Finite Group Databasebeta

← #27351290

Subgroups — #27351290

Order 13568.

1166 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288741C211yesmaximal, characteristic
2#20283751C211yesmaximal, characteristic, complemented
3#20277074C211yesmaximal, characteristic, complemented
4#20273237C211yesmaximal, characteristic, complemented
5#20273229C211yesmaximal, characteristic, complemented
6#20273221C211yesmaximal, characteristic, complemented
7#20273220C211yesmaximal, characteristic, complemented
8#20273216C211yesmaximal, characteristic, complemented
9#20273208C211yesmaximal, characteristic, complemented
10#20273204C211yesmaximal, characteristic, complemented
11#20273203C211yesmaximal, characteristic, complemented
12#20273198C211yesmaximal, characteristic, complemented
13C2×#16810357C211yesmaximal, characteristic, complemented
14#327×D53C211yesmaximal, characteristic, complemented
15C53×#1507C211yesmaximal, characteristic, complemented
16#16811337C411yescharacteristic, complemented
17#16811328C411yescharacteristic, complemented
18#16811321C411yescharacteristic, complemented
19#16811320C411yescharacteristic, complemented
20#16811316—21no—
21#16811291C411yescharacteristic, complemented
22#16811270C411yescharacteristic, complemented
23#16811267—21no—
24#16811267C411yescharacteristic, complemented
25#16811262—21no—
26D4×C22⋊D53—21no—
27D4×C22⋊D53C411yescharacteristic, complemented
28#16811223—21no—
29#16811211—21no—
30#16811205—21no—
31#16811168C2211yescharacteristic
32#16811154C2211yescharacteristic
33#16811134C2211yescharacteristic
34#16811133C2211yescharacteristic
35#121×D53C2211yescharacteristic
36#16811096—21no—
37C2×C4×C22⋊D53C2211yescharacteristic
38C2×#13133177—21no—
39#16810699—21no—
40#16810692—21no—
41#16810691—21no—
42#16810686—21no—
43#16810677C2211yescharacteristic, complemented
44#16810673C2211yescharacteristic, complemented
45#16810585C2211yescharacteristic, complemented
46C2×C22⋊#88322C2211yescharacteristic, complemented
47C22⋊C8×D53C2211yescharacteristic, complemented
48C4×#11719919—21no—
49#16810474C2211yescharacteristic, complemented
50C22⋊C4×Dic53—21no—
51C4×#11719921—21no—
52#16810470C2211yescharacteristic, complemented
53#16810468C2211yescharacteristic, complemented
54C2×#13133124C2211yescharacteristic, complemented
55#95×D53C2211yescharacteristic, complemented
56#16810361C2211yescharacteristic, complemented
57#16810361C2211yescharacteristic, complemented
58#16810359C2211yescharacteristic, complemented
59#16810359C2211yescharacteristic, complemented
60#16810358C2211yescharacteristic, complemented
61#16810358C2211yescharacteristic, complemented
62#16810357C2211yescharacteristic
63#16810357C2211yescharacteristic
64#16810357C2211yescharacteristic, complemented
65#16810357C2211yescharacteristic, complemented
66#16810356C2211yescharacteristic, complemented
67#16810356C2211yescharacteristic, complemented
68C2×#121×C53C2211yescharacteristic
69C53×#407C2211yescharacteristic, complemented
70C4×C22⋊C4×C53C2211yescharacteristic, complemented
71C53×#327C2211yescharacteristic
72C53×#327C2211yescharacteristic
73C53×#327C2211yescharacteristic, complemented
74C53×#327C2211yescharacteristic, complemented
75C2×#11719945C2×C411yescharacteristic, complemented
76C2×#11719947—21no—
77C2×#11719947C2×C411yescharacteristic, complemented
78C22×C22⋊D53—21no—
79C22×C22⋊D53D411yescharacteristic
80C2×D4×D53—21no—
81C2×D4×D53C2×C411yescharacteristic, complemented
82C23×Dic53—21no—
83C22×C4×D53—21no—
84C22×C4×D53C2311yescharacteristic
85C2×#11719912—21no—
86C22×#88322—21no—
87C2×C8×D53—21no—
88#13133216C2×C411yescharacteristic, complemented
89#13133213—21no—
90#13133213C2×C411yescharacteristic, complemented
91#13133212—21no—
92#13133210—21no—
93#13133210—21no—
94#13133208C2×C411yescharacteristic, complemented
95#13133207—21no—
96#13133204—21no—
97#13133204C2×C411yescharacteristic, complemented
98#13133203—21no—
99#13133203—21no—
100#13133202—21no—
101#13133200—21no—
102#13133199—21no—
103#13133199—21no—
104#13133198—21no—
105#13133198—21no—
106#13133198—21no—
107#13133197C2×C411yescharacteristic, complemented
108#13133196—21no—
109#13133196C2×C411yescharacteristic, complemented
110#13133196C2311yescharacteristic
111#13133195—21no—
112#13133192C2×C411yescharacteristic, complemented
113#13133191—21no—
114#13133191C2×C411yescharacteristic, complemented
115#13133191C2311yescharacteristic
116#13133190—21no—
117#13133190—21no—
118#13133189—21no—
119#13133189—21no—
120#13133189—21no—
121#13133189—21no—
122#13133189—21no—
123#13133189—21no—
124#13133188—21no—
125#13133188—21no—
126#13133188C2×C411yescharacteristic, complemented
127#13133188C2×C411yescharacteristic, complemented
128#13133186—21no—
129#13133186—21no—
130#13133186—21no—
131#13133185—21no—
132#13133185—21no—
133#13133185—21no—
134#13133182C2×C411yescharacteristic, complemented
135D4×Dic53—21no—
136D4×Dic53—21no—
137D4×Dic53C2×C411yescharacteristic, complemented
138D4×Dic53C2×C411yescharacteristic, complemented
139#13133179C2×C411yescharacteristic, complemented
140C4×C22⋊D53—21no—
141C4×C22⋊D53—21no—
142C4×C22⋊D53—21no—
143C4×C22⋊D53—21no—
144C4×C22⋊D53C2×C411yescharacteristic
145C4×C22⋊D53C2×C411yescharacteristic
146C4×C22⋊D53C2×C411yescharacteristic
147C4×C22⋊D53C2×C411yescharacteristic
148C4×C22⋊D53D411yescharacteristic
149C4×C22⋊D53D411yescharacteristic
150C4×C22⋊D53D411yescharacteristic
151C4×C22⋊D53D411yescharacteristic
152#13133177—28no—
153#13133177—21no—
154#13133177—21no—
155#13133177—21no—
156#13133177—21no—
157#13133176C2×C411yescharacteristic, complemented
158#13133175C2×C411yescharacteristic, complemented
159#13133173—21no—
160#13133173—21no—
161C2×#11719919—21no—
162C2×#11719919D411yescharacteristic
163C4⋊C4×D53C2×C411yescharacteristic, complemented
164C2×C22⋊Dic53—21no—
165C2×C22⋊Dic53D411yescharacteristic
166C2×#11719921—21no—
167C2×#11719921D411yescharacteristic
168C22⋊C4×D53—21no—
169C22⋊C4×D53—21no—
170C2×C4×Dic53—21no—
171C2×C4×Dic53—21no—
172C2×C4×Dic53—21no—
173C2×C4×Dic53C2311yescharacteristic
174#13133146—21no—
175#13133146—21no—
176C22⋊#88322—21no—
177C22⋊#88322C2311yescharacteristic
178C22⋊#88322C2311yescharacteristic
179#13133129—21no—
180#13133129—21no—
181#13133127—21no—
182C8×Dic53—21no—
183#13133124—21no—
184#13133124—21no—
185#13133124—21no—
186#13133124C2311yescharacteristic
187#13133124C2311yescharacteristic
188C22×D4×C53—21no—
189C22×D4×C53C2×C411yescharacteristic, complemented
190C23×C4×C53C2311yescharacteristic
191C2×M16×C53—21no—
192#121×C53—21no—
193#121×C53—21no—
194#121×C53C2×C411yescharacteristic, complemented
195#121×C53C2×C411yescharacteristic, complemented
196#121×C53C2311yescharacteristic
197#121×C53C2311yescharacteristic
198C2×C4⋊C4×C53C2×C411yescharacteristic, complemented
199C2×C22⋊C4×C53—21no—
200C2×C22⋊C4×C53—21no—
201C2×C42×C53—21no—
202C22⋊C8×C53—21no—
203C22⋊C8×C53C2311yescharacteristic
204C22⋊C8×C53C2311yescharacteristic
205#95×C53C2311yescharacteristic
206#95×C53C2311yescharacteristic
207C24×C53—21no—
208C24×C53C2×D411yescharacteristic
209C23×D53—21no—
210C23×D53C2×D411yescharacteristic
211C2×D4×C53—21no—
212C2×D4×C53—21no—
213C2×D4×C53—21no—
214C2×D4×C53—21no—
215C2×D4×C53—21no—
216C2×D4×C53—81no—
217C2×D4×C53—81no—
218C2×D4×C53—81no—
219C2×D4×C53C22×C411yescharacteristic
220C2×D4×C53C22×C411yescharacteristic
221C22×C4×C53—21no—
222C22×C4×C53—21no—
223C22×C4×C53—21no—
224C22×C4×C53—81no—
225C22×C4×C53C22×C411yescharacteristic
226C22×C4×C53C22×C411yescharacteristic
227C22×C4×C53C2×D411yescharacteristic
228C22×C4×C53C2×D411yescharacteristic
229C22×C4×C53C2×D411yescharacteristic
230C22×C4×C53C2411yescharacteristic
231C2×C22⋊D53—24no—
232C2×C22⋊D53—21no—
233C2×C22⋊D53—21no—
234C2×C22⋊D53—21no—
235C2×C22⋊D53—21no—
236C2×C22⋊D53—21no—
237C2×C22⋊D53—21no—
238C2×C22⋊D53—21no—
239C2×C22⋊D53—21no—
240C2×C22⋊D53—21no—
241C2×C22⋊D53—44no—
242C2×C22⋊D53C22⋊C411yescharacteristic
243C2×C22⋊D53C22⋊C411yescharacteristic
244C2×C22⋊D53C22⋊C411yescharacteristic
245C2×C22⋊D53C22⋊C411yescharacteristic
246C22×Dic53—21no—
247C22×Dic53—21no—
248C22×Dic53—24no—
249C22×Dic53—21no—
250C22×Dic53—21no—
251C22×Dic53—21no—
252C22×Dic53—81no—
253C22×Dic53—81no—
254C22×Dic53C2×D411yescharacteristic
255C22×Dic53C2×D411yescharacteristic
256C22×Dic53C2×D411yescharacteristic
257#11719947—81no—
258#11719947—81no—
259#11719947—81no—
260D4×D53—81no—
261D4×D53—81no—
262D4×D53—81no—
263#11719945—81no—
264C2×D212—21no—
265C2×D212C22×C411yescharacteristic
266C2×C4×D53—24no—
267C2×C4×D53—21no—
268C2×C4×D53—21no—
269C2×C4×D53—21no—
270C2×C4×D53—81no—
271C2×C4×D53—81no—
272C2×C4×D53—81no—
273C2×C4×D53C22×C411yescharacteristic
274C2×C4×D53C22×C411yescharacteristic
275C2×C4×D53C2×D411yescharacteristic
276C2×C4×D53C2×D411yescharacteristic
277C2×Dic106—21no—
278C2×Dic106C22×C411yescharacteristic
279M16×C53—81no—
280C2×C8×C53—21no—
281C2×C8×C53—21no—
282C4⋊C4×C53—21no—
283C4⋊C4×C53C22×C411yescharacteristic
284C4⋊C4×C53C22×C411yescharacteristic
285C22⋊C4×C53—24no—
286C22⋊C4×C53—21no—
287C22⋊C4×C53—21no—
288C22⋊C4×C53—21no—
289C22⋊C4×C53—21no—
290C42×C53—81no—
291C22⋊Dic53—21no—
292C22⋊Dic53—21no—
293C22⋊Dic53—21no—
294C22⋊Dic53—21no—
295C22⋊Dic53—21no—
296C22⋊Dic53—21no—
297C22⋊Dic53—21no—
298C22⋊Dic53—21no—
299C22⋊Dic53—21no—
300C22⋊Dic53C22⋊C411yescharacteristic
301C22⋊Dic53C22⋊C411yescharacteristic
302C22⋊Dic53C22⋊C411yescharacteristic
303C22⋊Dic53C22⋊C411yescharacteristic
304#11719921—24no—
305#11719921—21no—
306#11719921—21no—
307#11719921—21no—
308#11719921—21no—
309#11719921—21no—
310#11719921—21no—
311#11719921C22⋊C411yescharacteristic
312#11719921C22⋊C411yescharacteristic
313#11719921C22⋊C411yescharacteristic
314#11719921C22⋊C411yescharacteristic
315C4⋊Dic53—21no—
316C4⋊Dic53—21no—
317C4⋊Dic53C22×C411yescharacteristic
318C4⋊Dic53C22×C411yescharacteristic
319#11719919—24no—
320#11719919—21no—
321#11719919—21no—
322#11719919—21no—
323#11719919—21no—
324#11719919—21no—
325#11719919—21no—
326#11719919C22⋊C411yescharacteristic
327#11719919C22⋊C411yescharacteristic
328#11719919C22⋊C411yescharacteristic
329#11719919C22⋊C411yescharacteristic
330C4×Dic53—24no—
331C4×Dic53—21no—
332C4×Dic53—21no—
333C4×Dic53—21no—
334C4×Dic53—81no—
335C4×Dic53—81no—
336C4×Dic53C22×C411yescharacteristic
337C4×Dic53C22×C411yescharacteristic
338C4×Dic53C2×D411yescharacteristic
339C4×Dic53C2×D411yescharacteristic
340C2×#88322—21no—
341C2×#88322—21no—
342C2×#88322—81no—
343#11719912—81no—
344C8×D53—81no—
345C23×C53—21no—
346C23×C53—21no—
347C23×C53—22no—
348C23×C53—21no—
349C23×C53—21no—
350C23×C53—41no—
351C23×C53—42no—
352C23×C53—81no—
353C23×C53—81no—
354C23×C53C2×C22⋊C411yescharacteristic
355C23×C53C2×C22⋊C411yescharacteristic
356C23×C53C22×D411yescharacteristic
357C22×D53—21no—
358C22×D53—21no—
359C22×D53—22no—
360C22×D53—21no—
361C22×D53—41no—
362C22×D53—42no—
363C22×D53—81no—
364C22×D53—81no—
365C22×D53C2×C22⋊C411yescharacteristic
366C22×D53C2×C22⋊C411yescharacteristic
367D4×C53—41no—
368D4×C53—41no—
369D4×C53—41no—
370D4×C53—41no—
371D4×C53—41no—
372D4×C53—41no—
373D4×C53—81no—
374D4×C53—81no—
375D4×C53—81no—
376C2×C4×C53—22no—
377C2×C4×C53—22no—
378C2×C4×C53—21no—
379C2×C4×C53—21no—
380C2×C4×C53—41no—
381C2×C4×C53—41no—
382C2×C4×C53—41no—
383C2×C4×C53—41no—
384C2×C4×C53—41no—
385C2×C4×C53—41no—
386C2×C4×C53—41no—
387C2×C4×C53—41no—
388C2×C4×C53—41no—
389C2×C4×C53—41no—
390C2×C4×C53—81no—
391C2×C4×C53C2×C22⋊C411yescharacteristic
392C2×C4×C53C2×C22⋊C411yescharacteristic
393C2×C4×C53C23×C411yescharacteristic
394C2×C4×C53C22×D411yescharacteristic
395C22⋊D53—22no—
396C22⋊D53—22no—
397C22⋊D53—22no—
398C22⋊D53—41no—
399C22⋊D53—41no—
400C22⋊D53—42no—
401C22⋊D53—42no—
402C22⋊D53—42no—
403C22⋊D53—81no—
404C22⋊D53—81no—
405C22⋊D53—81no—
406C22⋊D53—81no—
407C22⋊D53—81no—
408C22⋊D53#10414yes—
409C2×Dic53—21no—
410C2×Dic53—21no—
411C2×Dic53—22no—
412C2×Dic53—22no—
413C2×Dic53—22no—
414C2×Dic53—21no—
415C2×Dic53—21no—
416C2×Dic53—21no—
417C2×Dic53—41no—
418C2×Dic53—41no—
419C2×Dic53—41no—
420C2×Dic53—41no—
421C2×Dic53—41no—
422C2×Dic53—42no—
423C2×Dic53—81no—
424C2×Dic53—81no—
425C2×Dic53—84no—
426C2×Dic53C2×C22⋊C411yescharacteristic
427C2×Dic53C2×C22⋊C411yescharacteristic
428C2×Dic53C2×C22⋊C411yescharacteristic
429C2×Dic53C2×C22⋊C411yescharacteristic
430C2×Dic53C2×C22⋊C411yescharacteristic
431C2×Dic53C2×C22⋊C411yescharacteristic
432D212—41no—
433D212—81no—
434C4×D53—41no—
435C4×D53—41no—
436C4×D53—41no—
437C4×D53—41no—
438C4×D53—81no—
439C4×D53—81no—
440C4×D53—81no—
441C4×D53—84no—
442Dic106—41no—
443Dic106—81no—
444C8×C53—41no—
445C8×C53—41no—
446#88322—41no—
447#88322—41no—
448#17547—531nomaximal, Sylow
449C22×C53—21no—
450C22×C53—21no—
451C22×C53—21no—
452C22×C53—21no—
453C22×C53—21no—
454C22×C53—21no—
455C22×C53—21no—
456C22×C53—42no—
457C22×C53—42no—
458C22×C53—41no—
459C22×C53—41no—
460C22×C53—41no—
461C22×C53—41no—
462C22×C53—41no—
463C22×C53—41no—
464C22×C53—162no—
465C22×C53C2×#10412yes—
466C22×C53C22×C22⋊C411yescharacteristic
467C22×C53#57611yescharacteristic
468C22×C53#57711yescharacteristic
469C2×D53—21no—
470C2×D53—21no—
471C2×D53—21no—
472C2×D53—21no—
473C2×D53—21no—
474C2×D53—42no—
475C2×D53—42no—
476C2×D53—41no—
477C2×D53—41no—
478C2×D53—41no—
479C2×D53—162no—
480C2×D53C2×#10412yes—
481C4×C53—21no—
482C4×C53—21no—
483C4×C53—21no—
484C4×C53—21no—
485C4×C53—42no—
486C4×C53—42no—
487C4×C53—41no—
488C4×C53—41no—
489Dic53—21no—
490Dic53—21no—
491Dic53—21no—
492Dic53—21no—
493Dic53—21no—
494Dic53—42no—
495Dic53—42no—
496Dic53—41no—
497Dic53—41no—
498Dic53—41no—
499Dic53C2×#10412yes—
500#3519—531no—
501#2974—531no—
502#2275—531no—
503#1509—531no—
504#1507—531no—
505#1507D5311yescharacteristic, complemented
506#1505—531no—
507#1504—531no—
508#1504—531no—
509#1502—531no—
510#1501—531no—
511#1501—531no—
512#1500—531no—
513C2×#327—531no—
514C2×#327—531no—
515C2×C53—21no—
516C2×C53—21no—
517C2×C53—22no—
518C2×C53—41no—
519C2×C53—81no—
520C2×C53—81no—
521C2×C53#288311yescharacteristic
522C2×C53#289711yescharacteristic
523C2×C53C22×#10411yescharacteristic
524D53—22no—
525D53—41no—
526D53—81no—
527#555—531no—
528#554—531no—
529#553—531no—
530#553—531no—
531#553—1061no—
532#550—531no—
533#546—531no—
534#546—531no—
535#546—1061no—
536#546—1061no—
537D42—531no—
538D42—1061no—
539#540—1061no—
540#538—1061no—
541#538—1061no—
542#532—531no—
543#529—531no—
544#525—531no—
545#525—531no—
546C2×#121—531no—
547C2×#121C2×D5311yescharacteristic
548#518—1061no—
549C2×C4×D4—531no—
550C2×C4×D4—1061no—
551#436—1061no—
552#435—1061no—
553#435—1061no—
554C8×D4—1061no—
555#432—531no—
556#431—531no—
557#407—531no—
558#407C2×D5311yescharacteristic, complemented
559C2×C22⋊C8—531no—
560C2×C22⋊C8—531no—
561C4×C4⋊C4—531no—
562C4×C4⋊C4—1061no—
563C4×C22⋊C4—531no—
564C4×C22⋊C4—1061no—
565C4×C22⋊C4—1061no—
566C4×C22⋊C4C2×D5311yescharacteristic, complemented
567#376—531no—
568C2×#95—531no—
569C2×#95—531no—
570#328—531no—
571#328—531no—
572#328—531no—
573#328—531no—
574#327—531no—
575#327—531no—
576#327—531no—
577#327—531no—
578#327—531no—
579#327—531no—
580#327—531no—
581#327—531no—
582#327C2×D5311yescharacteristic
583#327C2×D5311yescharacteristic
584#327C2×D5311yescharacteristic, complemented
585#327C2×D5311yescharacteristic, complemented
586C53#1754711yescharacteristic, complemented, Sylow
587C2×#41—531no—
588C2×#41—531no—
589C2×#41—1061no—
590C22×D4—21no—
591C22×D4—531no—
592C22×D4—531no—
593C22×D4—1061no—
594C22×D4—1061no—
595C22×D4C4×D5311yescharacteristic, complemented
596C23×C4—531no—
597C23×C4—1061no—
598C23×C4—1061no—
599C23×C4C22×D5311yescharacteristic
600C2×M16—21no—
601C2×M16—1061no—
602C22×C8—1061no—
603C22×C8—1061no—
604C4⋊Q8—531no—
605#127—531no—
606#127—1061no—
607#126—1061no—
608#126—1061no—
609#126—1061no—
610#125—531no—
611#125—1061no—
612#124—531no—
613#124—1061no—
614#124—1061no—
615#124—1061no—
616#123—1061no—
617#123—1061no—
618#123—1061no—
619#123—1061no—
620#123—1061no—
621#123—1061no—
622#123—1061no—
623C22⋊Q8—531no—
624C22⋊Q8—531no—
625C22⋊Q8—531no—
626C22⋊Q8—1061no—
627C22⋊Q8—1061no—
628#121—21no—
629#121—21no—
630#121—531no—
631#121—531no—
632#121—531no—
633#121—531no—
634#121—531no—
635#121—1061no—
636#121—1061no—
637#121—1061no—
638#121—1061no—
639#121—1061no—
640#121—1061no—
641#121—1061no—
642#121—1061no—
643#121—1061no—
644#121—1061no—
645#121—1061no—
646#121C4×D5311yescharacteristic, complemented
647#121C4×D5311yescharacteristic, complemented
648#121C22×D5311yescharacteristic
649#121C22×D5311yescharacteristic
650#120—1061no—
651#120—1061no—
652#120—1061no—
653#120—1061no—
654#120—1061no—
655#120—1061no—
656C4×Q8—531no—
657C4×D4—531no—
658C4×D4—531no—
659C4×D4—531no—
660C4×D4—531no—
661C4×D4—531no—
662C4×D4—531no—
663C4×D4—531no—
664C4×D4—531no—
665C4×D4—531no—
666C4×D4—531no—
667C4×D4—531no—
668C4×D4—1061no—
669C4×D4—1061no—
670C4×D4—1061no—
671C4×D4—1061no—
672C4×D4—1068no—
673C4×D4—1061no—
674C4×D4—1061no—
675C4×D4—1061no—
676C4×D4—1061no—
677C4×D4—1061no—
678C4×D4—1061no—
679#117—531no—
680#117—531no—
681#117—1061no—
682#117—1061no—
683C2×C4⋊C4—531no—
684C2×C4⋊C4—531no—
685C2×C4⋊C4—1061no—
686C2×C4⋊C4C4×D5311yescharacteristic, complemented
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—531no—
690C2×C22⋊C4—531no—
691C2×C22⋊C4—1061no—
692C2×C22⋊C4—1061no—
693C2×C22⋊C4—1061no—
694C2×C22⋊C4—1061no—
695C2×C42—21no—
696C2×C42—531no—
697C2×C42—1061no—
698C2×C42—1061no—
699C2×C42—1061no—
700C4⋊C8—1061no—
701C4⋊C8—1061no—
702C22⋊C8—21no—
703C22⋊C8—531no—
704C22⋊C8—531no—
705C22⋊C8—1061no—
706C22⋊C8—1061no—
707C22⋊C8—1061no—
708C22⋊C8C22×D5311yescharacteristic
709C22⋊C8C22×D5311yescharacteristic
710#97—1061no—
711C4×C8—1061no—
712#95—531no—
713#95—531no—
714#95—1061no—
715#95—1061no—
716#95—1061no—
717#95C22×D5311yescharacteristic
718#95C22×D5311yescharacteristic
719C24—21no—
720C24—531no—
721C24—1061no—
722C24D4×D5311yescharacteristic
723#41—4241no—
724#41—4241no—
725#41—4241no—
726#41—4241no—
727C2×Q8—531no—
728C2×Q8—1061no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—81no—
735C2×D4—81no—
736C2×D4—81no—
737C2×D4—531no—
738C2×D4—531no—
739C2×D4—531no—
740C2×D4—531no—
741C2×D4—531no—
742C2×D4—1061no—
743C2×D4—1061no—
744C2×D4—1061no—
745C2×D4—1061no—
746C2×D4—1064no—
747C2×D4—1061no—
748C2×D4—1061no—
749C2×D4—1061no—
750C2×D4—1061no—
751C2×D4—1061no—
752C2×D4—1061no—
753C2×D4—4241no—
754C2×D4—4241no—
755C2×D4—4241no—
756C2×D4—2124no—
757C2×D4C2×C4×D5311yescharacteristic
758C2×D4C2×C4×D5311yescharacteristic
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—81no—
763C22×C4—531no—
764C22×C4—531no—
765C22×C4—531no—
766C22×C4—531no—
767C22×C4—531no—
768C22×C4—531no—
769C22×C4—531no—
770C22×C4—1061no—
771C22×C4—1061no—
772C22×C4—1064no—
773C22×C4—1061no—
774C22×C4—1061no—
775C22×C4—1061no—
776C22×C4—1064no—
777C22×C4—1061no—
778C22×C4—1061no—
779C22×C4—1061no—
780C22×C4—4241no—
781C22×C4—4241no—
782C22×C4—4241no—
783C22×C4—4241no—
784C22×C4—4241no—
785C22×C4C2×C4×D5311yescharacteristic
786C22×C4C2×C4×D5311yescharacteristic
787C22×C4D4×D5311yescharacteristic
788C22×C4D4×D5311yescharacteristic
789C22×C4D4×D5311yescharacteristic
790C22×C4C23×D5311yescharacteristic
791M16—81no—
792M16—4241no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—1061no—
796C2×C8—1061no—
797C2×C8—4241no—
798C2×C8—4241no—
799C4⋊C4—21no—
800C4⋊C4—531no—
801C4⋊C4—531no—
802C4⋊C4—531no—
803C4⋊C4—531no—
804C4⋊C4—531no—
805C4⋊C4—531no—
806C4⋊C4—1061no—
807C4⋊C4—1061no—
808C4⋊C4—1061no—
809C4⋊C4—1061no—
810C4⋊C4—1061no—
811C4⋊C4—1061no—
812C4⋊C4—1064no—
813C4⋊C4—1061no—
814C4⋊C4—1061no—
815C4⋊C4C2×C4×D5311yescharacteristic
816C4⋊C4C2×C4×D5311yescharacteristic
817C22⋊C4—24no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—531no—
823C22⋊C4—531no—
824C22⋊C4—531no—
825C22⋊C4—531no—
826C22⋊C4—531no—
827C22⋊C4—531no—
828C22⋊C4—531no—
829C22⋊C4—531no—
830C22⋊C4—1061no—
831C22⋊C4—1061no—
832C22⋊C4—1061no—
833C22⋊C4—1061no—
834C22⋊C4—1064no—
835C22⋊C4—1061no—
836C22⋊C4—1061no—
837C22⋊C4—1061no—
838C22⋊C4—1061no—
839C22⋊C4—1061no—
840C22⋊C4—1061no—
841C22⋊C4—1061no—
842C22⋊C4—1061no—
843C22⋊C4—1061no—
844C22⋊C4—1061no—
845C22⋊C4—1061no—
846C42—81no—
847C42—531no—
848C42—531no—
849C42—531no—
850C42—531no—
851C42—1061no—
852C42—1061no—
853C42—1064no—
854C42—1061no—
855C42—4241no—
856C42—4241no—
857C23—22no—
858C23—21no—
859C23—21no—
860C23—21no—
861C23—21no—
862C23—41no—
863C23—42no—
864C23—81no—
865C23—81no—
866C23—531no—
867C23—531no—
868C23—1062no—
869C23—1061no—
870C23—1061no—
871C23—1061no—
872C23—4241no—
873C23—4241no—
874C23—2121no—
875C23—2122no—
876C23C22⋊C4×D5311yescharacteristic
877C23C22⋊C4×D5311yescharacteristic
878C23C2×D4×D5311yescharacteristic
879Q8—4241no—
880Q8—2121no—
881D4—41no—
882D4—41no—
883D4—41no—
884D4—41no—
885D4—41no—
886D4—41no—
887D4—81no—
888D4—81no—
889D4—81no—
890D4—534no—
891D4—1062no—
892D4—1062no—
893D4—1062no—
894D4—4241no—
895D4—4241no—
896D4—4241no—
897D4—4241no—
898D4—4241no—
899D4—4241no—
900D4—2121no—
901D4—2122no—
902D4—2122no—
903D4—2122no—
904D4—2121no—
905D4—2121no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—81no—
921C2×C4—531no—
922C2×C4—531no—
923C2×C4—531no—
924C2×C4—531no—
925C2×C4—531no—
926C2×C4—531no—
927C2×C4—1062no—
928C2×C4—1061no—
929C2×C4—1061no—
930C2×C4—1062no—
931C2×C4—1062no—
932C2×C4—1061no—
933C2×C4—1061no—
934C2×C4—1061no—
935C2×C4—4241no—
936C2×C4—4241no—
937C2×C4—4241no—
938C2×C4—4244no—
939C2×C4—4241no—
940C2×C4—4241no—
941C2×C4—4244no—
942C2×C4—2121no—
943C2×C4—2121no—
944C2×C4—2121no—
945C2×C4—2121no—
946C2×C4—2122no—
947C2×C4—2121no—
948C2×C4—2121no—
949C2×C4—2121no—
950C2×C4—2121no—
951C2×C4—2121no—
952C2×C4C22⋊C4×D5311yescharacteristic
953C2×C4C22⋊C4×D5311yescharacteristic
954C2×C4C22×C4×D5311yescharacteristic
955C2×C4C2×D4×D5311yescharacteristic
956C8—41no—
957C8—41no—
958C8—2121no—
959C8—2121no—
960C22—21no—
961C22—21no—
962C22—21no—
963C22—21no—
964C22—21no—
965C22—21no—
966C22—21no—
967C22—42no—
968C22—42no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—41no—
973C22—41no—
974C22—41no—
975C22—162no—
976C22—532no—
977C22—8482no—
978C22—1061no—
979C22—1061no—
980C22—1061no—
981C22—1061no—
982C22—1061no—
983C22—2122no—
984C22—2122no—
985C22—2121no—
986C22—2121no—
987C22—2121no—
988C22#104×D5312yes—
989C22C2×C22⋊C4×D5311yescharacteristic
990C22#1681142711yescharacteristic
991C22#1681143311yescharacteristic
992C4—21no—
993C4—21no—
994C4—21no—
995C4—21no—
996C4—42no—
997C4—42no—
998C4—41no—
999C4—41no—
1000C4—532no—
1001C4—1061no—
1002C4—1061no—
1003C4—1061no—
1004C4—1061no—
1005C4—1061no—
1006C4—2122no—
1007C4—2122no—
1008C4—2121no—
1009C4—2121no—
1010C4—2121no—
1011C2—21no—
1012C2—21no—
1013C2—22no—
1014C2—41no—
1015C2—81no—
1016C2—81no—
1017C2—1062no—
1018C2—4241no—
1019C2—2121no—
1020C2#2028317311yescharacteristic
1021C2#2028324011yescharacteristic
1022C2C2×#104×D5311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1507C2
socleC22×C53C22×C22⋊C4
prime radical#20288741C2
cosocleC22×C4×C53C24
hypercenter#1507D53
hypocenterC53#17547
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1507

Complements

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

NH ≅ G/Ntype
2. #20283751C2semidirect
3. #20277074C2semidirect
4. #20273237C2semidirect
5. #20273229C2semidirect
6. #20273221C2semidirect
7. #20273220C2semidirect
8. #20273216C2semidirect
9. #20273208C2semidirect
10. #20273204C2semidirect
11. #20273203C2semidirect
12. #20273198C2semidirect
13. C2×#16810357C2semidirect
14. #327×D53C2semidirect
15. C53×#1507C2semidirect
16. #16811337C4semidirect
17. #16811328C4semidirect
18. #16811321C4semidirect
19. #16811320C4semidirect
21. #16811291C4semidirect
22. #16811270C4semidirect
24. #16811267C4semidirect
27. D4×C22⋊D53C4semidirect
43. #16810677C22semidirect
44. #16810673C22semidirect
45. #16810585C22semidirect
46. C2×C22⋊#88322C22semidirect
47. C22⋊C8×D53C22semidirect
49. #16810474C22semidirect
52. #16810470C22semidirect
53. #16810468C22semidirect
54. C2×#13133124C22semidirect
55. #95×D53C22semidirect
56. #16810361C22semidirect
57. #16810361C22semidirect
58. #16810359C22semidirect
59. #16810359C22semidirect
60. #16810358C22semidirect
61. #16810358C22semidirect
64. #16810357C22semidirect
65. #16810357C22semidirect
66. #16810356C22semidirect
67. #16810356C22semidirect
69. C53×#407C22semidirect
70. C4×C22⋊C4×C53C22semidirect
73. C53×#327C22semidirect
74. C53×#327C22semidirect
75. C2×#11719945C2×C4semidirect
77. C2×#11719947C2×C4semidirect
81. C2×D4×D53C2×C4semidirect
88. #13133216C2×C4semidirect
90. #13133213C2×C4semidirect
94. #13133208C2×C4semidirect
97. #13133204C2×C4semidirect
107. #13133197C2×C4semidirect
109. #13133196C2×C4semidirect
112. #13133192C2×C4semidirect
114. #13133191C2×C4semidirect
126. #13133188C2×C4semidirect
127. #13133188C2×C4semidirect
134. #13133182C2×C4semidirect
137. D4×Dic53C2×C4semidirect
138. D4×Dic53C2×C4semidirect
139. #13133179C2×C4semidirect
157. #13133176C2×C4semidirect
158. #13133175C2×C4semidirect
163. C4⋊C4×D53C2×C4semidirect
189. C22×D4×C53C2×C4semidirect
194. #121×C53C2×C4semidirect
195. #121×C53C2×C4semidirect
198. C2×C4⋊C4×C53C2×C4semidirect
505. #1507D53semidirect
558. #407C2×D53semidirect
566. C4×C22⋊C4C2×D53semidirect
584. #327C2×D53semidirect
585. #327C2×D53semidirect
586. C53#17547semidirect
595. C22×D4C4×D53semidirect
646. #121C4×D53semidirect
647. #121C4×D53semidirect
686. C2×C4⋊C4C4×D53semidirect

Maximal subgroups

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

subgroupindex
#202887412
#202837512
#202770742
#202732372
#202732292
#202732212
#202732202
#202732162
#202732082
#202732042
#202732032
#202731982
C2×#168103572
#327×D532
C53×#15072
#1754753