Finite Group Databasebeta

← #27394382

Subgroups — #27394382

Order 13568.

1162 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810586C211yesmaximal, characteristic
2#20277097C211yesmaximal, characteristic
3#380×D53C211yesmaximal, characteristic
4#20274917C211yesmaximal, characteristic, complemented
5#20274915C211yesmaximal, characteristic, complemented
6#20274913C211yesmaximal, characteristic, complemented
7#20274911C211yesmaximal, characteristic, complemented
8#20274909C211yesmaximal, characteristic, complemented
9#20274906C211yesmaximal, characteristic, complemented
10#20274904C211yesmaximal, characteristic, complemented
11#20274901C211yesmaximal, characteristic, complemented
12#20274748C211yesmaximal, characteristic, complemented
13#20274746C211yesmaximal, characteristic, complemented
14#20274746C211yesmaximal, characteristic, complemented
15C53×#1809C211yesmaximal, characteristic, complemented
16C23×C4×D53C2211yescharacteristic
17C22×#11719917C2211yescharacteristic
18C2×#13133175C2211yescharacteristic
19C2×#13133175C2211yescharacteristic
20C2×C4⋊C4×D53C2211yescharacteristic
21C2×C4⋊C4×D53C2211yescharacteristic
22C2×C22⋊C4×D53—21no—
23C2×#13133151C2211yescharacteristic, complemented
24C2×#13133150C2211yescharacteristic, complemented
25C2×#13133150C2211yescharacteristic, complemented
26C2×#13133149C2211yescharacteristic, complemented
27C2×#13133148C2211yescharacteristic, complemented
28C2×#13133148C2211yescharacteristic, complemented
29#16810586C418yescomplemented
30C2×#13133129C2211yescharacteristic
31C2×#13133129C2211yescharacteristic
32C2×#13133129C2211yescharacteristic
33C2×#13133129C2211yescharacteristic
34#16810485—21no—
35#16810483C2211yescharacteristic
36#16810483C2211yescharacteristic
37#16810482—21no—
38#16810481—21no—
39#16810480C2211yescharacteristic
40#16810480C2211yescharacteristic
41#16810480C2211yescharacteristic
42#16810480C2211yescharacteristic
43#16810478—21no—
44C22⋊C4×Dic53—21no—
45#16810470—21no—
46#95×D53—21no—
47#16810386C2211yescharacteristic, complemented
48#16810386C2211yescharacteristic, complemented
49#16810385C2211yescharacteristic, complemented
50#16810385C2211yescharacteristic, complemented
51#16810385C2211yescharacteristic, complemented
52#16810385C2211yescharacteristic, complemented
53C22×M16×C53C2211yescharacteristic
54C2×#107×C53C2211yescharacteristic, complemented
55C2×#106×C53C2211yescharacteristic, complemented
56C53×#380C2211yescharacteristic
57C53×#380C2211yescharacteristic
58C53×#340C2211yescharacteristic, complemented
59C53×#340C2211yescharacteristic, complemented
60C24×D53D411yescharacteristic
61C23×Dic53D411yescharacteristic
62C22×C4×D53—21no—
63C22×C4×D53—21no—
64C22×C4×D53—41no—
65C22×C4×D53—41no—
66C22×C4×D53—41no—
67C22×C4×D53—41no—
68C22×C4×D53C2×C414yes—
69C22×C4×D53D411yescharacteristic
70C22×C4×D53D411yescharacteristic
71C22×C4×D53Q814yes—
72C22×C4×D53C2311yescharacteristic
73C22×C4×D53C2311yescharacteristic
74C2×#11719917—41no—
75C2×#11719917—41no—
76C2×#11719917C2×C414yescomplemented
77C22×#88322C2311yescharacteristic
78C22×#88322C2311yescharacteristic
79#13133175—41no—
80#13133175—41no—
81#13133175—41no—
82#13133175—41no—
83C2×C4⋊Dic53C2311yescharacteristic
84C2×C4⋊Dic53C2311yescharacteristic
85C2×C4⋊Dic53C2311yescharacteristic
86C2×C4⋊Dic53C2311yescharacteristic
87C2×#11719919—21no—
88C2×#11719919—21no—
89C4⋊C4×D53—41no—
90C4⋊C4×D53—41no—
91C4⋊C4×D53—41no—
92C4⋊C4×D53—41no—
93C2×C22⋊Dic53—21no—
94C2×C22⋊Dic53—21no—
95C2×#11719921—21no—
96C2×#11719921—21no—
97C2×#11719921—21no—
98C2×#11719921—21no—
99C2×#11719921—21no—
100C2×#11719921—21no—
101C22⋊C4×D53—44no—
102C2×C4×Dic53—21no—
103C2×C4×Dic53—21no—
104#13133151—41no—
105#13133150—41no—
106#13133150—41no—
107#13133149—41no—
108#13133148—41no—
109#13133148—41no—
110#13133129C2×C414yes—
111#13133129C2×C414yes—
112#13133129C2×C414yescomplemented
113#13133129C2×C414yescomplemented
114#13133124—21no—
115#13133124—21no—
116#13133124—21no—
117#13133124—21no—
118#13133124—21no—
119#13133124—21no—
120C23×C4×C53C2311yescharacteristic
121C2×M16×C53—41no—
122C2×M16×C53—41no—
123C2×M16×C53C2×C414yescomplemented
124C22×C8×C53C2311yescharacteristic
125C22×C8×C53C2311yescharacteristic
126C2×C4⋊C4×C53C2311yescharacteristic
127C2×C4⋊C4×C53C2311yescharacteristic
128C2×C4⋊C4×C53C2311yescharacteristic
129C2×C4⋊C4×C53C2311yescharacteristic
130C2×C22⋊C4×C53—21no—
131C2×C22⋊C4×C53—21no—
132#107×C53—41no—
133#106×C53—41no—
134#95×C53—21no—
135#95×C53—21no—
136C24×C53C2×D411yescharacteristic
137C23×D53—22no—
138C23×D53—22no—
139C23×D53—41no—
140C23×D53—41no—
141C23×D53—41no—
142C23×D53—41no—
143C23×D53C4⋊C414yes—
144C23×D53C2×D411yescharacteristic
145C23×D53C2×D411yescharacteristic
146C22×C4×C53—21no—
147C22×C4×C53—21no—
148C22×C4×C53—21no—
149C22×C4×C53—21no—
150C22×C4×C53—21no—
151C22×C4×C53—21no—
152C22×C4×C53—21no—
153C22×C4×C53—21no—
154C22×C4×C53C22×C412yes—
155C22×C4×C53C2×D411yescharacteristic
156C22×C4×C53C2×Q812yes—
157C22×C4×C53C2411yescharacteristic
158C22×Dic53—21no—
159C22×Dic53—21no—
160C22×Dic53—21no—
161C22×Dic53—21no—
162C22×Dic53—41no—
163C22×Dic53—41no—
164C22×Dic53C4⋊C414yes—
165C22×Dic53C2×D411yescharacteristic
166C22×Dic53C2×D411yescharacteristic
167C2×C4×D53—21no—
168C2×C4×D53—21no—
169C2×C4×D53—21no—
170C2×C4×D53—21no—
171C2×C4×D53—21no—
172C2×C4×D53—21no—
173C2×C4×D53—21no—
174C2×C4×D53—21no—
175C2×C4×D53—44no—
176C2×C4×D53—44no—
177C2×C4×D53—44no—
178C2×C4×D53—44no—
179C2×C4×D53—41no—
180C2×C4×D53—41no—
181C2×C4×D53—41no—
182C2×C4×D53—41no—
183C2×C4×D53—42no—
184C2×C4×D53—42no—
185C2×C4×D53—42no—
186C2×C4×D53—42no—
187C2×C4×D53—42no—
188C2×C4×D53—42no—
189C2×C4×D53C4⋊C414yes—
190C2×C4×D53C4⋊C414yes—
191C2×C4×D53C22×C412yes—
192C2×C4×D53C22×C412yes—
193C2×C4×D53C2×Q812yes—
194C2×C4×D53C2×Q812yes—
195M16×C53—44no—
196C2×C8×C53—21no—
197C2×C8×C53—21no—
198C2×C8×C53—21no—
199C2×C8×C53—21no—
200C2×C8×C53C22×C412yes—
201C2×C8×C53C22×C412yes—
202C4⋊C4×C53—21no—
203C4⋊C4×C53—21no—
204C4⋊C4×C53—21no—
205C4⋊C4×C53—21no—
206C4⋊C4×C53—21no—
207C4⋊C4×C53—21no—
208C4⋊C4×C53—21no—
209C4⋊C4×C53—21no—
210C22⋊C4×C53—42no—
211C22⋊C4×C53—42no—
212C22⋊Dic53—42no—
213C22⋊Dic53—42no—
214#11719921—42no—
215#11719921—42no—
216#11719921—42no—
217#11719921—42no—
218#11719921—42no—
219#11719921—42no—
220C4⋊Dic53—21no—
221C4⋊Dic53—21no—
222C4⋊Dic53—21no—
223C4⋊Dic53—21no—
224C4⋊Dic53—21no—
225C4⋊Dic53—21no—
226C4⋊Dic53—21no—
227C4⋊Dic53—21no—
228#11719919—42no—
229#11719919—42no—
230C4×Dic53—42no—
231C4×Dic53—42no—
232#11719917—44no—
233C2×#88322—21no—
234C2×#88322—21no—
235C2×#88322—21no—
236C2×#88322—21no—
237C2×#88322C22×C412yes—
238C2×#88322C22×C412yes—
239C23×C53—21no—
240C23×C53—21no—
241C23×C53—21no—
242C23×C53—21no—
243C23×C53—21no—
244C23×C53—21no—
245C23×C53C2×C4⋊C412yes—
246C23×C53C22×D411yescharacteristic
247C22×D53—21no—
248C22×D53—21no—
249C22×D53—21no—
250C22×D53—21no—
251C22×D53—21no—
252C22×D53—21no—
253C22×D53—21no—
254C22×D53—21no—
255C22×D53—21no—
256C22×D53—21no—
257C22×D53—28no—
258C22×D53—44no—
259C22×D53—44no—
260C22×D53—44no—
261C22×D53—44no—
262C22×D53—44no—
263C22×D53—44no—
264C22×D53C2×C4⋊C412yes—
265C22×D53C2×C4⋊C412yes—
266C22×D53AGL(1,ℤ/8)12yes—
267C22×D53#13712yes—
268C2×C4×C53—21no—
269C2×C4×C53—21no—
270C2×C4×C53—22no—
271C2×C4×C53—22no—
272C2×C4×C53—22no—
273C2×C4×C53—22no—
274C2×C4×C53—41no—
275C2×C4×C53—41no—
276C2×C4×C53—41no—
277C2×C4×C53—41no—
278C2×C4×C53—41no—
279C2×C4×C53—41no—
280C2×C4×C53—41no—
281C2×C4×C53—41no—
282C2×C4×C53—41no—
283C2×C4×C53—41no—
284C2×C4×C53—41no—
285C2×C4×C53—41no—
286C2×C4×C53C2×C4⋊C412yes—
287C2×C4×C53C23×C411yescharacteristic
288C2×C4×C53C22×Q811yescharacteristic
289C2×C4×C53H(5,𝔽2)11yescharacteristic
290C2×C4×C53H(5,𝔽2)11yescharacteristic
291C2×C4×C53H(5,𝔽2)11yescharacteristic
292C2×C4×C53H(5,𝔽2)11yescharacteristic
293C2×Dic53—21no—
294C2×Dic53—21no—
295C2×Dic53—21no—
296C2×Dic53—21no—
297C2×Dic53—44no—
298C2×Dic53—41no—
299C2×Dic53—41no—
300C2×Dic53—41no—
301C2×Dic53—41no—
302C2×Dic53—41no—
303C2×Dic53—41no—
304C2×Dic53—41no—
305C2×Dic53—41no—
306C2×Dic53—41no—
307C2×Dic53—41no—
308C2×Dic53—41no—
309C2×Dic53—41no—
310C2×Dic53C2×C4⋊C412yes—
311C2×Dic53C2×C4⋊C412yes—
312C4×D53—22no—
313C4×D53—22no—
314C4×D53—22no—
315C4×D53—22no—
316C4×D53—22no—
317C4×D53—22no—
318C4×D53—22no—
319C4×D53—22no—
320C4×D53—44no—
321C4×D53—44no—
322C4×D53—84no—
323C4×D53—84no—
324C8×C53—22no—
325C8×C53—22no—
326#88322—22no—
327#88322—22no—
328#21944—531nomaximal, Sylow
329C22×C53—22no—
330C22×C53—22no—
331C22×C53—22no—
332C22×C53—41no—
333C22×C53—41no—
334C22×C53—41no—
335C22×C53—41no—
336C22×C53C22×C4⋊C411yescharacteristic
337C22×C53#53411yescharacteristic
338C22×C53#53411yescharacteristic
339C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
340C22×C53C2×#13711yescharacteristic
341C22×C53#57511yescharacteristic
342C22×C53#57511yescharacteristic
343C2×D53—22no—
344C2×D53—22no—
345C2×D53—22no—
346C2×D53—22no—
347C2×D53—22no—
348C2×D53—22no—
349C2×D53—22no—
350C2×D53—22no—
351C2×D53—22no—
352C2×D53—416no—
353C2×D53—41no—
354C2×D53—41no—
355C2×D53—41no—
356C2×D53—41no—
357C2×D53#42814yes—
358C4×C53—22no—
359C4×C53—81no—
360C4×C53—81no—
361C4×C53—81no—
362C4×C53—81no—
363C4×C53#51811yescharacteristic
364C4×C53#51811yescharacteristic
365C4×C53#54311yescharacteristic
366C4×C53#54311yescharacteristic
367Dic53—22no—
368Dic53—22no—
369Dic53—81no—
370Dic53—81no—
371Dic53—81no—
372Dic53—81no—
373C2×#407—531no—
374#2280—531no—
375C2×#380—531no—
376#1854—531no—
377#1854—531no—
378#1854—531no—
379#1854—531no—
380#1853—531no—
381#1853—531no—
382#1852—531no—
383#1852—531no—
384#1809—531no—
385#1809—531no—
386#1809—531no—
387#1809D5311yescharacteristic, complemented
388C2×C53—42no—
389C2×C53#231511yescharacteristic
390C2×C53C2×#42811yescharacteristic
391C2×C53#291111yescharacteristic
392C2×C53#319411yescharacteristic
393C2×C53#319411yescharacteristic
394C2×C53#319611yescharacteristic
395C2×C53#319611yescharacteristic
396D53—24no—
397D53—42no—
398C24×C4—531no—
399C22×M16—531no—
400C22×M16C2×D5311yescharacteristic
401C2×#117—531no—
402C2×#117—531no—
403C22×C4⋊C4—531no—
404C22×C4⋊C4—531no—
405C22×C22⋊C4—1061no—
406C2×#107—531no—
407C2×#107—531no—
408C2×#107—531no—
409C2×#107C2×D5311yescharacteristic, complemented
410C2×#106—531no—
411C2×#106—531no—
412C2×#106—531no—
413C2×#106C2×D5311yescharacteristic, complemented
414#407—538no—
415C2×C22⋊C8—531no—
416C2×C22⋊C8—531no—
417C2×C22⋊C8—531no—
418C2×C22⋊C8—531no—
419#381—1061no—
420#380—531no—
421#380—531no—
422#380—531no—
423#380—531no—
424#380—531no—
425#380—531no—
426#380—1061no—
427#380—1061no—
428#380C2×D5311yescharacteristic
429#380C2×D5311yescharacteristic
430#379—1061no—
431C4×C22⋊C4—1061no—
432C4×C22⋊C4—1061no—
433C2×#95—1061no—
434#340—531no—
435#340—531no—
436#340—531no—
437#340—531no—
438#340—531no—
439#340—531no—
440#340C2×D5311yescharacteristic, complemented
441#340C2×D5311yescharacteristic, complemented
442C53#2194411yescharacteristic, complemented, Sylow
443C25—531no—
444C23×C4—531no—
445C23×C4—531no—
446C23×C4—531no—
447C23×C4—534no—
448C23×C4—531no—
449C23×C4—531no—
450C23×C4—534no—
451C23×C4—1061no—
452C23×C4—1061no—
453C23×C4—2121no—
454C23×C4—2121no—
455C23×C4—2121no—
456C23×C4—2121no—
457C23×C4C22×D5311yescharacteristic
458C2×M16—41no—
459C2×M16—41no—
460C2×M16—534no—
461C2×M16—2121no—
462C2×M16—2121no—
463C2×M16C4×D5314yescomplemented
464C22×C8—531no—
465C22×C8—531no—
466C22×C8C22×D5311yescharacteristic
467C22×C8C22×D5311yescharacteristic
468#117—2121no—
469#117—2121no—
470#117—2121no—
471#117—2121no—
472C2×C4⋊C4—531no—
473C2×C4⋊C4—531no—
474C2×C4⋊C4—531no—
475C2×C4⋊C4—531no—
476C2×C4⋊C4—1061no—
477C2×C4⋊C4—1061no—
478C2×C4⋊C4—2121no—
479C2×C4⋊C4—2121no—
480C2×C4⋊C4—2121no—
481C2×C4⋊C4—2121no—
482C2×C4⋊C4C22×D5311yescharacteristic
483C2×C4⋊C4C22×D5311yescharacteristic
484C2×C4⋊C4C22×D5311yescharacteristic
485C2×C4⋊C4C22×D5311yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—1061no—
489C2×C22⋊C4—1061no—
490C2×C22⋊C4—1061no—
491C2×C22⋊C4—1061no—
492C2×C22⋊C4—1061no—
493C2×C22⋊C4—1061no—
494C2×C22⋊C4—1061no—
495C2×C22⋊C4—1061no—
496C2×C22⋊C4—2124no—
497C2×C42—1061no—
498C2×C42—1061no—
499#107—41no—
500#107—2121no—
501#107—2121no—
502#107—2121no—
503#106—41no—
504#106—2121no—
505#106—2121no—
506#106—2121no—
507C22⋊C8—534no—
508C22⋊C8—534no—
509C22⋊C8—534no—
510C22⋊C8—534no—
511#95—21no—
512#95—21no—
513#95—1061no—
514#95—1061no—
515#95—1061no—
516#95—1061no—
517#95—1061no—
518#95—1061no—
519C24—531no—
520C24—531no—
521C24—534no—
522C24—1062no—
523C24—1062no—
524C24—2121no—
525C24—2121no—
526C24—2121no—
527C24—2121no—
528C24D4×D5311yescharacteristic
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—531no—
538C22×C4—531no—
539C22×C4—534no—
540C22×C4—532no—
541C22×C4—532no—
542C22×C4—532no—
543C22×C4—532no—
544C22×C4—534no—
545C22×C4—534no—
546C22×C4—1061no—
547C22×C4—1061no—
548C22×C4—1061no—
549C22×C4—1061no—
550C22×C4—1061no—
551C22×C4—1061no—
552C22×C4—1061no—
553C22×C4—1061no—
554C22×C4—1061no—
555C22×C4—1061no—
556C22×C4—1061no—
557C22×C4—1061no—
558C22×C4—2124no—
559C22×C4—2124no—
560C22×C4—2124no—
561C22×C4—2124no—
562C22×C4—2121no—
563C22×C4—2121no—
564C22×C4—2121no—
565C22×C4—2121no—
566C22×C4—2122no—
567C22×C4—2122no—
568C22×C4—2122no—
569C22×C4—2122no—
570C22×C4—2122no—
571C22×C4—2122no—
572C22×C4—2121no—
573C22×C4—2121no—
574C22×C4C2×C4×D5312yes—
575C22×C4D4×D5311yescharacteristic
576C22×C4Q8×D5312yes—
577C22×C4C23×D5311yescharacteristic
578M16—44no—
579M16—2124no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—532no—
585C2×C8—532no—
586C2×C8—1061no—
587C2×C8—1061no—
588C2×C8—1061no—
589C2×C8—1061no—
590C2×C8C2×C4×D5312yes—
591C2×C8C2×C4×D5312yes—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—1061no—
601C4⋊C4—1061no—
602C4⋊C4—1061no—
603C4⋊C4—1061no—
604C4⋊C4—1061no—
605C4⋊C4—1061no—
606C4⋊C4—1061no—
607C4⋊C4—1061no—
608C4⋊C4—2122no—
609C4⋊C4—2122no—
610C22⋊C4—42no—
611C22⋊C4—42no—
612C22⋊C4—2122no—
613C22⋊C4—2122no—
614C22⋊C4—2122no—
615C22⋊C4—2122no—
616C22⋊C4—2122no—
617C22⋊C4—2122no—
618C22⋊C4—2122no—
619C22⋊C4—2122no—
620C42—2122no—
621C42—2122no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—532no—
629C23—532no—
630C23—532no—
631C23—532no—
632C23—1068no—
633C23—1061no—
634C23—1061no—
635C23—1061no—
636C23—1061no—
637C23—1061no—
638C23—1061no—
639C23—1061no—
640C23—1061no—
641C23—1061no—
642C23—1061no—
643C23—2124no—
644C23—2124no—
645C23—2124no—
646C23—2124no—
647C23—2124no—
648C23—2124no—
649C23C4⋊C4×D5312yes—
650C23C2×D4×D5311yescharacteristic
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—532no—
670C2×C4—532no—
671C2×C4—1061no—
672C2×C4—1061no—
673C2×C4—1061no—
674C2×C4—1061no—
675C2×C4—1062no—
676C2×C4—1062no—
677C2×C4—1062no—
678C2×C4—1062no—
679C2×C4—1062no—
680C2×C4—1062no—
681C2×C4—1062no—
682C2×C4—1062no—
683C2×C4—4244no—
684C2×C4—4244no—
685C2×C4—2124no—
686C2×C4—2124no—
687C2×C4—2124no—
688C2×C4—2121no—
689C2×C4—2121no—
690C2×C4—2121no—
691C2×C4—2121no—
692C2×C4—2121no—
693C2×C4—2121no—
694C2×C4—2121no—
695C2×C4—2121no—
696C2×C4—2121no—
697C2×C4—2121no—
698C2×C4—2121no—
699C2×C4—2121no—
700C2×C4C4⋊C4×D5312yes—
701C2×C4C22×C4×D5311yescharacteristic
702C2×C4C2×Q8×D5311yescharacteristic
703C2×C4#1313326211yescharacteristic
704C2×C4#1313326211yescharacteristic
705C2×C4#1313326311yescharacteristic
706C2×C4#1313326311yescharacteristic
707C8—22no—
708C8—22no—
709C8—1062no—
710C8—1062no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—534no—
719C22—1062no—
720C22—1062no—
721C22—1062no—
722C22—1062no—
723C22—1062no—
724C22—1062no—
725C22—1062no—
726C22—1062no—
727C22—1062no—
728C22—21216no—
729C22—2121no—
730C22—2121no—
731C22—2121no—
732C22—2121no—
733C22C2×C4⋊C4×D5311yescharacteristic
734C22#1681118111yescharacteristic
735C22#1681118111yescharacteristic
736C22AGL(1,ℤ/8)×D5311yescharacteristic
737C22#137×D5311yescharacteristic
738C22#1681141911yescharacteristic
739C22#1681142211yescharacteristic
740C4—22no—
741C4—81no—
742C4—81no—
743C4—81no—
744C4—81no—
745C4—1062no—
746C4—1062no—
747C4—4241no—
748C4—4241no—
749C4—4241no—
750C4—4241no—
751C4#1681109611yescharacteristic
752C4#1681109711yescharacteristic
753C4#1681124811yescharacteristic
754C4#1681124811yescharacteristic
755C2—42no—
756C2—1064no—
757C2—2122no—
758C2#2027732811yescharacteristic
759C2#428×D5311yescharacteristic
760C2#2028330211yescharacteristic
761C2#2028552411yescharacteristic
762C2#2028553011yescharacteristic
763C2#2028554011yescharacteristic
764C2#2028554611yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1809C2
socleC23×C53C22×D4
prime radicalC24×D53D4
cosocleC22×C4×C53C24
hypercenter#1809D53
hypocenterC53#21944
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

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

NH ≅ G/Ntype
4. #20274917C2semidirect
5. #20274915C2semidirect
6. #20274913C2semidirect
7. #20274911C2semidirect
8. #20274909C2semidirect
9. #20274906C2semidirect
10. #20274904C2semidirect
11. #20274901C2semidirect
12. #20274748C2semidirect
13. #20274746C2semidirect
14. #20274746C2semidirect
15. C53×#1809C2semidirect
23. C2×#13133151C22semidirect
24. C2×#13133150C22semidirect
25. C2×#13133150C22semidirect
26. C2×#13133149C22semidirect
27. C2×#13133148C22semidirect
28. C2×#13133148C22semidirect
29. #16810586C4semidirect
47. #16810386C22semidirect
48. #16810386C22semidirect
49. #16810385C22semidirect
50. #16810385C22semidirect
51. #16810385C22semidirect
52. #16810385C22semidirect
54. C2×#107×C53C22semidirect
55. C2×#106×C53C22semidirect
58. C53×#340C22semidirect
59. C53×#340C22semidirect
76. C2×#11719917C2×C4semidirect
112. #13133129C2×C4semidirect
113. #13133129C2×C4semidirect
123. C2×M16×C53C2×C4semidirect
387. #1809D53semidirect
409. C2×#107C2×D53semidirect
413. C2×#106C2×D53semidirect
440. #340C2×D53semidirect
441. #340C2×D53semidirect
442. C53#21944semidirect
463. C2×M16C4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168105862
#202770972
#380×D532
#202749172
#202749152
#202749132
#202749112
#202749092
#202749062
#202749042
#202749012
#202747482
#202747462
C53×#18092
#2194453