Finite Group Databasebeta

← #27306641

Subgroups — #27306641

Order 13568.

2374 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D53C211yesmaximal, characteristic
2C2×#16810523C212yesmaximal
3C2×#16810487C211yesmaximal, characteristic, complemented
4C2×#16810474C211yesmaximal, characteristic, complemented
5#20272959C212yesmaximal, complemented
6#20272958C212yesmaximal, complemented
7#20272943C212yesmaximal, complemented
8#20272938C211yesmaximal, characteristic, complemented
9#20272936C211yesmaximal, characteristic, complemented
10#20272936C211yesmaximal, characteristic, complemented
11C53×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×C22⋊D53C2211yescharacteristic
13C23×C4×D53C2211yescharacteristic
14C2×C4×C22⋊D53—24no—
15C2×C4×C22⋊D53—24no—
16C2×C4×C22⋊D53C418yescomplemented
17C22×#11719919C2212yes—
18C22×#11719919C2212yes—
19C22×#11719919C2211yescharacteristic
20C22×C22⋊Dic53C2212yes—
21C22×C22⋊Dic53C2211yescharacteristic
22C22×#11719921C2212yes—
23C22×#11719921C2212yes—
24C22×#11719921C2211yescharacteristic
25C22×C4×Dic53C2212yes—
26C22×C4×Dic53C2211yescharacteristic
27#16810523—28no—
28#16810487—24no—
29#16810474—24no—
30C2×#13133124C2211yescharacteristic
31C2×#13133124C2211yescharacteristic
32C2×#13133124C2212yes—
33C2×#13133124C2212yes—
34C2×#13133124C2212yes—
35C2×#13133124C2212yes—
36C24×C4×C53C2211yescharacteristic
37C22×C22⋊C4×C53C2212yes—
38C2×#95×C53C2211yescharacteristic
39C2×#95×C53C2211yescharacteristic
40C2×#95×C53C2212yes—
41C24×D53C2311yescharacteristic
42C22×C22⋊D53—22no—
43C22×C22⋊D53—22no—
44C22×C22⋊D53—22no—
45C22×C22⋊D53—22no—
46C22×C22⋊D53C2×C414yes—
47C22×C22⋊D53D414yes—
48C22×C22⋊D53Q814yes—
49C23×Dic53C2312yes—
50C23×Dic53C2311yescharacteristic
51C23×Dic53C2312yes—
52C23×Dic53C2311yescharacteristic
53C23×Dic53C2311yescharacteristic
54C22×C4×D53—22no—
55C22×C4×D53—22no—
56C22×C4×D53—42no—
57C22×C4×D53—42no—
58C22×C4×D53C2×C414yes—
59C4×C22⋊D53—232no—
60C2×#11719919—24no—
61C2×#11719919—22no—
62C2×#11719919—22no—
63C2×#11719919—24no—
64C2×#11719919—24no—
65C2×#11719919—24no—
66C2×#11719919—24no—
67C2×#11719919—24no—
68C2×#11719919C2×C414yes—
69C2×C22⋊Dic53—24no—
70C2×C22⋊Dic53—22no—
71C2×C22⋊Dic53—22no—
72C2×C22⋊Dic53—24no—
73C2×C22⋊Dic53—42no—
74C2×C22⋊Dic53C2×C414yes—
75C2×#11719921—24no—
76C2×#11719921—24no—
77C2×#11719921—24no—
78C2×#11719921—22no—
79C2×#11719921—22no—
80C2×#11719921—24no—
81C2×#11719921—42no—
82C2×#11719921—42no—
83C2×#11719921C2×C414yes—
84C2×C4×Dic53—24no—
85C2×C4×Dic53—24no—
86C2×C4×Dic53—24no—
87C2×C4×Dic53C2×C414yes—
88C2×C4×Dic53D414yes—
89C2×C4×Dic53D414yes—
90#13133124—22no—
91#13133124—22no—
92#13133124—24no—
93#13133124—42no—
94#13133124—42no—
95#13133124—42no—
96C25×C53C2311yescharacteristic
97C23×C4×C53—22no—
98C23×C4×C53—22no—
99C23×C4×C53—42no—
100C23×C4×C53—42no—
101C23×C4×C53C2×C414yes—
102C23×C4×C53C2312yes—
103C23×C4×C53C2311yescharacteristic
104C23×C4×C53C2312yes—
105C23×C4×C53C2311yescharacteristic
106C2×C22⋊C4×C53—24no—
107C2×C22⋊C4×C53—24no—
108C2×C22⋊C4×C53—42no—
109#95×C53—22no—
110#95×C53—22no—
111#95×C53—42no—
112C24×C53—21no—
113C24×C53—21no—
114C24×C53—22no—
115C24×C53—22no—
116C24×C53—21no—
117C24×C53—21no—
118C24×C53—22no—
119C24×C53—22no—
120C24×C53C22×C412yes—
121C24×C53C2×D412yes—
122C24×C53C2×Q812yes—
123C24×C53C2411yescharacteristic
124C23×D53—21no—
125C23×D53—21no—
126C23×D53—22no—
127C23×D53—22no—
128C23×D53—21no—
129C23×D53—21no—
130C23×D53—22no—
131C23×D53—22no—
132C23×D53C22×C412yes—
133C23×D53C2×D412yes—
134C23×D53C2×Q812yes—
135C22×C4×C53—22no—
136C22×C4×C53—22no—
137C22×C4×C53—22no—
138C22×C4×C53—22no—
139C22×C4×C53—21no—
140C22×C4×C53—21no—
141C22×C4×C53—22no—
142C22×C4×C53—22no—
143C22×C4×C53—22no—
144C22×C4×C53—22no—
145C22×C4×C53—22no—
146C22×C4×C53—22no—
147C22×C4×C53—28no—
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—44no—
156C22×C4×C53—44no—
157C22×C4×C53—48no—
158C22×C4×C53—48no—
159C22×C4×C53C22×C412yes—
160C22×C4×C53C22×C412yes—
161C22×C4×C53C2×D412yes—
162C22×C4×C53C2×D412yes—
163C22×C4×C53#4114yes—
164C2×C22⋊D53—28no—
165C2×C22⋊D53—28no—
166C2×C22⋊D53—28no—
167C2×C22⋊D53—28no—
168C2×C22⋊D53—28no—
169C2×C22⋊D53—28no—
170C2×C22⋊D53C4⋊C4116yescomplemented
171C22×Dic53—22no—
172C22×Dic53—22no—
173C22×Dic53—22no—
174C22×Dic53—22no—
175C22×Dic53—21no—
176C22×Dic53—21no—
177C22×Dic53—22no—
178C22×Dic53—22no—
179C22×Dic53—22no—
180C22×Dic53—22no—
181C22×Dic53—22no—
182C22×Dic53—22no—
183C22×Dic53—22no—
184C22×Dic53—22no—
185C22×Dic53—22no—
186C22×Dic53—22no—
187C22×Dic53—22no—
188C22×Dic53—22no—
189C22×Dic53—22no—
190C22×Dic53C22×C412yes—
191C22×Dic53C22×C412yes—
192C22×Dic53C22×C412yes—
193C22×Dic53C2×D412yes—
194C22×Dic53C2×D412yes—
195C22×Dic53C2×D412yes—
196C22×Dic53C2×D412yes—
197C22×Dic53C2×D412yes—
198C22×Dic53C2×Q812yes—
199C22×Dic53#4114yes—
200C22×Dic53#4112yes—
201C22×Dic53#4112yes—
202C2×C4×D53—28no—
203C2×C4×D53—44no—
204C2×C4×D53—44no—
205C2×C4×D53—48no—
206C2×C4×D53—48no—
207C22⋊C4×C53—48no—
208C22⋊Dic53—28no—
209C22⋊Dic53—48no—
210#11719921—28no—
211#11719921—48no—
212#11719921—48no—
213#11719919—216no—
214#11719919—28no—
215#11719919—48no—
216C4×Dic53—48no—
217C4×Dic53C22⋊C4116yescomplemented
218C23×C53—22no—
219C23×C53—22no—
220C23×C53—22no—
221C23×C53—22no—
222C23×C53—22no—
223C23×C53—22no—
224C23×C53—22no—
225C23×C53—22no—
226C23×C53—22no—
227C23×C53—22no—
228C23×C53—24no—
229C23×C53—24no—
230C23×C53—24no—
231C23×C53—24no—
232C23×C53—42no—
233C23×C53—42no—
234C23×C53—42no—
235C23×C53—42no—
236C23×C53—42no—
237C23×C53—42no—
238C23×C53—42no—
239C23×C53—42no—
240C23×C53C2×C4⋊C414yes—
241C23×C53C23×C411yescharacteristic
242C23×C53C22×D411yescharacteristic
243C23×C53C22×D411yescharacteristic
244C23×C53C22×D411yescharacteristic
245C23×C53C22×Q811yescharacteristic
246C23×C53C2×#4111yescharacteristic
247C23×C53C2×#4111yescharacteristic
248C23×C53C2×#4112yes—
249C23×C53C2×#4112yes—
250C23×C53H(5,𝔽2)12yes—
251C23×C53H(5,𝔽2)12yes—
252C22×D53—22no—
253C22×D53—22no—
254C22×D53—22no—
255C22×D53—22no—
256C22×D53—22no—
257C22×D53—22no—
258C22×D53—22no—
259C22×D53—22no—
260C22×D53—22no—
261C22×D53—22no—
262C22×D53—24no—
263C22×D53—24no—
264C22×D53—24no—
265C22×D53—24no—
266C22×D53—42no—
267C22×D53—42no—
268C22×D53—42no—
269C22×D53—42no—
270C22×D53—42no—
271C22×D53—42no—
272C22×D53—42no—
273C22×D53—42no—
274C22×D53C2×C4⋊C414yes—
275C2×C4×C53—22no—
276C2×C4×C53—22no—
277C2×C4×C53—24no—
278C2×C4×C53—24no—
279C2×C4×C53—22no—
280C2×C4×C53—22no—
281C2×C4×C53—22no—
282C2×C4×C53—24no—
283C2×C4×C53—24no—
284C2×C4×C53—24no—
285C2×C4×C53—416no—
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×C4×C53—42no—
295C2×C4×C53—42no—
296C2×C4×C53—42no—
297C2×C4×C53—42no—
298C2×C4×C53—42no—
299C2×C4×C53C2×C22⋊C414yes—
300C22⋊D53—232no—
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—24no—
304C2×Dic53—24no—
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—24no—
309C2×Dic53—24no—
310C2×Dic53—24no—
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—42no—
321C2×Dic53—42no—
322C2×Dic53—42no—
323C2×Dic53—42no—
324C2×Dic53C2×C22⋊C414yes—
325C2×Dic53C2×C22⋊C414yes—
326C2×Dic53C2×C4⋊C414yes—
327C2×Dic53#11714yes—
328C2×Dic53#12114yes—
329C2×Dic53#12114yes—
330C2×Dic53C22⋊Q814yes—
331C2×Dic53C22⋊Q814yes—
332C4×D53—416no—
333#13941—531nomaximal, Sylow
334C22×C53—24no—
335C22×C53—24no—
336C22×C53—24no—
337C22×C53—42no—
338C22×C53—44no—
339C22×C53—44no—
340C22×C53—42no—
341C22×C53—42no—
342C22×C53—44no—
343C22×C53—44no—
344C22×C53—42no—
345C22×C53C22×C22⋊C411yescharacteristic
346C22×C53C22×C4⋊C411yescharacteristic
347C22×C53C2×#11711yescharacteristic
348C22×C53C4×#4111yescharacteristic
349C22×C53C4×#4111yescharacteristic
350C22×C53#51811yescharacteristic
351C22×C53#51811yescharacteristic
352C22×C53C2×#12111yescharacteristic
353C22×C53C2×#12111yescharacteristic
354C22×C53C2×C22⋊Q811yescharacteristic
355C22×C53C2×C22⋊Q811yescharacteristic
356C22×C53#52512yes—
357C22×C53#53212yes—
358C22×C53#53512yes—
359C22×C53#53512yes—
360C22×C53#54612yes—
361C22×C53#54612yes—
362C22×C53#55312yes—
363C22×C53#55312yes—
364C22×C53#55412yes—
365C22×C53#55412yes—
366C22×C53#55912yes—
367C22×C53#55912yes—
368C2×D53—24no—
369C2×D53—24no—
370C2×D53—24no—
371C2×D53—42no—
372C2×D53—44no—
373C2×D53—44no—
374C2×D53—42no—
375C2×D53—42no—
376C2×D53—44no—
377C2×D53—44no—
378C2×D53—42no—
379C4×C53—24no—
380C4×C53—42no—
381C4×C53—44no—
382C4×C53—82no—
383Dic53—24no—
384Dic53—42no—
385Dic53—44no—
386Dic53—82no—
387Dic53#38018yes—
388C22×C4×D4—531no—
389C2×#390—532no—
390C2×#382—531no—
391C2×C4×C4⋊C4—531no—
392#1439—532no—
393#1439—532no—
394C4⋊#95—532no—
395C22⋊#95—531no—
396C22⋊#95—531no—
397C22⋊#95—531no—
398C22⋊#95D5311yescharacteristic, complemented
399C2×C53—44no—
400C2×C53C2×#38011yescharacteristic
401C2×C53#229711yescharacteristic
402C2×C53#230911yescharacteristic
403C2×C53#234911yescharacteristic
404C2×C53#234911yescharacteristic
405C2×C53#235711yescharacteristic
406C2×C53#235711yescharacteristic
407C2×C53#253512yes—
408C2×C53#254412yes—
409C2×C53#256612yes—
410C2×C53#258012yes—
411D53—44no—
412C23×D4—531no—
413C24×C4—531no—
414C24×C4C2×D5311yescharacteristic
415C2×C4×D4—538no—
416C2×C4×D4—1064no—
417C2×C4×D4—1064no—
418C22×C4⋊C4—531no—
419C22×C4⋊C4—532no—
420C22×C4⋊C4—532no—
421C22×C22⋊C4—531no—
422C22×C22⋊C4—531no—
423C22×C22⋊C4—532no—
424C22×C22⋊C4—532no—
425C22×C22⋊C4—532no—
426C22×C22⋊C4C2×D5312yes—
427C22×C42—531no—
428C22×C42—532no—
429#390—1068no—
430#382—1064no—
431C4×C4⋊C4—1064no—
432C2×#95—531no—
433C2×#95—531no—
434C2×#95—532no—
435C2×#95—532no—
436C2×#95—532no—
437C2×#95—532no—
438C2×#95C2×D5311yescharacteristic
439C2×#95C2×D5311yescharacteristic
440C2×#95C2×D5312yes—
441C53#1394111yescharacteristic, complemented, Sylow
442C25—531no—
443C25C22×D5311yescharacteristic
444C22×D4—534no—
445C22×D4—534no—
446C22×D4—534no—
447C22×D4—1062no—
448C22×D4—1062no—
449C22×D4—1062no—
450C22×D4—1062no—
451C23×C4—22no—
452C23×C4—22no—
453C23×C4—42no—
454C23×C4—42no—
455C23×C4—531no—
456C23×C4—531no—
457C23×C4—532no—
458C23×C4—531no—
459C23×C4—534no—
460C23×C4—532no—
461C23×C4—1062no—
462C23×C4—1062no—
463C23×C4—2122no—
464C23×C4—2122no—
465C23×C4C4×D5314yes—
466C23×C4C22×D5312yes—
467C23×C4C22×D5311yescharacteristic
468C23×C4C22×D5312yes—
469C23×C4C22×D5311yescharacteristic
470C4×D4—10632no—
471C2×C4⋊C4—534no—
472C2×C4⋊C4—1062no—
473C2×C4⋊C4—1062no—
474C2×C4⋊C4—1064no—
475C2×C4⋊C4—1064no—
476C2×C4⋊C4—1064no—
477C2×C4⋊C4—1064no—
478C2×C4⋊C4—1064no—
479C2×C4⋊C4—1064no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—42no—
483C2×C22⋊C4—534no—
484C2×C22⋊C4—534no—
485C2×C22⋊C4—1062no—
486C2×C22⋊C4—1062no—
487C2×C22⋊C4—1062no—
488C2×C22⋊C4—1062no—
489C2×C22⋊C4—1064no—
490C2×C22⋊C4—1064no—
491C2×C22⋊C4—1064no—
492C2×C22⋊C4—1064no—
493C2×C22⋊C4—1064no—
494C2×C22⋊C4—1064no—
495C2×C22⋊C4—2122no—
496C2×C22⋊C4—2122no—
497C2×C22⋊C4—2122no—
498C2×C42—534no—
499C2×C42—534no—
500C2×C42—534no—
501C2×C42—1064no—
502C2×C42—1064no—
503C2×C42—1064no—
504#95—22no—
505#95—22no—
506#95—42no—
507#95—1064no—
508#95—1062no—
509#95—1062no—
510#95—2122no—
511#95—2122no—
512#95—2122no—
513C24—21no—
514C24—21no—
515C24—22no—
516C24—21no—
517C24—21no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—532no—
522C24—532no—
523C24—532no—
524C24—1061no—
525C24—1061no—
526C24—1062no—
527C24—1061no—
528C24—1061no—
529C24—1062no—
530C24—1062no—
531C24—1062no—
532C24C2×C4×D5312yes—
533C24D4×D5312yes—
534C24Q8×D5312yes—
535C24C23×D5311yescharacteristic
536C2×D4—5316no—
537C2×D4—1068no—
538C2×D4—1068no—
539C2×D4—1068no—
540C2×D4—1068no—
541C2×D4—1068no—
542C2×D4—1068no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—28no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4—532no—
568C22×C4—532no—
569C22×C4—532no—
570C22×C4—532no—
571C22×C4—532no—
572C22×C4—532no—
573C22×C4—532no—
574C22×C4—532no—
575C22×C4—532no—
576C22×C4—532no—
577C22×C4—532no—
578C22×C4—534no—
579C22×C4—1062no—
580C22×C4—1062no—
581C22×C4—1062no—
582C22×C4—1062no—
583C22×C4—1061no—
584C22×C4—1061no—
585C22×C4—1062no—
586C22×C4—1062no—
587C22×C4—1062no—
588C22×C4—1062no—
589C22×C4—1062no—
590C22×C4—1062no—
591C22×C4—1068no—
592C22×C4—1062no—
593C22×C4—1062no—
594C22×C4—1062no—
595C22×C4—1062no—
596C22×C4—1062no—
597C22×C4—1062no—
598C22×C4—1062no—
599C22×C4—2124no—
600C22×C4—2124no—
601C22×C4—2128no—
602C22×C4—2128no—
603C22×C4C2×C4×D5312yes—
604C22×C4C2×C4×D5312yes—
605C22×C4#1171994514yes—
606C22×C4D4×D5312yes—
607C22×C4D4×D5312yes—
608C4⋊C4—1068no—
609C4⋊C4—10616no—
610C4⋊C4—2128no—
611C22⋊C4—48no—
612C22⋊C4—1068no—
613C22⋊C4—1068no—
614C22⋊C4—2128no—
615C22⋊C4—2128no—
616C22⋊C4—2128no—
617C42—5316no—
618C42—2128no—
619C23—22no—
620C23—24no—
621C23—24no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—24no—
632C23—24no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—534no—
642C23—1062no—
643C23—1064no—
644C23—1064no—
645C23—1062no—
646C23—1062no—
647C23—1062no—
648C23—1062no—
649C23—1062no—
650C23—1062no—
651C23—1062no—
652C23—1062no—
653C23—1062no—
654C23—1064no—
655C23—1064no—
656C23—2122no—
657C23—2122no—
658C23—2122no—
659C23—2122no—
660C23—2122no—
661C23—2122no—
662C23—2122no—
663C23—2122no—
664C23C4⋊C4×D5314yes—
665C23C22×C4×D5311yescharacteristic
666C23C2×D4×D5311yescharacteristic
667C23C2×D4×D5311yescharacteristic
668C23C2×D4×D5311yescharacteristic
669C23C2×Q8×D5311yescharacteristic
670C23#41×D5311yescharacteristic
671C23#41×D5312yes—
672C23#41×D5311yescharacteristic
673C23C2×#1171994512yes—
674C23#1313326212yes—
675C23#1313326212yes—
676D4—10632no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—416no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—534no—
702C2×C4—534no—
703C2×C4—534no—
704C2×C4—534no—
705C2×C4—534no—
706C2×C4—534no—
707C2×C4—534no—
708C2×C4—534no—
709C2×C4—1062no—
710C2×C4—1062no—
711C2×C4—1064no—
712C2×C4—1064no—
713C2×C4—1064no—
714C2×C4—1062no—
715C2×C4—1062no—
716C2×C4—1062no—
717C2×C4—1064no—
718C2×C4—1064no—
719C2×C4—21216no—
720C2×C4—2122no—
721C2×C4—2122no—
722C2×C4—2122no—
723C2×C4—2122no—
724C2×C4—2122no—
725C2×C4—2122no—
726C2×C4—2122no—
727C2×C4—2122no—
728C2×C4—2122no—
729C2×C4—2122no—
730C2×C4—2122no—
731C2×C4—2122no—
732C2×C4—2122no—
733C2×C4C22⋊C4×D5314yes—
734C22—24no—
735C22—24no—
736C22—24no—
737C22—44no—
738C22—42no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—1064no—
746C22—1064no—
747C22—1064no—
748C22—2124no—
749C22—2122no—
750C22—2124no—
751C22—2124no—
752C22—2124no—
753C22—2122no—
754C22—2122no—
755C22—2122no—
756C22C2×C22⋊C4×D5311yescharacteristic
757C22C2×C4⋊C4×D5311yescharacteristic
758C22#117×D5311yescharacteristic
759C22#1681109111yescharacteristic
760C22C4×#1171994511yescharacteristic
761C22#1681109611yescharacteristic
762C22#1681109611yescharacteristic
763C22#121×D5311yescharacteristic
764C22#121×D5311yescharacteristic
765C22C22⋊Q8×D5311yescharacteristic
766C22C22⋊Q8×D5311yescharacteristic
767C22#1681113212yes—
768C22#1681117012yes—
769C22#1681118812yes—
770C22#1681118812yes—
771C22#1681126212yes—
772C22#1681126312yes—
773C22#1681131812yes—
774C22#1681132212yes—
775C22#1681132712yes—
776C22#1681132812yes—
777C22#1681135612yes—
778C22#1681135712yes—
779C4—24no—
780C4—42no—
781C4—44no—
782C4—82no—
783C4—538no—
784C4—1064no—
785C4—4242no—
786C4—2122no—
787C4—2124no—
788C2—44no—
789C2—2124no—
790C2#380×D5311yescharacteristic
791C2#2027720111yescharacteristic
792C2#2027729611yescharacteristic
793C2#2027761911yescharacteristic
794C2#2027762211yescharacteristic
795C2#2027768311yescharacteristic
796C2#2027768911yescharacteristic
797C2#2027961512yes—
798C2#2027968412yes—
799C2#2027991312yes—
800C2#2028007212yes—
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC53×C22⋊#95C2
socle, cosocleC24×C53C24
prime radicalC23×C22⋊D53C22
hypercenterC22⋊#95D53
hypocenterC53#13941
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#16810487C2semidirect
4. C2×#16810474C2semidirect
5. #20272959C2semidirect
6. #20272958C2semidirect
7. #20272943C2semidirect
8. #20272938C2semidirect
9. #20272936C2semidirect
10. #20272936C2semidirect
11. C53×C22⋊#95C2semidirect
16. C2×C4×C22⋊D53C4semidirect
170. C2×C22⋊D53C4⋊C4semidirect
217. C4×Dic53C22⋊C4semidirect
398. C22⋊#95D53semidirect
441. C53#13941semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D532
C2×#168105232
C2×#168104872
C2×#168104742
#202729592
#202729582
#202729432
#202729382
#202729362
C53×C22⋊#952
#1394153