Finite Group Databasebeta

← #29460196

Subgroups — #29460196

Order 15104.

2196 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837952C211yesmaximal, characteristic, complemented
2C2×#16837936C211yesmaximal, characteristic, complemented
3#21435135C214yesmaximal, complemented
4#21435125C212yesmaximal, complemented
5#21435116C212yesmaximal, complemented
6#21435074C214yesmaximal, complemented
7#21435063C214yesmaximal, complemented
8#21434562C212yesmaximal, complemented
9#21434497C212yesmaximal, complemented
10#21433570C212yesmaximal, complemented
11#21433562C212yesmaximal, complemented
12#21433358C212yesmaximal, complemented
13#21433350C212yesmaximal, complemented
14C59×#2920C211yesmaximal, characteristic, complemented
15C22×#11745685C2212yes—
16C2×#14273760C2214yescomplemented
17C2×#14273755C2214yescomplemented
18#16837952—21no—
19#16837952—21no—
20#16837952—21no—
21#16837952—21no—
22#16837952C2212yes—
23#16837952C2212yes—
24#16837952C2212yescomplemented
25#16837952C2212yescomplemented
26C2×#14273727C2211yescharacteristic, complemented
27C2×#14273724C2211yescharacteristic, complemented
28#16837936—21no—
29#16837936—21no—
30#16837936—21no—
31#16837936—21no—
32#16837936C2212yes—
33#16837936C2212yes—
34#16837936C2212yescomplemented
35#16837936C2212yescomplemented
36C2×#14273721—21no—
37C2×#14273719C2211yescharacteristic, complemented
38C2×#14273715C2211yescharacteristic, complemented
39C2×#14273715C2212yescomplemented
40C2×#14273710—21no—
41C2×#14273706C2211yescharacteristic
42C2×#14273701—21no—
43C2×#14273701—21no—
44C2×#14273701C2211yescharacteristic
45C2×C4×Dic118C2211yescharacteristic, complemented
46C2×C4×D236—21no—
47C2×C4×D236—21no—
48C2×C4×D236C2211yescharacteristic, complemented
49C2×C4×C22⋊D59—21no—
50C2×#14273684—21no—
51#16837796C2214yescomplemented
52#16837791C2214yescomplemented
53#16837786C2218yescomplemented
54#16837771C2214yescomplemented
55#16837767C2214yescomplemented
56#16837757C2218yescomplemented
57#16837625C2218yescomplemented
58#16837618C2218yescomplemented
59#16837613C2214yescomplemented
60#16837608C2214yescomplemented
61#16837603C2214yescomplemented
62#16837598C2214yescomplemented
63#16837566C2218yescomplemented
64#16837560C2214yescomplemented
65#16837555C2214yescomplemented
66#16837549C2218yescomplemented
67#16837543C2214yes—
68#16837538C2214yes—
69#16837404C2214yescomplemented
70#16837404C2214yescomplemented
71C22×C42×C59C2211yescharacteristic
72C59×#432C2212yescomplemented
73C59×#432C2212yescomplemented
74C59×#431C2212yescomplemented
75C59×#431C2212yescomplemented
76C59×#423C2212yescomplemented
77C59×#407C2212yes—
78C4×M16×C59C2212yescomplemented
79C2×#11745685—22no—
80C2×#11745685—22no—
81C2×#11745685—48no—
82C2×#11745685C2314yes—
83C2×#11745685C2314yes—
84C22×Dic118C2311yescharacteristic
85C22×Dic118C2312yes—
86C22×D236—21no—
87C22×D236—21no—
88C22×D236C2311yescharacteristic
89C22×D236C2312yes—
90C22×C22⋊D59—22no—
91C22×C22⋊D59—21no—
92C22×C4×D59—22no—
93C22×C4×D59—21no—
94#14273760—48no—
95#14273755—48no—
96C2×Dic236C2318yes—
97C2×#11745660C2318yes—
98C2×#11745660C2318yes—
99C2×D472C2318yes—
100#14273727—21no—
101#14273727—21no—
102#14273727C2312yes—
103#14273727C2312yes—
104#14273724—21no—
105#14273724—21no—
106#14273724C2312yes—
107#14273724C2312yes—
108#14273721—22no—
109#14273721—22no—
110#14273721—22no—
111#14273721—22no—
112#14273719—21no—
113#14273719—21no—
114#14273719C2312yes—
115#14273719C2312yes—
116#14273715—21no—
117#14273715—21no—
118#14273715—22no—
119#14273715—22no—
120#14273715C2312yes—
121#14273715C2312yes—
122#14273715C2314yes—
123#14273715C2314yes—
124#14273710—22no—
125#14273710—22no—
126#14273710—22no—
127#14273710—22no—
128#14273706—21no—
129#14273706—21no—
130#14273706C2312yes—
131#14273706C2312yes—
132#14273701—22no—
133#14273701—22no—
134#14273701—22no—
135#14273701—22no—
136#14273701—22no—
137#14273701—22no—
138#14273701—22no—
139#14273701—22no—
140#14273701—21no—
141#14273701—21no—
142#14273701C2312yes—
143#14273701C2312yes—
144C4×Dic118—21no—
145C4×Dic118—21no—
146C4×Dic118C2312yes—
147C4×Dic118C2312yes—
148C4×D236—21no—
149C4×D236—21no—
150C4×D236—22no—
151C4×D236—22no—
152C4×D236—22no—
153C4×D236—22no—
154C4×D236—22no—
155C4×D236—22no—
156C4×D236—22no—
157C4×D236—22no—
158C4×D236C2312yes—
159C4×D236C2312yes—
160C4×C22⋊D59—22no—
161C4×C22⋊D59—22no—
162C4×C22⋊D59—22no—
163C4×C22⋊D59—22no—
164#14273684—22no—
165#14273684—22no—
166#14273684—22no—
167#14273684—22no—
168C2×C4⋊Dic59—21no—
169C2×C4⋊Dic59—21no—
170C2×C4⋊Dic59C2311yescharacteristic
171C2×C4⋊Dic59C2311yescharacteristic
172C2×Dic59⋊C4—21no—
173C2×Dic59⋊C4—21no—
174C2×Dic59⋊C4—21no—
175C2×Dic59⋊C4—21no—
176C2×C22⋊Dic59—21no—
177C2×(C2×D59)⋊C4—22no—
178C2×(C2×D59)⋊C4—22no—
179C2×(C2×D59)⋊C4—21no—
180C2×(C2×D59)⋊C4—21no—
181C2×(C2×D59)⋊C4—21no—
182C2×(C2×D59)⋊C4—21no—
183C2×C4×Dic59—21no—
184#14273652C2318yes—
185#14273652C2318yes—
186#14273649C2318yes—
187#14273649C2318yes—
188C23×C4×C59D411yescharacteristic
189C23×C4×C59D411yescharacteristic
190C23×C4×C59C2311yescharacteristic
191C2×M16×C59C2314yes—
192C2×C42×C59D411yescharacteristic
193C2×C42×C59D411yescharacteristic
194C2×C42×C59D411yescharacteristic
195C2×C42×C59D411yescharacteristic
196C2×C42×C59D411yescharacteristic
197C2×C42×C59D411yescharacteristic
198C2×C42×C59C2311yescharacteristic
199C2×C42×C59C2311yescharacteristic
200C2×C42×C59C2311yescharacteristic
201C2×C42×C59C2311yescharacteristic
202C2×C42×C59C2311yescharacteristic
203C2×C42×C59C2311yescharacteristic
204C4⋊C8×C59C2314yes—
205C4⋊C8×C59C2314yes—
206C22⋊C8×C59C2314yes—
207C22⋊C8×C59C2314yes—
208#97×C59C2314yes—
209C4×C8×C59C2314yes—
210C24×C59C2×D411yescharacteristic
211C23×D59—21no—
212C23×D59—22no—
213C22×C4×C59—24no—
214C22×C4×C59—42no—
215C22×C4×C59—42no—
216C22×C4×C59C2×D411yescharacteristic
217C22×C4×C59C2×D411yescharacteristic
218C22×C4×C59C2×D411yescharacteristic
219C22×C4×C59C2×D411yescharacteristic
220C22×C4×C59C2×D411yescharacteristic
221C22×C4×C59C2×D411yescharacteristic
222C22×C4×C59C2×D411yescharacteristic
223C22×C4×C59C2×D411yescharacteristic
224C22×C4×C59C2×D411yescharacteristic
225C22×C4×C59C2×D411yescharacteristic
226C22×C4×C59C2×D411yescharacteristic
227C22×C4×C59C2×D411yescharacteristic
228C22×C4×C59C2×D411yescharacteristic
229C22×C4×C59C2×D411yescharacteristic
230C22×C4×C59C2×D411yescharacteristic
231C22×C4×C59C2411yescharacteristic
232C22×C4×C59C2411yescharacteristic
233C22×C4×C59C2411yescharacteristic
234C2×C22⋊D59—22no—
235C2×C22⋊D59—22no—
236C2×C22⋊D59—24no—
237C2×C22⋊D59—24no—
238C2×C22⋊D59—44no—
239C2×C22⋊D59—48no—
240C22×Dic59—21no—
241C22×Dic59—21no—
242C22×Dic59—22no—
243C22×Dic59—21no—
244#11745685—28no—
245#11745685—28no—
246#11745685—44no—
247#11745685—44no—
248#11745685—48no—
249#11745685—48no—
250C2×D236—24no—
251C2×D236—21no—
252C2×D236—22no—
253C2×D236—22no—
254C2×D236—22no—
255C2×D236—22no—
256C2×D236—22no—
257C2×D236—44no—
258C2×D236—44no—
259C2×D236—44no—
260C2×D236C2414yes—
261C2×D236C2412yes—
262C2×C4×D59—22no—
263C2×C4×D59—22no—
264C2×C4×D59—24no—
265C2×C4×D59—24no—
266C2×C4×D59—44no—
267C2×C4×D59—48no—
268C2×Dic118—24no—
269C2×Dic118—21no—
270C2×Dic118—22no—
271C2×Dic118—44no—
272C2×Dic118C2414yes—
273C2×Dic118C2412yes—
274M16×C59—28no—
275C2×C8×C59C2418yes—
276C42×C59C2×D411yescharacteristic
277C42×C59C2×D411yescharacteristic
278C42×C59C2×D411yescharacteristic
279C42×C59C2×D411yescharacteristic
280C42×C59C2×D411yescharacteristic
281C42×C59C2×D411yescharacteristic
282C42×C59C2×D411yescharacteristic
283C42×C59C2×D411yescharacteristic
284C42×C59C2×D411yescharacteristic
285C42×C59C2×D411yescharacteristic
286C42×C59C2×D411yescharacteristic
287C42×C59C2×D411yescharacteristic
288C42×C59C2411yescharacteristic
289C42×C59C2411yescharacteristic
290C42×C59C2411yescharacteristic
291C42×C59C2411yescharacteristic
292C22⋊Dic59—22no—
293C22⋊Dic59—22no—
294(C2×D59)⋊C4—22no—
295(C2×D59)⋊C4—22no—
296(C2×D59)⋊C4—22no—
297(C2×D59)⋊C4—22no—
298(C2×D59)⋊C4—22no—
299(C2×D59)⋊C4—22no—
300(C2×D59)⋊C4—24no—
301(C2×D59)⋊C4—24no—
302(C2×D59)⋊C4—24no—
303(C2×D59)⋊C4—24no—
304(C2×D59)⋊C4—22no—
305(C2×D59)⋊C4—22no—
306C4⋊Dic59—22no—
307C4⋊Dic59—22no—
308C4⋊Dic59—22no—
309C4⋊Dic59—22no—
310C4⋊Dic59—21no—
311C4⋊Dic59—21no—
312C4⋊Dic59C2412yes—
313C4⋊Dic59C2412yes—
314Dic59⋊C4—22no—
315Dic59⋊C4—22no—
316Dic59⋊C4—22no—
317Dic59⋊C4—22no—
318Dic59⋊C4—22no—
319Dic59⋊C4—22no—
320Dic59⋊C4—22no—
321Dic59⋊C4—22no—
322C4×Dic59—22no—
323C4×Dic59—22no—
324Dic236—48no—
325D472—48no—
326#11745660—48no—
327#11745660—48no—
328C23×C59—22no—
329C23×C59—22no—
330C23×C59—41no—
331C23×C59C22×D411yescharacteristic
332C23×C59C22×D411yescharacteristic
333C23×C59C22×D411yescharacteristic
334C22×D59—22no—
335C22×D59—24no—
336C22×D59—44no—
337C22×D59—42no—
338C22×D59—44no—
339C22×D59—42no—
340C22×D59—42no—
341C22×D59—44no—
342C2×C4×C59—22no—
343C2×C4×C59—22no—
344C2×C4×C59—22no—
345C2×C4×C59—22no—
346C2×C4×C59—22no—
347C2×C4×C59—22no—
348C2×C4×C59—22no—
349C2×C4×C59—22no—
350C2×C4×C59—22no—
351C2×C4×C59—22no—
352C2×C4×C59—41no—
353C2×C4×C59—41no—
354C2×C4×C59—41no—
355C2×C4×C59—41no—
356C2×C4×C59—41no—
357C2×C4×C59—41no—
358C2×C4×C59—41no—
359C2×C4×C59C22×D411yescharacteristic
360C2×C4×C59C22×D411yescharacteristic
361C2×C4×C59C22×D411yescharacteristic
362C2×C4×C59C22×D411yescharacteristic
363C2×C4×C59C22×D411yescharacteristic
364C2×C4×C59C22×D411yescharacteristic
365C2×C4×C59C22×D411yescharacteristic
366C2×C4×C59C22×D411yescharacteristic
367C2×C4×C59C22×D411yescharacteristic
368C2×C4×C59C22×D411yescharacteristic
369C2×C4×C59C22×D411yescharacteristic
370C2×C4×C59H(5,𝔽2)14yes—
371C2×C4×C59C2511yescharacteristic
372C22⋊D59—48no—
373C22⋊D59—44no—
374C22⋊D59—48no—
375C22⋊D59—44no—
376C2×Dic59—22no—
377C2×Dic59—22no—
378C2×Dic59—22no—
379C2×Dic59—24no—
380C2×Dic59—44no—
381C2×Dic59—42no—
382C2×Dic59—42no—
383C2×Dic59—42no—
384D236—24no—
385D236—24no—
386D236—24no—
387D236—44no—
388D236—44no—
389D236—44no—
390D236—44no—
391D236—42no—
392D236—44no—
393C4×D59—44no—
394C4×D59—48no—
395C4×D59—48no—
396C4×D59—44no—
397Dic118—24no—
398Dic118—24no—
399Dic118—24no—
400Dic118—44no—
401Dic118—42no—
402C8×C59—28no—
403#60805—591nomaximal, Sylow
404C22×C59—21no—
405C22×C59—21no—
406C22×C59—21no—
407C22×C59—21no—
408C22×C59—21no—
409C22×C59—21no—
410C22×C59—21no—
411C22×C59—44no—
412C22×C59#53512yes—
413C22×C59#57512yes—
414C22×C59C23×D411yescharacteristic
415C2×D59—44no—
416C2×D59—42no—
417C2×D59—42no—
418C2×D59—44no—
419C2×D59—44no—
420C2×D59—42no—
421C2×D59—88no—
422C2×D59—84no—
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#53512yes—
433C4×C59#57512yes—
434C4×C59C2×H(5,𝔽2)12yes—
435Dic59—44no—
436Dic59—42no—
437Dic59—42no—
438Dic59—42no—
439C2×#532—591no—
440C2×#529—591no—
441#3219—594no—
442#3218—592no—
443#3217—592no—
444#3212—594no—
445#3211—594no—
446#3153—592no—
447#3142—592no—
448#3037—592no—
449#3036—592no—
450#3007—592no—
451#3006—592no—
452#2920D5911yescharacteristic, complemented
453C2×C59—22no—
454C2×C59—22no—
455C2×C59—41no—
456C2×C59C2×#53511yescharacteristic
457C2×C59C2×#57511yescharacteristic
458C2×C59C2×#57511yescharacteristic
459D59—84no—
460D59—82no—
461C22×#41—592no—
462C2×#137—594no—
463C2×AGL(1,ℤ/8)—594no—
464#532—592no—
465#532—592no—
466#532—592no—
467#532—592no—
468#532—1181no—
469#532—1181no—
470#532—1181no—
471#532—1181no—
472C2×C4⋊Q8—591no—
473C2×#127—591no—
474#529—592no—
475#529—592no—
476#529—592no—
477#529—592no—
478#529—1181no—
479#529—1181no—
480#529—1181no—
481#529—1181no—
482C2×#126—1181no—
483C2×#125—591no—
484C2×#124—591no—
485C2×#124—592no—
486C2×#123—1181no—
487C2×C22⋊Q8—591no—
488C2×#121—591no—
489C2×#121—1181no—
490C2×#121—1181no—
491C2×C4×Q8—591no—
492C2×C4×D4—591no—
493C2×C4×D4—1181no—
494C2×C4×D4—1181no—
495C2×C4×D4—1181no—
496C2×#117—1181no—
497C22×C42C2×D5911yescharacteristic
498#497—594no—
499#496—594no—
500#495—598no—
501#491—594no—
502#490—594no—
503#488—598no—
504#464—598no—
505#463—598no—
506#462—594no—
507#461—594no—
508#460—594no—
509#459—594no—
510#452—598no—
511#451—594no—
512#450—594no—
513#449—598no—
514#448—594no—
515#447—594no—
516#432C2×D5912yescomplemented
517#432C2×D5912yescomplemented
518#431C2×D5912yescomplemented
519#431C2×D5912yescomplemented
520#423C2×D5912yescomplemented
521#417—594no—
522#417—594no—
523#407C2×D5912yes—
524C4×M16C2×D5912yescomplemented
525C59#6080511yescharacteristic, complemented, Sylow
526C2×#41—594no—
527C2×#41—594no—
528C2×#41—1182no—
529C2×#41—1182no—
530C2×#41—2368no—
531C22×Q8—591no—
532C22×Q8—592no—
533C22×D4—591no—
534C22×D4—592no—
535C22×D4—1181no—
536C22×D4—1182no—
537C22×D4—1181no—
538C22×D4—1181no—
539C23×C4—1181no—
540C23×C4—1182no—
541C23×C4D23611yescharacteristic
542C23×C4D23611yescharacteristic
543C23×C4C22×D5911yescharacteristic
544#137—2368no—
545AGL(1,ℤ/8)—2368no—
546C2×Q16—598no—
547C2×SD16—598no—
548C2×SD16—598no—
549C2×D8—598no—
550C2×M16C22×D5914yes—
551C4⋊Q8—592no—
552C4⋊Q8—592no—
553C4⋊Q8—1181no—
554C4⋊Q8—1181no—
555#127—592no—
556#127—592no—
557#127—1181no—
558#127—1181no—
559#126—1182no—
560#126—1182no—
561#126—1182no—
562#126—1182no—
563#125—592no—
564#125—592no—
565#125—1181no—
566#125—1181no—
567#124—592no—
568#124—592no—
569#124—594no—
570#124—594no—
571#124—1181no—
572#124—1181no—
573#124—1182no—
574#124—1182no—
575#123—1182no—
576#123—1182no—
577#123—1182no—
578#123—1182no—
579C22⋊Q8—592no—
580C22⋊Q8—592no—
581C22⋊Q8—1181no—
582C22⋊Q8—1181no—
583#121—592no—
584#121—592no—
585#121—1181no—
586#121—1181no—
587#121—1182no—
588#121—1182no—
589#121—1182no—
590#121—1182no—
591#121—1182no—
592#121—1182no—
593#121—1182no—
594#121—1182no—
595C4×Q8—592no—
596C4×Q8—592no—
597C4×Q8—1181no—
598C4×Q8—1181no—
599C4×D4—592no—
600C4×D4—592no—
601C4×D4—1182no—
602C4×D4—1182no—
603C4×D4—1182no—
604C4×D4—1182no—
605C4×D4—1181no—
606C4×D4—1181no—
607C4×D4—1182no—
608C4×D4—1182no—
609C4×D4—1182no—
610C4×D4—1182no—
611C4×D4—1182no—
612C4×D4—1182no—
613C4×D4—1182no—
614C4×D4—1182no—
615#117—1182no—
616#117—1182no—
617#117—1182no—
618#117—1182no—
619C2×C4⋊C4—591no—
620C2×C4⋊C4—591no—
621C2×C4⋊C4—1181no—
622C2×C4⋊C4—1181no—
623C2×C4⋊C4—1181no—
624C2×C4⋊C4—1181no—
625C2×C4⋊C4—1181no—
626C2×C4⋊C4—1181no—
627C2×C22⋊C4—1181no—
628C2×C22⋊C4—1181no—
629C2×C22⋊C4—1181no—
630C2×C22⋊C4—1181no—
631C2×C22⋊C4—1182no—
632C2×C22⋊C4—1182no—
633C2×C22⋊C4—1181no—
634C2×C42—1181no—
635C2×C42D23611yescharacteristic
636C2×C42D23611yescharacteristic
637C2×C42D23611yescharacteristic
638C2×C42D23611yescharacteristic
639C2×C42D23611yescharacteristic
640C2×C42D23611yescharacteristic
641C2×C42C22×D5911yescharacteristic
642C2×C42C22×D5911yescharacteristic
643C2×C42C22×D5911yescharacteristic
644C2×C42C22×D5911yescharacteristic
645C2×C42C22×D5911yescharacteristic
646C2×C42C22×D5911yescharacteristic
647C4⋊C8C22×D5914yes—
648C4⋊C8C22×D5914yes—
649#103—598no—
650#103—598no—
651#102—598no—
652#102—598no—
653C22⋊C8C22×D5914yes—
654C22⋊C8C22×D5914yes—
655#97C22×D5914yes—
656C4×C8C22×D5914yes—
657C24—1181no—
658C24—1182no—
659C24C2×D23611yescharacteristic
660#41—1188no—
661#41—1188no—
662#41—2364no—
663#41—2364no—
664#41—2368no—
665#41—2368no—
666C2×Q8—594no—
667C2×Q8—592no—
668C2×Q8—1181no—
669C2×Q8—1182no—
670C2×Q8—1184no—
671C2×Q8—2364no—
672C2×D4—594no—
673C2×D4—592no—
674C2×D4—1182no—
675C2×D4—1182no—
676C2×D4—1184no—
677C2×D4—1184no—
678C2×D4—1181no—
679C2×D4—1182no—
680C2×D4—1182no—
681C2×D4—1182no—
682C2×D4—1182no—
683C2×D4—1182no—
684C2×D4—1184no—
685C2×D4—2364no—
686C2×D4—2364no—
687C2×D4—2364no—
688C2×D4—2368no—
689C2×D4—2364no—
690C22×C4—24no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—1181no—
694C22×C4—1181no—
695C22×C4—1181no—
696C22×C4—1182no—
697C22×C4—1182no—
698C22×C4—1182no—
699C22×C4—1184no—
700C22×C4—1184no—
701C22×C4—2368no—
702C22×C4—2364no—
703C22×C4C2×D23611yescharacteristic
704C22×C4C2×D23611yescharacteristic
705C22×C4C2×D23611yescharacteristic
706C22×C4C2×D23611yescharacteristic
707C22×C4C2×D23611yescharacteristic
708C22×C4C2×D23611yescharacteristic
709C22×C4C2×D23611yescharacteristic
710C22×C4C2×D23611yescharacteristic
711C22×C4C2×D23611yescharacteristic
712C22×C4C2×D23611yescharacteristic
713C22×C4C2×D23611yescharacteristic
714C22×C4C2×D23611yescharacteristic
715C22×C4C2×D23611yescharacteristic
716C22×C4C2×D23611yescharacteristic
717C22×C4C2×D23611yescharacteristic
718C22×C4C23×D5911yescharacteristic
719C22×C4C23×D5911yescharacteristic
720C22×C4C23×D5911yescharacteristic
721Q16—2368no—
722SD16—2368no—
723SD16—2368no—
724D8—2368no—
725M16—28no—
726C2×C8C23×D5918yes—
727C4⋊C4—592no—
728C4⋊C4—592no—
729C4⋊C4—1181no—
730C4⋊C4—1181no—
731C4⋊C4—1182no—
732C4⋊C4—1182no—
733C4⋊C4—1182no—
734C4⋊C4—1182no—
735C4⋊C4—1182no—
736C4⋊C4—1182no—
737C4⋊C4—1182no—
738C4⋊C4—1182no—
739C4⋊C4—1182no—
740C4⋊C4—1182no—
741C4⋊C4—1182no—
742C4⋊C4—1182no—
743C22⋊C4—1182no—
744C22⋊C4—1182no—
745C22⋊C4—1182no—
746C22⋊C4—1182no—
747C22⋊C4—1182no—
748C22⋊C4—1182no—
749C22⋊C4—1182no—
750C22⋊C4—1182no—
751C22⋊C4—1184no—
752C22⋊C4—1184no—
753C22⋊C4—1184no—
754C22⋊C4—1184no—
755C22⋊C4—1182no—
756C22⋊C4—1182no—
757C42—1182no—
758C42—1182no—
759C42C2×D23611yescharacteristic
760C42C2×D23611yescharacteristic
761C42C2×D23611yescharacteristic
762C42C2×D23611yescharacteristic
763C42C2×D23611yescharacteristic
764C42C2×D23611yescharacteristic
765C42C2×D23611yescharacteristic
766C42C2×D23611yescharacteristic
767C42C2×D23611yescharacteristic
768C42C2×D23611yescharacteristic
769C42C2×D23611yescharacteristic
770C42C2×D23611yescharacteristic
771C42C23×D5911yescharacteristic
772C42C23×D5911yescharacteristic
773C42C23×D5911yescharacteristic
774C42C23×D5911yescharacteristic
775C23—22no—
776C23—22no—
777C23—41no—
778C23—1182no—
779C23—1184no—
780C23—2364no—
781C23—2362no—
782C23—2364no—
783C23—2362no—
784C23—2364no—
785C23—2362no—
786C23C22×D23611yescharacteristic
787C23C22×D23611yescharacteristic
788C23C22×D23611yescharacteristic
789Q8—1184no—
790Q8—1184no—
791Q8—1184no—
792Q8—2364no—
793Q8—2362no—
794D4—1184no—
795D4—1184no—
796D4—1184no—
797D4—2364no—
798D4—2364no—
799D4—2364no—
800D4—2364no—
801D4—2364no—
802D4—2368no—
803D4—2364no—
804D4—2368no—
805D4—2364no—
806D4—2362no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—1182no—
825C2×C4—1182no—
826C2×C4—1182no—
827C2×C4—1184no—
828C2×C4—2364no—
829C2×C4—2368no—
830C2×C4—2362no—
831C2×C4—2364no—
832C2×C4—2362no—
833C2×C4—2362no—
834C2×C4—2364no—
835C2×C4—2368no—
836C2×C4C22×D23611yescharacteristic
837C2×C4C22×D23611yescharacteristic
838C2×C4C22×D23611yescharacteristic
839C2×C4C22×D23611yescharacteristic
840C2×C4C22×D23611yescharacteristic
841C2×C4C22×D23611yescharacteristic
842C2×C4C22×D23611yescharacteristic
843C2×C4C22×D23611yescharacteristic
844C2×C4C22×D23611yescharacteristic
845C2×C4C22×D23611yescharacteristic
846C2×C4C22×D23611yescharacteristic
847C2×C4#1427377314yes—
848C2×C4C24×D5911yescharacteristic
849C8—28no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—44no—
858C22—4728no—
859C22—4724no—
860C22—2362no—
861C22—2364no—
862C22—2362no—
863C22—2364no—
864C22—2364no—
865C22—2362no—
866C22#1683797112yes—
867C22#1683820212yes—
868C22C23×D23611yescharacteristic
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—21no—
875C4—21no—
876C4—21no—
877C4—21no—
878C4—2362no—
879C4—2362no—
880C4—2364no—
881C4—2362no—
882C4#1683797112yes—
883C4#1683820212yes—
884C4C2×#1427377312yes—
885C2—22no—
886C2—22no—
887C2—41no—
888C2—4722no—
889C2—4724no—
890C2C2×#1683797111yescharacteristic
891C2C2×#1683820211yescharacteristic
892C2C2×#1683820211yescharacteristic
subgroupG/H
centerC22C23×D236
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC59×#2920C2
socleC22×C59C23×D4
hypercenter#2920D59
hypocenterC59#60805
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C42 ◁ #2920

Complements

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

NH ≅ G/Ntype
1. C2×#16837952C2semidirect
2. C2×#16837936C2semidirect
3. #21435135C2semidirect
4. #21435125C2semidirect
5. #21435116C2semidirect
6. #21435074C2semidirect
7. #21435063C2semidirect
8. #21434562C2semidirect
9. #21434497C2semidirect
10. #21433570C2semidirect
11. #21433562C2semidirect
12. #21433358C2semidirect
13. #21433350C2semidirect
14. C59×#2920C2semidirect
16. C2×#14273760C22semidirect
17. C2×#14273755C22semidirect
24. #16837952C22semidirect
25. #16837952C22semidirect
26. C2×#14273727C22semidirect
27. C2×#14273724C22semidirect
34. #16837936C22semidirect
35. #16837936C22semidirect
37. C2×#14273719C22semidirect
38. C2×#14273715C22semidirect
39. C2×#14273715C22semidirect
45. C2×C4×Dic118C22semidirect
48. C2×C4×D236C22semidirect
51. #16837796C22semidirect
52. #16837791C22semidirect
53. #16837786C22semidirect
54. #16837771C22semidirect
55. #16837767C22semidirect
56. #16837757C22semidirect
57. #16837625C22semidirect
58. #16837618C22semidirect
59. #16837613C22semidirect
60. #16837608C22semidirect
61. #16837603C22semidirect
62. #16837598C22semidirect
63. #16837566C22semidirect
64. #16837560C22semidirect
65. #16837555C22semidirect
66. #16837549C22semidirect
69. #16837404C22semidirect
70. #16837404C22semidirect
72. C59×#432C22semidirect
73. C59×#432C22semidirect
74. C59×#431C22semidirect
75. C59×#431C22semidirect
76. C59×#423C22semidirect
78. C4×M16×C59C22semidirect
452. #2920D59semidirect
516. #432C2×D59semidirect
517. #432C2×D59semidirect
518. #431C2×D59semidirect
519. #431C2×D59semidirect
520. #423C2×D59semidirect
524. C4×M16C2×D59semidirect
525. C59#60805semidirect

Maximal subgroups

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

subgroupindex
C2×#168379522
C2×#168379362
#214351352
#214351252
#214351162
#214350742
#214350632
#214345622
#214344972
#214335702
#214335622
#214333582
#214333502
C59×#29202
#6080559