Finite Group Databasebeta

← C2×#20289490 #28297928

Subgroups — C2×#20289490 #28297928

Order 13568.

11138 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811458C211yesmaximal, characteristic, complemented
2C2×H(5,𝔽2)×D53C211yesmaximal, characteristic, complemented
3#20289490C2132yesmaximal, direct product factor
4C2×#16811435C211yesmaximal, characteristic, complemented
5C2×#16811434C211yesmaximal, characteristic, complemented
6C2×#16811433C213yesmaximal, complemented
7C2×#16811430C213yesmaximal, complemented
8C2×#16811427C213yesmaximal, complemented
9C2×#16811426C211yesmaximal, characteristic, complemented
10C2×#16811424C213yesmaximal, complemented
11C2×#16811420C213yesmaximal, complemented
12C2×#16811419C213yesmaximal, complemented
13C22×#13133241C213yesmaximal, complemented
14C2×AGL(1,ℤ/8)×D53C213yesmaximal, complemented
15C2×#16811388C211yesmaximal, characteristic, complemented
16C2×C53×#576C211yesmaximal, characteristic, complemented
17#16811458—28no—
18#16811458C22116yescomplemented
19C2×#13133264—21no—
20C2×#13133264C2211yescharacteristic, complemented
21C2×#13133264C2213yescomplemented
22C2×#13133263—21no—
23C2×#13133263C2211yescharacteristic, complemented
24C2×#13133263C2213yescomplemented
25C2×#13133262—23no—
26C2×#13133262—23no—
27C2×#13133262C2213yescomplemented
28C2×#13133262C2213yescomplemented
29H(5,𝔽2)×D53—28no—
30H(5,𝔽2)×D53C22116yescomplemented
31C22×#11719947—23no—
32C22×#11719947C2213yescomplemented
33C2×#41×D53—21no—
34C2×#41×D53—21no—
35C2×#41×D53C2211yescharacteristic
36C2×#41×D53C2213yescomplemented
37C2×#41×D53C2213yescomplemented
38C22×D4×D53—23no—
39C22×D4×D53C2213yescomplemented
40#16811435C22116yescomplemented
41#16811434C22116yescomplemented
42#16811433C22148yescomplemented
43#16811430C22148yescomplemented
44#16811427C22148yescomplemented
45#16811426C22116yescomplemented
46#16811424C22148yescomplemented
47#16811420C22148yescomplemented
48#16811419C22148yescomplemented
49C2×#13133250C2213yescomplemented
50C2×#13133249C2211yescharacteristic, complemented
51C2×#13133249C2213yescomplemented
52C2×#13133247C2213yescomplemented
53C2×#13133246C2213yescomplemented
54C2×#13133246C2213yescomplemented
55C2×#13133245C2213yescomplemented
56C2×#13133244C2213yescomplemented
57C2×#13133244C2213yescomplemented
58C2×#13133243C2213yescomplemented
59C2×#13133243C2213yescomplemented
60C2×#13133242C2213yescomplemented
61C2×#13133241C2216yescomplemented
62C2×#13133241C2213yescomplemented
63C2×#13133241C2216yescomplemented
64C2×#13133241C2216yescomplemented
65C2×#13133241C2213yescomplemented
66C2×#13133241C22148yescomplemented
67AGL(1,ℤ/8)×D53C22148yescomplemented
68C2×#13133239C2213yescomplemented
69C2×#13133238C2216yescomplemented
70C2×#13133237C2213yescomplemented
71C2×#13133237C2213yescomplemented
72C2×#13133236C2216yescomplemented
73C22×#11719913C2213yescomplemented
74C22×#11719923C2213yescomplemented
75C2×SD16×D53C2216yescomplemented
76C22×#11719922C2213yescomplemented
77C2×D8×D53C2216yescomplemented
78#16811388C22116yescomplemented
79C2×#13133225C2213yescomplemented
80C2×#13133224C2211yescharacteristic, complemented
81C2×#13133223C2213yescomplemented
82C22×#11719912C2213yescomplemented
83C2×M16×D53C2213yescomplemented
84C2×H(5,𝔽2)×C53C2211yescharacteristic, complemented
85C2×H(5,𝔽2)×C53C2211yescharacteristic, complemented
86C53×#576C22116yescomplemented
87C2×AGL(1,ℤ/8)×C53C2213yescomplemented
88C2×AGL(1,ℤ/8)×C53C2213yescomplemented
89C2×#135×C53C2213yescomplemented
90C22×D8×C53C2213yescomplemented
91C2×#131×C53C2211yescharacteristic, complemented
92C24×D53—23no—
93#13133264—24no—
94#13133264—216no—
95#13133264—212no—
96#13133264C23124yescomplemented
97#13133264C2318yescomplemented
98#13133263—24no—
99#13133263—216no—
100#13133263—212no—
101#13133263C23124yescomplemented
102#13133263C2318yescomplemented
103#13133262—248no—
104#13133262—248no—
105#13133262—212no—
106#13133262—212no—
107#13133262C23124yescomplemented
108#13133262C23124yescomplemented
109C2×#11719949—21no—
110C2×#11719949D411yescharacteristic
111C2×#11719949C2313yes—
112C2×#11719949C2311yescharacteristic
113C2×#11719945—23no—
114C2×#11719945—23no—
115C2×#11719945—23no—
116C2×#11719945—23no—
117C2×#11719945C2313yes—
118C2×#11719945C2313yes—
119C2×#11719945C2313yescomplemented
120C2×#11719947—23no—
121C2×#11719947—26no—
122C2×#11719947—23no—
123C2×#11719947—23no—
124C2×#11719947—248no—
125C2×#11719947—23no—
126C2×#11719947—23no—
127C2×#11719947—212no—
128C2×#11719947—23no—
129C2×#11719947—23no—
130C2×#11719947D413yes—
131C2×#11719947C2313yes—
132C2×#11719947C2313yes—
133C2×#11719947C2316yescomplemented
134C2×#11719947C23124yescomplemented
135#41×D53—216no—
136#41×D53—216no—
137#41×D53—212no—
138#41×D53—212no—
139#41×D53D418yes—
140#41×D53C2318yes—
141#41×D53C23124yescomplemented
142#41×D53C23124yescomplemented
143C22×Dic106—23no—
144C22×Dic106C2313yescomplemented
145C2×Q8×D53—21no—
146C2×Q8×D53D411yescharacteristic
147C2×Q8×D53C2311yescharacteristic
148C2×Q8×D53C2313yescomplemented
149C22×D212—23no—
150C22×D212C2313yes—
151C22×C22⋊D53—23no—
152C22×C22⋊D53—26no—
153C22×C22⋊D53—26no—
154C22×C22⋊D53—23no—
155C2×D4×D53—23no—
156C2×D4×D53—23no—
157C2×D4×D53—23no—
158C2×D4×D53—26no—
159C2×D4×D53—248no—
160C2×D4×D53—23no—
161C2×D4×D53—23no—
162C2×D4×D53—23no—
163C2×D4×D53—212no—
164C2×D4×D53—23no—
165C2×D4×D53D413yes—
166C2×D4×D53C2316yes—
167C2×D4×D53C2313yes—
168C2×D4×D53C23124yescomplemented
169C2×D4×D53C2313yescomplemented
170C23×Dic53—23no—
171C22×C4×D53—23no—
172C22×C4×D53—23no—
173C22×C4×D53C2313yes—
174#13133250C23124yescomplemented
175#13133249C2318yescomplemented
176#13133249C23124yescomplemented
177#13133247C23124yescomplemented
178#13133246C23124yescomplemented
179#13133246C23124yescomplemented
180#13133245C23124yescomplemented
181#13133244C23124yescomplemented
182#13133244C23124yescomplemented
183#13133243C23124yescomplemented
184#13133243C23124yescomplemented
185#13133242C23124yescomplemented
186#13133241C23148yescomplemented
187#13133241C23124yescomplemented
188#13133241C23148yescomplemented
189#13133241C23148yescomplemented
190#13133241C23124yescomplemented
191#13133239C23124yescomplemented
192#13133238C23148yescomplemented
193#13133237C23124yescomplemented
194#13133237C23124yescomplemented
195#13133236C23148yescomplemented
196C2×Dic212C2313yescomplemented
197C2×#11719925C2311yescharacteristic, complemented
198C2×#11719925C2313yescomplemented
199C2×#11719913C2316yescomplemented
200C2×#11719913C2313yescomplemented
201C2×#11719913C2311yescharacteristic, complemented
202C2×#11719913C23124yescomplemented
203C2×#11719923C2316yescomplemented
204C2×#11719923C2313yescomplemented
205C2×#11719923C2313yescomplemented
206C2×#11719923C23124yescomplemented
207C2×#11719924C2313yescomplemented
208C2×#11719924C2311yescharacteristic, complemented
209SD16×D53C23148yescomplemented
210C2×D424C2313yescomplemented
211C2×#11719922C2313yescomplemented
212C2×#11719922C2316yescomplemented
213C2×#11719922C2313yescomplemented
214C2×#11719922C23124yescomplemented
215D8×D53C23148yescomplemented
216#13133225C23124yescomplemented
217#13133224C2318yescomplemented
218#13133223C23124yescomplemented
219C2×#11719917C2313yescomplemented
220C2×#11719912C2313yes—
221C2×#11719912C2311yescharacteristic
222C2×#11719912C23124yescomplemented
223C2×#11719912C2313yescomplemented
224C2×#11719912C2313yescomplemented
225M16×D53C23124yescomplemented
226C22×#88322C2313yescomplemented
227C2×C8×D53C2316yescomplemented
228H(5,𝔽2)×C53—24no—
229H(5,𝔽2)×C53—24no—
230H(5,𝔽2)×C53C2318yescomplemented
231H(5,𝔽2)×C53C2318yescomplemented
232C2×#41×C53—21no—
233C2×#41×C53—21no—
234C2×#41×C53C2313yes—
235C2×#41×C53C2311yescharacteristic
236C2×#41×C53C2313yescomplemented
237C22×D4×C53—23no—
238C22×D4×C53—23no—
239C22×D4×C53C2313yes—
240C22×D4×C53C2313yescomplemented
241AGL(1,ℤ/8)×C53C23124yescomplemented
242AGL(1,ℤ/8)×C53C23124yescomplemented
243#135×C53C23124yescomplemented
244C2×Q16×C53C2311yescharacteristic, complemented
245C2×SD16×C53C2313yescomplemented
246C2×SD16×C53C2313yescomplemented
247C2×D8×C53C2313yescomplemented
248C2×D8×C53C2316yescomplemented
249C2×D8×C53C23124yescomplemented
250#131×C53C2318yescomplemented
251C2×M16×C53C2313yescomplemented
252C22×C8×C53C2313yescomplemented
253C24×C53—23no—
254C24×C53—23no—
255C23×D53—23no—
256C23×D53—23no—
257C23×D53—23no—
258C23×D53—224no—
259C23×D53—26no—
260C23×D53—812no—
261C23×D53C2×D413yes—
262#41×C53—28no—
263#41×C53—28no—
264#41×C53—26no—
265#41×C53—26no—
266#41×C53C2×D414yes—
267#41×C53C24112yes—
268#41×C53C2414yes—
269#41×C53C24112yescomplemented
270C2×Q8×C53C2×D411yescharacteristic
271C2×Q8×C53C2411yescharacteristic
272C2×Q8×C53C2411yescharacteristic
273C2×D4×C53—23no—
274C2×D4×C53—23no—
275C2×D4×C53—224no—
276C2×D4×C53—224no—
277C2×D4×C53—23no—
278C2×D4×C53—23no—
279C2×D4×C53—26no—
280C2×D4×C53—26no—
281C2×D4×C53C2×D413yes—
282C2×D4×C53C2413yes—
283C2×D4×C53C2413yes—
284C2×D4×C53C24112yes—
285C2×D4×C53C24112yescomplemented
286C22×C4×C53—23no—
287C22×C4×C53—23no—
288C22×C4×C53C2413yes—
289C2×C22⋊D53—23no—
290C2×C22⋊D53—23no—
291C2×C22⋊D53—23no—
292C2×C22⋊D53—23no—
293C2×C22⋊D53—26no—
294C2×C22⋊D53—224no—
295C2×C22⋊D53—248no—
296C2×C22⋊D53—248no—
297C2×C22⋊D53—26no—
298C2×C22⋊D53—23no—
299C2×C22⋊D53—224no—
300C2×C22⋊D53—23no—
301C2×C22⋊D53C2×D416yes—
302C22×Dic53—23no—
303C22×Dic53—23no—
304C22×Dic53—23no—
305C22×Dic53—26no—
306C22×Dic53—224no—
307C22×Dic53C2×D413yes—
308#11719949—28no—
309#11719949—22no—
310#11719949—26no—
311#11719949C2×D418yes—
312#11719949C24112yes—
313#11719949C2414yes—
314Q8×D53—28no—
315Q8×D53—22no—
316Q8×D53—26no—
317Q8×D53C2×D418yes—
318Q8×D53C2414yes—
319Q8×D53C24112yescomplemented
320#11719947—224no—
321#11719947—248no—
322#11719947—224no—
323#11719947—224no—
324#11719947—26no—
325#11719947—224no—
326#11719947—26no—
327#11719947—212no—
328#11719947—224no—
329#11719947—224no—
330#11719947—224no—
331#11719947C2×D4124yes—
332#11719947C24112yes—
333#11719947C24112yes—
334#11719947C24124yescomplemented
335D4×D53—224no—
336D4×D53—224no—
337D4×D53—224no—
338D4×D53—248no—
339D4×D53—224no—
340D4×D53—224no—
341D4×D53—26no—
342D4×D53—224no—
343D4×D53—212no—
344D4×D53—224no—
345D4×D53—26no—
346D4×D53C2×D4124yes—
347D4×D53C24124yes—
348D4×D53C24112yes—
349D4×D53C24112yescomplemented
350#11719945—26no—
351#11719945—26no—
352#11719945—224no—
353#11719945—224no—
354#11719945—224no—
355#11719945—224no—
356#11719945C2×D4112yes—
357#11719945C24112yes—
358#11719945C24112yes—
359#11719945C24112yescomplemented
360C2×D212—23no—
361C2×D212—21no—
362C2×D212—23no—
363C2×D212—26no—
364C2×D212—224no—
365C2×D212C2×D413yes—
366C2×D212C2411yescharacteristic
367C2×D212C2413yes—
368C2×D212C24112yes—
369C2×C4×D53—21no—
370C2×C4×D53—23no—
371C2×C4×D53—23no—
372C2×C4×D53—23no—
373C2×C4×D53—21no—
374C2×C4×D53—23no—
375C2×C4×D53—224no—
376C2×C4×D53—224no—
377C2×C4×D53C2×D413yes—
378C2×C4×D53C2×D413yes—
379C2×C4×D53C2×D4112yes—
380C2×C4×D53C2413yes—
381C2×C4×D53C24112yes—
382C2×C4×D53C2411yescharacteristic
383C2×Dic106—23no—
384C2×Dic106—26no—
385C2×Dic106—21no—
386C2×Dic106—23no—
387C2×Dic106—224no—
388C2×Dic106C2×D413yes—
389C2×Dic106C2413yes—
390C2×Dic106C2411yescharacteristic
391C2×Dic106C24112yescomplemented
392Q16×C53C2414yescomplemented
393SD16×C53C24112yescomplemented
394SD16×C53C24112yescomplemented
395D8×C53C24112yescomplemented
396D8×C53C24124yescomplemented
397M16×C53C24112yescomplemented
398C2×C8×C53C2411yescharacteristic
399C2×C8×C53C2413yes—
400C2×C8×C53C24112yescomplemented
401#11719925C2414yescomplemented
402#11719925C24112yescomplemented
403#11719924C24112yescomplemented
404#11719924C2414yescomplemented
405#11719923C24124yescomplemented
406#11719923C24112yescomplemented
407#11719923C24112yescomplemented
408#11719922C24112yescomplemented
409#11719922C24124yescomplemented
410#11719922C24112yescomplemented
411#11719917C24112yescomplemented
412C2×#88322C2413yes—
413C2×#88322C2411yescharacteristic
414C2×#88322C24112yescomplemented
415Dic212C24112yescomplemented
416D424C24112yescomplemented
417#11719913C24124yescomplemented
418#11719913C24112yescomplemented
419#11719913C2414yescomplemented
420#11719912C24112yes—
421#11719912C2414yes—
422#11719912C24112yescomplemented
423#11719912C24112yescomplemented
424C8×D53C24124yescomplemented
425C23×C53—23no—
426C23×C53—23no—
427C23×C53—212no—
428C23×C53—212no—
429C23×C53—86no—
430C23×C53—86no—
431C23×C53C22×D413yes—
432C22×D53—21no—
433C22×D53—23no—
434C22×D53—212no—
435C22×D53—212no—
436C22×D53—212no—
437C22×D53—224no—
438C22×D53—46no—
439C22×D53—412no—
440C22×D53—86no—
441C22×D53—812no—
442C22×D53—848no—
443C22×D53—86no—
444C22×D53C22×D411yescharacteristic
445C22×D53C22×D413yes—
446C22×D53C22×D4112yes—
447Q8×C53—21no—
448Q8×C53—21no—
449Q8×C53C22×D414yes—
450Q8×C53C2512yes—
451Q8×C53C2512yes—
452D4×C53—212no—
453D4×C53—212no—
454D4×C53—23no—
455D4×C53—212no—
456D4×C53—23no—
457D4×C53—212no—
458D4×C53C22×D4112yes—
459D4×C53C2516yes—
460D4×C53C2516yes—
461C2×C4×C53—21no—
462C2×C4×C53—21no—
463C2×C4×C53—212no—
464C2×C4×C53—212no—
465C2×C4×C53C22×D413yes—
466C2×C4×C53C22×D416yes—
467C2×C4×C53C2511yescharacteristic
468C2×C4×C53C2516yes—
469C22⋊D53—212no—
470C22⋊D53—212no—
471C22⋊D53—212no—
472C22⋊D53—212no—
473C22⋊D53—224no—
474C22⋊D53—224no—
475C22⋊D53—212no—
476C22⋊D53—212no—
477C22⋊D53C22×D4124yes—
478C2×Dic53—23no—
479C2×Dic53—21no—
480C2×Dic53—212no—
481C2×Dic53—224no—
482C2×Dic53—212no—
483C2×Dic53—212no—
484C2×Dic53C22×D413yes—
485C2×Dic53C22×D411yescharacteristic
486C2×Dic53C22×D4112yes—
487D212—212no—
488D212—24no—
489D212—23no—
490D212—212no—
491D212—21no—
492D212C22×D4112yes—
493D212C2516yes—
494D212C2512yes—
495C4×D53—24no—
496C4×D53—212no—
497C4×D53—212no—
498C4×D53—212no—
499C4×D53—24no—
500C4×D53—212no—
501C4×D53C22×D4112yes—
502C4×D53C22×D4112yes—
503C4×D53C22×D412yes—
504C4×D53C22×D416yes—
505C4×D53C2512yes—
506C4×D53C2516yes—
507Dic106—23no—
508Dic106—212no—
509Dic106—21no—
510Dic106—212no—
511Dic106—24no—
512Dic106C22×D4112yes—
513Dic106C2516yes—
514Dic106C2512yes—
515C8×C53C2516yes—
516C8×C53C2512yes—
517#88322C2516yes—
518#88322C2512yes—
519C2×#3585—531nomaximal, Sylow
520C22×C53—26no—
521C22×C53—26no—
522C22×C53—26no—
523C22×C53—46no—
524C22×C53—46no—
525C22×C53—812no—
526C22×C53—812no—
527C22×C53C23×D416yes—
528C22×C53C23×D411yescharacteristic
529C2×D53—22no—
530C2×D53—26no—
531C2×D53—22no—
532C2×D53—26no—
533C2×D53—412no—
534C2×D53—424no—
535C2×D53—46no—
536C2×D53—42no—
537C2×D53—812no—
538C2×D53—824no—
539C2×D53—812no—
540C2×D53C23×D412yes—
541C2×D53C23×D416yes—
542C4×C53—22no—
543C4×C53—22no—
544C4×C53C23×D411yescharacteristic
545C4×C53C23×D416yes—
546C4×C53C2611yescharacteristic
547Dic53—26no—
548Dic53—22no—
549Dic53C23×D416yes—
550Dic53C23×D412yes—
551C2×#585—531no—
552C22×H(5,𝔽2)—531no—
553#3585—5332no—
554C2×#577—531no—
555C2×#577—533no—
556C2×#577—533no—
557C2×#577—531no—
558C2×#576—531no—
559C2×#576—533no—
560C2×#576—533no—
561C2×#576D5311yescharacteristic, complemented
562C2×#575—533no—
563C2×#575—533no—
564C22×AGL(1,ℤ/8)—533no—
565C22×AGL(1,ℤ/8)—533no—
566C2×#568—531no—
567C2×C53—26no—
568C2×C53—46no—
569C2×C53—46no—
570C2×C53#358512yescomplemented
571C2×C53C24×D411yescharacteristic
572D53—22no—
573D53—26no—
574D53—46no—
575D53—42no—
576#585—5316no—
577#585—1068no—
578C2×2−1+4—531no—
579C2×2−1+4—533no—
580C2×2−1+4—1061no—
581C2×H(5,𝔽2)—5316no—
582C2×H(5,𝔽2)—533no—
583C2×H(5,𝔽2)—531no—
584C2×H(5,𝔽2)—533no—
585C2×H(5,𝔽2)—533no—
586C2×H(5,𝔽2)—1063no—
587C2×H(5,𝔽2)—1063no—
588C2×H(5,𝔽2)—1061no—
589C2×H(5,𝔽2)—1068no—
590C2×H(5,𝔽2)C2×D5311yescharacteristic, complemented
591C2×H(5,𝔽2)C2×D5311yescharacteristic, complemented
592C22×#41—531no—
593C22×#41—533no—
594C22×#41—533no—
595C22×#41—533no—
596C22×#41—1063no—
597C22×#41—1061no—
598C22×#41—1061no—
599C23×D4—533no—
600C23×D4—1063no—
601#577—5316no—
602#577—5348no—
603#577—5348no—
604#577—5316no—
605#576—5316no—
606#576—5348no—
607#576—5348no—
608#576C2×D53116yescomplemented
609#575—5348no—
610#575—5348no—
611C2×#137—533no—
612C2×#137—531no—
613C2×#137—533no—
614C2×#137—533no—
615C2×#137—533no—
616C2×#137—533no—
617C2×AGL(1,ℤ/8)—533no—
618C2×AGL(1,ℤ/8)—533no—
619C2×AGL(1,ℤ/8)—533no—
620C2×AGL(1,ℤ/8)—5348no—
621C2×AGL(1,ℤ/8)—533no—
622C2×AGL(1,ℤ/8)—533no—
623C2×AGL(1,ℤ/8)—5348no—
624C2×AGL(1,ℤ/8)—536no—
625C2×AGL(1,ℤ/8)—533no—
626C2×AGL(1,ℤ/8)—536no—
627C2×AGL(1,ℤ/8)—536no—
628C2×AGL(1,ℤ/8)—533no—
629C2×AGL(1,ℤ/8)—533no—
630C2×AGL(1,ℤ/8)C2×D5313yescomplemented
631C2×AGL(1,ℤ/8)C2×D5313yescomplemented
632C2×#135—533no—
633C2×#135—533no—
634C2×#135—536no—
635C2×#135—536no—
636C2×#135—533no—
637C2×#135C2×D5313yescomplemented
638C22×SD16—533no—
639C22×SD16—536no—
640C22×SD16—533no—
641C22×D8—533no—
642C22×D8—536no—
643C22×D8C2×D5313yescomplemented
644#568—5316no—
645C2×#131—531no—
646C2×#131—533no—
647C2×#131—533no—
648C2×#131C2×D5311yescharacteristic, complemented
649C22×M16—533no—
650C22×M16—533no—
651C53C2×#358511yescharacteristic, complemented, Sylow
652C25—1063no—
6532−1+4—538no—
6542−1+4—5324no—
6552−1+4—10616no—
6562−1+4—10612no—
6572−1+4—1064no—
658H(5,𝔽2)—24no—
659H(5,𝔽2)—24no—
660H(5,𝔽2)—5324no—
661H(5,𝔽2)—538no—
662H(5,𝔽2)—5324no—
663H(5,𝔽2)—5324no—
664H(5,𝔽2)—10648no—
665H(5,𝔽2)—10648no—
666H(5,𝔽2)—10612no—
667H(5,𝔽2)—10612no—
668H(5,𝔽2)—10616no—
669H(5,𝔽2)—10612no—
670H(5,𝔽2)—1064no—
671H(5,𝔽2)C22×D5318yescomplemented
672H(5,𝔽2)C22×D5318yescomplemented
673C2×#41—21no—
674C2×#41—21no—
675C2×#41—538no—
676C2×#41—538no—
677C2×#41—531no—
678C2×#41—533no—
679C2×#41—533no—
680C2×#41—5324no—
681C2×#41—5324no—
682C2×#41—533no—
683C2×#41—531no—
684C2×#41—536no—
685C2×#41—533no—
686C2×#41—533no—
687C2×#41—5324no—
688C2×#41—533no—
689C2×#41—533no—
690C2×#41—1063no—
691C2×#41—1063no—
692C2×#41—1063no—
693C2×#41—1063no—
694C2×#41—1063no—
695C2×#41—1063no—
696C2×#41—1063no—
697C2×#41—1063no—
698C2×#41—10612no—
699C2×#41—10612no—
700C2×#41—10612no—
701C2×#41—1066no—
702C2×#41—1063no—
703C2×#41—1063no—
704C2×#41—10648no—
705C2×#41—10616no—
706C2×#41—10616no—
707C2×#41—1061no—
708C2×#41—1063no—
709C2×#41C22×D5313yes—
710C2×#41C22×D5311yescharacteristic
711C2×#41C22×D5313yescomplemented
712C22×Q8—531no—
713C22×Q8—533no—
714C22×Q8—531no—
715C22×Q8—533no—
716C22×Q8—1063no—
717C22×Q8—1061no—
718C22×D4—23no—
719C22×D4—23no—
720C22×D4—533no—
721C22×D4—533no—
722C22×D4—536no—
723C22×D4—533no—
724C22×D4—5324no—
725C22×D4—533no—
726C22×D4—1063no—
727C22×D4—1063no—
728C22×D4—1063no—
729C22×D4—10612no—
730C22×D4—1063no—
731C22×D4—1066no—
732C22×D4—10648no—
733C22×D4—1063no—
734C22×D4—1063no—
735C22×D4—1063no—
736C22×D4—1063no—
737C22×D4—1066no—
738C22×D4—1066no—
739C22×D4—1063no—
740C22×D4—1063no—
741C22×D4C22×D5313yes—
742C22×D4C22×D5313yescomplemented
743C23×C4—533no—
744C23×C4—1063no—
745C23×C4—1063no—
746C23×C4—1063no—
747#137—5324no—
748#137—538no—
749#137—5324no—
750#137—5324no—
751#137—5324no—
752#137—5324no—
753AGL(1,ℤ/8)—5324no—
754AGL(1,ℤ/8)—5324no—
755AGL(1,ℤ/8)—5324no—
756AGL(1,ℤ/8)—5324no—
757AGL(1,ℤ/8)—5324no—
758AGL(1,ℤ/8)—5348no—
759AGL(1,ℤ/8)—5324no—
760AGL(1,ℤ/8)—5348no—
761AGL(1,ℤ/8)—5348no—
762AGL(1,ℤ/8)—5324no—
763AGL(1,ℤ/8)—5324no—
764AGL(1,ℤ/8)C22×D53124yescomplemented
765AGL(1,ℤ/8)C22×D53124yescomplemented
766#135—5324no—
767#135—5324no—
768#135—5348no—
769#135—5348no—
770#135—5324no—
771#135C22×D53124yescomplemented
772C2×Q16—533no—
773C2×Q16—531no—
774C2×Q16—533no—
775C2×Q16C22×D5311yescharacteristic, complemented
776C2×SD16—533no—
777C2×SD16—531no—
778C2×SD16—533no—
779C2×SD16—536no—
780C2×SD16—5324no—
781C2×SD16—533no—
782C2×SD16—5348no—
783C2×SD16—536no—
784C2×SD16—533no—
785C2×SD16—531no—
786C2×SD16—5324no—
787C2×SD16C22×D5313yescomplemented
788C2×SD16C22×D5313yescomplemented
789C2×D8—533no—
790C2×D8—533no—
791C2×D8—536no—
792C2×D8—5324no—
793C2×D8—5348no—
794C2×D8—533no—
795C2×D8C22×D5316yescomplemented
796C2×D8C22×D5313yescomplemented
797C2×D8C22×D53124yescomplemented
798#131—538no—
799#131—5324no—
800#131—5324no—
801#131C22×D5318yescomplemented
802C2×M16—533no—
803C2×M16—5324no—
804C2×M16—533no—
805C2×M16—531no—
806C2×M16—533no—
807C2×M16—533no—
808C2×M16—5324no—
809C2×M16C22×D5313yescomplemented
810C22×C8—533no—
811C22×C8—536no—
812C22×C8C22×D5313yescomplemented
813C24—23no—
814C24—23no—
815C24—533no—
816C24—1063no—
817C24—1066no—
818C24—10624no—
819C24—1063no—
820C24—1063no—
821C24—42412no—
822#41—28no—
823#41—28no—
824#41—26no—
825#41—26no—
826#41—538no—
827#41—5324no—
828#41—5312no—
829#41—5312no—
830#41—5312no—
831#41—534no—
832#41—5312no—
833#41—5312no—
834#41—5324no—
835#41—5312no—
836#41—5312no—
837#41—10624no—
838#41—10624no—
839#41—10624no—
840#41—10624no—
841#41—10624no—
842#41—1066no—
843#41—10624no—
844#41—10624no—
845#41—1066no—
846#41—10624no—
847#41—10612no—
848#41—1062no—
849#41—1066no—
850#41—10648no—
851#41—10624no—
852#41—10624no—
853#41—1068no—
854#41—10624no—
855#41—1066no—
856#41—1066no—
857#41D4×D5314yes—
858#41C23×D53112yes—
859#41C23×D5314yes—
860#41C23×D53112yescomplemented
861C2×Q8—538no—
862C2×Q8—533no—
863C2×Q8—534no—
864C2×Q8—5312no—
865C2×Q8—533no—
866C2×Q8—531no—
867C2×Q8—5312no—
868C2×Q8—1063no—
869C2×Q8—1061no—
870C2×Q8—10624no—
871C2×Q8—1062no—
872C2×Q8—1066no—
873C2×Q8—1068no—
874C2×Q8—1063no—
875C2×Q8—1066no—
876C2×Q8D4×D5311yescharacteristic
877C2×Q8C23×D5311yescharacteristic
878C2×Q8C23×D5311yescharacteristic
879C2×D4—23no—
880C2×D4—23no—
881C2×D4—224no—
882C2×D4—224no—
883C2×D4—23no—
884C2×D4—23no—
885C2×D4—26no—
886C2×D4—26no—
887C2×D4—536no—
888C2×D4—5324no—
889C2×D4—5324no—
890C2×D4—5312no—
891C2×D4—5312no—
892C2×D4—533no—
893C2×D4—531no—
894C2×D4—533no—
895C2×D4—5312no—
896C2×D4—10624no—
897C2×D4—1063no—
898C2×D4—1061no—
899C2×D4—1066no—
900C2×D4—10624no—
901C2×D4—10624no—
902C2×D4—10612no—
903C2×D4—1066no—
904C2×D4—1063no—
905C2×D4—1066no—
906C2×D4—1063no—
907C2×D4—10624no—
908C2×D4—10648no—
909C2×D4—10624no—
910C2×D4—10624no—
911C2×D4—10624no—
912C2×D4—10624no—
913C2×D4—10648no—
914C2×D4—10648no—
915C2×D4—1063no—
916C2×D4—1063no—
917C2×D4—1066no—
918C2×D4—10624no—
919C2×D4—1063no—
920C2×D4—1063no—
921C2×D4—10624no—
922C2×D4—1063no—
923C2×D4—1066no—
924C2×D4D4×D5313yes—
925C2×D4C23×D5313yes—
926C2×D4C23×D5313yes—
927C2×D4C23×D53112yes—
928C2×D4C23×D53112yescomplemented
929C22×C4—23no—
930C22×C4—23no—
931C22×C4—533no—
932C22×C4—533no—
933C22×C4—533no—
934C22×C4—5312no—
935C22×C4—533no—
936C22×C4—531no—
937C22×C4—5312no—
938C22×C4—1061no—
939C22×C4—1063no—
940C22×C4—10624no—
941C22×C4—10624no—
942C22×C4—1061no—
943C22×C4—1063no—
944C22×C4—1063no—
945C22×C4—1063no—
946C22×C4—1066no—
947C22×C4—10624no—
948C22×C4—1063no—
949C22×C4—1063no—
950C22×C4—1063no—
951C22×C4C23×D5313yes—
952Q16—5312no—
953Q16—534no—
954Q16—5312no—
955Q16C23×D5314yescomplemented
956SD16—5312no—
957SD16—534no—
958SD16—5312no—
959SD16—5324no—
960SD16—5312no—
961SD16—5324no—
962SD16—5312no—
963SD16—534no—
964SD16C23×D53112yescomplemented
965SD16C23×D53112yescomplemented
966D8—5312no—
967D8—5312no—
968D8—5324no—
969D8—5312no—
970D8C23×D53124yescomplemented
971D8C23×D53112yescomplemented
972M16—5312no—
973M16—5312no—
974M16—534no—
975M16—5312no—
976M16—5312no—
977M16C23×D53112yescomplemented
978C2×C8—531no—
979C2×C8—533no—
980C2×C8—5312no—
981C2×C8—5324no—
982C2×C8C23×D5313yes—
983C2×C8C23×D5311yescharacteristic
984C2×C8C23×D53112yescomplemented
985C23—23no—
986C23—23no—
987C23—212no—
988C23—212no—
989C23—86no—
990C23—86no—
991C23—531no—
992C23—533no—
993C23—5312no—
994C23—10612no—
995C23—10624no—
996C23—10612no—
997C23—10612no—
998C23—1061no—
999C23—1063no—
1000C23—4246no—
1001C23—4246no—
1002C23—42412no—
1003C23—42448no—
1004C23—2126no—
1005C23—21212no—
1006C23C2×D4×D5313yes—
1007Q8—21no—
1008Q8—21no—
1009Q8—5312no—
1010Q8—536no—
1011Q8—532no—
1012Q8—10612no—
1013Q8—1064no—
1014Q8—10612no—
1015Q8—1063no—
1016Q8—1061no—
1017Q8C2×D4×D5314yes—
1018Q8C24×D5312yes—
1019Q8C24×D5312yes—
1020D4—212no—
1021D4—212no—
1022D4—212no—
1023D4—23no—
1024D4—23no—
1025D4—212no—
1026D4—5324no—
1027D4—5312no—
1028D4—532no—
1029D4—536no—
1030D4—10612no—
1031D4—1064no—
1032D4—10612no—
1033D4—10624no—
1034D4—10612no—
1035D4—10612no—
1036D4—10612no—
1037D4—10624no—
1038D4—10612no—
1039D4—10612no—
1040D4—10612no—
1041D4—1063no—
1042D4—1061no—
1043D4C2×D4×D53112yes—
1044D4C24×D5316yes—
1045D4C24×D5316yes—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—212no—
1049C2×C4—212no—
1050C2×C4—5312no—
1051C2×C4—531no—
1052C2×C4—533no—
1053C2×C4—532no—
1054C2×C4—5312no—
1055C2×C4—5312no—
1056C2×C4—536no—
1057C2×C4—536no—
1058C2×C4—532no—
1059C2×C4—1064no—
1060C2×C4—10612no—
1061C2×C4—1064no—
1062C2×C4—10612no—
1063C2×C4—10612no—
1064C2×C4—10612no—
1065C2×C4—10624no—
1066C2×C4—10612no—
1067C2×C4—1061no—
1068C2×C4—1063no—
1069C2×C4—10612no—
1070C2×C4—10612no—
1071C2×C4C2×D4×D5316yes—
1072C2×C4C2×D4×D5313yes—
1073C2×C4C24×D5316yes—
1074C2×C4C24×D5311yescharacteristic
1075C8—536no—
1076C8—532no—
1077C8C24×D5316yes—
1078C8C24×D5312yes—
1079C22—26no—
1080C22—26no—
1081C22—26no—
1082C22—46no—
1083C22—46no—
1084C22—812no—
1085C22—812no—
1086C22—532no—
1087C22—536no—
1088C22—1066no—
1089C22—1062no—
1090C22—1062no—
1091C22—1066no—
1092C22—42412no—
1093C22—42424no—
1094C22—42412no—
1095C22—21212no—
1096C22—21224no—
1097C22—2126no—
1098C22—2122no—
1099C22C22×D4×D5316yes—
1100C22C22×D4×D5311yescharacteristic
1101C4—22no—
1102C4—22no—
1103C4—532no—
1104C4—536no—
1105C4—1062no—
1106C4—1066no—
1107C4C22×D4×D5316yes—
1108C4C22×D4×D5311yescharacteristic
1109C4C25×D5311yescharacteristic
1110C2—26no—
1111C2—46no—
1112C2—46no—
1113C2—1066no—
1114C2—1062no—
1115C2—2126no—
1116C2—2122no—
1117C2#2028949012yesdirect product factor
1118C2C23×D4×D5311yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC4×C53C26
FrattiniC4C25×D53
FittingC2×C53×#576C2
socleC22×C53C23×D4
hypercenterC2×#576D53
hypocenterC53C2×#3585
LCSG ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#576

Complements

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

NH ≅ G/Ntype
1. C2×#16811458C2semidirect
2. C2×H(5,𝔽2)×D53C2semidirect
3. #20289490C2direct (N × H)
4. C2×#16811435C2semidirect
5. C2×#16811434C2semidirect
6. C2×#16811433C2semidirect
7. C2×#16811430C2semidirect
8. C2×#16811427C2semidirect
9. C2×#16811426C2semidirect
10. C2×#16811424C2semidirect
11. C2×#16811420C2semidirect
12. C2×#16811419C2semidirect
13. C22×#13133241C2semidirect
14. C2×AGL(1,ℤ/8)×D53C2semidirect
15. C2×#16811388C2semidirect
16. C2×C53×#576C2semidirect
18. #16811458C22semidirect
20. C2×#13133264C22semidirect
21. C2×#13133264C22semidirect
23. C2×#13133263C22semidirect
24. C2×#13133263C22semidirect
27. C2×#13133262C22semidirect
28. C2×#13133262C22semidirect
30. H(5,𝔽2)×D53C22semidirect
32. C22×#11719947C22semidirect
36. C2×#41×D53C22semidirect
37. C2×#41×D53C22semidirect
39. C22×D4×D53C22semidirect
40. #16811435C22semidirect
41. #16811434C22semidirect
42. #16811433C22semidirect
43. #16811430C22semidirect
44. #16811427C22semidirect
45. #16811426C22semidirect
46. #16811424C22semidirect
47. #16811420C22semidirect
48. #16811419C22semidirect
49. C2×#13133250C22semidirect
50. C2×#13133249C22semidirect
51. C2×#13133249C22semidirect
52. C2×#13133247C22semidirect
53. C2×#13133246C22semidirect
54. C2×#13133246C22semidirect
55. C2×#13133245C22semidirect
56. C2×#13133244C22semidirect
57. C2×#13133244C22semidirect
58. C2×#13133243C22semidirect
59. C2×#13133243C22semidirect
60. C2×#13133242C22semidirect
61. C2×#13133241C22semidirect
62. C2×#13133241C22semidirect
63. C2×#13133241C22semidirect
64. C2×#13133241C22semidirect
65. C2×#13133241C22semidirect
66. C2×#13133241C22semidirect
67. AGL(1,ℤ/8)×D53C22semidirect
68. C2×#13133239C22semidirect
69. C2×#13133238C22semidirect
70. C2×#13133237C22semidirect
71. C2×#13133237C22semidirect
72. C2×#13133236C22semidirect
73. C22×#11719913C22semidirect
74. C22×#11719923C22semidirect
75. C2×SD16×D53C22semidirect
76. C22×#11719922C22semidirect
77. C2×D8×D53C22semidirect
78. #16811388C22semidirect
79. C2×#13133225C22semidirect
80. C2×#13133224C22semidirect
81. C2×#13133223C22semidirect
82. C22×#11719912C22semidirect
83. C2×M16×D53C22semidirect
84. C2×H(5,𝔽2)×C53C22semidirect
85. C2×H(5,𝔽2)×C53C22semidirect
86. C53×#576C22semidirect
87. C2×AGL(1,ℤ/8)×C53C22semidirect
88. C2×AGL(1,ℤ/8)×C53C22semidirect
89. C2×#135×C53C22semidirect
90. C22×D8×C53C22semidirect
91. C2×#131×C53C22semidirect
96. #13133264C23semidirect
97. #13133264C23semidirect
101. #13133263C23semidirect
102. #13133263C23semidirect
107. #13133262C23semidirect
108. #13133262C23semidirect
119. C2×#11719945C23semidirect
133. C2×#11719947C23semidirect
134. C2×#11719947C23semidirect
141. #41×D53C23semidirect
142. #41×D53C23semidirect
144. C22×Dic106C23semidirect
148. C2×Q8×D53C23semidirect
168. C2×D4×D53C23semidirect
169. C2×D4×D53C23semidirect
174. #13133250C23semidirect
175. #13133249C23semidirect
176. #13133249C23semidirect
177. #13133247C23semidirect
178. #13133246C23semidirect
179. #13133246C23semidirect
180. #13133245C23semidirect
181. #13133244C23semidirect
182. #13133244C23semidirect
183. #13133243C23semidirect
184. #13133243C23semidirect
185. #13133242C23semidirect
186. #13133241C23semidirect
187. #13133241C23semidirect
188. #13133241C23semidirect
189. #13133241C23semidirect
190. #13133241C23semidirect
191. #13133239C23semidirect
192. #13133238C23semidirect
193. #13133237C23semidirect
194. #13133237C23semidirect
195. #13133236C23semidirect
196. C2×Dic212C23semidirect
197. C2×#11719925C23semidirect
198. C2×#11719925C23semidirect
199. C2×#11719913C23semidirect
200. C2×#11719913C23semidirect
201. C2×#11719913C23semidirect
202. C2×#11719913C23semidirect
203. C2×#11719923C23semidirect
204. C2×#11719923C23semidirect
205. C2×#11719923C23semidirect
206. C2×#11719923C23semidirect
207. C2×#11719924C23semidirect
208. C2×#11719924C23semidirect
209. SD16×D53C23semidirect
210. C2×D424C23semidirect
211. C2×#11719922C23semidirect
212. C2×#11719922C23semidirect
213. C2×#11719922C23semidirect
214. C2×#11719922C23semidirect
215. D8×D53C23semidirect
216. #13133225C23semidirect
217. #13133224C23semidirect
218. #13133223C23semidirect
219. C2×#11719917C23semidirect
222. C2×#11719912C23semidirect
223. C2×#11719912C23semidirect
224. C2×#11719912C23semidirect
225. M16×D53C23semidirect
226. C22×#88322C23semidirect
227. C2×C8×D53C23semidirect
230. H(5,𝔽2)×C53C23semidirect
231. H(5,𝔽2)×C53C23semidirect
236. C2×#41×C53C23semidirect
240. C22×D4×C53C23semidirect
241. AGL(1,ℤ/8)×C53C23semidirect
242. AGL(1,ℤ/8)×C53C23semidirect
243. #135×C53C23semidirect
244. C2×Q16×C53C23semidirect
245. C2×SD16×C53C23semidirect
246. C2×SD16×C53C23semidirect
247. C2×D8×C53C23semidirect
248. C2×D8×C53C23semidirect
249. C2×D8×C53C23semidirect
250. #131×C53C23semidirect
251. C2×M16×C53C23semidirect
252. C22×C8×C53C23semidirect
269. #41×C53C24semidirect
285. C2×D4×C53C24semidirect
319. Q8×D53C24semidirect
334. #11719947C24semidirect
349. D4×D53C24semidirect
359. #11719945C24semidirect
391. C2×Dic106C24semidirect
392. Q16×C53C24semidirect
393. SD16×C53C24semidirect
394. SD16×C53C24semidirect
395. D8×C53C24semidirect
396. D8×C53C24semidirect
397. M16×C53C24semidirect
400. C2×C8×C53C24semidirect
401. #11719925C24semidirect
402. #11719925C24semidirect
403. #11719924C24semidirect
404. #11719924C24semidirect
405. #11719923C24semidirect
406. #11719923C24semidirect
407. #11719923C24semidirect
408. #11719922C24semidirect
409. #11719922C24semidirect
410. #11719922C24semidirect
411. #11719917C24semidirect
414. C2×#88322C24semidirect
415. Dic212C24semidirect
416. D424C24semidirect
417. #11719913C24semidirect
418. #11719913C24semidirect
419. #11719913C24semidirect
422. #11719912C24semidirect
423. #11719912C24semidirect
424. C8×D53C24semidirect
561. C2×#576D53semidirect
570. C2×C53#3585semidirect
590. C2×H(5,𝔽2)C2×D53semidirect
591. C2×H(5,𝔽2)C2×D53semidirect
608. #576C2×D53semidirect
630. C2×AGL(1,ℤ/8)C2×D53semidirect
631. C2×AGL(1,ℤ/8)C2×D53semidirect
637. C2×#135C2×D53semidirect
643. C22×D8C2×D53semidirect
648. C2×#131C2×D53semidirect
651. C53C2×#3585semidirect
671. H(5,𝔽2)C22×D53semidirect
672. H(5,𝔽2)C22×D53semidirect
711. C2×#41C22×D53semidirect
742. C22×D4C22×D53semidirect
764. AGL(1,ℤ/8)C22×D53semidirect
765. AGL(1,ℤ/8)C22×D53semidirect
771. #135C22×D53semidirect
775. C2×Q16C22×D53semidirect
787. C2×SD16C22×D53semidirect
788. C2×SD16C22×D53semidirect
795. C2×D8C22×D53semidirect
796. C2×D8C22×D53semidirect
797. C2×D8C22×D53semidirect
801. #131C22×D53semidirect
809. C2×M16C22×D53semidirect
812. C22×C8C22×D53semidirect
860. #41C23×D53semidirect
928. C2×D4C23×D53semidirect
955. Q16C23×D53semidirect
964. SD16C23×D53semidirect
965. SD16C23×D53semidirect
970. D8C23×D53semidirect
971. D8C23×D53semidirect
977. M16C23×D53semidirect
984. C2×C8C23×D53semidirect
1117. C2#20289490direct (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×H(5,𝔽2)×D532
#202894902
C2×#168114352
C2×#168114342
C2×#168114332
C2×#168114302
C2×#168114272
C2×#168114262
C2×#168114242
C2×#168114202
C2×#168114192
C22×#131332412
C2×AGL(1,ℤ/8)×D532
C2×#168113882
C2×C53×#5762
C2×#358553