Finite Group Databasebeta

← #28495370

Subgroups — #28495370

Order 15104.

1292 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837419C211yesmaximal, characteristic, complemented
2C2×#16837419C211yesmaximal, characteristic, complemented
3C2×#16837419C211yesmaximal, characteristic, complemented
4#21432615C211yesmaximal, characteristic, complemented
5C2×#16837172C211yesmaximal, characteristic, complemented
6#21423828C211yesmaximal, characteristic, complemented
7C59×#3449C211yesmaximal, characteristic
8C22×#11745664C2211yescharacteristic
9C22×#11745664C2211yescharacteristic
10C2×#14273686C2211yescharacteristic
11C2×#14273686C2211yescharacteristic
12#16837419—22no—
13#16837419—22no—
14#16837419—22no—
15#16837419—22no—
16#16837419—22no—
17#16837419—22no—
18C2×#14273654—22no—
19C2×#14273654—22no—
20C2×#14273654—22no—
21#16837411—21no—
22#16837407—21no—
23#16837403—22no—
24#16837398—22no—
25#16837172—22no—
26#16837168—22no—
27C22×#41×C59C2211yescharacteristic
28C22×#41×C59C2211yescharacteristic
29C59×#537—22no—
30C59×#536—21no—
31C59×#536C412yescomplemented
32C59×#535—21no—
33C59×#535C412yescomplemented
34C59×#534—22no—
35C59×#532—22no—
36C59×#525—22no—
37C59×#525—22no—
38C2×#117×C59C2211yescharacteristic
39C2×#11745664—21no—
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×#11745664D412yescomplemented
50C2×#11745664D412yescomplemented
51C22×C59⋊C8—21no—
52C22×C59⋊C8—21no—
53#14273686—21no—
54#14273686—21no—
55#14273686—21no—
56#14273686—21no—
57#14273686—21no—
58#14273686—21no—
59#14273686—21no—
60#14273686D412yescomplemented
61C2×C4⋊Dic59—21no—
62C2×C4⋊Dic59—21no—
63C2×C22⋊Dic59—21no—
64C2×C22⋊Dic59—21no—
65C2×C4×Dic59—21no—
66C2×C4×Dic59D412yescomplemented
67#14273654—28no—
68#14273654—28no—
69#14273654—28no—
70#14273651—24no—
71#14273648—24no—
72C2×#41×C59—21no—
73C2×#41×C59—21no—
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×C59C2×C412yes—
93C2×#41×C59D412yes—
94C2×#41×C59D412yes—
95C2×#41×C59D412yes—
96C22×Q8×C59C2×C411yescharacteristic
97C22×Q8×C59D411yescharacteristic
98C22×D4×C59—21no—
99C22×D4×C59—21no—
100C22×D4×C59C2×C411yescharacteristic
101C22×D4×C59D411yescharacteristic
102C23×C4×C59—21no—
103C23×C4×C59—21no—
104C23×C4×C59C2311yescharacteristic
105C4⋊Q8×C59—22no—
106#127×C59—22no—
107#124×C59—22no—
108#124×C59—22no—
109#123×C59—24no—
110#123×C59—24no—
111C22⋊Q8×C59—24no—
112C22⋊Q8×C59—24no—
113#121×C59—24no—
114#121×C59—28no—
115#121×C59—24no—
116#120×C59—24no—
117#120×C59—24no—
118C4×D4×C59—28no—
119#117×C59—21no—
120#117×C59—21no—
121#117×C59C2×C412yes—
122#117×C59D412yes—
123C2×C4⋊C4×C59—21no—
124C2×C22⋊C4×C59D412yes—
125C2×C42×C59—21no—
126C24×C59—21no—
127C24×C59—21no—
128C24×C59C2×D411yescharacteristic
129#41×C59—22no—
130#41×C59—22no—
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—22no—
140#41×C59—22no—
141#41×C59—22no—
142#41×C59—22no—
143#41×C59—22no—
144#41×C59—22no—
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—
161C2×Q8×C59—21no—
162C2×Q8×C59—21no—
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×C59C22⋊C412yes—
172C2×Q8×C59C22⋊C412yes—
173C2×D4×C59—22no—
174C2×D4×C59—22no—
175C2×D4×C59—22no—
176C2×D4×C59—22no—
177C2×D4×C59—28no—
178C2×D4×C59—21no—
179C2×D4×C59—21no—
180C2×D4×C59—21no—
181C2×D4×C59—21no—
182C2×D4×C59—21no—
183C2×D4×C59—21no—
184C2×D4×C59—21no—
185C2×D4×C59—21no—
186C2×D4×C59—21no—
187C2×D4×C59—21no—
188C2×D4×C59—41no—
189C2×D4×C59—41no—
190C2×D4×C59—41no—
191C2×D4×C59—41no—
192C2×D4×C59—41no—
193C2×D4×C59—41no—
194C2×D4×C59—41no—
195C2×D4×C59—41no—
196C2×D4×C59C22⋊C412yes—
197C2×D4×C59C22⋊C412yes—
198C22×C4×C59—21no—
199C22×C4×C59—21no—
200C22×C4×C59—22no—
201C22×C4×C59—22no—
202C22×C4×C59—22no—
203C22×C4×C59—22no—
204C22×C4×C59—22no—
205C22×C4×C59—41no—
206C22×C4×C59—41no—
207C22×C4×C59—41no—
208C22×C4×C59—41no—
209C22×C4×C59—41no—
210C22×C4×C59—41no—
211C22×C4×C59—41no—
212C22×C4×C59—41no—
213C22×C4×C59C22×C411yescharacteristic
214C22×C4×C59C2×D411yescharacteristic
215C22×C4×C59C2×D411yescharacteristic
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×C59#4111yescharacteristic
224C22×C4×C59#4111yescharacteristic
225C22×C4×C59#4111yescharacteristic
226C22×C4×C59#4111yescharacteristic
227C22×Dic59—22no—
228C22×Dic59—41no—
229C4⋊C4×C59—28no—
230C4⋊C4×C59—22no—
231C4⋊C4×C59—22no—
232C22⋊C4×C59—28no—
233C22⋊C4×C59—28no—
234C22⋊C4×C59—22no—
235C22⋊C4×C59C22⋊C414yes—
236C42×C59—22no—
237C42×C59—22no—
238C22⋊Dic59—22no—
239C22⋊Dic59—41no—
240C22⋊Dic59—41no—
241C22⋊Dic59—41no—
242C4⋊Dic59—22no—
243C4⋊Dic59—41no—
244C4⋊Dic59—41no—
245C4⋊Dic59—41no—
246C4×Dic59—22no—
247C4×Dic59—22no—
248C4×Dic59—22no—
249C4×Dic59—41no—
250#11745664—22no—
251#11745664—22no—
252#11745664—22no—
253#11745664—22no—
254#11745664—41no—
255#11745664—41no—
256#11745664—41no—
257#11745664—41no—
258C2×C59⋊C8—22no—
259C2×C59⋊C8—22no—
260C2×C59⋊C8—41no—
261C2×C59⋊C8—41no—
262C2×C59⋊C8—41no—
263C2×C59⋊C8—41no—
264C23×C59—22no—
265C23×C59—22no—
266C23×C59—41no—
267C23×C59—41no—
268C23×C59—41no—
269C23×C59—41no—
270C23×C59—81no—
271C23×C59—82no—
272C23×C59—82no—
273C23×C59C2×C22⋊C411yescharacteristic
274C23×C59#12011yescharacteristic
275C23×C59#12011yescharacteristic
276C23×C59#12111yescharacteristic
277C23×C59#12111yescharacteristic
278C23×C59#12411yescharacteristic
279C23×C59#12711yescharacteristic
280Q8×C59—22no—
281Q8×C59—22no—
282Q8×C59—22no—
283Q8×C59—22no—
284Q8×C59—41no—
285Q8×C59—41no—
286Q8×C59—41no—
287Q8×C59—41no—
288D4×C59—22no—
289D4×C59—22no—
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—88no—
305C2×C4×C59—24no—
306C2×C4×C59—22no—
307C2×C4×C59—22no—
308C2×C4×C59—41no—
309C2×C4×C59—41no—
310C2×C4×C59—41no—
311C2×C4×C59—41no—
312C2×C4×C59—42no—
313C2×C4×C59—42no—
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—82no—
321C2×C4×C59C2×C22⋊C411yescharacteristic
322C2×C4×C59C2×C22⋊C411yescharacteristic
323C2×C4×C59C4×D411yescharacteristic
324C2×C4×C59C4×D411yescharacteristic
325C2×C4×C59C4×D411yescharacteristic
326C2×C4×C59C4×D411yescharacteristic
327C2×C4×C59#12011yescharacteristic
328C2×C4×C59#12011yescharacteristic
329C2×C4×C59#12011yescharacteristic
330C2×C4×C59#12011yescharacteristic
331C2×C4×C59#12011yescharacteristic
332C2×C4×C59#12011yescharacteristic
333C2×C4×C59#12111yescharacteristic
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#12311yescharacteristic
344C2×C4×C59#12311yescharacteristic
345C2×C4×C59#12311yescharacteristic
346C2×C4×C59#12311yescharacteristic
347C2×C4×C59#12411yescharacteristic
348C2×C4×C59#12711yescharacteristic
349C2×Dic59—42no—
350C2×Dic59—42no—
351C2×Dic59—82no—
352C2×Dic59—82no—
353C59⋊C8—42no—
354C59⋊C8—42no—
355#11003—591nomaximal, Sylow
356C22×C59—41no—
357C22×C59—41no—
358C22×C59—41no—
359C22×C59—41no—
360C22×C59—41no—
361C22×C59—41no—
362C22×C59—41no—
363C22×C59—44no—
364C22×C59—44no—
365C22×C59—42no—
366C22×C59—42no—
367C22×C59—82no—
368C22×C59—82no—
369C22×C59—82no—
370C22×C59—82no—
371C22×C59#37911yescharacteristic
372C22×C59#39011yescharacteristic
373C22×C59#39011yescharacteristic
374C22×C59#39211yescharacteristic
375C22×C59#39211yescharacteristic
376C22×C59#39411yescharacteristic
377C22×C59#39411yescharacteristic
378C4×C59—44no—
379C4×C59—42no—
380C4×C59—42no—
381C4×C59#38611yescharacteristic
382C4×C59#38611yescharacteristic
383C4×C59#38611yescharacteristic
384C4×C59#38611yescharacteristic
385C4×C59#39211yescharacteristic
386C4×C59#39211yescharacteristic
387C4×C59#39411yescharacteristic
388C4×C59#39411yescharacteristic
389Dic59—82no—
390Dic59—82no—
391#3449D5911yescharacteristic
392C2×#421—591no—
393C2×#421—591no—
394C2×#421—591no—
395#2896—591no—
396C2×#344—591no—
397#1740—591no—
398C2×C59—21no—
399C2×C59—21no—
400C2×C59—21no—
401C2×C59—21no—
402C2×C59—21no—
403C2×C59—21no—
404C2×C59—21no—
405C2×C59—82no—
406C2×C59—82no—
407C2×C59#143811yescharacteristic
408C22×#41C2×D5911yescharacteristic
409C22×#41C2×D5911yescharacteristic
410C22×M16—591no—
411C22×M16—591no—
412#537—22no—
413#536—21no—
414#536Dic5912yescomplemented
415#535—21no—
416#535Dic5912yescomplemented
417#534—22no—
418#532—22no—
419#525—22no—
420#525—22no—
421C2×#117—591no—
422C2×#117—591no—
423C2×#117C2×D5911yescharacteristic
424#421—1182no—
425#421—1182no—
426#421—1182no—
427#421—1182no—
428#421—1182no—
429#421—1182no—
430C2×#104—1182no—
431C2×#104—1182no—
432C2×#104—1182no—
433#419—1181no—
434#418—1181no—
435#417—1182no—
436#416—1182no—
437#344—1182no—
438#342—1182no—
439C59#1100311yescharacteristic, complemented, Sylow
440C2×#41—21no—
441C2×#41—21no—
442C2×#41—21no—
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×#41C2×Dic5912yes—
461C2×#41C22⋊D5912yes—
462C2×#41C22⋊D5912yes—
463C2×#41C22⋊D5912yes—
464C22×Q8C2×Dic5911yescharacteristic
465C22×Q8C22⋊D5911yescharacteristic
466C22×D4—21no—
467C22×D4—21no—
468C22×D4C2×Dic5911yescharacteristic
469C22×D4C22⋊D5911yescharacteristic
470C23×C4—21no—
471C23×C4—21no—
472C23×C4C22×D5911yescharacteristic
473C2×M16—592no—
474C2×M16—592no—
475C2×M16—1181no—
476C2×M16—1181no—
477C2×M16—1181no—
478C2×M16—1181no—
479C2×M16—1181no—
480C2×M16—1181no—
481C2×M16—1181no—
482C2×M16—1181no—
483C2×M16—1181no—
484C2×M16—1181no—
485C22×C8—1181no—
486C22×C8—1181no—
487C4⋊Q8—22no—
488#127—22no—
489#124—22no—
490#124—22no—
491#123—24no—
492#123—24no—
493C22⋊Q8—24no—
494C22⋊Q8—24no—
495#121—24no—
496#121—28no—
497#121—24no—
498#120—24no—
499#120—24no—
500C4×D4—28no—
501#117—21no—
502#117—21no—
503#117—592no—
504#117—1181no—
505#117—1181no—
506#117—1181no—
507#117—1181no—
508#117—1181no—
509#117—1181no—
510#117—1181no—
511#117C2×Dic5912yes—
512#117C22⋊D5912yes—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—1181no—
515C2×C4⋊C4—1181no—
516C2×C22⋊C4—1181no—
517C2×C22⋊C4—1181no—
518C2×C22⋊C4C22⋊D5912yes—
519C2×C42—21no—
520C2×C42—592no—
521C2×C42—1181no—
522#104—1188no—
523#104—1188no—
524#104—1188no—
525#103—1184no—
526#102—1184no—
527C24—21no—
528C24—21no—
529C24C2×C22⋊D5911yescharacteristic
530#41—22no—
531#41—22no—
532#41—22no—
533#41—22no—
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—22no—
543#41—22no—
544#41—22no—
545#41—22no—
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—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8C22⋊Dic5912yes—
573C2×Q8C22⋊Dic5912yes—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—28no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—41no—
590C2×D4—41no—
591C2×D4—41no—
592C2×D4—41no—
593C2×D4—41no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4—41no—
597C2×D4C22⋊Dic5912yes—
598C2×D4C22⋊Dic5912yes—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—1182no—
615C22×C4—2361no—
616C22×C4D4×D5911yescharacteristic
617C22×C4D4×D5911yescharacteristic
618C22×C4D4×D5911yescharacteristic
619C22×C4D4×D5911yescharacteristic
620C22×C4#1174568711yescharacteristic
621C22×C4#1174568711yescharacteristic
622C22×C4#1174568711yescharacteristic
623C22×C4#1174568711yescharacteristic
624C22×C4C22×Dic5911yescharacteristic
625C22×C4C2×C22⋊D5911yescharacteristic
626C22×C4C2×C22⋊D5911yescharacteristic
627C22×C4C2×C22⋊D5911yescharacteristic
628C22×C4C2×C22⋊D5911yescharacteristic
629C22×C4C2×C22⋊D5911yescharacteristic
630M16—1182no—
631M16—1182no—
632M16—1182no—
633M16—1182no—
634M16—2361no—
635M16—2361no—
636M16—2361no—
637M16—2361no—
638C2×C8—1182no—
639C2×C8—1182no—
640C2×C8—2361no—
641C2×C8—2361no—
642C2×C8—2361no—
643C2×C8—2361no—
644C4⋊C4—28no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—1182no—
648C4⋊C4—2361no—
649C4⋊C4—2361no—
650C4⋊C4—2361no—
651C22⋊C4—28no—
652C22⋊C4—28no—
653C22⋊C4—22no—
654C22⋊C4—1182no—
655C22⋊C4—2361no—
656C22⋊C4—2361no—
657C22⋊C4—2361no—
658C22⋊C4C22⋊Dic5914yes—
659C42—22no—
660C42—22no—
661C42—1182no—
662C42—1182no—
663C42—1182no—
664C42—2361no—
665C23—22no—
666C23—22no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—81no—
672C23—82no—
673C23—82no—
674C23C2×C22⋊Dic5911yescharacteristic
675C23#1427369611yescharacteristic
676C23#1427369611yescharacteristic
677C23#1427369811yescharacteristic
678C23#1427369811yescharacteristic
679C23#1427371411yescharacteristic
680C23#1427372311yescharacteristic
681Q8—22no—
682Q8—22no—
683Q8—22no—
684Q8—22no—
685Q8—41no—
686Q8—41no—
687Q8—41no—
688Q8—41no—
689D4—22no—
690D4—22no—
691D4—22no—
692D4—22no—
693D4—42no—
694D4—42no—
695D4—42no—
696D4—42no—
697D4—42no—
698D4—42no—
699D4—42no—
700D4—42no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—88no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—82no—
722C2×C4—4722no—
723C2×C4—4722no—
724C2×C4—2362no—
725C2×C4—2362no—
726C2×C4C2×C22⋊Dic5911yescharacteristic
727C2×C4C2×C22⋊Dic5911yescharacteristic
728C2×C4D4×Dic5911yescharacteristic
729C2×C4D4×Dic5911yescharacteristic
730C2×C4D4×Dic5911yescharacteristic
731C2×C4D4×Dic5911yescharacteristic
732C2×C4#1427369511yescharacteristic
733C2×C4#1427369511yescharacteristic
734C2×C4#1427369511yescharacteristic
735C2×C4#1427369511yescharacteristic
736C2×C4#1427369611yescharacteristic
737C2×C4#1427369611yescharacteristic
738C2×C4#1427369811yescharacteristic
739C2×C4#1427369811yescharacteristic
740C2×C4#1427369911yescharacteristic
741C2×C4#1427369911yescharacteristic
742C2×C4#1427369911yescharacteristic
743C2×C4#1427369911yescharacteristic
744C2×C4#1427369911yescharacteristic
745C2×C4#1427369911yescharacteristic
746C2×C4#1427369911yescharacteristic
747C2×C4#1427369911yescharacteristic
748C2×C4#1427370811yescharacteristic
749C2×C4#1427370811yescharacteristic
750C2×C4#1427370811yescharacteristic
751C2×C4#1427370811yescharacteristic
752C2×C4#1427371411yescharacteristic
753C2×C4#1427372311yescharacteristic
754C8—2362no—
755C8—2362no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—44no—
764C22—44no—
765C22—42no—
766C22—42no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22#1683725811yescharacteristic
772C22#1683730511yescharacteristic
773C22#1683730511yescharacteristic
774C22#1683731011yescharacteristic
775C22#1683731011yescharacteristic
776C22#1683731611yescharacteristic
777C22#1683731611yescharacteristic
778C4—44no—
779C4—42no—
780C4—42no—
781C4—4722no—
782C4—4722no—
783C4#1683728211yescharacteristic
784C4#1683728211yescharacteristic
785C4#1683728211yescharacteristic
786C4#1683728211yescharacteristic
787C4#1683731011yescharacteristic
788C4#1683731011yescharacteristic
789C4#1683731611yescharacteristic
790C4#1683731611yescharacteristic
791C2—21no—
792C2—21no—
793C2—21no—
794C2—21no—
795C2—21no—
796C2—21no—
797C2—21no—
798C2—82no—
799C2—82no—
800C2#2142233711yescharacteristic
subgroupG/H
centerC4#16837310
commutatorC22×C4×C59C22×C4
FrattiniC23×C4C22×D59
Fitting, prime radicalC59×#3449C2
socleC2×C59#1438
cosocleC23×C4×C59C23
hypercenter#3449D59
hypocenterC59#11003
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. C2×#16837419C2semidirect
3. C2×#16837419C2semidirect
4. #21432615C2semidirect
5. C2×#16837172C2semidirect
6. #21423828C2semidirect
31. C59×#536C4semidirect
33. C59×#535C4semidirect
49. C2×#11745664D4semidirect
50. C2×#11745664D4semidirect
60. #14273686D4semidirect
66. C2×C4×Dic59D4semidirect
414. #536Dic59semidirect
416. #535Dic59semidirect
439. C59#11003semidirect

Maximal subgroups

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

subgroupindex
C2×#168374192
#214326152
C2×#168371722
#214238282
C59×#34492
#1100359