Finite Group Databasebeta

← #27390663

Subgroups — #27390663

Order 13568.

1098 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810849C211yesmaximal, characteristic
2C2×#97×D53C211yesmaximal, characteristic, complemented
3C4×#13133193C211yesmaximal, characteristic, complemented
4C4×#13133188C211yesmaximal, characteristic
5#20275598C211yesmaximal, characteristic, complemented
6#20275456C211yesmaximal, characteristic, complemented
7#20275409C211yesmaximal, characteristic, complemented
8#20275402C211yesmaximal, characteristic, complemented
9#20275140C211yesmaximal, characteristic
10#20275135C211yesmaximal, characteristic, complemented
11#20274741C211yesmaximal, characteristic, complemented
12#20274612C211yesmaximal, characteristic, complemented
13#20274545C211yesmaximal, characteristic, complemented
14#20274540C211yesmaximal, characteristic, complemented
15C2×C53×#440C211yesmaximal, characteristic, complemented
16C22×C8×D53C2211yescharacteristic
17C22×C8×D53C2211yescharacteristic
18C2×#13133193C2211yescharacteristic
19C2×#13133188C2211yescharacteristic
20C2×C4×C22⋊D53—21no—
21C2×C42×D53C2211yescharacteristic
22#16810849C418yescomplemented
23C2×#13133151C2211yescharacteristic
24C2×#13133149C2211yescharacteristic
25C2×#13133141C2211yescharacteristic
26C2×#13133141C2211yescharacteristic
27C2×#13133138C2211yescharacteristic
28C2×#13133138C2211yescharacteristic
29C2×#13133128C2211yescharacteristic
30C2×#13133127C2211yescharacteristic
31C2×#13133127C2211yescharacteristic
32#97×D53—24no—
33#16810530C2211yescharacteristic
34#16810526C2211yescharacteristic
35#16810519C2211yescharacteristic
36#16810519C2211yescharacteristic
37#16810511—21no—
38#16810504—21no—
39#16810499—21no—
40#16810494—21no—
41#16810480C2211yescharacteristic
42#16810480C2211yescharacteristic
43C4×#11719919—21no—
44C4×C4⋊Dic53C2211yescharacteristic
45C4×C4⋊Dic53C2211yescharacteristic
46C4×#11719921—21no—
47C4×C22⋊Dic53—21no—
48#16810386C2211yescharacteristic
49#16810386C2211yescharacteristic
50#16810385C2211yescharacteristic
51#16810385C2211yescharacteristic
52#16810385C2211yescharacteristic
53#16810385C2211yescharacteristic
54C22×SD16×C53C2211yescharacteristic
55C2×C4×Q8×C53C2211yescharacteristic
56C2×C4×D4×C53C2211yescharacteristic
57C53×#440—24no—
58C2×#107×C53C2211yescharacteristic
59C2×#103×C53C2211yescharacteristic
60C2×#102×C53C2211yescharacteristic
61C2×#97×C53C2211yescharacteristic
62C22×C22⋊D53—21no—
63C22×C4×D53D411yescharacteristic
64C22×C4×D53D411yescharacteristic
65C22×C4×D53C2311yescharacteristic
66C22×#88322C2311yescharacteristic
67C22×#88322C2311yescharacteristic
68C2×C8×D53—22no—
69C2×C8×D53—22no—
70C2×C8×D53—22no—
71C2×C8×D53—22no—
72C2×C8×D53—22no—
73C2×C8×D53C2×C414yescomplemented
74#13133193—22no—
75#13133193C2×C414yescomplemented
76#13133188—22no—
77#13133188C2×C414yes—
78C4×C22⋊D53—44no—
79C2×C4⋊Dic53C2311yescharacteristic
80C2×C4⋊Dic53C2311yescharacteristic
81C2×C4⋊Dic53C2311yescharacteristic
82C2×C4⋊Dic53C2311yescharacteristic
83C2×#11719919—21no—
84C2×#11719919—21no—
85C2×#11719919—21no—
86C2×C22⋊Dic53—21no—
87C2×C22⋊Dic53—21no—
88C2×C22⋊Dic53—21no—
89C2×#11719921—21no—
90C2×#11719921—21no—
91C2×#11719921—21no—
92C2×C4×Dic53—21no—
93C2×C4×Dic53—21no—
94C2×C4×Dic53D411yescharacteristic
95C2×C4×Dic53D411yescharacteristic
96C2×C4×Dic53C2311yescharacteristic
97C42×D53—22no—
98C42×D53—22no—
99#13133151—22no—
100#13133149C2×C414yescomplemented
101#13133141—22no—
102#13133141C2×C414yescomplemented
103#13133138—22no—
104#13133138C2×C414yescomplemented
105#13133128—22no—
106#13133127—22no—
107#13133127—22no—
108#13133124—21no—
109#13133124—21no—
110#13133124—21no—
111#13133124—21no—
112#13133124—21no—
113#13133124—21no—
114#13133124—21no—
115#13133124—21no—
116C22×Q8×C53C2311yescharacteristic
117C22×D4×C53C2311yescharacteristic
118C23×C4×C53—21no—
119C2×SD16×C53—22no—
120C2×SD16×C53—22no—
121C2×SD16×C53C2×C414yescomplemented
122C22×C8×C53C2311yescharacteristic
123C22×C8×C53C2311yescharacteristic
124C4×Q8×C53—22no—
125C4×Q8×C53—22no—
126C4×D4×C53—22no—
127C4×D4×C53—22no—
128C2×C4⋊C4×C53—21no—
129C2×C4⋊C4×C53C2311yescharacteristic
130C2×C4⋊C4×C53C2311yescharacteristic
131C2×C22⋊C4×C53—21no—
132C2×C42×C53—21no—
133C2×C42×C53C2311yescharacteristic
134#107×C53—22no—
135#103×C53—22no—
136#102×C53—22no—
137#97×C53D414yescomplemented
138C24×C53—21no—
139C23×D53C2×D411yescharacteristic
140C2×Q8×C53—21no—
141C2×Q8×C53—21no—
142C2×Q8×C53—21no—
143C2×Q8×C53—21no—
144C2×Q8×C53—21no—
145C2×Q8×C53C22×C412yes—
146C2×D4×C53—21no—
147C2×D4×C53—21no—
148C2×D4×C53—21no—
149C2×D4×C53—21no—
150C2×D4×C53—21no—
151C2×D4×C53C22×C412yes—
152C22×C4×C53—21no—
153C22×C4×C53—21no—
154C22×C4×C53—21no—
155C22×C4×C53—42no—
156C22×C4×C53—42no—
157C22×C4×C53—42no—
158C22×C4×C53C2×D411yescharacteristic
159C22×C4×C53C2×D411yescharacteristic
160C22×C4×C53C2411yescharacteristic
161C2×C22⋊D53—24no—
162C2×C22⋊D53—42no—
163C2×C22⋊D53—42no—
164C22×Dic53—21no—
165C22×Dic53—21no—
166C22×Dic53—21no—
167C22×Dic53—21no—
168C22×Dic53C2×D411yescharacteristic
169C22×Dic53C2×D411yescharacteristic
170C22×Dic53C2×D411yescharacteristic
171C2×C4×D53—21no—
172C2×C4×D53—21no—
173C2×C4×D53—21no—
174C2×C4×D53—21no—
175C2×C4×D53—22no—
176C2×C4×D53—22no—
177C2×C4×D53—22no—
178C2×C4×D53—22no—
179C2×C4×D53—41no—
180C2×C4×D53—41no—
181C2×C4×D53C22×C412yes—
182C2×C4×D53#4112yes—
183SD16×C53—28no—
184C2×C8×C53—21no—
185C2×C8×C53—21no—
186C2×C8×C53C22×C412yes—
187C2×C8×C53C2×D412yes—
188C2×C8×C53C2×D412yes—
189C2×C8×C53#4112yes—
190C4⋊C4×C53—21no—
191C4⋊C4×C53—21no—
192C4⋊C4×C53—21no—
193C4⋊C4×C53—21no—
194C4⋊C4×C53—42no—
195C22⋊C4×C53—42no—
196C42×C53—42no—
197C42×C53C2×D412yes—
198C42×C53#4112yes—
199C22⋊Dic53—24no—
200C22⋊Dic53—42no—
201C22⋊Dic53—42no—
202#11719921—24no—
203#11719921—42no—
204#11719921—42no—
205C4⋊Dic53—21no—
206C4⋊Dic53—21no—
207C4⋊Dic53—21no—
208C4⋊Dic53—21no—
209C4⋊Dic53—21no—
210C4⋊Dic53—21no—
211C4⋊Dic53C22×C412yes—
212C4⋊Dic53C22×C412yes—
213#11719919—24no—
214#11719919—42no—
215#11719919—42no—
216C4×Dic53—22no—
217C4×Dic53—22no—
218C4×Dic53—21no—
219C4×Dic53—21no—
220C4×Dic53—42no—
221C4×Dic53—42no—
222C2×#88322—21no—
223C2×#88322—21no—
224C2×#88322—21no—
225C2×#88322—21no—
226C2×#88322C22×C412yes—
227C2×#88322#4112yes—
228C8×D53—28no—
229C8×D53—28no—
230C23×C53—22no—
231C23×C53—41no—
232C23×C53—41no—
233C23×C53—41no—
234C23×C53—41no—
235C23×C53—41no—
236C23×C53—41no—
237C23×C53C22×D411yescharacteristic
238C22×D53—21no—
239C22×D53—21no—
240C22×D53—21no—
241C22×D53—21no—
242C22×D53C4×D412yes—
243C22×D53AGL(1,ℤ/8)12yes—
244C22×D53#13712yes—
245Q8×C53—22no—
246Q8×C53—22no—
247Q8×C53—41no—
248Q8×C53—41no—
249D4×C53—22no—
250D4×C53—22no—
251D4×C53—41no—
252D4×C53—41no—
253C2×C4×C53—21no—
254C2×C4×C53—21no—
255C2×C4×C53—21no—
256C2×C4×C53—21no—
257C2×C4×C53—22no—
258C2×C4×C53—41no—
259C2×C4×C53—41no—
260C2×C4×C53—41no—
261C2×C4×C53—41no—
262C2×C4×C53—41no—
263C2×C4×C53—41no—
264C2×C4×C53—41no—
265C2×C4×C53—41no—
266C2×C4×C53—84no—
267C2×C4×C53#12112yes—
268C2×C4×C53#12112yes—
269C2×C4×C53C23×C411yescharacteristic
270C2×C4×C53C22×D411yescharacteristic
271C2×C4×C53C2×#4111yescharacteristic
272C2×C4×C53C2×#4111yescharacteristic
273C2×C4×C53C2×#4111yescharacteristic
274C2×C4×C53C2×#4111yescharacteristic
275C22⋊D53—48no—
276C2×Dic53—21no—
277C2×Dic53—21no—
278C2×Dic53—22no—
279C2×Dic53—22no—
280C2×Dic53—21no—
281C2×Dic53—21no—
282C2×Dic53—21no—
283C2×Dic53—21no—
284C2×Dic53—21no—
285C2×Dic53—21no—
286C2×Dic53—41no—
287C2×Dic53—41no—
288C2×Dic53—41no—
289C2×Dic53—41no—
290C2×Dic53—41no—
291C2×Dic53—41no—
292C2×Dic53—41no—
293C2×Dic53—41no—
294C2×Dic53—41no—
295C2×Dic53—41no—
296C2×Dic53C4×D412yes—
297C4×D53—22no—
298C4×D53—22no—
299C4×D53—22no—
300C4×D53—22no—
301C4×D53—44no—
302C4×D53—44no—
303C8×C53—22no—
304C8×C53C4×D414yescomplemented
305#88322—22no—
306#88322—22no—
307#21528—531nomaximal, Sylow
308C22×C53—42no—
309C22×C53—42no—
310C22×C53—42no—
311C22×C53—81no—
312C22×C53—81no—
313C22×C53—81no—
314C22×C53—81no—
315C22×C53C2×C4×D411yescharacteristic
316C22×C53C2×#12111yescharacteristic
317C22×C53#53211yescharacteristic
318C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
319C22×C53C2×#13711yescharacteristic
320C22×C53#57511yescharacteristic
321C22×C53#57511yescharacteristic
322C2×D53—22no—
323C2×D53—22no—
324C2×D53—22no—
325C2×D53—22no—
326C2×D53—22no—
327C2×D53—22no—
328C2×D53#44014yescomplemented
329C4×C53—22no—
330C4×C53—22no—
331C4×C53—42no—
332C4×C53—81no—
333C4×C53—81no—
334C4×C53C2×C4×D411yescharacteristic
335C4×C53C4×#4111yescharacteristic
336C4×C53#52511yescharacteristic
337C4×C53#52911yescharacteristic
338Dic53—22no—
339Dic53—42no—
340Dic53—42no—
341Dic53—41no—
342Dic53—41no—
343Dic53—81no—
344Dic53—81no—
345C2×#465—531no—
346C2×#440D5311yescharacteristic, complemented
347C22×#97—531no—
348C4×C22⋊Q8—531no—
349C4×#121—531no—
350#1973—531no—
351#1944—531no—
352#1936—531no—
353#1935—531no—
354#1893—531no—
355#1892—531no—
356#1808—531no—
357#1776—531no—
358#1763—531no—
359#1762—531no—
360C2×C53—82no—
361C2×C53C4×#12111yescharacteristic
362C2×C53C2×#44011yescharacteristic
363C2×C53#294311yescharacteristic
364C2×C53#305511yescharacteristic
365C2×C53#305611yescharacteristic
366C2×C53#318011yescharacteristic
367C2×C53#318111yescharacteristic
368D53—24no—
369C22×SD16C2×D5311yescharacteristic
370C23×C8—531no—
371C23×C8—531no—
372C2×C22⋊Q8—531no—
373C2×#121—531no—
374C2×C4×Q8C2×D5311yescharacteristic
375C2×C4×D4—1061no—
376C2×C4×D4C2×D5311yescharacteristic
377C22×C42—531no—
378#465—538no—
379#440—24no—
380C2×#107—531no—
381C2×#107C2×D5311yescharacteristic
382C2×#106—531no—
383C2×#103—531no—
384C2×#103—531no—
385C2×#103C2×D5311yescharacteristic
386C2×#102—531no—
387C2×#102—531no—
388C2×#102C2×D5311yescharacteristic
389C2×#97—531no—
390C2×#97—531no—
391C2×#97—531no—
392C2×#97—1064no—
393C2×#97C2×D5311yescharacteristic
394#391—531no—
395#390—531no—
396#389—531no—
397#389—531no—
398#388—1061no—
399#387—1061no—
400#386—1061no—
401#385—1061no—
402#380—531no—
403#380—531no—
404C4×C4⋊C4—531no—
405C4×C4⋊C4—531no—
406C4×C4⋊C4—1061no—
407C4×C22⋊C4—1061no—
408C4×C22⋊C4—1061no—
409#340—531no—
410#340—531no—
411#340—531no—
412#340—531no—
413#340—531no—
414#340—531no—
415C53#2152811yescharacteristic, complemented, Sylow
416C22×Q8C22×D5311yescharacteristic
417C22×D4—1061no—
418C22×D4C22×D5311yescharacteristic
419C23×C4—21no—
420C23×C4—531no—
421C23×C4—531no—
422C23×C4—531no—
423C2×SD16—22no—
424C2×SD16—22no—
425C2×SD16C4×D5314yescomplemented
426C22×C8—531no—
427C22×C8—531no—
428C22×C8—534no—
429C22×C8—1062no—
430C22×C8—1062no—
431C22×C8—1062no—
432C22×C8—1062no—
433C22×C8—1062no—
434C22×C8C22×D5311yescharacteristic
435C22×C8C22×D5311yescharacteristic
436C22⋊Q8—534no—
437C22⋊Q8—1062no—
438#121—534no—
439#121—1062no—
440C4×Q8—22no—
441C4×Q8—22no—
442C4×D4—22no—
443C4×D4—22no—
444C4×D4—2124no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—531no—
447C2×C4⋊C4—531no—
448C2×C4⋊C4—531no—
449C2×C4⋊C4—531no—
450C2×C4⋊C4—1061no—
451C2×C4⋊C4—1061no—
452C2×C4⋊C4—1061no—
453C2×C4⋊C4C22×D5311yescharacteristic
454C2×C4⋊C4C22×D5311yescharacteristic
455C2×C22⋊C4—21no—
456C2×C22⋊C4—1061no—
457C2×C22⋊C4—1061no—
458C2×C22⋊C4—1061no—
459C2×C22⋊C4—1061no—
460C2×C22⋊C4—1061no—
461C2×C22⋊C4—1061no—
462C2×C42—21no—
463C2×C42—531no—
464C2×C42—531no—
465C2×C42—531no—
466C2×C42—1062no—
467C2×C42—1062no—
468C2×C42—1061no—
469C2×C42—1061no—
470C2×C42C22×D5311yescharacteristic
471#107—22no—
472#107—1062no—
473#106—534no—
474#103—22no—
475#103—534no—
476#103—1062no—
477#102—22no—
478#102—534no—
479#102—1062no—
480#97—1062no—
481#97—1062no—
482#97—1062no—
483#97C22⋊D5314yescomplemented
484#95—1061no—
485#95—1061no—
486#95—1061no—
487#95—1061no—
488#95—1061no—
489#95—1061no—
490#95—1061no—
491#95—1061no—
492C24—21no—
493C24—531no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8C2×C4×D5312yes—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—1064no—
506C2×D4—2122no—
507C2×D4—2122no—
508C2×D4C2×C4×D5312yes—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—531no—
516C22×C4—532no—
517C22×C4—532no—
518C22×C4—531no—
519C22×C4—531no—
520C22×C4—1062no—
521C22×C4—1062no—
522C22×C4—1061no—
523C22×C4—1061no—
524C22×C4—1061no—
525C22×C4—1061no—
526C22×C4—1061no—
527C22×C4—1061no—
528C22×C4—1062no—
529C22×C4—1062no—
530C22×C4—1061no—
531C22×C4—1061no—
532C22×C4—2121no—
533C22×C4—2121no—
534C22×C4D4×D5311yescharacteristic
535C22×C4D4×D5311yescharacteristic
536C22×C4C23×D5311yescharacteristic
537SD16—28no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—532no—
541C2×C8—532no—
542C2×C8—1068no—
543C2×C8—1061no—
544C2×C8—1061no—
545C2×C8—1061no—
546C2×C8—1061no—
547C2×C8—1068no—
548C2×C8C2×C4×D5312yes—
549C2×C8#1171994512yes—
550C2×C8C2×C22⋊D5312yes—
551C2×C8C2×C22⋊D5312yes—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—42no—
557C4⋊C4—532no—
558C4⋊C4—532no—
559C4⋊C4—1064no—
560C4⋊C4—1061no—
561C4⋊C4—1061no—
562C4⋊C4—1061no—
563C4⋊C4—1061no—
564C4⋊C4—1061no—
565C4⋊C4—1061no—
566C4⋊C4—2122no—
567C4⋊C4—2122no—
568C22⋊C4—42no—
569C22⋊C4—1064no—
570C22⋊C4—1064no—
571C22⋊C4—2122no—
572C22⋊C4—2122no—
573C22⋊C4—2122no—
574C22⋊C4—2122no—
575C42—42no—
576C42—1062no—
577C42—1062no—
578C42—1061no—
579C42—1061no—
580C42—2122no—
581C42—2122no—
582C42#1171994712yes—
583C42C2×C22⋊D5312yes—
584C23—22no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—532no—
592C23—532no—
593C23—532no—
594C23—1061no—
595C23—1061no—
596C23—1061no—
597C23—1061no—
598C23C2×D4×D5311yescharacteristic
599Q8—22no—
600Q8—22no—
601Q8—41no—
602Q8—41no—
603D4—22no—
604D4—22no—
605D4—41no—
606D4—41no—
607D4—2128no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—22no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—84no—
622C2×C4—532no—
623C2×C4—1061no—
624C2×C4—1061no—
625C2×C4—1062no—
626C2×C4—1062no—
627C2×C4—1062no—
628C2×C4—1062no—
629C2×C4—1062no—
630C2×C4—1062no—
631C2×C4—1061no—
632C2×C4—1061no—
633C2×C4—1061no—
634C2×C4—1061no—
635C2×C4—1061no—
636C2×C4—1061no—
637C2×C4—2124no—
638C2×C4—2124no—
639C2×C4—2121no—
640C2×C4—2121no—
641C2×C4—2121no—
642C2×C4—2121no—
643C2×C4—2121no—
644C2×C4—2121no—
645C2×C4—2121no—
646C2×C4—2121no—
647C2×C4—2121no—
648C2×C4—2121no—
649C2×C4#1313318812yes—
650C2×C4#1313318812yes—
651C2×C4C22×C4×D5311yescharacteristic
652C2×C4C22×C22⋊D5311yescharacteristic
653C2×C4#41×D5311yescharacteristic
654C2×C4#41×D5311yescharacteristic
655C2×C4C2×#1171994711yescharacteristic
656C2×C4C2×#1171994511yescharacteristic
657C8—22no—
658C8—1062no—
659C8—1062no—
660C8C4×C22⋊D5314yescomplemented
661C22—42no—
662C22—42no—
663C22—42no—
664C22—81no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—534no—
669C22—1062no—
670C22—1062no—
671C22—1062no—
672C22—1062no—
673C22—1062no—
674C22—1062no—
675C22C4×D4×D5311yescharacteristic
676C22C2×#1313318811yescharacteristic
677C22#1681117011yescharacteristic
678C22AGL(1,ℤ/8)×D5311yescharacteristic
679C22#137×D5311yescharacteristic
680C22#1681141911yescharacteristic
681C22#1681142211yescharacteristic
682C4—22no—
683C4—22no—
684C4—42no—
685C4—81no—
686C4—81no—
687C4—1062no—
688C4—4241no—
689C4—4241no—
690C4—2122no—
691C4—2122no—
692C4—2121no—
693C4—2121no—
694C4C2×C4×C22⋊D5311yescharacteristic
695C4C4×#1171994711yescharacteristic
696C4#1681113011yescharacteristic
697C4#1681115511yescharacteristic
698C2—82no—
699C2—1064no—
700C2C4×#1313318811yescharacteristic
701C2#440×D5311yescharacteristic
702C2#2028351011yescharacteristic
703C2#2028432811yescharacteristic
704C2#2028433911yescharacteristic
705C2#2028540911yescharacteristic
706C2#2028542011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#440C2
socleC23×C53C22×D4
prime radicalC2×#13133188C22
cosocleC22×C4×C53C24
hypercenterC2×#440D53
hypocenterC53#21528
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. C2×#97×D53C2semidirect
3. C4×#13133193C2semidirect
5. #20275598C2semidirect
6. #20275456C2semidirect
7. #20275409C2semidirect
8. #20275402C2semidirect
10. #20275135C2semidirect
11. #20274741C2semidirect
12. #20274612C2semidirect
13. #20274545C2semidirect
14. #20274540C2semidirect
15. C2×C53×#440C2semidirect
22. #16810849C4semidirect
73. C2×C8×D53C2×C4semidirect
75. #13133193C2×C4semidirect
100. #13133149C2×C4semidirect
102. #13133141C2×C4semidirect
104. #13133138C2×C4semidirect
121. C2×SD16×C53C2×C4semidirect
137. #97×C53D4semidirect
304. C8×C53C4×D4semidirect
328. C2×D53#440semidirect
346. C2×#440D53semidirect
415. C53#21528semidirect
425. C2×SD16C4×D53semidirect
483. #97C22⋊D53semidirect
660. C8C4×C22⋊D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168108492
C2×#97×D532
C4×#131331932
C4×#131331882
#202755982
#202754562
#202754092
#202754022
#202751402
#202751352
#202747412
#202746122
#202745452
#202745402
C2×C53×#4402
#2152853