Finite Group Databasebeta

← #28600112

Subgroups — #28600112

Order 15104.

900 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21433314C211yesmaximal, characteristic
2#21432799C211yesmaximal, characteristic, complemented
3#21424988C211yesmaximal, characteristic, complemented
4#21424983C211yesmaximal, characteristic, complemented
5#21424810C211yesmaximal, characteristic, complemented
6#21424803C211yesmaximal, characteristic, complemented
7#21424741C211yesmaximal, characteristic, complemented
8#21424741C211yesmaximal, characteristic, complemented
9#21424426C211yesmaximal, characteristic, complemented
10#21424426C211yesmaximal, characteristic, complemented
11#21424398C211yesmaximal, characteristic, complemented
12#21424301C211yesmaximal, characteristic, complemented
13#21424040C211yesmaximal, characteristic, complemented
14#21423877C211yesmaximal, characteristic, complemented
15C59×#2879C211yesmaximal, characteristic, complemented
16C2×#14273747C2211yescharacteristic
17C2×#14273747C2211yescharacteristic
18C2×#14273733C2211yescharacteristic, complemented
19#16837913C2211yescharacteristic
20#16837564C411yescharacteristic, complemented
21#16837564C411yescharacteristic, complemented
22#16837558C411yescharacteristic, complemented
23#16837553C411yescharacteristic, complemented
24#16837547C411yescharacteristic, complemented
25#16837547C411yescharacteristic, complemented
26#16837541C411yescharacteristic, complemented
27#16837536C411yescharacteristic, complemented
28#16837478—21no—
29#16837478—21no—
30#16837471—21no—
31#16837471—21no—
32C2×#14273662C2211yescharacteristic, complemented
33C2×#14273662C2211yescharacteristic, complemented
34#16837428C2211yescharacteristic, complemented
35C2×#14273654C2211yescharacteristic
36C2×#14273654C2211yescharacteristic
37C2×#14273654C2211yescharacteristic
38C2×#14273654C2211yescharacteristic
39C2×#14273653C2211yescharacteristic, complemented
40C2×#14273653C2211yescharacteristic, complemented
41#16837398C2211yescharacteristic
42#16837398C2211yescharacteristic
43#16837368C2211yescharacteristic, complemented
44#16837366C2211yescharacteristic
45C2×C22⋊(C59⋊C8)C2211yescharacteristic
46#16837357C2211yescharacteristic, complemented
47C2×#14273637C2211yescharacteristic, complemented
48C2×C8×Dic59C2211yescharacteristic, complemented
49C4×C22⋊Dic59C2211yescharacteristic
50#16837166C2211yescharacteristic, complemented
51#16837166C2211yescharacteristic, complemented
52#16837163C2211yescharacteristic, complemented
53#16837163C2211yescharacteristic, complemented
54#16837156C2211yescharacteristic, complemented
55#16837156C2211yescharacteristic, complemented
56C22×#41×C59C2211yescharacteristic
57C22×M16×C59C2211yescharacteristic
58C22×M16×C59C2211yescharacteristic
59C59×#408—21no—
60C59×#408—21no—
61C59×#408C2211yescharacteristic
62C59×#408C2211yescharacteristic
63C59×#408C2211yescharacteristic
64C59×#408C2211yescharacteristic
65C59×#407—21no—
66C59×#407—21no—
67C2×#11745685C2311yescharacteristic
68#14273747—41no—
69#14273747—41no—
70#14273747—41no—
71#14273747—41no—
72C2×#11745672C2×C411yescharacteristic
73C2×#11745672C2×C411yescharacteristic
74C2×#11745670C2×C411yescharacteristic
75C2×#11745670C2×C411yescharacteristic
76C2×#11745671C2×C411yescharacteristic
77C2×#11745671C2×C411yescharacteristic
78C2×#11745669C2×C411yescharacteristic
79C2×#11745669C2×C411yescharacteristic
80#14273733—41no—
81#14273733—41no—
82C2×#11745664C2311yescharacteristic
83C2×#11745664C2311yescharacteristic
84C2×#11745659—21no—
85C22×C59⋊C8C2311yescharacteristic
86C22×C59⋊C8C2311yescharacteristic
87C2×C8×D59—21no—
88#14273710—21no—
89#14273706C2×C411yescharacteristic
90#14273706C2×C411yescharacteristic
91#14273701C2×C411yescharacteristic
92#14273701C2×C411yescharacteristic
93#14273696—21no—
94C4×C22⋊D59—21no—
95C4×C22⋊D59—21no—
96#14273686C2311yescharacteristic
97C2×C22⋊Dic59—21no—
98C2×C4×Dic59C2311yescharacteristic
99C2×C4×Dic59C2311yescharacteristic
100#14273662—41no—
101#14273662—41no—
102Dic59⋊C8—21no—
103Dic59⋊C8—21no—
104#14273654—41no—
105#14273654—41no—
106#14273654—41no—
107#14273654—41no—
108#14273653—41no—
109#14273653—41no—
110#14273651C2×C411yescharacteristic
111#14273651C2×C411yescharacteristic
112#14273651C2×C411yescharacteristic
113#14273651C2×C411yescharacteristic
114#14273648C2×C411yescharacteristic
115#14273648C2×C411yescharacteristic
116#14273648C2×C411yescharacteristic
117#14273648C2×C411yescharacteristic
118C22⋊(C59⋊C8)—21no—
119C22⋊(C59⋊C8)—21no—
120C22⋊(C59⋊C8)C2×C411yescharacteristic
121C22⋊(C59⋊C8)C2×C411yescharacteristic
122C22⋊(C59⋊C8)C2×C411yescharacteristic
123C22⋊(C59⋊C8)C2×C411yescharacteristic
124(C2×D59)⋊C8—21no—
125(C2×D59)⋊C8—21no—
126#14273637—21no—
127#14273637—41no—
128C8×Dic59—21no—
129C8×Dic59—41no—
130C59⋊#95—21no—
131C2×#41×C59—21no—
132C2×#41×C59—21no—
133C2×#41×C59—41no—
134C2×#41×C59—41no—
135C2×#41×C59—41no—
136C2×#41×C59—41no—
137C2×#41×C59C2×C411yescharacteristic
138C2×#41×C59C2×C411yescharacteristic
139C2×#41×C59C2311yescharacteristic
140C2×#41×C59C2311yescharacteristic
141C22×Q8×C59C2×C411yescharacteristic
142C22×D4×C59—21no—
143C22×D4×C59C2×C411yescharacteristic
144C23×C4×C59—21no—
145C23×C4×C59C2311yescharacteristic
146C2×M16×C59—21no—
147C2×M16×C59—41no—
148C2×M16×C59—41no—
149C2×M16×C59—41no—
150C2×M16×C59—41no—
151C2×M16×C59D411yescharacteristic
152C2×M16×C59D411yescharacteristic
153C2×M16×C59D411yescharacteristic
154C2×M16×C59D411yescharacteristic
155C2×M16×C59C2311yescharacteristic
156C2×M16×C59C2311yescharacteristic
157C22×C8×C59—21no—
158C22×C8×C59C2311yescharacteristic
159C22×C8×C59C2311yescharacteristic
160C22⋊C8×C59—21no—
161C22⋊C8×C59—21no—
162C22⋊C8×C59—21no—
163C22⋊C8×C59—21no—
164C22⋊C8×C59—21no—
165C22⋊C8×C59—21no—
166C22⋊C8×C59—21no—
167C22⋊C8×C59—21no—
168C24×C59—21no—
169C24×C59#4111yescharacteristic
170#41×C59—21no—
171#41×C59—21no—
172#41×C59—21no—
173#41×C59—21no—
174#41×C59—21no—
175#41×C59—21no—
176#41×C59—21no—
177#41×C59—21no—
178#41×C59—41no—
179#41×C59—41no—
180#41×C59—41no—
181#41×C59—41no—
182#41×C59—42no—
183#41×C59—42no—
184#41×C59—42no—
185#41×C59—42no—
186C2×Q8×C59—21no—
187C2×Q8×C59—41no—
188C2×Q8×C59—41no—
189C2×Q8×C59C22×C411yescharacteristic
190C2×Q8×C59C22×C411yescharacteristic
191C2×D4×C59—21no—
192C2×D4×C59—21no—
193C2×D4×C59—21no—
194C2×D4×C59—21no—
195C2×D4×C59—21no—
196C2×D4×C59—41no—
197C2×D4×C59—41no—
198C2×D4×C59—42no—
199C2×D4×C59—42no—
200C2×D4×C59C22×C411yescharacteristic
201C2×D4×C59C22×C411yescharacteristic
202C22×C4×C59—21no—
203C22×C4×C59—21no—
204C22×C4×C59—21no—
205C22×C4×C59—21no—
206C22×C4×C59—21no—
207C22×C4×C59—21no—
208C22×C4×C59—21no—
209C22×C4×C59—21no—
210C22×C4×C59—21no—
211C22×C4×C59—42no—
212C22×C4×C59—42no—
213C22×C4×C59C22×C411yescharacteristic
214C22×C4×C59C22×C411yescharacteristic
215C22×C4×C59C2×D411yescharacteristic
216C22×C4×C59C2×D411yescharacteristic
217C22×C4×C59#4111yescharacteristic
218C22×C4×C59C2411yescharacteristic
219C2×C22⋊D59—21no—
220C2×C22⋊D59—21no—
221C2×C22⋊D59—21no—
222C22×Dic59—21no—
223C22×Dic59—21no—
224#11745685—21no—
225#11745685—21no—
226#11745685—21no—
227#11745685—21no—
228C2×D236C22×C411yescharacteristic
229C2×C4×D59—21no—
230C2×Dic118C22×C411yescharacteristic
231M16×C59—21no—
232M16×C59—21no—
233M16×C59—21no—
234M16×C59—21no—
235M16×C59—41no—
236M16×C59—41no—
237M16×C59—41no—
238M16×C59—41no—
239M16×C59—42no—
240C2×C8×C59—21no—
241C2×C8×C59—21no—
242C2×C8×C59—21no—
243C2×C8×C59—21no—
244C2×C8×C59—21no—
245C2×C8×C59—21no—
246C2×C8×C59—42no—
247C2×C8×C59C2×D411yescharacteristic
248C2×C8×C59C2×D411yescharacteristic
249C2×C8×C59C2×D411yescharacteristic
250C2×C8×C59C2×D411yescharacteristic
251C22⋊Dic59—21no—
252C22⋊Dic59—21no—
253C22⋊Dic59—21no—
254C22⋊Dic59—42no—
255#11745672—41no—
256#11745672—41no—
257#11745671—41no—
258#11745671—41no—
259#11745670—41no—
260#11745670—41no—
261#11745669—41no—
262#11745669—41no—
263(C2×D59)⋊C4—21no—
264(C2×D59)⋊C4—21no—
265C4⋊Dic59C22×C411yescharacteristic
266C4⋊Dic59C22×C411yescharacteristic
267Dic59⋊C4—21no—
268Dic59⋊C4—21no—
269C4×Dic59—21no—
270C4×Dic59—21no—
271C4×Dic59—21no—
272C4×Dic59—21no—
273C4×Dic59—21no—
274#11745664—21no—
275#11745664—21no—
276#11745664—21no—
277#11745664—21no—
278C2×C59⋊C8—21no—
279C2×C59⋊C8—21no—
280C2×C59⋊C8—21no—
281C2×C59⋊C8—21no—
282C2×C59⋊C8—21no—
283C2×C59⋊C8—21no—
284C2×C59⋊C8C22×C411yescharacteristic
285C2×C59⋊C8C22×C411yescharacteristic
286C2×C59⋊C8C22×C411yescharacteristic
287C2×C59⋊C8C22×C411yescharacteristic
288#11745659—42no—
289C8×D59—42no—
290C23×C59—21no—
291C23×C59—21no—
292C23×C59—21no—
293C23×C59—21no—
294C23×C59—41no—
295C23×C59—41no—
296C23×C59—42no—
297C23×C59—81no—
298C23×C59—81no—
299C23×C59C4×D411yescharacteristic
300C23×C59C4×D411yescharacteristic
301C23×C59C2×#4111yescharacteristic
302C22×D59—21no—
303Q8×C59—21no—
304Q8×C59—21no—
305Q8×C59—21no—
306Q8×C59—21no—
307Q8×C59—42no—
308D4×C59—21no—
309D4×C59—21no—
310D4×C59—21no—
311D4×C59—21no—
312D4×C59—42no—
313D4×C59—42no—
314D4×C59—42no—
315D4×C59—41no—
316D4×C59—41no—
317D4×C59—41no—
318D4×C59—41no—
319C2×C4×C59—21no—
320C2×C4×C59—21no—
321C2×C4×C59—21no—
322C2×C4×C59—21no—
323C2×C4×C59—21no—
324C2×C4×C59—21no—
325C2×C4×C59—21no—
326C2×C4×C59—21no—
327C2×C4×C59—21no—
328C2×C4×C59—21no—
329C2×C4×C59—21no—
330C2×C4×C59—21no—
331C2×C4×C59—42no—
332C2×C4×C59—42no—
333C2×C4×C59—42no—
334C2×C4×C59—41no—
335C2×C4×C59—41no—
336C2×C4×C59—41no—
337C2×C4×C59—41no—
338C2×C4×C59C4×D411yescharacteristic
339C2×C4×C59C4×D411yescharacteristic
340C2×C4×C59C23×C411yescharacteristic
341C2×C4×C59C22×D411yescharacteristic
342C2×C4×C59H(5,𝔽2)11yescharacteristic
343C2×C4×C59H(5,𝔽2)11yescharacteristic
344C2×C4×C59H(5,𝔽2)11yescharacteristic
345C2×C4×C59H(5,𝔽2)11yescharacteristic
346C22⋊D59—41no—
347C22⋊D59—41no—
348C22⋊D59—81no—
349C22⋊D59—81no—
350C2×Dic59—22no—
351C2×Dic59—21no—
352C2×Dic59—21no—
353C2×Dic59—21no—
354C2×Dic59—41no—
355C2×Dic59—41no—
356C2×Dic59—41no—
357C2×Dic59—41no—
358C2×Dic59—41no—
359D236—21no—
360D236—21no—
361C4×D59—41no—
362C4×D59—41no—
363Dic118—21no—
364Dic118—21no—
365C8×C59—21no—
366C8×C59—21no—
367C8×C59—21no—
368C8×C59—21no—
369C8×C59—41no—
370C8×C59—41no—
371C59⋊C8—21no—
372C59⋊C8—21no—
373C59⋊C8—21no—
374C59⋊C8—21no—
375C59⋊C8—41no—
376C59⋊C8—41no—
377#22062—591nomaximal, Sylow
378C22×C59—21no—
379C22×C59—21no—
380C22×C59—21no—
381C22×C59—21no—
382C22×C59—21no—
383C22×C59—21no—
384C22×C59—21no—
385C22×C59—21no—
386C22×C59—41no—
387C22×C59—41no—
388C22×C59—41no—
389C22×C59—41no—
390C22×C59—41no—
391C22×C59—41no—
392C22×C59—81no—
393C22×C59—81no—
394C22×C59—84no—
395C22×C59C2×C4×D411yescharacteristic
396C22×C59#53811yescharacteristic
397C22×C59#53811yescharacteristic
398C2×D59—41no—
399C2×D59—41no—
400C2×D59—41no—
401C4×C59—21no—
402C4×C59—21no—
403C4×C59—41no—
404C4×C59—41no—
405C4×C59#51811yescharacteristic
406C4×C59#51811yescharacteristic
407C4×C59#53411yescharacteristic
408C4×C59#53511yescharacteristic
409Dic59—42no—
410Dic59—41no—
411Dic59—41no—
412Dic59—41no—
413Dic59—81no—
414#3002—591no—
415#2930—591no—
416#2879D5911yescharacteristic, complemented
417#1975—591no—
418#1974—591no—
419#1938—591no—
420#1937—591no—
421#1929—591no—
422#1929—591no—
423#1876—591no—
424#1876—591no—
425#1871—591no—
426#1855—591no—
427#1789—591no—
428#1753—591no—
429C2×C59—21no—
430C2×C59—21no—
431C2×C59—41no—
432C2×C59—41no—
433C2×C59—81no—
434C2×C59—81no—
435C2×C59#232111yescharacteristic
436C2×C59#295611yescharacteristic
437C2×C59#295711yescharacteristic
438D59—81no—
439C22×#41C2×D5911yescharacteristic
440C2×#135—591no—
441C2×#135—591no—
442C2×#131—591no—
443C22×M16C2×D5911yescharacteristic
444C22×M16C2×D5911yescharacteristic
445#525—591no—
446#452—591no—
447#452—591no—
448#451—591no—
449#450—591no—
450#449—591no—
451#449—591no—
452#448—591no—
453#447—591no—
454#436—1181no—
455#436—1181no—
456#435—1181no—
457#435—1181no—
458C2×#108—591no—
459C2×#108—591no—
460#424—591no—
461C2×#104—591no—
462C2×#104—591no—
463C2×#104—591no—
464C2×#104—591no—
465C2×#104—591no—
466C2×#104—591no—
467#416—591no—
468#416—591no—
469#408—21no—
470#408—21no—
471#408—591no—
472#408C2×D5911yescharacteristic
473#408C2×D5911yescharacteristic
474#408C2×D5911yescharacteristic
475#408C2×D5911yescharacteristic
476#407—21no—
477#407—21no—
478#407—591no—
479C2×C22⋊C8—591no—
480#405—591no—
481C2×#97—591no—
482C2×C4×C8—591no—
483C4×C22⋊C4—591no—
484#341—591no—
485#341—591no—
486#339—591no—
487#339—591no—
488#336—591no—
489#336—591no—
490C59#2206211yescharacteristic, complemented, Sylow
491C2×#41—21no—
492C2×#41—21no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—41no—
497C2×#41—591no—
498C2×#41C4×D5911yescharacteristic
499C2×#41C4×D5911yescharacteristic
500C2×#41C22×D5911yescharacteristic
501C2×#41C22×D5911yescharacteristic
502C22×Q8C4×D5911yescharacteristic
503C22×D4—21no—
504C22×D4C4×D5911yescharacteristic
505C23×C4—21no—
506C23×C4C22×D5911yescharacteristic
507#135—2361no—
508#135—2361no—
509#135—2361no—
510#135—2361no—
511C2×Q16—591no—
512C2×Q16—591no—
513C2×SD16—591no—
514C2×SD16—591no—
515C2×SD16—591no—
516C2×SD16—591no—
517C2×D8—591no—
518C2×D8—591no—
519#131—2361no—
520#131—2361no—
521C2×M16—21no—
522C2×M16—41no—
523C2×M16—41no—
524C2×M16—41no—
525C2×M16—41no—
526C2×M16—591no—
527C2×M16—591no—
528C2×M16—1181no—
529C2×M16C22⋊D5911yescharacteristic
530C2×M16C22⋊D5911yescharacteristic
531C2×M16C22⋊D5911yescharacteristic
532C2×M16C22⋊D5911yescharacteristic
533C2×M16C22×D5911yescharacteristic
534C2×M16C22×D5911yescharacteristic
535C22×C8—21no—
536C22×C8—591no—
537C22×C8—591no—
538C22×C8—1181no—
539C22×C8C22×D5911yescharacteristic
540C22×C8C22×D5911yescharacteristic
541#123—1181no—
542C22⋊Q8—591no—
543C22⋊Q8—591no—
544#121—591no—
545#121—591no—
546#120—1181no—
547C4×D4—1181no—
548C4×D4—1181no—
549#117—591no—
550C2×C22⋊C4—1181no—
551C2×C42—591no—
552C2×C42—591no—
553#108—2361no—
554#108—2361no—
555C4⋊C8—1181no—
556C4⋊C8—1181no—
557#104—2361no—
558#104—2361no—
559#104—2361no—
560#104—2361no—
561#104—2361no—
562#104—2361no—
563#103—591no—
564#103—591no—
565#103—591no—
566#103—591no—
567#102—591no—
568#102—591no—
569#102—591no—
570#102—591no—
571C22⋊C8—21no—
572C22⋊C8—21no—
573C22⋊C8—21no—
574C22⋊C8—21no—
575C22⋊C8—21no—
576C22⋊C8—21no—
577C22⋊C8—21no—
578C22⋊C8—21no—
579C22⋊C8—591no—
580C22⋊C8—591no—
581C22⋊C8—591no—
582C22⋊C8—591no—
583C22⋊C8—1181no—
584C22⋊C8—1181no—
585C22⋊C8—1181no—
586C22⋊C8—1181no—
587#97—1181no—
588#97—2361no—
589C4×C8—1181no—
590C4×C8—2361no—
591#95—1181no—
592C24—21no—
593C24#1174568511yescharacteristic
594#41—21no—
595#41—21no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—21no—
601#41—21no—
602#41—41no—
603#41—41no—
604#41—41no—
605#41—41no—
606#41—42no—
607#41—42no—
608#41—42no—
609#41—42no—
610#41—1181no—
611#41—1181no—
612#41—1181no—
613#41—1181no—
614C2×Q8—21no—
615C2×Q8—41no—
616C2×Q8—41no—
617C2×Q8—591no—
618C2×Q8C2×C4×D5911yescharacteristic
619C2×Q8C2×C4×D5911yescharacteristic
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—591no—
630C2×D4—1181no—
631C2×D4—1181no—
632C2×D4—1181no—
633C2×D4C2×C4×D5911yescharacteristic
634C2×D4C2×C4×D5911yescharacteristic
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—42no—
645C22×C4—42no—
646C22×C4—1181no—
647C22×C4—1181no—
648C22×C4—1181no—
649C22×C4C2×C4×D5911yescharacteristic
650C22×C4C2×C4×D5911yescharacteristic
651C22×C4#1174568511yescharacteristic
652C22×C4C2×C22⋊D5911yescharacteristic
653C22×C4C2×C22⋊D5911yescharacteristic
654C22×C4C23×D5911yescharacteristic
655Q16—2361no—
656Q16—2361no—
657SD16—2361no—
658SD16—2361no—
659SD16—2361no—
660SD16—2361no—
661D8—2361no—
662D8—2361no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—41no—
668M16—41no—
669M16—41no—
670M16—41no—
671M16—42no—
672M16—1181no—
673M16—1181no—
674M16—1181no—
675M16—1181no—
676M16—2362no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—42no—
684C2×C8—591no—
685C2×C8—591no—
686C2×C8—591no—
687C2×C8—591no—
688C2×C8—1181no—
689C2×C8—1181no—
690C2×C8—1181no—
691C2×C8—1181no—
692C2×C8—1181no—
693C2×C8—1181no—
694C2×C8—2362no—
695C2×C8C2×C22⋊D5911yescharacteristic
696C2×C8C2×C22⋊D5911yescharacteristic
697C2×C8C2×C22⋊D5911yescharacteristic
698C2×C8C2×C22⋊D5911yescharacteristic
699C4⋊C4—591no—
700C4⋊C4—591no—
701C4⋊C4—1181no—
702C4⋊C4—1181no—
703C22⋊C4—1181no—
704C22⋊C4—1181no—
705C22⋊C4—1181no—
706C22⋊C4—1181no—
707C22⋊C4—1181no—
708C22⋊C4—2362no—
709C42—1181no—
710C42—1181no—
711C42—1181no—
712C42—1181no—
713C42—1181no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—41no—
719C23—41no—
720C23—42no—
721C23—81no—
722C23—81no—
723C23—1181no—
724C23C4×C22⋊D5911yescharacteristic
725C23C4×C22⋊D5911yescharacteristic
726C23C2×#1174568511yescharacteristic
727Q8—21no—
728Q8—21no—
729Q8—21no—
730Q8—21no—
731Q8—42no—
732Q8—1181no—
733Q8—1181no—
734D4—21no—
735D4—21no—
736D4—21no—
737D4—21no—
738D4—42no—
739D4—42no—
740D4—42no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—1181no—
746D4—1181no—
747D4—4721no—
748D4—4721no—
749D4—2361no—
750D4—2361no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—1182no—
771C2×C4—1181no—
772C2×C4—1181no—
773C2×C4—1181no—
774C2×C4—2361no—
775C2×C4—2361no—
776C2×C4—2361no—
777C2×C4—2361no—
778C2×C4—2361no—
779C2×C4—2361no—
780C2×C4—2361no—
781C2×C4C4×C22⋊D5911yescharacteristic
782C2×C4C4×C22⋊D5911yescharacteristic
783C2×C4C22×C4×D5911yescharacteristic
784C2×C4C22×C22⋊D5911yescharacteristic
785C2×C4#1427377211yescharacteristic
786C2×C4#1427377211yescharacteristic
787C2×C4#1427377211yescharacteristic
788C2×C4#1427377211yescharacteristic
789C8—21no—
790C8—21no—
791C8—21no—
792C8—21no—
793C8—41no—
794C8—41no—
795C8—1181no—
796C8—1181no—
797C8—1181no—
798C8—1181no—
799C8—2361no—
800C8—2361no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—81no—
816C22—81no—
817C22—84no—
818C22—2361no—
819C22—2361no—
820C22—2361no—
821C22C2×C4×C22⋊D5911yescharacteristic
822C22#1683799011yescharacteristic
823C22#1683799011yescharacteristic
824C4—21no—
825C4—21no—
826C4—41no—
827C4—41no—
828C4—4721no—
829C4—2362no—
830C4—2361no—
831C4—2361no—
832C4—2361no—
833C4#1683787511yescharacteristic
834C4#1683787511yescharacteristic
835C4#1683796111yescharacteristic
836C4#1683796911yescharacteristic
837C2—21no—
838C2—21no—
839C2—41no—
840C2—41no—
841C2—81no—
842C2—81no—
843C2—4721no—
844C2#2142675411yescharacteristic
845C2#2143300311yescharacteristic
846C2#2143301111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2879C2
socleC22×C59C2×C4×D4
prime radical#21433314C2
cosocleC22×C4×C59C24
hypercenter#2879D59
hypocenterC59#22062
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C22×M16 ◁ #2879

Complements

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

NH ≅ G/Ntype
2. #21432799C2semidirect
3. #21424988C2semidirect
4. #21424983C2semidirect
5. #21424810C2semidirect
6. #21424803C2semidirect
7. #21424741C2semidirect
8. #21424741C2semidirect
9. #21424426C2semidirect
10. #21424426C2semidirect
11. #21424398C2semidirect
12. #21424301C2semidirect
13. #21424040C2semidirect
14. #21423877C2semidirect
15. C59×#2879C2semidirect
18. C2×#14273733C22semidirect
20. #16837564C4semidirect
21. #16837564C4semidirect
22. #16837558C4semidirect
23. #16837553C4semidirect
24. #16837547C4semidirect
25. #16837547C4semidirect
26. #16837541C4semidirect
27. #16837536C4semidirect
32. C2×#14273662C22semidirect
33. C2×#14273662C22semidirect
34. #16837428C22semidirect
39. C2×#14273653C22semidirect
40. C2×#14273653C22semidirect
43. #16837368C22semidirect
46. #16837357C22semidirect
47. C2×#14273637C22semidirect
48. C2×C8×Dic59C22semidirect
50. #16837166C22semidirect
51. #16837166C22semidirect
52. #16837163C22semidirect
53. #16837163C22semidirect
54. #16837156C22semidirect
55. #16837156C22semidirect
416. #2879D59semidirect
490. C59#22062semidirect

Maximal subgroups

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

subgroupindex
#214333142
#214327992
#214249882
#214249832
#214248102
#214248032
#214247412
#214244262
#214243982
#214243012
#214240402
#214238772
C59×#28792
#2206259