Finite Group Databasebeta

← #28495353

Subgroups — #28495353

Order 15104.

1292 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837419C211yesmaximal, characteristic, complemented
2#21432615C211yesmaximal, characteristic, complemented
3C2×#16837386C211yesmaximal, characteristic, complemented
4C2×#16837376C211yesmaximal, characteristic, complemented
5#21423806C211yesmaximal, characteristic, complemented
6C2×#16837158C211yesmaximal, characteristic, complemented
7C59×#3449C211yesmaximal, characteristic
8C22×#11745664C2211yescharacteristic
9C22×#11745664C2211yescharacteristic
10C2×#14273686C2211yescharacteristic
11C2×#14273686C2211yescharacteristic
12#16837419—22no—
13#16837419—22no—
14C2×#14273654—22no—
15#16837411—21no—
16#16837407—21no—
17#16837403—22no—
18#16837398—22no—
19#16837386—22no—
20#16837386—22no—
21C2×#14273646—21no—
22C2×#14273644—21no—
23#16837376—22no—
24#16837376—22no—
25C2×#14273642—22no—
26#16837162—22no—
27#16837158—22no—
28C22×#41×C59C2211yescharacteristic
29C22×#41×C59C2211yescharacteristic
30C59×#537—22no—
31C59×#536—21no—
32C59×#536—21no—
33C59×#535—21no—
34C59×#535—21no—
35C59×#534—22no—
36C59×#532—22no—
37C59×#525—22no—
38C59×#525C414yescomplemented
39C2×#117×C59C2211yescharacteristic
40C2×#11745664—21no—
41C2×#11745664—21no—
42C2×#11745664—21no—
43C2×#11745664—21no—
44C2×#11745664—21no—
45C2×#11745664—21no—
46C2×#11745664—21no—
47C2×#11745664—21no—
48C2×#11745664—21no—
49C2×#11745664—21no—
50C2×#11745664D412yescomplemented
51C2×#11745664D412yescomplemented
52C22×C59⋊C8—21no—
53C22×C59⋊C8—21no—
54#14273686—21no—
55#14273686—21no—
56#14273686—21no—
57#14273686—21no—
58#14273686—21no—
59#14273686—21no—
60#14273686D412yescomplemented
61#14273686D412yescomplemented
62C2×C4⋊Dic59—21no—
63C2×C4⋊Dic59—21no—
64C2×C22⋊Dic59—21no—
65C2×C22⋊Dic59—21no—
66C2×C4×Dic59—21no—
67C2×C4×Dic59—21no—
68#14273654—28no—
69#14273651—24no—
70#14273648—24no—
71#14273646—24no—
72#14273644—24no—
73#14273642—28no—
74C2×#41×C59—21no—
75C2×#41×C59—21no—
76C2×#41×C59—21no—
77C2×#41×C59—21no—
78C2×#41×C59—21no—
79C2×#41×C59—21no—
80C2×#41×C59—21no—
81C2×#41×C59—21no—
82C2×#41×C59—21no—
83C2×#41×C59—21no—
84C2×#41×C59—21no—
85C2×#41×C59—21no—
86C2×#41×C59—21no—
87C2×#41×C59—21no—
88C2×#41×C59—21no—
89C2×#41×C59—21no—
90C2×#41×C59—21no—
91C2×#41×C59—21no—
92C2×#41×C59—21no—
93C2×#41×C59—21no—
94C2×#41×C59—21no—
95C2×#41×C59—21no—
96C2×#41×C59C2×C412yes—
97C2×#41×C59D412yes—
98C22×Q8×C59D411yescharacteristic
99C22×Q8×C59D411yescharacteristic
100C22×D4×C59—21no—
101C22×D4×C59D412yes—
102C22×D4×C59D411yescharacteristic
103C22×D4×C59D411yescharacteristic
104C23×C4×C59—21no—
105C23×C4×C59C2×C412yes—
106C23×C4×C59C2311yescharacteristic
107C4⋊Q8×C59—22no—
108#127×C59—22no—
109#124×C59—22no—
110#124×C59—22no—
111#123×C59—24no—
112#123×C59—24no—
113C22⋊Q8×C59—24no—
114C22⋊Q8×C59—24no—
115#121×C59—24no—
116#121×C59—28no—
117#121×C59—24no—
118#120×C59—24no—
119#120×C59—24no—
120C4×D4×C59—28no—
121#117×C59—21no—
122#117×C59—21no—
123#117×C59C2×C412yes—
124#117×C59D412yes—
125C2×C4⋊C4×C59—21no—
126C2×C22⋊C4×C59—21no—
127C2×C42×C59D412yes—
128C24×C59—21no—
129C24×C59C22⋊C412yes—
130C24×C59C2×D411yescharacteristic
131#41×C59—22no—
132#41×C59—22no—
133#41×C59—22no—
134#41×C59—22no—
135#41×C59—22no—
136#41×C59—22no—
137#41×C59—22no—
138#41×C59—22no—
139#41×C59—41no—
140#41×C59—41no—
141#41×C59—41no—
142#41×C59—41no—
143#41×C59—41no—
144#41×C59—41no—
145#41×C59—41no—
146#41×C59—41no—
147#41×C59—41no—
148#41×C59—41no—
149#41×C59—41no—
150#41×C59—41no—
151#41×C59—41no—
152#41×C59—41no—
153#41×C59—41no—
154#41×C59—41no—
155#41×C59—41no—
156#41×C59—41no—
157#41×C59—41no—
158#41×C59—41no—
159#41×C59—41no—
160#41×C59—41no—
161#41×C59—41no—
162#41×C59—41no—
163C2×Q8×C59—21no—
164C2×Q8×C59—21no—
165C2×Q8×C59—21no—
166C2×Q8×C59—21no—
167C2×Q8×C59—21no—
168C2×Q8×C59—21no—
169C2×Q8×C59—21no—
170C2×Q8×C59—21no—
171C2×Q8×C59—21no—
172C2×Q8×C59—21no—
173C2×Q8×C59—21no—
174C2×Q8×C59C22⋊C412yes—
175C2×D4×C59—22no—
176C2×D4×C59—22no—
177C2×D4×C59—22no—
178C2×D4×C59—22no—
179C2×D4×C59—22no—
180C2×D4×C59—22no—
181C2×D4×C59—22no—
182C2×D4×C59—22no—
183C2×D4×C59—28no—
184C2×D4×C59—21no—
185C2×D4×C59—21no—
186C2×D4×C59—21no—
187C2×D4×C59—21no—
188C2×D4×C59—21no—
189C2×D4×C59—21no—
190C2×D4×C59—21no—
191C2×D4×C59—21no—
192C2×D4×C59—21no—
193C2×D4×C59—21no—
194C2×D4×C59—21no—
195C2×D4×C59—41no—
196C2×D4×C59—41no—
197C2×D4×C59—41no—
198C2×D4×C59—41no—
199C2×D4×C59C22⋊C412yes—
200C22×C4×C59—21no—
201C22×C4×C59—22no—
202C22×C4×C59—22no—
203C22×C4×C59—22no—
204C22×C4×C59—22no—
205C22×C4×C59—22no—
206C22×C4×C59—22no—
207C22×C4×C59—22no—
208C22×C4×C59—22no—
209C22×C4×C59—22no—
210C22×C4×C59—41no—
211C22×C4×C59—41no—
212C22×C4×C59—41no—
213C22×C4×C59—41no—
214C22×C4×C59C22⋊C412yes—
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
222C22×C4×C59C2×D411yescharacteristic
223C22×C4×C59C2×D411yescharacteristic
224C22×C4×C59C2×D411yescharacteristic
225C22×C4×C59#4111yescharacteristic
226C22×C4×C59#4111yescharacteristic
227C22×C4×C59#4111yescharacteristic
228C22×C4×C59#4111yescharacteristic
229C22×Dic59—41no—
230C22×Dic59—41no—
231C4⋊C4×C59—28no—
232C4⋊C4×C59—22no—
233C4⋊C4×C59—22no—
234C22⋊C4×C59—28no—
235C22⋊C4×C59—28no—
236C22⋊C4×C59—22no—
237C22⋊C4×C59—22no—
238C42×C59—22no—
239C42×C59C22⋊C414yes—
240C22⋊Dic59—22no—
241C22⋊Dic59—22no—
242C22⋊Dic59—41no—
243C22⋊Dic59—41no—
244C4⋊Dic59—22no—
245C4⋊Dic59—22no—
246C4⋊Dic59—41no—
247C4⋊Dic59—41no—
248C4×Dic59—22no—
249C4×Dic59—22no—
250C4×Dic59—41no—
251C4×Dic59—41no—
252#11745664—22no—
253#11745664—22no—
254#11745664—22no—
255#11745664—22no—
256#11745664—41no—
257#11745664—41no—
258#11745664—41no—
259#11745664—41no—
260C2×C59⋊C8—22no—
261C2×C59⋊C8—22no—
262C2×C59⋊C8—41no—
263C2×C59⋊C8—41no—
264C2×C59⋊C8—41no—
265C2×C59⋊C8—41no—
266C23×C59—22no—
267C23×C59—22no—
268C23×C59—22no—
269C23×C59—22no—
270C23×C59—41no—
271C23×C59—41no—
272C23×C59—81no—
273C23×C59—82no—
274C23×C59—82no—
275C23×C59C2×C22⋊C411yescharacteristic
276C23×C59#12011yescharacteristic
277C23×C59#12011yescharacteristic
278C23×C59#12011yescharacteristic
279C23×C59#12111yescharacteristic
280C23×C59#12111yescharacteristic
281C23×C59#12311yescharacteristic
282Q8×C59—22no—
283Q8×C59—22no—
284Q8×C59—41no—
285Q8×C59—41no—
286Q8×C59—41no—
287Q8×C59—41no—
288Q8×C59—41no—
289Q8×C59—41no—
290D4×C59—22no—
291D4×C59—22no—
292D4×C59—42no—
293D4×C59—42no—
294D4×C59—42no—
295D4×C59—42no—
296D4×C59—42no—
297D4×C59—42no—
298D4×C59—42no—
299D4×C59—42no—
300D4×C59—41no—
301D4×C59—41no—
302D4×C59—41no—
303D4×C59—41no—
304D4×C59—41no—
305D4×C59—41no—
306D4×C59—88no—
307C2×C4×C59—24no—
308C2×C4×C59—22no—
309C2×C4×C59—22no—
310C2×C4×C59—22no—
311C2×C4×C59—22no—
312C2×C4×C59—41no—
313C2×C4×C59—41no—
314C2×C4×C59—42no—
315C2×C4×C59—42no—
316C2×C4×C59—42no—
317C2×C4×C59—42no—
318C2×C4×C59—42no—
319C2×C4×C59—42no—
320C2×C4×C59—42no—
321C2×C4×C59—42no—
322C2×C4×C59—82no—
323C2×C4×C59C2×C22⋊C411yescharacteristic
324C2×C4×C59C2×C22⋊C411yescharacteristic
325C2×C4×C59C4×D411yescharacteristic
326C2×C4×C59C4×D411yescharacteristic
327C2×C4×C59C4×D411yescharacteristic
328C2×C4×C59C4×D411yescharacteristic
329C2×C4×C59#12011yescharacteristic
330C2×C4×C59#12011yescharacteristic
331C2×C4×C59#12011yescharacteristic
332C2×C4×C59#12011yescharacteristic
333C2×C4×C59#12011yescharacteristic
334C2×C4×C59#12111yescharacteristic
335C2×C4×C59#12111yescharacteristic
336C2×C4×C59#12111yescharacteristic
337C2×C4×C59#12111yescharacteristic
338C2×C4×C59#12111yescharacteristic
339C2×C4×C59#12111yescharacteristic
340C2×C4×C59#12111yescharacteristic
341C2×C4×C59#12111yescharacteristic
342C2×C4×C59#12111yescharacteristic
343C2×C4×C59#12111yescharacteristic
344C2×C4×C59#12311yescharacteristic
345C2×C4×C59#12311yescharacteristic
346C2×C4×C59#12311yescharacteristic
347C2×C4×C59#12411yescharacteristic
348C2×C4×C59#12411yescharacteristic
349C2×C4×C59#12711yescharacteristic
350C2×C4×C59#12711yescharacteristic
351C2×Dic59—42no—
352C2×Dic59—42no—
353C2×Dic59—82no—
354C2×Dic59—82no—
355C59⋊C8—42no—
356C59⋊C8—42no—
357#11000—591nomaximal, Sylow
358C22×C59—41no—
359C22×C59—41no—
360C22×C59—41no—
361C22×C59—41no—
362C22×C59—41no—
363C22×C59—41no—
364C22×C59—41no—
365C22×C59—44no—
366C22×C59—44no—
367C22×C59—42no—
368C22×C59—42no—
369C22×C59—82no—
370C22×C59—82no—
371C22×C59—82no—
372C22×C59—82no—
373C22×C59#37911yescharacteristic
374C22×C59#38611yescharacteristic
375C22×C59#38611yescharacteristic
376C22×C59#39211yescharacteristic
377C22×C59#39211yescharacteristic
378C22×C59#39411yescharacteristic
379C22×C59#39411yescharacteristic
380C4×C59—44no—
381C4×C59—42no—
382C4×C59—42no—
383C4×C59#38611yescharacteristic
384C4×C59#38611yescharacteristic
385C4×C59#39011yescharacteristic
386C4×C59#39011yescharacteristic
387C4×C59#39211yescharacteristic
388C4×C59#39211yescharacteristic
389C4×C59#39411yescharacteristic
390C4×C59#39411yescharacteristic
391Dic59—82no—
392Dic59—82no—
393#3449D5911yescharacteristic
394C2×#421—591no—
395#2896—591no—
396C2×#413—591no—
397C2×#410—591no—
398#1733—591no—
399C2×H(3,ℤ/4)—591no—
400C2×C59—21no—
401C2×C59—21no—
402C2×C59—21no—
403C2×C59—21no—
404C2×C59—21no—
405C2×C59—21no—
406C2×C59—21no—
407C2×C59—82no—
408C2×C59—82no—
409C2×C59#143811yescharacteristic
410C22×#41C2×D5911yescharacteristic
411C22×#41C2×D5911yescharacteristic
412C22×M16—591no—
413C22×M16—591no—
414#537—22no—
415#536—21no—
416#536—21no—
417#535—21no—
418#535—21no—
419#534—22no—
420#532—22no—
421#525—22no—
422#525Dic5914yescomplemented
423C2×#117—591no—
424C2×#117—591no—
425C2×#117C2×D5911yescharacteristic
426#421—1182no—
427#421—1182no—
428C2×#104—1182no—
429#419—1181no—
430#418—1181no—
431#417—1182no—
432#416—1182no—
433#413—1182no—
434#413—1182no—
435C2×#101—1181no—
436C2×#100—1181no—
437#410—1182no—
438#410—1182no—
439C2×#99—1182no—
440#339—1182no—
441H(3,ℤ/4)—1182no—
442C59#1100011yescharacteristic, complemented, Sylow
443C2×#41—21no—
444C2×#41—21no—
445C2×#41—21no—
446C2×#41—21no—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C2×#41—21no—
453C2×#41—21no—
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—21no—
465C2×#41C2×Dic5912yes—
466C2×#41C22⋊D5912yes—
467C22×Q8C22⋊D5911yescharacteristic
468C22×Q8C22⋊D5911yescharacteristic
469C22×D4—21no—
470C22×D4C22⋊D5912yes—
471C22×D4C22⋊D5911yescharacteristic
472C22×D4C22⋊D5911yescharacteristic
473C23×C4—21no—
474C23×C4C2×Dic5912yes—
475C23×C4C22×D5911yescharacteristic
476C2×M16—592no—
477C2×M16—592no—
478C2×M16—1181no—
479C2×M16—1181no—
480C2×M16—1181no—
481C2×M16—1181no—
482C2×M16—1181no—
483C2×M16—1181no—
484C2×M16—1181no—
485C2×M16—1181no—
486C2×M16—1181no—
487C2×M16—1181no—
488C22×C8—1181no—
489C22×C8—1181no—
490C4⋊Q8—22no—
491#127—22no—
492#124—22no—
493#124—22no—
494#123—24no—
495#123—24no—
496C22⋊Q8—24no—
497C22⋊Q8—24no—
498#121—24no—
499#121—28no—
500#121—24no—
501#120—24no—
502#120—24no—
503C4×D4—28no—
504#117—21no—
505#117—21no—
506#117—592no—
507#117—592no—
508#117—1181no—
509#117—1181no—
510#117—1181no—
511#117—1181no—
512#117—1181no—
513#117—1181no—
514#117C2×Dic5912yes—
515#117C22⋊D5912yes—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—1181no—
518C2×C4⋊C4—1181no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—1181no—
521C2×C22⋊C4—1181no—
522C2×C42—1181no—
523C2×C42—1181no—
524C2×C42C22⋊D5912yes—
525#104—1188no—
526#103—1184no—
527#102—1184no—
528#101—1184no—
529#100—1184no—
530#99—1188no—
531C24—21no—
532C24C22⋊Dic5912yes—
533C24C2×C22⋊D5911yescharacteristic
534#41—22no—
535#41—22no—
536#41—22no—
537#41—22no—
538#41—22no—
539#41—22no—
540#41—22no—
541#41—22no—
542#41—41no—
543#41—41no—
544#41—41no—
545#41—41no—
546#41—41no—
547#41—41no—
548#41—41no—
549#41—41no—
550#41—41no—
551#41—41no—
552#41—41no—
553#41—41no—
554#41—41no—
555#41—41no—
556#41—41no—
557#41—41no—
558#41—41no—
559#41—41no—
560#41—41no—
561#41—41no—
562#41—41no—
563#41—41no—
564#41—41no—
565#41—41no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8C22⋊Dic5912yes—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—28no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—41no—
599C2×D4—41no—
600C2×D4—41no—
601C2×D4—41no—
602C2×D4C22⋊Dic5912yes—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—2361no—
618C22×C4—2361no—
619C22×C4C22⋊Dic5912yes—
620C22×C4D4×D5911yescharacteristic
621C22×C4D4×D5911yescharacteristic
622C22×C4D4×D5911yescharacteristic
623C22×C4D4×D5911yescharacteristic
624C22×C4#1174568711yescharacteristic
625C22×C4#1174568711yescharacteristic
626C22×C4#1174568711yescharacteristic
627C22×C4#1174568711yescharacteristic
628C22×C4C22×Dic5911yescharacteristic
629C22×C4C2×C22⋊D5911yescharacteristic
630C22×C4C2×C22⋊D5911yescharacteristic
631C22×C4C2×C22⋊D5911yescharacteristic
632C22×C4C2×C22⋊D5911yescharacteristic
633C22×C4C2×C22⋊D5911yescharacteristic
634M16—1182no—
635M16—1182no—
636M16—1182no—
637M16—1182no—
638M16—2361no—
639M16—2361no—
640M16—2361no—
641M16—2361no—
642C2×C8—1182no—
643C2×C8—1182no—
644C2×C8—2361no—
645C2×C8—2361no—
646C2×C8—2361no—
647C2×C8—2361no—
648C4⋊C4—28no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—1182no—
652C4⋊C4—1182no—
653C4⋊C4—2361no—
654C4⋊C4—2361no—
655C22⋊C4—28no—
656C22⋊C4—28no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—1182no—
660C22⋊C4—1182no—
661C22⋊C4—2361no—
662C22⋊C4—2361no—
663C42—22no—
664C42—1182no—
665C42—1182no—
666C42—2361no—
667C42—2361no—
668C42C22⋊Dic5914yes—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—41no—
674C23—41no—
675C23—81no—
676C23—82no—
677C23—82no—
678C23C2×C22⋊Dic5911yescharacteristic
679C23#1427369511yescharacteristic
680C23#1427369611yescharacteristic
681C23#1427369611yescharacteristic
682C23#1427369911yescharacteristic
683C23#1427369911yescharacteristic
684C23#1427370811yescharacteristic
685Q8—22no—
686Q8—22no—
687Q8—41no—
688Q8—41no—
689Q8—41no—
690Q8—41no—
691Q8—41no—
692Q8—41no—
693D4—22no—
694D4—22no—
695D4—42no—
696D4—42no—
697D4—42no—
698D4—42no—
699D4—42no—
700D4—42no—
701D4—42no—
702D4—42no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—88no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—82no—
726C2×C4—4722no—
727C2×C4—4722no—
728C2×C4—2362no—
729C2×C4—2362no—
730C2×C4C2×C22⋊Dic5911yescharacteristic
731C2×C4C2×C22⋊Dic5911yescharacteristic
732C2×C4D4×Dic5911yescharacteristic
733C2×C4D4×Dic5911yescharacteristic
734C2×C4D4×Dic5911yescharacteristic
735C2×C4D4×Dic5911yescharacteristic
736C2×C4#1427369511yescharacteristic
737C2×C4#1427369511yescharacteristic
738C2×C4#1427369511yescharacteristic
739C2×C4#1427369611yescharacteristic
740C2×C4#1427369611yescharacteristic
741C2×C4#1427369811yescharacteristic
742C2×C4#1427369811yescharacteristic
743C2×C4#1427369811yescharacteristic
744C2×C4#1427369811yescharacteristic
745C2×C4#1427369911yescharacteristic
746C2×C4#1427369911yescharacteristic
747C2×C4#1427369911yescharacteristic
748C2×C4#1427369911yescharacteristic
749C2×C4#1427369911yescharacteristic
750C2×C4#1427369911yescharacteristic
751C2×C4#1427370811yescharacteristic
752C2×C4#1427370811yescharacteristic
753C2×C4#1427370811yescharacteristic
754C2×C4#1427371411yescharacteristic
755C2×C4#1427371411yescharacteristic
756C2×C4#1427372311yescharacteristic
757C2×C4#1427372311yescharacteristic
758C8—2362no—
759C8—2362no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—44no—
768C22—44no—
769C22—42no—
770C22—42no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—82no—
775C22#1683725811yescharacteristic
776C22#1683728211yescharacteristic
777C22#1683728211yescharacteristic
778C22#1683731011yescharacteristic
779C22#1683731011yescharacteristic
780C22#1683731611yescharacteristic
781C22#1683731611yescharacteristic
782C4—44no—
783C4—42no—
784C4—42no—
785C4—4722no—
786C4—4722no—
787C4#1683728211yescharacteristic
788C4#1683728211yescharacteristic
789C4#1683730511yescharacteristic
790C4#1683730511yescharacteristic
791C4#1683731011yescharacteristic
792C4#1683731011yescharacteristic
793C4#1683731611yescharacteristic
794C4#1683731611yescharacteristic
795C2—21no—
796C2—21no—
797C2—21no—
798C2—21no—
799C2—21no—
800C2—21no—
801C2—21no—
802C2—82no—
803C2—82no—
804C2#2142233711yescharacteristic
subgroupG/H
centerC4#16837305
commutatorC22×C4×C59C22×C4
FrattiniC23×C4C22×D59
Fitting, prime radicalC59×#3449C2
socleC2×C59#1438
cosocleC23×C4×C59C23
hypercenter#3449D59
hypocenterC59#11000
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C4 ◁ C23×C4 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. C2×#16837419C2semidirect
2. #21432615C2semidirect
3. C2×#16837386C2semidirect
4. C2×#16837376C2semidirect
5. #21423806C2semidirect
6. C2×#16837158C2semidirect
38. C59×#525C4semidirect
50. C2×#11745664D4semidirect
51. C2×#11745664D4semidirect
60. #14273686D4semidirect
61. #14273686D4semidirect
422. #525Dic59semidirect
442. C59#11000semidirect

Maximal subgroups

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

subgroupindex
C2×#168374192
#214326152
C2×#168373862
C2×#168373762
#214238062
C2×#168371582
C59×#34492
#1100059