Finite Group Databasebeta

← C2×#20289487 #28297924

Subgroups — C2×#20289487 #28297924

Order 13568.

10858 conjugacy classes of subgroups.

The subgroup lattice has 1108 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811460C211yesmaximal, characteristic, complemented
2C2×#16811458C211yesmaximal, characteristic, complemented
3#20289487C2132yesmaximal, direct product factor
4C2×#16811439C213yesmaximal, complemented
5C2×#16811438C211yesmaximal, characteristic, complemented
6C2×#16811435C211yesmaximal, characteristic, complemented
7C2×#16811430C213yesmaximal, complemented
8C2×#16811429C213yesmaximal, complemented
9C2×#16811427C213yesmaximal, complemented
10C2×#16811426C211yesmaximal, characteristic, complemented
11C2×#16811422C213yesmaximal, complemented
12C2×#16811419C213yesmaximal, complemented
13C22×#13133238C213yesmaximal, complemented
14C2×#135×D53C213yesmaximal, complemented
15C2×#131×D53C211yesmaximal, characteristic, complemented
16C2×C53×#577C211yesmaximal, characteristic, complemented
17#16811460—28no—
18#16811460C22116yescomplemented
19#16811458—28no—
20#16811458C22116yescomplemented
21C2×#13133265—21no—
22C2×#13133265C2213yescomplemented
23C2×#13133264—21no—
24C2×#13133264C2211yescharacteristic, complemented
25C2×#13133264C2213yescomplemented
26C2×#13133263—23no—
27C2×#13133263C2211yescharacteristic, complemented
28C2×#13133263C2213yescomplemented
29C2×#13133262—23no—
30C2×#13133262C2213yescomplemented
31C22×#11719949—21no—
32C22×#11719949C2213yescomplemented
33C22×#11719947—23no—
34C22×#11719947C2213yescomplemented
35C2×#41×D53—21no—
36C2×#41×D53—23no—
37C2×#41×D53C2211yescharacteristic
38C2×#41×D53C2213yescomplemented
39C2×#41×D53C2213yescomplemented
40#16811439C22148yescomplemented
41#16811438C22116yescomplemented
42#16811435C22116yescomplemented
43#16811430C22148yescomplemented
44#16811429C22148yescomplemented
45#16811427C22148yescomplemented
46#16811426C22116yescomplemented
47#16811422C22148yescomplemented
48#16811419C22148yescomplemented
49C2×#13133250C2213yescomplemented
50C2×#13133249C2216yescomplemented
51C2×#13133248C2213yescomplemented
52C2×#13133247C2213yescomplemented
53C2×#13133246C2216yescomplemented
54C2×#13133245C2213yescomplemented
55C2×#13133244C2216yescomplemented
56C2×#13133243C2213yescomplemented
57C2×#13133242C2213yescomplemented
58C2×#13133241C2216yescomplemented
59C2×#13133240C2213yescomplemented
60C2×#13133239C2213yescomplemented
61C2×#13133238C2211yescharacteristic, complemented
62C2×#13133238C2213yescomplemented
63C2×#13133238C2216yescomplemented
64C2×#13133238C2216yescomplemented
65C2×#13133238C2216yescomplemented
66C2×#13133238C22148yescomplemented
67C2×#13133237C2213yescomplemented
68C2×#13133237C2213yescomplemented
69C2×#13133236C2213yescomplemented
70#135×D53C22148yescomplemented
71C22×#11719925C2213yescomplemented
72C2×Q16×D53C2213yescomplemented
73C22×#11719913C2213yescomplemented
74C2×SD16×D53C2213yescomplemented
75C2×SD16×D53C2213yescomplemented
76C22×#11719922C2213yescomplemented
77C2×D8×D53C2213yescomplemented
78C2×#13133225C2213yescomplemented
79C2×#13133224C2211yescharacteristic, complemented
80C2×#13133223C2213yescomplemented
81#131×D53C22116yescomplemented
82C2×M16×D53C2213yescomplemented
83C22×C8×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—216no—
97#13133264—212no—
98#13133264C23124yescomplemented
99#13133264C2318yescomplemented
100#13133263—24no—
101#13133263—248no—
102#13133263—212no—
103#13133263C23124yescomplemented
104#13133263C2318yescomplemented
105#13133262—248no—
106#13133262—212no—
107#13133262C23124yescomplemented
108C2×#11719949—21no—
109C2×#11719949—216no—
110C2×#11719949—23no—
111C2×#11719949—23no—
112C2×#11719949—23no—
113C2×#11719949—212no—
114C2×#11719949D411yescharacteristic
115C2×#11719949C2313yes—
116C2×#11719949C2316yes—
117C2×#11719949C2311yescharacteristic
118C2×#11719949C23124yescomplemented
119C2×#11719945—26no—
120C2×#11719945—23no—
121C2×#11719945—23no—
122C2×#11719945—23no—
123C2×#11719945—23no—
124C2×#11719945C2313yes—
125C2×#11719945C2313yes—
126C2×#11719945C2313yes—
127C2×#11719947—23no—
128C2×#11719947—26no—
129C2×#11719947—23no—
130C2×#11719947—23no—
131C2×#11719947—248no—
132C2×#11719947—23no—
133C2×#11719947—23no—
134C2×#11719947—212no—
135C2×#11719947—23no—
136C2×#11719947D413yes—
137C2×#11719947C2311yescharacteristic
138C2×#11719947C2313yes—
139C2×#11719947C2316yes—
140C2×#11719947C23124yescomplemented
141#41×D53—216no—
142#41×D53—248no—
143#41×D53—212no—
144#41×D53—212no—
145#41×D53D418yes—
146#41×D53C2318yes—
147#41×D53C23124yescomplemented
148#41×D53C23124yescomplemented
149C22×Dic106—23no—
150C22×Dic106C2313yes—
151C2×Q8×D53—21no—
152C2×Q8×D53—23no—
153C2×Q8×D53D411yescharacteristic
154C2×Q8×D53C2313yes—
155C2×Q8×D53C2313yes—
156C22×D212—23no—
157C22×D212—23no—
158C22×D212C2313yes—
159C22×C22⋊D53—23no—
160C22×C22⋊D53—26no—
161C2×D4×D53—23no—
162C2×D4×D53—23no—
163C2×D4×D53—23no—
164C2×D4×D53—26no—
165C2×D4×D53—23no—
166C2×D4×D53D413yes—
167C2×D4×D53C2313yes—
168C2×D4×D53C2313yes—
169C23×Dic53—23no—
170C22×C4×D53—23no—
171C22×C4×D53—23no—
172C22×C4×D53—23no—
173C22×C4×D53C2313yes—
174#13133250C23124yescomplemented
175#13133249C23148yescomplemented
176#13133248C23124yescomplemented
177#13133247C23124yescomplemented
178#13133246C23148yescomplemented
179#13133245C23124yescomplemented
180#13133244C23148yescomplemented
181#13133243C23124yescomplemented
182#13133242C23124yescomplemented
183#13133241C23148yescomplemented
184#13133240C23124yescomplemented
185#13133239C23124yescomplemented
186#13133238C2318yescomplemented
187#13133238C23124yescomplemented
188#13133238C23148yescomplemented
189#13133238C23148yescomplemented
190#13133238C23148yescomplemented
191#13133237C23124yescomplemented
192#13133237C23124yescomplemented
193#13133236C23124yescomplemented
194C2×Dic212C2313yes—
195C2×#11719925C2311yescharacteristic
196C2×#11719925C2313yes—
197C2×#11719925C2316yes—
198C2×#11719925C23124yescomplemented
199Q16×D53C23124yescomplemented
200C2×#11719913C2311yescharacteristic
201C2×#11719913C2313yes—
202C2×#11719913C2316yes—
203C2×#11719913C23124yescomplemented
204C2×#11719923C2313yes—
205C2×#11719923C2313yes—
206C2×#11719924C2313yes—
207C2×#11719924C2313yes—
208SD16×D53C23124yescomplemented
209SD16×D53C23124yescomplemented
210C2×D424C2313yes—
211C2×#11719922C2311yescharacteristic
212C2×#11719922C2313yes—
213C2×#11719922C2316yes—
214C2×#11719922C23124yescomplemented
215D8×D53C23124yescomplemented
216#13133225C23124yescomplemented
217#13133224C2318yescomplemented
218#13133223C23124yescomplemented
219C2×#11719917C2313yes—
220C2×#11719912C2316yes—
221M16×D53C23124yescomplemented
222C22×#88322C2313yes—
223C2×C8×D53C2311yescharacteristic
224C2×C8×D53C2313yes—
225C2×C8×D53C2313yes—
226C2×C8×D53C2313yes—
227C2×C8×D53C23124yescomplemented
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—23no—
255C23×D53—23no—
256C23×D53—23no—
257C23×D53C2×D413yes—
258#41×C53—28no—
259#41×C53—224no—
260#41×C53—26no—
261#41×C53—26no—
262#41×C53C2×D414yes—
263#41×C53C24112yes—
264#41×C53C24112yes—
265#41×C53C2414yes—
266C2×Q8×C53—28no—
267C2×Q8×C53—23no—
268C2×Q8×C53—26no—
269C2×Q8×C53C2×D411yescharacteristic
270C2×Q8×C53C2413yes—
271C2×Q8×C53C2411yescharacteristic
272C2×Q8×C53C24112yes—
273C2×D4×C53—23no—
274C2×D4×C53—23no—
275C2×D4×C53—224no—
276C2×D4×C53—23no—
277C2×D4×C53—26no—
278C2×D4×C53C2×D413yes—
279C2×D4×C53C2411yescharacteristic
280C2×D4×C53C2413yes—
281C2×D4×C53C24112yes—
282C22×C4×C53—23no—
283C22×C4×C53—23no—
284C22×C4×C53—23no—
285C22×C4×C53C2413yes—
286C2×C22⋊D53—23no—
287C2×C22⋊D53—23no—
288C2×C22⋊D53—21no—
289C2×C22⋊D53—26no—
290C2×C22⋊D53—23no—
291C2×C22⋊D53—224no—
292C2×C22⋊D53—248no—
293C2×C22⋊D53—23no—
294C2×C22⋊D53—23no—
295C2×C22⋊D53C2×D416yes—
296C22×Dic53—23no—
297C22×Dic53—21no—
298C22×Dic53—23no—
299C22×Dic53—26no—
300C22×Dic53—224no—
301C22×Dic53C2×D413yes—
302#11719949—28no—
303#11719949—224no—
304#11719949—22no—
305#11719949—26no—
306#11719949—224no—
307#11719949—212no—
308#11719949—224no—
309#11719949C2×D418yes—
310#11719949C24112yes—
311#11719949C24124yes—
312#11719949C2414yes—
313Q8×D53—28no—
314Q8×D53—26no—
315Q8×D53—26no—
316Q8×D53—224no—
317Q8×D53C2×D418yes—
318Q8×D53C24112yes—
319Q8×D53C24112yes—
320#11719947—224no—
321#11719947—248no—
322#11719947—224no—
323#11719947—224no—
324#11719947—22no—
325#11719947—26no—
326#11719947—224no—
327#11719947—212no—
328#11719947—224no—
329#11719947—224no—
330#11719947C2×D4124yes—
331#11719947C2414yes—
332#11719947C24112yes—
333#11719947C24124yes—
334D4×D53—224no—
335D4×D53—224no—
336D4×D53—224no—
337D4×D53—248no—
338D4×D53—224no—
339D4×D53—26no—
340D4×D53—26no—
341D4×D53C2×D4124yes—
342D4×D53C24112yes—
343D4×D53C24112yes—
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—26no—
357C2×D212—23no—
358C2×D212—224no—
359C2×D212—23no—
360C2×D212—26no—
361C2×D212—224no—
362C2×D212C2×D413yes—
363C2×D212C2413yes—
364C2×D212C2411yescharacteristic
365C2×D212C24112yes—
366C2×C4×D53—23no—
367C2×C4×D53—23no—
368C2×C4×D53—23no—
369C2×C4×D53—23no—
370C2×C4×D53—21no—
371C2×C4×D53—23no—
372C2×C4×D53—26no—
373C2×C4×D53—224no—
374C2×C4×D53—224no—
375C2×C4×D53—224no—
376C2×C4×D53C2×D413yes—
377C2×C4×D53C2×D413yes—
378C2×C4×D53C2×D4112yes—
379C2×C4×D53C2411yescharacteristic
380C2×C4×D53C2413yes—
381C2×C4×D53C24112yes—
382C2×Dic106—23no—
383C2×Dic106—26no—
384C2×Dic106—23no—
385C2×Dic106—23no—
386C2×Dic106—224no—
387C2×Dic106C2×D413yes—
388C2×Dic106C2411yescharacteristic
389C2×Dic106C2413yes—
390C2×Dic106C24112yes—
391Q16×C53C24112yes—
392SD16×C53C24112yes—
393SD16×C53C24124yes—
394SD16×C53C2414yes—
395D8×C53C24112yes—
396M16×C53C24112yes—
397C2×C8×C53C2411yescharacteristic
398C2×C8×C53C2413yes—
399C2×C8×C53C24112yes—
400#11719925C2414yes—
401#11719925C24112yes—
402#11719925C24124yes—
403#11719924C24112yes—
404#11719924C24112yes—
405#11719923C24112yes—
406#11719923C24112yes—
407#11719922C2414yes—
408#11719922C24112yes—
409#11719922C24124yes—
410#11719917C24112yes—
411C2×#88322C2411yescharacteristic
412C2×#88322C2413yes—
413C2×#88322C24112yes—
414Dic212C24112yes—
415D424C24112yes—
416#11719913C2414yes—
417#11719913C24112yes—
418#11719913C24124yes—
419#11719912C24124yes—
420C8×D53C2414yes—
421C8×D53C24112yes—
422C8×D53C24112yes—
423C8×D53C24112yes—
424C23×C53—23no—
425C23×C53—21no—
426C23×C53—212no—
427C23×C53—86no—
428C23×C53C22×D413yes—
429C22×D53—23no—
430C22×D53—21no—
431C22×D53—212no—
432C22×D53—212no—
433C22×D53—212no—
434C22×D53—46no—
435C22×D53—86no—
436C22×D53—86no—
437C22×D53—86no—
438C22×D53C22×D413yes—
439C22×D53C22×D411yescharacteristic
440C22×D53C22×D4112yes—
441Q8×C53—21no—
442Q8×C53—23no—
443Q8×C53—212no—
444Q8×C53C22×D414yes—
445Q8×C53C2512yes—
446Q8×C53C2516yes—
447D4×C53—212no—
448D4×C53—212no—
449D4×C53—21no—
450D4×C53—23no—
451D4×C53—212no—
452D4×C53C22×D4112yes—
453D4×C53C2512yes—
454D4×C53C2516yes—
455C2×C4×C53—21no—
456C2×C4×C53—23no—
457C2×C4×C53—212no—
458C2×C4×C53—212no—
459C2×C4×C53—212no—
460C2×C4×C53C22×D413yes—
461C2×C4×C53C22×D416yes—
462C2×C4×C53C2511yescharacteristic
463C2×C4×C53C2516yes—
464C22⋊D53—212no—
465C22⋊D53—212no—
466C22⋊D53—24no—
467C22⋊D53—224no—
468C22⋊D53—212no—
469C22⋊D53—212no—
470C22⋊D53—212no—
471C22⋊D53C22×D4124yes—
472C2×Dic53—21no—
473C2×Dic53—23no—
474C2×Dic53—212no—
475C2×Dic53—224no—
476C2×Dic53—24no—
477C2×Dic53—212no—
478C2×Dic53C22×D413yes—
479C2×Dic53C22×D411yescharacteristic
480C2×Dic53C22×D4112yes—
481D212—224no—
482D212—212no—
483D212—24no—
484D212—23no—
485D212—212no—
486D212—21no—
487D212C22×D4112yes—
488D212C2516yes—
489D212C2512yes—
490C4×D53—212no—
491C4×D53—212no—
492C4×D53—212no—
493C4×D53—212no—
494C4×D53—24no—
495C4×D53—212no—
496C4×D53—224no—
497C4×D53C22×D4112yes—
498C4×D53C22×D412yes—
499C4×D53C22×D4112yes—
500C4×D53C22×D416yes—
501C4×D53C2512yes—
502C4×D53C2516yes—
503Dic106—23no—
504Dic106—212no—
505Dic106—21no—
506Dic106—212no—
507Dic106—212no—
508Dic106C22×D4112yes—
509Dic106C2516yes—
510Dic106C2512yes—
511C8×C53C2512yes—
512C8×C53C2516yes—
513#88322C2512yes—
514#88322C2516yes—
515C2×#3584—531nomaximal, Sylow
516C22×C53—26no—
517C22×C53—26no—
518C22×C53—22no—
519C22×C53—42no—
520C22×C53—46no—
521C22×C53—812no—
522C22×C53C23×D416yes—
523C22×C53C23×D411yescharacteristic
524C2×D53—22no—
525C2×D53—26no—
526C2×D53—26no—
527C2×D53—22no—
528C2×D53—412no—
529C2×D53—46no—
530C2×D53—42no—
531C2×D53—812no—
532C2×D53—812no—
533C2×D53—812no—
534C2×D53C23×D416yes—
535C2×D53C23×D412yes—
536C4×C53—22no—
537C4×C53—26no—
538C4×C53C23×D411yescharacteristic
539C4×C53C23×D416yes—
540C4×C53C2611yescharacteristic
541Dic53—22no—
542Dic53—26no—
543Dic53C23×D416yes—
544Dic53C23×D412yes—
545C2×#585—531no—
546C2×#585—531no—
547#3584—5332no—
548C2×#578—531no—
549C2×#578—533no—
550C2×#577—533no—
551C2×#577—533no—
552C2×#577—531no—
553C2×#577D5311yescharacteristic, complemented
554C2×#576—531no—
555C2×#576—533no—
556C2×#575—533no—
557C2×#575—533no—
558C22×#135—533no—
559C22×#135—533no—
560C22×#131—531no—
561C2×C53—26no—
562C2×C53—42no—
563C2×C53—46no—
564C2×C53#358412yescomplemented
565C2×C53C24×D411yescharacteristic
566D53—22no—
567D53—26no—
568D53—46no—
569D53—42no—
570#585—5316no—
571#585—5316no—
572#585—1068no—
573#585—1068no—
574C2×2−1+4—533no—
575C2×2−1+4—531no—
576C2×2−1+4—533no—
577C2×2−1+4—1061no—
578C2×2−1+4—1061no—
579C2×2−1+4C2×D5311yescharacteristic, complemented
580C2×H(5,𝔽2)—533no—
581C2×H(5,𝔽2)—531no—
582C2×H(5,𝔽2)—533no—
583C2×H(5,𝔽2)—1063no—
584C2×H(5,𝔽2)—1063no—
585C2×H(5,𝔽2)C2×D5311yescharacteristic, complemented
586C22×#41—531no—
587C22×#41—533no—
588C22×#41—533no—
589C22×#41—533no—
590C22×#41—533no—
591C22×#41—1063no—
592C22×#41—1061no—
593C22×#41—1061no—
594C22×#41—1063no—
595#578—5316no—
596#578—5348no—
597#577—5348no—
598#577—5348no—
599#577—5316no—
600#577C2×D53116yescomplemented
601#576—5316no—
602#576—5348no—
603#575—5348no—
604#575—5348no—
605C2×#137—533no—
606C2×#137—533no—
607C2×#137—536no—
608C2×#137—536no—
609C2×#137—533no—
610C2×#137C2×D5313yescomplemented
611C2×AGL(1,ℤ/8)—533no—
612C2×AGL(1,ℤ/8)—533no—
613C2×AGL(1,ℤ/8)—536no—
614C2×AGL(1,ℤ/8)—536no—
615C2×AGL(1,ℤ/8)—533no—
616C2×AGL(1,ℤ/8)C2×D5313yescomplemented
617C2×#135—533no—
618C2×#135—533no—
619C2×#135—5348no—
620C2×#135—533no—
621C2×#135—531no—
622C2×#135—533no—
623C2×#135—536no—
624C2×#135—536no—
625C2×#135—536no—
626C2×#135—5348no—
627C2×#135—533no—
628C2×#135—533no—
629C2×#135C2×D5313yescomplemented
630C22×Q16—533no—
631C22×Q16—533no—
632C22×SD16—533no—
633C22×SD16—533no—
634C22×SD16—533no—
635C22×SD16C2×D5313yescomplemented
636C22×D8—533no—
637C22×D8—533no—
638C2×#131—531no—
639C2×#131—5316no—
640C2×#131—533no—
641C2×#131—533no—
642C2×#131C2×D5311yescharacteristic, complemented
643C22×M16—533no—
644C23×C8—533no—
645C53C2×#358411yescharacteristic, complemented, Sylow
6462−1+4—24no—
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—10612no—
6542−1+4—1064no—
6552−1+4C22×D5318yescomplemented
656H(5,𝔽2)—24no—
657H(5,𝔽2)—5324no—
658H(5,𝔽2)—538no—
659H(5,𝔽2)—5324no—
660H(5,𝔽2)—10648no—
661H(5,𝔽2)—10612no—
662H(5,𝔽2)—10648no—
663H(5,𝔽2)—10612no—
664H(5,𝔽2)—1064no—
665H(5,𝔽2)C22×D5318yescomplemented
666C2×#41—21no—
667C2×#41—23no—
668C2×#41—538no—
669C2×#41—538no—
670C2×#41—531no—
671C2×#41—533no—
672C2×#41—533no—
673C2×#41—5324no—
674C2×#41—5324no—
675C2×#41—531no—
676C2×#41—533no—
677C2×#41—536no—
678C2×#41—5324no—
679C2×#41—533no—
680C2×#41—531no—
681C2×#41—536no—
682C2×#41—5324no—
683C2×#41—533no—
684C2×#41—533no—
685C2×#41—1063no—
686C2×#41—1063no—
687C2×#41—1066no—
688C2×#41—1063no—
689C2×#41—1063no—
690C2×#41—1063no—
691C2×#41—1063no—
692C2×#41—1063no—
693C2×#41—1063no—
694C2×#41—10612no—
695C2×#41—1063no—
696C2×#41—1063no—
697C2×#41—10612no—
698C2×#41—10612no—
699C2×#41—10612no—
700C2×#41—1066no—
701C2×#41—1063no—
702C2×#41—10648no—
703C2×#41—1063no—
704C2×#41—10616no—
705C2×#41—10616no—
706C2×#41—10648no—
707C2×#41—1061no—
708C2×#41—1063no—
709C2×#41C22×D5313yes—
710C2×#41C22×D5313yes—
711C2×#41C22×D5311yescharacteristic
712C22×Q8—21no—
713C22×Q8—531no—
714C22×Q8—533no—
715C22×Q8—533no—
716C22×Q8—533no—
717C22×Q8—1063no—
718C22×Q8—1063no—
719C22×Q8—1061no—
720C22×Q8C22×D5313yes—
721C22×D4—23no—
722C22×D4—533no—
723C22×D4—533no—
724C22×D4—533no—
725C22×D4—533no—
726C22×D4—1063no—
727C22×D4—1063no—
728C22×D4—1066no—
729C22×D4—1063no—
730C22×D4—1063no—
731C22×D4—1063no—
732C22×D4—1066no—
733C22×D4—1063no—
734C22×D4—1063no—
735C22×D4C22×D5313yes—
736C23×C4—533no—
737C23×C4—1063no—
738C23×C4—1063no—
739C23×C4—1063no—
740C23×C4—1063no—
741#137—5324no—
742#137—5324no—
743#137—5348no—
744#137—5348no—
745#137—5324no—
746#137C22×D53124yescomplemented
747AGL(1,ℤ/8)—5324no—
748AGL(1,ℤ/8)—5324no—
749AGL(1,ℤ/8)—5348no—
750AGL(1,ℤ/8)—5348no—
751AGL(1,ℤ/8)—5324no—
752AGL(1,ℤ/8)C22×D53124yescomplemented
753#135—5324no—
754#135—5324no—
755#135—5324no—
756#135—538no—
757#135—5324no—
758#135—5348no—
759#135—5348no—
760#135—5348no—
761#135—5324no—
762#135—5324no—
763#135C22×D53124yescomplemented
764C2×Q16—531no—
765C2×Q16—533no—
766C2×Q16—536no—
767C2×Q16—5324no—
768C2×Q16—5324no—
769C2×Q16—533no—
770C2×Q16C22×D5313yes—
771C2×SD16—533no—
772C2×SD16—533no—
773C2×SD16—533no—
774C2×SD16—533no—
775C2×SD16—5324no—
776C2×SD16—5324no—
777C2×SD16—531no—
778C2×SD16—533no—
779C2×SD16—536no—
780C2×SD16—5324no—
781C2×SD16C22×D5311yescharacteristic
782C2×SD16C22×D5313yes—
783C2×SD16C22×D5316yes—
784C2×SD16C22×D53124yescomplemented
785C2×D8—533no—
786C2×D8—531no—
787C2×D8—536no—
788C2×D8—5324no—
789C2×D8—5324no—
790C2×D8—533no—
791C2×D8C22×D5313yes—
792#131—538no—
793#131—5324no—
794#131—5324no—
795#131C22×D5318yescomplemented
796C2×M16—533no—
797C2×M16—5324no—
798C2×M16—536no—
799C2×M16C22×D5313yes—
800C22×C8—533no—
801C22×C8—531no—
802C22×C8—533no—
803C22×C8—533no—
804C22×C8—533no—
805C22×C8—5324no—
806C22×C8C22×D5313yes—
807C24—23no—
808C24—533no—
809C24—1063no—
810C24—1063no—
811C24—1063no—
812#41—28no—
813#41—224no—
814#41—26no—
815#41—26no—
816#41—538no—
817#41—5324no—
818#41—5312no—
819#41—5312no—
820#41—534no—
821#41—5312no—
822#41—5324no—
823#41—5312no—
824#41—534no—
825#41—5324no—
826#41—5312no—
827#41—5312no—
828#41—10624no—
829#41—10624no—
830#41—10648no—
831#41—10624no—
832#41—10624no—
833#41—10624no—
834#41—10624no—
835#41—1066no—
836#41—1062no—
837#41—10624no—
838#41—10624no—
839#41—10612no—
840#41—1066no—
841#41—1062no—
842#41—10624no—
843#41—10624no—
844#41—10612no—
845#41—10648no—
846#41—10624no—
847#41—10624no—
848#41—1068no—
849#41—10624no—
850#41—1066no—
851#41—1066no—
852#41D4×D5314yes—
853#41C23×D53112yes—
854#41C23×D53112yes—
855#41C23×D5314yes—
856C2×Q8—28no—
857C2×Q8—23no—
858C2×Q8—26no—
859C2×Q8—538no—
860C2×Q8—533no—
861C2×Q8—5312no—
862C2×Q8—5312no—
863C2×Q8—531no—
864C2×Q8—533no—
865C2×Q8—5312no—
866C2×Q8—1063no—
867C2×Q8—1063no—
868C2×Q8—10624no—
869C2×Q8—1066no—
870C2×Q8—1066no—
871C2×Q8—10624no—
872C2×Q8—1068no—
873C2×Q8—1063no—
874C2×Q8—1066no—
875C2×Q8D4×D5311yescharacteristic
876C2×Q8C23×D5311yescharacteristic
877C2×Q8C23×D5313yes—
878C2×Q8C23×D53112yes—
879C2×D4—23no—
880C2×D4—23no—
881C2×D4—224no—
882C2×D4—23no—
883C2×D4—26no—
884C2×D4—536no—
885C2×D4—5324no—
886C2×D4—5312no—
887C2×D4—5312no—
888C2×D4—533no—
889C2×D4—533no—
890C2×D4—531no—
891C2×D4—5312no—
892C2×D4—10624no—
893C2×D4—1061no—
894C2×D4—1063no—
895C2×D4—1066no—
896C2×D4—10624no—
897C2×D4—1066no—
898C2×D4—1066no—
899C2×D4—1063no—
900C2×D4—1063no—
901C2×D4—10648no—
902C2×D4—10624no—
903C2×D4—10624no—
904C2×D4—10624no—
905C2×D4—10648no—
906C2×D4—1061no—
907C2×D4—1063no—
908C2×D4—1066no—
909C2×D4—10624no—
910C2×D4—1063no—
911C2×D4—1063no—
912C2×D4—10624no—
913C2×D4—1063no—
914C2×D4—1066no—
915C2×D4D4×D5313yes—
916C2×D4C23×D5313yes—
917C2×D4C23×D53112yes—
918C2×D4C23×D5311yescharacteristic
919C22×C4—23no—
920C22×C4—23no—
921C22×C4—23no—
922C22×C4—533no—
923C22×C4—533no—
924C22×C4—533no—
925C22×C4—5312no—
926C22×C4—531no—
927C22×C4—533no—
928C22×C4—5312no—
929C22×C4—1061no—
930C22×C4—1063no—
931C22×C4—1066no—
932C22×C4—10624no—
933C22×C4—10624no—
934C22×C4—10624no—
935C22×C4—1063no—
936C22×C4—1063no—
937C22×C4—1061no—
938C22×C4—1063no—
939C22×C4—1066no—
940C22×C4—10624no—
941C22×C4—1063no—
942C22×C4—1063no—
943C22×C4—1063no—
944C22×C4C23×D5313yes—
945Q16—534no—
946Q16—5312no—
947Q16—5324no—
948Q16—5312no—
949Q16C23×D53112yes—
950SD16—5312no—
951SD16—5312no—
952SD16—5312no—
953SD16—5312no—
954SD16—534no—
955SD16—5312no—
956SD16—5324no—
957SD16C23×D5314yes—
958SD16C23×D53112yes—
959SD16C23×D53124yes—
960D8—5312no—
961D8—534no—
962D8—5324no—
963D8—5312no—
964D8C23×D53112yes—
965M16—5312no—
966M16—5324no—
967M16C23×D53112yes—
968C2×C8—531no—
969C2×C8—533no—
970C2×C8—5312no—
971C2×C8—534no—
972C2×C8—5312no—
973C2×C8—5312no—
974C2×C8—5312no—
975C2×C8C23×D5311yescharacteristic
976C2×C8C23×D5313yes—
977C2×C8C23×D53112yes—
978C23—21no—
979C23—23no—
980C23—212no—
981C23—86no—
982C23—531no—
983C23—533no—
984C23—5312no—
985C23—10612no—
986C23—10612no—
987C23—10612no—
988C23—1063no—
989C23—1061no—
990C23—4246no—
991C23—4246no—
992C23—4246no—
993C23—2126no—
994C23C2×D4×D5313yes—
995Q8—212no—
996Q8—23no—
997Q8—21no—
998Q8—5312no—
999Q8—536no—
1000Q8—532no—
1001Q8—10612no—
1002Q8—10612no—
1003Q8—10612no—
1004Q8—1063no—
1005Q8—1061no—
1006Q8C2×D4×D5314yes—
1007Q8C24×D5312yes—
1008Q8C24×D5316yes—
1009D4—212no—
1010D4—212no—
1011D4—212no—
1012D4—23no—
1013D4—21no—
1014D4—5324no—
1015D4—5312no—
1016D4—536no—
1017D4—532no—
1018D4—1064no—
1019D4—10612no—
1020D4—10624no—
1021D4—10612no—
1022D4—10612no—
1023D4—1064no—
1024D4—10612no—
1025D4—10624no—
1026D4—10612no—
1027D4—10612no—
1028D4—10612no—
1029D4—1063no—
1030D4—1061no—
1031D4C2×D4×D53112yes—
1032D4C24×D5316yes—
1033D4C24×D5312yes—
1034C2×C4—212no—
1035C2×C4—21no—
1036C2×C4—23no—
1037C2×C4—212no—
1038C2×C4—212no—
1039C2×C4—5312no—
1040C2×C4—531no—
1041C2×C4—533no—
1042C2×C4—532no—
1043C2×C4—5312no—
1044C2×C4—5312no—
1045C2×C4—536no—
1046C2×C4—532no—
1047C2×C4—536no—
1048C2×C4—1064no—
1049C2×C4—10612no—
1050C2×C4—10624no—
1051C2×C4—10612no—
1052C2×C4—10612no—
1053C2×C4—1064no—
1054C2×C4—10612no—
1055C2×C4—10624no—
1056C2×C4—10612no—
1057C2×C4—1061no—
1058C2×C4—1063no—
1059C2×C4—10612no—
1060C2×C4—10612no—
1061C2×C4C2×D4×D5316yes—
1062C2×C4C2×D4×D5313yes—
1063C2×C4C24×D5316yes—
1064C2×C4C24×D5311yescharacteristic
1065C8—532no—
1066C8—536no—
1067C8C24×D5312yes—
1068C8C24×D5316yes—
1069C22—26no—
1070C22—22no—
1071C22—26no—
1072C22—46no—
1073C22—42no—
1074C22—812no—
1075C22—532no—
1076C22—536no—
1077C22—1066no—
1078C22—1062no—
1079C22—1066no—
1080C22—1062no—
1081C22—42412no—
1082C22—42412no—
1083C22—42412no—
1084C22—21212no—
1085C22—2126no—
1086C22—2122no—
1087C22C22×D4×D5316yes—
1088C22C22×D4×D5311yescharacteristic
1089C4—22no—
1090C4—26no—
1091C4—532no—
1092C4—536no—
1093C4—1062no—
1094C4—1066no—
1095C4C22×D4×D5316yes—
1096C4C22×D4×D5311yescharacteristic
1097C4C25×D5311yescharacteristic
1098C2—26no—
1099C2—46no—
1100C2—42no—
1101C2—1066no—
1102C2—1062no—
1103C2—2126no—
1104C2—2122no—
1105C2#2028948712yesdirect product factor
1106C2C23×D4×D5311yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC4×C53C26
FrattiniC4C25×D53
FittingC2×C53×#577C2
socleC22×C53C23×D4
hypercenterC2×#577D53
hypocenterC53C2×#3584
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×#16811460C2semidirect
2. C2×#16811458C2semidirect
3. #20289487C2direct (N × H)
4. C2×#16811439C2semidirect
5. C2×#16811438C2semidirect
6. C2×#16811435C2semidirect
7. C2×#16811430C2semidirect
8. C2×#16811429C2semidirect
9. C2×#16811427C2semidirect
10. C2×#16811426C2semidirect
11. C2×#16811422C2semidirect
12. C2×#16811419C2semidirect
13. C22×#13133238C2semidirect
14. C2×#135×D53C2semidirect
15. C2×#131×D53C2semidirect
16. C2×C53×#577C2semidirect
18. #16811460C22semidirect
20. #16811458C22semidirect
22. C2×#13133265C22semidirect
24. C2×#13133264C22semidirect
25. C2×#13133264C22semidirect
27. C2×#13133263C22semidirect
28. C2×#13133263C22semidirect
30. C2×#13133262C22semidirect
32. C22×#11719949C22semidirect
34. C22×#11719947C22semidirect
38. C2×#41×D53C22semidirect
39. C2×#41×D53C22semidirect
40. #16811439C22semidirect
41. #16811438C22semidirect
42. #16811435C22semidirect
43. #16811430C22semidirect
44. #16811429C22semidirect
45. #16811427C22semidirect
46. #16811426C22semidirect
47. #16811422C22semidirect
48. #16811419C22semidirect
49. C2×#13133250C22semidirect
50. C2×#13133249C22semidirect
51. C2×#13133248C22semidirect
52. C2×#13133247C22semidirect
53. C2×#13133246C22semidirect
54. C2×#13133245C22semidirect
55. C2×#13133244C22semidirect
56. C2×#13133243C22semidirect
57. C2×#13133242C22semidirect
58. C2×#13133241C22semidirect
59. C2×#13133240C22semidirect
60. C2×#13133239C22semidirect
61. C2×#13133238C22semidirect
62. C2×#13133238C22semidirect
63. C2×#13133238C22semidirect
64. C2×#13133238C22semidirect
65. C2×#13133238C22semidirect
66. C2×#13133238C22semidirect
67. C2×#13133237C22semidirect
68. C2×#13133237C22semidirect
69. C2×#13133236C22semidirect
70. #135×D53C22semidirect
71. C22×#11719925C22semidirect
72. C2×Q16×D53C22semidirect
73. C22×#11719913C22semidirect
74. C2×SD16×D53C22semidirect
75. C2×SD16×D53C22semidirect
76. C22×#11719922C22semidirect
77. C2×D8×D53C22semidirect
78. C2×#13133225C22semidirect
79. C2×#13133224C22semidirect
80. C2×#13133223C22semidirect
81. #131×D53C22semidirect
82. C2×M16×D53C22semidirect
83. C22×C8×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
98. #13133264C23semidirect
99. #13133264C23semidirect
103. #13133263C23semidirect
104. #13133263C23semidirect
107. #13133262C23semidirect
118. C2×#11719949C23semidirect
140. C2×#11719947C23semidirect
147. #41×D53C23semidirect
148. #41×D53C23semidirect
174. #13133250C23semidirect
175. #13133249C23semidirect
176. #13133248C23semidirect
177. #13133247C23semidirect
178. #13133246C23semidirect
179. #13133245C23semidirect
180. #13133244C23semidirect
181. #13133243C23semidirect
182. #13133242C23semidirect
183. #13133241C23semidirect
184. #13133240C23semidirect
185. #13133239C23semidirect
186. #13133238C23semidirect
187. #13133238C23semidirect
188. #13133238C23semidirect
189. #13133238C23semidirect
190. #13133238C23semidirect
191. #13133237C23semidirect
192. #13133237C23semidirect
193. #13133236C23semidirect
198. C2×#11719925C23semidirect
199. Q16×D53C23semidirect
203. C2×#11719913C23semidirect
208. SD16×D53C23semidirect
209. SD16×D53C23semidirect
214. C2×#11719922C23semidirect
215. D8×D53C23semidirect
216. #13133225C23semidirect
217. #13133224C23semidirect
218. #13133223C23semidirect
221. M16×D53C23semidirect
227. C2×C8×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
564. C2×C53#3584semidirect
579. C2×2−1+4C2×D53semidirect
585. C2×H(5,𝔽2)C2×D53semidirect
600. #577C2×D53semidirect
610. C2×#137C2×D53semidirect
616. C2×AGL(1,ℤ/8)C2×D53semidirect
629. C2×#135C2×D53semidirect
635. C22×SD16C2×D53semidirect
642. C2×#131C2×D53semidirect
645. C53C2×#3584semidirect
655. 2−1+4C22×D53semidirect
665. H(5,𝔽2)C22×D53semidirect
746. #137C22×D53semidirect
752. AGL(1,ℤ/8)C22×D53semidirect
763. #135C22×D53semidirect
784. C2×SD16C22×D53semidirect
795. #131C22×D53semidirect
1105. C2#20289487direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168114602
C2×#168114582
#202894872
C2×#168114392
C2×#168114382
C2×#168114352
C2×#168114302
C2×#168114292
C2×#168114272
C2×#168114262
C2×#168114222
C2×#168114192
C22×#131332382
C2×#135×D532
C2×#131×D532
C2×C53×#5772
C2×#358453