Finite Group Databasebeta

← #27310482

Subgroups — #27310482

Order 13568.

2098 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810503C211yesmaximal, characteristic
2C2×#16810503C211yesmaximal, characteristic
3C2×#16810496C211yesmaximal, characteristic, complemented
4C22×#13133124C211yesmaximal, characteristic, complemented
5#20272975C212yesmaximal, complemented
6#20272973C212yesmaximal, complemented
7#20272962C212yesmaximal, complemented
8#20272958C212yesmaximal, complemented
9#20272937C211yesmaximal, characteristic, complemented
10#20272937C211yesmaximal, characteristic, complemented
11C2×C53×#386C211yesmaximal, characteristic
12C24×Dic53C2211yescharacteristic
13C24×Dic53C2211yescharacteristic
14C22×#11719919C2212yes—
15C22×C22⋊Dic53C2211yescharacteristic
16C22×C22⋊Dic53C2211yescharacteristic
17C22×C22⋊Dic53C2211yescharacteristic
18C22×C22⋊Dic53C2211yescharacteristic
19C22×C22⋊Dic53C2212yes—
20#16810503—24no—
21#16810503C418yescomplemented
22#16810496—24no—
23C2×#13133124—24no—
24C2×#13133124C2212yes—
25C2×#13133124C2212yes—
26C2×#13133124C2212yes—
27C2×#13133124C2211yescharacteristic
28C2×#13133124C2211yescharacteristic
29C2×#13133124C2212yes—
30C2×#13133124C2212yes—
31C2×#13133124C2212yes—
32C2×#13133124C2212yes—
33C2×#13133124C2212yes—
34C23×D4×C53C2211yescharacteristic
35C24×C4×C53C2211yescharacteristic
36C22×C22⋊C4×C53C2211yescharacteristic
37C22×C22⋊C4×C53C2212yes—
38C53×#386—24no—
39C2×#95×C53C2212yes—
40C23×Dic53—22no—
41C23×Dic53—22no—
42C23×Dic53—22no—
43C23×Dic53—22no—
44C23×Dic53—42no—
45C23×Dic53—42no—
46C23×Dic53—42no—
47C23×Dic53—42no—
48C23×Dic53C2×C414yes—
49C23×Dic53D414yes—
50C23×Dic53C2311yescharacteristic
51C23×Dic53C2311yescharacteristic
52C23×Dic53C2312yes—
53C23×Dic53C2312yes—
54C23×Dic53C2311yescharacteristic
55C23×Dic53C2311yescharacteristic
56C2×#11719919—24no—
57C2×#11719919—42no—
58C2×#11719919—42no—
59C2×C22⋊Dic53—22no—
60C2×C22⋊Dic53—22no—
61C2×C22⋊Dic53—22no—
62C2×C22⋊Dic53—22no—
63C2×C22⋊Dic53—22no—
64C2×C22⋊Dic53—22no—
65C2×C22⋊Dic53—22no—
66C2×C22⋊Dic53—42no—
67C2×C22⋊Dic53—42no—
68C2×C22⋊Dic53—42no—
69C2×C22⋊Dic53—42no—
70C2×C22⋊Dic53C2×C414yes—
71C2×C22⋊Dic53C2×C418yescomplemented
72#13133124—24no—
73#13133124—22no—
74#13133124—22no—
75#13133124—24no—
76#13133124—24no—
77#13133124—42no—
78#13133124—42no—
79#13133124—42no—
80#13133124—42no—
81#13133124C2×C418yescomplemented
82C25×C53C2311yescharacteristic
83C25×C53C2311yescharacteristic
84C22×D4×C53—22no—
85C22×D4×C53—22no—
86C22×D4×C53—22no—
87C22×D4×C53—22no—
88C22×D4×C53—22no—
89C22×D4×C53—22no—
90C22×D4×C53C2×C414yes—
91C23×C4×C53—22no—
92C23×C4×C53—22no—
93C23×C4×C53—42no—
94C23×C4×C53—42no—
95C23×C4×C53D414yes—
96C23×C4×C53C2312yes—
97C23×C4×C53C2311yescharacteristic
98C23×C4×C53C2312yes—
99C2×C22⋊C4×C53—22no—
100C2×C22⋊C4×C53—22no—
101C2×C22⋊C4×C53—22no—
102C2×C22⋊C4×C53—24no—
103C2×C22⋊C4×C53—42no—
104C2×C22⋊C4×C53—42no—
105#95×C53—24no—
106C24×C53—22no—
107C24×C53—22no—
108C24×C53—22no—
109C24×C53—22no—
110C24×C53—21no—
111C24×C53—21no—
112C24×C53—21no—
113C24×C53—21no—
114C24×C53—21no—
115C24×C53—21no—
116C24×C53—22no—
117C24×C53—22no—
118C24×C53—22no—
119C24×C53—22no—
120C24×C53C22×C412yes—
121C24×C53C22×C412yes—
122C24×C53C2×D412yes—
123C24×C53C2×D412yes—
124C24×C53#4112yes—
125C24×C53#4112yes—
126C24×C53#4112yes—
127C24×C53#4112yes—
128C24×C53C2411yescharacteristic
129C2×D4×C53—28no—
130C2×D4×C53—28no—
131C2×D4×C53—28no—
132C2×D4×C53—44no—
133C2×D4×C53—44no—
134C2×D4×C53—44no—
135C2×D4×C53—44no—
136C22×C4×C53—28no—
137C22×C4×C53—21no—
138C22×C4×C53—22no—
139C22×C4×C53—21no—
140C22×C4×C53—22no—
141C22×C4×C53—21no—
142C22×C4×C53—21no—
143C22×C4×C53—21no—
144C22×C4×C53—21no—
145C22×C4×C53—22no—
146C22×C4×C53—22no—
147C22×C4×C53—22no—
148C22×C4×C53—22no—
149C22×C4×C53—22no—
150C22×C4×C53—22no—
151C22×C4×C53—22no—
152C22×C4×C53—22no—
153C22×C4×C53—22no—
154C22×C4×C53—22no—
155C22×C4×C53—22no—
156C22×C4×C53—48no—
157C22×C4×C53—44no—
158C22×C4×C53—44no—
159C22×C4×C53—48no—
160C22×C4×C53C22×C412yes—
161C22×C4×C53C2×D414yes—
162C22×Dic53—28no—
163C22×Dic53—28no—
164C22×Dic53—22no—
165C22×Dic53—22no—
166C22×Dic53—22no—
167C22×Dic53—22no—
168C22×Dic53—21no—
169C22×Dic53—21no—
170C22×Dic53—21no—
171C22×Dic53—21no—
172C22×Dic53—22no—
173C22×Dic53—22no—
174C22×Dic53—22no—
175C22×Dic53—22no—
176C22×Dic53—22no—
177C22×Dic53—22no—
178C22×Dic53—22no—
179C22×Dic53—22no—
180C22×Dic53—22no—
181C22×Dic53—22no—
182C22×Dic53—22no—
183C22×Dic53—22no—
184C22×Dic53—21no—
185C22×Dic53—21no—
186C22×Dic53—21no—
187C22×Dic53—21no—
188C22×Dic53—21no—
189C22×Dic53—21no—
190C22×Dic53—22no—
191C22×Dic53—22no—
192C22×Dic53—22no—
193C22×Dic53—22no—
194C22×Dic53—48no—
195C22×Dic53—44no—
196C22×Dic53—44no—
197C22×Dic53—44no—
198C22×Dic53—44no—
199C22×Dic53—48no—
200C22×Dic53—48no—
201C22×Dic53—48no—
202C22×Dic53C22×C414yes—
203C22×Dic53C22×C414yes—
204C22×Dic53C2×D412yes—
205C22×Dic53C2×D412yes—
206C22⋊C4×C53—48no—
207C22⋊C4×C53—44no—
208C22⋊Dic53—28no—
209C22⋊Dic53—48no—
210C22⋊Dic53—44no—
211C22⋊Dic53—44no—
212C22⋊Dic53—44no—
213#11719919—48no—
214C23×C53—24no—
215C23×C53—24no—
216C23×C53—22no—
217C23×C53—22no—
218C23×C53—24no—
219C23×C53—22no—
220C23×C53—22no—
221C23×C53—24no—
222C23×C53—24no—
223C23×C53—24no—
224C23×C53—24no—
225C23×C53—24no—
226C23×C53—24no—
227C23×C53—24no—
228C23×C53—24no—
229C23×C53—24no—
230C23×C53—22no—
231C23×C53—22no—
232C23×C53—22no—
233C23×C53—24no—
234C23×C53—24no—
235C23×C53—41no—
236C23×C53—41no—
237C23×C53—41no—
238C23×C53—41no—
239C23×C53—41no—
240C23×C53—41no—
241C23×C53—42no—
242C23×C53—41no—
243C23×C53—41no—
244C23×C53—42no—
245C23×C53—42no—
246C23×C53—42no—
247C23×C53—42no—
248C23×C53—42no—
249C23×C53—42no—
250C23×C53—42no—
251C23×C53—42no—
252C23×C53—42no—
253C23×C53#11714yes—
254C23×C53C4×D414yes—
255C23×C53C4×D414yes—
256C23×C53#12114yes—
257C23×C53#12314yes—
258C23×C53#12414yes—
259C23×C53#12614yes—
260C23×C53C23×C411yescharacteristic
261C23×C53C22×D411yescharacteristic
262C23×C53C22×D411yescharacteristic
263C23×C53C2×#4111yescharacteristic
264C23×C53C2×#4111yescharacteristic
265C23×C53C2×#4111yescharacteristic
266C23×C53C2×#4111yescharacteristic
267C23×C53H(5,𝔽2)12yes—
268C23×C53H(5,𝔽2)12yes—
269C23×C53H(5,𝔽2)12yes—
270C23×C532−1+412yes—
271D4×C53—416no—
272C2×C4×C53—22no—
273C2×C4×C53—22no—
274C2×C4×C53—22no—
275C2×C4×C53—24no—
276C2×C4×C53—24no—
277C2×C4×C53—24no—
278C2×C4×C53—416no—
279C2×C4×C53—41no—
280C2×C4×C53—41no—
281C2×C4×C53—41no—
282C2×C4×C53—41no—
283C2×C4×C53—42no—
284C2×C4×C53—42no—
285C2×C4×C53—42no—
286C2×C4×C53—42no—
287C2×C4×C53—42no—
288C2×C4×C53—42no—
289C2×C4×C53—42no—
290C2×C4×C53—42no—
291C2×C4×C53—42no—
292C2×C4×C53—42no—
293C2×C4×C53—42no—
294C2×Dic53—24no—
295C2×Dic53—24no—
296C2×Dic53—24no—
297C2×Dic53—24no—
298C2×Dic53—24no—
299C2×Dic53—24no—
300C2×Dic53—22no—
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—22no—
304C2×Dic53—22no—
305C2×Dic53—22no—
306C2×Dic53—416no—
307C2×Dic53—416no—
308C2×Dic53—42no—
309C2×Dic53—42no—
310C2×Dic53—42no—
311C2×Dic53—42no—
312C2×Dic53—42no—
313C2×Dic53—42no—
314C2×Dic53—42no—
315C2×Dic53—42no—
316C2×Dic53—42no—
317C2×Dic53—42no—
318C2×Dic53—42no—
319C2×Dic53—42no—
320C2×Dic53—41no—
321C2×Dic53—41no—
322C2×Dic53—42no—
323C2×Dic53—41no—
324C2×Dic53—41no—
325C2×Dic53—41no—
326C2×Dic53—41no—
327C2×Dic53—42no—
328C2×Dic53—42no—
329C2×Dic53—42no—
330#14259—531nomaximal, Sylow
331C22×C53—28no—
332C22×C53—24no—
333C22×C53—24no—
334C22×C53—28no—
335C22×C53—24no—
336C22×C53—24no—
337C22×C53—24no—
338C22×C53—24no—
339C22×C53—28no—
340C22×C53—28no—
341C22×C53—44no—
342C22×C53—42no—
343C22×C53—42no—
344C22×C53—44no—
345C22×C53—42no—
346C22×C53—81no—
347C22×C53—81no—
348C22×C53—81no—
349C22×C53—81no—
350C22×C53—82no—
351C22×C53—82no—
352C22×C53#38818yes—
353C22×C53C2×#11711yescharacteristic
354C22×C53C2×C4×D411yescharacteristic
355C22×C53C2×C4×D411yescharacteristic
356C22×C53#51812yes—
357C22×C53#52012yes—
358C22×C53C2×#12111yescharacteristic
359C22×C53C2×#12311yescharacteristic
360C22×C53C2×#12411yescharacteristic
361C22×C53C2×#12611yescharacteristic
362C22×C53#53412yes—
363C22×C53#53411yescharacteristic
364C22×C53#53411yescharacteristic
365C22×C53#53511yescharacteristic
366C22×C53#53611yescharacteristic
367C22×C53#53712yes—
368C22×C53#53812yes—
369C22×C53#53812yes—
370C22×C53#53812yes—
371C22×C53#53812yes—
372C22×C53#53912yes—
373C22×C53#53912yes—
374C22×C53#53912yes—
375C22×C53#53912yes—
376C4×C53—44no—
377C4×C53—42no—
378C4×C53—82no—
379Dic53—44no—
380Dic53—44no—
381Dic53—42no—
382Dic53—42no—
383Dic53—81no—
384Dic53—81no—
385C2×#386—531no—
386C2×#386—531no—
387C2×#386D5311yescharacteristic
388C2×#385—531no—
389C22×#95—531no—
390#1443—532no—
391#1442—532no—
392#1440—532no—
393#1439—532no—
394C22⋊#95—531no—
395C22⋊#95—531no—
396C2×C53—28no—
397C2×C53—82no—
398C2×C53C2×#38811yescharacteristic
399C2×C53#231812yes—
400C2×C53#232111yescharacteristic
401C2×C53#232211yescharacteristic
402C2×C53#232512yes—
403C2×C53#261711yescharacteristic
404C2×C53#261811yescharacteristic
405C2×C53#262211yescharacteristic
406C2×C53#262311yescharacteristic
407C2×C53#263912yes—
408C2×C53#264312yes—
409C23×D4C2×D5311yescharacteristic
410C24×C4—531no—
411C24×C4—531no—
412C24×C4C2×D5311yescharacteristic
413C22×C4⋊C4—532no—
414C22×C22⋊C4—531no—
415C22×C22⋊C4—532no—
416C22×C22⋊C4—531no—
417C22×C22⋊C4—531no—
418C22×C22⋊C4—531no—
419C22×C22⋊C4C2×D5311yescharacteristic
420C22×C22⋊C4C2×D5312yes—
421#386—24no—
422#386—538no—
423#386—1064no—
424#385—1064no—
425C2×#95—532no—
426C2×#95—532no—
427C2×#95—532no—
428C2×#95—532no—
429C2×#95—531no—
430C2×#95—531no—
431C2×#95—532no—
432C2×#95—532no—
433C2×#95—532no—
434C2×#95—532no—
435C2×#95—1064no—
436C2×#95C2×D5312yes—
437C53#1425911yescharacteristic, complemented, Sylow
438C25C22×D5311yescharacteristic
439C25C22×D5311yescharacteristic
440C22×D4—22no—
441C22×D4—22no—
442C22×D4—22no—
443C22×D4—22no—
444C22×D4—22no—
445C22×D4—22no—
446C22×D4C4×D5314yes—
447C23×C4—22no—
448C23×C4—22no—
449C23×C4—42no—
450C23×C4—42no—
451C23×C4—532no—
452C23×C4—532no—
453C23×C4—531no—
454C23×C4—531no—
455C23×C4—534no—
456C23×C4—534no—
457C23×C4—531no—
458C23×C4—531no—
459C23×C4—1062no—
460C23×C4—1062no—
461C23×C4—1062no—
462C23×C4—1062no—
463C23×C4—2122no—
464C23×C4—2122no—
465C23×C4—2122no—
466C23×C4—2122no—
467C23×C4C22⋊D5314yes—
468C23×C4C22×D5312yes—
469C23×C4C22×D5311yescharacteristic
470C23×C4C22×D5312yes—
471C2×C4⋊C4—1064no—
472C2×C4⋊C4—2122no—
473C2×C4⋊C4—2122no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—42no—
479C2×C22⋊C4—42no—
480C2×C22⋊C4—534no—
481C2×C22⋊C4—538no—
482C2×C22⋊C4—1062no—
483C2×C22⋊C4—1062no—
484C2×C22⋊C4—1062no—
485C2×C22⋊C4—1062no—
486C2×C22⋊C4—1062no—
487C2×C22⋊C4—1062no—
488C2×C22⋊C4—1062no—
489C2×C22⋊C4—2122no—
490C2×C22⋊C4—2122no—
491C2×C22⋊C4—2122no—
492C2×C22⋊C4—2122no—
493#95—24no—
494#95—538no—
495#95—1064no—
496#95—1064no—
497#95—1062no—
498#95—1062no—
499#95—1064no—
500#95—2122no—
501#95—2122no—
502#95—2122no—
503#95—2122no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—21no—
509C24—21no—
510C24—21no—
511C24—21no—
512C24—21no—
513C24—21no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24C2×C4×D5312yes—
519C24C2×C4×D5312yes—
520C24#1171994512yes—
521C24D4×D5312yes—
522C24#1171994712yes—
523C24#1171994712yes—
524C24#1171994712yes—
525C24C2×C22⋊D5312yes—
526C24C23×D5311yescharacteristic
527C2×D4—28no—
528C2×D4—28no—
529C2×D4—28no—
530C2×D4—44no—
531C2×D4—44no—
532C2×D4—44no—
533C2×D4—44no—
534C22×C4—28no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—48no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—48no—
558C22×C4—534no—
559C22×C4—534no—
560C22×C4—532no—
561C22×C4—532no—
562C22×C4—1068no—
563C22×C4—1068no—
564C22×C4—1062no—
565C22×C4—1062no—
566C22×C4—1062no—
567C22×C4—1061no—
568C22×C4—1061no—
569C22×C4—1062no—
570C22×C4—1061no—
571C22×C4—1061no—
572C22×C4—1062no—
573C22×C4—1062no—
574C22×C4—1062no—
575C22×C4—1062no—
576C22×C4—1062no—
577C22×C4—1062no—
578C22×C4—1062no—
579C22×C4—1062no—
580C22×C4—1062no—
581C22×C4—1062no—
582C22×C4—1062no—
583C22×C4—1062no—
584C22×C4—1061no—
585C22×C4—1061no—
586C22×C4—1061no—
587C22×C4—1061no—
588C22×C4—1061no—
589C22×C4—1061no—
590C22×C4—1062no—
591C22×C4—1062no—
592C22×C4—1062no—
593C22×C4—1062no—
594C22×C4—2128no—
595C22×C4—2124no—
596C22×C4—2124no—
597C22×C4—2124no—
598C22×C4—2124no—
599C22×C4—2128no—
600C22×C4—2128no—
601C22×C4—2128no—
602C22×C4C2×C4×D5312yes—
603C22×C4C2×C22⋊D5314yes—
604C4⋊C4—2128no—
605C22⋊C4—48no—
606C22⋊C4—44no—
607C22⋊C4—1068no—
608C22⋊C4—2128no—
609C22⋊C4—2124no—
610C22⋊C4—2124no—
611C22⋊C4—2124no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—24no—
632C23—24no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—42no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23#1313317314yes—
652C23#1313317714yes—
653C23C4×C22⋊D5314yes—
654C23#1313318914yes—
655C23#1313319914yes—
656C23#1313320414yes—
657C23#1313321014yes—
658C23C22×C4×D5311yescharacteristic
659C23C2×D4×D5311yescharacteristic
660C23C22×C22⋊D5311yescharacteristic
661C23C2×#1171994711yescharacteristic
662C23C2×#1171994711yescharacteristic
663C23C2×#1171994711yescharacteristic
664C23C2×#1171994511yescharacteristic
665C23#1313326212yes—
666C23#1313326212yes—
667C23#1313326312yes—
668C23#1313326412yes—
669D4—416no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—416no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—1064no—
693C2×C4—1064no—
694C2×C4—1064no—
695C2×C4—1064no—
696C2×C4—1064no—
697C2×C4—1064no—
698C2×C4—1062no—
699C2×C4—1062no—
700C2×C4—1062no—
701C2×C4—1062no—
702C2×C4—1062no—
703C2×C4—1062no—
704C2×C4—2121no—
705C2×C4—2121no—
706C2×C4—2122no—
707C2×C4—2121no—
708C2×C4—2121no—
709C2×C4—2121no—
710C2×C4—2121no—
711C2×C4—2122no—
712C2×C4—2122no—
713C2×C4—2122no—
714C2×C4—21216no—
715C2×C4—21216no—
716C2×C4—2122no—
717C2×C4—2122no—
718C2×C4—2122no—
719C2×C4—2122no—
720C2×C4—2122no—
721C2×C4—2122no—
722C2×C4—2122no—
723C2×C4—2122no—
724C2×C4—2122no—
725C2×C4—2122no—
726C2×C4—2122no—
727C2×C4—2122no—
728C22—28no—
729C22—28no—
730C22—28no—
731C22—24no—
732C22—24no—
733C22—24no—
734C22—24no—
735C22—28no—
736C22—24no—
737C22—24no—
738C22—44no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—44no—
743C22—82no—
744C22—82no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22#1681051718yes—
750C22C2×#1313317311yescharacteristic
751C22C2×#1313317711yescharacteristic
752C22C2×C4×C22⋊D5311yescharacteristic
753C22#1681109512yes—
754C22#1681110212yes—
755C22C2×#1313318911yescharacteristic
756C22C2×#1313319911yescharacteristic
757C22C2×#1313320411yescharacteristic
758C22C2×#1313321011yescharacteristic
759C22#1681118212yes—
760C22#1681118311yescharacteristic
761C22#1681118411yescharacteristic
762C22#1681118811yescharacteristic
763C22#1681119511yescharacteristic
764C22#1681120112yes—
765C22#1681120612yes—
766C22#1681120812yes—
767C22#1681121012yes—
768C22#1681121012yes—
769C22#1681121512yes—
770C22#1681121712yes—
771C22#1681121812yes—
772C22#1681121812yes—
773C4—44no—
774C4—42no—
775C4—82no—
776C4—4241no—
777C4—4241no—
778C4—2124no—
779C4—2124no—
780C4—2122no—
781C4—2122no—
782C2—28no—
783C2—82no—
784C2C2×#1681051711yescharacteristic
785C2#2027734112yes—
786C2#2027737811yescharacteristic
787C2#2027738911yescharacteristic
788C2#2027741312yes—
789C2#2028045311yescharacteristic
790C2#2028046111yescharacteristic
791C2#2028049211yescharacteristic
792C2#2028049911yescharacteristic
793C2#2028064812yes—
794C2#2028067012yes—
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C53×#386C2
socle, cosocleC24×C53C24
prime radicalC23×D4×C53C22
hypercenterC2×#386D53
hypocenterC53#14259
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
3. C2×#16810496C2semidirect
4. C22×#13133124C2semidirect
5. #20272975C2semidirect
6. #20272973C2semidirect
7. #20272962C2semidirect
8. #20272958C2semidirect
9. #20272937C2semidirect
10. #20272937C2semidirect
21. #16810503C4semidirect
71. C2×C22⋊Dic53C2×C4semidirect
81. #13133124C2×C4semidirect
437. C53#14259semidirect

Maximal subgroups

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

subgroupindex
C2×#168105032
C2×#168104962
C22×#131331242
#202729752
#202729732
#202729622
#202729582
#202729372
C2×C53×#3862
#1425953