Finite Group Databasebeta

← #27385238

Subgroups — #27385238

Order 13568.

2230 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M16×D53C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D53C211yesmaximal, characteristic
3C2×#16810587C211yesmaximal, characteristic, complemented
4C2×#16810586C211yesmaximal, characteristic, complemented
5#20275009C214yesmaximal, complemented
6#20275004C214yesmaximal, complemented
7#20274408C211yesmaximal, characteristic, complemented
8#20274408C211yesmaximal, characteristic, complemented
9C2×C53×#407C211yesmaximal, characteristic, complemented
10C23×C22⋊D53C411yescharacteristic
11C23×C4×D53C2211yescharacteristic
12C22×#11719917C2211yescharacteristic
13C22×#11719917C2211yescharacteristic
14C22×#11719912C2212yescomplemented
15C2×M16×D53—24no—
16C2×M16×D53—24no—
17C2×M16×D53—24no—
18C22×C8×D53C2212yescomplemented
19C2×C4×C22⋊D53—24no—
20C2×C4×C22⋊D53—24no—
21C2×C4×C22⋊D53C412yes—
22C2×C4×C22⋊D53C412yes—
23C2×C4×C22⋊D53C2212yes—
24C2×C4×C22⋊D53C2212yes—
25C22×#11719919C411yescharacteristic
26C22×C22⋊Dic53C411yescharacteristic
27C22×#11719921C411yescharacteristic
28C22×C4×Dic53C2211yescharacteristic
29#16810587—24no—
30#16810586—24no—
31C2×C22⋊#88322C2214yescomplemented
32C2×#13133129C2212yescomplemented
33C2×#13133129C2212yescomplemented
34#16810377C2214yescomplemented
35#16810377C2214yescomplemented
36C24×C4×C53C2211yescharacteristic
37C22×M16×C53C2211yescharacteristic
38C22×M16×C53C2211yescharacteristic
39C53×#407—24no—
40C2×C22⋊C8×C53C2214yescomplemented
41C24×D53C2×C411yescharacteristic
42C22×C22⋊D53—24no—
43C22×C22⋊D53—28no—
44C22×C22⋊D53C2×C412yes—
45C22×C22⋊D53C2×C412yes—
46C23×Dic53C2×C411yescharacteristic
47C23×Dic53C2×C411yescharacteristic
48C23×Dic53C2×C411yescharacteristic
49C22×C4×D53—22no—
50C22×C4×D53—22no—
51C22×C4×D53—22no—
52C22×C4×D53—22no—
53C22×C4×D53C2×C411yescharacteristic
54C22×C4×D53C2×C411yescharacteristic
55C22×C4×D53D414yes—
56C22×C4×D53D414yes—
57C22×C4×D53C2311yescharacteristic
58C22×C4×D53C2311yescharacteristic
59C2×#11719917—22no—
60C2×#11719917—22no—
61C2×#11719917—22no—
62C2×#11719917—22no—
63C2×#11719917—22no—
64C2×#11719917D414yescomplemented
65C2×#11719912—24no—
66C2×#11719912—24no—
67C2×#11719912—24no—
68M16×D53—232no—
69C22×#88322C2312yes—
70C22×#88322C2312yes—
71C2×C8×D53—24no—
72C2×C8×D53—24no—
73C2×C8×D53—24no—
74C4×C22⋊D53—28no—
75C4×C22⋊D53—28no—
76C4×C22⋊D53—24no—
77C4×C22⋊D53—24no—
78C4×C22⋊D53—24no—
79C4×C22⋊D53—24no—
80C2×#11719919—24no—
81C2×#11719919C2×C412yes—
82C2×#11719919C2×C412yes—
83C2×C22⋊Dic53—24no—
84C2×C22⋊Dic53C2×C412yes—
85C2×C22⋊Dic53C2×C412yes—
86C2×#11719921—24no—
87C2×#11719921C2×C412yes—
88C2×#11719921C2×C412yes—
89C2×C4×Dic53—22no—
90C2×C4×Dic53—22no—
91C2×C4×Dic53C2×C412yes—
92C2×C4×Dic53C2312yes—
93C22⋊#88322—28no—
94#13133129—24no—
95#13133129—24no—
96C25×C53C2×C411yescharacteristic
97C23×C4×C53—22no—
98C23×C4×C53—22no—
99C23×C4×C53—22no—
100C23×C4×C53—22no—
101C23×C4×C53—22no—
102C23×C4×C53—22no—
103C23×C4×C53C2×C411yescharacteristic
104C23×C4×C53C2×C412yes—
105C23×C4×C53C2312yes—
106C23×C4×C53C2311yescharacteristic
107C2×M16×C53—22no—
108C2×M16×C53—22no—
109C2×M16×C53—22no—
110C2×M16×C53—22no—
111C2×M16×C53—22no—
112C2×M16×C53D414yescomplemented
113C22×C8×C53C2312yes—
114C22×C8×C53C2312yes—
115C22⋊C8×C53—28no—
116C24×C53—22no—
117C24×C53—24no—
118C24×C53—22no—
119C24×C53—22no—
120C24×C53—42no—
121C24×C53C22×C412yes—
122C24×C53C22×C411yescharacteristic
123C23×D53—22no—
124C23×D53—22no—
125C23×D53—24no—
126C23×D53—42no—
127C23×D53C22⋊C414yes—
128C23×D53C22×C411yescharacteristic
129C23×D53C22×C411yescharacteristic
130C22×C4×C53—22no—
131C22×C4×C53—22no—
132C22×C4×C53—22no—
133C22×C4×C53—24no—
134C22×C4×C53—24no—
135C22×C4×C53—24no—
136C22×C4×C53—22no—
137C22×C4×C53—22no—
138C22×C4×C53—22no—
139C22×C4×C53—22no—
140C22×C4×C53—22no—
141C22×C4×C53—22no—
142C22×C4×C53—44no—
143C22×C4×C53—44no—
144C22×C4×C53—44no—
145C22×C4×C53—44no—
146C22×C4×C53C22×C412yes—
147C22×C4×C53C22×C411yescharacteristic
148C22×C4×C53C2×D412yes—
149C22×C4×C53C2×D412yes—
150C22×C4×C53C2×D412yes—
151C22×C4×C53C2×D412yes—
152C22×C4×C53#4112yes—
153C22×C4×C53#4112yes—
154C22×C4×C53C2411yescharacteristic
155C2×C22⋊D53—232no—
156C2×C22⋊D53—24no—
157C2×C22⋊D53—24no—
158C2×C22⋊D53—24no—
159C2×C22⋊D53—24no—
160C2×C22⋊D53—24no—
161C2×C22⋊D53M1618yescomplemented
162C22×Dic53—22no—
163C22×Dic53—22no—
164C22×Dic53—22no—
165C22×Dic53—24no—
166C22×Dic53—22no—
167C22×Dic53—42no—
168C22×Dic53C22⋊C414yes—
169C22×Dic53C22×C412yes—
170C22×Dic53C22×C411yescharacteristic
171C22×Dic53C22×C411yescharacteristic
172C22×Dic53C22×C412yes—
173C2×C4×D53—22no—
174C2×C4×D53—22no—
175C2×C4×D53—22no—
176C2×C4×D53—22no—
177C2×C4×D53—28no—
178C2×C4×D53—28no—
179C2×C4×D53—28no—
180C2×C4×D53—28no—
181C2×C4×D53—21no—
182C2×C4×D53—21no—
183C2×C4×D53—21no—
184C2×C4×D53—21no—
185C2×C4×D53—21no—
186C2×C4×D53—21no—
187C2×C4×D53—21no—
188C2×C4×D53—21no—
189C2×C4×D53C22⋊C414yes—
190C2×C4×D53C22⋊C414yes—
191C2×C4×D53C2×D412yes—
192C2×C4×D53C2×D412yes—
193C2×C4×D53C2×D412yes—
194C2×C4×D53C2×D412yes—
195M16×C53—28no—
196M16×C53—44no—
197C2×C8×C53—22no—
198C2×C8×C53—22no—
199C2×C8×C53—22no—
200C2×C8×C53—22no—
201C2×C8×C53—22no—
202C2×C8×C53C2×D414yescomplemented
203C22⋊Dic53—24no—
204C22⋊Dic53—24no—
205#11719921—24no—
206#11719921—24no—
207#11719919—24no—
208#11719919—24no—
209C4×Dic53—24no—
210C4×Dic53—22no—
211C4×Dic53—22no—
212#11719917—28no—
213#11719917—44no—
214C2×#88322—22no—
215C2×#88322—22no—
216C2×#88322—22no—
217C2×#88322—22no—
218C2×#88322—22no—
219C2×#88322C2×D414yescomplemented
220#11719912—216no—
221C8×D53—216no—
222C23×C53—22no—
223C23×C53—22no—
224C23×C53—28no—
225C23×C53—22no—
226C23×C53—22no—
227C23×C53—22no—
228C23×C53—22no—
229C23×C53—22no—
230C23×C53—22no—
231C23×C53—48no—
232C23×C53—48no—
233C23×C53—44no—
234C23×C53—44no—
235C23×C53C2×C22⋊C412yes—
236C23×C53C4×D412yes—
237C23×C53C4×D412yes—
238C23×C53C2×M1614yescomplemented
239C23×C53C23×C411yescharacteristic
240C22×D53—21no—
241C22×D53—21no—
242C22×D53—22no—
243C22×D53—21no—
244C22×D53—21no—
245C22×D53—22no—
246C22×D53—22no—
247C22×D53—28no—
248C22×D53—28no—
249C22×D53—44no—
250C22×D53—48no—
251C22×D53—48no—
252C22×D53C2×C22⋊C412yes—
253C22×D53C2×C22⋊C412yes—
254C22×D53C2×M1614yes—
255C2×C4×C53—22no—
256C2×C4×C53—22no—
257C2×C4×C53—22no—
258C2×C4×C53—44no—
259C2×C4×C53—42no—
260C2×C4×C53—42no—
261C2×C4×C53—42no—
262C2×C4×C53—42no—
263C2×C4×C53—48no—
264C2×C4×C53C2×C22⋊C412yes—
265C2×C4×C53C4×D412yes—
266C2×C4×C53C4×D412yes—
267C2×C4×C53#12014yes—
268C2×C4×C53#12114yes—
269C2×C4×C53#12114yes—
270C2×C4×C53#12314yes—
271C2×C4×C53C22×D411yescharacteristic
272C2×C4×C53C22×D411yescharacteristic
273C2×C4×C53C22×D411yescharacteristic
274C2×C4×C53C22×D411yescharacteristic
275C2×C4×C53C2×#4111yescharacteristic
276C2×C4×C53C2×#4111yescharacteristic
277C22⋊D53—216no—
278C22⋊D53—216no—
279C2×Dic53—28no—
280C2×Dic53—22no—
281C2×Dic53—21no—
282C2×Dic53—21no—
283C2×Dic53—21no—
284C2×Dic53—21no—
285C2×Dic53—22no—
286C2×Dic53—28no—
287C2×Dic53—22no—
288C2×Dic53—24no—
289C2×Dic53—44no—
290C2×Dic53C2×C22⋊C412yes—
291C2×Dic53C2×C22⋊C412yes—
292C2×Dic53C2×M1614yescomplemented
293C4×D53—22no—
294C4×D53—22no—
295C4×D53—22no—
296C4×D53—22no—
297C4×D53—22no—
298C4×D53—22no—
299C4×D53—22no—
300C4×D53—22no—
301C4×D53—28no—
302C4×D53—28no—
303C8×C53—24no—
304C8×C53—42no—
305#88322—24no—
306#88322—42no—
307#20898—531nomaximal, Sylow
308C22×C53—22no—
309C22×C53—22no—
310C22×C53—24no—
311C22×C53—24no—
312C22×C53—24no—
313C22×C53—24no—
314C22×C53—24no—
315C22×C53—416no—
316C22×C53—42no—
317C22×C53—42no—
318C22×C53—42no—
319C22×C53—42no—
320C22×C53#38614yes—
321C22×C53C22×C22⋊C411yescharacteristic
322C22×C53C2×C4×D411yescharacteristic
323C22×C53C2×C4×D411yescharacteristic
324C22×C53C22×M1612yes—
325C22×C53#56812yes—
326C2×D53—22no—
327C2×D53—24no—
328C2×D53—24no—
329C2×D53—22no—
330C2×D53—22no—
331C2×D53—22no—
332C2×D53—22no—
333C2×D53—416no—
334C2×D53—42no—
335C2×D53—42no—
336C2×D53#40714yescomplemented
337C4×C53—42no—
338C4×C53#38614yes—
339C4×C53C2×#12011yescharacteristic
340C4×C53C2×#12111yescharacteristic
341C4×C53C2×#12111yescharacteristic
342C4×C53C2×#12311yescharacteristic
343Dic53—24no—
344Dic53—22no—
345Dic53—22no—
346Dic53—42no—
347C23×M16—531no—
348C22×C4×D4—531no—
349C2×#407—531no—
350C2×#407—531no—
351C2×#407D5311yescharacteristic, complemented
352#1870—534no—
353#1869—534no—
354#1728—531no—
355#1728—531no—
356C2×C53—24no—
357C2×C53—44no—
358C2×C53C2×#38611yescharacteristic
359C2×C53C2×#40711yescharacteristic
360C2×C53#287911yescharacteristic
361C2×C53D4×M1612yes—
362C2×C53D4×M1612yes—
363D53—24no—
364D53—42no—
365C23×D4—531no—
366C24×C4—531no—
367C24×C4C2×D5311yescharacteristic
368C22×M16—531no—
369C22×M16—531no—
370C22×M16—532no—
371C22×M16—1064no—
372C22×M16—1064no—
373C22×M16—1064no—
374C22×M16C2×D5311yescharacteristic
375C22×M16C2×D5311yescharacteristic
376C23×C8—532no—
377C2×C4×D4—532no—
378C2×C4×D4—532no—
379C2×C4×D4—532no—
380C2×C4×D4—532no—
381C2×C4×D4—1064no—
382C2×C4×D4—1064no—
383C22×C4⋊C4—531no—
384C22×C22⋊C4—531no—
385C22×C22⋊C4—531no—
386C22×C42—531no—
387#407—24no—
388#407—1064no—
389#407—1064no—
390C2×C22⋊C8—534no—
391C2×C22⋊C8—532no—
392C2×C22⋊C8—532no—
393C2×C22⋊C8C2×D5314yescomplemented
394#336—534no—
395#336—534no—
396C53#2089811yescharacteristic, complemented, Sylow
397C25—531no—
398C25C4×D5311yescharacteristic
399C22×D4—532no—
400C22×D4—532no—
401C22×D4—1068no—
402C22×D4—1064no—
403C23×C4—22no—
404C23×C4—22no—
405C23×C4—22no—
406C23×C4—22no—
407C23×C4—22no—
408C23×C4—22no—
409C23×C4—531no—
410C23×C4—531no—
411C23×C4—531no—
412C23×C4—534no—
413C23×C4—534no—
414C23×C4—531no—
415C23×C4—531no—
416C23×C4—531no—
417C23×C4—531no—
418C23×C4—1062no—
419C23×C4—1062no—
420C23×C4—1062no—
421C23×C4—1062no—
422C23×C4C4×D5311yescharacteristic
423C23×C4C4×D5312yes—
424C23×C4C22×D5312yes—
425C23×C4C22×D5311yescharacteristic
426C2×M16—22no—
427C2×M16—22no—
428C2×M16—22no—
429C2×M16—22no—
430C2×M16—22no—
431C2×M16—534no—
432C2×M16—1064no—
433C2×M16—1064no—
434C2×M16—10632no—
435C2×M16—1062no—
436C2×M16—1062no—
437C2×M16—1062no—
438C2×M16—1062no—
439C2×M16—1062no—
440C2×M16—1064no—
441C2×M16C22⋊D5314yescomplemented
442C22×C8—532no—
443C22×C8—532no—
444C22×C8—1064no—
445C22×C8—1064no—
446C22×C8—1064no—
447C22×C8C22×D5312yes—
448C22×C8C22×D5312yes—
449C4×D4—1068no—
450C4×D4—1068no—
451C4×D4—1064no—
452C4×D4—1064no—
453C4×D4—1064no—
454C4×D4—1064no—
455C2×C4⋊C4—532no—
456C2×C4⋊C4—532no—
457C2×C4⋊C4—1064no—
458C2×C22⋊C4—532no—
459C2×C22⋊C4—532no—
460C2×C22⋊C4—532no—
461C2×C22⋊C4—532no—
462C2×C22⋊C4—1064no—
463C2×C22⋊C4—1064no—
464C2×C42—532no—
465C2×C42—532no—
466C2×C42—1062no—
467C2×C42—1062no—
468C22⋊C8—28no—
469C22⋊C8—1064no—
470C22⋊C8—1064no—
471C22⋊C8—1068no—
472C24—22no—
473C24—24no—
474C24—22no—
475C24—22no—
476C24—42no—
477C24—531no—
478C24—531no—
479C24—534no—
480C24—1064no—
481C24—1062no—
482C24—1062no—
483C24—2122no—
484C24C2×C4×D5312yes—
485C24C2×C4×D5311yescharacteristic
486C2×D4—538no—
487C2×D4—1064no—
488C2×D4—1064no—
489C2×D4—1064no—
490C2×D4—1064no—
491C2×D4—10632no—
492C2×D4—1064no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—44no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4—534no—
510C22×C4—532no—
511C22×C4—531no—
512C22×C4—531no—
513C22×C4—534no—
514C22×C4—534no—
515C22×C4—532no—
516C22×C4—532no—
517C22×C4—532no—
518C22×C4—532no—
519C22×C4—532no—
520C22×C4—1064no—
521C22×C4—1062no—
522C22×C4—1062no—
523C22×C4—1062no—
524C22×C4—1062no—
525C22×C4—1062no—
526C22×C4—1062no—
527C22×C4—1062no—
528C22×C4—1068no—
529C22×C4—1068no—
530C22×C4—1068no—
531C22×C4—1068no—
532C22×C4—1061no—
533C22×C4—1061no—
534C22×C4—1061no—
535C22×C4—1061no—
536C22×C4—1061no—
537C22×C4—1061no—
538C22×C4—1061no—
539C22×C4—1061no—
540C22×C4—1062no—
541C22×C4—2122no—
542C22×C4C2×C4×D5312yes—
543C22×C4C2×C4×D5311yescharacteristic
544C22×C4#1171994512yes—
545C22×C4D4×D5312yes—
546C22×C4D4×D5312yes—
547C22×C4D4×D5312yes—
548C22×C4#1171994712yes—
549C22×C4C2×C22⋊D5312yes—
550C22×C4C23×D5311yescharacteristic
551M16—28no—
552M16—44no—
553M16—10616no—
554M16—1068no—
555M16—2124no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—534no—
562C2×C8—10616no—
563C2×C8—1062no—
564C2×C8—1062no—
565C2×C8—1062no—
566C2×C8—1062no—
567C2×C8—1062no—
568C2×C8C2×C22⋊D5314yescomplemented
569C4⋊C4—1064no—
570C4⋊C4—1064no—
571C22⋊C4—1064no—
572C22⋊C4—1064no—
573C22⋊C4—1064no—
574C22⋊C4—1064no—
575C42—1064no—
576C42—1062no—
577C42—1062no—
578C23—22no—
579C23—22no—
580C23—28no—
581C23—22no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—48no—
588C23—48no—
589C23—44no—
590C23—44no—
591C23—532no—
592C23—534no—
593C23—532no—
594C23—1068no—
595C23—1061no—
596C23—1061no—
597C23—1062no—
598C23—1068no—
599C23—1061no—
600C23—1061no—
601C23—1062no—
602C23—1062no—
603C23—2124no—
604C23—2128no—
605C23—2128no—
606C23C22⋊C4×D5312yes—
607C23#1313317712yes—
608C23C4×C22⋊D5312yes—
609C23M16×D5314yescomplemented
610C23C22×C4×D5311yescharacteristic
611D4—10616no—
612D4—10616no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—44no—
617C2×C4—48no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—532no—
623C2×C4—532no—
624C2×C4—534no—
625C2×C4—1068no—
626C2×C4—1068no—
627C2×C4—1062no—
628C2×C4—1061no—
629C2×C4—1061no—
630C2×C4—1061no—
631C2×C4—1061no—
632C2×C4—1062no—
633C2×C4—1068no—
634C2×C4—1068no—
635C2×C4—1062no—
636C2×C4—1062no—
637C2×C4—1062no—
638C2×C4—1062no—
639C2×C4—1062no—
640C2×C4—1062no—
641C2×C4—1062no—
642C2×C4—1062no—
643C2×C4—1062no—
644C2×C4—1064no—
645C2×C4—2124no—
646C2×C4C22⋊C4×D5312yes—
647C2×C4#1313317712yes—
648C2×C4C4×C22⋊D5312yes—
649C2×C4#1313318514yes—
650C2×C4#1313318814yes—
651C2×C4#1313319014yes—
652C2×C4#1313319914yes—
653C2×C4C2×D4×D5311yescharacteristic
654C2×C4C2×D4×D5311yescharacteristic
655C2×C4C2×D4×D5311yescharacteristic
656C2×C4C22×C22⋊D5311yescharacteristic
657C2×C4C2×#1171994711yescharacteristic
658C2×C4C2×#1171994511yescharacteristic
659C8—24no—
660C8—42no—
661C8—1064no—
662C8—2122no—
663C22—22no—
664C22—22no—
665C22—24no—
666C22—24no—
667C22—24no—
668C22—24no—
669C22—24no—
670C22—416no—
671C22—42no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—534no—
676C22—1062no—
677C22—1064no—
678C22—1064no—
679C22—1062no—
680C22—1062no—
681C22—1062no—
682C22—1062no—
683C22—21216no—
684C22—2122no—
685C22—2122no—
686C22#1681049914yes—
687C22C2×C22⋊C4×D5311yescharacteristic
688C22C2×#1313317711yescharacteristic
689C22C2×C4×C22⋊D5311yescharacteristic
690C22C2×M16×D5312yes—
691C22#1681138912yes—
692C4—42no—
693C4—1064no—
694C4—1062no—
695C4—1062no—
696C4—2122no—
697C4#1681049914yes—
698C4C2×#1313318511yescharacteristic
699C4C2×#1313318811yescharacteristic
700C4C2×#1313319011yescharacteristic
701C4C2×#1313319911yescharacteristic
702C2—24no—
703C2—44no—
704C2—1064no—
705C2—2122no—
706C2C2×#1681049911yescharacteristic
707C2#407×D5311yescharacteristic
708C2#2028315811yescharacteristic
709C2#2028344712yes—
710C2M16×C22⋊D5312yes—
subgroupG/H
center, FrattiniC22×C4C23×D53
commutator, socleC23×C53C23×C4
FittingC2×C53×#407C2
prime radicalC23×C22⋊D53C4
cosocleC22×C4×C53C24
hypercenterC2×#407D53
hypocenterC53#20898
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
1. C22×M16×D53C2semidirect
3. C2×#16810587C2semidirect
4. C2×#16810586C2semidirect
5. #20275009C2semidirect
6. #20275004C2semidirect
7. #20274408C2semidirect
8. #20274408C2semidirect
9. C2×C53×#407C2semidirect
14. C22×#11719912C22semidirect
18. C22×C8×D53C22semidirect
31. C2×C22⋊#88322C22semidirect
32. C2×#13133129C22semidirect
33. C2×#13133129C22semidirect
34. #16810377C22semidirect
35. #16810377C22semidirect
40. C2×C22⋊C8×C53C22semidirect
64. C2×#11719917D4semidirect
112. C2×M16×C53D4semidirect
161. C2×C22⋊D53M16semidirect
202. C2×C8×C53C2×D4semidirect
219. C2×#88322C2×D4semidirect
238. C23×C53C2×M16semidirect
292. C2×Dic53C2×M16semidirect
336. C2×D53#407semidirect
351. C2×#407D53semidirect
393. C2×C22⋊C8C2×D53semidirect
396. C53#20898semidirect
441. C2×M16C22⋊D53semidirect
568. C2×C8C2×C22⋊D53semidirect
609. C23M16×D53semidirect

Maximal subgroups

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

subgroupindex
C22×M16×D532
C22×C4×C22⋊D532
C2×#168105872
C2×#168105862
#202750092
#202750042
#202744082
C2×C53×#4072
#2089853