4—21no—
585C23×C4—21no—
586C23×C4C22×D5911yescharacteristic
587C23×C4C22×D5911yescharacteristic
588#137—2364no—
589AGL(1,ℤ/8)—2364no—
590AGL(1,ℤ/8)—2368no—
591C2×Q16—594no—
592C2×SD16—594no—
593C2×SD16—594no—
594C2×SD16—594no—
595C2×D8—594no—
596C2×D8—594no—
597C2×M16—592no—
598C2×M16—594no—
599C2×M16—592no—
600#126—1182no—
601#126—1182no—
602#126—1182no—
603#125—592no—
604#125—1182no—
605#124—22no—
606#124—592no—
607#124—1182no—
608#124C22×D5914yes—
609#123—24no—
610#123—24no—
611#123—1182no—
612#123—1182no—
613#123—1182no—
614#123—1182no—
615#123—1182no—
616C22⋊Q8—22no—
617C22⋊Q8—592no—
618C22⋊Q8—592no—
619C22⋊Q8—592no—
620C22⋊Q8—1181no—
621C22⋊Q8—1181no—
622C22⋊Q8—1182no—
623C22⋊Q8C22×D5914yes—
624#121—21no—
625#121—21no—
626#121—24no—
627#121—24no—
628#121—592no—
629#121—592no—
630#121—592no—
631#121—1182no—
632#121—1182no—
633#121—1181no—
634#121—1181no—
635#121—1182no—
636#121C22×D5912yes—
637#121C22×D5912yes—
638#120—24no—
639#120—24no—
640#120—1182no—
641#120—1182no—
642C4×Q8—592no—
643C4×D4—22no—
644C4×D4—592no—
645C4×D4—1182no—
646C4×D4—1182no—
647C4×D4—1182no—
648C4×D4—1182no—
649C4×D4—1182no—
650C4×D4C22⋊D5912yes—
651C4×D4C22⋊D5912yes—
652C4×D4C22×D5914yes—
653C4×D4C22×D5912yes—
654C4×D4C22×D5912yes—
655#117—592no—
656#117—1182no—
657#117—1182no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—591no—
660C2×C4⋊C4—591no—
661C2×C4⋊C4—1181no—
662C2×C4⋊C4C22⋊D5911yescharacteristic
663C2×C4⋊C4C22×D5911yescharacteristic
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—24no—
670C2×C22⋊C4—24no—
671C2×C22⋊C4—1181no—
672C2×C22⋊C4—1181no—
673C2×C22⋊C4—1182no—
674C2×C22⋊C4C22⋊D5911yescharacteristic
675C2×C22⋊C4C22⋊D5911yescharacteristic
676C2×C42C22×D5911yescharacteristic
677#107—594no—
678#106—594no—
679C4⋊C8—594no—
680#103—594no—
681#103—594no—
682#103—594no—
683#102—594no—
684#102—594no—
685#102—594no—
686#102—594no—
687#102—594no—
688C22⋊C8—592no—
689C22⋊C8—592no—
690C22⋊C8—594no—
691C22⋊C8—592no—
692C22⋊C8—592no—
693C4×C8—594no—
694C24—21no—
695C24—21no—
696C24—24no—
697C24—44no—
698C24—44no—
699C24—82no—
700C24—1181no—
701C24C2×C22⋊D5911yescharacteristic
702C24C2×C22⋊D5911yescharacteristic
703#41—24no—
704#41—24no—
705#41—42no—
706#41—42no—
707#41—44no—
708#41—44no—
709#41—2364no—
710C2×Q8—21no—
711C2×Q8—42no—
712C2×Q8—592no—
713C2×Q8—1181no—
714C2×Q8—2362no—
715C2×Q8C23×D5912yes—
716C2×D4—24no—
717C2×D4—28no—
718C2×D4—22no—
719C2×D4—22no—
720C2×D4—22no—
721C2×D4—22no—
722C2×D4—21no—
723C2×D4—24no—
724C2×D4—21no—
725C2×D4—44no—
726C2×D4—42no—
727C2×D4—42no—
728C2×D4—48no—
729C2×D4—44no—
730C2×D4—44no—
731C2×D4—82no—
732C2×D4—592no—
733C2×D4—1182no—
734C2×D4—1182no—
735C2×D4—1182no—
736C2×D4—1182no—
737C2×D4—1181no—
738C2×D4—2362no—
739C2×D4—2364no—
740C2×D4C2×C22⋊D5912yes—
741C2×D4C2×C22⋊D5912yes—
742C2×D4C23×D5912yes—
743C2×D4C23×D5912yes—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—24no—
749C22×C4—42no—
750C22×C4—42no—
751C22×C4—44no—
752C22×C4—82no—
753C22×C4—1181no—
754C22×C4—1181no—
755C22×C4—1181no—
756C22×C4—1182no—
757C22×C4—1182no—
758C22×C4C2×C22⋊D5911yescharacteristic
759C22×C4C2×C22⋊D5911yescharacteristic
760C22×C4C2×C22⋊D5911yescharacteristic
761C22×C4C2×C22⋊D5911yescharacteristic
762C22×C4C2×C22⋊D5911yescharacteristic
763C22×C4C2×C22⋊D5911yescharacteristic
764C22×C4C2×C22⋊D5912yes—
765C22×C4C23×D5911yescharacteristic
766C22×C4C23×D5911yescharacteristic
767C22×C4C23×D5911yescharacteristic
768C22×C4C23×D5912yes—
769Q16—2364no—
770SD16—1188no—
771SD16—2364no—
772SD16—2364no—
773D8—1188no—
774D8—2364no—
775M16—2362no—
776M16—2364no—
777M16—2362no—
778C2×C8—594no—
779C2×C8—594no—
780C4⋊C4—24no—
781C4⋊C4—21no—
782C4⋊C4—592no—
783C4⋊C4—592no—
784C4⋊C4—1181no—
785C4⋊C4—1181no—
786C4⋊C4—1182no—
787C4⋊C4—1182no—
788C4⋊C4—1182no—
789C4⋊C4—1182no—
790C4⋊C4—1182no—
791C4⋊C4—1182no—
792C4⋊C4C2×C22⋊D5912yes—
793C4⋊C4C2×C22⋊D5912yes—
794C4⋊C4C23×D5912yes—
795C22⋊C4—24no—
796C22⋊C4—24no—
797C22⋊C4—22no—
798C22⋊C4—22no—
799C22⋊C4—24no—
800C22⋊C4—24no—
801C22⋊C4—1182no—
802C22⋊C4—1182no—
803C22⋊C4—1182no—
804C22⋊C4—1182no—
805C22⋊C4—1182no—
806C22⋊C4—1182no—
807C22⋊C4—1182no—
808C22⋊C4—1182no—
809C22⋊C4—1182no—
810C22⋊C4—1182no—
811C22⋊C4C2×C22⋊D5912yes—
812C22⋊C4C2×C22⋊D5912yes—
813C22⋊C4C2×C22⋊D5912yes—
814C22⋊C4C2×C22⋊D5912yes—
815C42—1182no—
816C42—1182no—
817C42C2×C22⋊D5912yes—
818C42C23×D5912yes—
819C23—24no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—48no—
829C23—42no—
830C23—42no—
831C23—42no—
832C23—48no—
833C23—42no—
834C23—42no—
835C23—84no—
836C23—816no—
837C23—1182no—
838C23—4721no—
839C23—4721no—
840C23—2362no—
841C23C22×C22⋊D5912yes—
842C23C22×C22⋊D5911yescharacteristic
843C23C22×C22⋊D5911yescharacteristic
844C23C22×C22⋊D5911yescharacteristic
845Q8—22no—
846Q8—22no—
847Q8—42no—
848Q8—1184no—
849Q8—4721no—
850D4—24no—
851D4—22no—
852D4—24no—
853D4—42no—
854D4—42no—
855D4—48no—
856D4—42no—
857D4—44no—
858D4—44no—
859D4—82no—
860D4—82no—
861D4—1184no—
862D4—4721no—
863D4—4722no—
864D4—4722no—
865D4—2364no—
866D4—2364no—
867D4#1427377214yes—
868C2×C4—22no—
869C2×C4—24no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—41no—
876C2×C4—42no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—44no—
882C2×C4—44no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—84no—
886C2×C4—1182no—
887C2×C4—1182no—
888C2×C4—1182no—
889C2×C4—4722no—
890C2×C4—4722no—
891C2×C4—4721no—
892C2×C4—4721no—
893C2×C4—2362no—
894C2×C4C22×C22⋊D5912yes—
895C2×C4C22×C22⋊D5912yes—
896C2×C4C22×C22⋊D5911yescharacteristic
897C2×C4C22×C22⋊D5912yes—
898C2×C4C22×C22⋊D5911yescharacteristic
899C2×C4C22×C22⋊D5911yescharacteristic
900C2×C4C24×D5911yescharacteristic
901C8—1184no—
902C8—1184no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—21no—
907C22—22no—
908C22—24no—
909C22—21no—
910C22—21no—
911C22—22no—
912C22—21no—
913C22—21no—
914C22—22no—
915C22—44no—
916C22—48no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—82no—
923C22—84no—
924C22—816no—
925C22—9442no—
926C22—2362no—
927C22—2362no—
928C22—2362no—
929C22#1683820012yes—
930C22C23×C22⋊D5911yescharacteristic
931C4—21no—
932C4—21no—
933C4—21no—
934C4—22no—
935C4—22no—
936C4—22no—
937C4—42no—
938C4—42no—
939C4—2362no—
940C4—2362no—
941C4—2362no—
942C4C2×#1427377212yes—
943C2—22no—
944C2—42no—
945C2—41no—
946C2—41no—
947C2—44no—
948C2—82no—
949C2—4722no—
950C2#2143773111yescharacteristic
951C2C2×#1683820011yescharacteristic
952C2#2143887611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#546C2
socleC22×C59C23×D4
hypercenterC2×#546D59
hypocenterC59#61581
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. #21437935C2semidirect
2. #21436312C2semidirect
3. #21436297C2semidirect
4. #21435723C2semidirect
5. #21435703C2semidirect
6. #21435061C2semidirect
7. #21434926C2semidirect
8. #21434902C2semidirect
9. #21434893C2semidirect
10. #21434143C2semidirect
11. #21433356C2semidirect
12. #21433348C2semidirect
13. #21433323C2semidirect
14. #21433137C2semidirect
15. C2×C59×#546C2semidirect
16. C2×#14273757C22semidirect
17. C2×#14273753C22semidirect
18. C2×#14273752C22semidirect
20. #16838098C22semidirect
21. #16838092C22semidirect
23. #16838061C22semidirect
24. #16838048C22semidirect
28. #16837936C22semidirect
30. C2×#14273706C22semidirect
31. C2×#14273701C22semidirect
33. #16837784C22semidirect
34. #16837756C22semidirect
35. #16837740C22semidirect
36. #16837737C22semidirect
37. #16837720C22semidirect
38. #16837718C22semidirect
39. #16837713C22semidirect
40. #16837702C22semidirect
41. #16837658C22semidirect
42. #16837653C22semidirect
43. #16837650C22semidirect
44. #16837646C22semidirect
45. #16837621C22semidirect
46. #16837617C22semidirect
47. #16837614C22semidirect
48. #16837564C22semidirect
49. #16837562C22semidirect
50. #16837558C22semidirect
51. #16837553C22semidirect
52. #16837553C22semidirect
53. #16837553C22semidirect
54. #16837547C22semidirect
55. #16837541C22semidirect
56. #16837540C22semidirect
59. #16837536C22semidirect
60. #16837535C22semidirect
61. C4×#11745670C22semidirect
62. C4×#11745669C22semidirect
63. #16837480C22semidirect
64. #16837480C22semidirect
65. #16837455C22semidirect
66. #16837407C22semidirect
67. #16837403C22semidirect
68. #16837403C22semidirect
69. #16837366C22semidirect
70. #16837366C22semidirect
71. #16837366C22semidirect
73. C23×D4×C59C22semidirect
77. C59×#546C22semidirect
78. C2×#124×C59C22semidirect
80. C2×C22⋊Q8×C59C22semidirect
85. C2×C4×D4×C59C22semidirect
88. C22×Dic118C23semidirect
89. C22×D236C23semidirect
94. C2×#11745672C23semidirect
97. C2×#11745671C23semidirect
101. C2×#11745664C23semidirect
102. C2×#11745664C23semidirect
106. #14273719C23semidirect
108. #14273715C23semidirect
119. #14273706C23semidirect
125. #14273701C23semidirect
131. C4×Dic118C23semidirect
132. C4×D236C23semidirect
141. C2×C4⋊Dic59C23semidirect
142. C2×C4⋊Dic59C23semidirect
147. #14273660C23semidirect
148. #14273658C23semidirect
149. C4⋊(C59⋊C8)C23semidirect
150. #14273651C23semidirect
151. #14273651C23semidirect
152. #14273650C23semidirect
157. #14273647C23semidirect
161. C22⋊(C59⋊C8)C23semidirect
162. C22⋊(C59⋊C8)C23semidirect
163. C4×C59⋊C8C23semidirect
468. C2×#546D59semidirect
493. C23×D4C2×D59semidirect
506. #546C2×D59semidirect
511. C2×#124C2×D59semidirect
515. C2×C22⋊Q8C2×D59semidirect
522. C2×C4×D4C2×D59semidirect
563. C59#61581semidirect

Maximal subgroups

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

subgroupindex
#214379352
#214363122
#214362972
#214357232
#214357032
#214350612
#214349262
#214349022
#214348932
#214341432
#214333562
#214333482
#214333232
#214331372
C2×C59×#5462
#6158159