Finite Group Databasebeta

← #29452672

Subgroups — #29452672

Order 15104.

2756 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838167C211yesmaximal, characteristic, complemented
2C2×#131×D59C211yesmaximal, characteristic, complemented
3#41×D236C211yesmaximal, characteristic
4#21432842C213yesmaximal, complemented
5M16×D236C213yesmaximal, complemented
6#21432824C213yesmaximal, complemented
7#21432824C213yesmaximal, complemented
8#21432815C213yesmaximal, complemented
9#21432801C213yesmaximal, complemented
10#21432792C213yesmaximal, complemented
11C2×#16837475C213yesmaximal, complemented
12#21432664C211yesmaximal, characteristic, complemented
13#21432543C211yesmaximal, characteristic, complemented
14#21432543C211yesmaximal, characteristic, complemented
15C59×#2875C211yesmaximal, characteristic, complemented
16C2×#41×D59C2211yescharacteristic
17C2×#41×D59C2211yescharacteristic
18#16838167—28no—
19C2×#14273735C2213yescomplemented
20C2×#14273735C2213yescomplemented
21C2×#14273734C2211yescharacteristic
22C2×#14273734C2211yescharacteristic
23C2×#14273733C2213yescomplemented
24C2×#14273733C2213yescomplemented
25#131×D59—28no—
26C22×#11745659C2213yescomplemented
27C2×M16×D59C2213yescomplemented
28C2×M16×D59C2213yescomplemented
29C22×C8×D59C2213yescomplemented
30#16838074C411yescharacteristic
31Q8×D236C411yescharacteristic
32#16838064C411yescharacteristic
33#16838064C411yescharacteristic
34#16838056C413yes—
35#16838047C413yes—
36#16838047C413yes—
37D4×D236C413yes—
38#16837952C2213yes—
39#16837914C2213yes—
40#16837914C2213yes—
41C2×C4×D236C2213yes—
42#16837481C2216yescomplemented
43#16837481C2216yescomplemented
44#16837475C2213yes—
45#16837475C2211yescharacteristic
46#16837475C2216yescomplemented
47#16837475C2213yescomplemented
48#16837475C2213yescomplemented
49#16837475C2213yescomplemented
50#16837475C2213yescomplemented
51#16837475C2213yescomplemented
52#16837475C2213yescomplemented
53#16837475C2216yescomplemented
54#16837475C2216yescomplemented
55C8×D236C2216yescomplemented
56C8×D236C2216yescomplemented
57#16837429C2213yescomplemented
58#16837429C2213yescomplemented
59#16837426C2213yescomplemented
60C2×C4⋊(C59⋊C8)C2213yescomplemented
61#16837370C2213yescomplemented
62#16837370C2213yescomplemented
63#16837368C2213yescomplemented
64#16837368C2213yescomplemented
65#16837365C2213yescomplemented
66#16837365C2213yescomplemented
67C2×(C2×D59)⋊C8C2213yescomplemented
68C2×(C2×D59)⋊C8C2213yescomplemented
69C2×#131×C59C2211yescharacteristic
70C2×#131×C59C2211yescharacteristic
71C4×#41×C59C2211yescharacteristic
72C59×#405C2213yescomplemented
73C59×#405C2213yescomplemented
74C4×M16×C59C2213yescomplemented
75C2×#97×C59C2213yescomplemented
76C2×#11745689C2×C411yescharacteristic
77C2×#11745689C2×C411yescharacteristic
78C2×#11745685C2313yes—
79C2×#11745685C2313yes—
80C2×#11745687C2×C413yes—
81C2×#11745687C2×C413yes—
82#41×D59—24no—
83#41×D59—24no—
84#41×D59—24no—
85#41×D59—24no—
86C2×Q8×D59C2×C411yescharacteristic
87C2×Q8×D59C2×C411yescharacteristic
88C22×D236C2×C413yes—
89C2×D4×D59C2×C413yes—
90C2×D4×D59C2×C413yes—
91C22×C4×D59C2313yes—
92C22×C4×D59C2313yes—
93#14273735—212no—
94#14273735—212no—
95#14273734—24no—
96#14273734—24no—
97#14273733—212no—
98#14273733—212no—
99C2×#11745664C2313yes—
100C2×#11745664C2313yes—
101C2×#11745659—212no—
102C2×#11745659C2313yes—
103C2×#11745659C2316yes—
104C2×#11745659C2311yescharacteristic
105C2×#11745659C2313yes—
106C2×#11745659C2313yes—
107M16×D59—212no—
108M16×D59—212no—
109C22×C59⋊C8C2313yes—
110C22×C59⋊C8C2313yes—
111C2×C8×D59—212no—
112C2×C8×D59C2311yescharacteristic
113C2×C8×D59C2313yes—
114C2×C8×D59C2313yes—
115C2×C8×D59C2313yes—
116C2×C8×D59C2316yes—
117#14273727C2×C413yes—
118#14273724C2×C413yes—
119#14273715C2×C413yes—
120#14273715C2×C413yes—
121#14273711C2×C416yes—
122#14273711C2×C416yes—
123#14273707C2×C413yes—
124#14273707C2×C413yes—
125#14273707C2×C413yes—
126#14273707C2×C413yes—
127#14273702C2×C413yes—
128#14273702C2×C413yes—
129#14273702C2×C413yes—
130#14273702C2×C413yes—
131#14273701C2×C416yes—
132#14273701C2×C416yes—
133#14273697C2×C416yes—
134#14273697C2×C416yes—
135C4×D236C2×C413yes—
136C4×D236C2×C413yes—
137C4×D236C2×C413yes—
138C4×D236C2×C413yes—
139C4×D236C2316yes—
140C4×D236C2313yes—
141C4×D236C2313yes—
142C4×D236C2313yes—
143C4×D236C2311yescharacteristic
144C2×C4⋊Dic59C2×C413yes—
145C2×(C2×D59)⋊C4C2×C413yes—
146C2×(C2×D59)⋊C4C2×C413yes—
147C4⋊(C59⋊C8)C2311yescharacteristic
148C4⋊(C59⋊C8)C2313yes—
149C4⋊(C59⋊C8)C2313yes—
150C4⋊(C59⋊C8)C2313yes—
151C4⋊(C59⋊C8)C2316yes—
152(C2×D59)⋊C8C2313yes—
153(C2×D59)⋊C8C2313yes—
154(C2×D59)⋊C8C2316yes—
155(C2×D59)⋊C8C2316yes—
156(C2×D59)⋊C8C2311yescharacteristic
157(C2×D59)⋊C8C2311yescharacteristic
158(C2×D59)⋊C8C2313yes—
159(C2×D59)⋊C8C2313yes—
160(C2×D59)⋊C8C2313yes—
161(C2×D59)⋊C8C2313yes—
162C2×#41×C59C2311yescharacteristic
163#131×C59—24no—
164#131×C59D418yescomplemented
165C2×M16×C59C2313yes—
166C2×M16×C59C2313yes—
167C22×C8×C59C2313yes—
168C22×C8×C59C2313yes—
169C4×Q8×C59C2×C411yescharacteristic
170C4×Q8×C59C2×C411yescharacteristic
171C4×D4×C59C2×C413yes—
172C4×D4×C59C2×C413yes—
173#117×C59C2313yes—
174C2×C42×C59C2313yes—
175#97×C59C2311yescharacteristic
176#97×C59C2313yes—
177#97×C59C2313yes—
178#97×C59C2313yes—
179C4×C8×C59C2316yes—
180C23×D59C22×C413yes—
181C23×D59C22×C413yes—
182#41×C59C2×D414yes—
183#41×C59#4114yes—
184C2×Q8×C59C22×C411yescharacteristic
185C2×D4×C59C22×C413yes—
186C22×C4×C59C22×C413yes—
187C22×C4×C59C22×C413yes—
188C22×C4×C59C2413yes—
189C2×C22⋊D59C22×C416yes—
190C2×C22⋊D59C22×C416yes—
191C22×Dic59C22×C413yes—
192C22×Dic59C22×C413yes—
193#11745689—24no—
194#11745689—24no—
195Q8×D59—24no—
196Q8×D59—24no—
197#11745687—212no—
198#11745687—212no—
199D4×D59—212no—
200D4×D59—212no—
201#11745685—26no—
202#11745685—26no—
203#11745685—26no—
204#11745685—26no—
205C2×D236—46no—
206C2×D236C22×C411yescharacteristic
207C2×D236C22×C413yes—
208C2×D236C22×C413yes—
209C2×D236C22×C413yes—
210C2×D236C22×C413yes—
211C2×D236C22×C413yes—
212C2×D236C22×C416yes—
213C2×C4×D59—26no—
214C2×C4×D59—26no—
215C2×C4×D59—26no—
216C2×C4×D59—26no—
217C2×C4×D59C22×C413yes—
218C2×C4×D59C22×C413yes—
219C2×C4×D59C22×C413yes—
220C2×C4×D59C22×C413yes—
221C2×C4×D59C2411yescharacteristic
222C2×C4×D59C2413yes—
223C2×C4×D59C2413yes—
224C2×C4×D59C2411yescharacteristic
225C2×Dic118C22×C413yes—
226C2×Dic118C22×C413yes—
227M16×C59—26no—
228M16×C59C2×D4112yescomplemented
229C2×C8×C59—26no—
230C2×C8×C59C2×D4112yescomplemented
231C2×C8×C59C2413yes—
232C2×C8×C59C2411yescharacteristic
233C2×C8×C59C2413yes—
234C2×C8×C59C2411yescharacteristic
235C4⋊C4×C59C22×C413yes—
236C4⋊C4×C59C22×C413yes—
237C22⋊C4×C59C22×C416yes—
238C42×C59C22×C413yes—
239C42×C59C22×C413yes—
240C42×C59C2413yes—
241C42×C59C2411yescharacteristic
242(C2×D59)⋊C4C22×C411yescharacteristic
243(C2×D59)⋊C4C22×C411yescharacteristic
244(C2×D59)⋊C4C22×C413yes—
245(C2×D59)⋊C4C22×C413yes—
246(C2×D59)⋊C4C22×C413yes—
247(C2×D59)⋊C4C22×C413yes—
248(C2×D59)⋊C4C22×C413yes—
249(C2×D59)⋊C4C22×C413yes—
250(C2×D59)⋊C4C22×C416yes—
251(C2×D59)⋊C4C22×C416yes—
252C4⋊Dic59C22×C411yescharacteristic
253C4⋊Dic59C22×C413yes—
254C4⋊Dic59C22×C413yes—
255C4⋊Dic59C22×C413yes—
256C4⋊Dic59C22×C416yes—
257#11745664—26no—
258#11745664—26no—
259C2×C59⋊C8—26no—
260C2×C59⋊C8—26no—
261C2×C59⋊C8C2411yescharacteristic
262C2×C59⋊C8C2413yes—
263C2×C59⋊C8C2413yes—
264C2×C59⋊C8C2411yescharacteristic
265#11745659—26no—
266#11745659—212no—
267#11745659—22no—
268#11745659—26no—
269#11745659—26no—
270C8×D59—22no—
271C8×D59—26no—
272C8×D59—26no—
273C8×D59—26no—
274C8×D59—212no—
275C23×C59C23×C413yes—
276C22×D59—26no—
277C22×D59—26no—
278C22×D59—26no—
279C22×D59—43no—
280C22×D59—43no—
281C22×D59—43no—
282C22×D59C23×C411yescharacteristic
283C22×D59C23×C413yes—
284C22×D59C23×C413yes—
285C22×D59C23×C411yescharacteristic
286Q8×C59C4×D414yes—
287D4×C59C4×D4112yes—
288C2×C4×C59—43no—
289C2×C4×C59—43no—
290C2×C4×C59C23×C411yescharacteristic
291C2×C4×C59C23×C413yes—
292C2×C4×C59C23×C413yes—
293C2×C4×C59C23×C411yescharacteristic
294C2×C4×C59C23×C413yes—
295C2×C4×C59C22×D416yes—
296C2×C4×C59C2×#4116yes—
297C2×C4×C59C2511yescharacteristic
298C22⋊D59—212no—
299C22⋊D59—212no—
300C2×Dic59—26no—
301C2×Dic59—26no—
302C2×Dic59C23×C413yes—
303C2×Dic59C23×C413yes—
304C2×Dic59C23×C411yescharacteristic
305C2×Dic59C23×C411yescharacteristic
306D236—22no—
307D236—26no—
308D236—26no—
309D236—26no—
310D236—43no—
311D236—43no—
312D236—46no—
313C4×D59—26no—
314C4×D59—26no—
315C4×D59—26no—
316C4×D59—26no—
317C4×D59—21no—
318C4×D59—23no—
319C4×D59—23no—
320C4×D59—21no—
321C4×D59—21no—
322C4×D59—21no—
323C4×D59—23no—
324C4×D59—23no—
325Dic118—26no—
326Dic118—26no—
327C8×C59—21no—
328C8×C59—23no—
329C8×C59C22×D412yes—
330C8×C59C22×D416yes—
331C59⋊C8—21no—
332C59⋊C8—23no—
333C59⋊C8—23no—
334C59⋊C8—21no—
335#60146—591nomaximal, Sylow
336C22×C59—23no—
337C22×C59—23no—
338C22×C59C2×C4×D416yes—
339C22×C59C24×C411yescharacteristic
340C2×D59—21no—
341C2×D59—21no—
342C2×D59—21no—
343C2×D59—23no—
344C2×D59—23no—
345C2×D59—21no—
346C2×D59—23no—
347C2×D59—23no—
348C2×D59—23no—
349C2×D59—23no—
350C2×D59—21no—
351C2×D59—412no—
352C2×D59—86no—
353C2×D59#56812yescomplemented
354C4×C59—21no—
355C4×C59—23no—
356C4×C59—23no—
357C4×C59—21no—
358C4×C59C2×C4×D416yes—
359C4×C59C23×D411yescharacteristic
360C4×C59C22×#4111yescharacteristic
361Dic59—23no—
362Dic59—23no—
363Dic59—21no—
364Dic59—21no—
365C2×#568—591no—
366C22×#131—591no—
367D4×#41—591no—
368#2935—593no—
369D4×M16—593no—
370#2933—593no—
371#2933—593no—
372#2932—593no—
373#2930—593no—
374#2929—593no—
375C2×#435—593no—
376#2906—591no—
377#2880—591no—
378#2880—591no—
379#2875D5911yescharacteristic, complemented
380C2×C59—26no—
381C2×C59C22×C4×D411yescharacteristic
382C2×C59C2×#56811yescharacteristic
383C2×C59#357311yescharacteristic
384D59—22no—
385D59—43no—
386D59—43no—
387D59—41no—
388C22×#41—591no—
389C22×#41—591no—
390#568—1188no—
391C2×#131—591no—
392C2×#131—591no—
393C2×#131—593no—
394C2×#131—593no—
395C2×#131—593no—
396C2×#131—593no—
397C2×#131—1188no—
398C2×#131C2×D5911yescharacteristic
399C2×#131C2×D5911yescharacteristic
400C22×M16—593no—
401C22×M16—593no—
402C22×M16—593no—
403C23×C8—593no—
404#550—591no—
405D4×Q8—591no—
406#548—591no—
407#548—591no—
408#547—593no—
409#546—593no—
410#546—593no—
411D42—593no—
412#532—593no—
413#525—593no—
414#525—593no—
415C4×#41C2×D5911yescharacteristic
416C2×C4×D4—593no—
417#436—596no—
418#436—596no—
419#435—591no—
420#435—593no—
421#435—593no—
422#435—593no—
423#435—593no—
424#435—593no—
425#435—593no—
426#435—593no—
427#435—596no—
428#435—596no—
429#435—596no—
430C8×D4—596no—
431C8×D4—596no—
432#424—593no—
433#424—593no—
434#423—593no—
435C2×C4⋊C8—593no—
436#408—593no—
437#408—593no—
438#408—593no—
439#408—593no—
440#407—593no—
441#407—593no—
442C2×C22⋊C8—593no—
443C2×C22⋊C8—593no—
444#405C2×D5913yescomplemented
445#405C2×D5913yescomplemented
446C4×M16C2×D5913yescomplemented
447C2×#97C2×D5913yescomplemented
448C59#6014611yescharacteristic, complemented, Sylow
449C2×#41—591no—
450C2×#41—591no—
451C2×#41—593no—
452C2×#41—593no—
453C2×#41—593no—
454C2×#41—593no—
455C2×#41—1184no—
456C2×#41—1184no—
457C2×#41—1184no—
458C2×#41—1184no—
459C2×#41C22×D5911yescharacteristic
460C22×Q8—591no—
461C22×Q8—591no—
462C22×D4—593no—
463C22×D4—593no—
464C22×D4—593no—
465C23×C4—593no—
466C23×C4—593no—
467#131—24no—
468#131—1184no—
469#131—1184no—
470#131—11812no—
471#131—11812no—
472#131—11812no—
473#131—11812no—
474#131D23618yescomplemented
475C2×M16—593no—
476C2×M16—593no—
477C2×M16—591no—
478C2×M16—593no—
479C2×M16—593no—
480C2×M16—596no—
481C2×M16—593no—
482C2×M16—11812no—
483C2×M16—11812no—
484C2×M16—11812no—
485C2×M16C22×D5913yes—
486C2×M16C22×D5913yes—
487C22×C8—593no—
488C22×C8—593no—
489C22×C8—591no—
490C22×C8—593no—
491C22×C8—593no—
492C22×C8—593no—
493C22×C8—596no—
494C22×C8—11812no—
495C22×C8C22×D5913yes—
496C22×C8C22×D5913yes—
497C4⋊Q8—593no—
498#127—593no—
499#124—593no—
500#124—593no—
501#123—596no—
502#123—596no—
503C22⋊Q8—593no—
504C22⋊Q8—593no—
505C22⋊Q8—593no—
506C22⋊Q8—593no—
507#121—596no—
508#121—596no—
509#121—593no—
510#121—593no—
511#121—593no—
512#121—593no—
513#120—596no—
514#120—596no—
515C4×Q8C4×D5911yescharacteristic
516C4×Q8C4×D5911yescharacteristic
517C4×D4—593no—
518C4×D4—593no—
519C4×D4—593no—
520C4×D4—593no—
521C4×D4—591no—
522C4×D4—593no—
523C4×D4—593no—
524C4×D4—593no—
525C4×D4—596no—
526C4×D4C4×D5913yes—
527C4×D4C4×D5913yes—
528#117C22×D5913yes—
529C2×C4⋊C4—593no—
530C2×C22⋊C4—593no—
531C2×C22⋊C4—593no—
532C2×C42C22×D5913yes—
533C4⋊C8—591no—
534C4⋊C8—593no—
535C4⋊C8—593no—
536C4⋊C8—593no—
537C4⋊C8—596no—
538C22⋊C8—591no—
539C22⋊C8—591no—
540C22⋊C8—593no—
541C22⋊C8—593no—
542C22⋊C8—593no—
543C22⋊C8—593no—
544C22⋊C8—593no—
545C22⋊C8—593no—
546C22⋊C8—596no—
547C22⋊C8—596no—
548#97C22×D5911yescharacteristic
549#97C22×D5913yes—
550#97C22×D5913yes—
551#97C22×D5913yes—
552C4×C8C22×D5916yes—
553C24—593no—
554C24—593no—
555#41—1184no—
556#41—1184no—
557#41—11812no—
558#41—11812no—
559#41—1186no—
560#41—1186no—
561#41—1186no—
562#41—1186no—
563#41C2×D23614yes—
564#41#1174568514yes—
565C2×Q8—593no—
566C2×Q8—593no—
567C2×Q8—1184no—
568C2×Q8—1184no—
569C2×Q8C2×C4×D5911yescharacteristic
570C2×D4—596no—
571C2×D4—596no—
572C2×D4—591no—
573C2×D4—593no—
574C2×D4—593no—
575C2×D4—593no—
576C2×D4—593no—
577C2×D4—593no—
578C2×D4—596no—
579C2×D4—11812no—
580C2×D4—11812no—
581C2×D4—2366no—
582C2×D4C2×C4×D5913yes—
583C22×C4—593no—
584C22×C4—593no—
585C22×C4—593no—
586C22×C4—593no—
587C22×C4—593no—
588C22×C4—593no—
589C22×C4—591no—
590C22×C4—593no—
591C22×C4—593no—
592C22×C4—591no—
593C22×C4—1186no—
594C22×C4—1186no—
595C22×C4—1186no—
596C22×C4—1186no—
597C22×C4C2×C4×D5913yes—
598C22×C4C2×C4×D5913yes—
599C22×C4C23×D5913yes—
600M16—26no—
601M16—1186no—
602M16—1186no—
603M16—1182no—
604M16—1186no—
605M16—1186no—
606M16—11812no—
607M16—1186no—
608M16C2×D236112yescomplemented
609C2×C8—26no—
610C2×C8—591no—
611C2×C8—591no—
612C2×C8—593no—
613C2×C8—593no—
614C2×C8—1186no—
615C2×C8—1186no—
616C2×C8—1182no—
617C2×C8—1186no—
618C2×C8—1186no—
619C2×C8—1186no—
620C2×C8—11812no—
621C2×C8C2×D236112yescomplemented
622C2×C8C23×D5913yes—
623C2×C8C23×D5911yescharacteristic
624C2×C8C23×D5913yes—
625C2×C8C23×D5911yescharacteristic
626C4⋊C4—591no—
627C4⋊C4—593no—
628C4⋊C4—593no—
629C4⋊C4—593no—
630C4⋊C4—596no—
631C4⋊C4C2×C4×D5913yes—
632C4⋊C4C2×C4×D5913yes—
633C22⋊C4—591no—
634C22⋊C4—591no—
635C22⋊C4—593no—
636C22⋊C4—593no—
637C22⋊C4—593no—
638C22⋊C4—593no—
639C22⋊C4—593no—
640C22⋊C4—593no—
641C22⋊C4—596no—
642C22⋊C4—596no—
643C22⋊C4C2×C4×D5916yes—
644C42C2×C4×D5913yes—
645C42C2×C4×D5913yes—
646C42C23×D5913yes—
647C42C23×D5911yescharacteristic
648C23—591no—
649C23—591no—
650C23—593no—
651C23—593no—
652C23—1186no—
653C23—1186no—
654C23—1186no—
655C23—2363no—
656C23—2363no—
657C23—2363no—
658C23C22×C4×D5913yes—
659Q8—1186no—
660Q8—1186no—
661Q8C4×D23614yes—
662D4—1186no—
663D4—1182no—
664D4—11812no—
665D4—11812no—
666D4—1186no—
667D4—1186no—
668D4—2366no—
669D4—2363no—
670D4—2363no—
671D4C4×D236112yes—
672C2×C4—43no—
673C2×C4—43no—
674C2×C4—591no—
675C2×C4—591no—
676C2×C4—593no—
677C2×C4—593no—
678C2×C4—1186no—
679C2×C4—1186no—
680C2×C4—1181no—
681C2×C4—1183no—
682C2×C4—1183no—
683C2×C4—1181no—
684C2×C4—1181no—
685C2×C4—1181no—
686C2×C4—1183no—
687C2×C4—1183no—
688C2×C4—1186no—
689C2×C4—1186no—
690C2×C4—1186no—
691C2×C4—1186no—
692C2×C4C22×C4×D5911yescharacteristic
693C2×C4C22×C4×D5911yescharacteristic
694C2×C4C22×C4×D5913yes—
695C2×C4C22×C4×D5913yes—
696C2×C4C22×C4×D5913yes—
697C2×C4C22×D23616yes—
698C2×C4C2×#1174568516yes—
699C2×C4C24×D5911yescharacteristic
700C8—21no—
701C8—23no—
702C8—1181no—
703C8—1183no—
704C8—1183no—
705C8—1181no—
706C8C22×D23612yes—
707C8C22×D23616yes—
708C22—23no—
709C22—23no—
710C22—592no—
711C22—1181no—
712C22—1181no—
713C22—1181no—
714C22—1183no—
715C22—1183no—
716C22—1181no—
717C22—1183no—
718C22—1183no—
719C22—1183no—
720C22—1183no—
721C22—1181no—
722C22—4726no—
723C22—23612no—
724C22C2×C4×D23616yes—
725C22C23×C4×D5911yescharacteristic
726C4—21no—
727C4—23no—
728C4—21no—
729C4—23no—
730C4—1181no—
731C4—1181no—
732C4—1183no—
733C4—1183no—
734C4C2×C4×D23616yes—
735C4C23×D23611yescharacteristic
736C4C22×#1174568511yescharacteristic
737C2—26no—
738C2—1182no—
739C2—2361no—
740C2—2363no—
741C2—2363no—
742C2C22×C4×D23611yescharacteristic
743C2#568×D5911yescharacteristic
744C2#2143880911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D59
commutator, socleC22×C59C24×C4
FittingC59×#2875C2
prime radical#41×D236C2
cosocleC2×C4×C59C25
hypercenter#2875D59
hypocenterC59#60146
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ #2875

Complements

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

NH ≅ G/Ntype
1. C2×#16838167C2semidirect
2. C2×#131×D59C2semidirect
4. #21432842C2semidirect
5. M16×D236C2semidirect
6. #21432824C2semidirect
7. #21432824C2semidirect
8. #21432815C2semidirect
9. #21432801C2semidirect
10. #21432792C2semidirect
11. C2×#16837475C2semidirect
12. #21432664C2semidirect
13. #21432543C2semidirect
14. #21432543C2semidirect
15. C59×#2875C2semidirect
19. C2×#14273735C22semidirect
20. C2×#14273735C22semidirect
23. C2×#14273733C22semidirect
24. C2×#14273733C22semidirect
26. C22×#11745659C22semidirect
27. C2×M16×D59C22semidirect
28. C2×M16×D59C22semidirect
29. C22×C8×D59C22semidirect
42. #16837481C22semidirect
43. #16837481C22semidirect
46. #16837475C22semidirect
47. #16837475C22semidirect
48. #16837475C22semidirect
49. #16837475C22semidirect
50. #16837475C22semidirect
51. #16837475C22semidirect
52. #16837475C22semidirect
53. #16837475C22semidirect
54. #16837475C22semidirect
55. C8×D236C22semidirect
56. C8×D236C22semidirect
57. #16837429C22semidirect
58. #16837429C22semidirect
59. #16837426C22semidirect
60. C2×C4⋊(C59⋊C8)C22semidirect
61. #16837370C22semidirect
62. #16837370C22semidirect
63. #16837368C22semidirect
64. #16837368C22semidirect
65. #16837365C22semidirect
66. #16837365C22semidirect
67. C2×(C2×D59)⋊C8C22semidirect
68. C2×(C2×D59)⋊C8C22semidirect
72. C59×#405C22semidirect
73. C59×#405C22semidirect
74. C4×M16×C59C22semidirect
75. C2×#97×C59C22semidirect
164. #131×C59D4semidirect
228. M16×C59C2×D4semidirect
230. C2×C8×C59C2×D4semidirect
353. C2×D59#568semidirect
379. #2875D59semidirect
444. #405C2×D59semidirect
445. #405C2×D59semidirect
446. C4×M16C2×D59semidirect
447. C2×#97C2×D59semidirect
448. C59#60146semidirect
474. #131D236semidirect
608. M16C2×D236semidirect
621. C2×C8C2×D236semidirect

Maximal subgroups

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

subgroupindex
C2×#168381672
C2×#131×D592
#41×D2362
#214328422
M16×D2362
#214328242
#214328152
#214328012
#214327922
C2×#168374752
#214326642
#214325432
C59×#28752
#6014659