Finite Group Databasebeta

← C2×#20289497 #28297936

Subgroups — C2×#20289497 #28297936

Order 13568.

10794 conjugacy classes of subgroups.

The subgroup lattice has 1104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811458C211yesmaximal, characteristic, complemented
2C2×2−1+4×D53C211yesmaximal, characteristic, complemented
3#20289497C2132yesmaximal, direct product factor
4C2×#16811440C211yesmaximal, characteristic, complemented
5C2×#16811439C213yesmaximal, complemented
6C2×#16811438C211yesmaximal, characteristic, complemented
7C2×#16811437C213yesmaximal, complemented
8C2×#16811434C211yesmaximal, characteristic, complemented
9C2×#16811433C213yesmaximal, complemented
10C2×#16811429C213yesmaximal, complemented
11C2×#16811420C213yesmaximal, complemented
12C2×#16811419C213yesmaximal, complemented
13C22×#13133246C213yesmaximal, complemented
14C2×#137×D53C213yesmaximal, complemented
15C2×#16811388C211yesmaximal, characteristic, complemented
16C2×C53×#577C211yesmaximal, characteristic, complemented
17#16811458—28no—
18#16811458C22116yescomplemented
19C2×#13133265—21no—
20C2×#13133265C2213yescomplemented
21C2×#13133264—23no—
22C2×#13133264—21no—
23C2×#13133264C2211yescharacteristic, complemented
24C2×#13133264C2211yescharacteristic, complemented
25C2×#13133264C2213yescomplemented
26C2×#13133264C2213yescomplemented
272−1+4×D53—28no—
282−1+4×D53C22116yescomplemented
29C2×#13133262—23no—
30C2×#13133262C2213yescomplemented
31C22×#11719947—23no—
32C22×#11719947C2213yes—
33C2×#41×D53—21no—
34C2×#41×D53—23no—
35C2×#41×D53C2213yes—
36C2×#41×D53C2211yescharacteristic
37C2×#41×D53C2213yescomplemented
38C22×Q8×D53—21no—
39C22×Q8×D53C2213yescomplemented
40#16811440C22116yescomplemented
41#16811439C22148yescomplemented
42#16811438C22116yescomplemented
43#16811437C22148yescomplemented
44#16811434C22116yescomplemented
45#16811433C22148yescomplemented
46#16811429C22148yescomplemented
47#16811420C22148yescomplemented
48#16811419C22148yescomplemented
49C2×#13133250C2213yescomplemented
50C2×#13133250C2213yescomplemented
51C2×#13133249C2213yescomplemented
52C2×#13133249C2213yescomplemented
53C2×#13133248C2213yescomplemented
54C2×#13133247C2213yescomplemented
55C2×#13133247C2213yescomplemented
56C2×#13133246C2216yescomplemented
57C2×#13133246C2213yescomplemented
58C2×#13133246C2216yescomplemented
59C2×#13133246C2216yescomplemented
60C2×#13133246C2213yescomplemented
61C2×#13133246C22148yescomplemented
62#137×D53C22148yescomplemented
63C2×#13133244C2211yescharacteristic, complemented
64C2×#13133244C2213yescomplemented
65C2×#13133243C2213yescomplemented
66C2×#13133241C2213yescomplemented
67C2×#13133241C2213yescomplemented
68C2×#13133239C2213yescomplemented
69C2×#13133238C2216yescomplemented
70C2×#13133237C2213yescomplemented
71C2×#13133237C2213yescomplemented
72C2×#13133236C2216yescomplemented
73C22×Dic212C2213yescomplemented
74C22×#11719925C2213yescomplemented
75C2×Q16×D53C2216yescomplemented
76C22×#11719923C2213yescomplemented
77C2×SD16×D53C2216yescomplemented
78#16811388C22116yescomplemented
79C2×#13133225C2213yescomplemented
80C2×#13133224C2211yescharacteristic, complemented
81C2×#13133223C2213yescomplemented
82C22×#11719912C2213yescomplemented
83C2×M16×D53C2213yescomplemented
84C2×2−1+4×C53C2211yescharacteristic, complemented
85C2×H(5,𝔽2)×C53C2211yescharacteristic, complemented
86C53×#577C22116yescomplemented
87C2×#137×C53C2213yescomplemented
88C2×AGL(1,ℤ/8)×C53C2213yescomplemented
89C2×#135×C53C2213yescomplemented
90C22×SD16×C53C2213yescomplemented
91C2×#131×C53C2211yescharacteristic, complemented
92#13133265—216no—
93#13133265—212no—
94#13133265C23124yescomplemented
95#13133264—24no—
96#13133264—24no—
97#13133264—216no—
98#13133264—248no—
99#13133264—212no—
100#13133264—212no—
101#13133264C23124yescomplemented
102#13133264C23124yescomplemented
103#13133264C2318yescomplemented
104#13133264C2318yescomplemented
105#13133262—248no—
106#13133262—212no—
107#13133262C23124yescomplemented
108C2×#11719949—23no—
109C2×#11719949D411yescharacteristic
110C2×#11719949C2313yes—
111C2×#11719949C2311yescharacteristic
112C2×#11719945—26no—
113C2×#11719945—23no—
114C2×#11719945—23no—
115C2×#11719945—23no—
116C2×#11719945—23no—
117C2×#11719945C2313yes—
118C2×#11719945C2313yes—
119C2×#11719945C2313yes—
120C2×#11719947—23no—
121C2×#11719947—23no—
122C2×#11719947—26no—
123C2×#11719947—26no—
124C2×#11719947—23no—
125C2×#11719947—23no—
126C2×#11719947—248no—
127C2×#11719947—23no—
128C2×#11719947—23no—
129C2×#11719947—212no—
130C2×#11719947—23no—
131C2×#11719947D413yes—
132C2×#11719947C2313yes—
133C2×#11719947C2316yes—
134C2×#11719947C2313yes—
135C2×#11719947C23124yes—
136#41×D53—216no—
137#41×D53—248no—
138#41×D53—212no—
139#41×D53—212no—
140#41×D53D418yes—
141#41×D53C23124yes—
142#41×D53C2318yes—
143#41×D53C23124yescomplemented
144C22×Dic106—23no—
145C22×Dic106—23no—
146C22×Dic106—23no—
147C22×Dic106C2313yes—
148C22×Dic106C2313yes—
149C2×Q8×D53—21no—
150C2×Q8×D53—21no—
151C2×Q8×D53—216no—
152C2×Q8×D53—23no—
153C2×Q8×D53—212no—
154C2×Q8×D53—23no—
155C2×Q8×D53—23no—
156C2×Q8×D53D411yescharacteristic
157C2×Q8×D53C2316yes—
158C2×Q8×D53C2313yes—
159C2×Q8×D53C2313yes—
160C2×Q8×D53C23124yescomplemented
161C22×C22⋊D53—23no—
162C22×C22⋊D53—26no—
163C2×D4×D53—23no—
164C2×D4×D53—23no—
165C2×D4×D53—23no—
166C2×D4×D53D413yes—
167C2×D4×D53C2313yes—
168C2×D4×D53C2311yescharacteristic
169C23×Dic53—23no—
170C22×C4×D53—23no—
171C22×C4×D53—23no—
172C22×C4×D53—23no—
173C22×C4×D53C2313yes—
174#13133250C23124yescomplemented
175#13133250C23124yescomplemented
176#13133249C23124yescomplemented
177#13133249C23124yescomplemented
178#13133248C23124yescomplemented
179#13133247C23124yescomplemented
180#13133247C23124yescomplemented
181#13133246C23148yescomplemented
182#13133246C23124yescomplemented
183#13133246C23148yescomplemented
184#13133246C23148yescomplemented
185#13133246C23124yescomplemented
186#13133244C2318yescomplemented
187#13133244C23124yescomplemented
188#13133243C23124yescomplemented
189#13133241C23124yescomplemented
190#13133241C23124yescomplemented
191#13133239C23124yescomplemented
192#13133238C23148yescomplemented
193#13133237C23124yescomplemented
194#13133237C23124yescomplemented
195#13133236C23148yescomplemented
196C2×Dic212C2316yes—
197C2×Dic212C2313yes—
198C2×Dic212C23124yescomplemented
199C2×#11719925C2313yes—
200C2×#11719925C2316yes—
201C2×#11719925C2313yes—
202C2×#11719925C23124yescomplemented
203Q16×D53C23148yescomplemented
204C2×#11719913C2313yes—
205C2×#11719913C2313yes—
206C2×#11719923C2316yes—
207C2×#11719923C2313yes—
208C2×#11719923C2313yes—
209C2×#11719923C23124yescomplemented
210C2×#11719924C2313yes—
211C2×#11719924C2311yescharacteristic
212SD16×D53C23148yescomplemented
213C2×D424C2311yescharacteristic
214C2×#11719922C2311yescharacteristic
215C2×#11719922C2313yes—
216#13133225C23124yescomplemented
217#13133224C2318yescomplemented
218#13133223C23124yescomplemented
219C2×#11719917C2313yes—
220C2×#11719912C2313yes—
221C2×#11719912C2311yescharacteristic
222C2×#11719912C2313yes—
223C2×#11719912C2313yes—
224C2×#11719912C23124yescomplemented
225M16×D53C23124yescomplemented
226C22×#88322C2313yes—
227C2×C8×D53C2316yes—
2282−1+4×C53—24no—
2292−1+4×C53C2318yescomplemented
230H(5,𝔽2)×C53—24no—
231H(5,𝔽2)×C53C2318yescomplemented
232C2×#41×C53—21no—
233C2×#41×C53—23no—
234C2×#41×C53C2313yes—
235C2×#41×C53C2313yes—
236C2×#41×C53C2311yescharacteristic
237C22×Q8×C53—21no—
238C22×Q8×C53C2313yes—
239C22×D4×C53—23no—
240C22×D4×C53C2313yes—
241#137×C53C23124yescomplemented
242AGL(1,ℤ/8)×C53C23124yescomplemented
243#135×C53C23124yescomplemented
244C2×Q16×C53C2313yes—
245C2×SD16×C53C2313yes—
246C2×SD16×C53C2316yes—
247C2×SD16×C53C2311yescharacteristic
248C2×SD16×C53C23124yescomplemented
249C2×D8×C53C2313yes—
250#131×C53C2318yescomplemented
251C2×M16×C53C2313yes—
252C22×C8×C53C2313yes—
253C24×C53—23no—
254C23×D53—21no—
255C23×D53—23no—
256C23×D53C2×D413yes—
257#41×C53—28no—
258#41×C53—224no—
259#41×C53—26no—
260#41×C53—26no—
261#41×C53C2×D414yes—
262#41×C53C24112yes—
263#41×C53C24112yes—
264#41×C53C2414yes—
265C2×Q8×C53—28no—
266C2×Q8×C53—23no—
267C2×Q8×C53—26no—
268C2×Q8×C53C2×D411yescharacteristic
269C2×Q8×C53C2413yes—
270C2×Q8×C53C2411yescharacteristic
271C2×Q8×C53C24112yes—
272C2×D4×C53—23no—
273C2×D4×C53—23no—
274C2×D4×C53—224no—
275C2×D4×C53—23no—
276C2×D4×C53—26no—
277C2×D4×C53C2×D413yes—
278C2×D4×C53C2411yescharacteristic
279C2×D4×C53C2413yes—
280C2×D4×C53C24112yes—
281C22×C4×C53—23no—
282C22×C4×C53—23no—
283C22×C4×C53—23no—
284C22×C4×C53C2413yes—
285C2×C22⋊D53—23no—
286C2×C22⋊D53—23no—
287C2×C22⋊D53—23no—
288C2×C22⋊D53—26no—
289C2×C22⋊D53—23no—
290C2×C22⋊D53—224no—
291C2×C22⋊D53—248no—
292C2×C22⋊D53—23no—
293C2×C22⋊D53—21no—
294C2×C22⋊D53C2×D416yes—
295C22×Dic53—23no—
296C22×Dic53—23no—
297C22×Dic53—23no—
298C22×Dic53—23no—
299C22×Dic53—26no—
300C22×Dic53—224no—
301C22×Dic53C2×D413yes—
302#11719949—224no—
303#11719949—22no—
304#11719949—26no—
305#11719949C2×D418yes—
306#11719949C24112yes—
307#11719949C2414yes—
308Q8×D53—28no—
309Q8×D53—28no—
310Q8×D53—26no—
311Q8×D53—224no—
312Q8×D53—212no—
313Q8×D53—224no—
314Q8×D53—26no—
315Q8×D53—224no—
316Q8×D53C2×D418yes—
317Q8×D53C24124yes—
318Q8×D53C24112yes—
319Q8×D53C24112yes—
320#11719947—224no—
321#11719947—224no—
322#11719947—248no—
323#11719947—248no—
324#11719947—224no—
325#11719947—224no—
326#11719947—224no—
327#11719947—26no—
328#11719947—26no—
329#11719947—224no—
330#11719947—212no—
331#11719947—224no—
332#11719947C2×D4124yes—
333#11719947C24112yes—
334#11719947C24124yes—
335#11719947C24112yes—
336D4×D53—224no—
337D4×D53—224no—
338D4×D53—224no—
339D4×D53—22no—
340D4×D53—26no—
341D4×D53C2×D4124yes—
342D4×D53C24112yes—
343D4×D53C2414yes—
344#11719945—26no—
345#11719945—26no—
346#11719945—248no—
347#11719945—224no—
348#11719945—224no—
349#11719945—224no—
350#11719945—224no—
351#11719945C2×D4112yes—
352#11719945C24112yes—
353#11719945C24112yes—
354#11719945C24112yes—
355C2×D212—21no—
356C2×D212—23no—
357C2×D212C2×D413yes—
358C2×D212C2411yescharacteristic
359C2×D212C2411yescharacteristic
360C2×C4×D53—23no—
361C2×C4×D53—23no—
362C2×C4×D53—26no—
363C2×C4×D53—224no—
364C2×C4×D53—23no—
365C2×C4×D53—23no—
366C2×C4×D53—21no—
367C2×C4×D53—23no—
368C2×C4×D53—224no—
369C2×C4×D53—224no—
370C2×C4×D53C2×D413yes—
371C2×C4×D53C2×D413yes—
372C2×C4×D53C2×D4112yes—
373C2×C4×D53C2413yes—
374C2×C4×D53C24112yes—
375C2×C4×D53C2411yescharacteristic
376C2×Dic106—23no—
377C2×Dic106—26no—
378C2×Dic106—23no—
379C2×Dic106—26no—
380C2×Dic106—26no—
381C2×Dic106—23no—
382C2×Dic106—224no—
383C2×Dic106—23no—
384C2×Dic106—224no—
385C2×Dic106—224no—
386C2×Dic106C2×D413yes—
387C2×Dic106C2413yes—
388C2×Dic106C2413yes—
389C2×Dic106C24112yes—
390C2×Dic106C24112yes—
391Q16×C53C24112yes—
392SD16×C53C24112yes—
393SD16×C53C24124yes—
394SD16×C53C2414yes—
395D8×C53C24112yes—
396M16×C53C24112yes—
397C2×C8×C53C2411yescharacteristic
398C2×C8×C53C2413yes—
399C2×C8×C53C24112yes—
400#11719925C24112yes—
401#11719925C24124yes—
402#11719925C24112yes—
403#11719924C24112yes—
404#11719924C2414yes—
405#11719923C24124yes—
406#11719923C24112yes—
407#11719923C24112yes—
408#11719922C2414yes—
409#11719922C24112yes—
410#11719917C24112yes—
411C2×#88322C2413yes—
412C2×#88322C2411yescharacteristic
413C2×#88322C24112yes—
414Dic212C24124yes—
415Dic212C24112yes—
416D424C2414yes—
417#11719913C24112yes—
418#11719913C24112yes—
419#11719912C24112yes—
420#11719912C2414yes—
421#11719912C24112yes—
422#11719912C24112yes—
423C8×D53C24124yes—
424C23×C53—21no—
425C23×C53—23no—
426C23×C53—212no—
427C23×C53—86no—
428C23×C53C22×D413yes—
429C22×D53—21no—
430C22×D53—21no—
431C22×D53—24no—
432C22×D53—212no—
433C22×D53—46no—
434C22×D53—44no—
435C22×D53—86no—
436C22×D53C22×D411yescharacteristic
437C22×D53C22×D413yes—
438C22×D53C22×D4112yes—
439Q8×C53—23no—
440Q8×C53—212no—
441Q8×C53—21no—
442Q8×C53C22×D414yes—
443Q8×C53C2516yes—
444Q8×C53C2512yes—
445D4×C53—212no—
446D4×C53—212no—
447D4×C53—23no—
448D4×C53—212no—
449D4×C53—21no—
450D4×C53C22×D4112yes—
451D4×C53C2516yes—
452D4×C53C2512yes—
453C2×C4×C53—21no—
454C2×C4×C53—23no—
455C2×C4×C53—212no—
456C2×C4×C53—212no—
457C2×C4×C53—212no—
458C2×C4×C53C22×D413yes—
459C2×C4×C53C22×D416yes—
460C2×C4×C53C2511yescharacteristic
461C2×C4×C53C2516yes—
462C22⋊D53—212no—
463C22⋊D53—212no—
464C22⋊D53—212no—
465C22⋊D53—212no—
466C22⋊D53—224no—
467C22⋊D53—24no—
468C22⋊D53—212no—
469C22⋊D53C22×D4124yes—
470C2×Dic53—23no—
471C2×Dic53—212no—
472C2×Dic53—23no—
473C2×Dic53—212no—
474C2×Dic53—212no—
475C2×Dic53—224no—
476C2×Dic53—212no—
477C2×Dic53C22×D413yes—
478C2×Dic53C22×D411yescharacteristic
479C2×Dic53C22×D4112yes—
480D212—24no—
481D212—212no—
482D212—21no—
483D212—21no—
484D212C22×D4112yes—
485D212C2512yes—
486D212C2512yes—
487C4×D53—212no—
488C4×D53—212no—
489C4×D53—224no—
490C4×D53—212no—
491C4×D53—212no—
492C4×D53—24no—
493C4×D53—212no—
494C4×D53C22×D4112yes—
495C4×D53C22×D4112yes—
496C4×D53C22×D412yes—
497C4×D53C22×D416yes—
498C4×D53C2512yes—
499C4×D53C2516yes—
500Dic106—23no—
501Dic106—212no—
502Dic106—23no—
503Dic106—212no—
504Dic106—212no—
505Dic106—224no—
506Dic106—212no—
507Dic106C22×D4112yes—
508Dic106C2516yes—
509Dic106C2516yes—
510C8×C53C2516yes—
511C8×C53C2512yes—
512#88322C2516yes—
513#88322C2512yes—
514C2×#3586—531nomaximal, Sylow
515C22×C53—26no—
516C22×C53—22no—
517C22×C53—26no—
518C22×C53—42no—
519C22×C53—46no—
520C22×C53—812no—
521C22×C53C23×D416yes—
522C22×C53C23×D411yescharacteristic
523C2×D53—22no—
524C2×D53—26no—
525C2×D53—22no—
526C2×D53—22no—
527C2×D53—412no—
528C2×D53—48no—
529C2×D53—42no—
530C2×D53—42no—
531C2×D53—812no—
532C2×D53C23×D412yes—
533C2×D53C23×D416yes—
534C4×C53—22no—
535C4×C53—26no—
536C4×C53C23×D411yescharacteristic
537C4×C53C23×D416yes—
538C4×C53C2611yescharacteristic
539Dic53—26no—
540Dic53—26no—
541Dic53C23×D416yes—
542Dic53C23×D412yes—
543C2×#585—531no—
544C22×2−1+4—531no—
545#3586—5332no—
546C2×#578—531no—
547C2×#578—533no—
548C2×#578—533no—
549C2×#578—531no—
550C2×#577—531no—
551C2×#577—533no—
552C2×#577—533no—
553C2×#577D5311yescharacteristic, complemented
554C2×#575—533no—
555C2×#575—533no—
556C22×#137—533no—
557C22×#137—533no—
558C2×#568—531no—
559C2×C53—26no—
560C2×C53—42no—
561C2×C53—46no—
562C2×C53#358612yescomplemented
563C2×C53C24×D411yescharacteristic
564D53—22no—
565D53—26no—
566D53—42no—
567D53—42no—
568#585—5316no—
569#585—1068no—
570C2×2−1+4—5316no—
571C2×2−1+4—533no—
572C2×2−1+4—533no—
573C2×2−1+4—531no—
574C2×2−1+4—531no—
575C2×2−1+4—533no—
576C2×2−1+4—1061no—
577C2×2−1+4—1061no—
578C2×2−1+4—1063no—
579C2×2−1+4—1068no—
580C2×2−1+4C2×D5311yescharacteristic, complemented
581C2×H(5,𝔽2)—533no—
582C2×H(5,𝔽2)—1063no—
583C2×H(5,𝔽2)C2×D5311yescharacteristic, complemented
584C22×#41—531no—
585C22×#41—533no—
586C22×#41—533no—
587C22×#41—533no—
588C22×#41—1063no—
589C22×#41—1063no—
590C22×#41—1061no—
591C23×Q8—533no—
592C23×Q8—1061no—
593#578—5316no—
594#578—5348no—
595#578—5348no—
596#578—5316no—
597#577—5316no—
598#577—5348no—
599#577—5348no—
600#577C2×D53116yescomplemented
601#575—5348no—
602#575—5348no—
603C2×#137—533no—
604C2×#137—533no—
605C2×#137—533no—
606C2×#137—5348no—
607C2×#137—533no—
608C2×#137—533no—
609C2×#137—536no—
610C2×#137—533no—
611C2×#137—536no—
612C2×#137—536no—
613C2×#137—533no—
614C2×#137—5348no—
615C2×#137—533no—
616C2×#137—533no—
617C2×#137C2×D5313yescomplemented
618C2×AGL(1,ℤ/8)—533no—
619C2×AGL(1,ℤ/8)—531no—
620C2×AGL(1,ℤ/8)—533no—
621C2×AGL(1,ℤ/8)—533no—
622C2×AGL(1,ℤ/8)—533no—
623C2×AGL(1,ℤ/8)C2×D5313yescomplemented
624C2×#135—533no—
625C2×#135—533no—
626C2×#135—536no—
627C2×#135—536no—
628C2×#135—533no—
629C2×#135C2×D5313yescomplemented
630C22×Q16—533no—
631C22×Q16—536no—
632C22×Q16—533no—
633C22×SD16—533no—
634C22×SD16—536no—
635C22×SD16C2×D5313yescomplemented
636#568—5316no—
637C2×#131—531no—
638C2×#131—533no—
639C2×#131—533no—
640C2×#131C2×D5311yescharacteristic, complemented
641C22×M16—533no—
642C22×M16—533no—
643C53C2×#358611yescharacteristic, complemented, Sylow
6442−1+4—24no—
6452−1+4—5324no—
6462−1+4—538no—
6472−1+4—5324no—
6482−1+4—538no—
6492−1+4—5324no—
6502−1+4—10616no—
6512−1+4—10612no—
6522−1+4—10616no—
6532−1+4—10648no—
6542−1+4—10612no—
6552−1+4—10612no—
6562−1+4—1064no—
6572−1+4—1064no—
6582−1+4C22×D5318yescomplemented
659H(5,𝔽2)—24no—
660H(5,𝔽2)—5324no—
661H(5,𝔽2)—10648no—
662H(5,𝔽2)—10612no—
663H(5,𝔽2)C22×D5318yescomplemented
664C2×#41—21no—
665C2×#41—23no—
666C2×#41—538no—
667C2×#41—538no—
668C2×#41—531no—
669C2×#41—533no—
670C2×#41—533no—
671C2×#41—5324no—
672C2×#41—5324no—
673C2×#41—533no—
674C2×#41—531no—
675C2×#41—533no—
676C2×#41—536no—
677C2×#41—533no—
678C2×#41—5324no—
679C2×#41—533no—
680C2×#41—533no—
681C2×#41—1063no—
682C2×#41—1063no—
683C2×#41—1063no—
684C2×#41—1066no—
685C2×#41—1063no—
686C2×#41—1063no—
687C2×#41—1063no—
688C2×#41—1063no—
689C2×#41—1063no—
690C2×#41—10612no—
691C2×#41—10612no—
692C2×#41—10612no—
693C2×#41—1066no—
694C2×#41—1066no—
695C2×#41—1063no—
696C2×#41—10648no—
697C2×#41—1063no—
698C2×#41—10648no—
699C2×#41—10616no—
700C2×#41—1063no—
701C2×#41—1063no—
702C2×#41C22×D5313yes—
703C2×#41C22×D5313yes—
704C2×#41C22×D5311yescharacteristic
705C22×Q8—21no—
706C22×Q8—531no—
707C22×Q8—536no—
708C22×Q8—533no—
709C22×Q8—533no—
710C22×Q8—5324no—
711C22×Q8—533no—
712C22×Q8—533no—
713C22×Q8—1063no—
714C22×Q8—1063no—
715C22×Q8—1063no—
716C22×Q8—1063no—
717C22×Q8—1063no—
718C22×Q8—10612no—
719C22×Q8—10616no—
720C22×Q8—1063no—
721C22×Q8—1061no—
722C22×Q8—1061no—
723C22×Q8C22×D5313yes—
724C22×D4—23no—
725C22×D4—533no—
726C22×D4—533no—
727C22×D4—531no—
728C22×D4—1063no—
729C22×D4—1063no—
730C22×D4—1063no—
731C22×D4—1066no—
732C22×D4—1063no—
733C22×D4C22×D5313yes—
734C23×C4—533no—
735C23×C4—1063no—
736C23×C4—1063no—
737C23×C4—1063no—
738C23×C4—1063no—
739#137—5324no—
740#137—5324no—
741#137—5324no—
742#137—5324no—
743#137—5324no—
744#137—5348no—
745#137—5324no—
746#137—5348no—
747#137—5348no—
748#137—5324no—
749#137—5324no—
750#137—5324no—
751#137C22×D53124yescomplemented
752AGL(1,ℤ/8)—5324no—
753AGL(1,ℤ/8)—538no—
754AGL(1,ℤ/8)—5324no—
755AGL(1,ℤ/8)—5324no—
756AGL(1,ℤ/8)—5324no—
757AGL(1,ℤ/8)C22×D53124yescomplemented
758#135—5324no—
759#135—5324no—
760#135—5348no—
761#135—5348no—
762#135—5324no—
763#135C22×D53124yescomplemented
764C2×Q16—533no—
765C2×Q16—533no—
766C2×Q16—536no—
767C2×Q16—5324no—
768C2×Q16—5348no—
769C2×Q16—536no—
770C2×Q16—533no—
771C2×Q16—5324no—
772C2×Q16C22×D5313yes—
773C2×SD16—533no—
774C2×SD16—531no—
775C2×SD16—533no—
776C2×SD16—536no—
777C2×SD16—5324no—
778C2×SD16—533no—
779C2×SD16—5348no—
780C2×SD16—533no—
781C2×SD16—533no—
782C2×SD16C22×D5316yes—
783C2×SD16C22×D5313yes—
784C2×SD16C22×D5311yescharacteristic
785C2×SD16C22×D53124yescomplemented
786C2×D8—533no—
787C2×D8—531no—
788C2×D8—531no—
789C2×D8C22×D5313yes—
790#131—538no—
791#131—5324no—
792#131—5324no—
793#131C22×D5318yescomplemented
794C2×M16—533no—
795C2×M16—5324no—
796C2×M16—533no—
797C2×M16—531no—
798C2×M16—533no—
799C2×M16—533no—
800C2×M16—5324no—
801C2×M16C22×D5313yes—
802C22×C8—533no—
803C22×C8—536no—
804C22×C8C22×D5313yes—
805C24—23no—
806C24—533no—
807C24—1063no—
808C24—1061no—
809#41—28no—
810#41—224no—
811#41—26no—
812#41—26no—
813#41—538no—
814#41—5324no—
815#41—5312no—
816#41—5312no—
817#41—5312no—
818#41—534no—
819#41—5312no—
820#41—5324no—
821#41—5312no—
822#41—5312no—
823#41—5312no—
824#41—10624no—
825#41—10624no—
826#41—10624no—
827#41—10648no—
828#41—10624no—
829#41—10624no—
830#41—1066no—
831#41—10624no—
832#41—10624no—
833#41—10612no—
834#41—10624no—
835#41—1066no—
836#41—1062no—
837#41—1066no—
838#41—10648no—
839#41—10648no—
840#41—10624no—
841#41—10624no—
842#41—10624no—
843#41—10624no—
844#41—1066no—
845#41—1066no—
846#41D4×D5314yes—
847#41C23×D53112yes—
848#41C23×D53112yes—
849#41C23×D5314yes—
850C2×Q8—28no—
851C2×Q8—23no—
852C2×Q8—26no—
853C2×Q8—538no—
854C2×Q8—533no—
855C2×Q8—5324no—
856C2×Q8—5312no—
857C2×Q8—5312no—
858C2×Q8—533no—
859C2×Q8—533no—
860C2×Q8—5312no—
861C2×Q8—5312no—
862C2×Q8—1063no—
863C2×Q8—1066no—
864C2×Q8—1063no—
865C2×Q8—10624no—
866C2×Q8—10624no—
867C2×Q8—10624no—
868C2×Q8—1066no—
869C2×Q8—10624no—
870C2×Q8—10624no—
871C2×Q8—10612no—
872C2×Q8—1066no—
873C2×Q8—10624no—
874C2×Q8—1068no—
875C2×Q8—1068no—
876C2×Q8—1063no—
877C2×Q8—1063no—
878C2×Q8—1066no—
879C2×Q8—1066no—
880C2×Q8D4×D5311yescharacteristic
881C2×Q8C23×D5313yes—
882C2×Q8C23×D5311yescharacteristic
883C2×Q8C23×D53112yes—
884C2×D4—23no—
885C2×D4—23no—
886C2×D4—224no—
887C2×D4—23no—
888C2×D4—26no—
889C2×D4—536no—
890C2×D4—5324no—
891C2×D4—5312no—
892C2×D4—534no—
893C2×D4—533no—
894C2×D4—531no—
895C2×D4—531no—
896C2×D4—1061no—
897C2×D4—1063no—
898C2×D4—1062no—
899C2×D4—1066no—
900C2×D4—1063no—
901C2×D4—1061no—
902C2×D4—10624no—
903C2×D4—10624no—
904C2×D4—10624no—
905C2×D4—10648no—
906C2×D4—1063no—
907C2×D4—1066no—
908C2×D4—1063no—
909C2×D4—10624no—
910C2×D4—1063no—
911C2×D4—1063no—
912C2×D4D4×D5313yes—
913C2×D4C23×D5311yescharacteristic
914C2×D4C23×D5313yes—
915C2×D4C23×D53112yes—
916C22×C4—23no—
917C22×C4—23no—
918C22×C4—23no—
919C22×C4—533no—
920C22×C4—533no—
921C22×C4—533no—
922C22×C4—5312no—
923C22×C4—533no—
924C22×C4—531no—
925C22×C4—5312no—
926C22×C4—1061no—
927C22×C4—1063no—
928C22×C4—10624no—
929C22×C4—10624no—
930C22×C4—1063no—
931C22×C4—1063no—
932C22×C4—10624no—
933C22×C4—1066no—
934C22×C4—1063no—
935C22×C4—1066no—
936C22×C4—1063no—
937C22×C4—10624no—
938C22×C4—1063no—
939C22×C4—1063no—
940C22×C4—1063no—
941C22×C4—1063no—
942C22×C4C23×D5313yes—
943Q16—5312no—
944Q16—5312no—
945Q16—5324no—
946Q16—5324no—
947Q16—5312no—
948Q16C23×D53112yes—
949SD16—5312no—
950SD16—534no—
951SD16—5312no—
952SD16—5324no—
953SD16—5312no—
954SD16—5312no—
955SD16—5312no—
956SD16C23×D53124yes—
957SD16C23×D53112yes—
958SD16C23×D5314yes—
959D8—5312no—
960D8—534no—
961D8—534no—
962D8C23×D53112yes—
963M16—5312no—
964M16—5312no—
965M16—534no—
966M16—5312no—
967M16—5312no—
968M16C23×D53112yes—
969C2×C8—531no—
970C2×C8—533no—
971C2×C8—5312no—
972C2×C8—5324no—
973C2×C8C23×D5313yes—
974C2×C8C23×D5311yescharacteristic
975C2×C8C23×D53112yes—
976C23—21no—
977C23—23no—
978C23—212no—
979C23—86no—
980C23—531no—
981C23—533no—
982C23—5312no—
983C23—10612no—
984C23—1064no—
985C23—1061no—
986C23—1061no—
987C23—4246no—
988C23—2126no—
989C23—2124no—
990C23C2×D4×D5313yes—
991Q8—212no—
992Q8—23no—
993Q8—21no—
994Q8—5312no—
995Q8—536no—
996Q8—536no—
997Q8—10612no—
998Q8—10624no—
999Q8—10612no—
1000Q8—10612no—
1001Q8—1063no—
1002Q8—10612no—
1003Q8—1063no—
1004Q8C2×D4×D5314yes—
1005Q8C24×D5316yes—
1006Q8C24×D5312yes—
1007D4—212no—
1008D4—212no—
1009D4—212no—
1010D4—23no—
1011D4—21no—
1012D4—5324no—
1013D4—5312no—
1014D4—532no—
1015D4—532no—
1016D4—1064no—
1017D4—10612no—
1018D4—10612no—
1019D4—1064no—
1020D4—10612no—
1021D4—10624no—
1022D4—10612no—
1023D4—10612no—
1024D4—10612no—
1025D4—1061no—
1026D4—1061no—
1027D4C2×D4×D53112yes—
1028D4C24×D5312yes—
1029D4C24×D5316yes—
1030C2×C4—212no—
1031C2×C4—21no—
1032C2×C4—23no—
1033C2×C4—212no—
1034C2×C4—212no—
1035C2×C4—5312no—
1036C2×C4—531no—
1037C2×C4—533no—
1038C2×C4—532no—
1039C2×C4—5312no—
1040C2×C4—5312no—
1041C2×C4—536no—
1042C2×C4—536no—
1043C2×C4—532no—
1044C2×C4—1064no—
1045C2×C4—10612no—
1046C2×C4—10612no—
1047C2×C4—10612no—
1048C2×C4—10624no—
1049C2×C4—10612no—
1050C2×C4—10624no—
1051C2×C4—10612no—
1052C2×C4—10612no—
1053C2×C4—10612no—
1054C2×C4—1063no—
1055C2×C4—1063no—
1056C2×C4—10612no—
1057C2×C4—10612no—
1058C2×C4C2×D4×D5316yes—
1059C2×C4C2×D4×D5313yes—
1060C2×C4C24×D5316yes—
1061C2×C4C24×D5311yescharacteristic
1062C8—536no—
1063C8—532no—
1064C8C24×D5316yes—
1065C8C24×D5312yes—
1066C22—26no—
1067C22—22no—
1068C22—26no—
1069C22—46no—
1070C22—42no—
1071C22—812no—
1072C22—532no—
1073C22—536no—
1074C22—1066no—
1075C22—1062no—
1076C22—1062no—
1077C22—1062no—
1078C22—42412no—
1079C22—21212no—
1080C22—2128no—
1081C22—2122no—
1082C22—2122no—
1083C22C22×D4×D5316yes—
1084C22C22×D4×D5311yescharacteristic
1085C4—22no—
1086C4—26no—
1087C4—532no—
1088C4—536no—
1089C4—1066no—
1090C4—1066no—
1091C4C22×D4×D5316yes—
1092C4C22×D4×D5311yescharacteristic
1093C4C25×D5311yescharacteristic
1094C2—26no—
1095C2—46no—
1096C2—42no—
1097C2—1066no—
1098C2—1062no—
1099C2—2122no—
1100C2—2122no—
1101C2#2028949712yesdirect product factor
1102C2C23×D4×D5311yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC4×C53C26
FrattiniC4C25×D53
FittingC2×C53×#577C2
socleC22×C53C23×D4
hypercenterC2×#577D53
hypocenterC53C2×#3586
LCSG ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#577

Complements

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

NH ≅ G/Ntype
1. C2×#16811458C2semidirect
2. C2×2−1+4×D53C2semidirect
3. #20289497C2direct (N × H)
4. C2×#16811440C2semidirect
5. C2×#16811439C2semidirect
6. C2×#16811438C2semidirect
7. C2×#16811437C2semidirect
8. C2×#16811434C2semidirect
9. C2×#16811433C2semidirect
10. C2×#16811429C2semidirect
11. C2×#16811420C2semidirect
12. C2×#16811419C2semidirect
13. C22×#13133246C2semidirect
14. C2×#137×D53C2semidirect
15. C2×#16811388C2semidirect
16. C2×C53×#577C2semidirect
18. #16811458C22semidirect
20. C2×#13133265C22semidirect
23. C2×#13133264C22semidirect
24. C2×#13133264C22semidirect
25. C2×#13133264C22semidirect
26. C2×#13133264C22semidirect
28. 2−1+4×D53C22semidirect
30. C2×#13133262C22semidirect
37. C2×#41×D53C22semidirect
39. C22×Q8×D53C22semidirect
40. #16811440C22semidirect
41. #16811439C22semidirect
42. #16811438C22semidirect
43. #16811437C22semidirect
44. #16811434C22semidirect
45. #16811433C22semidirect
46. #16811429C22semidirect
47. #16811420C22semidirect
48. #16811419C22semidirect
49. C2×#13133250C22semidirect
50. C2×#13133250C22semidirect
51. C2×#13133249C22semidirect
52. C2×#13133249C22semidirect
53. C2×#13133248C22semidirect
54. C2×#13133247C22semidirect
55. C2×#13133247C22semidirect
56. C2×#13133246C22semidirect
57. C2×#13133246C22semidirect
58. C2×#13133246C22semidirect
59. C2×#13133246C22semidirect
60. C2×#13133246C22semidirect
61. C2×#13133246C22semidirect
62. #137×D53C22semidirect
63. C2×#13133244C22semidirect
64. C2×#13133244C22semidirect
65. C2×#13133243C22semidirect
66. C2×#13133241C22semidirect
67. C2×#13133241C22semidirect
68. C2×#13133239C22semidirect
69. C2×#13133238C22semidirect
70. C2×#13133237C22semidirect
71. C2×#13133237C22semidirect
72. C2×#13133236C22semidirect
73. C22×Dic212C22semidirect
74. C22×#11719925C22semidirect
75. C2×Q16×D53C22semidirect
76. C22×#11719923C22semidirect
77. C2×SD16×D53C22semidirect
78. #16811388C22semidirect
79. C2×#13133225C22semidirect
80. C2×#13133224C22semidirect
81. C2×#13133223C22semidirect
82. C22×#11719912C22semidirect
83. C2×M16×D53C22semidirect
84. C2×2−1+4×C53C22semidirect
85. C2×H(5,𝔽2)×C53C22semidirect
86. C53×#577C22semidirect
87. C2×#137×C53C22semidirect
88. C2×AGL(1,ℤ/8)×C53C22semidirect
89. C2×#135×C53C22semidirect
90. C22×SD16×C53C22semidirect
91. C2×#131×C53C22semidirect
94. #13133265C23semidirect
101. #13133264C23semidirect
102. #13133264C23semidirect
103. #13133264C23semidirect
104. #13133264C23semidirect
107. #13133262C23semidirect
143. #41×D53C23semidirect
160. C2×Q8×D53C23semidirect
174. #13133250C23semidirect
175. #13133250C23semidirect
176. #13133249C23semidirect
177. #13133249C23semidirect
178. #13133248C23semidirect
179. #13133247C23semidirect
180. #13133247C23semidirect
181. #13133246C23semidirect
182. #13133246C23semidirect
183. #13133246C23semidirect
184. #13133246C23semidirect
185. #13133246C23semidirect
186. #13133244C23semidirect
187. #13133244C23semidirect
188. #13133243C23semidirect
189. #13133241C23semidirect
190. #13133241C23semidirect
191. #13133239C23semidirect
192. #13133238C23semidirect
193. #13133237C23semidirect
194. #13133237C23semidirect
195. #13133236C23semidirect
198. C2×Dic212C23semidirect
202. C2×#11719925C23semidirect
203. Q16×D53C23semidirect
209. C2×#11719923C23semidirect
212. SD16×D53C23semidirect
216. #13133225C23semidirect
217. #13133224C23semidirect
218. #13133223C23semidirect
224. C2×#11719912C23semidirect
225. M16×D53C23semidirect
229. 2−1+4×C53C23semidirect
231. H(5,𝔽2)×C53C23semidirect
241. #137×C53C23semidirect
242. AGL(1,ℤ/8)×C53C23semidirect
243. #135×C53C23semidirect
248. C2×SD16×C53C23semidirect
250. #131×C53C23semidirect
553. C2×#577D53semidirect
562. C2×C53#3586semidirect
580. C2×2−1+4C2×D53semidirect
583. C2×H(5,𝔽2)C2×D53semidirect
600. #577C2×D53semidirect
617. C2×#137C2×D53semidirect
623. C2×AGL(1,ℤ/8)C2×D53semidirect
629. C2×#135C2×D53semidirect
635. C22×SD16C2×D53semidirect
640. C2×#131C2×D53semidirect
643. C53C2×#3586semidirect
658. 2−1+4C22×D53semidirect
663. H(5,𝔽2)C22×D53semidirect
751. #137C22×D53semidirect
757. AGL(1,ℤ/8)C22×D53semidirect
763. #135C22×D53semidirect
785. C2×SD16C22×D53semidirect
793. #131C22×D53semidirect
1101. C2#20289497direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168114582
C2×2−1+4×D532
#202894972
C2×#168114402
C2×#168114392
C2×#168114382
C2×#168114372
C2×#168114342
C2×#168114332
C2×#168114292
C2×#168114202
C2×#168114192
C22×#131332462
C2×#137×D532
C2×#168113882
C2×C53×#5772
C2×#358653