Finite Group Databasebeta

← #28556830

Subgroups — #28556830

Order 15104.

942 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21438057C211yesmaximal, characteristic
2#21433110C211yesmaximal, characteristic, complemented
3#21422730C211yesmaximal, characteristic, complemented
4#21422728C211yesmaximal, characteristic, complemented
5#21422725C211yesmaximal, characteristic, complemented
6#21422719C211yesmaximal, characteristic, complemented
7#21422717C211yesmaximal, characteristic, complemented
8#21422714C211yesmaximal, characteristic, complemented
9#21422708C211yesmaximal, characteristic, complemented
10#21422704C211yesmaximal, characteristic, complemented
11#21422695C211yesmaximal, characteristic, complemented
12#21422693C211yesmaximal, characteristic, complemented
13#21422685C211yesmaximal, characteristic, complemented
14C2×#16837141C211yesmaximal, characteristic, complemented
15C59×#2923C211yesmaximal, characteristic, complemented
16#16838137C411yescharacteristic
17#16838125C411yescharacteristic
18#16838115—21no—
19#16838076—21no—
20#16838076—21no—
21D4×Dic118C411yescharacteristic
22#16838061C411yescharacteristic
23#16838061C411yescharacteristic
24#16838048C411yescharacteristic
25#16838048C411yescharacteristic
26#16838040—21no—
27D4×D236C411yescharacteristic
28#16838024—21no—
29#16837985—21no—
30#16837985—21no—
31#16837952C2211yescharacteristic
32#16837936C2211yescharacteristic
33#16837936C2211yescharacteristic
34#16837936C2211yescharacteristic
35C2×#14273715C2211yescharacteristic
36C2×#14273715C2211yescharacteristic
37#16837874—21no—
38#16837533—21no—
39#16837474—21no—
40#16837474—21no—
41D4×C59⋊C8—21no—
42#16837459C2211yescharacteristic, complemented
43#16837459C2211yescharacteristic, complemented
44#16837459C2211yescharacteristic, complemented
45C4×#11745664C2211yescharacteristic, complemented
46C2×#14273638C2211yescharacteristic, complemented
47C2×#14273638C2211yescharacteristic, complemented
48#16837143C2211yescharacteristic, complemented
49#16837143C2211yescharacteristic, complemented
50#16837143C2211yescharacteristic, complemented
51#16837143C2211yescharacteristic, complemented
52#16837141C2211yescharacteristic
53#16837141C2211yescharacteristic
54#16837141C2211yescharacteristic
55#16837141C2211yescharacteristic
56#16837141C2211yescharacteristic, complemented
57#16837141C2211yescharacteristic, complemented
58#16837141C2211yescharacteristic, complemented
59#16837141C2211yescharacteristic, complemented
60#16837141C2211yescharacteristic, complemented
61#16837141C2211yescharacteristic, complemented
62#16837141C2211yescharacteristic, complemented
63#16837141C2211yescharacteristic, complemented
64C4×#41×C59C2211yescharacteristic
65C59×#433—21no—
66C59×#433—21no—
67C59×#432C2211yescharacteristic, complemented
68C59×#432C2211yescharacteristic, complemented
69C59×#432C2211yescharacteristic, complemented
70C59×#432C2211yescharacteristic, complemented
71C59×#424—21no—
72C59×#408—21no—
73C4×M16×C59C2211yescharacteristic, complemented
74C2×#97×C59C2211yescharacteristic, complemented
75C2×#11745685C2×C411yescharacteristic
76C2×#11745685C2×C411yescharacteristic
77C22×Dic118C2×C411yescharacteristic
78C22×Dic118C2×C411yescharacteristic
79C22×D236C2×C411yescharacteristic
80C22×D236C2×C411yescharacteristic
81C2×D4×D59—21no—
82C2×#11745664—21no—
83C22×C59⋊C8—21no—
84C22×C59⋊C8—21no—
85#14273727C2×C411yescharacteristic
86#14273726—21no—
87#14273724C2×C411yescharacteristic
88#14273722—21no—
89#14273722—21no—
90#14273721—21no—
91#14273721—21no—
92#14273721—21no—
93#14273719C2311yescharacteristic
94#14273716—21no—
95#14273715—21no—
96#14273715—21no—
97#14273715—21no—
98#14273715—21no—
99#14273715C2×C411yescharacteristic
100#14273715C2×C411yescharacteristic
101#14273715C2×C411yescharacteristic
102#14273715C2×C411yescharacteristic
103#14273715C2311yescharacteristic
104#14273715C2311yescharacteristic
105#14273715C2311yescharacteristic
106#14273713—21no—
107#14273713—21no—
108#14273712—21no—
109#14273712—21no—
110#14273712—21no—
111#14273712—21no—
112#14273710—21no—
113#14273710—21no—
114#14273710—21no—
115#14273706C2×C411yescharacteristic
116#14273706C2×C411yescharacteristic
117#14273706C2×C411yescharacteristic
118#14273705—21no—
119#14273705—21no—
120#14273704—21no—
121#14273704—21no—
122#14273703—21no—
123#14273702—21no—
124#14273701—21no—
125#14273701—21no—
126#14273701C2×C411yescharacteristic
127#14273701C2×C411yescharacteristic
128#14273701C2×C411yescharacteristic
129#14273700—21no—
130#14273700—21no—
131#14273699—21no—
132#14273699—21no—
133#14273697—21no—
134#14273697—21no—
135#14273695—21no—
136#14273695—21no—
137C4×Dic118C2×C411yescharacteristic
138C4×Dic118C2×C411yescharacteristic
139C4×Dic118C2×C411yescharacteristic
140C4×D236—21no—
141C4×D236—21no—
142C4×D236C2×C411yescharacteristic
143C4×D236C2×C411yescharacteristic
144C4×D236C2×C411yescharacteristic
145D4×Dic59—21no—
146#14273689—21no—
147C4×C22⋊D59—21no—
148C4×C22⋊D59—21no—
149C4×C22⋊D59—21no—
150(C22⋊D59)⋊C4—21no—
151(C22⋊D59)⋊C4—21no—
152#14273685—21no—
153#14273684—21no—
154#14273684—21no—
155#14273684—21no—
156C2×(C2×D59)⋊C4—21no—
157C2×(C2×D59)⋊C4—21no—
158C2×(C2×D59)⋊C4—21no—
159C2×(C2×D59)⋊C4—21no—
160C22⋊C4×D59—21no—
161C22⋊C4×D59—21no—
162C4⋊(C59⋊C8)—21no—
163C4⋊(C59⋊C8)—21no—
164C4⋊(C59⋊C8)—21no—
165C22⋊(C59⋊C8)—21no—
166C22⋊(C59⋊C8)—21no—
167C22⋊(C59⋊C8)—21no—
168#14273638—21no—
169#14273638—21no—
170#14273638C2311yescharacteristic
171#14273638C2311yescharacteristic
172#14273638C2311yescharacteristic
173#14273638C2311yescharacteristic
174C4×C59⋊C8—21no—
175C2×#41×C59D411yescharacteristic
176C2×M16×C59—21no—
177C22×C8×C59—21no—
178C4×Q8×C59C2×C411yescharacteristic
179C4×Q8×C59D411yescharacteristic
180C4×D4×C59C2×C411yescharacteristic
181C4×D4×C59C2×C411yescharacteristic
182C4×D4×C59C2×C411yescharacteristic
183C4×D4×C59D411yescharacteristic
184C4×D4×C59D411yescharacteristic
185C4×D4×C59D411yescharacteristic
186#117×C59D411yescharacteristic
187#117×C59D411yescharacteristic
188#117×C59D411yescharacteristic
189C2×C42×C59C2311yescharacteristic
190C2×C42×C59C2311yescharacteristic
191C2×C42×C59C2311yescharacteristic
192C4⋊C8×C59—21no—
193C4⋊C8×C59—21no—
194C4⋊C8×C59—21no—
195C4⋊C8×C59—21no—
196C22⋊C8×C59—21no—
197C22⋊C8×C59—21no—
198C22⋊C8×C59—21no—
199C22⋊C8×C59—21no—
200#97×C59—21no—
201#97×C59C2311yescharacteristic
202#97×C59C2311yescharacteristic
203#97×C59C2311yescharacteristic
204#97×C59C2311yescharacteristic
205C4×C8×C59—21no—
206C23×D59—21no—
207C23×D59—21no—
208#41×C59—42no—
209C2×Q8×C59C22⋊C411yescharacteristic
210C2×D4×C59C22⋊C411yescharacteristic
211C2×D4×C59C22⋊C411yescharacteristic
212C2×D4×C59C22⋊C411yescharacteristic
213C22×C4×C59C22×C411yescharacteristic
214C22×C4×C59C22×C411yescharacteristic
215C22×C4×C59C22×C411yescharacteristic
216C22×C4×C59C2×D411yescharacteristic
217C22×C4×C59C2×D411yescharacteristic
218C22×C4×C59C2×D411yescharacteristic
219C22×C4×C59C2×D411yescharacteristic
220C22×C4×C59C2×D411yescharacteristic
221C22×C4×C59C2×D411yescharacteristic
222C2×C22⋊D59—21no—
223C2×C22⋊D59—21no—
224C2×C22⋊D59—21no—
225C2×C22⋊D59—21no—
226C2×C22⋊D59—21no—
227C22×Dic59—21no—
228C22×Dic59—21no—
229D4×D59—44no—
230#11745685—81no—
231#11745685—81no—
232C2×D236—21no—
233C2×D236—21no—
234C2×D236—21no—
235C2×D236—21no—
236C2×D236—81no—
237C2×D236—81no—
238C2×D236C22×C411yescharacteristic
239C2×D236C22×C411yescharacteristic
240C2×D236C22×C411yescharacteristic
241C2×C4×D59—21no—
242C2×C4×D59—21no—
243C2×C4×D59—21no—
244C2×C4×D59—21no—
245C2×C4×D59—21no—
246C2×Dic118—21no—
247C2×Dic118—21no—
248C2×Dic118—81no—
249C2×Dic118—81no—
250C2×Dic118C22×C411yescharacteristic
251C2×Dic118C22×C411yescharacteristic
252C2×Dic118C22×C411yescharacteristic
253M16×C59—42no—
254C2×C8×C59—21no—
255C2×C8×C59—21no—
256C2×C8×C59—21no—
257C2×C8×C59—21no—
258C2×C8×C59—42no—
259C4⋊C4×C59C22⋊C411yescharacteristic
260C4⋊C4×C59C22⋊C411yescharacteristic
261C4⋊C4×C59C22⋊C411yescharacteristic
262C4⋊C4×C59C22⋊C411yescharacteristic
263C4⋊C4×C59C22⋊C411yescharacteristic
264C4⋊C4×C59C22⋊C411yescharacteristic
265C22⋊C4×C59C22⋊C411yescharacteristic
266C22⋊C4×C59C22⋊C411yescharacteristic
267C22⋊C4×C59C22⋊C411yescharacteristic
268C22⋊C4×C59C22⋊C411yescharacteristic
269C22⋊C4×C59C22⋊C411yescharacteristic
270C22⋊C4×C59C22⋊C411yescharacteristic
271C42×C59C22×C411yescharacteristic
272C42×C59C22×C411yescharacteristic
273C42×C59C22×C411yescharacteristic
274C42×C59C2×D411yescharacteristic
275C42×C59C2×D411yescharacteristic
276C42×C59C2×D411yescharacteristic
277C42×C59C2×D411yescharacteristic
278C42×C59C2×D411yescharacteristic
279C42×C59C2×D411yescharacteristic
280C42×C59C2411yescharacteristic
281C22⋊Dic59—21no—
282C22⋊Dic59—21no—
283C22⋊Dic59—21no—
284(C2×D59)⋊C4—21no—
285(C2×D59)⋊C4—21no—
286(C2×D59)⋊C4—21no—
287(C2×D59)⋊C4—21no—
288(C2×D59)⋊C4—21no—
289(C2×D59)⋊C4—21no—
290(C2×D59)⋊C4—21no—
291(C2×D59)⋊C4—21no—
292(C2×D59)⋊C4—21no—
293(C2×D59)⋊C4—21no—
294(C2×D59)⋊C4—21no—
295(C2×D59)⋊C4—21no—
296(C2×D59)⋊C4—21no—
297(C2×D59)⋊C4—21no—
298(C2×D59)⋊C4—21no—
299(C2×D59)⋊C4—21no—
300(C2×D59)⋊C4—21no—
301(C2×D59)⋊C4—21no—
302(C2×D59)⋊C4—21no—
303(C2×D59)⋊C4—21no—
304C4⋊Dic59—21no—
305C4⋊Dic59—21no—
306C4⋊Dic59C22×C411yescharacteristic
307C4⋊Dic59C22×C411yescharacteristic
308Dic59⋊C4—21no—
309Dic59⋊C4—21no—
310Dic59⋊C4—21no—
311Dic59⋊C4—21no—
312Dic59⋊C4—21no—
313Dic59⋊C4—21no—
314Dic59⋊C4—21no—
315Dic59⋊C4—21no—
316C4×Dic59—21no—
317C4×Dic59—21no—
318C4×Dic59—21no—
319#11745664—42no—
320C2×C59⋊C8—21no—
321C2×C59⋊C8—21no—
322C2×C59⋊C8—21no—
323C2×C59⋊C8—21no—
324C2×C59⋊C8—42no—
325C2×C59⋊C8—42no—
326C23×C59C2×C22⋊C411yescharacteristic
327C23×C59C2×C22⋊C411yescharacteristic
328C23×C59C2×C22⋊C411yescharacteristic
329C22×D59—21no—
330C22×D59—21no—
331C22×D59—21no—
332C22×D59—42no—
333C22×D59—42no—
334C22×D59—81no—
335C22×D59—81no—
336C22×D59—81no—
337C22×D59—81no—
338Q8×C59—41no—
339D4×C59—22no—
340D4×C59—22no—
341D4×C59—41no—
342C2×C4×C59—22no—
343C2×C4×C59—41no—
344C2×C4×C59—41no—
345C2×C4×C59—41no—
346C2×C4×C59—41no—
347C2×C4×C59—41no—
348C2×C4×C59—41no—
349C2×C4×C59—41no—
350C2×C4×C59—41no—
351C2×C4×C59C2×C22⋊C411yescharacteristic
352C2×C4×C59C2×C22⋊C411yescharacteristic
353C2×C4×C59C2×C22⋊C411yescharacteristic
354C2×C4×C59C2×C22⋊C411yescharacteristic
355C2×C4×C59C2×C22⋊C411yescharacteristic
356C2×C4×C59C2×C22⋊C411yescharacteristic
357C2×C4×C59C2×C22⋊C411yescharacteristic
358C2×C4×C59C2×C22⋊C411yescharacteristic
359C2×C4×C59C2×C22⋊C411yescharacteristic
360C2×C4×C59C23×C411yescharacteristic
361C2×C4×C59C22×D411yescharacteristic
362C2×C4×C59C22×D411yescharacteristic
363C22⋊D59—42no—
364C22⋊D59—42no—
365C22⋊D59—81no—
366C22⋊D59—81no—
367C22⋊D59—81no—
368C2×Dic59—21no—
369C2×Dic59—21no—
370C2×Dic59—21no—
371C2×Dic59—21no—
372C2×Dic59—21no—
373C2×Dic59—81no—
374C2×Dic59—81no—
375D236—41no—
376D236—41no—
377D236—41no—
378D236—42no—
379D236—81no—
380D236—81no—
381D236—81no—
382C4×D59—42no—
383C4×D59—81no—
384C4×D59—81no—
385C4×D59—81no—
386C4×D59—81no—
387Dic118—41no—
388Dic118—41no—
389Dic118—41no—
390Dic118—81no—
391Dic118—81no—
392C8×C59—41no—
393C8×C59—41no—
394C8×C59—41no—
395C8×C59—41no—
396C59⋊C8—22no—
397C59⋊C8—41no—
398C59⋊C8—41no—
399C59⋊C8—41no—
400#17679—591nomaximal, Sylow
401C22×C59—21no—
402C22×C59—21no—
403C22×C59—21no—
404C22×C59—21no—
405C22×C59—21no—
406C22×C59—21no—
407C22×C59—21no—
408C22×C59—21no—
409C22×C59#42112yes—
410C22×C59C22×C22⋊C411yescharacteristic
411C2×D59—41no—
412C2×D59—41no—
413C2×D59—41no—
414C2×D59—41no—
415C2×D59—41no—
416C2×D59—41no—
417C2×D59—41no—
418C2×D59—41no—
419C2×D59—41no—
420C2×D59—162no—
421C2×D59—162no—
422C4×C59—21no—
423C4×C59—21no—
424C4×C59—21no—
425C4×C59—21no—
426C4×C59—21no—
427C4×C59—21no—
428C4×C59—21no—
429C4×C59—21no—
430C4×C59—21no—
431C4×C59—21no—
432C4×C59—21no—
433C4×C59—21no—
434Dic59—41no—
435Dic59—41no—
436Dic59—41no—
437Dic59—41no—
438Dic59—41no—
439#3514—591no—
440#2970—591no—
441#2923D5911yescharacteristic, complemented
442#1536—591no—
443#1535—591no—
444#1535—591no—
445#1533—591no—
446#1532—591no—
447#1532—591no—
448#1530—591no—
449#1529—591no—
450#1527—591no—
451#1527—591no—
452#1524—591no—
453C2×#329—591no—
454C2×C59—22no—
455C2×C59—41no—
456C2×C59—41no—
457C2×C59#288811yescharacteristic
458C2×C59C2×#42111yescharacteristic
459C2×C59#290111yescharacteristic
460D59—81no—
461D59—81no—
462D59—81no—
463#559—591no—
464#556—591no—
465#555—1181no—
466#551—1181no—
467#551—1181no—
468D4×Q8—591no—
469#548—591no—
470#548—591no—
471#546—591no—
472#546—591no—
473#546—1181no—
474D42—591no—
475#542—1181no—
476#538—1181no—
477#538—1181no—
478#532—591no—
479#529—591no—
480#529—591no—
481#529—591no—
482C2×#124—591no—
483C2×#124—591no—
484#518—1181no—
485C4×#41C2×D5911yescharacteristic
486#446—1181no—
487#435—1181no—
488#435—1181no—
489C8×D4—1181no—
490#433—21no—
491#433—21no—
492#432—591no—
493#432—591no—
494#432—591no—
495#432C2×D5911yescharacteristic, complemented
496#432C2×D5911yescharacteristic, complemented
497#432C2×D5911yescharacteristic, complemented
498#432C2×D5911yescharacteristic, complemented
499#424—21no—
500#408—21no—
501C4×M16—591no—
502C4×M16C2×D5911yescharacteristic, complemented
503C2×#97—591no—
504C2×#97—591no—
505C2×#97C2×D5911yescharacteristic, complemented
506#330—591no—
507#330—591no—
508#330—591no—
509#330—591no—
510#329—591no—
511#329—591no—
512#329—591no—
513#329—591no—
514#329—591no—
515#329—591no—
516#329—591no—
517#329—591no—
518#329—591no—
519#329—591no—
520#329—591no—
521#329—591no—
522C59#1767911yescharacteristic, complemented, Sylow
523C2×#41—591no—
524C2×#41—591no—
525C2×#41C22⋊D5911yescharacteristic
526C22×Q8—591no—
527C22×Q8—591no—
528C22×D4—591no—
529C22×D4—591no—
530C22×D4—1181no—
531C2×M16—21no—
532C2×M16—1181no—
533C22×C8—21no—
534C22×C8—1181no—
535C22×C8—1181no—
536C4⋊Q8—591no—
537C4⋊Q8—1181no—
538#127—591no—
539#126—1181no—
540#126—1181no—
541#126—1181no—
542#126—1181no—
543#126—1181no—
544#125—591no—
545#124—591no—
546#124—591no—
547#124—591no—
548#124—591no—
549#124—591no—
550#124—591no—
551#124—591no—
552#124—1181no—
553#124—1181no—
554#124—1181no—
555#124—1181no—
556#124—1181no—
557#124—1181no—
558#124—1181no—
559#123—1181no—
560#123—1181no—
561#123—1181no—
562#123—1181no—
563#123—1181no—
564#123—1181no—
565#123—1181no—
566C22⋊Q8—591no—
567C22⋊Q8—591no—
568C22⋊Q8—591no—
569C22⋊Q8—1181no—
570C22⋊Q8—1181no—
571C22⋊Q8—1181no—
572C22⋊Q8—1181no—
573C22⋊Q8—1181no—
574#121—591no—
575#121—591no—
576#121—591no—
577#121—1181no—
578#121—1181no—
579#121—1181no—
580#121—1181no—
581#121—1181no—
582#121—1181no—
583#121—1181no—
584#120—1181no—
585#120—1181no—
586#120—1181no—
587#120—1181no—
588C4×Q8—591no—
589C4×Q8—591no—
590C4×Q8—591no—
591C4×Q8C4×D5911yescharacteristic
592C4×Q8D23611yescharacteristic
593C4×D4—591no—
594C4×D4—591no—
595C4×D4—591no—
596C4×D4—1181no—
597C4×D4—1181no—
598C4×D4—1181no—
599C4×D4—1181no—
600C4×D4—1181no—
601C4×D4—1181no—
602C4×D4—1181no—
603C4×D4—1181no—
604C4×D4—1181no—
605C4×D4C4×D5911yescharacteristic
606C4×D4C4×D5911yescharacteristic
607C4×D4C4×D5911yescharacteristic
608C4×D4D23611yescharacteristic
609C4×D4D23611yescharacteristic
610C4×D4D23611yescharacteristic
611#117—1181no—
612#117—1181no—
613#117—1181no—
614#117—1181no—
615#117C22⋊D5911yescharacteristic
616#117C22⋊D5911yescharacteristic
617#117C22⋊D5911yescharacteristic
618C2×C22⋊C4—1181no—
619C2×C22⋊C4—1181no—
620C2×C22⋊C4—1181no—
621C2×C22⋊C4—1181no—
622C2×C22⋊C4—1181no—
623C2×C22⋊C4—1181no—
624C2×C42C22×D5911yescharacteristic
625C2×C42C22×D5911yescharacteristic
626C2×C42C22×D5911yescharacteristic
627C4⋊C8—21no—
628C4⋊C8—21no—
629C4⋊C8—21no—
630C4⋊C8—21no—
631C4⋊C8—1181no—
632C4⋊C8—1181no—
633C4⋊C8—1181no—
634C22⋊C8—21no—
635C22⋊C8—21no—
636C22⋊C8—21no—
637C22⋊C8—21no—
638C22⋊C8—1181no—
639C22⋊C8—1181no—
640C22⋊C8—1181no—
641#97—21no—
642#97—591no—
643#97—591no—
644#97—591no—
645#97—591no—
646#97—1181no—
647#97—1181no—
648#97C22×D5911yescharacteristic
649#97C22×D5911yescharacteristic
650#97C22×D5911yescharacteristic
651#97C22×D5911yescharacteristic
652C4×C8—21no—
653C4×C8—1181no—
654C24—1181no—
655C24—1181no—
656#41—42no—
657#41—4721no—
658#41—4721no—
659C2×Q8—591no—
660C2×Q8—591no—
661C2×Q8—591no—
662C2×Q8—1181no—
663C2×Q8—1181no—
664C2×Q8—4721no—
665C2×Q8—4721no—
666C2×Q8(C2×D59)⋊C411yescharacteristic
667C2×D4—591no—
668C2×D4—591no—
669C2×D4—591no—
670C2×D4—1181no—
671C2×D4—1181no—
672C2×D4—1181no—
673C2×D4—1181no—
674C2×D4—1181no—
675C2×D4—1181no—
676C2×D4—1181no—
677C2×D4—1181no—
678C2×D4—1181no—
679C2×D4—4721no—
680C2×D4—4721no—
681C2×D4—2364no—
682C2×D4(C2×D59)⋊C411yescharacteristic
683C2×D4(C2×D59)⋊C411yescharacteristic
684C2×D4(C2×D59)⋊C411yescharacteristic
685C22×C4—1181no—
686C22×C4—1181no—
687C22×C4—1181no—
688C22×C4—1181no—
689C22×C4—1181no—
690C22×C4—1181no—
691C22×C4—1181no—
692C22×C4C2×C4×D5911yescharacteristic
693C22×C4C2×C4×D5911yescharacteristic
694C22×C4C2×C4×D5911yescharacteristic
695C22×C4C2×D23611yescharacteristic
696C22×C4C2×D23611yescharacteristic
697C22×C4C2×D23611yescharacteristic
698C22×C4C2×C22⋊D5911yescharacteristic
699C22×C4C2×C22⋊D5911yescharacteristic
700C22×C4C2×C22⋊D5911yescharacteristic
701M16—42no—
702M16—2362no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—42no—
708C2×C8—1181no—
709C2×C8—1181no—
710C2×C8—1181no—
711C2×C8—1181no—
712C2×C8—2362no—
713C2×C8—2362no—
714C4⋊C4—591no—
715C4⋊C4—591no—
716C4⋊C4—1181no—
717C4⋊C4—1181no—
718C4⋊C4—1181no—
719C4⋊C4—1181no—
720C4⋊C4—1181no—
721C4⋊C4—1181no—
722C4⋊C4—1181no—
723C4⋊C4—1181no—
724C4⋊C4—1181no—
725C4⋊C4—1181no—
726C4⋊C4(C2×D59)⋊C411yescharacteristic
727C4⋊C4(C2×D59)⋊C411yescharacteristic
728C4⋊C4(C2×D59)⋊C411yescharacteristic
729C4⋊C4(C2×D59)⋊C411yescharacteristic
730C4⋊C4(C2×D59)⋊C411yescharacteristic
731C4⋊C4(C2×D59)⋊C411yescharacteristic
732C22⋊C4—1181no—
733C22⋊C4—1181no—
734C22⋊C4—1181no—
735C22⋊C4—1181no—
736C22⋊C4—1181no—
737C22⋊C4—1181no—
738C22⋊C4—1181no—
739C22⋊C4—1181no—
740C22⋊C4—1181no—
741C22⋊C4—1181no—
742C22⋊C4—1181no—
743C22⋊C4—1181no—
744C22⋊C4—1181no—
745C22⋊C4—1181no—
746C22⋊C4—1181no—
747C22⋊C4—1181no—
748C22⋊C4—1181no—
749C22⋊C4—1181no—
750C22⋊C4—1181no—
751C22⋊C4—1181no—
752C22⋊C4—1181no—
753C22⋊C4—1181no—
754C22⋊C4—1181no—
755C22⋊C4(C2×D59)⋊C411yescharacteristic
756C22⋊C4(C2×D59)⋊C411yescharacteristic
757C22⋊C4(C2×D59)⋊C411yescharacteristic
758C22⋊C4(C2×D59)⋊C411yescharacteristic
759C22⋊C4(C2×D59)⋊C411yescharacteristic
760C22⋊C4(C2×D59)⋊C411yescharacteristic
761C42—1181no—
762C42—1181no—
763C42—1181no—
764C42C2×C4×D5911yescharacteristic
765C42C2×C4×D5911yescharacteristic
766C42C2×C4×D5911yescharacteristic
767C42C2×D23611yescharacteristic
768C42C2×D23611yescharacteristic
769C42C2×D23611yescharacteristic
770C42C2×C22⋊D5911yescharacteristic
771C42C2×C22⋊D5911yescharacteristic
772C42C2×C22⋊D5911yescharacteristic
773C42C23×D5911yescharacteristic
774C23—1181no—
775C23—1181no—
776C23—1181no—
777C23—4721no—
778C23—4721no—
779C23—4721no—
780C23—4721no—
781C23—2362no—
782C23—2362no—
783C23C2×(C2×D59)⋊C411yescharacteristic
784C23C2×(C2×D59)⋊C411yescharacteristic
785C23C2×(C2×D59)⋊C411yescharacteristic
786Q8—41no—
787Q8—4721no—
788Q8—4721no—
789Q8—2361no—
790Q8—2361no—
791Q8—2361no—
792D4—22no—
793D4—22no—
794D4—41no—
795D4—4721no—
796D4—4721no—
797D4—4721no—
798D4—4721no—
799D4—4721no—
800D4—4721no—
801D4—2361no—
802D4—2361no—
803D4—2361no—
804D4—2362no—
805D4—2362no—
806D4—2362no—
807C2×C4—22no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—1181no—
817C2×C4—1181no—
818C2×C4—1181no—
819C2×C4—1181no—
820C2×C4—1181no—
821C2×C4—4721no—
822C2×C4—4721no—
823C2×C4—4721no—
824C2×C4—4721no—
825C2×C4—4721no—
826C2×C4—4721no—
827C2×C4—2362no—
828C2×C4C2×(C2×D59)⋊C411yescharacteristic
829C2×C4C2×(C2×D59)⋊C411yescharacteristic
830C2×C4C2×(C2×D59)⋊C411yescharacteristic
831C2×C4C2×(C2×D59)⋊C411yescharacteristic
832C2×C4C2×(C2×D59)⋊C411yescharacteristic
833C2×C4C2×(C2×D59)⋊C411yescharacteristic
834C2×C4C2×(C2×D59)⋊C411yescharacteristic
835C2×C4C2×(C2×D59)⋊C411yescharacteristic
836C2×C4C2×(C2×D59)⋊C411yescharacteristic
837C2×C4C22×C4×D5911yescharacteristic
838C2×C4C22×C22⋊D5911yescharacteristic
839C2×C4C22×D23611yescharacteristic
840C8—41no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—1182no—
845C8—2361no—
846C8—2361no—
847C8—2361no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—9442no—
857C22—9442no—
858C22—2361no—
859C22—2361no—
860C22—2361no—
861C22—2361no—
862C22—2361no—
863C22—2361no—
864C22—2361no—
865C22—2361no—
866C22—2361no—
867C22#1683742012yes—
868C22C22×(C2×D59)⋊C411yescharacteristic
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—21no—
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—21no—
880C4—21no—
881C4—2361no—
882C4—2361no—
883C4—2361no—
884C4—2361no—
885C4—2361no—
886C2—22no—
887C2—41no—
888C2—41no—
889C2—4721no—
890C2—4721no—
891C2—4721no—
892C2#2143257411yescharacteristic
893C2C2×#1683742011yescharacteristic
894C2#2143264111yescharacteristic
subgroupG/H
centerC22C22×(C2×D59)⋊C4
commutatorC2×C4×C59C23×C4
FrattiniC42C23×D59
FittingC59×#2923C2
socleC22×C59C22×C22⋊C4
prime radical#21438057C2
cosocleC42×C59C24
hypercenter#2923D59
hypocenterC59#17679
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2923

Complements

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

NH ≅ G/Ntype
2. #21433110C2semidirect
3. #21422730C2semidirect
4. #21422728C2semidirect
5. #21422725C2semidirect
6. #21422719C2semidirect
7. #21422717C2semidirect
8. #21422714C2semidirect
9. #21422708C2semidirect
10. #21422704C2semidirect
11. #21422695C2semidirect
12. #21422693C2semidirect
13. #21422685C2semidirect
14. C2×#16837141C2semidirect
15. C59×#2923C2semidirect
42. #16837459C22semidirect
43. #16837459C22semidirect
44. #16837459C22semidirect
45. C4×#11745664C22semidirect
46. C2×#14273638C22semidirect
47. C2×#14273638C22semidirect
48. #16837143C22semidirect
49. #16837143C22semidirect
50. #16837143C22semidirect
51. #16837143C22semidirect
56. #16837141C22semidirect
57. #16837141C22semidirect
58. #16837141C22semidirect
59. #16837141C22semidirect
60. #16837141C22semidirect
61. #16837141C22semidirect
62. #16837141C22semidirect
63. #16837141C22semidirect
67. C59×#432C22semidirect
68. C59×#432C22semidirect
69. C59×#432C22semidirect
70. C59×#432C22semidirect
73. C4×M16×C59C22semidirect
74. C2×#97×C59C22semidirect
441. #2923D59semidirect
495. #432C2×D59semidirect
496. #432C2×D59semidirect
497. #432C2×D59semidirect
498. #432C2×D59semidirect
502. C4×M16C2×D59semidirect
505. C2×#97C2×D59semidirect
522. C59#17679semidirect

Maximal subgroups

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

subgroupindex
#214380572
#214331102
#214227302
#214227282
#214227252
#214227192
#214227172
#214227142
#214227082
#214227042
#214226952
#214226932
#214226852
C2×#168371412
C59×#29232
#1767959