Finite Group Databasebeta

← #27416874

Subgroups — #27416874

Order 13568.

1340 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810961C211yesmaximal, characteristic, complemented
2C2×#16810944C211yesmaximal, characteristic, complemented
3#20277307C211yesmaximal, characteristic, complemented
4#20275915C211yesmaximal, characteristic, complemented
5#20275908C211yesmaximal, characteristic, complemented
6#20275901C211yesmaximal, characteristic, complemented
7#20275894C211yesmaximal, characteristic, complemented
8#20275033C211yesmaximal, characteristic, complemented
9#20275023C211yesmaximal, characteristic, complemented
10#20274908C211yesmaximal, characteristic, complemented
11#20274903C211yesmaximal, characteristic, complemented
12#20274655C211yesmaximal, characteristic, complemented
13#20274655C211yesmaximal, characteristic, complemented
14#20274627C211yesmaximal, characteristic, complemented
15C2×C53×#537C211yesmaximal, characteristic
16C2×#13133176C2211yescharacteristic
17C22×C4⋊Dic53C2211yescharacteristic
18#16810961—24no—
19#16810944—24no—
20C2×#13133150C2211yescharacteristic
21C2×#13133150C2211yescharacteristic
22C2×#13133148C2211yescharacteristic
23C2×#13133148C2211yescharacteristic
24C2×#13133141C2211yescharacteristic
25C2×#13133141C2211yescharacteristic
26C2×#13133141C2211yescharacteristic
27C2×#13133141C2211yescharacteristic
28C2×#13133138C2211yescharacteristic
29C2×#13133138C2211yescharacteristic
30C2×#13133138C2211yescharacteristic
31C2×#13133138C2211yescharacteristic
32C2×C22⋊#88322C2211yescharacteristic
33C2×C22⋊#88322C2211yescharacteristic
34C2×C22⋊#88322C2211yescharacteristic
35C2×C22⋊#88322C2211yescharacteristic
36C2×C22⋊#88322C2211yescharacteristic
37C2×C22⋊#88322C2211yescharacteristic
38#16810530—21no—
39#16810526—21no—
40#16810503—21no—
41#16810503—21no—
42#16810483C2211yescharacteristic
43#16810483C2211yescharacteristic
44#16810483C2211yescharacteristic
45#16810483C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810385C2211yescharacteristic
49#16810385C2211yescharacteristic
50C22×#41×C53C2211yescharacteristic
51C22×#41×C53C2211yescharacteristic
52C53×#537—24no—
53C53×#537—24no—
54C2×C22⋊Q8×C53—21no—
55C2×C22⋊Q8×C53C2211yescharacteristic
56C2×C22⋊Q8×C53C2211yescharacteristic
57C2×#121×C53—21no—
58C2×#121×C53—21no—
59C2×#121×C53—21no—
60C2×#121×C53C2211yescharacteristic
61C2×#121×C53C2211yescharacteristic
62C22×C4⋊C4×C53C2211yescharacteristic
63C23×Dic53—21no—
64C22×#88322C2311yescharacteristic
65C22×#88322C2311yescharacteristic
66C22×#88322C2311yescharacteristic
67C22×#88322C2311yescharacteristic
68#13133176—22no—
69#13133176—22no—
70C2×C4⋊Dic53—21no—
71C2×C4⋊Dic53—41no—
72C2×C4⋊Dic53—41no—
73C2×C4⋊Dic53C2311yescharacteristic
74C2×C4⋊Dic53C2311yescharacteristic
75C2×C4⋊Dic53C2311yescharacteristic
76C2×C4⋊Dic53C2311yescharacteristic
77C2×C22⋊Dic53—21no—
78C2×C22⋊Dic53—21no—
79C2×C22⋊Dic53—21no—
80C2×C22⋊Dic53—21no—
81C2×C22⋊Dic53—21no—
82C2×C4×Dic53—21no—
83#13133150—22no—
84#13133150—22no—
85#13133148—22no—
86#13133148—22no—
87#13133141—22no—
88#13133141—22no—
89#13133141—41no—
90#13133141—41no—
91#13133138—22no—
92#13133138—22no—
93#13133138—41no—
94#13133138—41no—
95C22⋊#88322—22no—
96C22⋊#88322—22no—
97C22⋊#88322—22no—
98C22⋊#88322—22no—
99C22⋊#88322—41no—
100C22⋊#88322—41no—
101#13133124—21no—
102#13133124—21no—
103#13133124—21no—
104#13133124—21no—
105C2×#41×C53—22no—
106C2×#41×C53—22no—
107C2×#41×C53—22no—
108C2×#41×C53—22no—
109C2×#41×C53—22no—
110C2×#41×C53—22no—
111C2×#41×C53—22no—
112C2×#41×C53—22no—
113C2×#41×C53—41no—
114C2×#41×C53—41no—
115C2×#41×C53—41no—
116C2×#41×C53—41no—
117C22×Q8×C53D411yescharacteristic
118C22×Q8×C53C2311yescharacteristic
119C22×D4×C53—21no—
120C22×D4×C53—21no—
121C22×D4×C53—21no—
122C22×D4×C53D411yescharacteristic
123C22×D4×C53D411yescharacteristic
124C22×D4×C53D411yescharacteristic
125C22×D4×C53C2311yescharacteristic
126C23×C4×C53—21no—
127C23×C4×C53—21no—
128C23×C4×C53C2311yescharacteristic
129C23×C4×C53C2311yescharacteristic
130C23×C4×C53C2311yescharacteristic
131C22⋊Q8×C53—28no—
132C22⋊Q8×C53—22no—
133C22⋊Q8×C53—22no—
134C22⋊Q8×C53—22no—
135C22⋊Q8×C53D414yes—
136#121×C53—28no—
137#121×C53—28no—
138#121×C53—28no—
139#121×C53—22no—
140#121×C53—22no—
141#121×C53—22no—
142#121×C53D414yes—
143C2×C4⋊C4×C53—22no—
144C2×C4⋊C4×C53—22no—
145C2×C4⋊C4×C53—21no—
146C2×C4⋊C4×C53—21no—
147C2×C4⋊C4×C53—21no—
148C2×C4⋊C4×C53C2311yescharacteristic
149C2×C4⋊C4×C53C2311yescharacteristic
150C2×C22⋊C4×C53—21no—
151C2×C22⋊C4×C53—21no—
152C2×C22⋊C4×C53—21no—
153C2×C22⋊C4×C53—21no—
154C24×C53—21no—
155C24×C53C2×D411yescharacteristic
156C24×C53C2×D411yescharacteristic
157C24×C53C2×D411yescharacteristic
158#41×C53—44no—
159#41×C53—44no—
160#41×C53—44no—
161#41×C53—44no—
162#41×C53—44no—
163#41×C53—44no—
164#41×C53—44no—
165#41×C53—44no—
166C2×Q8×C53—22no—
167C2×Q8×C53—22no—
168C2×Q8×C53—21no—
169C2×Q8×C53—21no—
170C2×Q8×C53—21no—
171C2×Q8×C53—21no—
172C2×Q8×C53—21no—
173C2×Q8×C53—41no—
174C2×Q8×C53C2×D412yes—
175C2×D4×C53—24no—
176C2×D4×C53—22no—
177C2×D4×C53—22no—
178C2×D4×C53—22no—
179C2×D4×C53—22no—
180C2×D4×C53—24no—
181C2×D4×C53—24no—
182C2×D4×C53—22no—
183C2×D4×C53—22no—
184C2×D4×C53—21no—
185C2×D4×C53—21no—
186C2×D4×C53—21no—
187C2×D4×C53—21no—
188C2×D4×C53—21no—
189C2×D4×C53—41no—
190C2×D4×C53—41no—
191C2×D4×C53—41no—
192C2×D4×C53—42no—
193C2×D4×C53—42no—
194C2×D4×C53—81no—
195C2×D4×C53—81no—
196C2×D4×C53—81no—
197C2×D4×C53—81no—
198C2×D4×C53C2×D412yes—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—21no—
202C22×C4×C53—21no—
203C22×C4×C53—21no—
204C22×C4×C53—21no—
205C22×C4×C53—21no—
206C22×C4×C53—21no—
207C22×C4×C53—24no—
208C22×C4×C53—21no—
209C22×C4×C53—21no—
210C22×C4×C53—21no—
211C22×C4×C53—24no—
212C22×C4×C53—21no—
213C22×C4×C53—21no—
214C22×C4×C53—21no—
215C22×C4×C53—21no—
216C22×C4×C53—21no—
217C22×C4×C53—21no—
218C22×C4×C53—42no—
219C22×C4×C53—42no—
220C22×C4×C53—81no—
221C22×C4×C53—81no—
222C22×C4×C53C2×D411yescharacteristic
223C22×C4×C53C2×D411yescharacteristic
224C22×C4×C53C2×D412yes—
225C22×C4×C53C2×D412yes—
226C22×C4×C53C2×D411yescharacteristic
227C22×C4×C53#4112yes—
228C22×C4×C53#4112yes—
229C22×C4×C53C2411yescharacteristic
230C22×Dic53—21no—
231C22×Dic53—21no—
232C22×Dic53—21no—
233C22×Dic53—21no—
234C22×Dic53—42no—
235C22×Dic53—81no—
236C22×Dic53—81no—
237C4⋊C4×C53—24no—
238C4⋊C4×C53—24no—
239C4⋊C4×C53—24no—
240C4⋊C4×C53—21no—
241C4⋊C4×C53—21no—
242C4⋊C4×C53C2×D412yes—
243C4⋊C4×C53C2×D412yes—
244C22⋊C4×C53—24no—
245C22⋊C4×C53—24no—
246C22⋊C4×C53—24no—
247C22⋊C4×C53—24no—
248C22⋊Dic53—42no—
249C22⋊Dic53—81no—
250C22⋊Dic53—81no—
251C22⋊Dic53—81no—
252C22⋊Dic53—81no—
253C4⋊Dic53—21no—
254C4⋊Dic53—21no—
255C4⋊Dic53—21no—
256C4⋊Dic53—21no—
257C4⋊Dic53—21no—
258C4⋊Dic53—21no—
259C4⋊Dic53—21no—
260C4⋊Dic53—21no—
261C4⋊Dic53—42no—
262C4×Dic53—42no—
263C2×#88322—21no—
264C2×#88322—21no—
265C2×#88322—21no—
266C2×#88322—21no—
267C2×#88322—21no—
268C2×#88322—21no—
269C2×#88322—21no—
270C2×#88322—21no—
271C2×#88322—21no—
272C2×#88322—21no—
273C2×#88322—21no—
274C2×#88322—21no—
275C23×C53—21no—
276C23×C53—21no—
277C23×C53—21no—
278C23×C53—21no—
279C23×C53—21no—
280C23×C53—21no—
281C23×C53—21no—
282C23×C53—21no—
283C23×C53—21no—
284C23×C53—21no—
285C23×C53—21no—
286C23×C53—21no—
287C23×C53—21no—
288C23×C53—22no—
289C23×C53—21no—
290C23×C53—21no—
291C23×C53—21no—
292C23×C53—21no—
293C23×C53—21no—
294C23×C53—21no—
295C23×C53—41no—
296C23×C53—41no—
297C23×C53—41no—
298C23×C53—41no—
299C23×C53—41no—
300C23×C53—41no—
301C23×C53#12012yes—
302C23×C53#12312yes—
303C23×C53C22×D411yescharacteristic
304Q8×C53—22no—
305Q8×C53—22no—
306Q8×C53—44no—
307Q8×C53—41no—
308Q8×C53—41no—
309D4×C53—22no—
310D4×C53—22no—
311D4×C53—44no—
312D4×C53—44no—
313D4×C53—44no—
314D4×C53—48no—
315D4×C53—41no—
316D4×C53—41no—
317D4×C53—84no—
318D4×C53—84no—
319C2×C4×C53—21no—
320C2×C4×C53—21no—
321C2×C4×C53—21no—
322C2×C4×C53—21no—
323C2×C4×C53—22no—
324C2×C4×C53—22no—
325C2×C4×C53—22no—
326C2×C4×C53—22no—
327C2×C4×C53—22no—
328C2×C4×C53—22no—
329C2×C4×C53—22no—
330C2×C4×C53—22no—
331C2×C4×C53—22no—
332C2×C4×C53—22no—
333C2×C4×C53—22no—
334C2×C4×C53—21no—
335C2×C4×C53—21no—
336C2×C4×C53—21no—
337C2×C4×C53—48no—
338C2×C4×C53—41no—
339C2×C4×C53—41no—
340C2×C4×C53—41no—
341C2×C4×C53—41no—
342C2×C4×C53—41no—
343C2×C4×C53—41no—
344C2×C4×C53—41no—
345C2×C4×C53—41no—
346C2×C4×C53—41no—
347C2×C4×C53—41no—
348C2×C4×C53—84no—
349C2×C4×C53#12012yes—
350C2×C4×C53#12312yes—
351C2×C4×C53C22×D411yescharacteristic
352C2×C4×C53C22×D411yescharacteristic
353C2×C4×C53C2×#4111yescharacteristic
354C2×C4×C53C2×#4111yescharacteristic
355C2×C4×C53H(5,𝔽2)11yescharacteristic
356C2×C4×C53H(5,𝔽2)11yescharacteristic
357C2×Dic53—41no—
358C2×Dic53—41no—
359C2×Dic53—41no—
360C2×Dic53—41no—
361C2×Dic53—41no—
362C2×Dic53—41no—
363C2×Dic53—41no—
364C2×Dic53—41no—
365C2×Dic53—41no—
366C2×Dic53—41no—
367C2×Dic53—41no—
368C2×Dic53—41no—
369C2×Dic53—84no—
370#88322—41no—
371#88322—41no—
372#88322—41no—
373#88322—41no—
374#24017—531nomaximal, Sylow
375C22×C53—22no—
376C22×C53—22no—
377C22×C53—22no—
378C22×C53—22no—
379C22×C53—22no—
380C22×C53—22no—
381C22×C53—41no—
382C22×C53—41no—
383C22×C53—41no—
384C22×C53—41no—
385C22×C53—41no—
386C22×C53—41no—
387C22×C53—41no—
388C22×C53—41no—
389C22×C53—41no—
390C22×C53—41no—
391C22×C53—42no—
392C22×C53—41no—
393C22×C53—41no—
394C22×C53—41no—
395C22×C53—41no—
396C22×C53—42no—
397C22×C53—41no—
398C22×C53—42no—
399C22×C53—81no—
400C22×C53—81no—
401C22×C53—81no—
402C22×C53—81no—
403C22×C53C2×#12011yescharacteristic
404C22×C53C2×#12311yescharacteristic
405C22×C53#53411yescharacteristic
406C22×C53#57611yescharacteristic
407C22×C53#57711yescharacteristic
408C22×C53#57711yescharacteristic
409C22×C53#57811yescharacteristic
410C4×C53—22no—
411C4×C53—22no—
412C4×C53—41no—
413C4×C53—42no—
414C4×C53—42no—
415C4×C53—42no—
416C4×C53#54611yescharacteristic
417C4×C53#54611yescharacteristic
418C4×C53#54611yescharacteristic
419C4×C53#54611yescharacteristic
420Dic53—81no—
421Dic53—81no—
422Dic53—81no—
423Dic53—81no—
424C2×#537D5311yescharacteristic
425C2×#485—531no—
426C2×#482—531no—
427#2311—531no—
428#2036—531no—
429#2035—531no—
430#2034—531no—
431#2033—531no—
432#1874—531no—
433#1872—531no—
434#1853—531no—
435#1852—531no—
436#1788—531no—
437#1788—531no—
438#1780—531no—
439C2×C53—42no—
440C2×C53—42no—
441C2×C53—81no—
442C2×C53—82no—
443C2×C53#240511yescharacteristic
444C2×C53#301211yescharacteristic
445C2×C53#301311yescharacteristic
446C2×C53#309811yescharacteristic
447C2×C53#309911yescharacteristic
448C2×C53#319811yescharacteristic
449C2×C53#320111yescharacteristic
450C22×#41C2×D5311yescharacteristic
451C22×#41C2×D5311yescharacteristic
452#537—24no—
453#537—24no—
454C2×C22⋊Q8—21no—
455C2×C22⋊Q8C2×D5311yescharacteristic
456C2×C22⋊Q8C2×D5311yescharacteristic
457C2×#121—21no—
458C2×#121—21no—
459C2×#121—21no—
460C2×#121C2×D5311yescharacteristic
461C2×#121C2×D5311yescharacteristic
462C2×#117—531no—
463C22×C4⋊C4—531no—
464C22×C4⋊C4C2×D5311yescharacteristic
465#485—1064no—
466#482—1064no—
467C2×#107—531no—
468C2×#107—531no—
469C2×#106—531no—
470C2×#106—531no—
471C2×#103—531no—
472C2×#103—531no—
473C2×#103—531no—
474C2×#103—531no—
475C2×#102—531no—
476C2×#102—531no—
477C2×#102—531no—
478C2×#102—531no—
479C2×C22⋊C8—531no—
480C2×C22⋊C8—531no—
481C2×C22⋊C8—531no—
482C2×C22⋊C8—531no—
483C2×C22⋊C8—531no—
484C2×C22⋊C8—531no—
485#391—1061no—
486#390—1061no—
487#386—1061no—
488#386—1061no—
489#380—531no—
490#380—531no—
491#380—531no—
492#380—531no—
493#340—531no—
494#340—531no—
495#340—531no—
496#340—531no—
497C53#2401711yescharacteristic, complemented, Sylow
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—41no—
510C22×Q8C22⋊D5311yescharacteristic
511C22×Q8C22×D5311yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4C22⋊D5311yescharacteristic
516C22×D4C22⋊D5311yescharacteristic
517C22×D4C22⋊D5311yescharacteristic
518C22×D4C22×D5311yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—1061no—
522C23×C4C22×D5311yescharacteristic
523C23×C4C22×D5311yescharacteristic
524C23×C4C22×D5311yescharacteristic
525C22×C8—531no—
526C22×C8—531no—
527C22×C8—531no—
528C22×C8—531no—
529C22⋊Q8—28no—
530C22⋊Q8—22no—
531C22⋊Q8—22no—
532C22⋊Q8—22no—
533C22⋊Q8C22⋊D5314yes—
534#121—28no—
535#121—28no—
536#121—28no—
537#121—22no—
538#121—22no—
539#121—22no—
540#121C22⋊D5314yes—
541#117—1062no—
542#117—1062no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—22no—
547C2×C4⋊C4—22no—
548C2×C4⋊C4—531no—
549C2×C4⋊C4—531no—
550C2×C4⋊C4—531no—
551C2×C4⋊C4—531no—
552C2×C4⋊C4—1061no—
553C2×C4⋊C4—2121no—
554C2×C4⋊C4—2121no—
555C2×C4⋊C4C22×D5311yescharacteristic
556C2×C4⋊C4C22×D5311yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—1061no—
562C2×C22⋊C4—1061no—
563C2×C22⋊C4—1061no—
564C2×C22⋊C4—1061no—
565C2×C22⋊C4—1061no—
566C2×C42—1061no—
567#107—1062no—
568#107—1062no—
569#106—1062no—
570#106—1062no—
571#103—1062no—
572#103—1062no—
573#103—2121no—
574#103—2121no—
575#102—1062no—
576#102—1062no—
577#102—2121no—
578#102—2121no—
579C22⋊C8—1062no—
580C22⋊C8—1062no—
581C22⋊C8—1062no—
582C22⋊C8—1062no—
583C22⋊C8—2121no—
584C22⋊C8—2121no—
585#95—1061no—
586#95—1061no—
587#95—1061no—
588#95—1061no—
589C24—21no—
590C24C2×C22⋊D5311yescharacteristic
591C24C2×C22⋊D5311yescharacteristic
592C24C2×C22⋊D5311yescharacteristic
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598#41—44no—
599#41—44no—
600#41—44no—
601C2×Q8—22no—
602C2×Q8—22no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—41no—
609C2×Q8C2×C22⋊D5312yes—
610C2×D4—24no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—24no—
616C2×D4—24no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—41no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4C2×C22⋊D5312yes—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—24no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—42no—
654C22×C4—42no—
655C22×C4—81no—
656C22×C4—81no—
657C22×C4—1061no—
658C22×C4—1061no—
659C22×C4—1061no—
660C22×C4—1061no—
661C22×C4—4241no—
662C22×C4—4241no—
663C22×C4—2122no—
664C22×C4#1171994712yes—
665C22×C4#1171994712yes—
666C22×C4C2×C22⋊D5311yescharacteristic
667C22×C4C2×C22⋊D5311yescharacteristic
668C22×C4C2×C22⋊D5312yes—
669C22×C4C2×C22⋊D5312yes—
670C22×C4C2×C22⋊D5311yescharacteristic
671C22×C4C23×D5311yescharacteristic
672C2×C8—1061no—
673C2×C8—1061no—
674C2×C8—1061no—
675C2×C8—1061no—
676C2×C8—1061no—
677C2×C8—1061no—
678C2×C8—1061no—
679C2×C8—1061no—
680C2×C8—1061no—
681C2×C8—1061no—
682C2×C8—1061no—
683C2×C8—1061no—
684C4⋊C4—24no—
685C4⋊C4—24no—
686C4⋊C4—24no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—1061no—
690C4⋊C4—1061no—
691C4⋊C4—1061no—
692C4⋊C4—1061no—
693C4⋊C4—1061no—
694C4⋊C4—1061no—
695C4⋊C4—1061no—
696C4⋊C4—1061no—
697C4⋊C4—2122no—
698C4⋊C4C2×C22⋊D5312yes—
699C4⋊C4C2×C22⋊D5312yes—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—4241no—
705C22⋊C4—4241no—
706C22⋊C4—4241no—
707C22⋊C4—4241no—
708C22⋊C4—2122no—
709C42—2122no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—22no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23#1313318612yes—
737C23#1313319812yes—
738C23C22×C22⋊D5311yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—44no—
742Q8—41no—
743Q8—41no—
744D4—22no—
745D4—22no—
746D4—44no—
747D4—44no—
748D4—44no—
749D4—48no—
750D4—41no—
751D4—41no—
752D4—84no—
753D4—84no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—48no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—84no—
784C2×C4—4244no—
785C2×C4—2121no—
786C2×C4—2121no—
787C2×C4—2121no—
788C2×C4—2121no—
789C2×C4—2121no—
790C2×C4—2121no—
791C2×C4—2121no—
792C2×C4—2121no—
793C2×C4—2121no—
794C2×C4—2121no—
795C2×C4—2121no—
796C2×C4—2121no—
797C2×C4#1313318612yes—
798C2×C4#1313319812yes—
799C2×C4C22×C22⋊D5311yescharacteristic
800C2×C4C22×C22⋊D5311yescharacteristic
801C2×C4C2×#1171994711yescharacteristic
802C2×C4C2×#1171994711yescharacteristic
803C2×C4#1313326211yescharacteristic
804C2×C4#1313326211yescharacteristic
805C8—2121no—
806C8—2121no—
807C8—2121no—
808C8—2121no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—42no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—42no—
829C22—41no—
830C22—41no—
831C22—42no—
832C22—41no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22C2×#1313318611yescharacteristic
838C22C2×#1313319811yescharacteristic
839C22#1681118211yescharacteristic
840C22#1681142611yescharacteristic
841C22#1681143111yescharacteristic
842C22#1681143411yescharacteristic
843C22#1681143811yescharacteristic
844C4—22no—
845C4—22no—
846C4—41no—
847C4—42no—
848C4—42no—
849C4—42no—
850C4—4241no—
851C4—4241no—
852C4—4241no—
853C4—4241no—
854C4#1681126711yescharacteristic
855C4#1681126711yescharacteristic
856C4#1681126711yescharacteristic
857C4#1681126711yescharacteristic
858C2—42no—
859C2—42no—
860C2—81no—
861C2—82no—
862C2#2027803811yescharacteristic
863C2#2028401911yescharacteristic
864C2#2028403011yescharacteristic
865C2#2028468911yescharacteristic
866C2#2028470011yescharacteristic
867C2#2028556111yescharacteristic
868C2#2028559111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
Fitting, prime radicalC2×C53×#537C2
socleC23×C53C22×D4
hypercenterC2×#537D53
hypocenterC53#24017
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C2×#16810961C2semidirect
2. C2×#16810944C2semidirect
3. #20277307C2semidirect
4. #20275915C2semidirect
5. #20275908C2semidirect
6. #20275901C2semidirect
7. #20275894C2semidirect
8. #20275033C2semidirect
9. #20275023C2semidirect
10. #20274908C2semidirect
11. #20274903C2semidirect
12. #20274655C2semidirect
13. #20274655C2semidirect
14. #20274627C2semidirect
497. C53#24017semidirect

Maximal subgroups

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

subgroupindex
C2×#168109612
C2×#168109442
#202773072
#202759152
#202759082
#202759012
#202758942
#202750332
#202750232
#202749082
#202749032
#202746552
#202746272
C2×C53×#5372
#2401753