Finite Group Databasebeta

← #27390666

Subgroups — #27390666

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×#16810854C211yesmaximal, characteristic
2C2×#16810726C211yesmaximal, characteristic, complemented
3C22×#13133127C211yesmaximal, characteristic, complemented
4C22⋊Q8×Dic53C211yesmaximal, characteristic, complemented
5#20277221C211yesmaximal, characteristic
6#20275593C211yesmaximal, characteristic, complemented
7#20275457C211yesmaximal, characteristic, complemented
8#20275413C211yesmaximal, characteristic, complemented
9#20275402C211yesmaximal, characteristic, complemented
10#20275143C211yesmaximal, characteristic
11#20274742C211yesmaximal, characteristic, complemented
12#20274611C211yesmaximal, characteristic, complemented
13#20274547C211yesmaximal, characteristic, complemented
14#20274539C211yesmaximal, characteristic, complemented
15C53×#1892C211yesmaximal, characteristic, complemented
16C22×#11719924C2211yescharacteristic
17C23×#88322C2211yescharacteristic
18C2×#13133191C2211yescharacteristic
19C2×Q8×Dic53C2211yescharacteristic
20C2×#13133179C2211yescharacteristic
21C2×#13133177—21no—
22C22×C4×Dic53C2211yescharacteristic
23#16810854C418yescomplemented
24#16810726—24no—
25C2×#13133150C2211yescharacteristic
26C2×#13133150C2211yescharacteristic
27C2×#13133148C2211yescharacteristic
28C2×#13133141C2211yescharacteristic
29C2×#13133139C2211yescharacteristic
30C2×#13133139C2211yescharacteristic
31C2×#13133137C2211yescharacteristic
32C2×#13133127—24no—
33C2×#13133127C2211yescharacteristic
34C2×#13133127C2211yescharacteristic
35C2×#13133127C2211yescharacteristic
36C2×#13133127C2211yescharacteristic
37#16810530C2211yescharacteristic
38#16810524C2211yescharacteristic
39#16810522C2211yescharacteristic
40#16810519C2211yescharacteristic
41#16810512—21no—
42#16810509—21no—
43#16810500—21no—
44#16810498—21no—
45#16810483C2211yescharacteristic
46C4⋊C4×Dic53—21no—
47C4⋊C4×Dic53C2211yescharacteristic
48C4⋊C4×Dic53C2211yescharacteristic
49C22⋊C4×Dic53—21no—
50#16810470—21no—
51#16810386C2211yescharacteristic
52#16810386C2211yescharacteristic
53#16810385C2211yescharacteristic
54#16810385C2211yescharacteristic
55C23×C8×C53C2211yescharacteristic
56C2×C22⋊Q8×C53C2211yescharacteristic
57C2×#103×C53C2211yescharacteristic
58C2×#103×C53C2211yescharacteristic
59C53×#380C2211yescharacteristic
60C53×#340C2211yescharacteristic
61C53×#340C2211yescharacteristic
62C22×D212C2311yescharacteristic
63C22×C22⋊D53—21no—
64C23×Dic53D411yescharacteristic
65C23×Dic53D411yescharacteristic
66C22×C4×D53—21no—
67C2×#11719924—22no—
68C2×#11719924—22no—
69C2×#11719924C2×C414yescomplemented
70C22×#88322—22no—
71C22×#88322—22no—
72C22×#88322C2×C414yescomplemented
73C22×#88322C2311yescharacteristic
74C22×#88322C2311yescharacteristic
75#13133191—22no—
76#13133191C2×C414yes—
77Q8×Dic53—22no—
78Q8×Dic53—22no—
79#13133179—22no—
80#13133179—22no—
81#13133177—44no—
82C2×C4⋊Dic53—21no—
83C2×C4⋊Dic53—21no—
84C2×C4⋊Dic53C2311yescharacteristic
85C2×C4⋊Dic53C2311yescharacteristic
86C2×C4⋊Dic53C2311yescharacteristic
87C2×#11719919—21no—
88C2×C22⋊Dic53—21no—
89C2×#11719921—21no—
90C2×#11719921—21no—
91C2×#11719921—21no—
92C2×#11719921—21no—
93C2×C4×Dic53—22no—
94C2×C4×Dic53—22no—
95C2×C4×Dic53—21no—
96C2×C4×Dic53—21no—
97C2×C4×Dic53—21no—
98C2×C4×Dic53D411yescharacteristic
99C2×C4×Dic53D411yescharacteristic
100C2×C4×Dic53C2311yescharacteristic
101C2×C4×Dic53C2311yescharacteristic
102#13133150—22no—
103#13133150—22no—
104#13133148C2×C414yescomplemented
105#13133141C2×C414yescomplemented
106#13133139—22no—
107#13133139—22no—
108#13133137C2×C414yescomplemented
109#13133127—22no—
110#13133127—22no—
111#13133127—22no—
112#13133127D414yescomplemented
113#13133124—21no—
114#13133124—21no—
115#13133124—21no—
116#13133124—21no—
117#13133124—21no—
118#13133124—21no—
119#13133124—21no—
120C22×Q8×C53C2311yescharacteristic
121C23×C4×C53C2311yescharacteristic
122C22×C8×C53—22no—
123C22×C8×C53—22no—
124C22×C8×C53—22no—
125C22×C8×C53C2311yescharacteristic
126C22×C8×C53C2311yescharacteristic
127C22⋊Q8×C53—22no—
128C22⋊Q8×C53C2×C414yescomplemented
129C2×C4⋊C4×C53—21no—
130C2×C4⋊C4×C53C2311yescharacteristic
131C2×C4⋊C4×C53C2311yescharacteristic
132C2×C4⋊C4×C53C2311yescharacteristic
133C2×C22⋊C4×C53—21no—
134C2×C22⋊C4×C53—21no—
135#103×C53—22no—
136#103×C53—22no—
137#95×C53—21no—
138C24×C53C2×D411yescharacteristic
139C23×D53—21no—
140C2×Q8×C53—21no—
141C2×Q8×C53—21no—
142C2×Q8×C53—21no—
143C2×Q8×C53—21no—
144C2×Q8×C53—21no—
145C2×Q8×C53C22×C412yes—
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×C53#4112yes—
157C22×C4×C53C2411yescharacteristic
158C2×C22⋊D53—24no—
159C2×C22⋊D53—42no—
160C2×C22⋊D53—42no—
161C22×Dic53—22no—
162C22×Dic53—22no—
163C22×Dic53—21no—
164C22×Dic53—22no—
165C22×Dic53—22no—
166C22×Dic53—21no—
167C22×Dic53—21no—
168C22×Dic53—41no—
169C22×Dic53—41no—
170C22×Dic53C2×D411yescharacteristic
171C22×Dic53C2×D411yescharacteristic
172C22×Dic53C2×D411yescharacteristic
173C22×Dic53C2×D411yescharacteristic
174C2×D212—21no—
175C2×D212—21no—
176C2×D212—21no—
177C2×D212—21no—
178C2×D212—21no—
179C2×D212C22×C412yes—
180C2×C4×D53—42no—
181C2×C4×D53—42no—
182C2×C4×D53—42no—
183C2×C8×C53—28no—
184C2×C8×C53—21no—
185C2×C8×C53—21no—
186C2×C8×C53—21no—
187C2×C8×C53—21no—
188C2×C8×C53C2×D412yes—
189C2×C8×C53#4112yes—
190C4⋊C4×C53—24no—
191C4⋊C4×C53—21no—
192C4⋊C4×C53—21no—
193C4⋊C4×C53—21no—
194C4⋊C4×C53—21no—
195C4⋊C4×C53—21no—
196C4⋊C4×C53C22×C412yes—
197C22⋊C4×C53—24no—
198C22⋊C4×C53—42no—
199C22⋊Dic53—42no—
200#11719924—28no—
201#11719921—24no—
202#11719921—42no—
203#11719921—42no—
204#11719921—42no—
205C4⋊Dic53—21no—
206C4⋊Dic53—21no—
207C4⋊Dic53—21no—
208C4⋊Dic53—21no—
209C4⋊Dic53—21no—
210C4⋊Dic53—42no—
211C4⋊Dic53—42no—
212C4⋊Dic53C22×C412yes—
213#11719919—42no—
214C4×Dic53—21no—
215C4×Dic53—21no—
216C4×Dic53—22no—
217C4×Dic53—22no—
218C4×Dic53—42no—
219C4×Dic53—42no—
220C4×Dic53—42no—
221C4×Dic53C2×D412yes—
222C4×Dic53#4112yes—
223C2×#88322—21no—
224C2×#88322—21no—
225C2×#88322—28no—
226C2×#88322C22×C412yes—
227C2×#88322C22×C412yes—
228C2×#88322C2×D412yes—
229C2×#88322#4112yes—
230C23×C53—21no—
231C23×C53—21no—
232C23×C53—21no—
233C23×C53—21no—
234C23×C53C4×D412yes—
235C23×C53AGL(1,ℤ/8)12yes—
236C23×C53#13712yes—
237C23×C53C22×D411yescharacteristic
238C22×D53—22no—
239C22×D53—41no—
240C22×D53—41no—
241C22×D53—41no—
242C22×D53—41no—
243C22×D53—41no—
244C22×D53—41no—
245Q8×C53—22no—
246Q8×C53—22no—
247Q8×C53—41no—
248Q8×C53—41no—
249C2×C4×C53—21no—
250C2×C4×C53—21no—
251C2×C4×C53—22no—
252C2×C4×C53—22no—
253C2×C4×C53—22no—
254C2×C4×C53—22no—
255C2×C4×C53—22no—
256C2×C4×C53—22no—
257C2×C4×C53—41no—
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—41no—
267C2×C4×C53C4×D412yes—
268C2×C4×C53C23×C411yescharacteristic
269C2×C4×C53C22×D411yescharacteristic
270C2×C4×C53C2×#4111yescharacteristic
271C2×C4×C53C2×#4111yescharacteristic
272C2×C4×C53C2×#4111yescharacteristic
273C2×C4×C53C2×#4111yescharacteristic
274C22⋊D53—48no—
275C2×Dic53—21no—
276C2×Dic53—21no—
277C2×Dic53—21no—
278C2×Dic53—21no—
279C2×Dic53—22no—
280C2×Dic53—21no—
281C2×Dic53—21no—
282C2×Dic53—21no—
283C2×Dic53—21no—
284C2×Dic53—21no—
285C2×Dic53—21no—
286C2×Dic53—44no—
287C2×Dic53—44no—
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×Dic53#12112yes—
297C2×Dic53#12112yes—
298D212—22no—
299D212—22no—
300D212—41no—
301D212—41no—
302C4×D53—84no—
303C8×C53—22no—
304C8×C53—22no—
305#88322—22no—
306#88322C4×D414yescomplemented
307#21528—531nomaximal, Sylow
308C22×C53—22no—
309C22×C53—22no—
310C22×C53—22no—
311C22×C53—22no—
312C22×C53—22no—
313C22×C53—22no—
314C22×C53#44014yescomplemented
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—42no—
323C2×D53—42no—
324C2×D53—42no—
325C2×D53—81no—
326C2×D53—81no—
327C2×D53—81no—
328C2×D53—81no—
329C4×C53—22no—
330C4×C53—42no—
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—22no—
340Dic53—42no—
341Dic53—41no—
342Dic53—41no—
343Dic53—81no—
344Dic53—81no—
345C2×#465—531no—
346C2×#440—531no—
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#1892D5311yescharacteristic, complemented
356#1808—531no—
357#1776—531no—
358#1763—531no—
359#1762—531no—
360C2×C53—24no—
361C2×C53C4×#12111yescharacteristic
362C2×C53C2×#44011yescharacteristic
363C2×C53#294311yescharacteristic
364C2×C53#305511yescharacteristic
365C2×C53#305611yescharacteristic
366C2×C53#318011yescharacteristic
367C2×C53#318111yescharacteristic
368D53—82no—
369C22×SD16—531no—
370C23×C8—531no—
371C23×C8C2×D5311yescharacteristic
372C2×C22⋊Q8C2×D5311yescharacteristic
373C2×#121—531no—
374C2×C4×Q8—531no—
375C2×C4×D4—531no—
376C2×C4×D4—1061no—
377C22×C42—531no—
378#465—538no—
379#440—1064no—
380C2×#107—531no—
381C2×#107—531no—
382C2×#106—531no—
383C2×#103—531no—
384C2×#103C2×D5311yescharacteristic
385C2×#103C2×D5311yescharacteristic
386C2×#102—531no—
387C2×#102—531no—
388C2×#102—531no—
389C2×#97—531no—
390C2×#97—531no—
391C2×#97—531no—
392C2×#97—531no—
393C2×#97—1064no—
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#380C2×D5311yescharacteristic
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#340C2×D5311yescharacteristic
414#340C2×D5311yescharacteristic
415C53#2152811yescharacteristic, complemented, Sylow
416C22×Q8C22×D5311yescharacteristic
417C22×D4—531no—
418C22×D4—1061no—
419C23×C4—531no—
420C23×C4—531no—
421C23×C4—1061no—
422C23×C4C22×D5311yescharacteristic
423C2×SD16—534no—
424C2×SD16—1062no—
425C2×SD16—1062no—
426C22×C8—22no—
427C22×C8—22no—
428C22×C8—22no—
429C22×C8—531no—
430C22×C8—534no—
431C22×C8—531no—
432C22×C8—1062no—
433C22×C8—1062no—
434C22×C8C22×D5311yescharacteristic
435C22×C8C22×D5311yescharacteristic
436C22⋊Q8—22no—
437C22⋊Q8C4×D5314yescomplemented
438#121—534no—
439#121—1062no—
440C4×Q8—1062no—
441C4×Q8—1062no—
442C4×D4—1062no—
443C4×D4—1062no—
444C4×D4—2124no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—531no—
447C2×C4⋊C4—531no—
448C2×C4⋊C4—531no—
449C2×C4⋊C4—1061no—
450C2×C4⋊C4—1061no—
451C2×C4⋊C4—1061no—
452C2×C4⋊C4C22×D5311yescharacteristic
453C2×C4⋊C4C22×D5311yescharacteristic
454C2×C4⋊C4C22×D5311yescharacteristic
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—1061no—
458C2×C22⋊C4—1061no—
459C2×C22⋊C4—1061no—
460C2×C22⋊C4—1061no—
461C2×C22⋊C4—1061no—
462C2×C42—531no—
463C2×C42—531no—
464C2×C42—531no—
465C2×C42—531no—
466C2×C42—1062no—
467C2×C42—1062no—
468C2×C42—1061no—
469C2×C42—1061no—
470C2×C42—1061no—
471#107—1062no—
472#107—1062no—
473#106—534no—
474#103—22no—
475#103—22no—
476#103—534no—
477#102—534no—
478#102—1062no—
479#102—1062no—
480#97—534no—
481#97—1062no—
482#97—1062no—
483#97—1062no—
484#95—21no—
485#95—1061no—
486#95—1061no—
487#95—1061no—
488#95—1061no—
489#95—1061no—
490#95—1061no—
491#95—1061no—
492C24—1061no—
493C24D4×D5311yescharacteristic
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8C2×C4×D5312yes—
500C2×D4—532no—
501C2×D4—1064no—
502C2×D4—1061no—
503C2×D4—1061no—
504C2×D4—1061no—
505C2×D4—1061no—
506C2×D4—1061no—
507C2×D4—2122no—
508C2×D4—2122no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—531no—
518C22×C4—531no—
519C22×C4—531no—
520C22×C4—531no—
521C22×C4—1062no—
522C22×C4—1062no—
523C22×C4—1062no—
524C22×C4—1062no—
525C22×C4—1061no—
526C22×C4—1061no—
527C22×C4—1061no—
528C22×C4—2122no—
529C22×C4—2122no—
530C22×C4—2122no—
531C22×C4—2121no—
532C22×C4—2121no—
533C22×C4C2×C4×D5312yes—
534C22×C4D4×D5311yescharacteristic
535C22×C4#1171994712yes—
536C22×C4C23×D5311yescharacteristic
537SD16—1068no—
538C2×C8—28no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—532no—
544C2×C8—532no—
545C2×C8—532no—
546C2×C8—532no—
547C2×C8—1068no—
548C2×C8—1061no—
549C2×C8—1061no—
550C2×C8D4×D5312yes—
551C2×C8#1171994712yes—
552C4⋊C4—24no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—532no—
559C4⋊C4—1061no—
560C4⋊C4—1061no—
561C4⋊C4—1061no—
562C4⋊C4—1061no—
563C4⋊C4—1061no—
564C4⋊C4—2122no—
565C4⋊C4—2122no—
566C4⋊C4—2122no—
567C4⋊C4C2×C4×D5312yes—
568C22⋊C4—24no—
569C22⋊C4—42no—
570C22⋊C4—1064no—
571C22⋊C4—2122no—
572C22⋊C4—2122no—
573C22⋊C4—2122no—
574C22⋊C4—2122no—
575C42—532no—
576C42—532no—
577C42—1062no—
578C42—1062no—
579C42—1061no—
580C42—1061no—
581C42—2122no—
582C42—2122no—
583C42—2122no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—1062no—
589C23—2121no—
590C23—2121no—
591C23—2121no—
592C23—2121no—
593C23—2121no—
594C23—2121no—
595C23#1313317712yes—
596C23#1313324412yes—
597C23#1313324912yes—
598C23C2×D4×D5311yescharacteristic
599Q8—22no—
600Q8—22no—
601Q8—41no—
602Q8—41no—
603D4—1062no—
604D4—1062no—
605D4—2128no—
606D4—2121no—
607D4—2121no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—532no—
627C2×C4—532no—
628C2×C4—1061no—
629C2×C4—1061no—
630C2×C4—1061no—
631C2×C4—1061no—
632C2×C4—1062no—
633C2×C4—1061no—
634C2×C4—1061no—
635C2×C4—1061no—
636C2×C4—1061no—
637C2×C4—1061no—
638C2×C4—1061no—
639C2×C4—4244no—
640C2×C4—2124no—
641C2×C4—2124no—
642C2×C4—2121no—
643C2×C4—2121no—
644C2×C4—2121no—
645C2×C4—2121no—
646C2×C4—2121no—
647C2×C4—2121no—
648C2×C4—2121no—
649C2×C4—2121no—
650C2×C4#1313317712yes—
651C2×C4C22×C4×D5311yescharacteristic
652C2×C4C2×D4×D5311yescharacteristic
653C2×C4#41×D5311yescharacteristic
654C2×C4#41×D5311yescharacteristic
655C2×C4C2×#1171994711yescharacteristic
656C2×C4C2×#1171994711yescharacteristic
657C8—22no—
658C8—22no—
659C8—534no—
660C8—1062no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—22no—
667C22—4241no—
668C22—4241no—
669C22—4241no—
670C22—4241no—
671C22—2122no—
672C22—2122no—
673C22—2122no—
674C22#1681072614yescomplemented
675C22C2×#1313317711yescharacteristic
676C22#121×D5311yescharacteristic
677C22#1681116811yescharacteristic
678C22C2×#1313324411yescharacteristic
679C22C2×#1313324911yescharacteristic
680C22#1681142011yescharacteristic
681C22#1681142011yescharacteristic
682C4—22no—
683C4—42no—
684C4—42no—
685C4—81no—
686C4—81no—
687C4—1062no—
688C4—1062no—
689C4—4241no—
690C4—4241no—
691C4—2122no—
692C4—2121no—
693C4—2121no—
694C4C4×D4×D5311yescharacteristic
695C4C4×#1171994711yescharacteristic
696C4#1681112911yescharacteristic
697C4#1681115011yescharacteristic
698C2—24no—
699C2—4242no—
700C2#2027722511yescharacteristic
701C2C2×#1681072611yescharacteristic
702C2#2028351111yescharacteristic
703C2#2028432711yescharacteristic
704C2#2028434211yescharacteristic
705C2#2028540611yescharacteristic
706C2#2028541911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1892C2
socleC23×C53C22×D4
prime radicalC2×#13133191C22
cosocleC22×C4×C53C24
hypercenter#1892D53
hypocenterC53#21528
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1892

Complements

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

NH ≅ G/Ntype
2. C2×#16810726C2semidirect
3. C22×#13133127C2semidirect
4. C22⋊Q8×Dic53C2semidirect
6. #20275593C2semidirect
7. #20275457C2semidirect
8. #20275413C2semidirect
9. #20275402C2semidirect
11. #20274742C2semidirect
12. #20274611C2semidirect
13. #20274547C2semidirect
14. #20274539C2semidirect
15. C53×#1892C2semidirect
23. #16810854C4semidirect
69. C2×#11719924C2×C4semidirect
72. C22×#88322C2×C4semidirect
104. #13133148C2×C4semidirect
105. #13133141C2×C4semidirect
108. #13133137C2×C4semidirect
112. #13133127D4semidirect
128. C22⋊Q8×C53C2×C4semidirect
306. #88322C4×D4semidirect
314. C22×C53#440semidirect
355. #1892D53semidirect
415. C53#21528semidirect
437. C22⋊Q8C4×D53semidirect
674. C22#16810726semidirect

Maximal subgroups

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

subgroupindex
C2×#168108542
C2×#168107262
C22×#131331272
C22⋊Q8×Dic532
#202772212
#202755932
#202754572
#202754132
#202754022
#202751432
#202747422
#202746112
#202745472
#202745392
C53×#18922
#2152853