Finite Group Databasebeta

← #27306332

Subgroups — #27306332

Order 13568.

2574 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133177C211yesmaximal, characteristic
2C2×#16810523C212yesmaximal
3C2×#16810492C211yesmaximal, characteristic, complemented
4C2×#16810482C212yesmaximal, complemented
5C2×#16810481C212yesmaximal, complemented
6C2×#16810474C211yesmaximal, characteristic, complemented
7#20272961C211yesmaximal, characteristic, complemented
8#20272960C211yesmaximal, characteristic, complemented
9#20272957C211yesmaximal, characteristic, complemented
10#20272943C212yesmaximal, complemented
11C53×#1439C211yesmaximal, characteristic, complemented
12C23×C22⋊D53C2211yescharacteristic
13C24×Dic53C2211yescharacteristic
14C23×C4×D53C2211yescharacteristic
15C2×#13133177—24no—
16C2×#13133177—24no—
17C2×#13133177C418yescomplemented
18C22×C4⋊Dic53C2211yescharacteristic
19C22×#11719919C2212yes—
20C22×#11719919C2212yes—
21C22×#11719919C2211yescharacteristic
22C22×#11719919C2212yes—
23C22×C22⋊Dic53C2212yes—
24C22×#11719921C2212yes—
25C22×#11719921C2212yes—
26C22×#11719921C2211yescharacteristic
27C22×C4×Dic53C2212yes—
28C22×C4×Dic53C2211yescharacteristic
29#16810523—28no—
30#16810492—24no—
31#16810482—28no—
32#16810481—28no—
33#16810474—24no—
34C2×#13133124C2212yes—
35C2×#13133124C2212yes—
36C2×#13133124C2212yes—
37C2×#13133124C2211yescharacteristic
38C22×C4⋊C4×C53C2211yescharacteristic
39C22×C22⋊C4×C53C2212yes—
40C22×C22⋊C4×C53C2211yescharacteristic
41C2×#95×C53C2212yes—
42C2×#95×C53C2211yescharacteristic
43C24×D53C2311yescharacteristic
44C22×C22⋊D53—22no—
45C22×C22⋊D53—22no—
46C22×C22⋊D53—22no—
47C22×C22⋊D53—22no—
48C22×C22⋊D53C2×C414yes—
49C22×C22⋊D53D414yes—
50C22×C22⋊D53Q814yes—
51C23×Dic53—22no—
52C23×Dic53—22no—
53C23×Dic53—24no—
54C23×Dic53—24no—
55C23×Dic53C2×C414yes—
56C23×Dic53C2312yes—
57C23×Dic53C2311yescharacteristic
58C23×Dic53C2312yes—
59C23×Dic53C2311yescharacteristic
60C23×Dic53C2311yescharacteristic
61C22×C4×D53—22no—
62C22×C4×D53—22no—
63C22×C4×D53—24no—
64C22×C4×D53—24no—
65C22×C4×D53C2×C414yes—
66#13133177—232no—
67C2×C4⋊Dic53—22no—
68C2×C4⋊Dic53—42no—
69C2×#11719919—22no—
70C2×#11719919—22no—
71C2×#11719919—24no—
72C2×#11719919—24no—
73C2×#11719919—24no—
74C2×#11719919—24no—
75C2×#11719919—24no—
76C2×#11719919—24no—
77C2×#11719919—24no—
78C2×#11719919—24no—
79C2×#11719919C2×C414yes—
80C2×#11719919D418yescomplemented
81C2×C22⋊Dic53—24no—
82C2×C22⋊Dic53—24no—
83C2×C22⋊Dic53—42no—
84C2×#11719921—24no—
85C2×#11719921—24no—
86C2×#11719921—22no—
87C2×#11719921—22no—
88C2×#11719921—24no—
89C2×#11719921—24no—
90C2×#11719921—42no—
91C2×#11719921—42no—
92C2×#11719921C2×C414yes—
93C2×C4×Dic53—24no—
94C2×C4×Dic53—24no—
95C2×C4×Dic53—24no—
96C2×C4×Dic53C2×C414yes—
97C2×C4×Dic53D414yes—
98C2×C4×Dic53D414yes—
99#13133124—22no—
100#13133124—24no—
101#13133124—24no—
102#13133124—24no—
103C25×C53C2311yescharacteristic
104C23×C4×C53C2312yes—
105C23×C4×C53C2311yescharacteristic
106C23×C4×C53C2312yes—
107C23×C4×C53C2311yescharacteristic
108C2×C4⋊C4×C53—22no—
109C2×C4⋊C4×C53—42no—
110C2×C22⋊C4×C53—24no—
111C2×C22⋊C4×C53—22no—
112C2×C22⋊C4×C53—22no—
113C2×C22⋊C4×C53—24no—
114C2×C22⋊C4×C53—42no—
115C2×C22⋊C4×C53C2×C414yes—
116#95×C53—22no—
117#95×C53—24no—
118C24×C53—22no—
119C24×C53—21no—
120C24×C53—21no—
121C24×C53—22no—
122C24×C53—21no—
123C24×C53—21no—
124C24×C53—22no—
125C24×C53—22no—
126C24×C53C22×C412yes—
127C24×C53C2×D412yes—
128C24×C53C2×Q812yes—
129C24×C53C2411yescharacteristic
130C23×D53—22no—
131C23×D53—21no—
132C23×D53—21no—
133C23×D53—22no—
134C23×D53—21no—
135C23×D53—21no—
136C23×D53—22no—
137C23×D53—22no—
138C23×D53C22×C412yes—
139C23×D53C2×D412yes—
140C23×D53C2×Q812yes—
141C22×C4×C53—22no—
142C22×C4×C53—22no—
143C22×C4×C53—22no—
144C22×C4×C53—22no—
145C22×C4×C53—22no—
146C22×C4×C53—21no—
147C22×C4×C53—21no—
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—22no—
157C22×C4×C53—22no—
158C22×C4×C53—22no—
159C22×C4×C53—22no—
160C22×C4×C53C22×C412yes—
161C22×C4×C53C22×C412yes—
162C22×C4×C53C2×D414yes—
163C22×C4×C53C2×D412yes—
164C22×C4×C53C2×D412yes—
165C2×C22⋊D53—28no—
166C2×C22⋊D53—28no—
167C2×C22⋊D53—28no—
168C2×C22⋊D53—28no—
169C2×C22⋊D53—28no—
170C2×C22⋊D53—28no—
171C2×C22⋊D53C4⋊C4116yescomplemented
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—28no—
183C22×Dic53—216no—
184C22×Dic53—22no—
185C22×Dic53—22no—
186C22×Dic53—22no—
187C22×Dic53—22no—
188C22×Dic53—22no—
189C22×Dic53—22no—
190C22×Dic53—22no—
191C22×Dic53—48no—
192C22×Dic53—44no—
193C22×Dic53—44no—
194C22×Dic53C22×C412yes—
195C22×Dic53C22×C412yes—
196C22×Dic53C22×C412yes—
197C22×Dic53C2×D414yes—
198C22×Dic53C2×D412yes—
199C22×Dic53C2×D412yes—
200C22×Dic53C2×D412yes—
201C22×Dic53C2×D412yes—
202C22×Dic53C2×D412yes—
203C22×Dic53C2×D414yes—
204C22×Dic53C2×Q812yes—
205C22×Dic53#4112yes—
206C22×Dic53#4112yes—
207C22×Dic53#4114yes—
208C2×C4×D53—28no—
209C2×C4×D53—216no—
210C2×C4×D53—48no—
211C2×C4×D53—44no—
212C2×C4×D53—44no—
213C4⋊C4×C53—44no—
214C22⋊C4×C53—28no—
215C22⋊C4×C53—48no—
216C22⋊Dic53—48no—
217#11719921—28no—
218#11719921—48no—
219#11719921—48no—
220C4⋊Dic53—44no—
221#11719919—28no—
222#11719919—216no—
223#11719919—48no—
224#11719919—48no—
225C4×Dic53—48no—
226C4×Dic53C22⋊C4116yescomplemented
227C23×C53—22no—
228C23×C53—22no—
229C23×C53—24no—
230C23×C53—24no—
231C23×C53—22no—
232C23×C53—22no—
233C23×C53—22no—
234C23×C53—22no—
235C23×C53—24no—
236C23×C53—24no—
237C23×C53—24no—
238C23×C53—24no—
239C23×C53—42no—
240C23×C53—41no—
241C23×C53—41no—
242C23×C53—41no—
243C23×C53—41no—
244C23×C53—42no—
245C23×C53—42no—
246C23×C53—42no—
247C23×C53—42no—
248C23×C53—42no—
249C23×C53C2×C4⋊C414yes—
250C23×C53C23×C411yescharacteristic
251C23×C53C22×D411yescharacteristic
252C23×C53C22×D411yescharacteristic
253C23×C53C22×D411yescharacteristic
254C23×C53C22×D412yes—
255C23×C53C22×Q811yescharacteristic
256C23×C53C2×#4111yescharacteristic
257C23×C53C2×#4111yescharacteristic
258C23×C53C2×#4112yes—
259C23×C53H(5,𝔽2)12yes—
260C23×C532−1+412yes—
261C22×D53—22no—
262C22×D53—22no—
263C22×D53—24no—
264C22×D53—24no—
265C22×D53—22no—
266C22×D53—22no—
267C22×D53—22no—
268C22×D53—22no—
269C22×D53—24no—
270C22×D53—24no—
271C22×D53—24no—
272C22×D53—24no—
273C22×D53—42no—
274C22×D53—41no—
275C22×D53—41no—
276C22×D53—41no—
277C22×D53—41no—
278C22×D53—42no—
279C22×D53—42no—
280C22×D53—42no—
281C22×D53—42no—
282C22×D53—42no—
283C22×D53C2×C4⋊C414yes—
284C2×C4×C53—24no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—24no—
288C2×C4×C53—22no—
289C2×C4×C53—24no—
290C2×C4×C53—24no—
291C2×C4×C53—24no—
292C2×C4×C53—24no—
293C2×C4×C53—42no—
294C2×C4×C53—42no—
295C2×C4×C53—41no—
296C2×C4×C53—41no—
297C2×C4×C53—42no—
298C2×C4×C53—42no—
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×C53—42no—
306C2×C4×C53—42no—
307C2×C4×C53C2×C22⋊C414yes—
308C22⋊D53—232no—
309C2×Dic53—22no—
310C2×Dic53—24no—
311C2×Dic53—24no—
312C2×Dic53—24no—
313C2×Dic53—24no—
314C2×Dic53—42no—
315C2×Dic53—42no—
316C2×Dic53—41no—
317C2×Dic53—41no—
318C2×Dic53—42no—
319C2×Dic53—42no—
320C2×Dic53—42no—
321C2×Dic53—416no—
322C2×Dic53—42no—
323C2×Dic53—42no—
324C2×Dic53—42no—
325C2×Dic53—42no—
326C2×Dic53—42no—
327C2×Dic53—42no—
328C2×Dic53—42no—
329C2×Dic53C2×C22⋊C414yes—
330C2×Dic53C2×C22⋊C414yes—
331C2×Dic53C2×C4⋊C414yes—
332C2×Dic53#11714yes—
333C2×Dic53C4×D418yes—
334C2×Dic53#12114yes—
335C2×Dic53#12114yes—
336C2×Dic53#12118yes—
337C2×Dic53C22⋊Q814yes—
338C2×Dic53C22⋊Q814yes—
339C2×Dic53#12414yes—
340C2×Dic53#12714yes—
341C4×D53—416no—
342#13906—531nomaximal, Sylow
343C22×C53—28no—
344C22×C53—24no—
345C22×C53—42no—
346C22×C53—42no—
347C22×C53—44no—
348C22×C53—44no—
349C22×C53—44no—
350C22×C53—42no—
351C22×C53—42no—
352C22×C53—42no—
353C22×C53—42no—
354C22×C53C22×C22⋊C411yescharacteristic
355C22×C53C22×C4⋊C411yescharacteristic
356C22×C53C2×#11711yescharacteristic
357C22×C53C2×C4×D412yes—
358C22×C53#52012yes—
359C22×C53C2×#12111yescharacteristic
360C22×C53C2×#12111yescharacteristic
361C22×C53C2×#12112yes—
362C22×C53C2×C22⋊Q811yescharacteristic
363C22×C53C2×C22⋊Q811yescharacteristic
364C22×C53C2×#12411yescharacteristic
365C22×C53C2×#12711yescharacteristic
366C22×C53#53511yescharacteristic
367C22×C53#53611yescharacteristic
368C22×C53#53712yes—
369C22×C53D4212yes—
370C22×C53#54712yes—
371C22×C53#54712yes—
372C22×C53D4×Q812yes—
373C22×C53#55012yes—
374C22×C53#55412yes—
375C22×C53#55512yes—
376C22×C53#55612yes—
377C2×D53—28no—
378C2×D53—24no—
379C2×D53—42no—
380C2×D53—42no—
381C2×D53—44no—
382C2×D53—44no—
383C2×D53—44no—
384C2×D53—42no—
385C2×D53—42no—
386C2×D53—42no—
387C2×D53—42no—
388C4×C53—24no—
389C4×C53—44no—
390C4×C53—42no—
391C4×C53—82no—
392Dic53—44no—
393Dic53—42no—
394Dic53—82no—
395Dic53#38018yescomplemented
396Dic53#39018yescomplemented
397C22×C4×D4—531no—
398C2×#390—532no—
399C2×#384—531no—
400C2×#380—532no—
401C2×#380—532no—
402C2×C4×C4⋊C4—531no—
403#1439—531no—
404#1439—531no—
405#1439—531no—
406#1439D5311yescharacteristic, complemented
407C4⋊#95—532no—
408C2×C53—44no—
409C2×C53C2×#38011yescharacteristic
410C2×C53C2×#39011yescharacteristic
411C2×C53#231111yescharacteristic
412C2×C53D4×C4⋊C412yes—
413C2×C53#235412yes—
414C2×C53#253712yes—
415C2×C53#253812yes—
416C2×C53#254111yescharacteristic
417C2×C53#254211yescharacteristic
418C2×C53#254711yescharacteristic
419C2×C53#256311yescharacteristic
420D53—44no—
421C23×D4—531no—
422C24×C4—531no—
423C24×C4—531no—
424C2×C4×D4—538no—
425C2×C4×D4—1064no—
426C2×C4×D4—1064no—
427C22×C4⋊C4—531no—
428C22×C4⋊C4—532no—
429C22×C4⋊C4—532no—
430C22×C4⋊C4—532no—
431C22×C4⋊C4—531no—
432C22×C4⋊C4C2×D5311yescharacteristic
433C22×C22⋊C4—531no—
434C22×C22⋊C4—532no—
435C22×C22⋊C4—532no—
436C22×C22⋊C4—532no—
437C22×C22⋊C4C2×D5312yes—
438C22×C22⋊C4C2×D5311yescharacteristic
439C22×C42—531no—
440C22×C42—532no—
441#390—1068no—
442#384—1064no—
443#380—1068no—
444#380—1068no—
445C4×C4⋊C4—1064no—
446C2×#95—532no—
447C2×#95—532no—
448C2×#95—532no—
449C2×#95—531no—
450C2×#95C2×D5312yes—
451C2×#95C2×D5311yescharacteristic
452C53#1390611yescharacteristic, complemented, Sylow
453C25—531no—
454C25C22×D5311yescharacteristic
455C22×D4—534no—
456C22×D4—534no—
457C22×D4—534no—
458C22×D4—1062no—
459C22×D4—1062no—
460C22×D4—1062no—
461C22×D4—1062no—
462C23×C4—531no—
463C23×C4—531no—
464C23×C4—534no—
465C23×C4—532no—
466C23×C4—531no—
467C23×C4—534no—
468C23×C4—532no—
469C23×C4—1062no—
470C23×C4—1062no—
471C23×C4—1064no—
472C23×C4—1064no—
473C23×C4—1062no—
474C23×C4—1062no—
475C23×C4—1064no—
476C23×C4—1064no—
477C23×C4C22×D5312yes—
478C23×C4C22×D5311yescharacteristic
479C23×C4C22×D5312yes—
480C23×C4C22×D5311yescharacteristic
481C4×D4—10632no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—42no—
484C2×C4⋊C4—534no—
485C2×C4⋊C4—538no—
486C2×C4⋊C4—1062no—
487C2×C4⋊C4—1062no—
488C2×C4⋊C4—1064no—
489C2×C4⋊C4—1064no—
490C2×C4⋊C4—1064no—
491C2×C4⋊C4—1064no—
492C2×C4⋊C4—1064no—
493C2×C4⋊C4—1064no—
494C2×C4⋊C4—1064no—
495C2×C4⋊C4—1064no—
496C2×C4⋊C4—1062no—
497C2×C4⋊C4—2122no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—42no—
503C2×C22⋊C4—534no—
504C2×C22⋊C4—1062no—
505C2×C22⋊C4—1062no—
506C2×C22⋊C4—1064no—
507C2×C22⋊C4—1064no—
508C2×C22⋊C4—1064no—
509C2×C22⋊C4—1064no—
510C2×C22⋊C4—1064no—
511C2×C22⋊C4—1064no—
512C2×C22⋊C4—2122no—
513C2×C22⋊C4—2122no—
514C2×C22⋊C4—2122no—
515C2×C22⋊C4C4×D5314yes—
516C2×C42—534no—
517C2×C42—534no—
518C2×C42—534no—
519C2×C42—1064no—
520C2×C42—1064no—
521C2×C42—1064no—
522#95—22no—
523#95—24no—
524#95—1064no—
525#95—1064no—
526#95—1062no—
527#95—1064no—
528C24—22no—
529C24—21no—
530C24—21no—
531C24—22no—
532C24—21no—
533C24—21no—
534C24—22no—
535C24—22no—
536C24—532no—
537C24—532no—
538C24—532no—
539C24—1062no—
540C24—1061no—
541C24—1061no—
542C24—1062no—
543C24—1061no—
544C24—1061no—
545C24—1062no—
546C24—1062no—
547C24C2×C4×D5312yes—
548C24D4×D5312yes—
549C24Q8×D5312yes—
550C24C23×D5311yescharacteristic
551C2×D4—5316no—
552C2×D4—1068no—
553C2×D4—1068no—
554C2×D4—1068no—
555C2×D4—1068no—
556C2×D4—1068no—
557C2×D4—1068no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—532no—
578C22×C4—532no—
579C22×C4—532no—
580C22×C4—532no—
581C22×C4—532no—
582C22×C4—532no—
583C22×C4—532no—
584C22×C4—534no—
585C22×C4—532no—
586C22×C4—532no—
587C22×C4—532no—
588C22×C4—534no—
589C22×C4—532no—
590C22×C4—534no—
591C22×C4—1068no—
592C22×C4—10616no—
593C22×C4—1068no—
594C22×C4—10616no—
595C22×C4—1062no—
596C22×C4—1062no—
597C22×C4—1062no—
598C22×C4—1061no—
599C22×C4—1061no—
600C22×C4—1062no—
601C22×C4—1062no—
602C22×C4—1062no—
603C22×C4—1062no—
604C22×C4—1062no—
605C22×C4—1062no—
606C22×C4—1062no—
607C22×C4—1062no—
608C22×C4—1062no—
609C22×C4—1062no—
610C22×C4—1062no—
611C22×C4—1062no—
612C22×C4—2128no—
613C22×C4—2124no—
614C22×C4—2124no—
615C22×C4—2128no—
616C22×C4—2124no—
617C22×C4—2124no—
618C22×C4C2×C4×D5312yes—
619C22×C4C2×C4×D5312yes—
620C22×C4D4×D5314yes—
621C22×C4D4×D5312yes—
622C22×C4D4×D5312yes—
623C4⋊C4—44no—
624C4⋊C4—1068no—
625C4⋊C4—10616no—
626C4⋊C4—2124no—
627C4⋊C4—2128no—
628C4⋊C4—2128no—
629C22⋊C4—28no—
630C22⋊C4—48no—
631C22⋊C4—1068no—
632C22⋊C4—2128no—
633C22⋊C4—2128no—
634C22⋊C4—2128no—
635C42—5316no—
636C42—2128no—
637C23—24no—
638C23—24no—
639C23—22no—
640C23—24no—
641C23—22no—
642C23—24no—
643C23—24no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—24no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—42no—
659C23—534no—
660C23—1064no—
661C23—1064no—
662C23—1062no—
663C23—1064no—
664C23—1062no—
665C23—1064no—
666C23—1064no—
667C23—1062no—
668C23—1062no—
669C23—1062no—
670C23—1062no—
671C23—1064no—
672C23—2122no—
673C23—2122no—
674C23—2122no—
675C23—2122no—
676C23—2122no—
677C23—2121no—
678C23—2121no—
679C23—2121no—
680C23—2121no—
681C23—2122no—
682C23C4⋊C4×D5314yes—
683C23C22×C4×D5311yescharacteristic
684C23C2×D4×D5311yescharacteristic
685C23C2×D4×D5312yes—
686C23C2×D4×D5311yescharacteristic
687C23C2×D4×D5311yescharacteristic
688C23C2×Q8×D5311yescharacteristic
689C23#41×D5311yescharacteristic
690C23#41×D5312yes—
691C23#41×D5311yescharacteristic
692C23#1313326212yes—
693C23#1313326412yes—
694D4—10632no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—534no—
719C2×C4—534no—
720C2×C4—534no—
721C2×C4—534no—
722C2×C4—538no—
723C2×C4—534no—
724C2×C4—538no—
725C2×C4—534no—
726C2×C4—534no—
727C2×C4—534no—
728C2×C4—534no—
729C2×C4—534no—
730C2×C4—1064no—
731C2×C4—1062no—
732C2×C4—1064no—
733C2×C4—1064no—
734C2×C4—1064no—
735C2×C4—21216no—
736C2×C4—21216no—
737C2×C4—2122no—
738C2×C4—2122no—
739C2×C4—2122no—
740C2×C4—2122no—
741C2×C4—2122no—
742C2×C4—2122no—
743C2×C4—2122no—
744C2×C4—2122no—
745C2×C4—2122no—
746C2×C4—2122no—
747C2×C4—2122no—
748C2×C4—2121no—
749C2×C4—2121no—
750C2×C4—2122no—
751C2×C4C22⋊C4×D5314yes—
752C22—24no—
753C22—28no—
754C22—42no—
755C22—44no—
756C22—42no—
757C22—44no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—44no—
762C22—42no—
763C22—1064no—
764C22—1068no—
765C22—2122no—
766C22—2124no—
767C22—2122no—
768C22—2124no—
769C22—2122no—
770C22—2122no—
771C22—2122no—
772C22—2124no—
773C22—2122no—
774C22C2×C22⋊C4×D5311yescharacteristic
775C22C2×C4⋊C4×D5311yescharacteristic
776C22#117×D5311yescharacteristic
777C22C4×D4×D5312yes—
778C22#1681110212yes—
779C22#121×D5311yescharacteristic
780C22#121×D5312yes—
781C22#121×D5311yescharacteristic
782C22C22⋊Q8×D5311yescharacteristic
783C22C22⋊Q8×D5311yescharacteristic
784C22#124×D5311yescharacteristic
785C22#127×D5311yescharacteristic
786C22#1681118811yescharacteristic
787C22#1681119511yescharacteristic
788C22#1681120012yes—
789C22#1681125512yes—
790C22#1681127112yes—
791C22#1681127112yes—
792C22#1681128612yes—
793C22#1681129112yes—
794C22#1681132712yes—
795C22#1681133512yes—
796C22#1681134012yes—
797C4—24no—
798C4—44no—
799C4—42no—
800C4—82no—
801C4—538no—
802C4—538no—
803C4—4242no—
804C4—2124no—
805C4—2122no—
806C2—44no—
807C2—2124no—
808C2#380×D5311yescharacteristic
809C2#390×D5311yescharacteristic
810C2#2027730211yescharacteristic
811C2#2027761312yes—
812C2#2027766112yes—
813C2#2027962712yes—
814C2#2027963212yes—
815C2#2027965611yescharacteristic
816C2#2027966311yescharacteristic
817C2#2027970611yescharacteristic
818C2#2027988311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC53×#1439C2
socle, cosocleC24×C53C24
prime radicalC23×C22⋊D53C22
hypercenter#1439D53
hypocenterC53#13906
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
3. C2×#16810492C2semidirect
4. C2×#16810482C2semidirect
5. C2×#16810481C2semidirect
6. C2×#16810474C2semidirect
7. #20272961C2semidirect
8. #20272960C2semidirect
9. #20272957C2semidirect
10. #20272943C2semidirect
11. C53×#1439C2semidirect
17. C2×#13133177C4semidirect
80. C2×#11719919D4semidirect
171. C2×C22⋊D53C4⋊C4semidirect
226. C4×Dic53C22⋊C4semidirect
395. Dic53#380semidirect
396. Dic53#390semidirect
406. #1439D53semidirect
452. C53#13906semidirect

Maximal subgroups

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

subgroupindex
C22×#131331772
C2×#168105232
C2×#168104922
C2×#168104822
C2×#168104812
C2×#168104742
#202729612
#202729602
#202729572
#202729432
C53×#14392
#1390653