Finite Group Databasebeta

← #28247774

Subgroups — #28247774

Order 13568.

2694 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811389C211yesmaximal, characteristic
2#20287916C211yesmaximal, characteristic
3C2×#16811103C211yesmaximal, characteristic
4#20283314C214yesmaximal, complemented
5#20283312C214yesmaximal, complemented
6#20283309C214yesmaximal, complemented
7#20283307C214yesmaximal, complemented
8#20283304C211yesmaximal, characteristic, complemented
9#20283302C214yesmaximal, complemented
10C2×#16810666C211yesmaximal, characteristic, complemented
11C2×#16810665C211yesmaximal, characteristic, complemented
12#428×D53C214yesmaximal, complemented
13C53×#2911C211yesmaximal, characteristic, complemented
14C22×#11719945C2211yescharacteristic
15#16811389C4116yescomplemented
16C2×#13133225C2214yes—
17C2×#13133223C2214yes—
18C22×#11719917C2211yescharacteristic
19C2×M16×D53C2214yes—
20#16811104C2212yes—
21#16811104C2212yes—
22#16811103—22no—
23#16811103—22no—
24#16811103C2214yes—
25#16811103C2214yes—
26#16811103C2212yes—
27#16811103C2212yes—
28#16811100—21no—
29#16811097—21no—
30#16811096—22no—
31C4×#11719945—22no—
32#16811091—22no—
33C2×C4×Dic106—21no—
34C2×C4×D212—21no—
35C2×#13133177—22no—
36C2×#13133176C2211yescharacteristic
37C2×#13133175C2212yes—
38#117×D53C2214yes—
39C22×C4⋊Dic53C2211yescharacteristic
40C2×C4⋊C4×D53C2212yes—
41#16810666C2214yes—
42#16810666C2214yescomplemented
43#16810666C2212yescomplemented
44#16810666C2212yescomplemented
45#16810665C2214yes—
46#16810665C2214yescomplemented
47#16810664C2218yescomplemented
48#16810664C2218yescomplemented
49#16810663C2212yes—
50#16810663C2212yes—
51#16810662C2218yescomplemented
52#16810662C2218yescomplemented
53#16810660C2218yescomplemented
54#16810659C2214yescomplemented
55#16810658C2218yescomplemented
56C2×#13133151C2212yescomplemented
57C2×#13133150C2212yescomplemented
58#107×D53C2218yescomplemented
59C2×#13133149C2212yescomplemented
60C2×#13133148C2212yescomplemented
61#106×D53C2218yescomplemented
62C22×M16×C53C2211yescharacteristic
63C2×#117×C53C2211yescharacteristic
64C2×#117×C53C2211yescharacteristic
65C53×#428C2212yes—
66C53×#428C2212yes—
67C53×#428C2212yescomplemented
68C53×#428C2212yescomplemented
69C53×#427C2214yescomplemented
70C2×#11719945C2×C418yes—
71C2×#11719945D412yes—
72C2×#11719945D412yes—
73C2×#11719945Q818yes—
74C2×#11719945C2312yes—
75C2×#11719945C2312yes—
76C22×Dic106D411yescharacteristic
77C22×D212D411yescharacteristic
78C22×C22⋊D53D412yes—
79C23×Dic53—21no—
80C22×C4×D53—22no—
81C22×C4×D53C2312yes—
82#13133225C2×C4132yescomplemented
83#13133223C2×C4132yescomplemented
84C2×#11719917C2×C418yescomplemented
85C2×#11719917C2312yes—
86C2×#11719917C2312yes—
87C2×#11719912C2318yes—
88M16×D53C2×C4132yescomplemented
89C22×#88322C2312yes—
90C2×C8×D53C2318yes—
91C4×Dic106—24no—
92C4×Dic106—24no—
93C4×Dic106—22no—
94C4×Dic106—22no—
95#13133182—22no—
96#13133182—22no—
97C4×D212—24no—
98C4×D212—24no—
99C4×D212—22no—
100C4×D212—22no—
101#13133179—22no—
102#13133179—22no—
103C4×C22⋊D53—24no—
104C4×C22⋊D53—24no—
105#13133177—28no—
106#13133177—28no—
107#13133177—24no—
108#13133177—24no—
109#13133176—21no—
110#13133176—21no—
111#13133176C2312yes—
112#13133176C2312yes—
113#13133175—24no—
114#13133175C2314yes—
115#13133175C2314yes—
116#13133175C2318yes—
117#13133174—24no—
118#13133173—24no—
119C2×C4⋊Dic53—21no—
120C2×C4⋊Dic53—21no—
121C2×C4⋊Dic53—21no—
122C2×C4⋊Dic53C2312yes—
123C2×C4⋊Dic53C2312yes—
124C2×C4⋊Dic53C2312yes—
125C2×C4⋊Dic53C2311yescharacteristic
126C2×C4⋊Dic53C2311yescharacteristic
127C2×#11719919—22no—
128C4⋊C4×D53—24no—
129C4⋊C4×D53C2318yes—
130C4⋊C4×D53C2314yes—
131C4⋊C4×D53C2314yes—
132C2×C22⋊Dic53—21no—
133C2×#11719921—22no—
134C22⋊C4×D53—24no—
135C2×C4×Dic53—21no—
136C2×C4×Dic53—22no—
137C42×D53—24no—
138#13133151C2318yes—
139#13133150C2314yes—
140#13133150C2318yes—
141#13133150C2314yes—
142#13133149C2318yes—
143#13133148C2314yes—
144#13133148C2318yes—
145#13133148C2314yes—
146C23×C4×C53C2311yescharacteristic
147C2×M16×C53C2×C418yescomplemented
148C2×M16×C53C2312yes—
149C2×M16×C53C2312yes—
150C22×C8×C53C2312yes—
151#117×C53—21no—
152#117×C53—21no—
153#117×C53—21no—
154#117×C53—21no—
155#117×C53C2312yes—
156#117×C53C2312yes—
157#117×C53C2312yes—
158#117×C53C2312yes—
159C2×C4⋊C4×C53C2311yescharacteristic
160C2×C4⋊C4×C53C2311yescharacteristic
161C2×C4⋊C4×C53C2311yescharacteristic
162C2×C4⋊C4×C53C2311yescharacteristic
163C2×C22⋊C4×C53—21no—
164C2×C22⋊C4×C53—21no—
165C2×C42×C53—21no—
166C2×C42×C53—21no—
167#107×C53C2314yes—
168#107×C53C2314yes—
169#106×C53C2314yes—
170#106×C53C2314yes—
171C24×C53C2×D411yescharacteristic
172C23×D53C2×D412yes—
173C22×C4×C53—21no—
174C22×C4×C53—21no—
175C22×C4×C53—21no—
176C22×C4×C53—21no—
177C22×C4×C53C22×C414yes—
178C22×C4×C53C2×D411yescharacteristic
179C22×C4×C53C2×D411yescharacteristic
180C22×C4×C53C2×D411yescharacteristic
181C22×C4×C53C2×Q814yes—
182C22×C4×C53C2411yescharacteristic
183C22×C4×C53C2411yescharacteristic
184C22×C4×C53C2411yescharacteristic
185C2×C22⋊D53C4⋊C4116yes—
186C2×C22⋊D53C2×D414yes—
187C2×C22⋊D53C2×D414yes—
188C22×Dic53—22no—
189C22×Dic53—21no—
190C22×Dic53—21no—
191C22×Dic53—22no—
192C22×Dic53—22no—
193C22×Dic53—82no—
194C22×Dic53C2×D412yes—
195#11719945C4⋊C4116yes—
196#11719945C4⋊C4116yes—
197#11719945C22×C418yes—
198#11719945C22×C418yes—
199#11719945C2×Q818yes—
200#11719945C2×Q818yes—
201C2×D212C4⋊C418yes—
202C2×D212C2×D412yes—
203C2×D212C2×D412yes—
204C2×C4×D53—24no—
205C2×C4×D53—24no—
206C2×C4×D53—28no—
207C2×C4×D53—84no—
208C2×C4×D53C22×C418yes—
209C2×C4×D53C2×D414yes—
210C2×C4×D53C2×Q818yes—
211C2×C4×D53C2414yes—
212C2×Dic106C4⋊C418yes—
213C2×Dic106C2×D412yes—
214C2×Dic106C2×D412yes—
215M16×C53C22×C418yes—
216M16×C53C22×C418yescomplemented
217C2×C8×C53C22×C418yescomplemented
218C2×C8×C53C2414yes—
219C4⋊C4×C53—21no—
220C4⋊C4×C53—21no—
221C4⋊C4×C53—21no—
222C4⋊C4×C53—21no—
223C4⋊C4×C53C2412yes—
224C4⋊C4×C53C2412yes—
225C4⋊C4×C53C2412yes—
226C4⋊C4×C53C2412yes—
227C22⋊C4×C53—22no—
228C22⋊C4×C53—22no—
229C22⋊C4×C53—22no—
230C22⋊C4×C53—22no—
231C42×C53—22no—
232C42×C53—22no—
233C42×C53—22no—
234C42×C53—22no—
235C22⋊Dic53—22no—
236C22⋊Dic53—22no—
237#11719921—24no—
238#11719921—24no—
239#11719921—28no—
240C4⋊Dic53—22no—
241C4⋊Dic53—22no—
242C4⋊Dic53—22no—
243C4⋊Dic53—21no—
244C4⋊Dic53—21no—
245C4⋊Dic53C2412yes—
246C4⋊Dic53C2414yes—
247C4⋊Dic53C2412yes—
248#11719919—28no—
249#11719919—24no—
250#11719919—24no—
251C4×Dic53—22no—
252C4×Dic53—22no—
253C4×Dic53—24no—
254C4×Dic53—24no—
255C4×Dic53—28no—
256#11719917C22×C418yes—
257#11719917C22×C418yescomplemented
258C2×#88322C22×C418yescomplemented
259C2×#88322C2414yes—
260#11719912C22×C4132yescomplemented
261C8×D53C22×C4132yescomplemented
262C23×C53—41no—
263C23×C53—41no—
264C23×C53C2×C4⋊C414yes—
265C23×C53C22×D411yescharacteristic
266C23×C53C22×D411yescharacteristic
267C23×C53C22×D411yescharacteristic
268C22×D53—42no—
269C22×D53—42no—
270C22×D53C2×C4⋊C418yes—
271C22×D53C22×D414yes—
272C2×C4×C53—22no—
273C2×C4×C53—22no—
274C2×C4×C53—22no—
275C2×C4×C53—22no—
276C2×C4×C53—42no—
277C2×C4×C53—42no—
278C2×C4×C53—81no—
279C2×C4×C53—81no—
280C2×C4×C53C2×C4⋊C414yes—
281C2×C4×C53C2×C4⋊C414yes—
282C2×C4×C53C2×C4⋊C414yes—
283C2×C4×C53C23×C412yes—
284C2×C4×C53C23×C412yes—
285C2×C4×C53C23×C412yes—
286C2×C4×C53C22×D411yescharacteristic
287C2×C4×C53C22×D411yescharacteristic
288C2×C4×C53C22×D411yescharacteristic
289C2×C4×C53C22×Q812yes—
290C2×C4×C53C22×Q812yes—
291C2×C4×C53C22×Q812yes—
292C2×C4×C53C2511yescharacteristic
293C22⋊D53C2×C4⋊C4116yes—
294C22⋊D53C2×C4⋊C4116yes—
295C2×Dic53—24no—
296C2×Dic53—22no—
297C2×Dic53—22no—
298C2×Dic53—44no—
299C2×Dic53—81no—
300C2×Dic53—81no—
301C2×Dic53—82no—
302C2×Dic53—82no—
303C2×Dic53C2×C4⋊C418yes—
304C2×Dic53C22×D414yes—
305D212C2×C4⋊C418yes—
306D212C2×C4⋊C418yes—
307C4×D53—84no—
308C4×D53—84no—
309C4×D53—88no—
310C4×D53C2×C4⋊C4116yes—
311C4×D53C23×C418yes—
312C4×D53C22×Q818yes—
313Dic106C2×C4⋊C418yes—
314Dic106C2×C4⋊C418yes—
315C8×C53C23×C418yes—
316#88322C23×C418yes—
317#60109—531nomaximal, Sylow
318C22×C53—21no—
319C22×C53—21no—
320C22×C53—21no—
321C22×C53—21no—
322C22×C53—21no—
323C22×C53—21no—
324C22×C53—44no—
325C22×C53C22×C4⋊C412yes—
326C22×C53C22×C4⋊C412yes—
327C22×C53C22×C4⋊C412yes—
328C22×C53C23×D411yescharacteristic
329C2×D53—24no—
330C2×D53—24no—
331C2×D53—48no—
332C2×D53C22×C4⋊C418yes—
333C4×C53—42no—
334C4×C53—42no—
335C4×C53—42no—
336C4×C53—42no—
337C4×C53C22×C4⋊C412yes—
338C4×C53C22×C4⋊C412yes—
339C4×C53C22×C4⋊C412yes—
340C4×C53C24×C411yescharacteristic
341C4×C53C23×Q811yescharacteristic
342Dic53—44no—
343Dic53—42no—
344Dic53—42no—
345Dic53C22×C4⋊C418yes—
346C2×#568—531no—
347#3428—531no—
348C2×#520—531no—
349#2913—534no—
350#2913—534no—
351#2912—534no—
352#2912—534no—
353#2911—534no—
354#2911—531no—
355#2911D5311yescharacteristic, complemented
356C2×#428—534no—
357C2×#428—531no—
358C2×#428—531no—
359C2×C53—22no—
360C2×C53—22no—
361C2×C53—22no—
362C2×C53C23×C4⋊C411yescharacteristic
363C2×C53#358511yescharacteristic
364C2×C53#358611yescharacteristic
365D53—28no—
366C22×#41—531no—
367#568—5316no—
368C2×#131—534no—
369C2×#131—534no—
370C22×M16—531no—
371C22×M16—534no—
372C22×M16C2×D5311yescharacteristic
373#520—532no—
374#520—534no—
375#520—534no—
376#520—532no—
377#520—532no—
378#520—532no—
379#520—1062no—
380#520—1062no—
381#519—1061no—
382#518—1062no—
383#518—1061no—
384C4×#41—1062no—
385C4×#41—1062no—
386C2×C4×Q8—1061no—
387C2×C4×D4—1061no—
388C2×C4×D4—1062no—
389C2×#117—531no—
390C2×#117—534no—
391C2×#117—532no—
392C2×#117C2×D5311yescharacteristic
393C2×#117C2×D5311yescharacteristic
394C22×C4⋊C4—531no—
395C22×C4⋊C4—532no—
396#428—534no—
397#428—534no—
398#428—534no—
399#428—534no—
400#428—532no—
401#428—532no—
402#428—532no—
403#428—532no—
404#428—538no—
405#428—538no—
406#428—538no—
407#428—538no—
408#428C2×D5312yes—
409#428C2×D5312yes—
410#428C2×D5312yescomplemented
411#428C2×D5312yescomplemented
412#427—534no—
413#427—538no—
414#427—538no—
415#427C2×D5314yescomplemented
416C2×#107—532no—
417C2×#107—532no—
418C2×#107—538no—
419C2×#106—532no—
420C2×#106—532no—
421C2×#106—538no—
422C53#6010911yescharacteristic, complemented, Sylow
423C2×#41—538no—
424C2×#41—532no—
425C2×#41—532no—
426C2×#41—538no—
427C2×#41—532no—
428C2×#41—532no—
429C22×Q8—531no—
430C22×D4—532no—
431C22×D4—531no—
432C23×C4—532no—
433C23×C4—1062no—
434C23×C4—1061no—
435C23×C4C22×D5311yescharacteristic
436#131—5332no—
437#131—5332no—
438C2×M16—538no—
439C2×M16—532no—
440C2×M16—532no—
441C2×M16—5332no—
442C2×M16—538no—
443C2×M16C4×D5318yescomplemented
444C2×M16C22×D5312yes—
445C2×M16C22×D5312yes—
446C22×C8—532no—
447C22×C8—538no—
448C22×C8C22×D5312yes—
449C4×Q8—1064no—
450C4×Q8—1064no—
451C4×Q8—1062no—
452C4×Q8—1062no—
453C4×Q8—1062no—
454C4×Q8—1062no—
455C4×D4—1064no—
456C4×D4—1064no—
457C4×D4—1062no—
458C4×D4—1062no—
459C4×D4—1068no—
460C4×D4—1068no—
461C4×D4—1064no—
462C4×D4—1064no—
463C4×D4—1062no—
464C4×D4—1062no—
465C4×D4—1064no—
466C4×D4—1064no—
467#117—21no—
468#117—21no—
469#117—21no—
470#117—21no—
471#117—532no—
472#117—532no—
473#117—534no—
474#117—538no—
475#117—534no—
476#117—1064no—
477#117—1064no—
478#117—1064no—
479#117—1061no—
480#117—1061no—
481#117C22×D5312yes—
482#117C22×D5312yes—
483#117C22×D5312yes—
484#117C22×D5312yes—
485C2×C4⋊C4—532no—
486C2×C4⋊C4—532no—
487C2×C4⋊C4—532no—
488C2×C4⋊C4—531no—
489C2×C4⋊C4—531no—
490C2×C4⋊C4—538no—
491C2×C4⋊C4—534no—
492C2×C4⋊C4—534no—
493C2×C4⋊C4—1064no—
494C2×C4⋊C4—1062no—
495C2×C4⋊C4—1061no—
496C2×C4⋊C4—1061no—
497C2×C4⋊C4—1061no—
498C2×C4⋊C4C22×D5311yescharacteristic
499C2×C4⋊C4C22×D5311yescharacteristic
500C2×C4⋊C4C22×D5311yescharacteristic
501C2×C4⋊C4C22×D5311yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—1064no—
505C2×C22⋊C4—1062no—
506C2×C22⋊C4—1061no—
507C2×C42—21no—
508C2×C42—21no—
509C2×C42—1064no—
510C2×C42—1062no—
511C2×C42—1061no—
512#107—538no—
513#107—538no—
514#107—534no—
515#107—534no—
516#107C22×D5314yes—
517#107C22×D5314yes—
518#106—538no—
519#106—534no—
520#106—538no—
521#106—534no—
522#106C22×D5314yes—
523#106C22×D5314yes—
524C24—532no—
525C24D4×D5311yescharacteristic
526#41—5316no—
527#41—5316no—
528#41—538no—
529#41—538no—
530#41—538no—
531#41—538no—
532C2×Q8—538no—
533C2×Q8—532no—
534C2×Q8—532no—
535C2×D4—5316no—
536C2×D4—534no—
537C2×D4—534no—
538C2×D4—538no—
539C2×D4—532no—
540C2×D4—532no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—532no—
546C22×C4—538no—
547C22×C4—534no—
548C22×C4—538no—
549C22×C4—534no—
550C22×C4—1064no—
551C22×C4—1064no—
552C22×C4—1068no—
553C22×C4—1061no—
554C22×C4—1061no—
555C22×C4—1062no—
556C22×C4—1062no—
557C22×C4—1062no—
558C22×C4—4244no—
559C22×C4—4242no—
560C22×C4C2×C4×D5314yes—
561C22×C4D4×D5311yescharacteristic
562C22×C4D4×D5311yescharacteristic
563C22×C4D4×D5311yescharacteristic
564C22×C4Q8×D5314yes—
565C22×C4C23×D5311yescharacteristic
566C22×C4C23×D5311yescharacteristic
567C22×C4C23×D5311yescharacteristic
568M16—538no—
569M16—538no—
570M16—5332no—
571M16C2×C4×D5318yes—
572M16C2×C4×D5318yescomplemented
573C2×C8—538no—
574C2×C8—534no—
575C2×C8—5332no—
576C2×C8C2×C4×D5318yescomplemented
577C2×C8C23×D5314yes—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—532no—
583C4⋊C4—534no—
584C4⋊C4—532no—
585C4⋊C4—1068no—
586C4⋊C4—1064no—
587C4⋊C4—1064no—
588C4⋊C4—1062no—
589C4⋊C4—1062no—
590C4⋊C4—1062no—
591C4⋊C4—1061no—
592C4⋊C4—1061no—
593C4⋊C4C23×D5312yes—
594C4⋊C4C23×D5312yes—
595C4⋊C4C23×D5312yes—
596C4⋊C4C23×D5312yes—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—1068no—
602C22⋊C4—1064no—
603C22⋊C4—1064no—
604C22⋊C4—1062no—
605C22⋊C4—1062no—
606C42—22no—
607C42—22no—
608C42—22no—
609C42—22no—
610C42—1068no—
611C42—1064no—
612C42—1064no—
613C42—1062no—
614C42—1062no—
615C23—41no—
616C23—41no—
617C23—534no—
618C23—538no—
619C23—2122no—
620C23—2122no—
621C23C4⋊C4×D5314yes—
622C23C2×D4×D5311yescharacteristic
623C23C2×D4×D5311yescharacteristic
624C23C2×D4×D5311yescharacteristic
625Q8—538no—
626Q8—538no—
627D4—5316no—
628D4—5316no—
629D4—538no—
630D4—538no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—81no—
638C2×C4—81no—
639C2×C4—538no—
640C2×C4—534no—
641C2×C4—5316no—
642C2×C4—538no—
643C2×C4—538no—
644C2×C4—1062no—
645C2×C4—1062no—
646C2×C4—1064no—
647C2×C4—4244no—
648C2×C4—4244no—
649C2×C4—4248no—
650C2×C4—4241no—
651C2×C4—4241no—
652C2×C4—4242no—
653C2×C4—4242no—
654C2×C4—2124no—
655C2×C4C4⋊C4×D5314yes—
656C2×C4C4⋊C4×D5314yes—
657C2×C4C4⋊C4×D5314yes—
658C2×C4C22×C4×D5312yes—
659C2×C4C22×C4×D5312yes—
660C2×C4C22×C4×D5312yes—
661C2×C4C2×D4×D5311yescharacteristic
662C2×C4C2×D4×D5311yescharacteristic
663C2×C4C2×D4×D5311yescharacteristic
664C2×C4C2×Q8×D5312yes—
665C2×C4C2×Q8×D5312yes—
666C2×C4C2×Q8×D5312yes—
667C2×C4C24×D5311yescharacteristic
668C8—538no—
669C8C22×C4×D5318yes—
670C22—21no—
671C22—21no—
672C22—21no—
673C22—21no—
674C22—21no—
675C22—21no—
676C22—44no—
677C22—538no—
678C22—1064no—
679C22—1064no—
680C22—2128no—
681C22C2×C4⋊C4×D5312yes—
682C22C2×C4⋊C4×D5312yes—
683C22C2×C4⋊C4×D5312yes—
684C22C22×D4×D5311yescharacteristic
685C4—42no—
686C4—42no—
687C4—42no—
688C4—42no—
689C4—538no—
690C4—2124no—
691C4—2122no—
692C4—2122no—
693C4C2×C4⋊C4×D5312yes—
694C4C2×C4⋊C4×D5312yes—
695C4C2×C4⋊C4×D5312yes—
696C4C23×C4×D5311yescharacteristic
697C4C22×Q8×D5311yescharacteristic
698C2—22no—
699C2—22no—
700C2—22no—
701C2—1068no—
702C2C22×C4⋊C4×D5311yescharacteristic
703C2#2028949211yescharacteristic
704C2#2028949911yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutatorC4×C53C24×C4
FrattiniC2×C4C24×D53
FittingC53×#2911C2
socleC22×C53C23×D4
prime radicalC22×#11719945C22
cosocleC2×C4×C53C25
hypercenter#2911D53
hypocenterC53#60109
LCSG ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2911

Complements

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

NH ≅ G/Ntype
4. #20283314C2semidirect
5. #20283312C2semidirect
6. #20283309C2semidirect
7. #20283307C2semidirect
8. #20283304C2semidirect
9. #20283302C2semidirect
10. C2×#16810666C2semidirect
11. C2×#16810665C2semidirect
12. #428×D53C2semidirect
13. C53×#2911C2semidirect
15. #16811389C4semidirect
42. #16810666C22semidirect
43. #16810666C22semidirect
44. #16810666C22semidirect
46. #16810665C22semidirect
47. #16810664C22semidirect
48. #16810664C22semidirect
51. #16810662C22semidirect
52. #16810662C22semidirect
53. #16810660C22semidirect
54. #16810659C22semidirect
55. #16810658C22semidirect
56. C2×#13133151C22semidirect
57. C2×#13133150C22semidirect
58. #107×D53C22semidirect
59. C2×#13133149C22semidirect
60. C2×#13133148C22semidirect
61. #106×D53C22semidirect
67. C53×#428C22semidirect
68. C53×#428C22semidirect
69. C53×#427C22semidirect
82. #13133225C2×C4semidirect
83. #13133223C2×C4semidirect
84. C2×#11719917C2×C4semidirect
88. M16×D53C2×C4semidirect
147. C2×M16×C53C2×C4semidirect
216. M16×C53C22×C4semidirect
217. C2×C8×C53C22×C4semidirect
257. #11719917C22×C4semidirect
258. C2×#88322C22×C4semidirect
260. #11719912C22×C4semidirect
261. C8×D53C22×C4semidirect
355. #2911D53semidirect
410. #428C2×D53semidirect
411. #428C2×D53semidirect
415. #427C2×D53semidirect
422. C53#60109semidirect
443. C2×M16C4×D53semidirect
572. M16C2×C4×D53semidirect
576. C2×C8C2×C4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168113892
#202879162
C2×#168111032
#202833142
#202833122
#202833092
#202833072
#202833042
#202833022
C2×#168106662
C2×#168106652
#428×D532
C53×#29112
#6010953