Finite Group Databasebeta

← #27315331

Subgroups — #27315331

Order 13568.

2574 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C42×D53C211yesmaximal, characteristic
2C2×#16810519C211yesmaximal, characteristic, complemented
3C2×#16810494C212yesmaximal
4C2×#16810480C211yesmaximal, characteristic
5C2×#16810480C211yesmaximal, characteristic
6#20272947C212yesmaximal, complemented
7#20272946C212yesmaximal, complemented
8#20272945C211yesmaximal, characteristic, complemented
9#20272944C211yesmaximal, characteristic, complemented
10#20272936C212yesmaximal
11C2×C53×#389C211yesmaximal, characteristic, complemented
12C23×C4×D53C2211yescharacteristic
13C23×C4×D53C2211yescharacteristic
14C23×C4×D53C2211yescharacteristic
15C22×C4⋊Dic53C2211yescharacteristic
16C22×C4⋊Dic53C2211yescharacteristic
17C22×#11719919C2212yes—
18C22×#11719921C2212yes—
19C22×#11719921C2212yes—
20C22×C4×Dic53C2211yescharacteristic
21C22×C4×Dic53C2211yescharacteristic
22C22×C4×Dic53C2211yescharacteristic
23C2×C42×D53—24no—
24C2×C42×D53—24no—
25C2×C42×D53—24no—
26#16810519—24no—
27#16810494—28no—
28#16810480—24no—
29#16810480C418yescomplemented
30C2×#13133124C2212yes—
31C2×#13133124C2212yes—
32C2×#13133124C2212yes—
33C2×#13133124C2212yes—
34C2×#13133124C2212yes—
35C2×#13133124C2212yes—
36C2×#13133124C2212yes—
37C22×C4⋊C4×C53C2212yes—
38C22×C4⋊C4×C53C2211yescharacteristic
39C22×C4⋊C4×C53C2211yescharacteristic
40C22×C42×C53C2211yescharacteristic
41C53×#389—24no—
42C2×#95×C53C2212yes—
43C24×D53C2311yescharacteristic
44C23×Dic53C2312yes—
45C23×Dic53C2312yes—
46C23×Dic53C2311yescharacteristic
47C23×Dic53C2311yescharacteristic
48C23×Dic53C2311yescharacteristic
49C22×C4×D53—22no—
50C22×C4×D53—22no—
51C22×C4×D53—22no—
52C22×C4×D53—22no—
53C22×C4×D53—22no—
54C22×C4×D53—22no—
55C22×C4×D53—22no—
56C22×C4×D53—22no—
57C22×C4×D53—22no—
58C22×C4×D53—22no—
59C22×C4×D53—22no—
60C22×C4×D53—22no—
61C22×C4×D53—22no—
62C22×C4×D53—22no—
63C22×C4×D53—22no—
64C22×C4×D53—22no—
65C22×C4×D53C2×C414yes—
66C22×C4×D53D414yes—
67C22×C4×D53D414yes—
68C22×C4×D53Q814yes—
69C22×C4×D53Q814yes—
70C2×C4⋊Dic53—22no—
71C2×C4⋊Dic53—22no—
72C2×C4⋊Dic53—22no—
73C2×C4⋊Dic53—22no—
74C2×C4⋊Dic53—22no—
75C2×C4⋊Dic53C2×C414yescomplemented
76C2×#11719919—24no—
77C2×#11719919—24no—
78C2×#11719919—24no—
79C2×#11719921—24no—
80C2×#11719921—24no—
81C2×#11719921—24no—
82C2×#11719921—24no—
83C2×#11719921—24no—
84C2×#11719921C2×C418yes—
85C2×C4×Dic53—22no—
86C2×C4×Dic53—22no—
87C2×C4×Dic53—22no—
88C2×C4×Dic53—22no—
89C2×C4×Dic53—22no—
90C2×C4×Dic53—22no—
91C2×C4×Dic53—22no—
92C2×C4×Dic53—22no—
93C2×C4×Dic53D414yes—
94C42×D53—232no—
95#13133124—24no—
96#13133124—24no—
97#13133124—24no—
98#13133124—24no—
99#13133124—24no—
100#13133124—24no—
101#13133124C2×C418yescomplemented
102C23×C4×C53C2312yes—
103C23×C4×C53C2312yes—
104C23×C4×C53C2311yescharacteristic
105C23×C4×C53C2311yescharacteristic
106C23×C4×C53C2311yescharacteristic
107C2×C4⋊C4×C53—22no—
108C2×C4⋊C4×C53—22no—
109C2×C4⋊C4×C53—24no—
110C2×C4⋊C4×C53—22no—
111C2×C4⋊C4×C53—22no—
112C2×C4⋊C4×C53—24no—
113C2×C4⋊C4×C53—22no—
114C2×C4⋊C4×C53—24no—
115C2×C4⋊C4×C53C2×C414yescomplemented
116C2×C42×C53—22no—
117C2×C42×C53—22no—
118C2×C42×C53D414yes—
119#95×C53—24no—
120C24×C53C2411yescharacteristic
121C23×D53—21no—
122C23×D53—21no—
123C23×D53—21no—
124C23×D53—21no—
125C23×D53—21no—
126C23×D53—21no—
127C23×D53—21no—
128C23×D53—21no—
129C23×D53C22×C412yes—
130C23×D53C2×D412yes—
131C23×D53C2×D412yes—
132C23×D53C2×Q812yes—
133C23×D53C2×Q812yes—
134C23×D53#4112yes—
135C23×D53#4112yes—
136C22×C4×C53—21no—
137C22×C4×C53—21no—
138C22×C4×C53—21no—
139C22×C4×C53—21no—
140C22×C4×C53—21no—
141C22×C4×C53—21no—
142C22×C4×C53—21no—
143C22×C4×C53—21no—
144C22×C4×C53—22no—
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—22no—
157C22×C4×C53C22×C414yes—
158C22×C4×C53C22×C412yes—
159C22×C4×C53C2×D412yes—
160C22×C4×C53C2×D412yes—
161C22×C4×C53C2×D412yes—
162C22×C4×C53C2×D412yes—
163C22×C4×C53C2×D412yes—
164C22×C4×C53C2×D412yes—
165C22×C4×C53C2×Q812yes—
166C22×C4×C53C2×Q812yes—
167C22×C4×C53#4112yes—
168C22×C4×C53#4112yes—
169C22×C4×C53#4112yes—
170C22×C4×C53#4112yes—
171C22×Dic53—21no—
172C22×Dic53—21no—
173C22×Dic53—21no—
174C22×Dic53—21no—
175C22×Dic53—21no—
176C22×Dic53—21no—
177C22×Dic53—21no—
178C22×Dic53—21no—
179C22×Dic53—21no—
180C22×Dic53—21no—
181C22×Dic53—21no—
182C22×Dic53—21no—
183C22×Dic53—22no—
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—22no—
193C22×Dic53—22no—
194C22×Dic53—22no—
195C22×Dic53—22no—
196C22×Dic53C22×C414yes—
197C22×Dic53C22×C412yes—
198C22×Dic53C2×D412yes—
199C22×Dic53C2×D412yes—
200C22×Dic53C2×D412yes—
201C22×Dic53C2×D412yes—
202C22×Dic53C2×Q812yes—
203C22×Dic53C2×Q812yes—
204C22×Dic53#4112yes—
205C22×Dic53#4112yes—
206C2×C4×D53—28no—
207C2×C4×D53—28no—
208C2×C4×D53—28no—
209C2×C4×D53—28no—
210C2×C4×D53—28no—
211C2×C4×D53—28no—
212C2×C4×D53—28no—
213C2×C4×D53—28no—
214C2×C4×D53—28no—
215C2×C4×D53—28no—
216C2×C4×D53—28no—
217C2×C4×D53—28no—
218C2×C4×D53—28no—
219C2×C4×D53—28no—
220C2×C4×D53—28no—
221C2×C4×D53—28no—
222C2×C4×D53—28no—
223C2×C4×D53—28no—
224C2×C4×D53—28no—
225C2×C4×D53—28no—
226C2×C4×D53C4⋊C4116yescomplemented
227C4⋊C4×C53—28no—
228C4⋊C4×C53—44no—
229C4⋊C4×C53—48no—
230C42×C53—28no—
231#11719921—216no—
232#11719921—48no—
233C4⋊Dic53—28no—
234C4⋊Dic53—44no—
235#11719919—48no—
236C4×Dic53—28no—
237C4×Dic53—28no—
238C4×Dic53—28no—
239C23×C53C23×C411yescharacteristic
240C23×C53C22×D411yescharacteristic
241C23×C53C22×D411yescharacteristic
242C23×C53C22×D411yescharacteristic
243C23×C53C22×D411yescharacteristic
244C23×C53C22×Q811yescharacteristic
245C23×C53C22×Q811yescharacteristic
246C23×C53C2×#4111yescharacteristic
247C23×C53C2×#4111yescharacteristic
248C23×C53C2×#4111yescharacteristic
249C23×C53C2×#4111yescharacteristic
250C23×C53C2×#4111yescharacteristic
251C23×C53C2×#4111yescharacteristic
252C23×C53C2×#4111yescharacteristic
253C23×C53C2×#4111yescharacteristic
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—22no—
263C22×D53—22no—
264C22×D53—22no—
265C22×D53—22no—
266C22×D53—22no—
267C22×D53—22no—
268C22×D53—22no—
269C22×D53—22no—
270C22×D53—22no—
271C22×D53—22no—
272C22×D53—22no—
273C22×D53—22no—
274C22×D53—22no—
275C22×D53—22no—
276C22×D53—22no—
277C22×D53—22no—
278C22×D53—22no—
279C22×D53—22no—
280C22×D53—22no—
281C22×D53—22no—
282C22×D53C2×C4⋊C414yes—
283C22×D53C4×D414yes—
284C22×D53C4×Q814yes—
285C22×D53#12114yes—
286C22×D53C22⋊Q814yes—
287C22×D53#12514yes—
288C22×D53C4⋊Q814yes—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—22no—
300C2×C4×C53—22no—
301C2×C4×C53—24no—
302C2×C4×C53—24no—
303C2×C4×C53—24no—
304C2×C4×C53—42no—
305C2×C4×C53—42no—
306C2×C4×C53—42no—
307C2×C4×C53—42no—
308C2×C4×C53—42no—
309C2×C4×C53—42no—
310C2×C4×C53—42no—
311C2×C4×C53—42no—
312C2×C4×C53—42no—
313C2×C4×C53—42no—
314C2×C4×C53—42no—
315C2×C4×C53C2×C4⋊C414yes—
316C2×C4×C53C4×D414yes—
317C2×C4×C53C4×D414yes—
318C2×C4×C53#12014yes—
319C2×C4×C53#12114yes—
320C2×C4×C53C22⋊Q814yes—
321C2×C4×C53C22⋊Q814yes—
322C2×C4×C53C22⋊Q814yes—
323C2×C4×C53#12314yes—
324C2×Dic53—22no—
325C2×Dic53—22no—
326C2×Dic53—22no—
327C2×Dic53—22no—
328C2×Dic53—22no—
329C2×Dic53—22no—
330C2×Dic53—22no—
331C2×Dic53—22no—
332C2×Dic53—22no—
333C2×Dic53—22no—
334C2×Dic53—22no—
335C2×Dic53—22no—
336C2×Dic53—22no—
337C2×Dic53—22no—
338C2×Dic53—22no—
339C2×Dic53—22no—
340C2×Dic53—22no—
341C2×Dic53—22no—
342C2×Dic53—24no—
343C2×Dic53—24no—
344C2×Dic53—24no—
345C2×Dic53—42no—
346C2×Dic53—42no—
347C2×Dic53—42no—
348C2×Dic53—42no—
349C2×Dic53—42no—
350C2×Dic53—42no—
351C2×Dic53—42no—
352C2×Dic53—42no—
353C2×Dic53—42no—
354C2×Dic53—42no—
355C2×Dic53—42no—
356C2×Dic53C2×C4⋊C414yes—
357C2×Dic53#12114yes—
358C2×Dic53C22⋊Q814yes—
359C4×D53—232no—
360C4×D53—232no—
361C4×D53—232no—
362#14697—531nomaximal, Sylow
363C22×C53C22×C4⋊C411yescharacteristic
364C22×C53C2×C4×D411yescharacteristic
365C22×C53C2×C4×D411yescharacteristic
366C22×C53C2×C4×D411yescharacteristic
367C22×C53C2×C4×Q811yescharacteristic
368C22×C53C4×#4111yescharacteristic
369C22×C53C4×#4111yescharacteristic
370C22×C53C2×#12011yescharacteristic
371C22×C53C2×#12111yescharacteristic
372C22×C53C2×#12111yescharacteristic
373C22×C53C2×#12111yescharacteristic
374C22×C53C2×C22⋊Q811yescharacteristic
375C22×C53C2×C22⋊Q811yescharacteristic
376C22×C53C2×C22⋊Q811yescharacteristic
377C22×C53C2×C22⋊Q811yescharacteristic
378C22×C53C2×C22⋊Q811yescharacteristic
379C22×C53C2×#12311yescharacteristic
380C22×C53#52511yescharacteristic
381C22×C53#52511yescharacteristic
382C22×C53#52511yescharacteristic
383C22×C53#52511yescharacteristic
384C22×C53#52511yescharacteristic
385C22×C53#52511yescharacteristic
386C22×C53C2×#12511yescharacteristic
387C22×C53#52911yescharacteristic
388C22×C53#52911yescharacteristic
389C22×C53#52911yescharacteristic
390C22×C53#52911yescharacteristic
391C22×C53C2×C4⋊Q811yescharacteristic
392C22×C53#53211yescharacteristic
393C22×C53#53211yescharacteristic
394C22×C53#53311yescharacteristic
395C22×C53#53311yescharacteristic
396C22×C53#53311yescharacteristic
397C22×C53#53311yescharacteristic
398C2×D53—24no—
399C2×D53—24no—
400C2×D53—24no—
401C2×D53—24no—
402C2×D53—24no—
403C2×D53—24no—
404C2×D53—24no—
405C2×D53—24no—
406C2×D53—24no—
407C2×D53—24no—
408C2×D53—24no—
409C2×D53—24no—
410C2×D53—24no—
411C2×D53—24no—
412C2×D53#38918yescomplemented
413C4×C53—24no—
414C4×C53—24no—
415C4×C53—44no—
416C4×C53—82no—
417C4×C53#38518yescomplemented
418Dic53—24no—
419Dic53—24no—
420Dic53—24no—
421Dic53—44no—
422Dic53—82no—
423C23×C42—531no—
424C2×#389—531no—
425C2×#389D5311yescharacteristic, complemented
426C2×#385—532no—
427C2×#380—531no—
428C2×#380—531no—
429#1436—532no—
430#1436—532no—
431C4⋊#95—531no—
432C4⋊#95—531no—
433C22⋊#95—532no—
434C2×C53C2×#38511yescharacteristic
435C2×C53C2×#38911yescharacteristic
436C2×C53#229611yescharacteristic
437C2×C53C4×#12111yescharacteristic
438C2×C53C4×#12111yescharacteristic
439C2×C53C4×C22⋊Q811yescharacteristic
440C2×C53C4×C22⋊Q811yescharacteristic
441C2×C53#284711yescharacteristic
442C2×C53#284811yescharacteristic
443C2×C53#285111yescharacteristic
444C2×C53#285111yescharacteristic
445C2×C53#285411yescharacteristic
446C2×C53#285511yescharacteristic
447C2×C53#285711yescharacteristic
448C2×C53#285711yescharacteristic
449D53—28no—
450C24×C4—531no—
451C24×C4—531no—
452C24×C4—531no—
453C22×C4⋊C4—531no—
454C22×C4⋊C4—532no—
455C22×C4⋊C4—531no—
456C22×C4⋊C4C2×D5312yes—
457C22×C4⋊C4C2×D5311yescharacteristic
458C22×C4⋊C4C2×D5311yescharacteristic
459C22×C22⋊C4—532no—
460C22×C22⋊C4—532no—
461C22×C42—531no—
462C22×C42—531no—
463C22×C42—531no—
464C22×C42—1064no—
465C22×C42—1064no—
466C22×C42—1064no—
467C22×C42C2×D5311yescharacteristic
468#389—24no—
469#389—1064no—
470#385—1068no—
471#380—538no—
472#380—1064no—
473C2×#95—532no—
474C2×#95—532no—
475C2×#95—532no—
476C2×#95—532no—
477C2×#95—532no—
478C2×#95—532no—
479C2×#95—532no—
480C2×#95C2×D5312yes—
481C53#1469711yescharacteristic, complemented, Sylow
482C25—531no—
483C23×C4—531no—
484C23×C4—531no—
485C23×C4—531no—
486C23×C4—534no—
487C23×C4—534no—
488C23×C4—534no—
489C23×C4—532no—
490C23×C4—534no—
491C23×C4—534no—
492C23×C4—532no—
493C23×C4—1062no—
494C23×C4—1062no—
495C23×C4—1062no—
496C23×C4—1062no—
497C23×C4—1062no—
498C23×C4—1062no—
499C23×C4—1062no—
500C23×C4—1062no—
501C23×C4—1062no—
502C23×C4—1062no—
503C23×C4—1062no—
504C23×C4—1062no—
505C23×C4—1062no—
506C23×C4—1062no—
507C23×C4—1062no—
508C23×C4—1062no—
509C23×C4C22×D5312yes—
510C23×C4C22×D5312yes—
511C23×C4C22×D5311yescharacteristic
512C23×C4C22×D5311yescharacteristic
513C23×C4C22×D5311yescharacteristic
514C2×C4⋊C4—22no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4—24no—
518C2×C4⋊C4—22no—
519C2×C4⋊C4—24no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—24no—
522C2×C4⋊C4—534no—
523C2×C4⋊C4—1062no—
524C2×C4⋊C4—1062no—
525C2×C4⋊C4—1064no—
526C2×C4⋊C4—1064no—
527C2×C4⋊C4—1064no—
528C2×C4⋊C4—1062no—
529C2×C4⋊C4—1062no—
530C2×C4⋊C4—1062no—
531C2×C4⋊C4C4×D5314yescomplemented
532C2×C22⋊C4—538no—
533C2×C22⋊C4—1064no—
534C2×C22⋊C4—1064no—
535C2×C22⋊C4—1064no—
536C2×C22⋊C4—1064no—
537C2×C22⋊C4—1064no—
538C2×C42—22no—
539C2×C42—22no—
540C2×C42—534no—
541C2×C42—10632no—
542C2×C42—1062no—
543C2×C42—1062no—
544C2×C42—1062no—
545C2×C42—1062no—
546C2×C42—1062no—
547C2×C42—1062no—
548C2×C42—1062no—
549C2×C42—1062no—
550C2×C42C22⋊D5314yes—
551#95—24no—
552#95—538no—
553#95—1064no—
554#95—1064no—
555#95—1064no—
556#95—1064no—
557#95—1064no—
558#95—1064no—
559C24—532no—
560C24—532no—
561C24—532no—
562C24—532no—
563C24—532no—
564C24—532no—
565C24—532no—
566C24—1061no—
567C24—1061no—
568C24—1061no—
569C24—1061no—
570C24—1061no—
571C24—1061no—
572C24—1061no—
573C24—1061no—
574C24C23×D5311yescharacteristic
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—532no—
597C22×C4—532no—
598C22×C4—532no—
599C22×C4—532no—
600C22×C4—532no—
601C22×C4—532no—
602C22×C4—532no—
603C22×C4—532no—
604C22×C4—532no—
605C22×C4—5316no—
606C22×C4—534no—
607C22×C4—1068no—
608C22×C4—1068no—
609C22×C4—1068no—
610C22×C4—1068no—
611C22×C4—1068no—
612C22×C4—1068no—
613C22×C4—1068no—
614C22×C4—1068no—
615C22×C4—1068no—
616C22×C4—1068no—
617C22×C4—1068no—
618C22×C4—1068no—
619C22×C4—1061no—
620C22×C4—1061no—
621C22×C4—1061no—
622C22×C4—1061no—
623C22×C4—1061no—
624C22×C4—1061no—
625C22×C4—1061no—
626C22×C4—1061no—
627C22×C4—1061no—
628C22×C4—1061no—
629C22×C4—1061no—
630C22×C4—1061no—
631C22×C4—1068no—
632C22×C4—1068no—
633C22×C4—1068no—
634C22×C4—1068no—
635C22×C4—1068no—
636C22×C4—1068no—
637C22×C4—1068no—
638C22×C4—1068no—
639C22×C4—1062no—
640C22×C4—1062no—
641C22×C4—1062no—
642C22×C4—1062no—
643C22×C4—1062no—
644C22×C4—1062no—
645C22×C4—1062no—
646C22×C4—1062no—
647C22×C4—1062no—
648C22×C4—1062no—
649C22×C4—1062no—
650C22×C4—1062no—
651C22×C4—1062no—
652C22×C4C2×C4×D5314yes—
653C22×C4C2×C4×D5312yes—
654C22×C4#1171994512yes—
655C22×C4D4×D5312yes—
656C22×C4D4×D5312yes—
657C22×C4D4×D5312yes—
658C22×C4#1171994712yes—
659C22×C4Q8×D5312yes—
660C22×C4Q8×D5312yes—
661C22×C4#1171994912yes—
662C22×C4#1171994912yes—
663C22×C4C2×C22⋊D5312yes—
664C22×C4C2×C22⋊D5312yes—
665C22×C4C2×C22⋊D5312yes—
666C4⋊C4—28no—
667C4⋊C4—44no—
668C4⋊C4—48no—
669C4⋊C4—1068no—
670C4⋊C4—2128no—
671C4⋊C4—2124no—
672C22⋊C4—10616no—
673C22⋊C4—2128no—
674C42—28no—
675C42—1068no—
676C42—1068no—
677C42—1068no—
678C23—534no—
679C23—534no—
680C23—534no—
681C23—534no—
682C23—534no—
683C23—534no—
684C23—534no—
685C23—1062no—
686C23—1062no—
687C23—1062no—
688C23—1062no—
689C23—1062no—
690C23—1062no—
691C23—1062no—
692C23—1062no—
693C23—1062no—
694C23—1062no—
695C23—1062no—
696C23—1062no—
697C23—1062no—
698C23—1062no—
699C23—1062no—
700C23—1062no—
701C23—1062no—
702C23—1062no—
703C23—1062no—
704C23—1062no—
705C23—1062no—
706C23—1062no—
707C23—1062no—
708C23—1062no—
709C23—1062no—
710C23—1062no—
711C23—1062no—
712C23—1062no—
713C23C22×C4×D5311yescharacteristic
714C23C2×D4×D5311yescharacteristic
715C23C2×D4×D5311yescharacteristic
716C23C2×D4×D5311yescharacteristic
717C23C22×C22⋊D5311yescharacteristic
718C23C2×Q8×D5311yescharacteristic
719C23C2×Q8×D5311yescharacteristic
720C23#41×D5311yescharacteristic
721C23#41×D5311yescharacteristic
722C23#41×D5311yescharacteristic
723C23#41×D5311yescharacteristic
724C23C2×#1171994711yescharacteristic
725C23C2×#1171994511yescharacteristic
726C23C2×#1171994911yescharacteristic
727C23C2×#1171994911yescharacteristic
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—534no—
755C2×C4—534no—
756C2×C4—534no—
757C2×C4—10632no—
758C2×C4—10632no—
759C2×C4—1062no—
760C2×C4—1062no—
761C2×C4—1062no—
762C2×C4—1062no—
763C2×C4—1062no—
764C2×C4—1062no—
765C2×C4—1062no—
766C2×C4—1062no—
767C2×C4—1062no—
768C2×C4—1062no—
769C2×C4—1062no—
770C2×C4—1062no—
771C2×C4—1062no—
772C2×C4—1062no—
773C2×C4—1062no—
774C2×C4—1062no—
775C2×C4—1062no—
776C2×C4—1062no—
777C2×C4—10632no—
778C2×C4—1064no—
779C2×C4—1064no—
780C2×C4—1064no—
781C2×C4—2122no—
782C2×C4—2122no—
783C2×C4—2122no—
784C2×C4—2122no—
785C2×C4—2122no—
786C2×C4—2122no—
787C2×C4—2122no—
788C2×C4—2122no—
789C2×C4—2122no—
790C2×C4—2122no—
791C2×C4—2122no—
792C2×C4C4⋊C4×D5314yes—
793C2×C4C4×C22⋊D5314yes—
794C2×C4#1313317914yes—
795C2×C4#1313318514yes—
796C2×C4#1313318814yes—
797C2×C4#1313319314yes—
798C2×C4#1313319314yes—
799C2×C4#1313319514yes—
800C2×C4#1313320214yes—
801C22—538no—
802C22—1064no—
803C22—1064no—
804C22—1064no—
805C22—1064no—
806C22—1064no—
807C22—1064no—
808C22—1064no—
809C22—1064no—
810C22—1064no—
811C22—1064no—
812C22—1064no—
813C22—1064no—
814C22—1064no—
815C22—1064no—
816C22C2×C4⋊C4×D5311yescharacteristic
817C22C4×D4×D5311yescharacteristic
818C22C2×C4×C22⋊D5311yescharacteristic
819C22C2×#1313317911yescharacteristic
820C22C4×Q8×D5311yescharacteristic
821C22C4×#1171994711yescharacteristic
822C22C4×#1171994911yescharacteristic
823C22C2×#1313318511yescharacteristic
824C22#121×D5311yescharacteristic
825C22#121×D5311yescharacteristic
826C22C2×#1313318811yescharacteristic
827C22C22⋊Q8×D5311yescharacteristic
828C22C22⋊Q8×D5311yescharacteristic
829C22C2×#1313319311yescharacteristic
830C22C2×#1313319311yescharacteristic
831C22C2×#1313319511yescharacteristic
832C22C2×#1313320211yescharacteristic
833C22#1681113011yescharacteristic
834C22#1681113011yescharacteristic
835C22#1681113311yescharacteristic
836C22#1681113311yescharacteristic
837C22#1681113611yescharacteristic
838C22#1681113611yescharacteristic
839C22#125×D5311yescharacteristic
840C22#1681115511yescharacteristic
841C22#1681115811yescharacteristic
842C22#1681115811yescharacteristic
843C22#1681116011yescharacteristic
844C22C4⋊Q8×D5311yescharacteristic
845C22#1681117011yescharacteristic
846C22#1681117411yescharacteristic
847C22#1681117711yescharacteristic
848C22#1681117811yescharacteristic
849C22#1681117811yescharacteristic
850C22#1681117911yescharacteristic
851C4—24no—
852C4—24no—
853C4—44no—
854C4—82no—
855C4—1064no—
856C4—1064no—
857C4—1064no—
858C4—4242no—
859C4—2124no—
860C4#1681049418yescomplemented
861C2—1068no—
862C2C2×#1681049411yescharacteristic
863C2#389×D5311yescharacteristic
864C2#2027719611yescharacteristic
865C2C4×#1313318811yescharacteristic
866C2#2027722311yescharacteristic
867C2C4×#1313319311yescharacteristic
868C2#2027724511yescharacteristic
869C2#2028299411yescharacteristic
870C2#2028299911yescharacteristic
871C2#2028302011yescharacteristic
872C2#2028302411yescharacteristic
873C2#2028304811yescharacteristic
874C2#2028305311yescharacteristic
875C2#2028306211yescharacteristic
876C2#2028306611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C53×#389C2
socle, cosocleC24×C53C24
prime radicalC24×D53C23
hypercenterC2×#389D53
hypocenterC53#14697
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C2×#16810519C2semidirect
6. #20272947C2semidirect
7. #20272946C2semidirect
8. #20272945C2semidirect
9. #20272944C2semidirect
11. C2×C53×#389C2semidirect
29. #16810480C4semidirect
75. C2×C4⋊Dic53C2×C4semidirect
101. #13133124C2×C4semidirect
115. C2×C4⋊C4×C53C2×C4semidirect
226. C2×C4×D53C4⋊C4semidirect
412. C2×D53#389semidirect
417. C4×C53#385semidirect
425. C2×#389D53semidirect
481. C53#14697semidirect
531. C2×C4⋊C4C4×D53semidirect
860. C4#16810494semidirect

Maximal subgroups

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

subgroupindex
C22×C42×D532
C2×#168105192
C2×#168104942
C2×#168104802
#202729472
#202729462
#202729452
#202729442
#202729362
C2×C53×#3892
#1469753