Finite Group Databasebeta

← #27308188

Subgroups — #27308188

Order 13568.

1946 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133173C211yesmaximal, characteristic
2C2×#16810518C211yesmaximal, characteristic, complemented
3C2×#16810504C211yesmaximal, characteristic, complemented
4C2×#16810495C211yesmaximal, characteristic
5#20272973C211yesmaximal, characteristic, complemented
6#20272966C211yesmaximal, characteristic, complemented
7#20272964C211yesmaximal, characteristic
8#20272958C211yesmaximal, characteristic
9#20272952C211yesmaximal, characteristic
10#20272948C211yesmaximal, characteristic, complemented
11#20272946C211yesmaximal, characteristic, complemented
12#20272946C211yesmaximal, characteristic, complemented
13#20272937C211yesmaximal, characteristic
14C4×#13133124C211yesmaximal, characteristic, complemented
15C2×C53×#388C211yesmaximal, characteristic
16C24×Dic53C2211yescharacteristic
17C2×#13133173—24no—
18C2×#13133173—24no—
19C2×#13133173—24no—
20C22×#11719919C2211yescharacteristic
21C22×#11719919C2211yescharacteristic
22C22×#11719919C2211yescharacteristic
23C22×#11719919C2211yescharacteristic
24C22×#11719919C2211yescharacteristic
25C22×C22⋊Dic53C2211yescharacteristic
26C22×C22⋊Dic53C2211yescharacteristic
27C22×C22⋊Dic53C2211yescharacteristic
28C22×C4×Dic53C2211yescharacteristic
29C22×C4×Dic53C2211yescharacteristic
30C22×C4×Dic53C2211yescharacteristic
31#16810518—24no—
32#16810504—24no—
33#16810495C418yescomplemented
34C2×#13133124C2211yescharacteristic
35C2×#13133124C2211yescharacteristic
36C2×#13133124C2211yescharacteristic
37C2×#13133124C2211yescharacteristic
38C2×#13133124C2211yescharacteristic
39C2×#13133124C2211yescharacteristic
40C2×#13133124C2211yescharacteristic
41C2×#13133124C2211yescharacteristic
42C2×#13133124C2211yescharacteristic
43C2×#13133124C2211yescharacteristic
44C2×#13133124C2211yescharacteristic
45C2×#13133124C2211yescharacteristic
46C2×#13133124C2211yescharacteristic
47C2×#13133124C2211yescharacteristic
48C2×#13133124C2211yescharacteristic
49C2×#13133124C2211yescharacteristic
50C22×C4⋊C4×C53C2211yescharacteristic
51C22×C22⋊C4×C53C2211yescharacteristic
52C22×C22⋊C4×C53C2211yescharacteristic
53C22×C22⋊C4×C53C2211yescharacteristic
54C22×C42×C53C2211yescharacteristic
55C53×#388—24no—
56C2×#95×C53C2211yescharacteristic
57C2×#95×C53C2211yescharacteristic
58C23×Dic53—22no—
59C23×Dic53—22no—
60C23×Dic53—22no—
61C23×Dic53—22no—
62C23×Dic53—22no—
63C23×Dic53—22no—
64C23×Dic53C2×C414yes—
65C23×Dic53C2311yescharacteristic
66C23×Dic53C2311yescharacteristic
67C23×Dic53C2311yescharacteristic
68C23×Dic53C2311yescharacteristic
69C23×Dic53C2311yescharacteristic
70C23×Dic53C2311yescharacteristic
71C23×Dic53C2311yescharacteristic
72C23×Dic53C2311yescharacteristic
73#13133173—232no—
74C2×#11719919—22no—
75C2×#11719919—22no—
76C2×#11719919—22no—
77C2×#11719919—22no—
78C2×#11719919—22no—
79C2×#11719919—22no—
80C2×#11719919—22no—
81C2×#11719919—22no—
82C2×#11719919—22no—
83C2×#11719919—22no—
84C2×#11719919—22no—
85C2×#11719919—41no—
86C2×#11719919C2×C414yes—
87C2×#11719919C2×C414yes—
88C2×#11719919D414yes—
89C2×C22⋊Dic53—22no—
90C2×C22⋊Dic53—22no—
91C2×C22⋊Dic53—22no—
92C2×C22⋊Dic53—22no—
93C2×C22⋊Dic53—22no—
94C2×C22⋊Dic53—22no—
95C2×C22⋊Dic53—22no—
96C2×C22⋊Dic53—41no—
97C2×C22⋊Dic53C2×C414yes—
98C2×C4×Dic53—22no—
99C2×C4×Dic53—22no—
100C2×C4×Dic53—22no—
101C2×C4×Dic53—22no—
102C2×C4×Dic53—22no—
103C2×C4×Dic53—22no—
104C2×C4×Dic53—22no—
105C2×C4×Dic53—41no—
106C2×C4×Dic53D414yes—
107#13133124—22no—
108#13133124—22no—
109#13133124—22no—
110#13133124—22no—
111#13133124—22no—
112#13133124—22no—
113#13133124—22no—
114#13133124—22no—
115#13133124—22no—
116#13133124—22no—
117#13133124—22no—
118#13133124—22no—
119#13133124—22no—
120#13133124—41no—
121#13133124C2×C414yes—
122#13133124C2×C414yes—
123C25×C53C2311yescharacteristic
124C23×C4×C53C2311yescharacteristic
125C23×C4×C53C2311yescharacteristic
126C23×C4×C53C2311yescharacteristic
127C23×C4×C53C2311yescharacteristic
128C23×C4×C53C2311yescharacteristic
129C23×C4×C53C2311yescharacteristic
130C2×C4⋊C4×C53—22no—
131C2×C4⋊C4×C53—22no—
132C2×C4⋊C4×C53—22no—
133C2×C22⋊C4×C53—22no—
134C2×C22⋊C4×C53—22no—
135C2×C22⋊C4×C53—22no—
136C2×C22⋊C4×C53—22no—
137C2×C22⋊C4×C53—22no—
138C2×C22⋊C4×C53—22no—
139C2×C22⋊C4×C53—41no—
140C2×C22⋊C4×C53C2×C414yes—
141C2×C22⋊C4×C53D414yes—
142C2×C42×C53—22no—
143C2×C42×C53—22no—
144C2×C42×C53—41no—
145#95×C53—22no—
146#95×C53—22no—
147C24×C53—21no—
148C24×C53—21no—
149C24×C53—21no—
150C24×C53—21no—
151C24×C53—21no—
152C24×C53—21no—
153C24×C53—21no—
154C24×C53—21no—
155C24×C53—21no—
156C24×C53—21no—
157C24×C53—21no—
158C24×C53—21no—
159C24×C53C22×C412yes—
160C24×C53C2×D412yes—
161C24×C53#4112yes—
162C24×C53C2411yescharacteristic
163C22×C4×C53—21no—
164C22×C4×C53—21no—
165C22×C4×C53—21no—
166C22×C4×C53—21no—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53—21no—
171C22×C4×C53—21no—
172C22×C4×C53—21no—
173C22×C4×C53—21no—
174C22×C4×C53—21no—
175C22×C4×C53—21no—
176C22×C4×C53—21no—
177C22×C4×C53—21no—
178C22×C4×C53—21no—
179C22×C4×C53—21no—
180C22×C4×C53—21no—
181C22×C4×C53—21no—
182C22×C4×C53—21no—
183C22×C4×C53—21no—
184C22×C4×C53—21no—
185C22×C4×C53—21no—
186C22×C4×C53—21no—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53C22×C412yes—
199C22×C4×C53C22×C412yes—
200C22×C4×C53C2×D412yes—
201C22×C4×C53C2×D412yes—
202C22×C4×C53C2×D412yes—
203C22×C4×C53C2×D412yes—
204C22×C4×C53#4112yes—
205C22×Dic53—28no—
206C22×Dic53—28no—
207C22×Dic53—28no—
208C22×Dic53—28no—
209C22×Dic53—28no—
210C22×Dic53—21no—
211C22×Dic53—21no—
212C22×Dic53—21no—
213C22×Dic53—21no—
214C22×Dic53—21no—
215C22×Dic53—21no—
216C22×Dic53—21no—
217C22×Dic53—21no—
218C22×Dic53—21no—
219C22×Dic53—21no—
220C22×Dic53—21no—
221C22×Dic53—21no—
222C22×Dic53—28no—
223C22×Dic53—28no—
224C22×Dic53—21no—
225C22×Dic53—21no—
226C22×Dic53—21no—
227C22×Dic53—21no—
228C22×Dic53—21no—
229C22×Dic53—21no—
230C22×Dic53—21no—
231C22×Dic53—21no—
232C22×Dic53—21no—
233C22×Dic53—21no—
234C22×Dic53—21no—
235C22×Dic53—21no—
236C22×Dic53—21no—
237C22×Dic53—21no—
238C22×Dic53—21no—
239C22×Dic53—21no—
240C22×Dic53—21no—
241C22×Dic53—21no—
242C22×Dic53—21no—
243C22×Dic53—21no—
244C22×Dic53—21no—
245C22×Dic53—21no—
246C22×Dic53—21no—
247C22×Dic53—21no—
248C22×Dic53—21no—
249C22×Dic53—21no—
250C22×Dic53—21no—
251C22×Dic53—21no—
252C22×Dic53—21no—
253C22×Dic53—21no—
254C22×Dic53—21no—
255C22×Dic53C22×C412yes—
256C22×Dic53C22×C412yes—
257C22×Dic53C22×C412yes—
258C22×Dic53C22×C412yes—
259C22×Dic53C2×D412yes—
260C22×Dic53C2×D412yes—
261C22×Dic53C2×D412yes—
262C22×Dic53C2×D412yes—
263C22×Dic53#4112yes—
264C22×Dic53#4112yes—
265C22×Dic53#4112yes—
266C22×Dic53#4112yes—
267C22×Dic53#4112yes—
268C4⋊C4×C53—44no—
269C22⋊C4×C53—28no—
270C22⋊C4×C53—28no—
271C22⋊C4×C53—44no—
272C42×C53—44no—
273C22⋊Dic53—28no—
274C22⋊Dic53—28no—
275C22⋊Dic53—44no—
276#11719919—28no—
277#11719919—28no—
278#11719919—28no—
279#11719919—28no—
280#11719919—44no—
281C4×Dic53—28no—
282C4×Dic53—28no—
283C4×Dic53—44no—
284C23×C53—22no—
285C23×C53—22no—
286C23×C53—22no—
287C23×C53—22no—
288C23×C53—22no—
289C23×C53—22no—
290C23×C53—22no—
291C23×C53—22no—
292C23×C53—22no—
293C23×C53—22no—
294C23×C53—22no—
295C23×C53—22no—
296C23×C53—22no—
297C23×C53—22no—
298C23×C53—22no—
299C23×C53—22no—
300C23×C53—22no—
301C23×C53—22no—
302C23×C53—41no—
303C23×C53—41no—
304C23×C53—41no—
305C23×C53—41no—
306C23×C53—41no—
307C23×C53—41no—
308C23×C53—41no—
309C23×C53—41no—
310C23×C53—41no—
311C23×C53—41no—
312C23×C53—41no—
313C23×C53—41no—
314C23×C53—41no—
315C23×C53—41no—
316C23×C53—41no—
317C23×C53—41no—
318C23×C53C4×D414yes—
319C23×C53C23×C411yescharacteristic
320C23×C53C22×D411yescharacteristic
321C23×C53C22×D411yescharacteristic
322C23×C53C22×D411yescharacteristic
323C23×C53C2×#4111yescharacteristic
324C23×C53C2×#4111yescharacteristic
325C23×C53C2×#4111yescharacteristic
326C23×C53C2×#4111yescharacteristic
327C23×C53C2×#4111yescharacteristic
328C23×C53C2×#4111yescharacteristic
329C23×C53C2×#4111yescharacteristic
330C23×C53H(5,𝔽2)11yescharacteristic
331C23×C532−1+411yescharacteristic
332C23×C532−1+411yescharacteristic
333C23×C532−1+411yescharacteristic
334C2×C4×C53—22no—
335C2×C4×C53—22no—
336C2×C4×C53—22no—
337C2×C4×C53—22no—
338C2×C4×C53—22no—
339C2×C4×C53—22no—
340C2×C4×C53—22no—
341C2×C4×C53—22no—
342C2×C4×C53—22no—
343C2×C4×C53—22no—
344C2×C4×C53—22no—
345C2×C4×C53—22no—
346C2×C4×C53—22no—
347C2×C4×C53—22no—
348C2×C4×C53—22no—
349C2×C4×C53—22no—
350C2×C4×C53—22no—
351C2×C4×C53—22no—
352C2×C4×C53—41no—
353C2×C4×C53—41no—
354C2×C4×C53—41no—
355C2×C4×C53—41no—
356C2×C4×C53—41no—
357C2×C4×C53—41no—
358C2×C4×C53—41no—
359C2×C4×C53—41no—
360C2×C4×C53—41no—
361C2×C4×C53—41no—
362C2×C4×C53—41no—
363C2×C4×C53—41no—
364C2×C4×C53—41no—
365C2×C4×C53—41no—
366C2×C4×C53—41no—
367C2×C4×C53—41no—
368C2×C4×C53—41no—
369C2×C4×C53—41no—
370C2×C4×C53—41no—
371C2×C4×C53—41no—
372C2×C4×C53—41no—
373C2×C4×C53—41no—
374C2×C4×C53—41no—
375C2×C4×C53#12014yes—
376C2×Dic53—232no—
377C2×Dic53—22no—
378C2×Dic53—22no—
379C2×Dic53—22no—
380C2×Dic53—22no—
381C2×Dic53—22no—
382C2×Dic53—22no—
383C2×Dic53—22no—
384C2×Dic53—22no—
385C2×Dic53—22no—
386C2×Dic53—22no—
387C2×Dic53—22no—
388C2×Dic53—22no—
389C2×Dic53—22no—
390C2×Dic53—22no—
391C2×Dic53—22no—
392C2×Dic53—22no—
393C2×Dic53—22no—
394C2×Dic53—22no—
395C2×Dic53—22no—
396C2×Dic53—22no—
397C2×Dic53—22no—
398C2×Dic53—22no—
399C2×Dic53—22no—
400C2×Dic53—22no—
401C2×Dic53—22no—
402C2×Dic53—22no—
403C2×Dic53—22no—
404C2×Dic53—22no—
405C2×Dic53—22no—
406C2×Dic53—22no—
407C2×Dic53—41no—
408C2×Dic53—41no—
409C2×Dic53—41no—
410C2×Dic53—41no—
411C2×Dic53—41no—
412C2×Dic53—41no—
413C2×Dic53—41no—
414C2×Dic53—41no—
415C2×Dic53—41no—
416C2×Dic53—41no—
417C2×Dic53—41no—
418C2×Dic53—41no—
419C2×Dic53—41no—
420C2×Dic53—41no—
421C2×Dic53—41no—
422C2×Dic53—41no—
423C2×Dic53—41no—
424C2×Dic53—41no—
425C2×Dic53—41no—
426C2×Dic53—41no—
427C2×Dic53—41no—
428C2×Dic53—41no—
429C2×Dic53—41no—
430C2×Dic53#11714yescomplemented
431C2×Dic53C4×D414yes—
432C2×Dic53C4×D414yes—
433#14072—531nomaximal, Sylow
434C22×C53—24no—
435C22×C53—24no—
436C22×C53—24no—
437C22×C53—42no—
438C22×C53—42no—
439C22×C53—42no—
440C22×C53—42no—
441C22×C53—42no—
442C22×C53—42no—
443C22×C53—42no—
444C22×C53—42no—
445C22×C53—42no—
446C22×C53—42no—
447C22×C53—42no—
448C22×C53—42no—
449C22×C53C2×#11711yescharacteristic
450C22×C53C2×C4×D411yescharacteristic
451C22×C53C2×C4×D411yescharacteristic
452C22×C53C2×C4×D411yescharacteristic
453C22×C53C4×#4111yescharacteristic
454C22×C53#51911yescharacteristic
455C22×C53#52011yescharacteristic
456C22×C53C2×#12011yescharacteristic
457C22×C53#52511yescharacteristic
458C22×C53#52511yescharacteristic
459C22×C53#52511yescharacteristic
460C22×C53#52911yescharacteristic
461C22×C53#52911yescharacteristic
462C22×C53#53211yescharacteristic
463C22×C53#53211yescharacteristic
464C22×C53#53611yescharacteristic
465C22×C53#53711yescharacteristic
466C22×C53#54111yescharacteristic
467C22×C53#54211yescharacteristic
468C22×C53#54611yescharacteristic
469C22×C53#54611yescharacteristic
470C22×C53#54711yescharacteristic
471C22×C53#54711yescharacteristic
472C22×C53#54711yescharacteristic
473C22×C53#54711yescharacteristic
474C22×C53#54811yescharacteristic
475C22×C53#54811yescharacteristic
476C22×C53#55111yescharacteristic
477C22×C53#55211yescharacteristic
478C22×C53#55211yescharacteristic
479C22×C53#55211yescharacteristic
480C22×C53#55211yescharacteristic
481C22×C53#55211yescharacteristic
482C22×C53#55311yescharacteristic
483C22×C53#55611yescharacteristic
484C4×C53—24no—
485C4×C53—42no—
486C4×C53—42no—
487C4×C53—42no—
488C4×C53—42no—
489C4×C53—81no—
490Dic53—24no—
491Dic53—24no—
492Dic53—24no—
493Dic53—42no—
494Dic53—42no—
495Dic53—42no—
496Dic53—42no—
497Dic53—81no—
498C22×#117—531no—
499C2×#389—531no—
500C2×#388D5311yescharacteristic
501C2×#387—531no—
502C2×#385—531no—
503#1442—531no—
504#1441—531no—
505#1440—531no—
506#1439—531no—
507#1437—531no—
508#1436—531no—
509#1436—531no—
510#1436—531no—
511C22⋊#95—531no—
512C4×#95—531no—
513C2×C53—44no—
514C2×C53#229311yescharacteristic
515C2×C53C4×#12011yescharacteristic
516C2×C53#232311yescharacteristic
517C2×C53#234411yescharacteristic
518C2×C53#235211yescharacteristic
519C2×C53#235911yescharacteristic
520C2×C53#236211yescharacteristic
521C2×C53#243011yescharacteristic
522C2×C53#243211yescharacteristic
523C2×C53#247011yescharacteristic
524C2×C53#247511yescharacteristic
525C2×C53#247711yescharacteristic
526C2×C53#247811yescharacteristic
527C2×C53#260111yescharacteristic
528C2×C53#261111yescharacteristic
529C24×C4—531no—
530C2×#117—1064no—
531C2×#117—1064no—
532C2×#117—1064no—
533C22×C4⋊C4—531no—
534C22×C4⋊C4—531no—
535C22×C4⋊C4—531no—
536C22×C4⋊C4—531no—
537C22×C4⋊C4—531no—
538C22×C4⋊C4C2×D5311yescharacteristic
539C22×C22⋊C4—531no—
540C22×C22⋊C4—531no—
541C22×C22⋊C4—531no—
542C22×C22⋊C4C2×D5311yescharacteristic
543C22×C22⋊C4C2×D5311yescharacteristic
544C22×C22⋊C4C2×D5311yescharacteristic
545C22×C42—531no—
546C22×C42—531no—
547C22×C42—531no—
548C22×C42C2×D5311yescharacteristic
549#389—1064no—
550#388—24no—
551#387—1064no—
552#385—538no—
553C2×#95—531no—
554C2×#95—531no—
555C2×#95—531no—
556C2×#95—531no—
557C2×#95—531no—
558C2×#95—531no—
559C2×#95—531no—
560C2×#95—531no—
561C2×#95—531no—
562C2×#95—531no—
563C2×#95—531no—
564C2×#95—531no—
565C2×#95—531no—
566C2×#95—531no—
567C2×#95—531no—
568C2×#95—531no—
569C2×#95C2×D5311yescharacteristic
570C2×#95C2×D5311yescharacteristic
571C53#1407211yescharacteristic, complemented, Sylow
572C25C22×D5311yescharacteristic
573C23×C4—531no—
574C23×C4—531no—
575C23×C4—531no—
576C23×C4—534no—
577C23×C4—531no—
578C23×C4—531no—
579C23×C4—531no—
580C23×C4—531no—
581C23×C4—531no—
582C23×C4—1062no—
583C23×C4—1062no—
584C23×C4—1062no—
585C23×C4—1062no—
586C23×C4—1062no—
587C23×C4—1062no—
588C23×C4C22×D5311yescharacteristic
589C23×C4C22×D5311yescharacteristic
590C23×C4C22×D5311yescharacteristic
591C23×C4C22×D5311yescharacteristic
592C23×C4C22×D5311yescharacteristic
593C23×C4C22×D5311yescharacteristic
594#117—10632no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—534no—
599C2×C4⋊C4—534no—
600C2×C4⋊C4—534no—
601C2×C4⋊C4—1062no—
602C2×C4⋊C4—1062no—
603C2×C4⋊C4—1062no—
604C2×C4⋊C4—1062no—
605C2×C4⋊C4—1062no—
606C2×C4⋊C4—1062no—
607C2×C4⋊C4—1062no—
608C2×C4⋊C4—1062no—
609C2×C4⋊C4—1062no—
610C2×C4⋊C4—1062no—
611C2×C4⋊C4—1062no—
612C2×C4⋊C4—2121no—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—22no—
619C2×C22⋊C4—41no—
620C2×C22⋊C4—534no—
621C2×C22⋊C4—1062no—
622C2×C22⋊C4—1062no—
623C2×C22⋊C4—1062no—
624C2×C22⋊C4—1062no—
625C2×C22⋊C4—1062no—
626C2×C22⋊C4—1062no—
627C2×C22⋊C4—1062no—
628C2×C22⋊C4—2121no—
629C2×C22⋊C4C4×D5314yes—
630C2×C22⋊C4C22⋊D5314yes—
631C2×C42—22no—
632C2×C42—22no—
633C2×C42—41no—
634C2×C42—534no—
635C2×C42—1062no—
636C2×C42—1062no—
637C2×C42—1062no—
638C2×C42—1062no—
639C2×C42—1062no—
640C2×C42—1062no—
641C2×C42—1062no—
642C2×C42—2121no—
643#95—22no—
644#95—22no—
645#95—534no—
646#95—534no—
647#95—1062no—
648#95—1062no—
649#95—1062no—
650#95—1062no—
651#95—1062no—
652#95—1062no—
653#95—1062no—
654#95—1062no—
655#95—1062no—
656#95—1062no—
657#95—1062no—
658#95—1062no—
659#95—1062no—
660#95—2121no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24C2×C4×D5312yes—
674C24#1171994512yes—
675C24C2×C22⋊D5312yes—
676C24C23×D5311yescharacteristic
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—532no—
713C22×C4—532no—
714C22×C4—532no—
715C22×C4—532no—
716C22×C4—532no—
717C22×C4—532no—
718C22×C4—532no—
719C22×C4—532no—
720C22×C4—532no—
721C22×C4—532no—
722C22×C4—532no—
723C22×C4—532no—
724C22×C4—532no—
725C22×C4—1068no—
726C22×C4—1068no—
727C22×C4—1068no—
728C22×C4—1068no—
729C22×C4—1068no—
730C22×C4—1068no—
731C22×C4—1068no—
732C22×C4—1061no—
733C22×C4—1061no—
734C22×C4—1061no—
735C22×C4—1061no—
736C22×C4—1061no—
737C22×C4—1061no—
738C22×C4—1061no—
739C22×C4—1061no—
740C22×C4—1061no—
741C22×C4—1061no—
742C22×C4—1061no—
743C22×C4—1061no—
744C22×C4—1061no—
745C22×C4—1061no—
746C22×C4—1061no—
747C22×C4—1061no—
748C22×C4—1061no—
749C22×C4—1061no—
750C22×C4—1061no—
751C22×C4—1061no—
752C22×C4—1061no—
753C22×C4—1061no—
754C22×C4—1061no—
755C22×C4—1061no—
756C22×C4—1061no—
757C22×C4—1061no—
758C22×C4—1061no—
759C22×C4—1061no—
760C22×C4—1061no—
761C22×C4—1061no—
762C22×C4—1061no—
763C22×C4—1061no—
764C22×C4—1061no—
765C22×C4—1061no—
766C22×C4—1061no—
767C22×C4—1061no—
768C22×C4—1061no—
769C22×C4—1061no—
770C22×C4—1061no—
771C22×C4—1061no—
772C22×C4—1061no—
773C22×C4—1061no—
774C22×C4—1061no—
775C22×C4C2×C4×D5312yes—
776C22×C4C2×C4×D5312yes—
777C22×C4D4×D5312yes—
778C22×C4D4×D5312yes—
779C22×C4#1171994712yes—
780C22×C4C2×C22⋊D5312yes—
781C22×C4C2×C22⋊D5312yes—
782C4⋊C4—44no—
783C4⋊C4—1068no—
784C4⋊C4—1068no—
785C4⋊C4—1068no—
786C4⋊C4—1068no—
787C4⋊C4—2124no—
788C22⋊C4—28no—
789C22⋊C4—28no—
790C22⋊C4—44no—
791C22⋊C4—1068no—
792C22⋊C4—1068no—
793C22⋊C4—2124no—
794C42—44no—
795C42—1068no—
796C42—1068no—
797C42—2124no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23C4×C22⋊D5314yes—
833C23C22×C4×D5311yescharacteristic
834C23C2×D4×D5311yescharacteristic
835C23C2×D4×D5311yescharacteristic
836C23C22×C22⋊D5311yescharacteristic
837C23#41×D5311yescharacteristic
838C23#41×D5311yescharacteristic
839C23#41×D5311yescharacteristic
840C23#41×D5311yescharacteristic
841C23#41×D5311yescharacteristic
842C23C2×#1171994711yescharacteristic
843C23C2×#1171994511yescharacteristic
844C23#1313326211yescharacteristic
845C23#1313326411yescharacteristic
846C23#1313326411yescharacteristic
847C23#1313326411yescharacteristic
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—534no—
890C2×C4—534no—
891C2×C4—534no—
892C2×C4—10632no—
893C2×C4—1062no—
894C2×C4—1062no—
895C2×C4—1062no—
896C2×C4—1062no—
897C2×C4—1062no—
898C2×C4—1062no—
899C2×C4—1062no—
900C2×C4—1062no—
901C2×C4—1062no—
902C2×C4—1062no—
903C2×C4—1062no—
904C2×C4—1062no—
905C2×C4—1062no—
906C2×C4—1062no—
907C2×C4—1062no—
908C2×C4—1062no—
909C2×C4—1062no—
910C2×C4—1062no—
911C2×C4—1062no—
912C2×C4—1062no—
913C2×C4—1062no—
914C2×C4—1062no—
915C2×C4—1062no—
916C2×C4—1062no—
917C2×C4—1062no—
918C2×C4—1062no—
919C2×C4—1062no—
920C2×C4—1062no—
921C2×C4—1062no—
922C2×C4—1062no—
923C2×C4—2121no—
924C2×C4—2121no—
925C2×C4—2121no—
926C2×C4—2121no—
927C2×C4—2121no—
928C2×C4—2121no—
929C2×C4—2121no—
930C2×C4—2121no—
931C2×C4—2121no—
932C2×C4—2121no—
933C2×C4—2121no—
934C2×C4—2121no—
935C2×C4—2121no—
936C2×C4—2121no—
937C2×C4—2121no—
938C2×C4—2121no—
939C2×C4—2121no—
940C2×C4—2121no—
941C2×C4—2121no—
942C2×C4—2121no—
943C2×C4—2121no—
944C2×C4—2121no—
945C2×C4—2121no—
946C2×C4#1313318514yes—
947C22—24no—
948C22—24no—
949C22—24no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22#117×D5311yescharacteristic
963C22C4×D4×D5311yescharacteristic
964C22C4×D4×D5311yescharacteristic
965C22C2×C4×C22⋊D5311yescharacteristic
966C22C4×#1171994711yescharacteristic
967C22#1681110011yescharacteristic
968C22#1681110211yescharacteristic
969C22C2×#1313318511yescharacteristic
970C22#1681113011yescharacteristic
971C22#1681113211yescharacteristic
972C22#1681113211yescharacteristic
973C22#1681115011yescharacteristic
974C22#1681115611yescharacteristic
975C22#1681116811yescharacteristic
976C22#1681117211yescharacteristic
977C22#1681119311yescharacteristic
978C22#1681120011yescharacteristic
979C22#1681123011yescharacteristic
980C22#1681124111yescharacteristic
981C22#1681126211yescharacteristic
982C22#1681126711yescharacteristic
983C22#1681127211yescharacteristic
984C22#1681127211yescharacteristic
985C22#1681127211yescharacteristic
986C22#1681127311yescharacteristic
987C22#1681128111yescharacteristic
988C22#1681128111yescharacteristic
989C22#1681130211yescharacteristic
990C22#1681130611yescharacteristic
991C22#1681130611yescharacteristic
992C22#1681130911yescharacteristic
993C22#1681131011yescharacteristic
994C22#1681131311yescharacteristic
995C22#1681131811yescharacteristic
996C22#1681134011yescharacteristic
997C4—24no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—42no—
1002C4—81no—
1003C4—1064no—
1004C4—1064no—
1005C4—1064no—
1006C4—4241no—
1007C4—2122no—
1008C4—2122no—
1009C4—2122no—
1010C4—2122no—
1011C2—44no—
1012C2#2027717511yescharacteristic
1013C2C4×#1313318511yescharacteristic
1014C2#2027739011yescharacteristic
1015C2#2027758511yescharacteristic
1016C2#2027764311yescharacteristic
1017C2#2027770111yescharacteristic
1018C2#2027773911yescharacteristic
1019C2#2027832111yescharacteristic
1020C2#2027834611yescharacteristic
1021C2#2027880711yescharacteristic
1022C2#2027889211yescharacteristic
1023C2#2027892211yescharacteristic
1024C2#2027892711yescharacteristic
1025C2#2028031711yescharacteristic
1026C2#2028041011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C53×#388C2
socle, cosocleC24×C53C24
prime radicalC25×C53C23
hypercenterC2×#388D53
hypocenterC53#14072
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#16810518C2semidirect
3. C2×#16810504C2semidirect
5. #20272973C2semidirect
6. #20272966C2semidirect
10. #20272948C2semidirect
11. #20272946C2semidirect
12. #20272946C2semidirect
14. C4×#13133124C2semidirect
33. #16810495C4semidirect
430. C2×Dic53#117semidirect
571. C53#14072semidirect

Maximal subgroups

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

subgroupindex
C22×#131331732
C2×#168105182
C2×#168105042
C2×#168104952
#202729732
#202729662
#202729642
#202729582
#202729522
#202729482
#202729462
#202729372
C4×#131331242
C2×C53×#3882
#1407253