Finite Group Databasebeta

← #41×#11719922 #28265493

Subgroups — #41×#11719922 #28265493

Order 13568.

2406 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×D212C211yesmaximal, characteristic, complemented
2#20287687C211yesmaximal, characteristic, complemented
3Q8×#11719922C211yesmaximal, characteristic, complemented
4#20287350C211yesmaximal, characteristic, complemented
5#20287346C211yesmaximal, characteristic, complemented
6#20287058C213yesmaximal, complemented
7#20286528C213yesmaximal, complemented
8#20286522C213yesmaximal, complemented
9D4×#11719922C213yesmaximal, complemented
10#20285290C213yesmaximal, complemented
11#20284715C213yesmaximal, complemented
12#20284711C213yesmaximal, complemented
13#41×#88322C211yesmaximal, characteristic, complemented
14C2×C4×#11719922C213yesmaximal, complemented
15D4×#41×C53C211yesmaximal, characteristic, complemented
16C2×#41×D53—21no—
17C22×#11719922C2213yes—
18#16811295C2211yescharacteristic, complemented
19Q8×D212C2211yescharacteristic, complemented
20#16811285—21no—
21#16811277C2213yescomplemented
22#16811268—23no—
23D4×D212C2213yescomplemented
24#16811173C2213yescomplemented
25#16811135—23no—
26C2×C4×D212C2213yescomplemented
27#16811026C2213yescomplemented
28#16810999C2213yescomplemented
29#16810971C2213yescomplemented
30#16810969C2213yescomplemented
31#16810936C2216yescomplemented
32#16810934C2216yescomplemented
33#16810903C2213yescomplemented
34#16810903C2213yescomplemented
35#16810900C2213yescomplemented
36#16810900C2213yescomplemented
37#16810857C2216yescomplemented
38#16810857C2216yescomplemented
39#16810818C2213yescomplemented
40#16810818C2213yescomplemented
41#16810815C2213yescomplemented
42#16810815C2213yescomplemented
43#16810757C2216yescomplemented
44#16810756C2216yescomplemented
45Q8×#88322C2211yescharacteristic, complemented
46Q8×#88322C2211yescharacteristic, complemented
47C4×#11719922C2211yescharacteristic
48C4×#11719922C2213yes—
49C4×#11719922C2213yescomplemented
50C4×#11719922C2216yescomplemented
51C4×#11719922C2213yescomplemented
52C4×#11719922C2213yescomplemented
53C4×#11719922C2213yescomplemented
54C4×#11719922C2213yescomplemented
55C4×#11719922C2213yescomplemented
56D4×#88322C2213yescomplemented
57D4×#88322C2213yescomplemented
58#16810676C2213yescomplemented
59C2×#13133150C2213yescomplemented
60C2×#13133138C2213yescomplemented
61C2×#13133137C2213yescomplemented
62C2×C4×#88322C2213yescomplemented
63C22×#41×C53—21no—
64C53×#550C2211yescharacteristic, complemented
65D4×Q8×C53C2211yescharacteristic, complemented
66C53×#548—21no—
67C53×#547C2213yescomplemented
68C53×#546—23no—
69D42×C53C2213yescomplemented
70C53×#532C2213yescomplemented
71C53×#525—23no—
72C4×#41×C53C2211yescharacteristic
73C2×C4×D4×C53C2213yescomplemented
74C2×#11719949—21no—
75C2×#11719945—23no—
76C2×#11719947—23no—
77#41×D53—48no—
78C2×Q8×D53—21no—
79C22×D212C2313yes—
80C2×D4×D53—23no—
81C22×C4×D53—23no—
82C2×#11719922—212no—
83C2×#11719922C2313yes—
84C2×#11719922C2313yes—
85C2×#11719922C2313yes—
86C2×#11719922C2316yes—
87C2×#11719922C2311yescharacteristic
88C22×#88322C2313yes—
89C22×#88322C2313yes—
90#13133217C2313yes—
91#13133214C2313yes—
92#13133205—23no—
93#13133201—26no—
94#13133197—23no—
95#13133197—23no—
96#13133192—23no—
97#13133192—23no—
98#13133191—23no—
99#13133191C2316yes—
100#13133187—26no—
101C4×D212—23no—
102C4×D212—23no—
103C4×D212—23no—
104C4×D212C2313yes—
105C4×D212C2313yes—
106C4×D212C2311yescharacteristic
107C4×D212C2313yes—
108C2×C4⋊Dic53C2313yes—
109C2×#11719921—23no—
110#13133150C2313yes—
111#13133150C2316yes—
112#13133150C2313yes—
113#13133150C2313yes—
114#13133150C2311yescharacteristic
115C4⋊#88322C2313yes—
116C4⋊#88322C2313yes—
117#13133138C2313yes—
118#13133138C2316yes—
119#13133138C2313yes—
120#13133138C2313yes—
121#13133138C2311yescharacteristic
122#13133137C2313yes—
123#13133137C2316yes—
124#13133137C2313yes—
125#13133137C2313yes—
126#13133137C2311yescharacteristic
127C22⋊#88322C2316yes—
128C4×#88322C2313yes—
129C4×#88322C2311yescharacteristic
130C4×#88322C2313yes—
131C4×#88322C2313yes—
132C2×#41×C53—21no—
133C2×#41×C53—23no—
134C2×#41×C53—23no—
135C2×#41×C53—48no—
136C2×#41×C53D411yescharacteristic
137C22×Q8×C53—21no—
138C22×D4×C53—23no—
139C22×D4×C53C2313yes—
140C23×C4×C53—23no—
141C4⋊Q8×C53C2313yes—
142#127×C53C2313yes—
143#124×C53—23no—
144#123×C53—26no—
145C22⋊Q8×C53—23no—
146C22⋊Q8×C53—23no—
147#121×C53—23no—
148#121×C53—23no—
149#121×C53—23no—
150#121×C53C2316yes—
151#120×C53—26no—
152C4×Q8×C53D411yescharacteristic
153C4×Q8×C53C2311yescharacteristic
154C4×D4×C53—23no—
155C4×D4×C53—23no—
156C4×D4×C53—23no—
157C4×D4×C53D413yes—
158C4×D4×C53C2311yescharacteristic
159C4×D4×C53C2313yes—
160C4×D4×C53C2313yes—
161C4×D4×C53C2313yes—
162C4×D4×C53C2313yes—
163#117×C53D413yes—
164C2×C4⋊C4×C53C2313yes—
165C2×C22⋊C4×C53—23no—
166C2×C42×C53C2313yes—
167C24×C53—23no—
168C23×D53—23no—
169#41×C53—44no—
170#41×C53—412no—
171#41×C53—412no—
172#41×C53D818yescomplemented
173C2×Q8×C53—23no—
174C2×Q8×C53—44no—
175C2×Q8×C53C2×D411yescharacteristic
176C2×D4×C53—26no—
177C2×D4×C53—26no—
178C2×D4×C53—23no—
179C2×D4×C53—23no—
180C2×D4×C53—23no—
181C2×D4×C53—43no—
182C2×D4×C53—412no—
183C2×D4×C53C2×D413yes—
184C2×D4×C53C2413yes—
185C2×D4×C53C2411yescharacteristic
186C22×C4×C53—23no—
187C22×C4×C53—21no—
188C22×C4×C53—23no—
189C22×C4×C53—23no—
190C22×C4×C53—23no—
191C22×C4×C53—412no—
192C22×C4×C53C2×D413yes—
193C22×C4×C53C2×D413yes—
194C22×C4×C53C2413yes—
195C2×C22⋊D53—26no—
196C22×Dic53—23no—
197#11719949—44no—
198Q8×D53—44no—
199#11719947—412no—
200D4×D53—412no—
201#11719945—412no—
202C2×D212—26no—
203C2×D212—23no—
204C2×D212—23no—
205C2×D212—23no—
206C2×D212—43no—
207C2×D212C2413yes—
208C2×D212C2411yescharacteristic
209C2×C4×D53—21no—
210C2×C4×D53—23no—
211C2×C4×D53—23no—
212C2×C4×D53—23no—
213C2×C4×D53—412no—
214C2×Dic106—23no—
215C4⋊C4×C53—23no—
216C4⋊C4×C53—23no—
217C4⋊C4×C53C2×D413yes—
218C4⋊C4×C53C2×D413yes—
219C4⋊C4×C53C2411yescharacteristic
220C4⋊C4×C53C2413yes—
221C22⋊C4×C53—21no—
222C22⋊C4×C53—23no—
223C22⋊C4×C53—23no—
224C22⋊C4×C53—23no—
225C22⋊C4×C53—26no—
226C22⋊C4×C53C2×D416yes—
227C42×C53C2×D413yes—
228C42×C53C2×D413yes—
229C42×C53C2411yescharacteristic
230C42×C53C2413yes—
231#11719922—26no—
232#11719922—26no—
233#11719922—26no—
234#11719922—46no—
235#11719922#4114yesdirect product factor
236#11719921—21no—
237#11719921—23no—
238#11719921—23no—
239#11719921—23no—
240#11719921—26no—
241C4⋊Dic53—23no—
242C4⋊Dic53—23no—
243C4⋊Dic53C2411yescharacteristic
244C4⋊Dic53C2413yes—
245C2×#88322—26no—
246C2×#88322—43no—
247C2×#88322C2411yescharacteristic
248C2×#88322C2413yes—
249C2×#88322C2413yes—
250C2×#88322C2411yescharacteristic
251C23×C53—21no—
252C23×C53—23no—
253C23×C53—46no—
254C23×C53—46no—
255C23×C53—83no—
256C23×C53C22×D413yes—
257C22×D53—21no—
258C22×D53—23no—
259C22×D53—46no—
260C22×D53—46no—
261C22×D53—83no—
262Q8×C53—46no—
263Q8×C53C2×D814yescomplemented
264D4×C53—23no—
265D4×C53—21no—
266D4×C53—23no—
267D4×C53—46no—
268D4×C53—412no—
269D4×C53—46no—
270D4×C53—83no—
271D4×C53C2×D8112yescomplemented
272D4×C53C2×#4112yescomplemented
273C2×C4×C53—23no—
274C2×C4×C53—23no—
275C2×C4×C53—21no—
276C2×C4×C53—23no—
277C2×C4×C53—43no—
278C2×C4×C53—46no—
279C2×C4×C53—42no—
280C2×C4×C53—46no—
281C2×C4×C53—46no—
282C2×C4×C53—46no—
283C2×C4×C53C2×D8112yescomplemented
284C2×C4×C53C22×D413yes—
285C2×C4×C53C22×D413yes—
286C2×C4×C53C22×D411yescharacteristic
287C2×C4×C53C22×D413yes—
288C2×C4×C53C22×D411yescharacteristic
289C2×C4×C53C2511yescharacteristic
290C22⋊D53—412no—
291C2×Dic53—23no—
292C2×Dic53—21no—
293C2×Dic53—46no—
294D212—23no—
295D212—21no—
296D212—23no—
297D212—46no—
298D212—46no—
299D212—83no—
300D212C2×#4112yescomplemented
301C4×D53—42no—
302C4×D53—46no—
303C4×D53—46no—
304C4×D53—46no—
305Dic106—46no—
306#88322—23no—
307#88322—21no—
308#88322—23no—
309#88322C2×#4112yescomplemented
310D8×#41—531nomaximal, Sylow
311C22×C53—23no—
312C22×C53—23no—
313C22×C53—22no—
314C22×C53—41no—
315C22×C53—41no—
316C22×C53—43no—
317C22×C53—43no—
318C22×C53—43no—
319C22×C53—812no—
320C22×C53C22×D816yes—
321C22×C53C23×D411yescharacteristic
322C2×D53—22no—
323C2×D53—41no—
324C2×D53—41no—
325C2×D53—43no—
326C2×D53—43no—
327C2×D53—43no—
328C2×D53—812no—
329C4×C53—23no—
330C4×C53—21no—
331C4×C53—23no—
332C4×C53—41no—
333C4×C53—43no—
334C4×C53C22×D816yes—
335C4×C53C22×D812yes—
336C4×C53C22×#4111yescharacteristic
337C4×C53#58511yescharacteristic
338Dic53—43no—
339Dic53—41no—
340D4×#41—531no—
341D4×#41D5311yescharacteristic, complemented
342#3391—531no—
343Q8×D8—531no—
344#3358—531no—
345#3358—531no—
346#3334—533no—
347#3294—533no—
348#3294—533no—
349D4×D8—533no—
350#3169—533no—
351#3100—533no—
352#3100—533no—
353C8×#41—531no—
354C2×C4×D8—533no—
355C2×C53—26no—
356C2×C53—42no—
357C2×C53—83no—
358C2×C53D4×#4111yescharacteristic
359C2×C53C23×D811yescharacteristic
360C2×C53#358411yescharacteristic
361D53—42no—
362D53—83no—
363C22×#41—21no—
364C22×#41—1061no—
365C22×D8—533no—
366#550—531no—
367#550C2×D5311yescharacteristic, complemented
368D4×Q8—531no—
369D4×Q8C2×D5311yescharacteristic, complemented
370#548—21no—
371#548—1061no—
372#547—533no—
373#547C2×D5313yescomplemented
374#546—23no—
375#546—1063no—
376D42—533no—
377D42C2×D5313yescomplemented
378#532—533no—
379#532C2×D5313yescomplemented
380#525—23no—
381#525—1063no—
382C4×#41C2×D5311yescharacteristic
383C2×C4×D4—533no—
384C2×C4×D4C2×D5313yescomplemented
385#500—533no—
386#493—533no—
387#486—533no—
388#486—533no—
389#480—536no—
390#480—536no—
391#474—533no—
392#474—533no—
393#474—533no—
394#474—533no—
395#466—536no—
396#466—536no—
397#459—533no—
398#459—533no—
399#459—533no—
400#459—533no—
401#447—536no—
402#447—536no—
403C8×Q8—531no—
404C8×Q8—531no—
405C4×D8—533no—
406C4×D8—536no—
407C4×D8—533no—
408C4×D8—533no—
409C4×D8—533no—
410C4×D8—533no—
411C4×D8—533no—
412C4×D8—533no—
413C4×D8—531no—
414C8×D4—533no—
415C8×D4—533no—
416#431—533no—
417C2×#107—533no—
418C2×#102—533no—
419C2×#102—533no—
420C2×C4×C8—533no—
421C53D8×#4111yescharacteristic, complemented, Sylow
422C2×#41—21no—
423C2×#41—23no—
424C2×#41—23no—
425C2×#41—48no—
426C2×#41—1061no—
427C2×#41—1063no—
428C2×#41—1063no—
429C2×#41—2128no—
430C2×#41C22⋊D5311yescharacteristic
431C22×Q8—21no—
432C22×Q8—1061no—
433C22×D4—23no—
434C22×D4—533no—
435C22×D4—1063no—
436C22×D4C22×D5313yes—
437C23×C4—23no—
438C23×C4—1063no—
439C2×D8—531no—
440C2×D8—533no—
441C2×D8—533no—
442C2×D8—533no—
443C2×D8—536no—
444C2×D8—10612no—
445C22×C8—533no—
446C22×C8—533no—
447C4⋊Q8—533no—
448C4⋊Q8C22×D5313yes—
449#127—533no—
450#127C22×D5313yes—
451#124—23no—
452#124—1063no—
453#123—26no—
454#123—1066no—
455C22⋊Q8—23no—
456C22⋊Q8—23no—
457C22⋊Q8—1063no—
458C22⋊Q8—1063no—
459#121—23no—
460#121—23no—
461#121—23no—
462#121—536no—
463#121—1063no—
464#121—1063no—
465#121—1063no—
466#121C22×D5316yes—
467#120—26no—
468#120—1066no—
469C4×Q8C22⋊D5311yescharacteristic
470C4×Q8C22×D5311yescharacteristic
471C4×D4—23no—
472C4×D4—23no—
473C4×D4—23no—
474C4×D4—531no—
475C4×D4—533no—
476C4×D4—533no—
477C4×D4—533no—
478C4×D4—1063no—
479C4×D4—1063no—
480C4×D4—1063no—
481C4×D4C22⋊D5313yes—
482C4×D4C22×D5311yescharacteristic
483C4×D4C22×D5313yes—
484C4×D4C22×D5313yes—
485C4×D4C22×D5313yes—
486C4×D4C22×D5313yes—
487#117C22⋊D5313yes—
488C2×C4⋊C4—533no—
489C2×C4⋊C4C22×D5313yes—
490C2×C22⋊C4—23no—
491C2×C22⋊C4—1063no—
492C2×C42C22×D5313yes—
493#107—531no—
494#107—533no—
495#107—533no—
496#107—533no—
497#107—536no—
498C4⋊C8—533no—
499C4⋊C8—533no—
500#102—531no—
501#102—533no—
502#102—533no—
503#102—533no—
504#102—536no—
505#102—531no—
506#102—533no—
507#102—533no—
508#102—533no—
509#102—536no—
510C22⋊C8—536no—
511C4×C8—531no—
512C4×C8—533no—
513C4×C8—533no—
514C4×C8—533no—
515C24—23no—
516C24—1063no—
517#41—44no—
518#41—412no—
519#41—412no—
520#41—2124no—
521#41—21212no—
522#41—21212no—
523#41#1171992218yesdirect product factor
524C2×Q8—23no—
525C2×Q8—44no—
526C2×Q8—1063no—
527C2×Q8—2124no—
528C2×Q8C2×C22⋊D5311yescharacteristic
529C2×D4—26no—
530C2×D4—26no—
531C2×D4—23no—
532C2×D4—23no—
533C2×D4—23no—
534C2×D4—43no—
535C2×D4—412no—
536C2×D4—531no—
537C2×D4—533no—
538C2×D4—1066no—
539C2×D4—1066no—
540C2×D4—1063no—
541C2×D4—1063no—
542C2×D4—1063no—
543C2×D4—2123no—
544C2×D4—21212no—
545C2×D4C2×C22⋊D5313yes—
546C2×D4C23×D5313yes—
547C2×D4C23×D5311yescharacteristic
548C22×C4—23no—
549C22×C4—23no—
550C22×C4—23no—
551C22×C4—21no—
552C22×C4—23no—
553C22×C4—412no—
554C22×C4—1063no—
555C22×C4—1063no—
556C22×C4—1063no—
557C22×C4—1061no—
558C22×C4—1063no—
559C22×C4—21212no—
560C22×C4C2×C22⋊D5313yes—
561C22×C4C2×C22⋊D5313yes—
562C22×C4C23×D5313yes—
563D8—534no—
564D8—1066no—
565D8—1066no—
566D8—1066no—
567D8—2126no—
568C2×C8—531no—
569C2×C8—531no—
570C2×C8—533no—
571C2×C8—533no—
572C2×C8—1066no—
573C2×C8—2123no—
574C4⋊C4—23no—
575C4⋊C4—23no—
576C4⋊C4—531no—
577C4⋊C4—533no—
578C4⋊C4—1063no—
579C4⋊C4—1063no—
580C4⋊C4C2×C22⋊D5313yes—
581C4⋊C4C2×C22⋊D5313yes—
582C4⋊C4C23×D5311yescharacteristic
583C4⋊C4C23×D5313yes—
584C22⋊C4—21no—
585C22⋊C4—23no—
586C22⋊C4—23no—
587C22⋊C4—23no—
588C22⋊C4—26no—
589C22⋊C4—1061no—
590C22⋊C4—1063no—
591C22⋊C4—1063no—
592C22⋊C4—1063no—
593C22⋊C4—1066no—
594C22⋊C4C2×C22⋊D5316yes—
595C42C2×C22⋊D5313yes—
596C42C2×C22⋊D5313yes—
597C42C23×D5313yes—
598C42C23×D5311yescharacteristic
599C23—21no—
600C23—23no—
601C23—46no—
602C23—46no—
603C23—83no—
604C23—1061no—
605C23—1063no—
606C23—4243no—
607C23—2126no—
608C23—2126no—
609C23C22×C22⋊D5313yes—
610Q8—46no—
611Q8—2126no—
612Q8C2×#1171992214yescomplemented
613D4—23no—
614D4—21no—
615D4—23no—
616D4—46no—
617D4—412no—
618D4—46no—
619D4—83no—
620D4—532no—
621D4—1063no—
622D4—1061no—
623D4—1063no—
624D4—4243no—
625D4—2126no—
626D4—21212no—
627D4—2126no—
628D4C2×#11719922112yescomplemented
629D4#41×D5312yescomplemented
630C2×C4—23no—
631C2×C4—23no—
632C2×C4—21no—
633C2×C4—23no—
634C2×C4—43no—
635C2×C4—46no—
636C2×C4—42no—
637C2×C4—46no—
638C2×C4—46no—
639C2×C4—46no—
640C2×C4—1061no—
641C2×C4—1063no—
642C2×C4—2126no—
643C2×C4—2122no—
644C2×C4—2126no—
645C2×C4—2126no—
646C2×C4—2126no—
647C2×C4C2×#11719922112yescomplemented
648C2×C4C22×C22⋊D5311yescharacteristic
649C2×C4C22×C22⋊D5313yes—
650C2×C4C22×C22⋊D5313yes—
651C2×C4C22×C22⋊D5313yes—
652C2×C4C22×C22⋊D5311yescharacteristic
653C2×C4C24×D5311yescharacteristic
654C8—532no—
655C8—1063no—
656C8—1061no—
657C8—1063no—
658C22—23no—
659C22—23no—
660C22—22no—
661C22—41no—
662C22—41no—
663C22—43no—
664C22—43no—
665C22—43no—
666C22—812no—
667C22—1062no—
668C22—42412no—
669C22—2123no—
670C22—2123no—
671C22—2123no—
672C22—2121no—
673C22—2121no—
674C22C22×#1171992216yes—
675C22C23×C22⋊D5311yescharacteristic
676C4—23no—
677C4—21no—
678C4—23no—
679C4—41no—
680C4—43no—
681C4—2121no—
682C4—2123no—
683C4C22×#1171992212yes—
684C4C22×#1171992216yes—
685C4C2×#41×D5311yescharacteristic
686C4#1681145911yescharacteristic
687C2—26no—
688C2—42no—
689C2—83no—
690C2—4243no—
691C2—2122no—
692C2#41×C22⋊D5311yescharacteristic
693C2C23×#1171992211yescharacteristic
694C2#2028948611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingD4×#41×C53C2
socleC22×C53C23×D4
hypercenterD4×#41D53
hypocenterC53D8×#41
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ D4×#41

Complements

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

NH ≅ G/Ntype
1. #41×D212C2semidirect
2. #20287687C2semidirect
3. Q8×#11719922C2semidirect
4. #20287350C2semidirect
5. #20287346C2semidirect
6. #20287058C2semidirect
7. #20286528C2semidirect
8. #20286522C2semidirect
9. D4×#11719922C2semidirect
10. #20285290C2semidirect
11. #20284715C2semidirect
12. #20284711C2semidirect
13. #41×#88322C2semidirect
14. C2×C4×#11719922C2semidirect
15. D4×#41×C53C2semidirect
18. #16811295C22semidirect
19. Q8×D212C22semidirect
21. #16811277C22semidirect
23. D4×D212C22semidirect
24. #16811173C22semidirect
26. C2×C4×D212C22semidirect
27. #16811026C22semidirect
28. #16810999C22semidirect
29. #16810971C22semidirect
30. #16810969C22semidirect
31. #16810936C22semidirect
32. #16810934C22semidirect
33. #16810903C22semidirect
34. #16810903C22semidirect
35. #16810900C22semidirect
36. #16810900C22semidirect
37. #16810857C22semidirect
38. #16810857C22semidirect
39. #16810818C22semidirect
40. #16810818C22semidirect
41. #16810815C22semidirect
42. #16810815C22semidirect
43. #16810757C22semidirect
44. #16810756C22semidirect
45. Q8×#88322C22semidirect
46. Q8×#88322C22semidirect
49. C4×#11719922C22semidirect
50. C4×#11719922C22semidirect
51. C4×#11719922C22semidirect
52. C4×#11719922C22semidirect
53. C4×#11719922C22semidirect
54. C4×#11719922C22semidirect
55. C4×#11719922C22semidirect
56. D4×#88322C22semidirect
57. D4×#88322C22semidirect
58. #16810676C22semidirect
59. C2×#13133150C22semidirect
60. C2×#13133138C22semidirect
61. C2×#13133137C22semidirect
62. C2×C4×#88322C22semidirect
64. C53×#550C22semidirect
65. D4×Q8×C53C22semidirect
67. C53×#547C22semidirect
69. D42×C53C22semidirect
70. C53×#532C22semidirect
73. C2×C4×D4×C53C22semidirect
172. #41×C53D8semidirect
235. #11719922#41direct (N × H)
263. Q8×C53C2×D8semidirect
271. D4×C53C2×D8semidirect
272. D4×C53C2×#41semidirect
283. C2×C4×C53C2×D8semidirect
300. D212C2×#41semidirect
309. #88322C2×#41semidirect
341. D4×#41D53semidirect
367. #550C2×D53semidirect
369. D4×Q8C2×D53semidirect
373. #547C2×D53semidirect
377. D42C2×D53semidirect
379. #532C2×D53semidirect
384. C2×C4×D4C2×D53semidirect
421. C53D8×#41semidirect
523. #41#11719922direct (N × H)
612. Q8C2×#11719922semidirect
628. D4C2×#11719922semidirect
629. D4#41×D53semidirect
647. C2×C4C2×#11719922semidirect

Maximal subgroups

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

subgroupindex
#41×D2122
#202876872
Q8×#117199222
#202873502
#202873462
#202870582
#202865282
#202865222
D4×#117199222
#202852902
#202847152
#202847112
#41×#883222
C2×C4×#117199222
D4×#41×C532
D8×#4153