Finite Group Databasebeta

← #27441301

Subgroups — #27441301

Order 13568.

1162 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810921C211yesmaximal, characteristic, complemented
2C22×#13133138C211yesmaximal, characteristic
3#20278440C211yesmaximal, characteristic, complemented
4D4×C22⋊Dic53C211yesmaximal, characteristic
5#20276234C211yesmaximal, characteristic, complemented
6#20276101C211yesmaximal, characteristic, complemented
7#20276085C211yesmaximal, characteristic, complemented
8#20275859C211yesmaximal, characteristic, complemented
9#20274974C211yesmaximal, characteristic, complemented
10#20274964C211yesmaximal, characteristic, complemented
11#20274905C211yesmaximal, characteristic, complemented
12#20274892C211yesmaximal, characteristic, complemented
13#20274738C211yesmaximal, characteristic, complemented
14#20274723C211yesmaximal, characteristic, complemented
15C53×#1786C211yesmaximal, characteristic
16C23×#88322C2211yescharacteristic
17C2×#13133208C2211yescharacteristic, complemented
18C2×D4×Dic53C2211yescharacteristic
19C2×D4×Dic53C2211yescharacteristic
20C22×C4⋊Dic53C2211yescharacteristic
21C22×C22⋊Dic53—21no—
22#16810921—24no—
23C2×#13133151C2211yescharacteristic, complemented
24C2×#13133151C2211yescharacteristic, complemented
25C2×#13133148C2211yescharacteristic, complemented
26C2×#13133148C2211yescharacteristic, complemented
27C2×#13133146C2211yescharacteristic, complemented
28C2×#13133146C2211yescharacteristic, complemented
29C2×#13133138—24no—
30C2×#13133138C2211yescharacteristic
31C2×#13133138C2211yescharacteristic
32C2×#13133138C2211yescharacteristic
33C2×#13133138C2211yescharacteristic
34#16810565—21no—
35#16810555—21no—
36#16810526C2211yescharacteristic
37#16810526C2211yescharacteristic
38#16810522C2211yescharacteristic, complemented
39#16810519C2211yescharacteristic, complemented
40#16810503—21no—
41#16810503—21no—
42#16810498—21no—
43#16810488C2211yescharacteristic, complemented
44#16810483C2211yescharacteristic
45#16810481—21no—
46#16810479—21no—
47C4×C22⋊Dic53C2211yescharacteristic
48#16810386C2211yescharacteristic, complemented
49#16810386C2211yescharacteristic, complemented
50#16810385C2211yescharacteristic, complemented
51#16810385C2211yescharacteristic, complemented
52#16810377C2211yescharacteristic, complemented
53#16810377C2211yescharacteristic, complemented
54C23×D4×C53C2211yescharacteristic
55C2×#102×C53C2211yescharacteristic
56C2×#102×C53C2211yescharacteristic
57C2×#102×C53C2211yescharacteristic
58C2×#102×C53C2211yescharacteristic
59C2×C22⋊C8×C53C2211yescharacteristic
60C53×#380C2211yescharacteristic
61C23×Dic53—21no—
62C23×Dic53—21no—
63C23×Dic53—21no—
64C22×#88322—22no—
65C22×#88322—22no—
66C22×#88322—41no—
67C22×#88322C2311yescharacteristic
68C22×#88322C2311yescharacteristic
69#13133208—22no—
70#13133208—41no—
71D4×Dic53—22no—
72D4×Dic53—22no—
73D4×Dic53—41no—
74D4×Dic53—41no—
75C2×C4⋊Dic53—21no—
76C2×C4⋊Dic53—21no—
77C2×C4⋊Dic53—21no—
78C2×C4⋊Dic53—22no—
79C2×C4⋊Dic53—41no—
80C2×C4⋊Dic53C2311yescharacteristic
81C2×C4⋊Dic53C2311yescharacteristic
82C2×C4⋊Dic53C2311yescharacteristic
83C2×C4⋊Dic53C2311yescharacteristic
84C2×#11719919—21no—
85C2×#11719919—21no—
86C2×C22⋊Dic53—21no—
87C2×C22⋊Dic53—21no—
88C2×C22⋊Dic53—21no—
89C2×C22⋊Dic53—21no—
90C2×C22⋊Dic53—21no—
91C2×C22⋊Dic53—21no—
92C2×C22⋊Dic53—21no—
93C2×C22⋊Dic53—44no—
94C2×C22⋊Dic53D411yescharacteristic
95C2×C22⋊Dic53D411yescharacteristic
96C2×C4×Dic53C2311yescharacteristic
97C2×C4×Dic53C2311yescharacteristic
98#13133151—22no—
99#13133151—41no—
100#13133148—22no—
101#13133148—41no—
102#13133146—22no—
103#13133146—41no—
104#13133138—22no—
105#13133138—22no—
106#13133138—22no—
107#13133138D414yes—
108#13133124—21no—
109#13133124—21no—
110#13133124—21no—
111#13133124—21no—
112#13133124—21no—
113#13133124D411yescharacteristic
114#13133124D411yescharacteristic
115C25×C53—21no—
116C22×D4×C53—22no—
117C22×D4×C53—22no—
118C22×D4×C53—21no—
119C22×D4×C53—22no—
120C22×D4×C53—41no—
121C22×D4×C53—41no—
122C22×D4×C53Q814yes—
123C22×D4×C53C2311yescharacteristic
124C22×D4×C53C2311yescharacteristic
125C23×C4×C53C2311yescharacteristic
126C22×C8×C53C2311yescharacteristic
127C22×C8×C53C2311yescharacteristic
128C2×C4⋊C4×C53C2311yescharacteristic
129C2×C4⋊C4×C53C2311yescharacteristic
130C2×C22⋊C4×C53—21no—
131#102×C53—22no—
132#102×C53—22no—
133#102×C53—41no—
134#102×C53—41no—
135C22⋊C8×C53—22no—
136#95×C53—21no—
137C24×C53—21no—
138C24×C53—21no—
139C24×C53—24no—
140C24×C53—42no—
141C24×C53—42no—
142C24×C53—42no—
143C24×C53—42no—
144C24×C53—81no—
145C24×C53—81no—
146C24×C53C2×D411yescharacteristic
147C2×D4×C53—28no—
148C2×D4×C53—24no—
149C2×D4×C53—21no—
150C2×D4×C53—21no—
151C2×D4×C53—21no—
152C2×D4×C53—21no—
153C2×D4×C53—21no—
154C2×D4×C53—21no—
155C2×D4×C53—21no—
156C2×D4×C53—21no—
157C2×D4×C53—44no—
158C2×D4×C53—44no—
159C2×D4×C53—44no—
160C2×D4×C53—42no—
161C2×D4×C53—42no—
162C2×D4×C53C2×D412yes—
163C2×D4×C53C2×Q812yes—
164C2×D4×C53C2×Q812yes—
165C2×D4×C53#4112yes—
166C22×C4×C53—21no—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53—21no—
171C22×C4×C53—21no—
172C22×C4×C53C2×D411yescharacteristic
173C22×C4×C53C2×Q812yes—
174C22×C4×C53#4112yes—
175C22×C4×C53C2411yescharacteristic
176C22×Dic53—21no—
177C22×Dic53—21no—
178C22×Dic53—21no—
179C22×Dic53—21no—
180C22×Dic53—42no—
181C22×Dic53—42no—
182C22×Dic53—42no—
183C22×Dic53—42no—
184C22×Dic53—42no—
185C22×Dic53—42no—
186C22×Dic53—81no—
187C22×Dic53—81no—
188C22×Dic53—81no—
189C22×Dic53C2×D411yescharacteristic
190C22×Dic53C2×D411yescharacteristic
191C22×Dic53C2×D411yescharacteristic
192C22×Dic53C2×D411yescharacteristic
193C2×C8×C53—21no—
194C2×C8×C53—21no—
195C2×C8×C53—21no—
196C2×C8×C53—21no—
197C2×C8×C53—21no—
198C2×C8×C53—21no—
199C4⋊C4×C53—21no—
200C4⋊C4×C53—21no—
201C4⋊C4×C53—21no—
202C4⋊C4×C53—21no—
203C22⋊C4×C53—42no—
204C22⋊Dic53—22no—
205C22⋊Dic53—22no—
206C22⋊Dic53—42no—
207C22⋊Dic53—42no—
208C22⋊Dic53—42no—
209C22⋊Dic53—42no—
210C22⋊Dic53—42no—
211C22⋊Dic53—81no—
212C22⋊Dic53—81no—
213C4⋊Dic53—21no—
214C4⋊Dic53—21no—
215C4⋊Dic53—21no—
216C4⋊Dic53—21no—
217C4⋊Dic53—21no—
218C4⋊Dic53—21no—
219C4⋊Dic53—21no—
220C4⋊Dic53—42no—
221C4⋊Dic53—42no—
222C4⋊Dic53—81no—
223C4⋊Dic53C2×D412yes—
224#11719919—42no—
225#11719919—81no—
226C4×Dic53—21no—
227C4×Dic53—21no—
228C4×Dic53—21no—
229C4×Dic53—21no—
230C2×#88322—21no—
231C2×#88322—21no—
232C2×#88322—21no—
233C2×#88322—21no—
234C2×#88322—21no—
235C2×#88322—44no—
236C2×#88322C2×D412yes—
237C23×C53—21no—
238C23×C53—21no—
239C23×C53—21no—
240C23×C53—21no—
241C23×C53—22no—
242C23×C53—22no—
243C23×C53—22no—
244C23×C53—22no—
245C23×C53—48no—
246C23×C53—41no—
247C23×C53—41no—
248C23×C53—41no—
249C23×C53—41no—
250C23×C53—41no—
251C23×C53—41no—
252C23×C53—41no—
253C23×C53—41no—
254C23×C53—41no—
255C23×C53—41no—
256C23×C53—48no—
257C23×C53—84no—
258C23×C53—84no—
259C23×C53—84no—
260C23×C53—84no—
261C23×C53—84no—
262C23×C53C22⋊Q812yes—
263C23×C53#13512yes—
264C23×C53AGL(1,ℤ/8)12yes—
265C23×C53C22×D411yescharacteristic
266D4×C53—22no—
267D4×C53—22no—
268D4×C53—22no—
269D4×C53—22no—
270D4×C53—22no—
271D4×C53—48no—
272D4×C53—41no—
273D4×C53—41no—
274D4×C53C22⋊Q814yes—
275C2×C4×C53—21no—
276C2×C4×C53—21no—
277C2×C4×C53—22no—
278C2×C4×C53—22no—
279C2×C4×C53—22no—
280C2×C4×C53—22no—
281C2×C4×C53—41no—
282C2×C4×C53—41no—
283C2×C4×C53—41no—
284C2×C4×C53—41no—
285C2×C4×C53—41no—
286C2×C4×C53—41no—
287C2×C4×C53C22⋊Q812yes—
288C2×C4×C53C22×D411yescharacteristic
289C2×C4×C53C22×Q811yescharacteristic
290C2×C4×C53C2×#4111yescharacteristic
291C2×C4×C53C2×#4111yescharacteristic
292C2×C4×C53H(5,𝔽2)11yescharacteristic
293C2×C4×C53H(5,𝔽2)11yescharacteristic
294C2×Dic53—22no—
295C2×Dic53—21no—
296C2×Dic53—21no—
297C2×Dic53—21no—
298C2×Dic53—21no—
299C2×Dic53—21no—
300C2×Dic53—21no—
301C2×Dic53—21no—
302C2×Dic53—21no—
303C2×Dic53—21no—
304C2×Dic53—21no—
305C2×Dic53—21no—
306C2×Dic53—21no—
307C2×Dic53—41no—
308C2×Dic53—41no—
309C2×Dic53—41no—
310C2×Dic53—41no—
311C2×Dic53—41no—
312C2×Dic53—41no—
313C2×Dic53—41no—
314C2×Dic53—41no—
315C2×Dic53—41no—
316C2×Dic53—41no—
317C2×Dic53—41no—
318C2×Dic53—84no—
319C2×Dic53—84no—
320C2×Dic53—84no—
321C8×C53—41no—
322C8×C53—41no—
323#88322—22no—
324#88322—41no—
325#25960—531nomaximal, Sylow
326C22×C53—22no—
327C22×C53—22no—
328C22×C53—22no—
329C22×C53—22no—
330C22×C53—22no—
331C22×C53—22no—
332C22×C53—24no—
333C22×C53—42no—
334C22×C53—42no—
335C22×C53—42no—
336C22×C53—42no—
337C22×C53—42no—
338C22×C53—42no—
339C22×C53—42no—
340C22×C53—42no—
341C22×C53—42no—
342C22×C53—816no—
343C22×C53—81no—
344C22×C53—81no—
345C22×C53—81no—
346C22×C53—81no—
347C22×C53#47814yescomplemented
348C22×C53C2×C22⋊Q811yescharacteristic
349C22×C53D4211yescharacteristic
350C22×C53#54611yescharacteristic
351C22×C53C2×#13511yescharacteristic
352C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
353C22×C53#57611yescharacteristic
354C22×C53#57711yescharacteristic
355C4×C53—22no—
356C4×C53—81no—
357C4×C53—81no—
358C4×C53C2×C22⋊Q811yescharacteristic
359C4×C53#54311yescharacteristic
360C4×C53#54611yescharacteristic
361C4×C53#55111yescharacteristic
362Dic53—41no—
363Dic53—42no—
364Dic53—41no—
365Dic53—41no—
366Dic53—41no—
367Dic53—81no—
368Dic53—81no—
369Dic53—81no—
370C2×#478—531no—
371C22×#102—531no—
372#2442—531no—
373D4×C22⋊C4—531no—
374#2092—531no—
375#2067—531no—
376#2065—531no—
377#2025—531no—
378#1864—531no—
379#1862—531no—
380#1852—531no—
381#1850—531no—
382#1807—531no—
383#1804—531no—
384#1786D5311yescharacteristic
385C2×C53—24no—
386C2×C53—44no—
387C2×C53—82no—
388C2×C53#243711yescharacteristic
389C2×C53C2×#47811yescharacteristic
390C2×C53#308111yescharacteristic
391C2×C53#326411yescharacteristic
392C2×C53#328211yescharacteristic
393C2×C53#329711yescharacteristic
394C2×C53#331011yescharacteristic
395C23×D4C2×D5311yescharacteristic
396C23×C8—531no—
397C2×#125—531no—
398C2×C4×D4—531no—
399C2×C4×D4—531no—
400C22×C4⋊C4—531no—
401C22×C22⋊C4—1061no—
402#478—1064no—
403C2×#107—531no—
404C2×#107—531no—
405C2×#106—531no—
406C2×#106—531no—
407C2×C4⋊C8—531no—
408C2×C4⋊C8—531no—
409C2×#102—531no—
410C2×#102—531no—
411C2×#102—531no—
412C2×#102—531no—
413C2×#102—1064no—
414C2×#102C2×D5311yescharacteristic
415C2×#102C2×D5311yescharacteristic
416C2×#102C2×D5311yescharacteristic
417C2×#102C2×D5311yescharacteristic
418C2×C22⋊C8C2×D5311yescharacteristic
419#400—1061no—
420#398—1061no—
421#390—531no—
422#390—531no—
423#389—531no—
424#389—531no—
425#386—1061no—
426#386—1061no—
427#385—1061no—
428#382—531no—
429#380—531no—
430#380—1061no—
431#380C2×D5311yescharacteristic
432#379—1061no—
433C4×C22⋊C4—531no—
434#340—531no—
435#340—531no—
436#340—531no—
437#340—531no—
438#336—531no—
439#336—531no—
440C53#2596011yescharacteristic, complemented, Sylow
441C25—21no—
442C22×D4—22no—
443C22×D4—22no—
444C22×D4—21no—
445C22×D4—22no—
446C22×D4—41no—
447C22×D4—41no—
448C22×D4Dic10614yes—
449C22×D4C22×D5311yescharacteristic
450C22×D4C22×D5311yescharacteristic
451C23×C4—1061no—
452C23×C4—1061no—
453C23×C4—1061no—
454C23×C4C22×D5311yescharacteristic
455C22×C8—531no—
456C22×C8—531no—
457C22×C8—1062no—
458C22×C8—1062no—
459C22×C8—2121no—
460C22×C8C22×D5311yescharacteristic
461C22×C8C22×D5311yescharacteristic
462#125—1062no—
463#125—2121no—
464C4×D4—1062no—
465C4×D4—1062no—
466C4×D4—2121no—
467C4×D4—2121no—
468C2×C4⋊C4—531no—
469C2×C4⋊C4—531no—
470C2×C4⋊C4—531no—
471C2×C4⋊C4—531no—
472C2×C4⋊C4—1062no—
473C2×C4⋊C4—1061no—
474C2×C4⋊C4—1061no—
475C2×C4⋊C4—1061no—
476C2×C4⋊C4—1061no—
477C2×C4⋊C4—1061no—
478C2×C4⋊C4—2121no—
479C2×C4⋊C4C22×D5311yescharacteristic
480C2×C4⋊C4C22×D5311yescharacteristic
481C2×C22⋊C4—21no—
482C2×C22⋊C4—531no—
483C2×C22⋊C4—531no—
484C2×C22⋊C4—1061no—
485C2×C22⋊C4—1061no—
486C2×C22⋊C4—1061no—
487C2×C22⋊C4—1061no—
488C2×C22⋊C4—1061no—
489C2×C22⋊C4—1061no—
490C2×C22⋊C4—1061no—
491C2×C22⋊C4—2124no—
492C2×C42—531no—
493C2×C42—531no—
494#107—1062no—
495#107—2121no—
496#106—1062no—
497#106—2121no—
498C4⋊C8—1062no—
499C4⋊C8—2121no—
500#102—22no—
501#102—22no—
502#102—41no—
503#102—41no—
504#102—534no—
505#102—1062no—
506#102—1062no—
507#102—1062no—
508C22⋊C8—22no—
509#95—21no—
510#95—531no—
511#95—531no—
512#95—1061no—
513#95—1061no—
514#95—1061no—
515#95—1061no—
516#95—1061no—
517C24—21no—
518C24—21no—
519C24—24no—
520C24—42no—
521C24—42no—
522C24—42no—
523C24—42no—
524C24—81no—
525C24—81no—
526C24D4×D5311yescharacteristic
527C2×D4—28no—
528C2×D4—24no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—44no—
538C2×D4—44no—
539C2×D4—44no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4C2×Dic10612yes—
543C2×D4C2×Dic10612yes—
544C2×D4D4×D5312yes—
545C2×D4#1171994712yes—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—531no—
553C22×C4—531no—
554C22×C4—531no—
555C22×C4—531no—
556C22×C4—1061no—
557C22×C4—1061no—
558C22×C4—1061no—
559C22×C4—1061no—
560C22×C4—4241no—
561C22×C4—4241no—
562C22×C4—4241no—
563C22×C4—2122no—
564C22×C4—2122no—
565C22×C4—2122no—
566C22×C4—2122no—
567C22×C4—2122no—
568C22×C4—2122no—
569C22×C4C2×Dic10612yes—
570C22×C4D4×D5311yescharacteristic
571C22×C4#1171994712yes—
572C22×C4C23×D5311yescharacteristic
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—532no—
580C2×C8—1061no—
581C2×C8—1061no—
582C2×C8—1061no—
583C2×C8—1061no—
584C2×C8—1061no—
585C2×C8—2124no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—532no—
591C4⋊C4—1061no—
592C4⋊C4—1061no—
593C4⋊C4—1061no—
594C4⋊C4—1061no—
595C4⋊C4—1061no—
596C4⋊C4—1061no—
597C4⋊C4—1061no—
598C4⋊C4—4241no—
599C4⋊C4—4241no—
600C4⋊C4—2122no—
601C4⋊C4—2122no—
602C4⋊C4—2122no—
603C22⋊C4—42no—
604C22⋊C4—1062no—
605C22⋊C4—1062no—
606C22⋊C4—4241no—
607C22⋊C4—4241no—
608C22⋊C4—2122no—
609C22⋊C4—2122no—
610C22⋊C4—2122no—
611C22⋊C4—2122no—
612C22⋊C4—2122no—
613C42—1061no—
614C42—1061no—
615C42—1061no—
616C42—1061no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—48no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—48no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—84no—
638C23—84no—
639C23—84no—
640C23—84no—
641C23—84no—
642C23#1313319412yes—
643C23#1313323612yes—
644C23#1313324412yes—
645C23C2×D4×D5311yescharacteristic
646D4—22no—
647D4—22no—
648D4—22no—
649D4—22no—
650D4—22no—
651D4—48no—
652D4—41no—
653D4—41no—
654D4#1313319414yes—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—1061no—
668C2×C4—1061no—
669C2×C4—1061no—
670C2×C4—1061no—
671C2×C4—1061no—
672C2×C4—1061no—
673C2×C4—1061no—
674C2×C4—1061no—
675C2×C4—1061no—
676C2×C4—1061no—
677C2×C4—1062no—
678C2×C4—1061no—
679C2×C4—1061no—
680C2×C4—4244no—
681C2×C4—4244no—
682C2×C4—4244no—
683C2×C4—2121no—
684C2×C4—2121no—
685C2×C4—2121no—
686C2×C4—2121no—
687C2×C4—2121no—
688C2×C4—2121no—
689C2×C4—2121no—
690C2×C4—2121no—
691C2×C4—2121no—
692C2×C4—2121no—
693C2×C4—2121no—
694C2×C4#1313319412yes—
695C2×C4C2×D4×D5311yescharacteristic
696C2×C4C22×Dic10611yescharacteristic
697C2×C4C2×#1171994711yescharacteristic
698C2×C4C2×#1171994711yescharacteristic
699C2×C4#1313326211yescharacteristic
700C2×C4#1313326211yescharacteristic
701C8—41no—
702C8—41no—
703C8—1062no—
704C8—2121no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—24no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—816no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22#1681092114yescomplemented
727C22C2×#1313319411yescharacteristic
728C22#1681125511yescharacteristic
729C22#1681126011yescharacteristic
730C22C2×#1313323611yescharacteristic
731C22C2×#1313324411yescharacteristic
732C22#1681142711yescharacteristic
733C22#1681143311yescharacteristic
734C4—22no—
735C4—81no—
736C4—81no—
737C4—4241no—
738C4—4241no—
739C4—4241no—
740C4—2121no—
741C4—2121no—
742C4—2121no—
743C4—2121no—
744C4—2122no—
745C4C2×#1313319411yescharacteristic
746C4#1681124911yescharacteristic
747C4#1681126011yescharacteristic
748C4#1681130411yescharacteristic
749C2—24no—
750C2—44no—
751C2—82no—
752C2#2027838111yescharacteristic
753C2C2×#1681092111yescharacteristic
754C2#2028454811yescharacteristic
755C2#2028619911yescharacteristic
756C2#2028642611yescharacteristic
757C2#2028656911yescharacteristic
758C2#2028674011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
FittingC53×#1786C2
socleC23×C53C22×D4
prime radicalC23×D4×C53C22
hypercenter#1786D53
hypocenterC53#25960
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1786

Complements

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

NH ≅ G/Ntype
1. C2×#16810921C2semidirect
3. #20278440C2semidirect
5. #20276234C2semidirect
6. #20276101C2semidirect
7. #20276085C2semidirect
8. #20275859C2semidirect
9. #20274974C2semidirect
10. #20274964C2semidirect
11. #20274905C2semidirect
12. #20274892C2semidirect
13. #20274738C2semidirect
14. #20274723C2semidirect
17. C2×#13133208C22semidirect
23. C2×#13133151C22semidirect
24. C2×#13133151C22semidirect
25. C2×#13133148C22semidirect
26. C2×#13133148C22semidirect
27. C2×#13133146C22semidirect
28. C2×#13133146C22semidirect
38. #16810522C22semidirect
39. #16810519C22semidirect
43. #16810488C22semidirect
48. #16810386C22semidirect
49. #16810386C22semidirect
50. #16810385C22semidirect
51. #16810385C22semidirect
52. #16810377C22semidirect
53. #16810377C22semidirect
347. C22×C53#478semidirect
440. C53#25960semidirect
726. C22#16810921semidirect

Maximal subgroups

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

subgroupindex
C2×#168109212
C22×#131331382
#202784402
D4×C22⋊Dic532
#202762342
#202761012
#202760852
#202758592
#202749742
#202749642
#202749052
#202748922
#202747382
#202747232
C53×#17862
#2596053