Finite Group Databasebeta

← #27306295

Subgroups — #27306295

Order 13568.

1818 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810490C211yesmaximal, characteristic, complemented
2C2×#16810470C211yesmaximal, characteristic
3C2×#95×D53C211yesmaximal, characteristic
4#20272977C211yesmaximal, characteristic, complemented
5#20272976C211yesmaximal, characteristic, complemented
6#20272975C211yesmaximal, characteristic, complemented
7#20272940C211yesmaximal, characteristic, complemented
8#20272940C211yesmaximal, characteristic, complemented
9#20272939C211yesmaximal, characteristic, complemented
10#20272936C211yesmaximal, characteristic
11#20272936C211yesmaximal, characteristic
12#20272936C211yesmaximal, characteristic
13#20272936C211yesmaximal, characteristic
14#20272936C211yesmaximal, characteristic
15C53×#1443C211yesmaximal, characteristic, complemented
16C23×C4×D53C2211yescharacteristic
17C23×C4×D53C2211yescharacteristic
18C23×C4×D53C2211yescharacteristic
19C22×#11719921C2211yescharacteristic
20C22×#11719921C2211yescharacteristic
21C22×#11719921C2211yescharacteristic
22C22×#11719921C2211yescharacteristic
23C22×C4×Dic53C2211yescharacteristic
24C22×C4×Dic53C2211yescharacteristic
25#16810490—24no—
26#16810470C418yescomplemented
27C2×#13133124C2211yescharacteristic
28C2×#13133124C2211yescharacteristic
29C2×#13133124C2211yescharacteristic
30C2×#13133124C2211yescharacteristic
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
46#95×D53—24no—
47C2×#95×C53C2211yescharacteristic
48C2×#95×C53C2211yescharacteristic
49C2×#95×C53C2211yescharacteristic
50C2×#95×C53C2211yescharacteristic
51C2×#95×C53C2211yescharacteristic
52C2×#95×C53C2211yescharacteristic
53C2×#95×C53C2211yescharacteristic
54C24×D53C2311yescharacteristic
55C23×Dic53C2311yescharacteristic
56C23×Dic53C2311yescharacteristic
57C23×Dic53C2311yescharacteristic
58C23×Dic53C2311yescharacteristic
59C23×Dic53C2311yescharacteristic
60C23×Dic53C2311yescharacteristic
61C23×Dic53C2311yescharacteristic
62C22×C4×D53—22no—
63C22×C4×D53—22no—
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—41no—
77C22×C4×D53—41no—
78C22×C4×D53—41no—
79C22×C4×D53—41no—
80C22×C4×D53—41no—
81C22×C4×D53—41no—
82C22×C4×D53C2×C414yes—
83C2×#11719921—22no—
84C2×#11719921—22no—
85C2×#11719921—22no—
86C2×#11719921—22no—
87C2×#11719921—22no—
88C2×#11719921—22no—
89C2×#11719921—22no—
90C2×#11719921—22no—
91C2×#11719921—22no—
92C2×#11719921—22no—
93C2×#11719921C2×C414yes—
94C2×#11719921C2×C414yes—
95C2×C4×Dic53—22no—
96C2×C4×Dic53—22no—
97C2×C4×Dic53—41no—
98C2×C4×Dic53—41no—
99C2×C4×Dic53C2×C414yescomplemented
100C2×C4×Dic53C2×C414yescomplemented
101#13133124—22no—
102#13133124—22no—
103#13133124—22no—
104#13133124—22no—
105#13133124—22no—
106#13133124—22no—
107#13133124—22no—
108#13133124—22no—
109#13133124—22no—
110#13133124—41no—
111#13133124—41no—
112#13133124—41no—
113#13133124—41no—
114#13133124—41no—
115#13133124—41no—
116#13133124—41no—
117#13133124—41no—
118#13133124C2×C414yescomplemented
119#13133124D414yes—
120C23×C4×C53C2311yescharacteristic
121C23×C4×C53C2311yescharacteristic
122C23×C4×C53C2311yescharacteristic
123C23×C4×C53C2311yescharacteristic
124C23×C4×C53C2311yescharacteristic
125C23×C4×C53C2311yescharacteristic
126C23×C4×C53C2311yescharacteristic
127#95×C53—22no—
128#95×C53—22no—
129#95×C53—22no—
130#95×C53—22no—
131#95×C53—41no—
132#95×C53—41no—
133#95×C53C2×C414yescomplemented
134C24×C53C2411yescharacteristic
135C23×D53—21no—
136C23×D53—21no—
137C23×D53—21no—
138C23×D53—21no—
139C23×D53—21no—
140C23×D53—21no—
141C23×D53—21no—
142C23×D53—21no—
143C23×D53C22×C412yes—
144C23×D53#4112yes—
145C23×D53#4112yes—
146C23×D53#4112yes—
147C23×D53#4112yes—
148C23×D53#4112yes—
149C23×D53#4112yes—
150C22×C4×C53—21no—
151C22×C4×C53—21no—
152C22×C4×C53—21no—
153C22×C4×C53—21no—
154C22×C4×C53—21no—
155C22×C4×C53—21no—
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×C53C22×C412yes—
195C22×C4×C53C22×C412yes—
196C22×C4×C53C22×C412yes—
197C22×C4×C53C2×D412yes—
198C22×C4×C53#4112yes—
199C22×Dic53—21no—
200C22×Dic53—21no—
201C22×Dic53—21no—
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53—21no—
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×Dic53C22×C412yes—
242C22×Dic53C22×C412yes—
243C22×Dic53C22×C412yes—
244C22×Dic53C2×D412yes—
245C22×Dic53C2×D412yes—
246C22×Dic53#4112yes—
247C22×Dic53#4112yes—
248C2×C4×D53—28no—
249C2×C4×D53—28no—
250C2×C4×D53—28no—
251C2×C4×D53—28no—
252C2×C4×D53—44no—
253C2×C4×D53—44no—
254C2×C4×D53—44no—
255C2×C4×D53—44no—
256C2×C4×D53—44no—
257C2×C4×D53—44no—
258C2×C4×D53—44no—
259C2×C4×D53—44no—
260C2×C4×D53—44no—
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—
269#11719921—28no—
270#11719921—28no—
271#11719921—44no—
272#11719921—44no—
273C4×Dic53—28no—
274C4×Dic53—44no—
275C23×C53C23×C411yescharacteristic
276C23×C53C22×D411yescharacteristic
277C23×C53C2×#4111yescharacteristic
278C23×C53C2×#4111yescharacteristic
279C23×C53C2×#4111yescharacteristic
280C23×C53C2×#4111yescharacteristic
281C23×C53C2×#4111yescharacteristic
282C23×C53C2×#4111yescharacteristic
283C23×C53C2×#4111yescharacteristic
284C23×C53C2×#4111yescharacteristic
285C23×C53C2×#4111yescharacteristic
286C23×C53H(5,𝔽2)11yescharacteristic
287C23×C53H(5,𝔽2)11yescharacteristic
288C23×C53H(5,𝔽2)11yescharacteristic
289C23×C532−1+411yescharacteristic
290C22×D53—22no—
291C22×D53—22no—
292C22×D53—22no—
293C22×D53—22no—
294C22×D53—22no—
295C22×D53—22no—
296C22×D53—22no—
297C22×D53—22no—
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#11714yes—
319C22×D53#11714yes—
320C22×D53#11714yes—
321C22×D53#12614yes—
322C22×D53#12614yes—
323C22×D53#12614yes—
324C22×D53#12614yes—
325C2×C4×C53—22no—
326C2×C4×C53—22no—
327C2×C4×C53—22no—
328C2×C4×C53—22no—
329C2×C4×C53—22no—
330C2×C4×C53—22no—
331C2×C4×C53—22no—
332C2×C4×C53—22no—
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—41no—
341C2×C4×C53—41no—
342C2×C4×C53—41no—
343C2×C4×C53—41no—
344C2×C4×C53—41no—
345C2×C4×C53—41no—
346C2×C4×C53—41no—
347C2×C4×C53—41no—
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×Dic53—22no—
375C2×Dic53—22no—
376C2×Dic53—22no—
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—41no—
393C2×Dic53—41no—
394C2×Dic53—41no—
395C2×Dic53—41no—
396C2×Dic53—41no—
397C2×Dic53—41no—
398C2×Dic53—41no—
399C2×Dic53—41no—
400C2×Dic53—41no—
401C2×Dic53—41no—
402C2×Dic53—41no—
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×Dic53C4×D414yes—
423C4×D53—416no—
424C4×D53—416no—
425C4×D53—416no—
426#13901—531nomaximal, Sylow
427C22×C53C2×#11711yescharacteristic
428C22×C53C2×#11711yescharacteristic
429C22×C53C2×#11711yescharacteristic
430C22×C53C2×C4×D411yescharacteristic
431C22×C53C4×#4111yescharacteristic
432C22×C53#51811yescharacteristic
433C22×C53#52011yescharacteristic
434C22×C53#52511yescharacteristic
435C22×C53#52511yescharacteristic
436C22×C53C2×#12611yescharacteristic
437C22×C53C2×#12611yescharacteristic
438C22×C53C2×#12611yescharacteristic
439C22×C53C2×#12611yescharacteristic
440C22×C53#52911yescharacteristic
441C22×C53#52911yescharacteristic
442C22×C53#53811yescharacteristic
443C22×C53#53811yescharacteristic
444C22×C53#53911yescharacteristic
445C22×C53#53911yescharacteristic
446C22×C53#54611yescharacteristic
447C22×C53#54611yescharacteristic
448C22×C53#54611yescharacteristic
449C22×C53#54811yescharacteristic
450C22×C53#55111yescharacteristic
451C22×C53#55111yescharacteristic
452C22×C53#55111yescharacteristic
453C22×C53#55111yescharacteristic
454C22×C53#55111yescharacteristic
455C22×C53#55111yescharacteristic
456C22×C53#55211yescharacteristic
457C22×C53#55211yescharacteristic
458C22×C53#55211yescharacteristic
459C22×C53#55311yescharacteristic
460C22×C53#55311yescharacteristic
461C22×C53#55311yescharacteristic
462C2×D53—24no—
463C2×D53—24no—
464C2×D53—24no—
465C2×D53—24no—
466C2×D53—24no—
467C2×D53—24no—
468C2×D53—24no—
469C2×D53—24no—
470C2×D53—24no—
471C2×D53—24no—
472C2×D53—24no—
473C2×D53—24no—
474C2×D53—24no—
475C2×D53—24no—
476C2×D53#38318yescomplemented
477C4×C53—42no—
478C4×C53—42no—
479C4×C53—42no—
480C4×C53—42no—
481C4×C53—42no—
482C4×C53—81no—
483C4×C53—81no—
484Dic53—24no—
485Dic53—42no—
486Dic53—42no—
487Dic53—42no—
488Dic53—42no—
489Dic53—81no—
490Dic53—81no—
491C2×#383—531no—
492C2×C4×C22⋊C4—531no—
493C22×#95—531no—
494#1443—531no—
495#1443—531no—
496#1443—531no—
497#1443D5311yescharacteristic, complemented
498#1434—531no—
499#1434—531no—
500#1434—531no—
501C22⋊#95—531no—
502C22⋊#95—531no—
503C22⋊#95—531no—
504C22⋊#95—531no—
505C22⋊#95—531no—
506C2×C53C2×#38311yescharacteristic
507C2×C53#229011yescharacteristic
508C2×C53#231811yescharacteristic
509C2×C53#234211yescharacteristic
510C2×C53#234311yescharacteristic
511C2×C53#235211yescharacteristic
512C2×C53#235311yescharacteristic
513C2×C53#248011yescharacteristic
514C2×C53#248011yescharacteristic
515C2×C53#248111yescharacteristic
516C2×C53#248111yescharacteristic
517C2×C53#249311yescharacteristic
518C2×C53#249311yescharacteristic
519C2×C53#251011yescharacteristic
520C2×C53#251011yescharacteristic
521D53—28no—
522C24×C4—531no—
523C24×C4—531no—
524C24×C4—531no—
525C22×C22⋊C4—531no—
526C22×C22⋊C4—531no—
527C22×C22⋊C4—531no—
528C22×C22⋊C4—531no—
529C22×C42—531no—
530C22×C42—531no—
531#383—1064no—
532C4×C22⋊C4—538no—
533C2×#95—531no—
534C2×#95—531no—
535C2×#95—531no—
536C2×#95—531no—
537C2×#95—531no—
538C2×#95—531no—
539C2×#95—531no—
540C2×#95—531no—
541C2×#95—531no—
542C2×#95—531no—
543C2×#95—531no—
544C2×#95—531no—
545C2×#95—531no—
546C2×#95—531no—
547C2×#95—531no—
548C2×#95—531no—
549C2×#95—531no—
550C2×#95—531no—
551C2×#95—531no—
552C2×#95—1064no—
553C2×#95C2×D5311yescharacteristic
554C2×#95C2×D5311yescharacteristic
555C2×#95C2×D5311yescharacteristic
556C2×#95C2×D5311yescharacteristic
557C2×#95C2×D5311yescharacteristic
558C2×#95C2×D5311yescharacteristic
559C2×#95C2×D5311yescharacteristic
560C53#1390111yescharacteristic, complemented, Sylow
561C25—531no—
562C23×C4—531no—
563C23×C4—531no—
564C23×C4—531no—
565C23×C4—531no—
566C23×C4—531no—
567C23×C4—534no—
568C23×C4—531no—
569C23×C4—531no—
570C23×C4—1062no—
571C23×C4—1062no—
572C23×C4—1062no—
573C23×C4—1062no—
574C23×C4—1062no—
575C23×C4—1062no—
576C23×C4—1062no—
577C23×C4—1062no—
578C23×C4—1062no—
579C23×C4—1062no—
580C23×C4—1062no—
581C23×C4—1062no—
582C23×C4—1062no—
583C23×C4—1062no—
584C23×C4—2121no—
585C23×C4—2121no—
586C23×C4—2121no—
587C23×C4—2121no—
588C23×C4—2121no—
589C23×C4—2121no—
590C23×C4C22×D5311yescharacteristic
591C23×C4C22×D5311yescharacteristic
592C23×C4C22×D5311yescharacteristic
593C23×C4C22×D5311yescharacteristic
594C23×C4C22×D5311yescharacteristic
595C23×C4C22×D5311yescharacteristic
596C23×C4C22×D5311yescharacteristic
597C2×C22⋊C4—534no—
598C2×C22⋊C4—534no—
599C2×C22⋊C4—1062no—
600C2×C22⋊C4—1062no—
601C2×C22⋊C4—1062no—
602C2×C22⋊C4—1062no—
603C2×C22⋊C4—1062no—
604C2×C22⋊C4—1062no—
605C2×C22⋊C4—1062no—
606C2×C22⋊C4—1062no—
607C2×C22⋊C4—1062no—
608C2×C22⋊C4—1062no—
609C2×C42—534no—
610C2×C42—534no—
611C2×C42—1062no—
612C2×C42—1062no—
613C2×C42—2121no—
614C2×C42—2121no—
615#95—22no—
616#95—22no—
617#95—22no—
618#95—22no—
619#95—41no—
620#95—41no—
621#95—534no—
622#95—534no—
623#95—1062no—
624#95—1062no—
625#95—1062no—
626#95—1062no—
627#95—1062no—
628#95—1062no—
629#95—1062no—
630#95—1062no—
631#95—1062no—
632#95—2121no—
633#95—2121no—
634#95—2121no—
635#95—2121no—
636#95—2121no—
637#95—2121no—
638#95—2121no—
639#95—2121no—
640#95C4×D5314yescomplemented
641C24—532no—
642C24—532no—
643C24—532no—
644C24—532no—
645C24—532no—
646C24—532no—
647C24—532no—
648C24—1061no—
649C24—1061no—
650C24—1061no—
651C24—1061no—
652C24—1061no—
653C24—1061no—
654C24—1061no—
655C24—1061no—
656C24C23×D5311yescharacteristic
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
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—532no—
702C22×C4—532no—
703C22×C4—532no—
704C22×C4—532no—
705C22×C4—532no—
706C22×C4—532no—
707C22×C4—532no—
708C22×C4—1068no—
709C22×C4—1068no—
710C22×C4—1068no—
711C22×C4—1068no—
712C22×C4—1061no—
713C22×C4—1061no—
714C22×C4—1061no—
715C22×C4—1061no—
716C22×C4—1061no—
717C22×C4—1061no—
718C22×C4—1061no—
719C22×C4—1061no—
720C22×C4—1061no—
721C22×C4—1061no—
722C22×C4—1061no—
723C22×C4—1061no—
724C22×C4—1061no—
725C22×C4—1061no—
726C22×C4—1061no—
727C22×C4—1061no—
728C22×C4—1061no—
729C22×C4—1061no—
730C22×C4—1061no—
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—2124no—
755C22×C4—2124no—
756C22×C4—2124no—
757C22×C4—2124no—
758C22×C4—2124no—
759C22×C4—2124no—
760C22×C4—2124no—
761C22×C4—2124no—
762C22×C4—2124no—
763C22×C4—2124no—
764C22×C4—2124no—
765C22×C4—2124no—
766C22×C4—2124no—
767C22×C4—2124no—
768C22×C4—2124no—
769C22×C4—2124no—
770C22×C4—2124no—
771C22×C4C2×C4×D5312yes—
772C22×C4C2×C4×D5312yes—
773C22×C4C2×C4×D5312yes—
774C22×C4D4×D5312yes—
775C22×C4#1171994712yes—
776C22⋊C4—1068no—
777C22⋊C4—1068no—
778C22⋊C4—2124no—
779C22⋊C4—2124no—
780C42—1068no—
781C42—2124no—
782C23—534no—
783C23—534no—
784C23—534no—
785C23—534no—
786C23—534no—
787C23—534no—
788C23—534no—
789C23—1062no—
790C23—1062no—
791C23—1062no—
792C23—1062no—
793C23—1062no—
794C23—1062no—
795C23—1062no—
796C23—1062no—
797C23—1062no—
798C23—1062no—
799C23—1062no—
800C23—1062no—
801C23—1062no—
802C23—1062no—
803C23—1062no—
804C23—1062no—
805C23—1062no—
806C23—1062no—
807C23—1062no—
808C23—1062no—
809C23—1062no—
810C23—1062no—
811C23—1062no—
812C23—1062no—
813C23—1062no—
814C23—1062no—
815C23—1062no—
816C23—1062no—
817C23C22×C4×D5311yescharacteristic
818C23C2×D4×D5311yescharacteristic
819C23#41×D5311yescharacteristic
820C23#41×D5311yescharacteristic
821C23#41×D5311yescharacteristic
822C23#41×D5311yescharacteristic
823C23#41×D5311yescharacteristic
824C23#41×D5311yescharacteristic
825C23#41×D5311yescharacteristic
826C23#41×D5311yescharacteristic
827C23C2×#1171994711yescharacteristic
828C23#1313326211yescharacteristic
829C23#1313326311yescharacteristic
830C23#1313326311yescharacteristic
831C23#1313326511yescharacteristic
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
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—534no—
882C2×C4—1062no—
883C2×C4—1062no—
884C2×C4—1062no—
885C2×C4—1062no—
886C2×C4—1062no—
887C2×C4—1062no—
888C2×C4—1062no—
889C2×C4—1062no—
890C2×C4—1062no—
891C2×C4—1062no—
892C2×C4—1062no—
893C2×C4—1062no—
894C2×C4—1062no—
895C2×C4—1062no—
896C2×C4—1062no—
897C2×C4—1062no—
898C2×C4—1062no—
899C2×C4—1062no—
900C2×C4—21216no—
901C2×C4—21216no—
902C2×C4—21216no—
903C2×C4—2121no—
904C2×C4—2121no—
905C2×C4—2121no—
906C2×C4—2121no—
907C2×C4—2121no—
908C2×C4—2121no—
909C2×C4—2121no—
910C2×C4—2121no—
911C2×C4—2121no—
912C2×C4—2121no—
913C2×C4—2121no—
914C2×C4—2121no—
915C2×C4—2121no—
916C2×C4—2121no—
917C2×C4—2121no—
918C2×C4—2121no—
919C2×C4—2121no—
920C2×C4—2121no—
921C2×C4—2121no—
922C2×C4—2121no—
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—
933C22—538no—
934C22—1064no—
935C22—1064no—
936C22—1064no—
937C22—1064no—
938C22—1064no—
939C22—1064no—
940C22—1064no—
941C22—1064no—
942C22—1064no—
943C22—1064no—
944C22—1064no—
945C22—1064no—
946C22—1064no—
947C22—1064no—
948C22#117×D5311yescharacteristic
949C22#117×D5311yescharacteristic
950C22#117×D5311yescharacteristic
951C22C4×D4×D5311yescharacteristic
952C22C4×#1171994711yescharacteristic
953C22#1681109511yescharacteristic
954C22#1681110511yescharacteristic
955C22#1681113111yescharacteristic
956C22#1681113311yescharacteristic
957C22#126×D5311yescharacteristic
958C22#126×D5311yescharacteristic
959C22#126×D5311yescharacteristic
960C22#126×D5311yescharacteristic
961C22#1681115211yescharacteristic
962C22#1681115611yescharacteristic
963C22#1681120911yescharacteristic
964C22#1681121211yescharacteristic
965C22#1681121911yescharacteristic
966C22#1681122111yescharacteristic
967C22#1681126211yescharacteristic
968C22#1681126511yescharacteristic
969C22#1681126611yescharacteristic
970C22#1681128311yescharacteristic
971C22#1681129611yescharacteristic
972C22#1681129611yescharacteristic
973C22#1681129811yescharacteristic
974C22#1681129811yescharacteristic
975C22#1681130111yescharacteristic
976C22#1681130311yescharacteristic
977C22#1681130511yescharacteristic
978C22#1681130511yescharacteristic
979C22#1681130711yescharacteristic
980C22#1681132011yescharacteristic
981C22#1681132411yescharacteristic
982C22#1681132411yescharacteristic
983C4—42no—
984C4—42no—
985C4—42no—
986C4—42no—
987C4—42no—
988C4—81no—
989C4—81no—
990C4—1064no—
991C4—4241no—
992C4—4241no—
993C4—2122no—
994C4—2122no—
995C4—2122no—
996C4—2122no—
997C2—1068no—
998C2#383×D5311yescharacteristic
999C2#2027715711yescharacteristic
1000C2#2027734711yescharacteristic
1001C2#2027756311yescharacteristic
1002C2#2027757011yescharacteristic
1003C2#2027763911yescharacteristic
1004C2#2027765011yescharacteristic
1005C2#2027895411yescharacteristic
1006C2#2027896211yescharacteristic
1007C2#2027896911yescharacteristic
1008C2#2027897711yescharacteristic
1009C2#2027910111yescharacteristic
1010C2#2027910311yescharacteristic
1011C2#2027926811yescharacteristic
1012C2#2027927011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC53×#1443C2
socle, cosocleC24×C53C24
prime radicalC24×D53C23
hypercenter#1443D53
hypocenterC53#13901
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ #1443

Complements

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

NH ≅ G/Ntype
1. C2×#16810490C2semidirect
4. #20272977C2semidirect
5. #20272976C2semidirect
6. #20272975C2semidirect
7. #20272940C2semidirect
8. #20272940C2semidirect
9. #20272939C2semidirect
15. C53×#1443C2semidirect
26. #16810470C4semidirect
99. C2×C4×Dic53C2×C4semidirect
100. C2×C4×Dic53C2×C4semidirect
118. #13133124C2×C4semidirect
133. #95×C53C2×C4semidirect
476. C2×D53#383semidirect
497. #1443D53semidirect
560. C53#13901semidirect
640. #95C4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168104902
C2×#168104702
C2×#95×D532
#202729772
#202729762
#202729752
#202729402
#202729392
#202729362
C53×#14432
#1390153