Finite Group Databasebeta

← #27395412

Subgroups — #27395412

Order 13568.

1024 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810766C211yesmaximal, characteristic
2#20277303C211yesmaximal, characteristic, complemented
3#20275595C211yesmaximal, characteristic, complemented
4#20275580C211yesmaximal, characteristic, complemented
5#20275411C211yesmaximal, characteristic, complemented
6#20275390C211yesmaximal, characteristic, complemented
7#20275356C211yesmaximal, characteristic, complemented
8#20275335C211yesmaximal, characteristic, complemented
9#20275063C211yesmaximal, characteristic, complemented
10#20275049C211yesmaximal, characteristic, complemented
11#20275033C211yesmaximal, characteristic, complemented
12#20274902C211yesmaximal, characteristic, complemented
13#20274653C211yesmaximal, characteristic, complemented
14#20274481C211yesmaximal, characteristic, complemented
15C53×#2324C211yesmaximal, characteristic, complemented
16C22×#11719945C2211yescharacteristic
17C22×#11719923C2211yescharacteristic
18C22×#11719922C2211yescharacteristic
19C22×C4⋊Dic53C2211yescharacteristic
20#16810766C418yescomplemented
21C2×#13133150C2211yescharacteristic
22C2×#13133150C2211yescharacteristic
23C2×#13133140C2211yescharacteristic
24C2×#13133140C2211yescharacteristic
25C2×#13133140C2211yescharacteristic
26C2×#13133138C2211yescharacteristic
27C2×#13133138C2211yescharacteristic
28C2×#13133137C2211yescharacteristic
29C2×#13133137C2211yescharacteristic
30C2×#13133137C2211yescharacteristic
31C2×C22⋊#88322C2211yescharacteristic
32C2×C22⋊#88322C2211yescharacteristic
33C2×#13133128C2211yescharacteristic
34C2×C4×#88322C2211yescharacteristic
35#16810529C2211yescharacteristic
36#16810529C2211yescharacteristic
37#16810525C2211yescharacteristic
38#16810525C2211yescharacteristic
39#16810500—21no—
40#16810500—21no—
41#16810480—21no—
42#16810480—21no—
43#16810385C2211yescharacteristic
44#16810385C2211yescharacteristic
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810378C2211yescharacteristic
48#16810378C2211yescharacteristic
49C2×#121×C53C2211yescharacteristic
50C2×C4×D4×C53C2211yescharacteristic
51C2×#117×C53C2211yescharacteristic
52C53×#390—21no—
53C53×#390C2211yescharacteristic
54C53×#389C2211yescharacteristic
55C53×#388—21no—
56C53×#386—21no—
57C53×#385—21no—
58C53×#380C2211yescharacteristic
59C4×C4⋊C4×C53C2211yescharacteristic
60C2×#11719945—22no—
61C2×#11719945—41no—
62C2×#11719945—41no—
63C2×#11719945—41no—
64C2×#11719945—41no—
65C2×#11719945C2×C414yescomplemented
66C22×Dic106C2311yescharacteristic
67C22×D212C2311yescharacteristic
68C22×C22⋊D53—21no—
69C23×Dic53—21no—
70C22×C4×D53—21no—
71C2×#11719923—41no—
72C2×#11719923—41no—
73C2×#11719923C2×C414yescomplemented
74C2×#11719922—41no—
75C2×#11719922—41no—
76C2×#11719922C2×C414yescomplemented
77C22×#88322C2311yescharacteristic
78C22×#88322C2311yescharacteristic
79C22×#88322C2311yescharacteristic
80C22×#88322C2311yescharacteristic
81C2×C4⋊Dic53—21no—
82C2×C4⋊Dic53—41no—
83C2×C4⋊Dic53—41no—
84C2×C4⋊Dic53C2311yescharacteristic
85C2×C4⋊Dic53C2311yescharacteristic
86C2×#11719921—21no—
87C2×#11719921—21no—
88C2×#11719921—21no—
89C2×#11719921—21no—
90#13133150—41no—
91#13133150—41no—
92#13133140—41no—
93#13133140—41no—
94#13133140C2×C414yescomplemented
95#13133138—41no—
96#13133138—41no—
97#13133137—41no—
98#13133137—41no—
99#13133137C2×C414yescomplemented
100C22⋊#88322—22no—
101C22⋊#88322C2×C414yescomplemented
102#13133128—41no—
103C4×#88322—41no—
104#13133124—21no—
105#13133124—21no—
106#13133124—21no—
107#13133124—21no—
108C22×D4×C53—21no—
109C22×D4×C53C2311yescharacteristic
110C23×C4×C53—21no—
111C23×C4×C53C2311yescharacteristic
112#121×C53—22no—
113#121×C53C2×C414yes—
114C4×D4×C53—41no—
115C4×D4×C53—41no—
116#117×C53—41no—
117#117×C53—41no—
118C2×C4⋊C4×C53—21no—
119C2×C4⋊C4×C53D411yescharacteristic
120C2×C4⋊C4×C53D411yescharacteristic
121C2×C4⋊C4×C53C2311yescharacteristic
122C2×C4⋊C4×C53C2311yescharacteristic
123C2×C4⋊C4×C53C2311yescharacteristic
124C2×C22⋊C4×C53—21no—
125C2×C22⋊C4×C53—21no—
126C2×C22⋊C4×C53—21no—
127C2×C22⋊C4×C53—21no—
128C2×C22⋊C4×C53—21no—
129C2×C22⋊C4×C53D411yescharacteristic
130C2×C22⋊C4×C53D411yescharacteristic
131C2×C42×C53—21no—
132C2×C42×C53C2311yescharacteristic
133C2×C42×C53C2311yescharacteristic
134#95×C53—21no—
135#95×C53—21no—
136#95×C53—21no—
137C24×C53—21no—
138C24×C53C2×D411yescharacteristic
139C23×D53—21no—
140C2×D4×C53—24no—
141C2×D4×C53—21no—
142C2×D4×C53—21no—
143C2×D4×C53—21no—
144C2×D4×C53—21no—
145C2×D4×C53—21no—
146C2×D4×C53—81no—
147C2×D4×C53—81no—
148C2×D4×C53C22×C412yes—
149C22×C4×C53—21no—
150C22×C4×C53—21no—
151C22×C4×C53—21no—
152C22×C4×C53—21no—
153C22×C4×C53—21no—
154C22×C4×C53—21no—
155C22×C4×C53—21no—
156C22×C4×C53—42no—
157C22×C4×C53—81no—
158C22×C4×C53—81no—
159C22×C4×C53C22×C412yes—
160C22×C4×C53C2×D411yescharacteristic
161C22×C4×C53C2×D411yescharacteristic
162C22×C4×C53C2×D411yescharacteristic
163C22×C4×C53C2×D411yescharacteristic
164C22×C4×C53C2×D411yescharacteristic
165C22×C4×C53#4112yes—
166C22×C4×C53C2411yescharacteristic
167C2×C22⋊D53—24no—
168C2×C22⋊D53—42no—
169C2×C22⋊D53—42no—
170C22×Dic53—21no—
171C22×Dic53—21no—
172C22×Dic53—21no—
173C22×Dic53—42no—
174C22×Dic53—81no—
175C22×Dic53—81no—
176#11719945—44no—
177#11719945—44no—
178#11719945—44no—
179#11719945—44no—
180C2×D212—21no—
181C2×D212—21no—
182C2×D212—21no—
183C2×D212—21no—
184C2×D212—21no—
185C2×D212C22×C412yes—
186C2×C4×D53—24no—
187C2×C4×D53—42no—
188C2×C4×D53—42no—
189C2×Dic106—21no—
190C2×Dic106—21no—
191C2×Dic106—21no—
192C2×Dic106—21no—
193C2×Dic106—21no—
194C2×Dic106C22×C412yes—
195C4⋊C4×C53—21no—
196C4⋊C4×C53—21no—
197C4⋊C4×C53—21no—
198C4⋊C4×C53—21no—
199C4⋊C4×C53—21no—
200C4⋊C4×C53—41no—
201C4⋊C4×C53—41no—
202C4⋊C4×C53—81no—
203C4⋊C4×C53C22×C412yes—
204C22⋊C4×C53—24no—
205C22⋊C4×C53—41no—
206C22⋊C4×C53—41no—
207C22⋊C4×C53—42no—
208C22⋊C4×C53—81no—
209C22⋊C4×C53—81no—
210C22⋊C4×C53—81no—
211C42×C53—21no—
212C42×C53—21no—
213C42×C53—21no—
214C42×C53—21no—
215C42×C53—81no—
216#11719923—44no—
217#11719922—44no—
218#11719921—81no—
219#11719921—81no—
220#11719921—81no—
221#11719921—81no—
222C4⋊Dic53—21no—
223C4⋊Dic53—21no—
224C4⋊Dic53—21no—
225C4⋊Dic53—21no—
226C4⋊Dic53—42no—
227C2×#88322—21no—
228C2×#88322—21no—
229C2×#88322—21no—
230C2×#88322—21no—
231C2×#88322—21no—
232C2×#88322—21no—
233C2×#88322—21no—
234C2×#88322—21no—
235C2×#88322—21no—
236C2×#88322—21no—
237C2×#88322C22×C412yes—
238C2×#88322C22×C412yes—
239C23×C53—21no—
240C23×C53—21no—
241C23×C53—21no—
242C23×C53—21no—
243C23×C53—21no—
244C23×C53—21no—
245C23×C53—22no—
246C23×C53—41no—
247C23×C53—41no—
248C23×C53—41no—
249C23×C53—41no—
250C23×C53—41no—
251C23×C53—41no—
252C23×C53C4×D412yes—
253C23×C53C22×D411yescharacteristic
254C22×D53—22no—
255C22×D53—41no—
256C22×D53—41no—
257C22×D53—41no—
258C22×D53—41no—
259C22×D53—41no—
260C22×D53—41no—
261D4×C53—22no—
262D4×C53—22no—
263D4×C53—41no—
264D4×C53—41no—
265D4×C53—84no—
266C2×C4×C53—21no—
267C2×C4×C53—21no—
268C2×C4×C53—22no—
269C2×C4×C53—22no—
270C2×C4×C53—22no—
271C2×C4×C53—22no—
272C2×C4×C53—22no—
273C2×C4×C53—21no—
274C2×C4×C53—21no—
275C2×C4×C53—21no—
276C2×C4×C53—21no—
277C2×C4×C53—21no—
278C2×C4×C53—21no—
279C2×C4×C53—21no—
280C2×C4×C53—21no—
281C2×C4×C53—21no—
282C2×C4×C53—21no—
283C2×C4×C53—21no—
284C2×C4×C53—21no—
285C2×C4×C53—41no—
286C2×C4×C53—41no—
287C2×C4×C53—41no—
288C2×C4×C53—41no—
289C2×C4×C53—41no—
290C2×C4×C53—41no—
291C2×C4×C53—41no—
292C2×C4×C53—41no—
293C2×C4×C53—84no—
294C2×C4×C53C4×D412yes—
295C2×C4×C53C23×C411yescharacteristic
296C2×C4×C53C2×#4111yescharacteristic
297C2×C4×C53H(5,𝔽2)11yescharacteristic
298C2×C4×C53H(5,𝔽2)11yescharacteristic
299C2×C4×C53H(5,𝔽2)11yescharacteristic
300C2×C4×C53H(5,𝔽2)11yescharacteristic
301C22⋊D53—48no—
302C2×Dic53—22no—
303C2×Dic53—41no—
304C2×Dic53—41no—
305C2×Dic53—41no—
306C2×Dic53—41no—
307C2×Dic53—41no—
308C2×Dic53—41no—
309C2×Dic53—41no—
310C2×Dic53—41no—
311C2×Dic53—84no—
312D212—22no—
313D212—22no—
314D212—41no—
315D212—41no—
316C4×D53—48no—
317Dic106—22no—
318Dic106—22no—
319Dic106—41no—
320Dic106—41no—
321#88322—22no—
322#88322—22no—
323#88322—41no—
324#88322—41no—
325#22055—531nomaximal, Sylow
326C22×C53—22no—
327C22×C53—22no—
328C22×C53—22no—
329C22×C53—41no—
330C22×C53—41no—
331C22×C53—41no—
332C22×C53—41no—
333C22×C53—42no—
334C22×C53—42no—
335C22×C53—42no—
336C22×C53—81no—
337C22×C53—81no—
338C22×C53—81no—
339C22×C53—81no—
340C22×C53C2×C4×D411yescharacteristic
341C22×C53#53411yescharacteristic
342C22×C53#53511yescharacteristic
343C22×C53#57611yescharacteristic
344C22×C53#57611yescharacteristic
345C22×C53#57711yescharacteristic
346C22×C53#57811yescharacteristic
347C2×D53—42no—
348C2×D53—42no—
349C2×D53—42no—
350C2×D53—81no—
351C2×D53—81no—
352C2×D53—81no—
353C2×D53—81no—
354C4×C53—22no—
355C4×C53—41no—
356C4×C53—41no—
357C4×C53—42no—
358C4×C53—41no—
359C4×C53—41no—
360C4×C53—81no—
361C4×C53—81no—
362C4×C53#51811yescharacteristic
363C4×C53#51811yescharacteristic
364C4×C53#53811yescharacteristic
365C4×C53#53811yescharacteristic
366Dic53—42no—
367Dic53—81no—
368Dic53—81no—
369C2×#449—531no—
370#2324D5311yescharacteristic, complemented
371#2311—531no—
372#1973—531no—
373#1970—531no—
374#1936—531no—
375#1933—531no—
376#1928—531no—
377#1925—531no—
378#1879—531no—
379#1877—531no—
380#1874—531no—
381#1852—531no—
382#1788—531no—
383#1750—531no—
384C2×C53—42no—
385C2×C53—82no—
386C2×C53#232111yescharacteristic
387C2×C53#294611yescharacteristic
388C2×C53#295111yescharacteristic
389C2×C53#319811yescharacteristic
390C2×C53#320311yescharacteristic
391C2×C53#322011yescharacteristic
392C2×C53#322511yescharacteristic
393D53—82no—
394C22×#41—531no—
395C22×SD16—531no—
396C22×D8—531no—
397C2×#121C2×D5311yescharacteristic
398C2×C4×D4C2×D5311yescharacteristic
399C2×#117C2×D5311yescharacteristic
400C22×C4⋊C4—531no—
401#449—538no—
402C2×#107—531no—
403C2×#107—531no—
404C2×#103—531no—
405C2×#103—531no—
406C2×#103—531no—
407C2×#102—531no—
408C2×#102—531no—
409C2×#102—531no—
410C2×#102—531no—
411C2×#102—531no—
412C2×C22⋊C8—531no—
413C2×C22⋊C8—531no—
414C2×#97—531no—
415C2×C4×C8—531no—
416#391—531no—
417#391—531no—
418#390—21no—
419#390—531no—
420#390—531no—
421#390C2×D5311yescharacteristic
422#389C2×D5311yescharacteristic
423#388—21no—
424#386—21no—
425#386—1061no—
426#386—1061no—
427#385—21no—
428#380—1061no—
429#380—1061no—
430#380C2×D5311yescharacteristic
431C4×C4⋊C4C2×D5311yescharacteristic
432#340—531no—
433#340—531no—
434#340—531no—
435#340—531no—
436#336—531no—
437#336—531no—
438C53#2205511yescharacteristic, complemented, Sylow
439C2×#41—534no—
440C2×#41—1062no—
441C2×#41—2121no—
442C2×#41—2121no—
443C2×#41—2121no—
444C2×#41—2121no—
445C22×Q8—531no—
446C22×D4—21no—
447C22×D4—531no—
448C22×D4—1061no—
449C22×D4C22×D5311yescharacteristic
450C23×C4—21no—
451C23×C4—1061no—
452C23×C4—1061no—
453C23×C4C22×D5311yescharacteristic
454C2×SD16—534no—
455C2×SD16—2121no—
456C2×SD16—2121no—
457C2×D8—534no—
458C2×D8—2121no—
459C2×D8—2121no—
460C22×C8—531no—
461C22×C8—531no—
462C22×C8—531no—
463C22×C8—531no—
464#121—22no—
465#121C4×D5314yes—
466C4×D4—41no—
467C4×D4—41no—
468#117—41no—
469#117—41no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—531no—
472C2×C4⋊C4—531no—
473C2×C4⋊C4—1061no—
474C2×C4⋊C4—2121no—
475C2×C4⋊C4—2121no—
476C2×C4⋊C4C22⋊D5311yescharacteristic
477C2×C4⋊C4C22⋊D5311yescharacteristic
478C2×C4⋊C4C22×D5311yescharacteristic
479C2×C4⋊C4C22×D5311yescharacteristic
480C2×C4⋊C4C22×D5311yescharacteristic
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—1061no—
487C2×C22⋊C4—1061no—
488C2×C22⋊C4—1061no—
489C2×C22⋊C4—1061no—
490C2×C22⋊C4C22⋊D5311yescharacteristic
491C2×C22⋊C4C22⋊D5311yescharacteristic
492C2×C42—21no—
493C2×C42C22×D5311yescharacteristic
494C2×C42C22×D5311yescharacteristic
495#107—2121no—
496#107—2121no—
497#103—534no—
498#103—2121no—
499#103—2121no—
500#102—534no—
501#102—2121no—
502#102—2121no—
503#102—2121no—
504#102—2121no—
505C22⋊C8—534no—
506C22⋊C8—1062no—
507#97—2121no—
508C4×C8—2121no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—1061no—
513#95—1061no—
514#95—1061no—
515#95—1061no—
516C24—21no—
517C24—1061no—
518C24C2×C22⋊D5311yescharacteristic
519#41—2124no—
520#41—2124no—
521#41—2124no—
522#41—2124no—
523C2×Q8—532no—
524C2×Q8—1061no—
525C2×Q8—1061no—
526C2×Q8—1061no—
527C2×Q8—1061no—
528C2×Q8—1061no—
529C2×D4—24no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—81no—
536C2×D4—81no—
537C2×D4—532no—
538C2×D4—1064no—
539C2×D4—1061no—
540C2×D4—1061no—
541C2×D4—1061no—
542C2×D4—1061no—
543C2×D4—1061no—
544C2×D4—2122no—
545C2×D4—2122no—
546C2×D4C2×C4×D5312yes—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—42no—
555C22×C4—81no—
556C22×C4—81no—
557C22×C4—1061no—
558C22×C4—1064no—
559C22×C4—1061no—
560C22×C4—1061no—
561C22×C4—4241no—
562C22×C4—4241no—
563C22×C4—2122no—
564C22×C4—2122no—
565C22×C4—2122no—
566C22×C4C2×C4×D5312yes—
567C22×C4#1171994512yes—
568C22×C4C2×C22⋊D5311yescharacteristic
569C22×C4C2×C22⋊D5311yescharacteristic
570C22×C4C2×C22⋊D5311yescharacteristic
571C22×C4C2×C22⋊D5311yescharacteristic
572C22×C4C2×C22⋊D5311yescharacteristic
573C22×C4C23×D5311yescharacteristic
574SD16—2124no—
575D8—2124no—
576C2×C8—532no—
577C2×C8—532no—
578C2×C8—1061no—
579C2×C8—1061no—
580C2×C8—1061no—
581C2×C8—1061no—
582C2×C8—1061no—
583C2×C8—1061no—
584C2×C8—1061no—
585C2×C8—1061no—
586C2×C8—1061no—
587C2×C8—1061no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—41no—
594C4⋊C4—41no—
595C4⋊C4—81no—
596C4⋊C4—1061no—
597C4⋊C4—1061no—
598C4⋊C4—1061no—
599C4⋊C4—1061no—
600C4⋊C4—2122no—
601C4⋊C4C2×C4×D5312yes—
602C22⋊C4—24no—
603C22⋊C4—41no—
604C22⋊C4—41no—
605C22⋊C4—42no—
606C22⋊C4—81no—
607C22⋊C4—81no—
608C22⋊C4—81no—
609C22⋊C4—4241no—
610C22⋊C4—4241no—
611C22⋊C4—4241no—
612C22⋊C4—4241no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—81no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—22no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—1062no—
632C23—2121no—
633C23—2121no—
634C23—2121no—
635C23—2121no—
636C23—2121no—
637C23—2121no—
638C23C4×C22⋊D5312yes—
639C23C22×C22⋊D5311yescharacteristic
640Q8—1062no—
641Q8—1062no—
642Q8—2121no—
643Q8—2121no—
644D4—22no—
645D4—22no—
646D4—41no—
647D4—41no—
648D4—84no—
649D4—1062no—
650D4—1062no—
651D4—2128no—
652D4—2121no—
653D4—2121no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—84no—
682C2×C4—1062no—
683C2×C4—4244no—
684C2×C4—2128no—
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×C4C4×C22⋊D5312yes—
694C2×C4C22×C4×D5311yescharacteristic
695C2×C4C2×#1171994511yescharacteristic
696C2×C4#1313326211yescharacteristic
697C2×C4#1313326211yescharacteristic
698C2×C4#1313326311yescharacteristic
699C2×C4#1313326311yescharacteristic
700C8—1062no—
701C8—1062no—
702C8—2121no—
703C8—2121no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—4241no—
719C22—4241no—
720C22—4241no—
721C22—4241no—
722C22—2122no—
723C22—2122no—
724C22—2122no—
725C22C2×C4×C22⋊D5311yescharacteristic
726C22#1681118211yescharacteristic
727C22#1681118711yescharacteristic
728C22#1681142611yescharacteristic
729C22#1681142611yescharacteristic
730C22#1681143411yescharacteristic
731C22#1681143811yescharacteristic
732C4—22no—
733C4—41no—
734C4—41no—
735C4—42no—
736C4—41no—
737C4—41no—
738C4—81no—
739C4—81no—
740C4—4241no—
741C4—4241no—
742C4—2122no—
743C4#1681109511yescharacteristic
744C4#1681109511yescharacteristic
745C4#1681120611yescharacteristic
746C4#1681120611yescharacteristic
747C2—42no—
748C2—82no—
749C2—4242no—
750C2#2027736911yescharacteristic
751C2#2028354711yescharacteristic
752C2#2028358811yescharacteristic
753C2#2028556711yescharacteristic
754C2#2028561211yescharacteristic
755C2#2028575911yescharacteristic
756C2#2028581811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2324C2
socleC23×C53C22×D4
prime radicalC2×#16810766C2
cosocleC22×C4×C53C24
hypercenter#2324D53
hypocenterC53#22055
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2324

Complements

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

NH ≅ G/Ntype
2. #20277303C2semidirect
3. #20275595C2semidirect
4. #20275580C2semidirect
5. #20275411C2semidirect
6. #20275390C2semidirect
7. #20275356C2semidirect
8. #20275335C2semidirect
9. #20275063C2semidirect
10. #20275049C2semidirect
11. #20275033C2semidirect
12. #20274902C2semidirect
13. #20274653C2semidirect
14. #20274481C2semidirect
15. C53×#2324C2semidirect
20. #16810766C4semidirect
65. C2×#11719945C2×C4semidirect
73. C2×#11719923C2×C4semidirect
76. C2×#11719922C2×C4semidirect
94. #13133140C2×C4semidirect
99. #13133137C2×C4semidirect
101. C22⋊#88322C2×C4semidirect
370. #2324D53semidirect
438. C53#22055semidirect

Maximal subgroups

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

subgroupindex
C2×#168107662
#202773032
#202755952
#202755802
#202754112
#202753902
#202753562
#202753352
#202750632
#202750492
#202750332
#202749022
#202746532
#202744812
C53×#23242
#2205553