Finite Group Databasebeta

← #27307500

Subgroups — #27307500

Order 13568.

2538 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810513C212yesmaximal, complemented
2C2×#16810502C211yesmaximal, characteristic
3C2×#16810502C211yesmaximal, characteristic
4C2×#16810502C211yesmaximal, characteristic
5C2×C4×C22⋊Dic53C211yesmaximal, characteristic, complemented
6#20272974C212yesmaximal, complemented
7#20272957C212yesmaximal, complemented
8#20272947C212yesmaximal, complemented
9#20272938C211yesmaximal, characteristic, complemented
10#20272938C211yesmaximal, characteristic, complemented
11C23×C4⋊C4×C53C211yesmaximal, characteristic, complemented
12C23×C22⋊D53C2211yescharacteristic
13C22×C22⋊Dic53C2211yescharacteristic
14C22×C22⋊Dic53C2211yescharacteristic
15C22×C22⋊Dic53C2211yescharacteristic
16C22×#11719921C2211yescharacteristic
17C22×#11719921C2212yes—
18C22×#11719921C2212yes—
19C22×#11719921C2211yescharacteristic
20C22×C4×Dic53C2212yes—
21#16810513—28no—
22#16810502—24no—
23#16810502—24no—
24#16810502C418yescomplemented
25C4×C22⋊Dic53—24no—
26C2×#13133124C2212yes—
27C2×#13133124C2212yes—
28C2×#13133124C2212yes—
29C2×#13133124C2211yescharacteristic
30C2×#13133124C2212yes—
31C2×#13133124C2212yes—
32C2×#13133124C2211yescharacteristic
33C2×#13133124C2212yes—
34C2×#13133124C2212yes—
35C24×C4×C53C2211yescharacteristic
36C24×C4×C53C2211yescharacteristic
37C24×C4×C53C2211yescharacteristic
38C22×C4⋊C4×C53—24no—
39C22×C4⋊C4×C53—28no—
40C22×C4⋊C4×C53C2212yes—
41C22×C4⋊C4×C53C2212yes—
42C24×D53C2311yescharacteristic
43C22×C22⋊D53—22no—
44C22×C22⋊D53—22no—
45C22×C22⋊D53—22no—
46C22×C22⋊D53—22no—
47C22×C22⋊D53—22no—
48C22×C22⋊D53—22no—
49C22×C22⋊D53C2×C414yes—
50C23×Dic53C2311yescharacteristic
51C23×Dic53C2311yescharacteristic
52C23×Dic53C2312yes—
53C23×Dic53C2311yescharacteristic
54C23×Dic53C2312yes—
55C2×C22⋊Dic53—22no—
56C2×C22⋊Dic53—22no—
57C2×C22⋊Dic53—22no—
58C2×C22⋊Dic53—22no—
59C2×C22⋊Dic53—22no—
60C2×C22⋊Dic53—22no—
61C2×C22⋊Dic53—22no—
62C2×C22⋊Dic53C2×C414yes—
63C2×C22⋊Dic53D414yes—
64C2×#11719921—24no—
65C2×#11719921—22no—
66C2×#11719921—22no—
67C2×#11719921—24no—
68C2×#11719921—24no—
69C2×#11719921—24no—
70C2×#11719921—24no—
71C2×#11719921—42no—
72C2×#11719921—42no—
73C2×#11719921C2×C418yescomplemented
74C2×C4×Dic53—24no—
75C2×C4×Dic53—24no—
76C2×C4×Dic53—42no—
77#13133124—22no—
78#13133124—22no—
79#13133124—24no—
80#13133124—24no—
81#13133124—24no—
82#13133124—24no—
83#13133124—24no—
84#13133124—42no—
85#13133124C2×C418yescomplemented
86C25×C53C2311yescharacteristic
87C23×C4×C53—22no—
88C23×C4×C53—22no—
89C23×C4×C53—24no—
90C23×C4×C53—24no—
91C23×C4×C53—22no—
92C23×C4×C53—22no—
93C23×C4×C53—22no—
94C23×C4×C53—24no—
95C23×C4×C53—24no—
96C23×C4×C53—22no—
97C23×C4×C53—22no—
98C23×C4×C53—42no—
99C23×C4×C53—42no—
100C23×C4×C53C2×C414yes—
101C23×C4×C53D414yes—
102C23×C4×C53C2311yescharacteristic
103C23×C4×C53C2312yes—
104C23×C4×C53C2312yes—
105C23×C4×C53C2311yescharacteristic
106C2×C4⋊C4×C53—232no—
107C2×C4⋊C4×C53—24no—
108C2×C4⋊C4×C53—24no—
109C2×C4⋊C4×C53—24no—
110C2×C4⋊C4×C53—24no—
111C2×C4⋊C4×C53—24no—
112C2×C4⋊C4×C53D418yescomplemented
113C24×C53—22no—
114C24×C53—22no—
115C24×C53—22no—
116C24×C53—22no—
117C24×C53C22×C412yes—
118C24×C53C2×D412yes—
119C24×C53C2×D412yes—
120C24×C53#4112yes—
121C24×C53#4112yes—
122C24×C53#4112yes—
123C24×C53#4112yes—
124C24×C53C2411yescharacteristic
125C23×D53—22no—
126C23×D53—21no—
127C23×D53—21no—
128C23×D53—22no—
129C23×D53—21no—
130C23×D53—21no—
131C23×D53—21no—
132C23×D53—21no—
133C23×D53—22no—
134C23×D53—22no—
135C23×D53C22×C412yes—
136C22×C4×C53—28no—
137C22×C4×C53—216no—
138C22×C4×C53—28no—
139C22×C4×C53—28no—
140C22×C4×C53—22no—
141C22×C4×C53—22no—
142C22×C4×C53—21no—
143C22×C4×C53—22no—
144C22×C4×C53—22no—
145C22×C4×C53—21no—
146C22×C4×C53—22no—
147C22×C4×C53—216no—
148C22×C4×C53—28no—
149C22×C4×C53—28no—
150C22×C4×C53—22no—
151C22×C4×C53—22no—
152C22×C4×C53—22no—
153C22×C4×C53—21no—
154C22×C4×C53—22no—
155C22×C4×C53—21no—
156C22×C4×C53—22no—
157C22×C4×C53—22no—
158C22×C4×C53—22no—
159C22×C4×C53—22no—
160C22×C4×C53—28no—
161C22×C4×C53—44no—
162C22×C4×C53—48no—
163C22×C4×C53—48no—
164C22×C4×C53—48no—
165C22×C4×C53—48no—
166C22×C4×C53—44no—
167C22×C4×C53—44no—
168C22×C4×C53C22×C414yes—
169C22×C4×C53C2×D412yes—
170C22×C4×C53C2×D414yes—
171C22×C4×C53C2×D414yes—
172C22×C4×C53C2×D412yes—
173C22×C4×C53C2×D414yes—
174C22×C4×C53#4114yes—
175C2×C22⋊D53—28no—
176C2×C22⋊D53—28no—
177C2×C22⋊D53—28no—
178C2×C22⋊D53—44no—
179C2×C22⋊D53—44no—
180C2×C22⋊D53—44no—
181C2×C22⋊D53—44no—
182C22×Dic53—21no—
183C22×Dic53—21no—
184C22×Dic53—22no—
185C22×Dic53—22no—
186C22×Dic53—22no—
187C22×Dic53—22no—
188C22×Dic53—22no—
189C22×Dic53—22no—
190C22×Dic53—22no—
191C22×Dic53—22no—
192C22×Dic53—21no—
193C22×Dic53—21no—
194C22×Dic53—21no—
195C22×Dic53—21no—
196C22×Dic53—22no—
197C22×Dic53—22no—
198C22×Dic53—22no—
199C22×Dic53—22no—
200C22×Dic53—22no—
201C22×Dic53—21no—
202C22×Dic53—21no—
203C22×Dic53—22no—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C22×Dic53—21no—
207C22×Dic53—21no—
208C22×Dic53—22no—
209C22×Dic53—22no—
210C22×Dic53C22×C412yes—
211C22×Dic53C22×C414yes—
212C22×Dic53C2×D414yes—
213C4⋊C4×C53—216no—
214C4⋊C4×C53—216no—
215C22⋊Dic53—28no—
216C22⋊Dic53—28no—
217C22⋊Dic53—44no—
218#11719921—216no—
219#11719921—48no—
220#11719921—44no—
221#11719921—44no—
222C4×Dic53—48no—
223C23×C53—24no—
224C23×C53—24no—
225C23×C53—22no—
226C23×C53—22no—
227C23×C53—24no—
228C23×C53—22no—
229C23×C53—22no—
230C23×C53—24no—
231C23×C53—24no—
232C23×C53—24no—
233C23×C53—24no—
234C23×C53—24no—
235C23×C53—24no—
236C23×C53—24no—
237C23×C53—24no—
238C23×C53—24no—
239C23×C53#11714yes—
240C23×C53C4×D414yes—
241C23×C53C4×D414yes—
242C23×C53#12114yes—
243C23×C53#12314yes—
244C23×C53#12414yes—
245C23×C53#12614yes—
246C23×C53C23×C411yescharacteristic
247C23×C53C22×D411yescharacteristic
248C23×C53C22×D411yescharacteristic
249C23×C53C22×D412yes—
250C23×C53C2×#4111yescharacteristic
251C23×C53C2×#4111yescharacteristic
252C23×C53C2×#4112yes—
253C23×C53C2×#4111yescharacteristic
254C23×C53C2×#4111yescharacteristic
255C23×C53H(5,𝔽2)12yes—
256C23×C532−1+412yes—
257C22×D53—22no—
258C22×D53—22no—
259C22×D53—22no—
260C22×D53—24no—
261C22×D53—24no—
262C22×D53—41no—
263C22×D53—41no—
264C22×D53—41no—
265C22×D53—41no—
266C22×D53—42no—
267C22×D53—41no—
268C22×D53—41no—
269C22×D53—41no—
270C22×D53—41no—
271C22×D53—42no—
272C22×D53—42no—
273C22×D53—42no—
274C22×D53—42no—
275C22×D53—42no—
276C22×D53—42no—
277C22×D53—42no—
278C22×D53—42no—
279C22×D53—42no—
280C2×C4×C53—232no—
281C2×C4×C53—24no—
282C2×C4×C53—24no—
283C2×C4×C53—24no—
284C2×C4×C53—22no—
285C2×C4×C53—24no—
286C2×C4×C53—24no—
287C2×C4×C53—24no—
288C2×C4×C53—22no—
289C2×C4×C53—24no—
290C2×C4×C53—24no—
291C2×C4×C53—24no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—24no—
296C2×C4×C53—24no—
297C2×C4×C53—416no—
298C2×C4×C53—416no—
299C2×C4×C53—42no—
300C2×C4×C53—42no—
301C2×C4×C53—42no—
302C2×C4×C53—42no—
303C2×C4×C53—42no—
304C2×C4×C53—42no—
305C2×C4×C53C4×D418yes—
306C2×C4×C53#12014yes—
307C22⋊D53—416no—
308C2×Dic53—22no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—24no—
312C2×Dic53—24no—
313C2×Dic53—24no—
314C2×Dic53—24no—
315C2×Dic53—24no—
316C2×Dic53—24no—
317C2×Dic53—41no—
318C2×Dic53—41no—
319C2×Dic53—42no—
320C2×Dic53—41no—
321C2×Dic53—41no—
322C2×Dic53—42no—
323C2×Dic53—42no—
324C2×Dic53—42no—
325C2×Dic53—42no—
326C2×Dic53—42no—
327C2×Dic53—42no—
328C2×Dic53—42no—
329C2×Dic53—41no—
330C2×Dic53—41no—
331C2×Dic53—41no—
332C2×Dic53—41no—
333C2×Dic53—41no—
334C2×Dic53—41no—
335C2×Dic53—42no—
336C2×Dic53—42no—
337C2×Dic53—42no—
338C2×Dic53—42no—
339#14019—531nomaximal, Sylow
340C22×C53—24no—
341C22×C53—24no—
342C22×C53—28no—
343C22×C53—28no—
344C22×C53—24no—
345C22×C53—24no—
346C22×C53—24no—
347C22×C53—28no—
348C22×C53—28no—
349C22×C53—24no—
350C22×C53#38818yescomplemented
351C22×C53C2×#11711yescharacteristic
352C22×C53C2×C4×D411yescharacteristic
353C22×C53C2×C4×D412yes—
354C22×C53C2×C4×D411yescharacteristic
355C22×C53#52012yes—
356C22×C53C2×#12011yescharacteristic
357C22×C53C2×#12111yescharacteristic
358C22×C53C2×#12311yescharacteristic
359C22×C53#52511yescharacteristic
360C22×C53#52512yes—
361C22×C53C2×#12411yescharacteristic
362C22×C53C2×#12611yescharacteristic
363C22×C53#53411yescharacteristic
364C22×C53#53611yescharacteristic
365C22×C53#53912yes—
366C22×C53D4212yes—
367C22×C53#54612yes—
368C22×C53#54712yes—
369C22×C53#54812yes—
370C22×C53#54812yes—
371C22×C53#55212yes—
372C22×C53#55312yes—
373C22×C53#55312yes—
374C2×D53—42no—
375C2×D53—44no—
376C2×D53—44no—
377C2×D53—42no—
378C2×D53—42no—
379C2×D53—81no—
380C2×D53—81no—
381C2×D53—81no—
382C2×D53—81no—
383C2×D53—82no—
384C2×D53—82no—
385C4×C53—24no—
386C4×C53—28no—
387C4×C53—42no—
388C4×C53—44no—
389Dic53—44no—
390Dic53—44no—
391Dic53—42no—
392Dic53—81no—
393Dic53—81no—
394C23×C4⋊C4D5311yescharacteristic, complemented
395C2×#388—532no—
396C2×#386—531no—
397C2×#386—531no—
398C2×#386—531no—
399C2×C4×C22⋊C4—531no—
400#1442—532no—
401#1439—532no—
402#1436—532no—
403C22⋊#95—531no—
404C22⋊#95—531no—
405C2×C53—28no—
406C2×C53C2×#38811yescharacteristic
407C2×C53C4×#12011yescharacteristic
408C2×C53#232211yescharacteristic
409C2×C53#235212yes—
410C2×C53#236112yes—
411C2×C53#241011yescharacteristic
412C2×C53#241311yescharacteristic
413C2×C53#243611yescharacteristic
414C2×C53#244312yes—
415C2×C53#248112yes—
416C2×C53#259111yescharacteristic
417D53—82no—
418C23×D4—531no—
419C24×C4C2×D5311yescharacteristic
420C24×C4C2×D5311yescharacteristic
421C24×C4C2×D5311yescharacteristic
422C22×C4⋊C4—24no—
423C22×C4⋊C4—28no—
424C22×C4⋊C4C2×D5312yes—
425C22×C4⋊C4C2×D5312yes—
426C22×C22⋊C4—531no—
427C22×C22⋊C4—531no—
428C22×C22⋊C4—532no—
429C22×C22⋊C4—531no—
430C22×C22⋊C4—531no—
431C22×C22⋊C4—532no—
432C22×C22⋊C4—531no—
433C22×C42—532no—
434#388—1068no—
435#386—538no—
436#386—1064no—
437#386—1064no—
438C4×C22⋊C4—1064no—
439C2×#95—532no—
440C2×#95—532no—
441C2×#95—532no—
442C2×#95—532no—
443C2×#95—531no—
444C2×#95—532no—
445C2×#95—532no—
446C2×#95—531no—
447C2×#95—532no—
448C53#1401911yescharacteristic, complemented, Sylow
449C25—531no—
450C25C22×D5311yescharacteristic
451C22×D4—534no—
452C22×D4—1062no—
453C22×D4—1062no—
454C22×D4—1062no—
455C22×D4—1062no—
456C22×D4—1062no—
457C22×D4—1062no—
458C23×C4—22no—
459C23×C4—22no—
460C23×C4—24no—
461C23×C4—24no—
462C23×C4—22no—
463C23×C4—22no—
464C23×C4—22no—
465C23×C4—24no—
466C23×C4—24no—
467C23×C4—22no—
468C23×C4—22no—
469C23×C4—42no—
470C23×C4—42no—
471C23×C4—532no—
472C23×C4—532no—
473C23×C4—531no—
474C23×C4—531no—
475C23×C4—531no—
476C23×C4C4×D5314yes—
477C23×C4C22⋊D5314yes—
478C23×C4C22×D5311yescharacteristic
479C23×C4C22×D5312yes—
480C23×C4C22×D5312yes—
481C23×C4C22×D5311yescharacteristic
482C2×C4⋊C4—232no—
483C2×C4⋊C4—24no—
484C2×C4⋊C4—24no—
485C2×C4⋊C4—24no—
486C2×C4⋊C4—24no—
487C2×C4⋊C4—24no—
488C2×C4⋊C4C22⋊D5318yescomplemented
489C2×C22⋊C4—534no—
490C2×C22⋊C4—534no—
491C2×C22⋊C4—538no—
492C2×C22⋊C4—1062no—
493C2×C22⋊C4—1062no—
494C2×C22⋊C4—1062no—
495C2×C22⋊C4—1062no—
496C2×C22⋊C4—1064no—
497C2×C22⋊C4—1064no—
498C2×C22⋊C4—1064no—
499C2×C22⋊C4—1062no—
500C2×C22⋊C4—1062no—
501C2×C22⋊C4—1062no—
502C2×C22⋊C4—1062no—
503C2×C22⋊C4—1062no—
504C2×C22⋊C4—1064no—
505C2×C22⋊C4—1064no—
506C2×C22⋊C4—2122no—
507C2×C22⋊C4—2122no—
508C2×C42—1064no—
509C2×C42—1064no—
510C2×C42—2122no—
511#95—538no—
512#95—1064no—
513#95—1064no—
514#95—1064no—
515#95—1062no—
516#95—1062no—
517#95—1064no—
518#95—1064no—
519#95—2122no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—532no—
525C24—1061no—
526C24—1062no—
527C24—1061no—
528C24—1061no—
529C24—1062no—
530C24—1061no—
531C24—1061no—
532C24—1061no—
533C24—1062no—
534C24—1062no—
535C24C2×C4×D5312yes—
536C24#1171994512yes—
537C24D4×D5312yes—
538C24#1171994712yes—
539C24#1171994912yes—
540C24#1171994912yes—
541C24C2×C22⋊D5312yes—
542C24C23×D5311yescharacteristic
543C2×D4—1068no—
544C2×D4—1068no—
545C2×D4—1068no—
546C2×D4—2124no—
547C2×D4—2124no—
548C2×D4—2124no—
549C2×D4—2124no—
550C22×C4—28no—
551C22×C4—28no—
552C22×C4—216no—
553C22×C4—28no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—216no—
562C22×C4—28no—
563C22×C4—28no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—28no—
575C22×C4—44no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4—48no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—532no—
583C22×C4—534no—
584C22×C4—534no—
585C22×C4—1061no—
586C22×C4—1062no—
587C22×C4—1061no—
588C22×C4—1062no—
589C22×C4—1062no—
590C22×C4—1061no—
591C22×C4—1062no—
592C22×C4—1062no—
593C22×C4—1062no—
594C22×C4—1061no—
595C22×C4—1062no—
596C22×C4—1062no—
597C22×C4—1061no—
598C22×C4—1061no—
599C22×C4—1062no—
600C22×C4—1062no—
601C22×C4—1062no—
602C22×C4—1062no—
603C22×C4—1062no—
604C22×C4—1061no—
605C22×C4—1061no—
606C22×C4—1062no—
607C22×C4—1061no—
608C22×C4—1061no—
609C22×C4—1061no—
610C22×C4—1061no—
611C22×C4—1062no—
612C22×C4—1062no—
613C22×C4C2×C4×D5314yes—
614C22×C4#1171994514yes—
615C22×C4C2×C22⋊D5312yes—
616C22×C4C2×C22⋊D5314yes—
617C22×C4C2×C22⋊D5314yes—
618C22×C4C2×C22⋊D5312yes—
619C22×C4C2×C22⋊D5314yes—
620C4⋊C4—216no—
621C4⋊C4—216no—
622C22⋊C4—1068no—
623C22⋊C4—1068no—
624C22⋊C4—10616no—
625C22⋊C4—2128no—
626C22⋊C4—2124no—
627C22⋊C4—2124no—
628C22⋊C4—2124no—
629C42—2128no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—22no—
640C23—24no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—24no—
645C23—24no—
646C23—1062no—
647C23—1064no—
648C23—1062no—
649C23—1062no—
650C23—1064no—
651C23—2122no—
652C23—2122no—
653C23—2122no—
654C23—2122no—
655C23—2122no—
656C23—2122no—
657C23—2122no—
658C23—2121no—
659C23—2121no—
660C23—2121no—
661C23—2121no—
662C23—2122no—
663C23—2121no—
664C23—2121no—
665C23—2121no—
666C23—2121no—
667C23—2122no—
668C23—2122no—
669C23#1313317514yes—
670C23C4×C22⋊D5314yes—
671C23#1313317914yes—
672C23#1313318914yes—
673C23#1313320214yes—
674C23#1313320614yes—
675C23#1313321214yes—
676C23C22×C4×D5311yescharacteristic
677C23C2×D4×D5311yescharacteristic
678C23C22×C22⋊D5312yes—
679C23C22×C22⋊D5311yescharacteristic
680C23C2×#1171994711yescharacteristic
681C23C2×#1171994512yes—
682C23C2×#1171994511yescharacteristic
683C23C2×#1171994911yescharacteristic
684C23C2×#1171994911yescharacteristic
685C23#1313326212yes—
686C23#1313326512yes—
687D4—21216no—
688C2×C4—232no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—416no—
706C2×C4—416no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—1064no—
714C2×C4—1062no—
715C2×C4—1064no—
716C2×C4—1062no—
717C2×C4—1064no—
718C2×C4—1062no—
719C2×C4—1064no—
720C2×C4—1064no—
721C2×C4—1064no—
722C2×C4—2122no—
723C2×C4—2122no—
724C2×C4—2122no—
725C2×C4—2122no—
726C2×C4—2121no—
727C2×C4—2121no—
728C2×C4—2121no—
729C2×C4—2121no—
730C2×C4—2121no—
731C2×C4—2121no—
732C2×C4—2122no—
733C2×C4—2122no—
734C2×C4—2122no—
735C2×C4—2122no—
736C2×C4—2122no—
737C2×C4—2121no—
738C2×C4—2121no—
739C2×C4—2122no—
740C2×C4—2121no—
741C2×C4—2121no—
742C2×C4—2122no—
743C2×C4—2122no—
744C2×C4C4×C22⋊D5318yes—
745C2×C4#1313318614yes—
746C22—24no—
747C22—24no—
748C22—24no—
749C22—24no—
750C22—24no—
751C22—28no—
752C22—28no—
753C22—28no—
754C22—24no—
755C22—28no—
756C22—4241no—
757C22—4241no—
758C22—4241no—
759C22—4241no—
760C22—4242no—
761C22—4242no—
762C22—2122no—
763C22—2124no—
764C22—2122no—
765C22—2122no—
766C22—2124no—
767C22#1681051318yescomplemented
768C22C2×#1313317511yescharacteristic
769C22C2×C4×C22⋊D5311yescharacteristic
770C22C2×C4×C22⋊D5312yes—
771C22C2×#1313317911yescharacteristic
772C22#1681110412yes—
773C22C2×#1313318611yescharacteristic
774C22C2×#1313318911yescharacteristic
775C22C2×#1313320211yescharacteristic
776C22#1681113411yescharacteristic
777C22#1681113412yes—
778C22C2×#1313320611yescharacteristic
779C22C2×#1313321211yescharacteristic
780C22#1681118211yescharacteristic
781C22#1681119711yescharacteristic
782C22#1681122012yes—
783C22D4×C22⋊D5312yes—
784C22#1681126712yes—
785C22#1681127412yes—
786C22#1681128412yes—
787C22#1681128412yes—
788C22#1681130812yes—
789C22#1681132112yes—
790C22#1681132112yes—
791C4—24no—
792C4—28no—
793C4—44no—
794C4—42no—
795C4—4241no—
796C4—4241no—
797C4—2122no—
798C4—2124no—
799C4—2124no—
800C2—28no—
801C2—4242no—
802C2C2×#1681051311yescharacteristic
803C2C4×#1313318611yescharacteristic
804C2#2027738411yescharacteristic
805C2#2027764012yes—
806C2#2027773112yes—
807C2#2027808911yescharacteristic
808C2#2027812211yescharacteristic
809C2#2027836911yescharacteristic
810C2#2027845012yes—
811C2#2027897012yes—
812C2#2028019511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC23×C4⋊C4×C53C2
socle, cosocleC24×C53C24
prime radicalC23×C22⋊D53C22
hypercenterC23×C4⋊C4D53
hypocenterC53#14019
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#16810513C2semidirect
5. C2×C4×C22⋊Dic53C2semidirect
6. #20272974C2semidirect
7. #20272957C2semidirect
8. #20272947C2semidirect
9. #20272938C2semidirect
10. #20272938C2semidirect
11. C23×C4⋊C4×C53C2semidirect
24. #16810502C4semidirect
73. C2×#11719921C2×C4semidirect
85. #13133124C2×C4semidirect
112. C2×C4⋊C4×C53D4semidirect
350. C22×C53#388semidirect
394. C23×C4⋊C4D53semidirect
448. C53#14019semidirect
488. C2×C4⋊C4C22⋊D53semidirect
767. C22#16810513semidirect

Maximal subgroups

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

subgroupindex
C2×#168105132
C2×#168105022
C2×C4×C22⋊Dic532
#202729742
#202729572
#202729472
#202729382
C23×C4⋊C4×C532
#1401953