Finite Group Databasebeta

← #27427937

Subgroups — #27427937

Order 13568.

1014 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810768C211yesmaximal, characteristic
2C2×C4×#11719924C211yesmaximal, characteristic, complemented
3#20278207C211yesmaximal, characteristic, complemented
4#20276236C211yesmaximal, characteristic, complemented
5#20276152C211yesmaximal, characteristic, complemented
6#20276025C211yesmaximal, characteristic, complemented
7#20275897C211yesmaximal, characteristic, complemented
8#20275401C211yesmaximal, characteristic, complemented
9#20275323C211yesmaximal, characteristic, complemented
10#20275070C211yesmaximal, characteristic, complemented
11#20275066C211yesmaximal, characteristic, complemented
12#20274969C211yesmaximal, characteristic, complemented
13#20274730C211yesmaximal, characteristic, complemented
14#20274655C211yesmaximal, characteristic, complemented
15C53×#2341C211yesmaximal, characteristic, complemented
16C22×#11719924C2211yescharacteristic
17C22×#11719922C2211yescharacteristic
18C2×#13133191C2211yescharacteristic
19C2×C4×D212C2211yescharacteristic
20#16810768—24no—
21C4×#11719924—24no—
22C2×#13133150C2211yescharacteristic
23C2×#13133148C2211yescharacteristic
24C2×C4⋊#88322C2211yescharacteristic
25C2×#13133141C2211yescharacteristic
26C2×#13133141C2211yescharacteristic
27C2×#13133141C2211yescharacteristic
28C2×#13133138C2211yescharacteristic
29C2×#13133138C2211yescharacteristic
30C2×#13133138C2211yescharacteristic
31C2×#13133137C2211yescharacteristic
32C2×#13133137C2211yescharacteristic
33C2×C22⋊#88322C2211yescharacteristic
34C2×C22⋊#88322C2211yescharacteristic
35C2×C4×#88322C2211yescharacteristic
36#16810552—21no—
37#16810538—21no—
38#16810525C2211yescharacteristic
39#16810521C2211yescharacteristic
40#16810499—21no—
41#16810489C2211yescharacteristic
42#16810485—21no—
43#16810483C2211yescharacteristic
44#16810385C2211yescharacteristic
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810378C2211yescharacteristic
49#16810378C2211yescharacteristic
50C22×#41×C53C2211yescharacteristic
51C2×C4×Q8×C53C2211yescharacteristic
52C2×C4×Q8×C53C2211yescharacteristic
53C53×#390—21no—
54C53×#390—21no—
55C53×#390C2211yescharacteristic
56C53×#390C2211yescharacteristic
57C53×#380—21no—
58C53×#380C2211yescharacteristic
59C4×C22⋊C4×C53—21no—
60C4×C22⋊C4×C53C2211yescharacteristic
61C22×D212C2311yescharacteristic
62C22×C22⋊D53—21no—
63C22×C4×D53—21no—
64C2×#11719924—22no—
65C2×#11719924—22no—
66C2×#11719924D414yes—
67C2×#11719922—22no—
68C2×#11719922—22no—
69C2×#11719922—41no—
70C22×#88322C2311yescharacteristic
71C22×#88322C2311yescharacteristic
72C22×#88322C2311yescharacteristic
73C22×#88322C2311yescharacteristic
74#13133191—22no—
75#13133191—41no—
76C4×D212—22no—
77C4×D212—41no—
78C2×C4⋊Dic53C2311yescharacteristic
79C2×C4⋊Dic53C2311yescharacteristic
80C2×C4⋊Dic53C2311yescharacteristic
81C2×#11719919—21no—
82C2×C22⋊Dic53—21no—
83C2×#11719921—21no—
84C2×#11719921—21no—
85C2×#11719921—21no—
86C2×#11719921—21no—
87#13133150—41no—
88#13133148—22no—
89C4⋊#88322—41no—
90#13133141—22no—
91#13133141—22no—
92#13133141—22no—
93#13133138—22no—
94#13133138—22no—
95#13133138—41no—
96#13133137—22no—
97#13133137—41no—
98C22⋊#88322—22no—
99C22⋊#88322—41no—
100C4×#88322—22no—
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—41no—
110C2×#41×C53—41no—
111C22×Q8×C53C2311yescharacteristic
112C22×D4×C53—21no—
113C22×D4×C53C2311yescharacteristic
114C23×C4×C53—21no—
115C23×C4×C53C2311yescharacteristic
116C4×Q8×C53—22no—
117C4×Q8×C53—22no—
118C4×Q8×C53—41no—
119C4×Q8×C53—41no—
120C2×C4⋊C4×C53—21no—
121C2×C4⋊C4×C53—21no—
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×C53—21no—
133C2×C42×C53C2311yescharacteristic
134C2×C42×C53C2311yescharacteristic
135#95×C53—21no—
136#95×C53D411yescharacteristic
137#95×C53D411yescharacteristic
138C24×C53—21no—
139C24×C53C2×D411yescharacteristic
140C23×D53—21no—
141#41×C53—44no—
142#41×C53—44no—
143#41×C53—44no—
144#41×C53—44no—
145C2×Q8×C53—21no—
146C2×Q8×C53—21no—
147C2×Q8×C53—21no—
148C2×Q8×C53C2×D412yes—
149C2×Q8×C53#4112yes—
150C2×Q8×C53#4112yes—
151C2×D4×C53—24no—
152C2×D4×C53—21no—
153C2×D4×C53—21no—
154C2×D4×C53—21no—
155C2×D4×C53—21no—
156C2×D4×C53—21no—
157C2×D4×C53—42no—
158C2×D4×C53—42no—
159C2×D4×C53#4112yes—
160C22×C4×C53—21no—
161C22×C4×C53—24no—
162C22×C4×C53—21no—
163C22×C4×C53—21no—
164C22×C4×C53—21no—
165C22×C4×C53—21no—
166C22×C4×C53—21no—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53—42no—
171C22×C4×C53—42no—
172C22×C4×C53C2×D411yescharacteristic
173C22×C4×C53C2×D411yescharacteristic
174C22×C4×C53C2×D411yescharacteristic
175C22×C4×C53C2×D411yescharacteristic
176C22×C4×C53C2×D411yescharacteristic
177C22×C4×C53C2411yescharacteristic
178C2×C22⋊D53—42no—
179C2×C22⋊D53—42no—
180C2×C22⋊D53—81no—
181C22×Dic53—21no—
182C22×Dic53—21no—
183C22×Dic53—21no—
184C2×D212—21no—
185C2×D212—21no—
186C2×D212—21no—
187C2×D212—21no—
188C2×D212—21no—
189C2×D212C2×D412yes—
190C2×C4×D53—42no—
191C2×C4×D53—42no—
192C2×C4×D53—81no—
193C4⋊C4×C53—21no—
194C4⋊C4×C53—21no—
195C4⋊C4×C53—21no—
196C4⋊C4×C53—21no—
197C4⋊C4×C53—42no—
198C4⋊C4×C53—42no—
199C22⋊C4×C53—22no—
200C22⋊C4×C53—41no—
201C22⋊C4×C53—42no—
202C22⋊C4×C53—42no—
203C22⋊C4×C53—81no—
204C22⋊C4×C53—81no—
205C22⋊C4×C53—81no—
206C42×C53—21no—
207C42×C53—21no—
208C42×C53—21no—
209C42×C53—21no—
210C42×C53—42no—
211C42×C53—42no—
212C22⋊Dic53—81no—
213#11719924—28no—
214#11719922—44no—
215#11719921—42no—
216#11719921—42no—
217#11719921—81no—
218#11719921—81no—
219C4⋊Dic53—21no—
220C4⋊Dic53—21no—
221C4⋊Dic53—21no—
222C4⋊Dic53—21no—
223C4⋊Dic53—21no—
224C4⋊Dic53—21no—
225#11719919—81no—
226C2×#88322—21no—
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×#88322C2×D412yes—
238C23×C53—21no—
239C23×C53—22no—
240C23×C53—21no—
241C23×C53—21no—
242C23×C53—21no—
243C23×C53—21no—
244C23×C53—21no—
245C23×C53—21no—
246C23×C53—41no—
247C23×C53—41no—
248C23×C53—41no—
249C23×C53—41no—
250C23×C53—41no—
251C23×C53—41no—
252C23×C53C22×D411yescharacteristic
253C22×D53—22no—
254C22×D53—41no—
255C22×D53—41no—
256C22×D53—41no—
257C22×D53—41no—
258C22×D53—41no—
259C22×D53—41no—
260Q8×C53—22no—
261Q8×C53—22no—
262Q8×C53—22no—
263Q8×C53#12314yes—
264D4×C53—22no—
265D4×C53—22no—
266D4×C53—48no—
267D4×C53—41no—
268D4×C53—41no—
269C2×C4×C53—22no—
270C2×C4×C53—21no—
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—21no—
286C2×C4×C53—48no—
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—41no—
294C2×C4×C53—41no—
295C2×C4×C53—41no—
296C2×C4×C53—41no—
297C2×C4×C53#13512yes—
298C2×C4×C53C22×D411yescharacteristic
299C2×C4×C53C2×#4111yescharacteristic
300C2×C4×C53C2×#4111yescharacteristic
301C2×C4×C53C2×#4111yescharacteristic
302C2×C4×C53H(5,𝔽2)11yescharacteristic
303C2×C4×C53H(5,𝔽2)11yescharacteristic
304C22⋊D53—84no—
305C2×Dic53—41no—
306C2×Dic53—41no—
307C2×Dic53—41no—
308C2×Dic53—41no—
309C2×Dic53—41no—
310C2×Dic53—41no—
311C2×Dic53—41no—
312C2×Dic53—41no—
313C2×Dic53—41no—
314D212—22no—
315D212—22no—
316D212—41no—
317D212—41no—
318C4×D53—84no—
319#88322—22no—
320#88322—41no—
321#88322—41no—
322#88322—41no—
323#24900—531nomaximal, Sylow
324C22×C53—41no—
325C22×C53—42no—
326C22×C53—41no—
327C22×C53—42no—
328C22×C53—42no—
329C22×C53—41no—
330C22×C53—41no—
331C22×C53—41no—
332C22×C53—41no—
333C22×C53—41no—
334C22×C53—81no—
335C22×C53—81no—
336C22×C53—81no—
337C22×C53—81no—
338C22×C53#52511yescharacteristic
339C22×C53D4211yescharacteristic
340C22×C53#54611yescharacteristic
341C22×C53C2×#13511yescharacteristic
342C22×C53#57511yescharacteristic
343C22×C53#57611yescharacteristic
344C22×C53#57711yescharacteristic
345C2×D53—42no—
346C2×D53—42no—
347C2×D53—42no—
348C2×D53—81no—
349C2×D53—81no—
350C2×D53—81no—
351C2×D53—81no—
352C4×C53—24no—
353C4×C53—22no—
354C4×C53—41no—
355C4×C53—41no—
356C4×C53—41no—
357C4×C53—41no—
358C4×C53—81no—
359C4×C53—81no—
360C4×C53C2×#12311yescharacteristic
361C4×C53#53811yescharacteristic
362C4×C53#54611yescharacteristic
363C4×C53#55111yescharacteristic
364Dic53—81no—
365Dic53—81no—
366Dic53—81no—
367C2×#449—531no—
368C2×C4×SD16—531no—
369#2420—531no—
370#2341D5311yescharacteristic, complemented
371#2092—531no—
372#2077—531no—
373#2054—531no—
374#2033—531no—
375#1934—531no—
376#1923—531no—
377#1880—531no—
378#1879—531no—
379#1863—531no—
380#1805—531no—
381#1788—531no—
382C2×C53—81no—
383C2×C53—82no—
384C2×C53#241811yescharacteristic
385C2×C53#310211yescharacteristic
386C2×C53#311911yescharacteristic
387C2×C53#326811yescharacteristic
388C2×C53#328211yescharacteristic
389C2×C53#330511yescharacteristic
390C2×C53#332611yescharacteristic
391D53—82no—
392C22×#41C2×D5311yescharacteristic
393C22×SD16—531no—
394C22×D8—531no—
395C2×#121—531no—
396C2×C4×Q8C2×D5311yescharacteristic
397C2×C4×Q8C2×D5311yescharacteristic
398C2×C4×D4—531no—
399#449—1064no—
400C4×SD16—1064no—
401C2×#107—531no—
402C2×#106—531no—
403C2×C4⋊C8—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×C4×C8—531no—
415#397—1061no—
416#394—1061no—
417#390—21no—
418#390—21no—
419#390—531no—
420#390C2×D5311yescharacteristic
421#390C2×D5311yescharacteristic
422#389—531no—
423#386—1061no—
424#382—531no—
425#381—1061no—
426#380—21no—
427#380—531no—
428#380C2×D5311yescharacteristic
429C4×C22⋊C4—21no—
430C4×C22⋊C4C2×D5311yescharacteristic
431#340—531no—
432#340—531no—
433#340—531no—
434#340—531no—
435#336—531no—
436#336—531no—
437C53#2490011yescharacteristic, complemented, Sylow
438C2×#41—22no—
439C2×#41—22no—
440C2×#41—22no—
441C2×#41—22no—
442C2×#41—41no—
443C2×#41—41no—
444C22×Q8C22×D5311yescharacteristic
445C22×D4—21no—
446C22×D4—531no—
447C22×D4—1061no—
448C22×D4C22×D5311yescharacteristic
449C23×C4—21no—
450C23×C4—1061no—
451C23×C4C22×D5311yescharacteristic
452C2×SD16—534no—
453C2×SD16—1062no—
454C2×SD16—1062no—
455C2×D8—1062no—
456C2×D8—1062no—
457C2×D8—2121no—
458C22×C8—531no—
459C22×C8—531no—
460C22×C8—531no—
461C22×C8—531no—
462#121—1062no—
463#121—2121no—
464C4×Q8—22no—
465C4×Q8—22no—
466C4×Q8—41no—
467C4×Q8—41no—
468C4×D4—1062no—
469C4×D4—2121no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—531no—
473C2×C4⋊C4—531no—
474C2×C4⋊C4—531no—
475C2×C4⋊C4—1061no—
476C2×C4⋊C4C22×D5311yescharacteristic
477C2×C4⋊C4C22×D5311yescharacteristic
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—1061no—
484C2×C22⋊C4—1061no—
485C2×C22⋊C4—1061no—
486C2×C22⋊C4—1061no—
487C2×C22⋊C4—1061no—
488C2×C22⋊C4C22⋊D5311yescharacteristic
489C2×C22⋊C4C22⋊D5311yescharacteristic
490C2×C42—21no—
491C2×C42—21no—
492C2×C42C22×D5311yescharacteristic
493C2×C42C22×D5311yescharacteristic
494#107—2121no—
495#106—1062no—
496C4⋊C8—2121no—
497#103—1062no—
498#103—1062no—
499#103—1062no—
500#102—1062no—
501#102—1062no—
502#102—1062no—
503#102—2121no—
504#102—2121no—
505C22⋊C8—1062no—
506C22⋊C8—2121no—
507C4×C8—1062no—
508#95—21no—
509#95—1061no—
510#95—1061no—
511#95—1061no—
512#95—1061no—
513#95C22⋊D5311yescharacteristic
514#95C22⋊D5311yescharacteristic
515C24—21no—
516C24—1061no—
517C24C2×C22⋊D5311yescharacteristic
518#41—44no—
519#41—44no—
520#41—44no—
521#41—44no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8#1171994512yes—
526C2×Q8D4×D5312yes—
527C2×Q8#1171994712yes—
528C2×D4—24no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—532no—
537C2×D4—1061no—
538C2×D4—1061no—
539C2×D4—1061no—
540C2×D4—1061no—
541C2×D4—1061no—
542C2×D4—4241no—
543C2×D4—2122no—
544C2×D4—2122no—
545C2×D4#1171994512yes—
546C22×C4—21no—
547C22×C4—24no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—1061no—
559C22×C4—1061no—
560C22×C4—1061no—
561C22×C4—4241no—
562C22×C4—2122no—
563C22×C4—2122no—
564C22×C4C2×C22⋊D5311yescharacteristic
565C22×C4C2×C22⋊D5311yescharacteristic
566C22×C4C2×C22⋊D5311yescharacteristic
567C22×C4C2×C22⋊D5311yescharacteristic
568C22×C4C2×C22⋊D5311yescharacteristic
569C22×C4C23×D5311yescharacteristic
570SD16—1068no—
571D8—2124no—
572C2×C8—532no—
573C2×C8—1061no—
574C2×C8—1061no—
575C2×C8—1061no—
576C2×C8—1061no—
577C2×C8—1061no—
578C2×C8—1061no—
579C2×C8—1061no—
580C2×C8—1061no—
581C2×C8—1061no—
582C2×C8—1061no—
583C2×C8—1061no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—1061no—
591C4⋊C4—1061no—
592C4⋊C4—1061no—
593C4⋊C4—1061no—
594C4⋊C4—1061no—
595C4⋊C4—1061no—
596C4⋊C4—4241no—
597C22⋊C4—22no—
598C22⋊C4—41no—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4—81no—
602C22⋊C4—81no—
603C22⋊C4—81no—
604C22⋊C4—4241no—
605C22⋊C4—4241no—
606C22⋊C4—4241no—
607C22⋊C4—2122no—
608C22⋊C4—2122no—
609C42—21no—
610C42—21no—
611C42—21no—
612C42—21no—
613C42—42no—
614C42—42no—
615C23—21no—
616C23—21no—
617C23—22no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—1062no—
630C23—2121no—
631C23—2121no—
632C23—2121no—
633C23—2121no—
634C23—2121no—
635C23—2121no—
636C23C22×C22⋊D5311yescharacteristic
637Q8—22no—
638Q8—22no—
639Q8—22no—
640Q8#1313319914yes—
641D4—22no—
642D4—22no—
643D4—48no—
644D4—41no—
645D4—41no—
646D4—1062no—
647D4—1062no—
648D4—4244no—
649D4—2121no—
650D4—2121no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—22no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—48no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—4244no—
680C2×C4—2121no—
681C2×C4—2121no—
682C2×C4—2121no—
683C2×C4—2121no—
684C2×C4—2121no—
685C2×C4—2121no—
686C2×C4—2121no—
687C2×C4—2121no—
688C2×C4—2121no—
689C2×C4#1313323712yes—
690C2×C4C2×D4×D5311yescharacteristic
691C2×C4C2×#1171994711yescharacteristic
692C2×C4C2×#1171994511yescharacteristic
693C2×C4C2×#1171994511yescharacteristic
694C2×C4#1313326211yescharacteristic
695C2×C4#1313326211yescharacteristic
696C8—1062no—
697C8—2121no—
698C8—2121no—
699C8—2121no—
700C22—41no—
701C22—41no—
702C22—42no—
703C22—42no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—42no—
709C22—41no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—4241no—
715C22—4241no—
716C22—4241no—
717C22—4241no—
718C22—2122no—
719C22—2122no—
720C22—2122no—
721C22#1681113411yescharacteristic
722C22D4×C22⋊D5311yescharacteristic
723C22#1681126711yescharacteristic
724C22C2×#1313323711yescharacteristic
725C22#1681142111yescharacteristic
726C22#1681142611yescharacteristic
727C22#1681143111yescharacteristic
728C4—24no—
729C4—22no—
730C4—41no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—81no—
735C4—81no—
736C4—4241no—
737C4—4241no—
738C4—4241no—
739C4C2×#1313319911yescharacteristic
740C4#1681121111yescharacteristic
741C4#1681126311yescharacteristic
742C4#1681129911yescharacteristic
743C2—81no—
744C2—82no—
745C2—4242no—
746C2#2027817711yescharacteristic
747C2#2028473311yescharacteristic
748C2#2028491411yescharacteristic
749C2#2028625611yescharacteristic
750C2#2028642311yescharacteristic
751C2#2028666511yescharacteristic
752C2#2028696811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
FittingC53×#2341C2
socleC23×C53C22×D4
prime radicalC2×#16810768C2
hypercenter#2341D53
hypocenterC53#24900
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2341

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11719924C2semidirect
3. #20278207C2semidirect
4. #20276236C2semidirect
5. #20276152C2semidirect
6. #20276025C2semidirect
7. #20275897C2semidirect
8. #20275401C2semidirect
9. #20275323C2semidirect
10. #20275070C2semidirect
11. #20275066C2semidirect
12. #20274969C2semidirect
13. #20274730C2semidirect
14. #20274655C2semidirect
15. C53×#2341C2semidirect
370. #2341D53semidirect
437. C53#24900semidirect

Maximal subgroups

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

subgroupindex
C2×#168107682
C2×C4×#117199242
#202782072
#202762362
#202761522
#202760252
#202758972
#202754012
#202753232
#202750702
#202750662
#202749692
#202747302
#202746552
C53×#23412
#2490053