Finite Group Databasebeta

← #27306016

Subgroups — #27306016

Order 13568.

1918 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810485C211yesmaximal, characteristic
2C2×#16810485C211yesmaximal, characteristic
3C2×#16810482C211yesmaximal, characteristic
4C2×#16810470C211yesmaximal, characteristic
5C2×#95×D53C211yesmaximal, characteristic
6#20272977C211yesmaximal, characteristic, complemented
7#20272973C211yesmaximal, characteristic, complemented
8#20272970C211yesmaximal, characteristic, complemented
9#20272950C211yesmaximal, characteristic, complemented
10#20272946C211yesmaximal, characteristic, complemented
11#20272941C211yesmaximal, characteristic, complemented
12#20272939C211yesmaximal, characteristic, complemented
13#20272936C211yesmaximal, characteristic
14#20272936C211yesmaximal, characteristic
15C53×#1443C211yesmaximal, characteristic, complemented
16C23×C4×D53C2211yescharacteristic
17C23×C4×D53C2211yescharacteristic
18C23×C4×D53C2211yescharacteristic
19C22×#11719919C2211yescharacteristic
20C22×#11719919C2211yescharacteristic
21C22×#11719921C2211yescharacteristic
22C22×#11719921C2211yescharacteristic
23C22×#11719921C2211yescharacteristic
24C22×#11719921C2211yescharacteristic
25C22×C4×Dic53C2211yescharacteristic
26C22×C4×Dic53C2211yescharacteristic
27#16810485—24no—
28#16810485—24no—
29#16810482—24no—
30#16810470—24no—
31C2×#13133124C2211yescharacteristic
32C2×#13133124C2211yescharacteristic
33C2×#13133124C2211yescharacteristic
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
48#95×D53C418yescomplemented
49C2×#95×C53C2211yescharacteristic
50C2×#95×C53C2211yescharacteristic
51C2×#95×C53C2211yescharacteristic
52C2×#95×C53C2211yescharacteristic
53C2×#95×C53C2211yescharacteristic
54C2×#95×C53C2211yescharacteristic
55C2×#95×C53C2211yescharacteristic
56C24×D53C2311yescharacteristic
57C23×Dic53C2311yescharacteristic
58C23×Dic53C2311yescharacteristic
59C23×Dic53C2311yescharacteristic
60C23×Dic53C2311yescharacteristic
61C23×Dic53C2311yescharacteristic
62C23×Dic53C2311yescharacteristic
63C23×Dic53C2311yescharacteristic
64C22×C4×D53—22no—
65C22×C4×D53—22no—
66C22×C4×D53—22no—
67C22×C4×D53—22no—
68C22×C4×D53—22no—
69C22×C4×D53—22no—
70C22×C4×D53—22no—
71C22×C4×D53—22no—
72C22×C4×D53—22no—
73C22×C4×D53—22no—
74C22×C4×D53—22no—
75C22×C4×D53—22no—
76C22×C4×D53—22no—
77C22×C4×D53—22no—
78C22×C4×D53—41no—
79C22×C4×D53—41no—
80C22×C4×D53—41no—
81C22×C4×D53—41no—
82C22×C4×D53C2×C414yes—
83C22×C4×D53C2×C414yes—
84C22×C4×D53C2×C414yes—
85C2×#11719919—22no—
86C2×#11719919—22no—
87C2×#11719919—22no—
88C2×#11719919—22no—
89C2×#11719919—41no—
90C2×#11719919—41no—
91C2×#11719921—22no—
92C2×#11719921—22no—
93C2×#11719921—22no—
94C2×#11719921—22no—
95C2×#11719921—22no—
96C2×#11719921—22no—
97C2×#11719921—22no—
98C2×#11719921—22no—
99C2×#11719921—22no—
100C2×#11719921—22no—
101C2×#11719921D414yes—
102C2×#11719921D414yes—
103C2×C4×Dic53—22no—
104C2×C4×Dic53—22no—
105C2×C4×Dic53—22no—
106C2×C4×Dic53—22no—
107C2×C4×Dic53—41no—
108C2×C4×Dic53—41no—
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—22no—
121#13133124—41no—
122#13133124—41no—
123#13133124C2×C414yes—
124#13133124C2×C414yes—
125#13133124C2×C414yes—
126C23×C4×C53C2311yescharacteristic
127C23×C4×C53C2311yescharacteristic
128C23×C4×C53C2311yescharacteristic
129C23×C4×C53C2311yescharacteristic
130C23×C4×C53C2311yescharacteristic
131C23×C4×C53C2311yescharacteristic
132C23×C4×C53C2311yescharacteristic
133#95×C53—22no—
134#95×C53—22no—
135#95×C53—22no—
136#95×C53—22no—
137#95×C53—41no—
138#95×C53—41no—
139#95×C53C2×C414yes—
140C24×C53C2411yescharacteristic
141C23×D53—21no—
142C23×D53—21no—
143C23×D53—21no—
144C23×D53—21no—
145C23×D53—21no—
146C23×D53—21no—
147C23×D53—21no—
148C23×D53—21no—
149C23×D53C22×C412yes—
150C23×D53C2×D412yes—
151C23×D53C2×D412yes—
152C23×D53#4112yes—
153C23×D53#4112yes—
154C23×D53#4112yes—
155C23×D53#4112yes—
156C22×C4×C53—21no—
157C22×C4×C53—21no—
158C22×C4×C53—21no—
159C22×C4×C53—21no—
160C22×C4×C53—21no—
161C22×C4×C53—21no—
162C22×C4×C53—21no—
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×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53C22×C412yes—
201C22×C4×C53C22×C412yes—
202C22×C4×C53C22×C412yes—
203C22×C4×C53C2×D412yes—
204C22×C4×C53C2×D412yes—
205C22×Dic53—21no—
206C22×Dic53—21no—
207C22×Dic53—21no—
208C22×Dic53—21no—
209C22×Dic53—21no—
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—21no—
223C22×Dic53—21no—
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×Dic53C22×C412yes—
246C22×Dic53C22×C412yes—
247C22×Dic53C22×C412yes—
248C22×Dic53C2×D412yes—
249C22×Dic53C2×D412yes—
250C22×Dic53#4112yes—
251C22×Dic53#4112yes—
252C22×Dic53#4112yes—
253C22×Dic53#4112yes—
254C2×C4×D53—28no—
255C2×C4×D53—28no—
256C2×C4×D53—28no—
257C2×C4×D53—28no—
258C2×C4×D53—28no—
259C2×C4×D53—28no—
260C2×C4×D53—28no—
261C2×C4×D53—44no—
262C2×C4×D53—44no—
263C2×C4×D53—44no—
264C2×C4×D53—44no—
265C2×C4×D53—44no—
266C2×C4×D53—44no—
267C2×C4×D53—44no—
268C2×C4×D53—44no—
269C2×C4×D53—44no—
270C2×C4×D53—44no—
271C2×C4×D53—44no—
272C2×C4×D53—44no—
273C2×C4×D53—44no—
274C2×C4×D53—44no—
275#11719921—28no—
276#11719921—28no—
277#11719921—44no—
278#11719921—44no—
279#11719919—44no—
280#11719919—44no—
281C4×Dic53—44no—
282C4×Dic53—44no—
283C23×C53C23×C411yescharacteristic
284C23×C53C22×D411yescharacteristic
285C23×C53C22×D411yescharacteristic
286C23×C53C2×#4111yescharacteristic
287C23×C53C2×#4111yescharacteristic
288C23×C53C2×#4111yescharacteristic
289C23×C53C2×#4111yescharacteristic
290C23×C53C2×#4111yescharacteristic
291C23×C53C2×#4111yescharacteristic
292C23×C53C2×#4111yescharacteristic
293C23×C53C2×#4111yescharacteristic
294C23×C53H(5,𝔽2)11yescharacteristic
295C23×C53H(5,𝔽2)11yescharacteristic
296C23×C532−1+411yescharacteristic
297C23×C532−1+411yescharacteristic
298C22×D53—22no—
299C22×D53—22no—
300C22×D53—22no—
301C22×D53—22no—
302C22×D53—22no—
303C22×D53—22no—
304C22×D53—22no—
305C22×D53—22no—
306C22×D53—22no—
307C22×D53—22no—
308C22×D53—22no—
309C22×D53—22no—
310C22×D53—22no—
311C22×D53—22no—
312C22×D53—22no—
313C22×D53—22no—
314C22×D53—22no—
315C22×D53—22no—
316C22×D53—22no—
317C22×D53—22no—
318C22×D53—22no—
319C22×D53—22no—
320C22×D53—22no—
321C22×D53—22no—
322C22×D53—22no—
323C22×D53—22no—
324C22×D53—22no—
325C22×D53—22no—
326C22×D53#11714yes—
327C22×D53C4×D414yes—
328C22×D53C4×D414yes—
329C22×D53#12114yes—
330C22×D53#12314yes—
331C22×D53#12414yes—
332C22×D53#12614yes—
333C2×C4×C53—22no—
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—41no—
349C2×C4×C53—41no—
350C2×C4×C53—41no—
351C2×C4×C53—41no—
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—41no—
376C2×C4×C53—41no—
377C2×C4×C53—41no—
378C2×C4×C53—41no—
379C2×C4×C53—41no—
380C2×C4×C53—41no—
381C2×C4×C53—41no—
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—41no—
404C2×Dic53—41no—
405C2×Dic53—41no—
406C2×Dic53—41no—
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#11714yes—
430C2×Dic53#11714yes—
431C4×D53—416no—
432C4×D53—416no—
433C4×D53—416no—
434#13874—531nomaximal, Sylow
435C22×C53C2×#11711yescharacteristic
436C22×C53C2×#11711yescharacteristic
437C22×C53C2×#11711yescharacteristic
438C22×C53C2×C4×D411yescharacteristic
439C22×C53C2×C4×D411yescharacteristic
440C22×C53#51811yescharacteristic
441C22×C53#51911yescharacteristic
442C22×C53C2×#12111yescharacteristic
443C22×C53C2×#12311yescharacteristic
444C22×C53C2×#12411yescharacteristic
445C22×C53C2×#12611yescharacteristic
446C22×C53#52911yescharacteristic
447C22×C53#52911yescharacteristic
448C22×C53#52911yescharacteristic
449C22×C53#52911yescharacteristic
450C22×C53#53911yescharacteristic
451C22×C53#53911yescharacteristic
452C22×C53#53911yescharacteristic
453C22×C53#53911yescharacteristic
454C22×C53#54611yescharacteristic
455C22×C53#54611yescharacteristic
456C22×C53#54611yescharacteristic
457C22×C53#54611yescharacteristic
458C22×C53#54711yescharacteristic
459C22×C53#54711yescharacteristic
460C22×C53#54711yescharacteristic
461C22×C53#54711yescharacteristic
462C22×C53#55111yescharacteristic
463C22×C53#55111yescharacteristic
464C22×C53#55111yescharacteristic
465C22×C53#55111yescharacteristic
466C22×C53#55211yescharacteristic
467C22×C53#55211yescharacteristic
468C22×C53#55211yescharacteristic
469C22×C53#55211yescharacteristic
470C2×D53—24no—
471C2×D53—24no—
472C2×D53—24no—
473C2×D53—24no—
474C2×D53—24no—
475C2×D53—24no—
476C2×D53—24no—
477C2×D53—24no—
478C2×D53—24no—
479C2×D53—24no—
480C2×D53—24no—
481C2×D53—24no—
482C2×D53—24no—
483C2×D53—24no—
484C2×D53#38818yes—
485C4×C53—42no—
486C4×C53—42no—
487C4×C53—42no—
488C4×C53—42no—
489C4×C53—42no—
490C4×C53—81no—
491C4×C53—81no—
492Dic53—24no—
493Dic53—24no—
494Dic53—42no—
495Dic53—42no—
496Dic53—42no—
497Dic53—81no—
498Dic53—81no—
499C2×#381—531no—
500C2×#381—531no—
501C2×#380—531no—
502C2×C4×C22⋊C4—531no—
503C22×#95—531no—
504#1443—531no—
505#1443D5311yescharacteristic, complemented
506#1442—531no—
507#1442—531no—
508#1436—531no—
509#1436—531no—
510#1434—531no—
511#1434—531no—
512C22⋊#95—531no—
513C22⋊#95—531no—
514C2×C53#228311yescharacteristic
515C2×C53C2×#38811yescharacteristic
516C2×C53#231311yescharacteristic
517C2×C53#234211yescharacteristic
518C2×C53#234211yescharacteristic
519C2×C53#234411yescharacteristic
520C2×C53#234411yescharacteristic
521C2×C53#241911yescharacteristic
522C2×C53#241911yescharacteristic
523C2×C53#242511yescharacteristic
524C2×C53#242511yescharacteristic
525C2×C53#248811yescharacteristic
526C2×C53#248811yescharacteristic
527C2×C53#249311yescharacteristic
528C2×C53#249311yescharacteristic
529D53—28no—
530C24×C4—531no—
531C24×C4—531no—
532C24×C4—531no—
533C22×C4⋊C4—531no—
534C22×C4⋊C4—531no—
535C22×C22⋊C4—531no—
536C22×C22⋊C4—531no—
537C22×C22⋊C4—531no—
538C22×C22⋊C4—531no—
539C22×C42—531no—
540C22×C42—531no—
541#381—1064no—
542#381—1064no—
543#380—1064no—
544C4×C22⋊C4—1064no—
545C2×#95—531no—
546C2×#95—531no—
547C2×#95—531no—
548C2×#95—538no—
549C2×#95—531no—
550C2×#95—531no—
551C2×#95—531no—
552C2×#95—531no—
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×#95C2×D5311yescharacteristic
564C2×#95C2×D5311yescharacteristic
565C2×#95C2×D5311yescharacteristic
566C2×#95C2×D5311yescharacteristic
567C2×#95C2×D5311yescharacteristic
568C2×#95C2×D5311yescharacteristic
569C2×#95C2×D5311yescharacteristic
570C53#1387411yescharacteristic, complemented, Sylow
571C25—531no—
572C23×C4—531no—
573C23×C4—531no—
574C23×C4—531no—
575C23×C4—531no—
576C23×C4—531no—
577C23×C4—534no—
578C23×C4—534no—
579C23×C4—534no—
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×C4—1062no—
589C23×C4—1062no—
590C23×C4—1062no—
591C23×C4—1062no—
592C23×C4—1062no—
593C23×C4—1062no—
594C23×C4—1062no—
595C23×C4—1062no—
596C23×C4—2121no—
597C23×C4—2121no—
598C23×C4—2121no—
599C23×C4—2121no—
600C23×C4C22×D5311yescharacteristic
601C23×C4C22×D5311yescharacteristic
602C23×C4C22×D5311yescharacteristic
603C23×C4C22×D5311yescharacteristic
604C23×C4C22×D5311yescharacteristic
605C23×C4C22×D5311yescharacteristic
606C23×C4C22×D5311yescharacteristic
607C2×C4⋊C4—1062no—
608C2×C4⋊C4—1062no—
609C2×C4⋊C4—1062no—
610C2×C4⋊C4—1062no—
611C2×C4⋊C4—2121no—
612C2×C4⋊C4—2121no—
613C2×C22⋊C4—534no—
614C2×C22⋊C4—534no—
615C2×C22⋊C4—1062no—
616C2×C22⋊C4—1062no—
617C2×C22⋊C4—1062no—
618C2×C22⋊C4—1062no—
619C2×C22⋊C4—1062no—
620C2×C22⋊C4—1062no—
621C2×C22⋊C4—1062no—
622C2×C22⋊C4—1062no—
623C2×C22⋊C4—1062no—
624C2×C22⋊C4—1062no—
625C2×C42—1062no—
626C2×C42—1062no—
627C2×C42—1062no—
628C2×C42—1062no—
629C2×C42—2121no—
630C2×C42—2121no—
631#95—22no—
632#95—22no—
633#95—22no—
634#95—22no—
635#95—41no—
636#95—41no—
637#95—534no—
638#95—534no—
639#95—534no—
640#95—1062no—
641#95—1062no—
642#95—1062no—
643#95—1062no—
644#95—1062no—
645#95—1062no—
646#95—1062no—
647#95—1062no—
648#95—1062no—
649#95—1062no—
650#95—1062no—
651#95—1062no—
652#95—2121no—
653#95—2121no—
654#95C4×D5314yes—
655C24—532no—
656C24—532no—
657C24—532no—
658C24—532no—
659C24—532no—
660C24—532no—
661C24—532no—
662C24—1061no—
663C24—1061no—
664C24—1061no—
665C24—1061no—
666C24—1061no—
667C24—1061no—
668C24—1061no—
669C24—1061no—
670C24C23×D5311yescharacteristic
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
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—21no—
713C22×C4—21no—
714C22×C4—21no—
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—1068no—
725C22×C4—1068no—
726C22×C4—1068no—
727C22×C4—1068no—
728C22×C4—1068no—
729C22×C4—1068no—
730C22×C4—1068no—
731C22×C4—1061no—
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—2124no—
772C22×C4—2124no—
773C22×C4—2124no—
774C22×C4—2124no—
775C22×C4—2124no—
776C22×C4—2124no—
777C22×C4—2124no—
778C22×C4—2124no—
779C22×C4—2124no—
780C22×C4—2124no—
781C22×C4—2124no—
782C22×C4—2124no—
783C22×C4—2124no—
784C22×C4—2124no—
785C22×C4C2×C4×D5312yes—
786C22×C4C2×C4×D5312yes—
787C22×C4C2×C4×D5312yes—
788C22×C4D4×D5312yes—
789C22×C4D4×D5312yes—
790C4⋊C4—2124no—
791C4⋊C4—2124no—
792C22⋊C4—1068no—
793C22⋊C4—1068no—
794C22⋊C4—2124no—
795C22⋊C4—2124no—
796C42—2124no—
797C42—2124no—
798C23—534no—
799C23—534no—
800C23—534no—
801C23—534no—
802C23—534no—
803C23—534no—
804C23—534no—
805C23—1062no—
806C23—1062no—
807C23—1062no—
808C23—1062no—
809C23—1062no—
810C23—1062no—
811C23—1062no—
812C23—1062no—
813C23—1062no—
814C23—1062no—
815C23—1062no—
816C23—1062no—
817C23—1062no—
818C23—1062no—
819C23—1062no—
820C23—1062no—
821C23—1062no—
822C23—1062no—
823C23—1062no—
824C23—1062no—
825C23—1062no—
826C23—1062no—
827C23—1062no—
828C23—1062no—
829C23—1062no—
830C23—1062no—
831C23—1062no—
832C23—1062no—
833C23C22×C4×D5311yescharacteristic
834C23C2×D4×D5311yescharacteristic
835C23C2×D4×D5311yescharacteristic
836C23#41×D5311yescharacteristic
837C23#41×D5311yescharacteristic
838C23#41×D5311yescharacteristic
839C23#41×D5311yescharacteristic
840C23#41×D5311yescharacteristic
841C23#41×D5311yescharacteristic
842C23#41×D5311yescharacteristic
843C23#41×D5311yescharacteristic
844C23#1313326211yescharacteristic
845C23#1313326311yescharacteristic
846C23#1313326411yescharacteristic
847C23#1313326511yescharacteristic
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—41no—
864C2×C4—41no—
865C2×C4—41no—
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—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—534no—
898C2×C4—534no—
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—21216no—
921C2×C4—21216no—
922C2×C4—21216no—
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—2121no—
947C2×C4—2121no—
948C2×C4—2121no—
949C22—538no—
950C22—1064no—
951C22—1064no—
952C22—1064no—
953C22—1064no—
954C22—1064no—
955C22—1064no—
956C22—1064no—
957C22—1064no—
958C22—1064no—
959C22—1064no—
960C22—1064no—
961C22—1064no—
962C22—1064no—
963C22—1064no—
964C22#117×D5311yescharacteristic
965C22#117×D5311yescharacteristic
966C22#117×D5311yescharacteristic
967C22C4×D4×D5311yescharacteristic
968C22C4×D4×D5311yescharacteristic
969C22#1681109511yescharacteristic
970C22#1681109911yescharacteristic
971C22#121×D5311yescharacteristic
972C22#123×D5311yescharacteristic
973C22#124×D5311yescharacteristic
974C22#126×D5311yescharacteristic
975C22#1681115611yescharacteristic
976C22#1681115611yescharacteristic
977C22#1681115611yescharacteristic
978C22#1681115611yescharacteristic
979C22#1681121411yescharacteristic
980C22#1681121611yescharacteristic
981C22#1681121911yescharacteristic
982C22#1681122111yescharacteristic
983C22#1681126211yescharacteristic
984C22#1681126511yescharacteristic
985C22#1681126611yescharacteristic
986C22#1681127011yescharacteristic
987C22#1681127111yescharacteristic
988C22#1681127111yescharacteristic
989C22#1681127511yescharacteristic
990C22#1681127511yescharacteristic
991C22#1681129811yescharacteristic
992C22#1681129811yescharacteristic
993C22#1681130111yescharacteristic
994C22#1681130311yescharacteristic
995C22#1681130511yescharacteristic
996C22#1681130511yescharacteristic
997C22#1681130911yescharacteristic
998C22#1681130911yescharacteristic
999C4—42no—
1000C4—42no—
1001C4—42no—
1002C4—42no—
1003C4—42no—
1004C4—81no—
1005C4—81no—
1006C4—1064no—
1007C4—1064no—
1008C4—4241no—
1009C4—4241no—
1010C4—2122no—
1011C4—2122no—
1012C4—2122no—
1013C2—1068no—
1014C2#2027711211yescharacteristic
1015C2#388×D5311yescharacteristic
1016C2#2027731411yescharacteristic
1017C2#2027755911yescharacteristic
1018C2#2027756311yescharacteristic
1019C2#2027758111yescharacteristic
1020C2#2027758111yescharacteristic
1021C2#2027818711yescharacteristic
1022C2#2027819511yescharacteristic
1023C2#2027826111yescharacteristic
1024C2#2027826911yescharacteristic
1025C2#2027903611yescharacteristic
1026C2#2027904411yescharacteristic
1027C2#2027909511yescharacteristic
1028C2#2027910311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC53×#1443C2
socle, cosocleC24×C53C24
prime radicalC24×D53C23
hypercenter#1443D53
hypocenterC53#13874
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ #1443

Complements

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

NH ≅ G/Ntype
6. #20272977C2semidirect
7. #20272973C2semidirect
8. #20272970C2semidirect
9. #20272950C2semidirect
10. #20272946C2semidirect
11. #20272941C2semidirect
12. #20272939C2semidirect
15. C53×#1443C2semidirect
48. #95×D53C4semidirect
505. #1443D53semidirect
570. C53#13874semidirect

Maximal subgroups

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

subgroupindex
C2×#168104852
C2×#168104822
C2×#168104702
C2×#95×D532
#202729772
#202729732
#202729702
#202729502
#202729462
#202729412
#202729392
#202729362
C53×#14432
#1387453