Finite Group Databasebeta

← #577×#6157 #28329543

Subgroups — #577×#6157 #28329543

Order 13568.

2742 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
12−1+4×#6157C211yesmaximal, characteristic, complemented
2H(5,𝔽2)×#6157C211yesmaximal, characteristic, complemented
3#20291478C213yesmaximal, complemented
4#20291475C213yesmaximal, complemented
5#20291473C213yesmaximal, complemented
6#20291472C213yesmaximal, complemented
7#137×#6157C213yesmaximal, complemented
8AGL(1,ℤ/8)×#6157C213yesmaximal, complemented
9#135×#6157C213yesmaximal, complemented
10C2×SD16×#6157C213yesmaximal, complemented
11#20291369C211yesmaximal, characteristic, complemented
12#20291337C211yesmaximal, characteristic, complemented
13#20291336C211yesmaximal, characteristic, complemented
14#131×#6157C211yesmaximal, characteristic, complemented
15#577×D53C211yesmaximal, characteristic
16D53⋊#131C2211yescharacteristic
17#16811692—21no—
18#16811692—23no—
19#16811692C2213yes—
20#16811692C2211yescharacteristic
21#16811692C2211yescharacteristic
22#16811692C2213yescomplemented
23#16811691—21no—
24#16811691C2213yescomplemented
25#16811690—23no—
26#16811690C2213yes—
27#41×#6157—21no—
28#41×#6157—23no—
29#41×#6157C2213yes—
30#41×#6157C2211yescharacteristic
31#41×#6157C2213yescomplemented
32C2×Q8×#6157—21no—
33C2×Q8×#6157C2213yescomplemented
34C2×D4×#6157—23no—
35C2×D4×#6157C2213yes—
36#16811664C2216yescomplemented
37#16811663C2216yescomplemented
38#16811662C2216yescomplemented
39#16811662C2216yescomplemented
40Q16×#6157C2213yescomplemented
41Q16×#6157C2213yescomplemented
42SD16×#6157C2213yescomplemented
43SD16×#6157C2216yescomplemented
44SD16×#6157C2216yescomplemented
45SD16×#6157C2216yescomplemented
46SD16×#6157C2211yescharacteristic, complemented
47SD16×#6157C2213yescomplemented
48SD16×#6157C2213yescomplemented
49D8×#6157C2213yescomplemented
50D8×#6157C2213yescomplemented
51#16811634C2213yescomplemented
52#16811634C2213yescomplemented
53#16811633C2213yescomplemented
54C2×#13133285C2213yescomplemented
55#16811616C2213yescomplemented
56#16811615C2213yes—
57#16811614C2213yes—
58#16811614C2213yescomplemented
59#16811613C2213yes—
60#16811613C2213yescomplemented
61C2×#13133280C2213yescomplemented
62C2×#13133279C2213yes—
63#16811589C2213yescomplemented
64#16811586C2213yescomplemented
65M16×#6157C2213yescomplemented
66C2×C8×#6157C2213yescomplemented
672−1+4×D53C2211yescharacteristic
68H(5,𝔽2)×D53C2211yescharacteristic
69#16811435C411yescharacteristic, complemented
70#16811434C411yescharacteristic, complemented
71#16811433C413yescomplemented
72#16811432C413yescomplemented
73#16811431C411yescharacteristic, complemented
74#16811430C413yescomplemented
75#16811429C413yescomplemented
76#137×D53C2213yes—
77AGL(1,ℤ/8)×D53C2213yes—
78#135×D53C2213yes—
79C2×SD16×D53C2213yes—
80#131×D53C2211yescharacteristic
81C53×#577C411yescharacteristic, complemented
82C23×#6157—23no—
83#13133305—21no—
84#13133304—23no—
85D53⋊M16C2313yes—
86C2×D53⋊C8C2313yes—
87Q8×#6157—21no—
88Q8×#6157—21no—
89Q8×#6157—23no—
90Q8×#6157—23no—
91Q8×#6157—23no—
92Q8×#6157—23no—
93Q8×#6157D411yescharacteristic
94Q8×#6157D411yescharacteristic
95Q8×#6157C2313yes—
96Q8×#6157C2316yes—
97Q8×#6157C2311yescharacteristic
98Q8×#6157C2313yes—
99Q8×#6157C2313yes—
100D4×#6157—23no—
101D4×#6157—23no—
102D4×#6157—23no—
103D4×#6157—23no—
104D4×#6157—23no—
105D4×#6157—23no—
106D4×#6157—26no—
107D4×#6157—26no—
108D4×#6157—23no—
109D4×#6157—23no—
110D4×#6157—23no—
111D4×#6157—23no—
112D4×#6157D413yes—
113D4×#6157D413yes—
114D4×#6157C2311yescharacteristic
115D4×#6157C2313yes—
116D4×#6157C2313yes—
117D4×#6157C2313yes—
118D4×#6157C2316yes—
119#13133296—26no—
120#13133296—23no—
121#13133296—23no—
122#13133296—23no—
123#13133296—23no—
124#13133296C2313yes—
125#13133296C2313yes—
126#13133296C2313yes—
127C2×C4⋊#6157—23no—
128C2×C4⋊#6157—23no—
129C2×C4⋊#6157—23no—
130C2×C4⋊#6157C2313yes—
131C2×C4⋊#6157C2313yes—
132C2×C22⋊#6157—23no—
133C2×C22⋊#6157—26no—
134C2×C4×#6157—23no—
135C2×C4×#6157—23no—
136C2×C4×#6157—23no—
137C2×C4×#6157C2313yes—
138#13133286C2313yes—
139#13133286C2313yes—
140#13133285C2313yes—
141#13133285C2316yes—
142#13133285C2311yescharacteristic
143#13133280C2313yes—
144#13133280C2316yes—
145#13133280C2311yescharacteristic
146#13133280C2313yes—
147#13133280C2313yes—
148#13133279C2313yes—
149#13133279C2316yes—
150#13133279C2313yes—
151#13133279C2311yescharacteristic
152#13133279C2313yes—
153#13133271C2316yes—
154C8×#6157C2311yescharacteristic
155C8×#6157C2313yes—
156C8×#6157C2313yes—
157C8×#6157C2313yes—
158#13133265—21no—
159#13133265C2×C413yescomplemented
160#13133264—23no—
161#13133264C2×C413yescomplemented
162#13133264C2×C411yescharacteristic, complemented
163#13133263—21no—
164#13133263C2×C413yescomplemented
165#13133263C2×C411yescharacteristic, complemented
166#13133262—23no—
167#13133262C2×C413yescomplemented
168#41×D53—21no—
169#41×D53—23no—
170#41×D53C2313yes—
171#41×D53C2313yes—
172#41×D53C2311yescharacteristic
173C2×Q8×D53—21no—
174C2×Q8×D53C2313yes—
175C2×D4×D53—23no—
176C2×D4×D53C2313yes—
177#13133250C2×C413yescomplemented
178#13133249C2×C416yescomplemented
179#13133248C2×C413yescomplemented
180#13133247C2×C413yescomplemented
181#13133246C2×C416yescomplemented
182#13133245C2×C413yescomplemented
183#13133244C2×C416yescomplemented
184#13133243C2×C413yescomplemented
185#13133242C2×C413yescomplemented
186#13133241C2×C416yescomplemented
187#13133240C2×C413yescomplemented
188#13133239C2×C413yescomplemented
189#13133238C2×C413yescomplemented
190#13133238C2×C413yescomplemented
191#13133237C2×C413yescomplemented
192#13133237C2×C413yescomplemented
193#13133236C2×C413yescomplemented
194Q16×D53C2313yes—
195C2×#11719913C2×C413yescomplemented
196C2×#11719923C2×C413yescomplemented
197C2×#11719924C2×C413yescomplemented
198SD16×D53C2×C416yescomplemented
199SD16×D53C2×C416yescomplemented
200SD16×D53C2313yes—
201SD16×D53C2316yes—
202SD16×D53C2311yescharacteristic
203D8×D53C2313yes—
204#13133225C2×C413yescomplemented
205#13133224C2×C411yescharacteristic, complemented
206#13133223C2×C413yescomplemented
207M16×D53C2313yes—
208C2×C8×D53C2313yes—
2092−1+4×C53C2×C411yescharacteristic, complemented
210H(5,𝔽2)×C53C2×C411yescharacteristic, complemented
211#137×C53C2×C413yescomplemented
212AGL(1,ℤ/8)×C53C2×C413yescomplemented
213#135×C53C2×C413yescomplemented
214C2×SD16×C53C2×C413yescomplemented
215#131×C53C2×C411yescharacteristic, complemented
216C23×D53—23no—
217C22×#6157—23no—
218C22×#6157—23no—
219C22×#6157—21no—
220C22×#6157—23no—
221C22×#6157—23no—
222C22×#6157—23no—
223C22×#6157—26no—
224C22×#6157—86no—
225C22×#6157C2×D413yes—
226C22×#6157C2×D413yes—
227#41×C53—21no—
228#41×C53—23no—
229#41×C53C22×C413yes—
230#41×C53C22×C411yescharacteristic
231#41×C53C22×C413yescomplemented
232C2×Q8×C53—21no—
233C2×Q8×C53C22×C413yescomplemented
234C2×D4×C53—23no—
235C2×D4×C53C22×C413yes—
236C2×C22⋊D53—26no—
237C2×C22⋊D53—23no—
238#11719949—21no—
239#11719949—23no—
240#11719949C22×C413yes—
241#11719949C22×C413yescomplemented
242#11719949#4111yescharacteristic
243Q8×D53—21no—
244Q8×D53—23no—
245Q8×D53—23no—
246Q8×D53—23no—
247Q8×D53C22×C416yescomplemented
248Q8×D53C2×D411yescharacteristic
249Q8×D53C2413yes—
250Q8×D53C2411yescharacteristic
251#11719947—23no—
252#11719947—26no—
253#11719947—23no—
254#11719947—23no—
255#11719947—23no—
256#11719947C22×C413yes—
257#11719947C22×C413yescomplemented
258#11719947#4113yes—
259D4×D53—23no—
260D4×D53—23no—
261D4×D53—23no—
262D4×D53—26no—
263D4×D53—23no—
264D4×D53—23no—
265D4×D53—23no—
266D4×D53C22×C416yes—
267D4×D53C2×D413yes—
268D4×D53C2411yescharacteristic
269D4×D53C2413yes—
270#11719945—26no—
271#11719945—23no—
272#11719945—23no—
273#11719945—23no—
274#11719945—23no—
275#11719945C22×C413yes—
276#11719945C22×C413yes—
277#11719945C22×C413yescomplemented
278C2×D212—23no—
279C2×D212C22×C413yes—
280C2×C4×D53—23no—
281C2×C4×D53—23no—
282C2×C4×D53—23no—
283C2×C4×D53C2413yes—
284C2×Dic106—23no—
285C2×Dic106—23no—
286C2×Dic106C22×C413yescomplemented
287C22⋊#6157—23no—
288C22⋊#6157—23no—
289C22⋊#6157—23no—
290C22⋊#6157—26no—
291C22⋊#6157—23no—
292C22⋊#6157—21no—
293C22⋊#6157—23no—
294C22⋊#6157C2×D416yes—
295#11719940—23no—
296C2×#88324—23no—
297C4⋊#6157—23no—
298C4⋊#6157—26no—
299C4⋊#6157—23no—
300C4⋊#6157—21no—
301C4⋊#6157—23no—
302C4⋊#6157—23no—
303C4⋊#6157—23no—
304C4⋊#6157C2×D413yes—
305C4⋊#6157C2×D413yes—
306C4⋊#6157C2413yes—
307C4⋊#6157C2411yescharacteristic
308C4⋊#6157C2413yes—
309C4⋊#6157C2411yescharacteristic
310C4×#6157—21no—
311C4×#6157—23no—
312C4×#6157—23no—
313C4×#6157—23no—
314C4×#6157—26no—
315C4×#6157—23no—
316C4×#6157—23no—
317C4×#6157C2×D413yes—
318C4×#6157C2×D413yes—
319C4×#6157C2411yescharacteristic
320C4×#6157C2413yes—
321#11719936—23no—
322D53⋊C8—23no—
323D53⋊C8C2411yescharacteristic
324D53⋊C8C2413yes—
325Q16×C53C22×C413yescomplemented
326SD16×C53C22×C413yescomplemented
327SD16×C53C22×C416yescomplemented
328SD16×C53C22×C411yescharacteristic, complemented
329D8×C53C22×C413yescomplemented
330M16×C53C22×C413yescomplemented
331C2×C8×C53C22×C413yescomplemented
332#11719925C22×C413yescomplemented
333#11719925C22×C413yescomplemented
334#11719924C22×C413yescomplemented
335#11719924C22×C416yescomplemented
336#11719924C22×C411yescharacteristic, complemented
337#11719923C22×C413yescomplemented
338#11719923C22×C416yescomplemented
339#11719923C22×C411yescharacteristic, complemented
340#11719922C22×C413yescomplemented
341#11719922C22×C413yescomplemented
342#11719917C22×C413yescomplemented
343C2×#88322C22×C413yescomplemented
344Dic212C22×C413yescomplemented
345D424C22×C413yescomplemented
346#11719913C22×C413yescomplemented
347#11719913C22×C416yescomplemented
348#11719913C22×C411yescharacteristic, complemented
349#11719912C22×C416yescomplemented
350C8×D53C22×C413yescomplemented
351C8×D53C22×C413yescomplemented
352C8×D53C2411yescharacteristic
353C8×D53C2413yes—
354C23×C53—23no—
355C22×D53—23no—
356C22×D53—21no—
357C22×D53—23no—
358C22×D53—26no—
359C22×D53—83no—
360C22×D53—83no—
361C22×D53C22×D413yes—
362C2×#6157—26no—
363C2×#6157—21no—
364C2×#6157—23no—
365C2×#6157—21no—
366C2×#6157—23no—
367C2×#6157—43no—
368C2×#6157—42no—
369C2×#6157—46no—
370C2×#6157—83no—
371C2×#6157—83no—
372C2×#6157—86no—
373C2×#6157—83no—
374C2×#6157—83no—
375C2×#6157C22×D413yes—
376C2×#6157C22×D413yes—
377C2×#6157C22×D411yescharacteristic
378C2×#6157C22×D411yescharacteristic
379Q8×C53—23no—
380Q8×C53C4×D411yescharacteristic
381Q8×C53C23×C413yes—
382Q8×C53C23×C411yescharacteristic
383D4×C53—23no—
384D4×C53—23no—
385D4×C53—23no—
386D4×C53C4×D413yes—
387D4×C53C23×C413yes—
388D4×C53C23×C411yescharacteristic
389C2×C4×C53—23no—
390C2×C4×C53—23no—
391C2×C4×C53—23no—
392C2×C4×C53C23×C413yes—
393C22⋊D53—23no—
394C22⋊D53—23no—
395C22⋊D53—23no—
396C22⋊D53—23no—
397C22⋊D53—26no—
398C22⋊D53—21no—
399C22⋊D53—23no—
400C22⋊D53C4×D416yes—
401C2×Dic53—23no—
402C2×Dic53—23no—
403C2×Dic53—23no—
404C2×Dic53C2×#4113yes—
405D212—23no—
406D212—23no—
407D212—23no—
408D212C4×D413yes—
409D212C23×C413yes—
410D212C23×C411yescharacteristic
411C4×D53—26no—
412C4×D53—21no—
413C4×D53—23no—
414C4×D53—23no—
415C4×D53—23no—
416C4×D53—23no—
417C4×D53—23no—
418C4×D53C23×C413yes—
419C4×D53C22×D413yes—
420C4×D53C2×#4113yes—
421C4×D53C2511yescharacteristic
422Dic106—23no—
423Dic106—26no—
424Dic106—23no—
425Dic106—21no—
426Dic106C4×D413yes—
427Dic106C23×C413yes—
428Dic106C23×C411yescharacteristic
429#88324—23no—
430#88324—21no—
431C8×C53C23×C411yescharacteristic
432C8×C53C23×C413yes—
433#88322C23×C411yescharacteristic
434#88322C23×C413yes—
435C4×#577—531nomaximal, Sylow
436C22×C53—21no—
437C22×C53—23no—
438C22×C53—83no—
439C22×C53C2×C4×D413yes—
440C2×D53—23no—
441C2×D53—23no—
442C2×D53—21no—
443C2×D53—23no—
444C2×D53—41no—
445C2×D53—43no—
446C2×D53—43no—
447C2×D53—41no—
448C2×D53—86no—
449C2×D53—83no—
450C2×D53C2×C4×D413yes—
451C2×D53C23×D411yescharacteristic
452#6157—21no—
453#6157—23no—
454#6157—23no—
455#6157—43no—
456#6157—41no—
457#6157—41no—
458#6157—43no—
459#6157#57712yesdirect product factor
460C4×C53—23no—
461C4×C53—21no—
462C4×C53C2×C4×D413yes—
463C4×C53C24×C411yescharacteristic
464Dic53—23no—
465Dic53—21no—
466Dic53C2×C4×D413yes—
467Dic53C22×#4111yescharacteristic
468C2×#577—531no—
469C4×2−1+4—531no—
470C4×H(5,𝔽2)—531no—
471#2952—533no—
472#2949—533no—
473#2947—533no—
474#2946—533no—
475C4×#137—533no—
476C4×AGL(1,ℤ/8)—533no—
477C4×#135—533no—
478C2×C4×SD16—533no—
479#2912—531no—
480#2898—531no—
481#2897—531no—
482C4×#131—531no—
483C2×C53—23no—
484C2×C53—43no—
485C2×C53—41no—
486C2×C53C22×C4×D411yescharacteristic
487D53—23no—
488D53—41no—
489D53—43no—
490D53C2×#57711yescharacteristic
491D53#358411yescharacteristic
492C2×2−1+4—531no—
493C2×H(5,𝔽2)—531no—
494#577—531no—
495#577—531no—
496#577—533no—
497#577—533no—
498#577—533no—
499#577—533no—
500#577—531no—
501#577#615711yescharacteristic, direct product factor
502C2×#137—533no—
503C2×AGL(1,ℤ/8)—533no—
504C2×#135—533no—
505C22×SD16—533no—
506C2×#131—531no—
507C2×#131—531no—
508#520—531no—
509#520—531no—
510#520—533no—
511#520—533no—
512#520—1063no—
513#520—1061no—
514#519—533no—
515#519—1061no—
516#518—533no—
517#518—1063no—
518C4×#41—531no—
519C4×#41—533no—
520C4×#41—533no—
521C4×#41—1063no—
522C4×#41—1061no—
523C2×C4×Q8—533no—
524C2×C4×Q8—1061no—
525C2×C4×D4—533no—
526C2×C4×D4—1063no—
527#442—536no—
528#441—536no—
529#440—536no—
530#440—536no—
531C4×Q16—533no—
532C4×Q16—533no—
533C4×SD16—533no—
534C4×SD16—536no—
535C4×SD16—536no—
536C4×SD16—536no—
537C4×SD16—531no—
538C4×SD16—533no—
539C4×SD16—533no—
540C4×D8—533no—
541C4×D8—533no—
542#428—533no—
543#428—533no—
544#427—533no—
545C2×#106—533no—
546#419—533no—
547#418—533no—
548#417—533no—
549#417—533no—
550#416—533no—
551#416—533no—
552C2×#103—533no—
553C2×#102—533no—
554#405—533no—
555#405—533no—
556C4×M16—533no—
557C2×C4×C8—533no—
558C53C4×#57711yescharacteristic, complemented, Sylow
5592−1+4—531no—
5602−1+4—533no—
5612−1+4—533no—
5622−1+4—1061no—
5632−1+4—1063no—
5642−1+4C2×#615711yescharacteristic, complemented
565H(5,𝔽2)—533no—
566H(5,𝔽2)—531no—
567H(5,𝔽2)—533no—
568H(5,𝔽2)—1063no—
569H(5,𝔽2)—1061no—
570H(5,𝔽2)C2×#615711yescharacteristic, complemented
571C2×#41—531no—
572C2×#41—533no—
573C2×#41—533no—
574C2×#41—1063no—
575C2×#41—1061no—
576C22×Q8—533no—
577C22×Q8—1061no—
578C22×D4—533no—
579C22×D4—1063no—
580C23×C4—1063no—
581#137—533no—
582#137—533no—
583#137—536no—
584#137—536no—
585#137—533no—
586#137C2×#615713yescomplemented
587AGL(1,ℤ/8)—533no—
588AGL(1,ℤ/8)—533no—
589AGL(1,ℤ/8)—536no—
590AGL(1,ℤ/8)—536no—
591AGL(1,ℤ/8)—533no—
592AGL(1,ℤ/8)C2×#615713yescomplemented
593#135—533no—
594#135—533no—
595#135—533no—
596#135—533no—
597#135—533no—
598#135—533no—
599#135—533no—
600#135C2×#615713yescomplemented
601C2×Q16—533no—
602C2×SD16—533no—
603C2×SD16—533no—
604C2×SD16—533no—
605C2×SD16—536no—
606C2×SD16—536no—
607C2×SD16—536no—
608C2×SD16—531no—
609C2×SD16—533no—
610C2×SD16C2×#615713yescomplemented
611C2×D8—533no—
612#131—531no—
613#131—533no—
614#131—533no—
615#131—1063no—
616#131—1061no—
617#131C2×#615711yescharacteristic, complemented
618C2×M16—533no—
619C2×M16—533no—
620C22×C8—533no—
621C22×C8—533no—
622C4×Q8—531no—
623C4×Q8—531no—
624C4×Q8—533no—
625C4×Q8—536no—
626C4×Q8—531no—
627C4×Q8—533no—
628C4×Q8—533no—
629C4×Q8—1063no—
630C4×Q8—1063no—
631C4×Q8—1063no—
632C4×Q8—1063no—
633C4×Q8—1061no—
634C4×Q8—1061no—
635C4×D4—533no—
636C4×D4—533no—
637C4×D4—533no—
638C4×D4—536no—
639C4×D4—531no—
640C4×D4—533no—
641C4×D4—533no—
642C4×D4—1063no—
643C4×D4—1063no—
644C4×D4—1066no—
645C4×D4—1066no—
646C4×D4—1063no—
647C4×D4—1063no—
648C4×D4—1063no—
649C4×D4—1063no—
650C4×D4—1063no—
651C4×D4—1063no—
652C4×D4—1063no—
653C4×D4—1063no—
654#117—533no—
655#117—533no—
656#117—533no—
657#117—1063no—
658#117—1063no—
659#117—1066no—
660#117—1063no—
661#117—1063no—
662C2×C4⋊C4—533no—
663C2×C4⋊C4—533no—
664C2×C4⋊C4—1063no—
665C2×C4⋊C4—1063no—
666C2×C4⋊C4—1063no—
667C2×C22⋊C4—1066no—
668C2×C22⋊C4—1063no—
669C2×C42—533no—
670C2×C42—1063no—
671C2×C42—1063no—
672C2×C42—1063no—
673#107—533no—
674#107—533no—
675#106—533no—
676#106—536no—
677#106—531no—
678#103—533no—
679#103—536no—
680#103—531no—
681#103—533no—
682#103—533no—
683#102—533no—
684#102—536no—
685#102—531no—
686#102—533no—
687#102—533no—
688#97—536no—
689C4×C8—531no—
690C4×C8—533no—
691C4×C8—533no—
692C4×C8—533no—
693C24—1063no—
694#41—21no—
695#41—23no—
696#41—531no—
697#41—533no—
698#41—533no—
699#41—533no—
700#41—533no—
701#41—533no—
702#41—533no—
703#41—533no—
704#41—533no—
705#41—1063no—
706#41—1063no—
707#41—1066no—
708#41—1063no—
709#41—1063no—
710#41—1063no—
711#41—1063no—
712#41—1066no—
713#41—1063no—
714#41—1063no—
715#41—1061no—
716#41—1063no—
717#41C22×#615713yes—
718#41C22×#615711yescharacteristic
719#41C22×#615713yescomplemented
720C2×Q8—21no—
721C2×Q8—531no—
722C2×Q8—536no—
723C2×Q8—533no—
724C2×Q8—531no—
725C2×Q8—533no—
726C2×Q8—1063no—
727C2×Q8—1063no—
728C2×Q8—1063no—
729C2×Q8—1063no—
730C2×Q8—1063no—
731C2×Q8—1061no—
732C2×Q8C22×#615713yescomplemented
733C2×D4—23no—
734C2×D4—533no—
735C2×D4—536no—
736C2×D4—531no—
737C2×D4—533no—
738C2×D4—533no—
739C2×D4—1063no—
740C2×D4—1063no—
741C2×D4—1063no—
742C2×D4—1063no—
743C2×D4—1066no—
744C2×D4—1063no—
745C2×D4—1063no—
746C2×D4—1063no—
747C2×D4—1066no—
748C2×D4—1063no—
749C2×D4C22×#615713yes—
750C22×C4—533no—
751C22×C4—533no—
752C22×C4—533no—
753C22×C4—1063no—
754C22×C4—1063no—
755C22×C4—1063no—
756C22×C4—1063no—
757C22×C4—1063no—
758C22×C4—1066no—
759C22×C4—1061no—
760C22×C4—1063no—
761C22×C4—1063no—
762C22×C4—1063no—
763C22×C4—4246no—
764Q16—533no—
765Q16—533no—
766Q16—533no—
767Q16C22×#615713yescomplemented
768SD16—533no—
769SD16—536no—
770SD16—531no—
771SD16—533no—
772SD16—536no—
773SD16—531no—
774SD16—533no—
775SD16—536no—
776SD16—531no—
777SD16C22×#615713yescomplemented
778SD16C22×#615716yescomplemented
779SD16C22×#615711yescharacteristic, complemented
780D8—533no—
781D8—533no—
782D8—533no—
783D8C22×#615713yescomplemented
784M16—533no—
785M16—536no—
786M16—1063no—
787M16—1063no—
788M16C22×#615713yescomplemented
789C2×C8—533no—
790C2×C8—531no—
791C2×C8—533no—
792C2×C8—533no—
793C2×C8—533no—
794C2×C8—531no—
795C2×C8—533no—
796C2×C8—1063no—
797C2×C8—1063no—
798C2×C8C22×#615713yescomplemented
799C4⋊C4—533no—
800C4⋊C4—533no—
801C4⋊C4—533no—
802C4⋊C4—531no—
803C4⋊C4—533no—
804C4⋊C4—531no—
805C4⋊C4—1063no—
806C4⋊C4—1063no—
807C4⋊C4—1063no—
808C4⋊C4—1063no—
809C4⋊C4—1066no—
810C4⋊C4—1061no—
811C4⋊C4—1063no—
812C22⋊C4—536no—
813C22⋊C4—1063no—
814C22⋊C4—1063no—
815C22⋊C4—1066no—
816C22⋊C4—1061no—
817C22⋊C4—1063no—
818C22⋊C4—1063no—
819C22⋊C4—1063no—
820C42—533no—
821C42—533no—
822C42—531no—
823C42—533no—
824C42—1061no—
825C42—1063no—
826C42—1063no—
827C42—1063no—
828C42—1063no—
829C42—1063no—
830C42—1066no—
831C23—23no—
832C23—533no—
833C23—1066no—
834C23—1061no—
835C23—1063no—
836C23—1063no—
837C23—4243no—
838C23—4243no—
839Q8—23no—
840Q8—533no—
841Q8—533no—
842Q8—531no—
843Q8—1063no—
844Q8—1066no—
845Q8—1061no—
846Q8—1063no—
847Q8D4×#615711yescharacteristic
848Q8C23×#615713yes—
849Q8C23×#615711yescharacteristic
850D4—23no—
851D4—23no—
852D4—23no—
853D4—536no—
854D4—533no—
855D4—531no—
856D4—533no—
857D4—1063no—
858D4—1063no—
859D4—1063no—
860D4—1066no—
861D4—1061no—
862D4—1063no—
863D4—1063no—
864D4—1063no—
865D4—1063no—
866D4—1063no—
867D4D4×#615713yes—
868D4C23×#615711yescharacteristic
869D4C23×#615713yes—
870C2×C4—23no—
871C2×C4—23no—
872C2×C4—23no—
873C2×C4—531no—
874C2×C4—533no—
875C2×C4—533no—
876C2×C4—533no—
877C2×C4—533no—
878C2×C4—531no—
879C2×C4—531no—
880C2×C4—533no—
881C2×C4—533no—
882C2×C4—1063no—
883C2×C4—1063no—
884C2×C4—1061no—
885C2×C4—1063no—
886C2×C4—1066no—
887C2×C4—1063no—
888C2×C4—1063no—
889C2×C4—1066no—
890C2×C4—1063no—
891C2×C4—1063no—
892C2×C4—1063no—
893C2×C4—1061no—
894C2×C4—1061no—
895C2×C4—1063no—
896C2×C4—1063no—
897C2×C4—4243no—
898C2×C4—4243no—
899C2×C4—4246no—
900C2×C4—4243no—
901C2×C4—4243no—
902C2×C4—2122no—
903C2×C4—2126no—
904C2×C4—2123no—
905C2×C4C23×#615713yes—
906C8—531no—
907C8—533no—
908C8—1061no—
909C8—1063no—
910C8C23×#615711yescharacteristic
911C8C23×#615713yes—
912C22—21no—
913C22—23no—
914C22—83no—
915C22—531no—
916C22—533no—
917C22—1063no—
918C22—1063no—
919C22—1061no—
920C22—1063no—
921C22—4243no—
922C22—4246no—
923C22—2121no—
924C22—2123no—
925C22—2123no—
926C22—2121no—
927C22C2×D4×#615713yes—
928C4—21no—
929C4—23no—
930C4—532no—
931C4—531no—
932C4—533no—
933C4—1063no—
934C4—1063no—
935C4—1061no—
936C4—1061no—
937C4—1063no—
938C4—2123no—
939C4—2121no—
940C4—2123no—
941C4—2121no—
942C4C2×D4×#615713yes—
943C4C24×#615711yescharacteristic
944C2—23no—
945C2—43no—
946C2—41no—
947C2—531no—
948C2—531no—
949C2—1063no—
950C2—2123no—
951C2—2121no—
952C2C22×D4×#615711yescharacteristic
subgroupG/H
centerC2C22×D4×#6157
commutatorC4×C53C24×C4
FrattiniC4C24×#6157
FittingC53×#577C4
socleC2×C53C22×C4×D4
prime radical#577×D53C2
cosocleC4×D53C25
hypercenter#577#6157
hypocenterC53C4×#577
LCSG ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2 ◁ #41 ◁ #577

Complements

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

NH ≅ G/Ntype
1. 2−1+4×#6157C2semidirect
2. H(5,𝔽2)×#6157C2semidirect
3. #20291478C2semidirect
4. #20291475C2semidirect
5. #20291473C2semidirect
6. #20291472C2semidirect
7. #137×#6157C2semidirect
8. AGL(1,ℤ/8)×#6157C2semidirect
9. #135×#6157C2semidirect
10. C2×SD16×#6157C2semidirect
11. #20291369C2semidirect
12. #20291337C2semidirect
13. #20291336C2semidirect
14. #131×#6157C2semidirect
22. #16811692C22semidirect
24. #16811691C22semidirect
31. #41×#6157C22semidirect
33. C2×Q8×#6157C22semidirect
36. #16811664C22semidirect
37. #16811663C22semidirect
38. #16811662C22semidirect
39. #16811662C22semidirect
40. Q16×#6157C22semidirect
41. Q16×#6157C22semidirect
42. SD16×#6157C22semidirect
43. SD16×#6157C22semidirect
44. SD16×#6157C22semidirect
45. SD16×#6157C22semidirect
46. SD16×#6157C22semidirect
47. SD16×#6157C22semidirect
48. SD16×#6157C22semidirect
49. D8×#6157C22semidirect
50. D8×#6157C22semidirect
51. #16811634C22semidirect
52. #16811634C22semidirect
53. #16811633C22semidirect
54. C2×#13133285C22semidirect
55. #16811616C22semidirect
58. #16811614C22semidirect
60. #16811613C22semidirect
61. C2×#13133280C22semidirect
63. #16811589C22semidirect
64. #16811586C22semidirect
65. M16×#6157C22semidirect
66. C2×C8×#6157C22semidirect
69. #16811435C4semidirect
70. #16811434C4semidirect
71. #16811433C4semidirect
72. #16811432C4semidirect
73. #16811431C4semidirect
74. #16811430C4semidirect
75. #16811429C4semidirect
81. C53×#577C4semidirect
159. #13133265C2×C4semidirect
161. #13133264C2×C4semidirect
162. #13133264C2×C4semidirect
164. #13133263C2×C4semidirect
165. #13133263C2×C4semidirect
167. #13133262C2×C4semidirect
177. #13133250C2×C4semidirect
178. #13133249C2×C4semidirect
179. #13133248C2×C4semidirect
180. #13133247C2×C4semidirect
181. #13133246C2×C4semidirect
182. #13133245C2×C4semidirect
183. #13133244C2×C4semidirect
184. #13133243C2×C4semidirect
185. #13133242C2×C4semidirect
186. #13133241C2×C4semidirect
187. #13133240C2×C4semidirect
188. #13133239C2×C4semidirect
189. #13133238C2×C4semidirect
190. #13133238C2×C4semidirect
191. #13133237C2×C4semidirect
192. #13133237C2×C4semidirect
193. #13133236C2×C4semidirect
195. C2×#11719913C2×C4semidirect
196. C2×#11719923C2×C4semidirect
197. C2×#11719924C2×C4semidirect
198. SD16×D53C2×C4semidirect
199. SD16×D53C2×C4semidirect
204. #13133225C2×C4semidirect
205. #13133224C2×C4semidirect
206. #13133223C2×C4semidirect
209. 2−1+4×C53C2×C4semidirect
210. H(5,𝔽2)×C53C2×C4semidirect
211. #137×C53C2×C4semidirect
212. AGL(1,ℤ/8)×C53C2×C4semidirect
213. #135×C53C2×C4semidirect
214. C2×SD16×C53C2×C4semidirect
215. #131×C53C2×C4semidirect
231. #41×C53C22×C4semidirect
233. C2×Q8×C53C22×C4semidirect
241. #11719949C22×C4semidirect
247. Q8×D53C22×C4semidirect
257. #11719947C22×C4semidirect
277. #11719945C22×C4semidirect
286. C2×Dic106C22×C4semidirect
325. Q16×C53C22×C4semidirect
326. SD16×C53C22×C4semidirect
327. SD16×C53C22×C4semidirect
328. SD16×C53C22×C4semidirect
329. D8×C53C22×C4semidirect
330. M16×C53C22×C4semidirect
331. C2×C8×C53C22×C4semidirect
332. #11719925C22×C4semidirect
333. #11719925C22×C4semidirect
334. #11719924C22×C4semidirect
335. #11719924C22×C4semidirect
336. #11719924C22×C4semidirect
337. #11719923C22×C4semidirect
338. #11719923C22×C4semidirect
339. #11719923C22×C4semidirect
340. #11719922C22×C4semidirect
341. #11719922C22×C4semidirect
342. #11719917C22×C4semidirect
343. C2×#88322C22×C4semidirect
344. Dic212C22×C4semidirect
345. D424C22×C4semidirect
346. #11719913C22×C4semidirect
347. #11719913C22×C4semidirect
348. #11719913C22×C4semidirect
349. #11719912C22×C4semidirect
350. C8×D53C22×C4semidirect
351. C8×D53C22×C4semidirect
459. #6157#577direct (N × H)
501. #577#6157direct (N × H)
558. C53C4×#577semidirect
564. 2−1+4C2×#6157semidirect
570. H(5,𝔽2)C2×#6157semidirect
586. #137C2×#6157semidirect
592. AGL(1,ℤ/8)C2×#6157semidirect
600. #135C2×#6157semidirect
610. C2×SD16C2×#6157semidirect
617. #131C2×#6157semidirect
719. #41C22×#6157semidirect
732. C2×Q8C22×#6157semidirect
767. Q16C22×#6157semidirect
777. SD16C22×#6157semidirect
778. SD16C22×#6157semidirect
779. SD16C22×#6157semidirect
783. D8C22×#6157semidirect
788. M16C22×#6157semidirect
798. C2×C8C22×#6157semidirect

Maximal subgroups

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

subgroupindex
2−1+4×#61572
H(5,𝔽2)×#61572
#202914782
#202914752
#202914732
#202914722
#137×#61572
AGL(1,ℤ/8)×#61572
#135×#61572
C2×SD16×#61572
#202913692
#202913372
#202913362
#131×#61572
#577×D532
C4×#57753