Finite Group Databasebeta

← #29457178

Subgroups — #29457178

Order 15104.

2078 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21437486C211yesmaximal, characteristic, complemented
2#21434373C214yesmaximal, complemented
3#21434358C214yesmaximal, complemented
4#21434310C214yesmaximal, complemented
5#21434295C214yesmaximal, complemented
6#21434019C212yesmaximal, complemented
7#21433901C211yesmaximal, characteristic, complemented
8#21433893C211yesmaximal, characteristic, complemented
9#21433568C211yesmaximal, characteristic, complemented
10#21433560C211yesmaximal, characteristic, complemented
11#21433338C212yesmaximal, complemented
12C4×#14273758C212yesmaximal, complemented
13C4×#14273753C212yesmaximal, complemented
14#21432734C211yesmaximal, characteristic, complemented
15C2×C59×#520C211yesmaximal, characteristic, complemented
16C2×#14273758C2212yes—
17C2×#14273753C2212yes—
18#16838023C2212yescomplemented
19#16838023C2212yescomplemented
20#16838014C2212yescomplemented
21#16838007C2212yescomplemented
22#16837999—21no—
23#16837999—21no—
24#16837990—21no—
25#16837990—21no—
26#16837959C2211yescharacteristic
27#16837952C2211yescharacteristic
28#16837930—22no—
29#16837930—22no—
30#16837913C2212yes—
31C4×#11745685C2212yes—
32#16837737C2214yescomplemented
33#16837732C2214yescomplemented
34#16837720C2214yescomplemented
35#16837715C2214yescomplemented
36#16837709C2214yescomplemented
37#16837702C2214yescomplemented
38#16837697C2212yescomplemented
39#16837692C2212yescomplemented
40#16837687C2212yescomplemented
41#16837682C2212yescomplemented
42#16837624C2214yescomplemented
43#16837617C2214yescomplemented
44#16837612C2212yescomplemented
45#16837607C2212yescomplemented
46#16837602C2212yescomplemented
47#16837597C2212yescomplemented
48#16837564C2214yes—
49#16837564C2214yes—
50#16837547C2214yes—
51#16837547C2214yes—
52#16837512C2214yescomplemented
53#16837507C2214yescomplemented
54#16837502C2214yescomplemented
55#16837500C2214yescomplemented
56C4×#11745672C2214yescomplemented
57C4×#11745671C2214yescomplemented
58C4×#11745670C2214yescomplemented
59C4×#11745669C2214yescomplemented
60#16837463C2214yescomplemented
61#16837463C2214yescomplemented
62#16837442C2212yes—
63#16837442C2212yes—
64#16837426C2211yescharacteristic
65#16837426C2211yescharacteristic
66#16837411C2212yes—
67#16837407C2212yes—
68#16837401C2212yes—
69#16837401C2212yes—
70#16837366C2212yes—
71C4×#11745664C2212yes—
72C22×#41×C59C2211yescharacteristic
73C59×#520—22no—
74C59×#520—22no—
75C59×#520C2214yes—
76C59×#520C2214yes—
77C2×C4×Q8×C59C2211yescharacteristic
78C2×C4×Q8×C59C2211yescharacteristic
79C2×C4×D4×C59—21no—
80C2×C4×D4×C59—21no—
81C2×C4×D4×C59C2211yescharacteristic
82C2×C4×D4×C59C2211yescharacteristic
83C2×#117×C59—21no—
84C2×#117×C59C2211yescharacteristic
85C22×C4⋊C4×C59—21no—
86C22×C4⋊C4×C59C2211yescharacteristic
87C2×#11745685C2312yes—
88#14273758—28no—
89#14273753—28no—
90C2×#11745672C2314yes—
91C2×#11745670C2314yes—
92C2×#11745671C2314yes—
93C2×#11745669C2314yes—
94C2×#11745664C2312yes—
95C2×#11745664C2312yes—
96#14273727C2311yescharacteristic
97#14273727C2311yescharacteristic
98#14273727C2311yescharacteristic
99#14273724C2311yescharacteristic
100#14273722—22no—
101#14273722—22no—
102#14273720—22no—
103#14273720—22no—
104#14273719C2312yes—
105#14273717—22no—
106#14273717—22no—
107#14273715C2312yes—
108#14273713—22no—
109#14273713—22no—
110#14273712—22no—
111#14273712—22no—
112#14273710—22no—
113#14273709—22no—
114#14273709—22no—
115#14273706—21no—
116#14273706—21no—
117#14273706C2312yes—
118#14273706C2312yes—
119#14273705—22no—
120#14273705—22no—
121#14273701—21no—
122#14273701—21no—
123#14273701C2312yes—
124#14273701C2312yes—
125#14273700—22no—
126#14273700—22no—
127#14273696—22no—
128C4×Dic118—21no—
129C4×Dic118—21no—
130C4×Dic118C2312yes—
131C4×Dic118C2312yes—
132C4×D236—21no—
133C4×D236—21no—
134C4×D236C2312yes—
135C4×D236C2312yes—
136C4×C22⋊D59—22no—
137C4×C22⋊D59—22no—
138C4×C22⋊D59—22no—
139C4×C22⋊D59—22no—
140#14273686C2312yes—
141#14273684—22no—
142C42×D59—22no—
143#14273660C2314yes—
144#14273660C2314yes—
145#14273658C2314yes—
146#14273658C2314yes—
147C4⋊(C59⋊C8)C2312yes—
148C4⋊(C59⋊C8)C2312yes—
149C4⋊(C59⋊C8)C2312yes—
150C4⋊(C59⋊C8)C2312yes—
151#14273651C2314yes—
152#14273651C2314yes—
153#14273650C2314yes—
154#14273650C2314yes—
155#14273648C2314yes—
156#14273648C2314yes—
157#14273647C2314yes—
158#14273647C2314yes—
159C22⋊(C59⋊C8)C2314yes—
160C22⋊(C59⋊C8)C2314yes—
161#14273638C2314yes—
162C4×C59⋊C8C2314yes—
163C2×#41×C59—24no—
164C2×#41×C59—24no—
165C2×#41×C59—22no—
166C2×#41×C59C2314yes—
167C22×Q8×C59C2311yescharacteristic
168C22×D4×C59—21no—
169C22×D4×C59C2311yescharacteristic
170C23×C4×C59—21no—
171C23×C4×C59—21no—
172C23×C4×C59—21no—
173C23×C4×C59—21no—
174C23×C4×C59C2311yescharacteristic
175C4×Q8×C59—22no—
176C4×Q8×C59—21no—
177C4×Q8×C59—21no—
178C4×Q8×C59C2312yes—
179C4×Q8×C59C2312yes—
180C4×Q8×C59C2314yes—
181C4×D4×C59—24no—
182C4×D4×C59—24no—
183C4×D4×C59—24no—
184C4×D4×C59—24no—
185C4×D4×C59—22no—
186C4×D4×C59—21no—
187C4×D4×C59—21no—
188C4×D4×C59C2312yes—
189C4×D4×C59C2312yes—
190C4×D4×C59C2314yes—
191#117×C59—24no—
192#117×C59—24no—
193#117×C59D412yes—
194#117×C59D412yes—
195#117×C59C2312yes—
196#117×C59C2312yes—
197C2×C4⋊C4×C59—21no—
198C2×C4⋊C4×C59—21no—
199C2×C4⋊C4×C59—21no—
200C2×C4⋊C4×C59—22no—
201C2×C4⋊C4×C59—24no—
202C2×C4⋊C4×C59—24no—
203C2×C4⋊C4×C59D411yescharacteristic
204C2×C4⋊C4×C59D411yescharacteristic
205C2×C4⋊C4×C59C2311yescharacteristic
206C2×C4⋊C4×C59C2311yescharacteristic
207C2×C4⋊C4×C59C2314yes—
208C2×C22⋊C4×C59—21no—
209C2×C22⋊C4×C59—21no—
210C2×C22⋊C4×C59D411yescharacteristic
211C2×C22⋊C4×C59D411yescharacteristic
212C2×C42×C59—21no—
213C2×C42×C59—21no—
214C2×C42×C59C2311yescharacteristic
215C2×C42×C59C2311yescharacteristic
216C24×C59—21no—
217C24×C59C2×D411yescharacteristic
218#41×C59—216no—
219#41×C59—28no—
220#41×C59—28no—
221C2×Q8×C59—21no—
222C2×Q8×C59—22no—
223C2×Q8×C59#4114yes—
224C2×Q8×C59C2412yes—
225C2×D4×C59—28no—
226C2×D4×C59—24no—
227C2×D4×C59—21no—
228C2×D4×C59—22no—
229C2×D4×C59#4114yes—
230C2×D4×C59C2412yes—
231C22×C4×C59—28no—
232C22×C4×C59—21no—
233C22×C4×C59—24no—
234C22×C4×C59—22no—
235C22×C4×C59—22no—
236C22×C4×C59—21no—
237C22×C4×C59—21no—
238C22×C4×C59—24no—
239C22×C4×C59—24no—
240C22×C4×C59—22no—
241C22×C4×C59—22no—
242C22×C4×C59—82no—
243C22×C4×C59—82no—
244C22×C4×C59—82no—
245C22×C4×C59C2×D411yescharacteristic
246C22×C4×C59C2×D412yes—
247C22×C4×C59C2×D411yescharacteristic
248C22×C4×C59C2×D411yescharacteristic
249C22×C4×C59C2×D411yescharacteristic
250C22×C4×C59C2×D411yescharacteristic
251C22×C4×C59C2412yes—
252C22×C4×C59C2411yescharacteristic
253C2×C22⋊D59—22no—
254C2×C22⋊D59—22no—
255C2×C22⋊D59—22no—
256#11745685—24no—
257#11745685—24no—
258C2×D236—21no—
259C2×D236—21no—
260C2×D236C2412yes—
261C2×C4×D59—22no—
262C2×C4×D59—22no—
263C2×C4×D59—22no—
264C2×Dic118—21no—
265C2×Dic118—21no—
266C2×Dic118C2412yes—
267C4⋊C4×C59—24no—
268C4⋊C4×C59—24no—
269C4⋊C4×C59—22no—
270C4⋊C4×C59—22no—
271C4⋊C4×C59—21no—
272C4⋊C4×C59—21no—
273C4⋊C4×C59C2×D412yes—
274C4⋊C4×C59C2×D412yes—
275C4⋊C4×C59C2×D412yes—
276C4⋊C4×C59C2×D412yes—
277C4⋊C4×C59C2412yes—
278C4⋊C4×C59C2412yes—
279C22⋊C4×C59—24no—
280C22⋊C4×C59—22no—
281C22⋊C4×C59—22no—
282C22⋊C4×C59C2×D412yes—
283C22⋊C4×C59C2×D412yes—
284C22⋊C4×C59C2×D412yes—
285C22⋊C4×C59C2×D412yes—
286C42×C59—24no—
287C42×C59—22no—
288C42×C59—22no—
289C42×C59C2×D412yes—
290C42×C59C2×D411yescharacteristic
291C42×C59C2×D411yescharacteristic
292C42×C59C2412yes—
293C42×C59C2411yescharacteristic
294C42×C59C2411yescharacteristic
295C22⋊Dic59—22no—
296C22⋊Dic59—22no—
297C22⋊Dic59—22no—
298#11745672—28no—
299#11745671—28no—
300#11745670—28no—
301#11745669—28no—
302(C2×D59)⋊C4—22no—
303(C2×D59)⋊C4—22no—
304(C2×D59)⋊C4—22no—
305(C2×D59)⋊C4—22no—
306(C2×D59)⋊C4—22no—
307(C2×D59)⋊C4—22no—
308C4⋊Dic59—21no—
309C4⋊Dic59—21no—
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—
320C4×Dic59—22no—
321C4×Dic59—22no—
322C4×Dic59—22no—
323#11745664—24no—
324#11745664—24no—
325C2×C59⋊C8C2414yes—
326C2×C59⋊C8C2414yes—
327C23×C59—22no—
328C23×C59—24no—
329C23×C59—22no—
330C23×C59—41no—
331C23×C59—41no—
332C23×C59—42no—
333C23×C59—42no—
334C23×C59C22×D412yes—
335C23×C59C22×D411yescharacteristic
336C22×D59—22no—
337Q8×C59—24no—
338Q8×C59—22no—
339Q8×C59C2×#4114yes—
340D4×C59—216no—
341D4×C59—24no—
342D4×C59—22no—
343D4×C59C2×#4114yes—
344C2×C4×C59—216no—
345C2×C4×C59—22no—
346C2×C4×C59—24no—
347C2×C4×C59—22no—
348C2×C4×C59—24no—
349C2×C4×C59—22no—
350C2×C4×C59—22no—
351C2×C4×C59—22no—
352C2×C4×C59—22no—
353C2×C4×C59—41no—
354C2×C4×C59—41no—
355C2×C4×C59—41no—
356C2×C4×C59—41no—
357C2×C4×C59—42no—
358C2×C4×C59—42no—
359C2×C4×C59—82no—
360C2×C4×C59—84no—
361C2×C4×C59—82no—
362C2×C4×C59—84no—
363C2×C4×C59C22×D412yes—
364C2×C4×C59C22×D412yes—
365C2×C4×C59C22×D411yescharacteristic
366C2×C4×C59C22×D411yescharacteristic
367C2×C4×C59C22×D412yes—
368C2×C4×C59C22×D411yescharacteristic
369C2×C4×C59C22×D411yescharacteristic
370C2×C4×C59C22×D411yescharacteristic
371C2×C4×C59C2×#4112yes—
372C2×C4×C59C2×#4112yes—
373C2×C4×C59C2511yescharacteristic
374C22⋊D59—44no—
375C22⋊D59—82no—
376C22⋊D59—82no—
377C2×Dic59—22no—
378C2×Dic59—22no—
379C2×Dic59—22no—
380D236—22no—
381D236—22no—
382D236—81no—
383D236—81no—
384C4×D59—44no—
385C4×D59—82no—
386C4×D59—82no—
387Dic118—22no—
388Dic118—22no—
389Dic118—81no—
390Dic118—81no—
391C59⋊C8—24no—
392C59⋊C8—24no—
393#60565—591nomaximal, Sylow
394C22×C59—21no—
395C22×C59—21no—
396C22×C59—22no—
397C22×C59—22no—
398C22×C59—22no—
399C22×C59—24no—
400C22×C59—44no—
401C22×C59—48no—
402C22×C59—42no—
403C22×C59—42no—
404C22×C59#52512yes—
405C22×C59C23×D411yescharacteristic
406C2×D59—42no—
407C2×D59—42no—
408C2×D59—42no—
409C4×C59—21no—
410C4×C59—22no—
411C4×C59—21no—
412C4×C59—21no—
413C4×C59—22no—
414C4×C59—21no—
415C4×C59—22no—
416C4×C59—24no—
417C4×C59—42no—
418C4×C59—42no—
419C4×C59#52512yes—
420C4×C59C22×#4111yescharacteristic
421C4×C59C22×#4111yescharacteristic
422Dic59—42no—
423Dic59—42no—
424Dic59—42no—
425#3455—591no—
426C2×#520D5911yescharacteristic, complemented
427#3125—594no—
428#3124—594no—
429#3120—594no—
430#3119—594no—
431#3092—592no—
432#3078—591no—
433#3077—591no—
434#3037—591no—
435#3036—591no—
436#3005—592no—
437C4×#137—592no—
438C4×AGL(1,ℤ/8)—592no—
439#2921—591no—
440C2×C59—22no—
441C2×C59—42no—
442C2×C59—44no—
443C2×C59C2×#52511yescharacteristic
444C2×C59#358511yescharacteristic
445C2×C59#358611yescharacteristic
446D59—82no—
447C22×#41C2×D5911yescharacteristic
448C2×#137—592no—
449C2×AGL(1,ℤ/8)—592no—
450#542—592no—
451#542—592no—
452#541—592no—
453#540—592no—
454#539—1181no—
455#539—1181no—
456#538—1181no—
457#538—1181no—
458#533—591no—
459#532—591no—
460#529—1182no—
461#529—1182no—
462#525—592no—
463#520—22no—
464#520—22no—
465#520C2×D5914yes—
466#520C2×D5914yes—
467C4×#41—592no—
468C2×C4×Q8C2×D5911yescharacteristic
469C2×C4×Q8C2×D5911yescharacteristic
470C2×C4×D4—21no—
471C2×C4×D4—21no—
472C2×C4×D4C2×D5911yescharacteristic
473C2×C4×D4C2×D5911yescharacteristic
474C2×#117—21no—
475C2×#117C2×D5911yescharacteristic
476C22×C4⋊C4—21no—
477C22×C4⋊C4C2×D5911yescharacteristic
478#484—594no—
479#483—594no—
480#481—594no—
481#480—594no—
482#479—594no—
483#478—594no—
484#477—592no—
485#476—592no—
486#475—592no—
487#474—592no—
488#464—594no—
489#463—594no—
490#462—592no—
491#461—592no—
492#460—592no—
493#459—592no—
494#452—594no—
495#452—594no—
496#449—594no—
497#449—594no—
498#442—594no—
499#441—594no—
500#440—594no—
501#440—594no—
502C4×Q16—594no—
503C4×SD16—594no—
504C4×SD16—594no—
505C4×D8—594no—
506#433—594no—
507#433—594no—
508#428—592no—
509#428—592no—
510#423—591no—
511#423—591no—
512#419—592no—
513#418—592no—
514#417—592no—
515#417—592no—
516#407—592no—
517C4×M16—592no—
518C59#6056511yescharacteristic, complemented, Sylow
519C2×#41—24no—
520C2×#41—24no—
521C2×#41—22no—
522C2×#41—592no—
523C2×#41C22×D5914yes—
524C22×Q8C22×D5911yescharacteristic
525C22×D4—21no—
526C22×D4C22×D5911yescharacteristic
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4C22×D5911yescharacteristic
532#137—1188no—
533AGL(1,ℤ/8)—1188no—
534C2×Q16—594no—
535C2×SD16—594no—
536C2×SD16—594no—
537C2×D8—594no—
538C2×M16—592no—
539C2×M16—592no—
540C4⋊Q8—591no—
541C4⋊Q8—591no—
542C4⋊Q8—591no—
543#127—591no—
544#126—1182no—
545#126—1182no—
546#126—1182no—
547#126—1182no—
548#125—592no—
549#125—1182no—
550#125—1182no—
551#124—592no—
552#124—1182no—
553#124—1182no—
554#123—1182no—
555#123—1182no—
556#123—1182no—
557#123—1182no—
558#123—1182no—
559C22⋊Q8—592no—
560C22⋊Q8—592no—
561C22⋊Q8—1181no—
562C22⋊Q8—1181no—
563C22⋊Q8—1182no—
564C22⋊Q8—1182no—
565#121—592no—
566#121—592no—
567#121—1181no—
568#121—1181no—
569#121—1182no—
570#121—1182no—
571#120—1182no—
572C4×Q8—22no—
573C4×Q8—21no—
574C4×Q8—21no—
575C4×Q8—592no—
576C4×Q8—592no—
577C4×Q8—1181no—
578C4×Q8—1181no—
579C4×Q8C22×D5914yes—
580C4×Q8C22×D5912yes—
581C4×Q8C22×D5912yes—
582C4×D4—24no—
583C4×D4—24no—
584C4×D4—24no—
585C4×D4—24no—
586C4×D4—22no—
587C4×D4—21no—
588C4×D4—21no—
589C4×D4—592no—
590C4×D4—592no—
591C4×D4—1182no—
592C4×D4—1182no—
593C4×D4—1182no—
594C4×D4—1182no—
595C4×D4—1181no—
596C4×D4—1181no—
597C4×D4C22×D5914yes—
598C4×D4C22×D5912yes—
599C4×D4C22×D5912yes—
600#117—24no—
601#117—24no—
602#117—592no—
603#117—1182no—
604#117C22⋊D5912yes—
605#117C22⋊D5912yes—
606#117C22×D5912yes—
607#117C22×D5912yes—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—24no—
613C2×C4⋊C4—24no—
614C2×C4⋊C4C22⋊D5911yescharacteristic
615C2×C4⋊C4C22⋊D5911yescharacteristic
616C2×C4⋊C4C22×D5911yescharacteristic
617C2×C4⋊C4C22×D5911yescharacteristic
618C2×C4⋊C4C22×D5914yes—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4C22⋊D5911yescharacteristic
622C2×C22⋊C4C22⋊D5911yescharacteristic
623C2×C42—21no—
624C2×C42—21no—
625C2×C42—1182no—
626C2×C42C22×D5911yescharacteristic
627C2×C42C22×D5911yescharacteristic
628#107—594no—
629#107—594no—
630#106—594no—
631#106—594no—
632C4⋊C8—592no—
633C4⋊C8—592no—
634C4⋊C8—592no—
635C4⋊C8—592no—
636#103—594no—
637#103—594no—
638#103—594no—
639#103—594no—
640#102—594no—
641#102—594no—
642#102—594no—
643#102—594no—
644C22⋊C8—594no—
645C22⋊C8—594no—
646#97—594no—
647C4×C8—594no—
648C24—21no—
649C24C2×C22⋊D5911yescharacteristic
650#41—216no—
651#41—28no—
652#41—28no—
653#41—1184no—
654#41—1184no—
655C2×Q8—21no—
656C2×Q8—22no—
657C2×Q8—592no—
658C2×Q8—1181no—
659C2×Q8—1181no—
660C2×Q8#1174568514yes—
661C2×Q8C23×D5912yes—
662C2×D4—28no—
663C2×D4—24no—
664C2×D4—21no—
665C2×D4—22no—
666C2×D4—592no—
667C2×D4—1182no—
668C2×D4—1182no—
669C2×D4—1182no—
670C2×D4—1181no—
671C2×D4—1181no—
672C2×D4#1174568514yes—
673C2×D4C23×D5912yes—
674C22×C4—28no—
675C22×C4—21no—
676C22×C4—24no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—24no—
682C22×C4—24no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—82no—
686C22×C4—82no—
687C22×C4—82no—
688C22×C4—1182no—
689C22×C4—1182no—
690C22×C4—1182no—
691C22×C4C2×C22⋊D5911yescharacteristic
692C22×C4C2×C22⋊D5912yes—
693C22×C4C2×C22⋊D5911yescharacteristic
694C22×C4C2×C22⋊D5911yescharacteristic
695C22×C4C2×C22⋊D5911yescharacteristic
696C22×C4C2×C22⋊D5911yescharacteristic
697C22×C4C23×D5912yes—
698C22×C4C23×D5911yescharacteristic
699Q16—1188no—
700SD16—1188no—
701SD16—1188no—
702D8—1188no—
703M16—1184no—
704M16—1184no—
705C2×C8—594no—
706C2×C8—594no—
707C4⋊C4—24no—
708C4⋊C4—24no—
709C4⋊C4—22no—
710C4⋊C4—22no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—592no—
714C4⋊C4—592no—
715C4⋊C4—1182no—
716C4⋊C4—1182no—
717C4⋊C4—1181no—
718C4⋊C4—1181no—
719C4⋊C4—1182no—
720C4⋊C4—1182no—
721C4⋊C4—1182no—
722C4⋊C4—1182no—
723C4⋊C4—1181no—
724C4⋊C4—1181no—
725C4⋊C4C2×C22⋊D5912yes—
726C4⋊C4C2×C22⋊D5912yes—
727C4⋊C4C2×C22⋊D5912yes—
728C4⋊C4C2×C22⋊D5912yes—
729C4⋊C4C23×D5912yes—
730C4⋊C4C23×D5912yes—
731C22⋊C4—24no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—1182no—
735C22⋊C4—1182no—
736C22⋊C4—1182no—
737C22⋊C4—1182no—
738C22⋊C4—1182no—
739C22⋊C4—1182no—
740C22⋊C4—1182no—
741C22⋊C4—1182no—
742C22⋊C4—1182no—
743C22⋊C4C2×C22⋊D5912yes—
744C22⋊C4C2×C22⋊D5912yes—
745C22⋊C4C2×C22⋊D5912yes—
746C22⋊C4C2×C22⋊D5912yes—
747C42—24no—
748C42—22no—
749C42—22no—
750C42—1182no—
751C42—1182no—
752C42—1182no—
753C42C2×C22⋊D5912yes—
754C42C2×C22⋊D5911yescharacteristic
755C42C2×C22⋊D5911yescharacteristic
756C42C23×D5912yes—
757C42C23×D5911yescharacteristic
758C42C23×D5911yescharacteristic
759C23—22no—
760C23—24no—
761C23—22no—
762C23—41no—
763C23—41no—
764C23—42no—
765C23—42no—
766C23—1182no—
767C23C22×C22⋊D5912yes—
768C23C22×C22⋊D5911yescharacteristic
769Q8—24no—
770Q8—22no—
771Q8—1182no—
772Q8—1182no—
773Q8—4721no—
774Q8—4721no—
775Q8C2×#1174568514yes—
776D4—216no—
777D4—24no—
778D4—22no—
779D4—1182no—
780D4—1182no—
781D4—4721no—
782D4—4721no—
783D4—4722no—
784D4—4722no—
785D4—2364no—
786D4C2×#1174568514yes—
787C2×C4—216no—
788C2×C4—22no—
789C2×C4—24no—
790C2×C4—22no—
791C2×C4—24no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—84no—
803C2×C4—82no—
804C2×C4—82no—
805C2×C4—84no—
806C2×C4—1182no—
807C2×C4—1182no—
808C2×C4—1182no—
809C2×C4—4722no—
810C2×C4—4722no—
811C2×C4—2364no—
812C2×C4C22×C22⋊D5912yes—
813C2×C4C22×C22⋊D5911yescharacteristic
814C2×C4C22×C22⋊D5911yescharacteristic
815C2×C4C22×C22⋊D5912yes—
816C2×C4C22×C22⋊D5911yescharacteristic
817C2×C4C22×C22⋊D5911yescharacteristic
818C2×C4C22×C22⋊D5912yes—
819C2×C4C22×C22⋊D5911yescharacteristic
820C2×C4C2×#1174568512yes—
821C2×C4C2×#1174568512yes—
822C2×C4C24×D5911yescharacteristic
823C8—1184no—
824C8—1184no—
825C22—21no—
826C22—21no—
827C22—22no—
828C22—24no—
829C22—22no—
830C22—22no—
831C22—44no—
832C22—48no—
833C22—42no—
834C22—42no—
835C22—2362no—
836C22—2362no—
837C22—2362no—
838C22#1683791312yes—
839C22C23×C22⋊D5911yescharacteristic
840C4—22no—
841C4—24no—
842C4—22no—
843C4—21no—
844C4—21no—
845C4—22no—
846C4—21no—
847C4—21no—
848C4—42no—
849C4—42no—
850C4—2362no—
851C4—2362no—
852C4—2362no—
853C4#1683791312yes—
854C4C22×#1174568511yescharacteristic
855C4C22×#1174568511yescharacteristic
856C2—22no—
857C2—42no—
858C2—44no—
859C2—4722no—
860C2C2×#1683791311yescharacteristic
861C2#2143887611yescharacteristic
862C2#2143888311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#520C2
socleC22×C59C23×D4
hypercenterC2×#520D59
hypocenterC59#60565
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #21437486C2semidirect
2. #21434373C2semidirect
3. #21434358C2semidirect
4. #21434310C2semidirect
5. #21434295C2semidirect
6. #21434019C2semidirect
7. #21433901C2semidirect
8. #21433893C2semidirect
9. #21433568C2semidirect
10. #21433560C2semidirect
11. #21433338C2semidirect
12. C4×#14273758C2semidirect
13. C4×#14273753C2semidirect
14. #21432734C2semidirect
15. C2×C59×#520C2semidirect
18. #16838023C22semidirect
19. #16838023C22semidirect
20. #16838014C22semidirect
21. #16838007C22semidirect
32. #16837737C22semidirect
33. #16837732C22semidirect
34. #16837720C22semidirect
35. #16837715C22semidirect
36. #16837709C22semidirect
37. #16837702C22semidirect
38. #16837697C22semidirect
39. #16837692C22semidirect
40. #16837687C22semidirect
41. #16837682C22semidirect
42. #16837624C22semidirect
43. #16837617C22semidirect
44. #16837612C22semidirect
45. #16837607C22semidirect
46. #16837602C22semidirect
47. #16837597C22semidirect
52. #16837512C22semidirect
53. #16837507C22semidirect
54. #16837502C22semidirect
55. #16837500C22semidirect
56. C4×#11745672C22semidirect
57. C4×#11745671C22semidirect
58. C4×#11745670C22semidirect
59. C4×#11745669C22semidirect
60. #16837463C22semidirect
61. #16837463C22semidirect
426. C2×#520D59semidirect
518. C59#60565semidirect

Maximal subgroups

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

subgroupindex
#214374862
#214343732
#214343582
#214343102
#214342952
#214340192
#214339012
#214338932
#214335682
#214335602
#214333382
C4×#142737582
C4×#142737532
#214327342
C2×C59×#5202
#6056559