Finite Group Databasebeta

← C2×#19149370 #26010433

Subgroups — C2×#19149370 #26010433

Order 11008.

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×#14583734C211yesmaximal, characteristic, complemented
2C2×H(5,𝔽2)×D43C211yesmaximal, characteristic, complemented
3#19149370C2132yesmaximal, direct product factor
4C2×#14583711C211yesmaximal, characteristic, complemented
5C2×#14583710C211yesmaximal, characteristic, complemented
6C2×#14583709C213yesmaximal, complemented
7C2×#14583706C213yesmaximal, complemented
8C2×#14583703C213yesmaximal, complemented
9C2×#14583702C211yesmaximal, characteristic, complemented
10C2×#14583700C213yesmaximal, complemented
11C2×#14583696C213yesmaximal, complemented
12C2×#14583695C213yesmaximal, complemented
13C22×#13063349C213yesmaximal, complemented
14C2×AGL(1,ℤ/8)×D43C213yesmaximal, complemented
15C2×#14583664C211yesmaximal, characteristic, complemented
16C2×C43×#576C211yesmaximal, characteristic, complemented
17#14583734—28no—
18#14583734C22116yescomplemented
19C2×#13063372—21no—
20C2×#13063372C2211yescharacteristic, complemented
21C2×#13063372C2213yescomplemented
22C2×#13063371—21no—
23C2×#13063371C2211yescharacteristic, complemented
24C2×#13063371C2213yescomplemented
25C2×#13063370—23no—
26C2×#13063370—23no—
27C2×#13063370C2213yescomplemented
28C2×#13063370C2213yescomplemented
29H(5,𝔽2)×D43—28no—
30H(5,𝔽2)×D43C22116yescomplemented
31C22×#10621900—23no—
32C22×#10621900C2213yescomplemented
33C2×#41×D43—21no—
34C2×#41×D43—21no—
35C2×#41×D43C2211yescharacteristic
36C2×#41×D43C2213yescomplemented
37C2×#41×D43C2213yescomplemented
38C22×D4×D43—23no—
39C22×D4×D43C2213yescomplemented
40#14583711C22116yescomplemented
41#14583710C22116yescomplemented
42#14583709C22148yescomplemented
43#14583706C22148yescomplemented
44#14583703C22148yescomplemented
45#14583702C22116yescomplemented
46#14583700C22148yescomplemented
47#14583696C22148yescomplemented
48#14583695C22148yescomplemented
49C2×#13063358C2213yescomplemented
50C2×#13063357C2211yescharacteristic, complemented
51C2×#13063357C2213yescomplemented
52C2×#13063355C2213yescomplemented
53C2×#13063354C2213yescomplemented
54C2×#13063354C2213yescomplemented
55C2×#13063353C2213yescomplemented
56C2×#13063352C2213yescomplemented
57C2×#13063352C2213yescomplemented
58C2×#13063351C2213yescomplemented
59C2×#13063351C2213yescomplemented
60C2×#13063350C2213yescomplemented
61C2×#13063349C2216yescomplemented
62C2×#13063349C2213yescomplemented
63C2×#13063349C2216yescomplemented
64C2×#13063349C2216yescomplemented
65C2×#13063349C2213yescomplemented
66C2×#13063349C22148yescomplemented
67AGL(1,ℤ/8)×D43C22148yescomplemented
68C2×#13063347C2213yescomplemented
69C2×#13063346C2216yescomplemented
70C2×#13063345C2213yescomplemented
71C2×#13063345C2213yescomplemented
72C2×#13063344C2216yescomplemented
73C22×#10621873C2213yescomplemented
74C22×#10621883C2213yescomplemented
75C2×SD16×D43C2216yescomplemented
76C22×#10621882C2213yescomplemented
77C2×D8×D43C2216yescomplemented
78#14583664C22116yescomplemented
79C2×#13063333C2213yescomplemented
80C2×#13063332C2211yescharacteristic, complemented
81C2×#13063331C2213yescomplemented
82C22×#10621872C2213yescomplemented
83C2×M16×D43C2213yescomplemented
84C2×H(5,𝔽2)×C43C2211yescharacteristic, complemented
85C2×H(5,𝔽2)×C43C2211yescharacteristic, complemented
86C43×#576C22116yescomplemented
87C2×AGL(1,ℤ/8)×C43C2213yescomplemented
88C2×AGL(1,ℤ/8)×C43C2213yescomplemented
89C2×#135×C43C2213yescomplemented
90C22×D8×C43C2213yescomplemented
91C2×#131×C43C2211yescharacteristic, complemented
92C24×D43—23no—
93#13063372—24no—
94#13063372—216no—
95#13063372—212no—
96#13063372C23124yescomplemented
97#13063372C2318yescomplemented
98#13063371—24no—
99#13063371—216no—
100#13063371—212no—
101#13063371C23124yescomplemented
102#13063371C2318yescomplemented
103#13063370—248no—
104#13063370—248no—
105#13063370—212no—
106#13063370—212no—
107#13063370C23124yescomplemented
108#13063370C23124yescomplemented
109C2×#10621902—21no—
110C2×#10621902D411yescharacteristic
111C2×#10621902C2313yes—
112C2×#10621902C2311yescharacteristic
113C2×#10621898—23no—
114C2×#10621898—23no—
115C2×#10621898—23no—
116C2×#10621898—23no—
117C2×#10621898C2313yes—
118C2×#10621898C2313yes—
119C2×#10621898C2313yescomplemented
120C2×#10621900—23no—
121C2×#10621900—26no—
122C2×#10621900—23no—
123C2×#10621900—23no—
124C2×#10621900—248no—
125C2×#10621900—23no—
126C2×#10621900—23no—
127C2×#10621900—212no—
128C2×#10621900—23no—
129C2×#10621900—23no—
130C2×#10621900D413yes—
131C2×#10621900C2313yes—
132C2×#10621900C2313yes—
133C2×#10621900C2316yescomplemented
134C2×#10621900C23124yescomplemented
135#41×D43—216no—
136#41×D43—216no—
137#41×D43—212no—
138#41×D43—212no—
139#41×D43D418yes—
140#41×D43C2318yes—
141#41×D43C23124yescomplemented
142#41×D43C23124yescomplemented
143C22×Dic86—23no—
144C22×Dic86C2313yescomplemented
145C2×Q8×D43—21no—
146C2×Q8×D43D411yescharacteristic
147C2×Q8×D43C2311yescharacteristic
148C2×Q8×D43C2313yescomplemented
149C22×D172—23no—
150C22×D172C2313yes—
151C22×C22⋊D43—23no—
152C22×C22⋊D43—26no—
153C22×C22⋊D43—26no—
154C22×C22⋊D43—23no—
155C2×D4×D43—23no—
156C2×D4×D43—23no—
157C2×D4×D43—23no—
158C2×D4×D43—26no—
159C2×D4×D43—248no—
160C2×D4×D43—23no—
161C2×D4×D43—23no—
162C2×D4×D43—23no—
163C2×D4×D43—212no—
164C2×D4×D43—23no—
165C2×D4×D43D413yes—
166C2×D4×D43C2316yes—
167C2×D4×D43C2313yes—
168C2×D4×D43C23124yescomplemented
169C2×D4×D43C2313yescomplemented
170C23×Dic43—23no—
171C22×C4×D43—23no—
172C22×C4×D43—23no—
173C22×C4×D43C2313yes—
174#13063358C23124yescomplemented
175#13063357C2318yescomplemented
176#13063357C23124yescomplemented
177#13063355C23124yescomplemented
178#13063354C23124yescomplemented
179#13063354C23124yescomplemented
180#13063353C23124yescomplemented
181#13063352C23124yescomplemented
182#13063352C23124yescomplemented
183#13063351C23124yescomplemented
184#13063351C23124yescomplemented
185#13063350C23124yescomplemented
186#13063349C23148yescomplemented
187#13063349C23124yescomplemented
188#13063349C23148yescomplemented
189#13063349C23148yescomplemented
190#13063349C23124yescomplemented
191#13063347C23124yescomplemented
192#13063346C23148yescomplemented
193#13063345C23124yescomplemented
194#13063345C23124yescomplemented
195#13063344C23148yescomplemented
196C2×Dic172C2313yescomplemented
197C2×#10621885C2311yescharacteristic, complemented
198C2×#10621885C2313yescomplemented
199C2×#10621873C2316yescomplemented
200C2×#10621873C2313yescomplemented
201C2×#10621873C2311yescharacteristic, complemented
202C2×#10621873C23124yescomplemented
203C2×#10621883C2316yescomplemented
204C2×#10621883C2313yescomplemented
205C2×#10621883C2313yescomplemented
206C2×#10621883C23124yescomplemented
207C2×#10621884C2313yescomplemented
208C2×#10621884C2311yescharacteristic, complemented
209SD16×D43C23148yescomplemented
210C2×D344C2313yescomplemented
211C2×#10621882C2313yescomplemented
212C2×#10621882C2316yescomplemented
213C2×#10621882C2313yescomplemented
214C2×#10621882C23124yescomplemented
215D8×D43C23148yescomplemented
216#13063333C23124yescomplemented
217#13063332C2318yescomplemented
218#13063331C23124yescomplemented
219C2×#10621877C2313yescomplemented
220C2×#10621872C2313yes—
221C2×#10621872C2311yescharacteristic
222C2×#10621872C23124yescomplemented
223C2×#10621872C2313yescomplemented
224C2×#10621872C2313yescomplemented
225M16×D43C23124yescomplemented
226C22×C43⋊C8C2313yescomplemented
227C2×C8×D43C2316yescomplemented
228H(5,𝔽2)×C43—24no—
229H(5,𝔽2)×C43—24no—
230H(5,𝔽2)×C43C2318yescomplemented
231H(5,𝔽2)×C43C2318yescomplemented
232C2×#41×C43—21no—
233C2×#41×C43—21no—
234C2×#41×C43C2313yes—
235C2×#41×C43C2311yescharacteristic
236C2×#41×C43C2313yescomplemented
237C22×D4×C43—23no—
238C22×D4×C43—23no—
239C22×D4×C43C2313yes—
240C22×D4×C43C2313yescomplemented
241AGL(1,ℤ/8)×C43C23124yescomplemented
242AGL(1,ℤ/8)×C43C23124yescomplemented
243#135×C43C23124yescomplemented
244C2×Q16×C43C2311yescharacteristic, complemented
245C2×SD16×C43C2313yescomplemented
246C2×SD16×C43C2313yescomplemented
247C2×D8×C43C2313yescomplemented
248C2×D8×C43C2316yescomplemented
249C2×D8×C43C23124yescomplemented
250#131×C43C2318yescomplemented
251C2×M16×C43C2313yescomplemented
252C22×C8×C43C2313yescomplemented
253C24×C43—23no—
254C24×C43—23no—
255C23×D43—23no—
256C23×D43—23no—
257C23×D43—23no—
258C23×D43—224no—
259C23×D43—26no—
260C23×D43—812no—
261C23×D43C2×D413yes—
262#41×C43—28no—
263#41×C43—28no—
264#41×C43—26no—
265#41×C43—26no—
266#41×C43C2×D414yes—
267#41×C43C24112yes—
268#41×C43C2414yes—
269#41×C43C24112yescomplemented
270C2×Q8×C43C2×D411yescharacteristic
271C2×Q8×C43C2411yescharacteristic
272C2×Q8×C43C2411yescharacteristic
273C2×D4×C43—224no—
274C2×D4×C43—224no—
275C2×D4×C43—23no—
276C2×D4×C43—23no—
277C2×D4×C43—26no—
278C2×D4×C43—26no—
279C2×D4×C43—23no—
280C2×D4×C43—23no—
281C2×D4×C43C2×D413yes—
282C2×D4×C43C2413yes—
283C2×D4×C43C2413yes—
284C2×D4×C43C24112yes—
285C2×D4×C43C24112yescomplemented
286C22×C4×C43—23no—
287C22×C4×C43—23no—
288C22×C4×C43C2413yes—
289C2×C22⋊D43—248no—
290C2×C22⋊D43—248no—
291C2×C22⋊D43—26no—
292C2×C22⋊D43—23no—
293C2×C22⋊D43—224no—
294C2×C22⋊D43—23no—
295C2×C22⋊D43—23no—
296C2×C22⋊D43—23no—
297C2×C22⋊D43—23no—
298C2×C22⋊D43—23no—
299C2×C22⋊D43—26no—
300C2×C22⋊D43—224no—
301C2×C22⋊D43C2×D416yes—
302C22×Dic43—23no—
303C22×Dic43—23no—
304C22×Dic43—26no—
305C22×Dic43—224no—
306C22×Dic43—23no—
307C22×Dic43C2×D413yes—
308#10621902—28no—
309#10621902—22no—
310#10621902—26no—
311#10621902C2×D418yes—
312#10621902C24112yes—
313#10621902C2414yes—
314Q8×D43—28no—
315Q8×D43—22no—
316Q8×D43—26no—
317Q8×D43C2×D418yes—
318Q8×D43C2414yes—
319Q8×D43C24112yescomplemented
320#10621900—224no—
321#10621900—248no—
322#10621900—224no—
323#10621900—224no—
324#10621900—26no—
325#10621900—224no—
326#10621900—26no—
327#10621900—212no—
328#10621900—224no—
329#10621900—224no—
330#10621900—224no—
331#10621900C2×D4124yes—
332#10621900C24112yes—
333#10621900C24112yes—
334#10621900C24124yescomplemented
335D4×D43—224no—
336D4×D43—248no—
337D4×D43—224no—
338D4×D43—224no—
339D4×D43—26no—
340D4×D43—224no—
341D4×D43—212no—
342D4×D43—224no—
343D4×D43—26no—
344D4×D43—224no—
345D4×D43—224no—
346D4×D43C2×D4124yes—
347D4×D43C24124yes—
348D4×D43C24112yes—
349D4×D43C24112yescomplemented
350#10621898—26no—
351#10621898—26no—
352#10621898—224no—
353#10621898—224no—
354#10621898—224no—
355#10621898—224no—
356#10621898C2×D4112yes—
357#10621898C24112yes—
358#10621898C24112yes—
359#10621898C24112yescomplemented
360C2×D172—23no—
361C2×D172—26no—
362C2×D172—224no—
363C2×D172—23no—
364C2×D172—21no—
365C2×D172C2×D413yes—
366C2×D172C2411yescharacteristic
367C2×D172C2413yes—
368C2×D172C24112yes—
369C2×C4×D43—23no—
370C2×C4×D43—23no—
371C2×C4×D43—21no—
372C2×C4×D43—23no—
373C2×C4×D43—224no—
374C2×C4×D43—224no—
375C2×C4×D43—21no—
376C2×C4×D43—23no—
377C2×C4×D43C2×D413yes—
378C2×C4×D43C2×D413yes—
379C2×C4×D43C2×D4112yes—
380C2×C4×D43C2413yes—
381C2×C4×D43C24112yes—
382C2×C4×D43C2411yescharacteristic
383C2×Dic86—23no—
384C2×Dic86—26no—
385C2×Dic86—21no—
386C2×Dic86—23no—
387C2×Dic86—224no—
388C2×Dic86C2×D413yes—
389C2×Dic86C2413yes—
390C2×Dic86C2411yescharacteristic
391C2×Dic86C24112yescomplemented
392Q16×C43C2414yescomplemented
393SD16×C43C24112yescomplemented
394SD16×C43C24112yescomplemented
395D8×C43C24112yescomplemented
396D8×C43C24124yescomplemented
397M16×C43C24112yescomplemented
398C2×C8×C43C2411yescharacteristic
399C2×C8×C43C2413yes—
400C2×C8×C43C24112yescomplemented
401#10621885C2414yescomplemented
402#10621885C24112yescomplemented
403#10621884C24112yescomplemented
404#10621884C2414yescomplemented
405#10621883C24124yescomplemented
406#10621883C24112yescomplemented
407#10621883C24112yescomplemented
408#10621882C24112yescomplemented
409#10621882C24124yescomplemented
410#10621882C24112yescomplemented
411#10621877C24112yescomplemented
412C2×C43⋊C8C2413yes—
413C2×C43⋊C8C2411yescharacteristic
414C2×C43⋊C8C24112yescomplemented
415Dic172C24112yescomplemented
416D344C24112yescomplemented
417#10621873C24124yescomplemented
418#10621873C24112yescomplemented
419#10621873C2414yescomplemented
420#10621872C24112yes—
421#10621872C2414yes—
422#10621872C24112yescomplemented
423#10621872C24112yescomplemented
424C8×D43C24124yescomplemented
425C23×C43—23no—
426C23×C43—23no—
427C23×C43—212no—
428C23×C43—212no—
429C23×C43—86no—
430C23×C43—86no—
431C23×C43C22×D413yes—
432C22×D43—21no—
433C22×D43—23no—
434C22×D43—212no—
435C22×D43—212no—
436C22×D43—212no—
437C22×D43—224no—
438C22×D43—46no—
439C22×D43—412no—
440C22×D43—86no—
441C22×D43—812no—
442C22×D43—848no—
443C22×D43—86no—
444C22×D43C22×D411yescharacteristic
445C22×D43C22×D413yes—
446C22×D43C22×D4112yes—
447Q8×C43—21no—
448Q8×C43—21no—
449Q8×C43C22×D414yes—
450Q8×C43C2512yes—
451Q8×C43C2512yes—
452D4×C43—212no—
453D4×C43—212no—
454D4×C43—23no—
455D4×C43—212no—
456D4×C43—23no—
457D4×C43—212no—
458D4×C43C22×D4112yes—
459D4×C43C2516yes—
460D4×C43C2516yes—
461C2×C4×C43—21no—
462C2×C4×C43—21no—
463C2×C4×C43—212no—
464C2×C4×C43—212no—
465C2×C4×C43C22×D413yes—
466C2×C4×C43C22×D416yes—
467C2×C4×C43C2511yescharacteristic
468C2×C4×C43C2516yes—
469C22⋊D43—212no—
470C22⋊D43—212no—
471C22⋊D43—212no—
472C22⋊D43—212no—
473C22⋊D43—224no—
474C22⋊D43—224no—
475C22⋊D43—212no—
476C22⋊D43—212no—
477C22⋊D43C22×D4124yes—
478C2×Dic43—23no—
479C2×Dic43—21no—
480C2×Dic43—212no—
481C2×Dic43—224no—
482C2×Dic43—212no—
483C2×Dic43—212no—
484C2×Dic43C22×D413yes—
485C2×Dic43C22×D411yescharacteristic
486C2×Dic43C22×D4112yes—
487D172—212no—
488D172—24no—
489D172—23no—
490D172—212no—
491D172—21no—
492D172C22×D4112yes—
493D172C2516yes—
494D172C2512yes—
495C4×D43—24no—
496C4×D43—212no—
497C4×D43—212no—
498C4×D43—212no—
499C4×D43—24no—
500C4×D43—212no—
501C4×D43C22×D4112yes—
502C4×D43C22×D4112yes—
503C4×D43C22×D412yes—
504C4×D43C22×D416yes—
505C4×D43C2516yes—
506C4×D43C2512yes—
507Dic86—23no—
508Dic86—212no—
509Dic86—21no—
510Dic86—212no—
511Dic86—24no—
512Dic86C22×D4112yes—
513Dic86C2516yes—
514Dic86C2512yes—
515C8×C43C2516yes—
516C8×C43C2512yes—
517C43⋊C8C2516yes—
518C43⋊C8C2512yes—
519C2×#3585—431nomaximal, Sylow
520C22×C43—26no—
521C22×C43—26no—
522C22×C43—26no—
523C22×C43—46no—
524C22×C43—46no—
525C22×C43—812no—
526C22×C43—812no—
527C22×C43C23×D416yes—
528C22×C43C23×D411yescharacteristic
529C2×D43—22no—
530C2×D43—26no—
531C2×D43—26no—
532C2×D43—22no—
533C2×D43—412no—
534C2×D43—424no—
535C2×D43—46no—
536C2×D43—42no—
537C2×D43—812no—
538C2×D43—824no—
539C2×D43—812no—
540C2×D43C23×D412yes—
541C2×D43C23×D416yes—
542C4×C43—22no—
543C4×C43—22no—
544C4×C43C23×D411yescharacteristic
545C4×C43C23×D416yes—
546C4×C43C2611yescharacteristic
547Dic43—26no—
548Dic43—22no—
549Dic43C23×D416yes—
550Dic43C23×D412yes—
551C2×#585—431no—
552C22×H(5,𝔽2)—431no—
553#3585—4332no—
554C2×#577—431no—
555C2×#577—433no—
556C2×#577—433no—
557C2×#577—431no—
558C2×#576—431no—
559C2×#576—433no—
560C2×#576—433no—
561C2×#576D4311yescharacteristic, complemented
562C2×#575—433no—
563C2×#575—433no—
564C22×AGL(1,ℤ/8)—433no—
565C22×AGL(1,ℤ/8)—433no—
566C2×#568—431no—
567C2×C43—26no—
568C2×C43—46no—
569C2×C43—46no—
570C2×C43#358512yescomplemented
571C2×C43C24×D411yescharacteristic
572D43—22no—
573D43—26no—
574D43—46no—
575D43—42no—
576#585—4316no—
577#585—868no—
578C2×2−1+4—431no—
579C2×2−1+4—433no—
580C2×2−1+4—861no—
581C2×H(5,𝔽2)—4316no—
582C2×H(5,𝔽2)—433no—
583C2×H(5,𝔽2)—431no—
584C2×H(5,𝔽2)—433no—
585C2×H(5,𝔽2)—433no—
586C2×H(5,𝔽2)—863no—
587C2×H(5,𝔽2)—863no—
588C2×H(5,𝔽2)—861no—
589C2×H(5,𝔽2)—868no—
590C2×H(5,𝔽2)C2×D4311yescharacteristic, complemented
591C2×H(5,𝔽2)C2×D4311yescharacteristic, complemented
592C22×#41—431no—
593C22×#41—433no—
594C22×#41—433no—
595C22×#41—433no—
596C22×#41—863no—
597C22×#41—861no—
598C22×#41—861no—
599C23×D4—433no—
600C23×D4—863no—
601#577—4316no—
602#577—4348no—
603#577—4348no—
604#577—4316no—
605#576—4316no—
606#576—4348no—
607#576—4348no—
608#576C2×D43116yescomplemented
609#575—4348no—
610#575—4348no—
611C2×#137—433no—
612C2×#137—431no—
613C2×#137—433no—
614C2×#137—433no—
615C2×#137—433no—
616C2×#137—433no—
617C2×AGL(1,ℤ/8)—433no—
618C2×AGL(1,ℤ/8)—433no—
619C2×AGL(1,ℤ/8)—433no—
620C2×AGL(1,ℤ/8)—4348no—
621C2×AGL(1,ℤ/8)—433no—
622C2×AGL(1,ℤ/8)—433no—
623C2×AGL(1,ℤ/8)—4348no—
624C2×AGL(1,ℤ/8)—436no—
625C2×AGL(1,ℤ/8)—433no—
626C2×AGL(1,ℤ/8)—436no—
627C2×AGL(1,ℤ/8)—436no—
628C2×AGL(1,ℤ/8)—433no—
629C2×AGL(1,ℤ/8)—433no—
630C2×AGL(1,ℤ/8)C2×D4313yescomplemented
631C2×AGL(1,ℤ/8)C2×D4313yescomplemented
632C2×#135—433no—
633C2×#135—433no—
634C2×#135—436no—
635C2×#135—436no—
636C2×#135—433no—
637C2×#135C2×D4313yescomplemented
638C22×SD16—433no—
639C22×SD16—436no—
640C22×SD16—433no—
641C22×D8—433no—
642C22×D8—436no—
643C22×D8C2×D4313yescomplemented
644#568—4316no—
645C2×#131—431no—
646C2×#131—433no—
647C2×#131—433no—
648C2×#131C2×D4311yescharacteristic, complemented
649C22×M16—433no—
650C22×M16—433no—
651C43C2×#358511yescharacteristic, complemented, Sylow
652C25—863no—
6532−1+4—438no—
6542−1+4—4324no—
6552−1+4—8616no—
6562−1+4—8612no—
6572−1+4—864no—
658H(5,𝔽2)—24no—
659H(5,𝔽2)—24no—
660H(5,𝔽2)—4324no—
661H(5,𝔽2)—438no—
662H(5,𝔽2)—4324no—
663H(5,𝔽2)—4324no—
664H(5,𝔽2)—8648no—
665H(5,𝔽2)—8648no—
666H(5,𝔽2)—8612no—
667H(5,𝔽2)—8612no—
668H(5,𝔽2)—8616no—
669H(5,𝔽2)—8612no—
670H(5,𝔽2)—864no—
671H(5,𝔽2)C22×D4318yescomplemented
672H(5,𝔽2)C22×D4318yescomplemented
673C2×#41—21no—
674C2×#41—21no—
675C2×#41—438no—
676C2×#41—438no—
677C2×#41—431no—
678C2×#41—433no—
679C2×#41—433no—
680C2×#41—4324no—
681C2×#41—4324no—
682C2×#41—433no—
683C2×#41—431no—
684C2×#41—436no—
685C2×#41—433no—
686C2×#41—433no—
687C2×#41—4324no—
688C2×#41—433no—
689C2×#41—433no—
690C2×#41—863no—
691C2×#41—863no—
692C2×#41—863no—
693C2×#41—863no—
694C2×#41—863no—
695C2×#41—863no—
696C2×#41—863no—
697C2×#41—863no—
698C2×#41—8612no—
699C2×#41—8612no—
700C2×#41—8612no—
701C2×#41—866no—
702C2×#41—863no—
703C2×#41—863no—
704C2×#41—8648no—
705C2×#41—8616no—
706C2×#41—8616no—
707C2×#41—861no—
708C2×#41—863no—
709C2×#41C22×D4313yes—
710C2×#41C22×D4311yescharacteristic
711C2×#41C22×D4313yescomplemented
712C22×Q8—431no—
713C22×Q8—433no—
714C22×Q8—431no—
715C22×Q8—433no—
716C22×Q8—863no—
717C22×Q8—861no—
718C22×D4—23no—
719C22×D4—23no—
720C22×D4—433no—
721C22×D4—433no—
722C22×D4—436no—
723C22×D4—433no—
724C22×D4—4324no—
725C22×D4—433no—
726C22×D4—863no—
727C22×D4—863no—
728C22×D4—863no—
729C22×D4—8612no—
730C22×D4—863no—
731C22×D4—866no—
732C22×D4—8648no—
733C22×D4—863no—
734C22×D4—863no—
735C22×D4—863no—
736C22×D4—863no—
737C22×D4—866no—
738C22×D4—866no—
739C22×D4—863no—
740C22×D4—863no—
741C22×D4C22×D4313yes—
742C22×D4C22×D4313yescomplemented
743C23×C4—433no—
744C23×C4—863no—
745C23×C4—863no—
746C23×C4—863no—
747#137—4324no—
748#137—438no—
749#137—4324no—
750#137—4324no—
751#137—4324no—
752#137—4324no—
753AGL(1,ℤ/8)—4324no—
754AGL(1,ℤ/8)—4324no—
755AGL(1,ℤ/8)—4324no—
756AGL(1,ℤ/8)—4324no—
757AGL(1,ℤ/8)—4324no—
758AGL(1,ℤ/8)—4348no—
759AGL(1,ℤ/8)—4324no—
760AGL(1,ℤ/8)—4348no—
761AGL(1,ℤ/8)—4348no—
762AGL(1,ℤ/8)—4324no—
763AGL(1,ℤ/8)—4324no—
764AGL(1,ℤ/8)C22×D43124yescomplemented
765AGL(1,ℤ/8)C22×D43124yescomplemented
766#135—4324no—
767#135—4324no—
768#135—4348no—
769#135—4348no—
770#135—4324no—
771#135C22×D43124yescomplemented
772C2×Q16—433no—
773C2×Q16—431no—
774C2×Q16—433no—
775C2×Q16C22×D4311yescharacteristic, complemented
776C2×SD16—433no—
777C2×SD16—431no—
778C2×SD16—433no—
779C2×SD16—436no—
780C2×SD16—4324no—
781C2×SD16—433no—
782C2×SD16—4348no—
783C2×SD16—436no—
784C2×SD16—433no—
785C2×SD16—431no—
786C2×SD16—4324no—
787C2×SD16C22×D4313yescomplemented
788C2×SD16C22×D4313yescomplemented
789C2×D8—433no—
790C2×D8—433no—
791C2×D8—436no—
792C2×D8—4324no—
793C2×D8—4348no—
794C2×D8—433no—
795C2×D8C22×D4316yescomplemented
796C2×D8C22×D4313yescomplemented
797C2×D8C22×D43124yescomplemented
798#131—438no—
799#131—4324no—
800#131—4324no—
801#131C22×D4318yescomplemented
802C2×M16—433no—
803C2×M16—4324no—
804C2×M16—433no—
805C2×M16—431no—
806C2×M16—433no—
807C2×M16—433no—
808C2×M16—4324no—
809C2×M16C22×D4313yescomplemented
810C22×C8—433no—
811C22×C8—436no—
812C22×C8C22×D4313yescomplemented
813C24—23no—
814C24—23no—
815C24—433no—
816C24—863no—
817C24—866no—
818C24—8624no—
819C24—863no—
820C24—863no—
821C24—34412no—
822#41—28no—
823#41—28no—
824#41—26no—
825#41—26no—
826#41—438no—
827#41—4324no—
828#41—4312no—
829#41—4312no—
830#41—4312no—
831#41—434no—
832#41—4324no—
833#41—4312no—
834#41—4312no—
835#41—4312no—
836#41—4312no—
837#41—8624no—
838#41—8624no—
839#41—8624no—
840#41—8624no—
841#41—8624no—
842#41—866no—
843#41—8624no—
844#41—8624no—
845#41—866no—
846#41—8624no—
847#41—8612no—
848#41—862no—
849#41—866no—
850#41—8648no—
851#41—8624no—
852#41—8624no—
853#41—868no—
854#41—8624no—
855#41—866no—
856#41—866no—
857#41D4×D4314yes—
858#41C23×D43112yes—
859#41C23×D4314yes—
860#41C23×D43112yescomplemented
861C2×Q8—438no—
862C2×Q8—433no—
863C2×Q8—4312no—
864C2×Q8—434no—
865C2×Q8—433no—
866C2×Q8—431no—
867C2×Q8—4312no—
868C2×Q8—863no—
869C2×Q8—861no—
870C2×Q8—8624no—
871C2×Q8—862no—
872C2×Q8—866no—
873C2×Q8—868no—
874C2×Q8—863no—
875C2×Q8—866no—
876C2×Q8D4×D4311yescharacteristic
877C2×Q8C23×D4311yescharacteristic
878C2×Q8C23×D4311yescharacteristic
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—436no—
888C2×D4—4324no—
889C2×D4—4312no—
890C2×D4—4324no—
891C2×D4—4312no—
892C2×D4—433no—
893C2×D4—431no—
894C2×D4—433no—
895C2×D4—4312no—
896C2×D4—8624no—
897C2×D4—863no—
898C2×D4—861no—
899C2×D4—866no—
900C2×D4—8624no—
901C2×D4—8624no—
902C2×D4—8612no—
903C2×D4—866no—
904C2×D4—863no—
905C2×D4—866no—
906C2×D4—863no—
907C2×D4—8624no—
908C2×D4—8648no—
909C2×D4—8624no—
910C2×D4—8624no—
911C2×D4—8624no—
912C2×D4—8624no—
913C2×D4—8648no—
914C2×D4—8648no—
915C2×D4—863no—
916C2×D4—863no—
917C2×D4—866no—
918C2×D4—8624no—
919C2×D4—863no—
920C2×D4—863no—
921C2×D4—8624no—
922C2×D4—863no—
923C2×D4—866no—
924C2×D4D4×D4313yes—
925C2×D4C23×D4313yes—
926C2×D4C23×D4313yes—
927C2×D4C23×D43112yes—
928C2×D4C23×D43112yescomplemented
929C22×C4—23no—
930C22×C4—23no—
931C22×C4—433no—
932C22×C4—433no—
933C22×C4—433no—
934C22×C4—4312no—
935C22×C4—433no—
936C22×C4—431no—
937C22×C4—4312no—
938C22×C4—861no—
939C22×C4—863no—
940C22×C4—8624no—
941C22×C4—8624no—
942C22×C4—861no—
943C22×C4—863no—
944C22×C4—863no—
945C22×C4—863no—
946C22×C4—866no—
947C22×C4—8624no—
948C22×C4—863no—
949C22×C4—863no—
950C22×C4—863no—
951C22×C4C23×D4313yes—
952Q16—4312no—
953Q16—434no—
954Q16—4312no—
955Q16C23×D4314yescomplemented
956SD16—4312no—
957SD16—434no—
958SD16—4312no—
959SD16—4324no—
960SD16—4312no—
961SD16—4324no—
962SD16—4312no—
963SD16—434no—
964SD16C23×D43112yescomplemented
965SD16C23×D43112yescomplemented
966D8—4312no—
967D8—4312no—
968D8—4324no—
969D8—4312no—
970D8C23×D43124yescomplemented
971D8C23×D43112yescomplemented
972M16—4312no—
973M16—4312no—
974M16—434no—
975M16—4312no—
976M16—4312no—
977M16C23×D43112yescomplemented
978C2×C8—431no—
979C2×C8—433no—
980C2×C8—4312no—
981C2×C8—4324no—
982C2×C8C23×D4313yes—
983C2×C8C23×D4311yescharacteristic
984C2×C8C23×D43112yescomplemented
985C23—23no—
986C23—23no—
987C23—212no—
988C23—212no—
989C23—86no—
990C23—86no—
991C23—431no—
992C23—433no—
993C23—4312no—
994C23—8612no—
995C23—8624no—
996C23—8612no—
997C23—8612no—
998C23—861no—
999C23—863no—
1000C23—3446no—
1001C23—3446no—
1002C23—34412no—
1003C23—34448no—
1004C23—1726no—
1005C23—17212no—
1006C23C2×D4×D4313yes—
1007Q8—21no—
1008Q8—21no—
1009Q8—4312no—
1010Q8—436no—
1011Q8—432no—
1012Q8—8612no—
1013Q8—864no—
1014Q8—8612no—
1015Q8—863no—
1016Q8—861no—
1017Q8C2×D4×D4314yes—
1018Q8C24×D4312yes—
1019Q8C24×D4312yes—
1020D4—212no—
1021D4—212no—
1022D4—212no—
1023D4—23no—
1024D4—23no—
1025D4—212no—
1026D4—4324no—
1027D4—4312no—
1028D4—432no—
1029D4—436no—
1030D4—8612no—
1031D4—864no—
1032D4—8612no—
1033D4—8624no—
1034D4—8612no—
1035D4—8612no—
1036D4—8612no—
1037D4—8624no—
1038D4—8612no—
1039D4—8612no—
1040D4—8612no—
1041D4—863no—
1042D4—861no—
1043D4C2×D4×D43112yes—
1044D4C24×D4316yes—
1045D4C24×D4316yes—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—212no—
1049C2×C4—212no—
1050C2×C4—4312no—
1051C2×C4—431no—
1052C2×C4—433no—
1053C2×C4—432no—
1054C2×C4—4312no—
1055C2×C4—4312no—
1056C2×C4—436no—
1057C2×C4—436no—
1058C2×C4—432no—
1059C2×C4—864no—
1060C2×C4—8612no—
1061C2×C4—864no—
1062C2×C4—8612no—
1063C2×C4—8612no—
1064C2×C4—8612no—
1065C2×C4—8624no—
1066C2×C4—8612no—
1067C2×C4—861no—
1068C2×C4—863no—
1069C2×C4—8612no—
1070C2×C4—8612no—
1071C2×C4C2×D4×D4316yes—
1072C2×C4C2×D4×D4313yes—
1073C2×C4C24×D4316yes—
1074C2×C4C24×D4311yescharacteristic
1075C8—432no—
1076C8—436no—
1077C8C24×D4316yes—
1078C8C24×D4312yes—
1079C22—26no—
1080C22—26no—
1081C22—26no—
1082C22—46no—
1083C22—46no—
1084C22—812no—
1085C22—812no—
1086C22—432no—
1087C22—436no—
1088C22—866no—
1089C22—862no—
1090C22—862no—
1091C22—866no—
1092C22—34412no—
1093C22—34424no—
1094C22—34412no—
1095C22—17212no—
1096C22—17224no—
1097C22—1726no—
1098C22—1722no—
1099C22C22×D4×D4316yes—
1100C22C22×D4×D4311yescharacteristic
1101C4—22no—
1102C4—22no—
1103C4—432no—
1104C4—436no—
1105C4—862no—
1106C4—866no—
1107C4C22×D4×D4316yes—
1108C4C22×D4×D4311yescharacteristic
1109C4C25×D4311yescharacteristic
1110C2—26no—
1111C2—46no—
1112C2—46no—
1113C2—866no—
1114C2—862no—
1115C2—1726no—
1116C2—1722no—
1117C2#1914937012yesdirect product factor
1118C2C23×D4×D4311yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC4×C43C26
FrattiniC4C25×D43
FittingC2×C43×#576C2
socleC22×C43C23×D4
hypercenterC2×#576D43
hypocenterC43C2×#3585
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#576

Complements

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

NH ≅ G/Ntype
1. C2×#14583734C2semidirect
2. C2×H(5,𝔽2)×D43C2semidirect
3. #19149370C2direct (N × H)
4. C2×#14583711C2semidirect
5. C2×#14583710C2semidirect
6. C2×#14583709C2semidirect
7. C2×#14583706C2semidirect
8. C2×#14583703C2semidirect
9. C2×#14583702C2semidirect
10. C2×#14583700C2semidirect
11. C2×#14583696C2semidirect
12. C2×#14583695C2semidirect
13. C22×#13063349C2semidirect
14. C2×AGL(1,ℤ/8)×D43C2semidirect
15. C2×#14583664C2semidirect
16. C2×C43×#576C2semidirect
18. #14583734C22semidirect
20. C2×#13063372C22semidirect
21. C2×#13063372C22semidirect
23. C2×#13063371C22semidirect
24. C2×#13063371C22semidirect
27. C2×#13063370C22semidirect
28. C2×#13063370C22semidirect
30. H(5,𝔽2)×D43C22semidirect
32. C22×#10621900C22semidirect
36. C2×#41×D43C22semidirect
37. C2×#41×D43C22semidirect
39. C22×D4×D43C22semidirect
40. #14583711C22semidirect
41. #14583710C22semidirect
42. #14583709C22semidirect
43. #14583706C22semidirect
44. #14583703C22semidirect
45. #14583702C22semidirect
46. #14583700C22semidirect
47. #14583696C22semidirect
48. #14583695C22semidirect
49. C2×#13063358C22semidirect
50. C2×#13063357C22semidirect
51. C2×#13063357C22semidirect
52. C2×#13063355C22semidirect
53. C2×#13063354C22semidirect
54. C2×#13063354C22semidirect
55. C2×#13063353C22semidirect
56. C2×#13063352C22semidirect
57. C2×#13063352C22semidirect
58. C2×#13063351C22semidirect
59. C2×#13063351C22semidirect
60. C2×#13063350C22semidirect
61. C2×#13063349C22semidirect
62. C2×#13063349C22semidirect
63. C2×#13063349C22semidirect
64. C2×#13063349C22semidirect
65. C2×#13063349C22semidirect
66. C2×#13063349C22semidirect
67. AGL(1,ℤ/8)×D43C22semidirect
68. C2×#13063347C22semidirect
69. C2×#13063346C22semidirect
70. C2×#13063345C22semidirect
71. C2×#13063345C22semidirect
72. C2×#13063344C22semidirect
73. C22×#10621873C22semidirect
74. C22×#10621883C22semidirect
75. C2×SD16×D43C22semidirect
76. C22×#10621882C22semidirect
77. C2×D8×D43C22semidirect
78. #14583664C22semidirect
79. C2×#13063333C22semidirect
80. C2×#13063332C22semidirect
81. C2×#13063331C22semidirect
82. C22×#10621872C22semidirect
83. C2×M16×D43C22semidirect
84. C2×H(5,𝔽2)×C43C22semidirect
85. C2×H(5,𝔽2)×C43C22semidirect
86. C43×#576C22semidirect
87. C2×AGL(1,ℤ/8)×C43C22semidirect
88. C2×AGL(1,ℤ/8)×C43C22semidirect
89. C2×#135×C43C22semidirect
90. C22×D8×C43C22semidirect
91. C2×#131×C43C22semidirect
96. #13063372C23semidirect
97. #13063372C23semidirect
101. #13063371C23semidirect
102. #13063371C23semidirect
107. #13063370C23semidirect
108. #13063370C23semidirect
119. C2×#10621898C23semidirect
133. C2×#10621900C23semidirect
134. C2×#10621900C23semidirect
141. #41×D43C23semidirect
142. #41×D43C23semidirect
144. C22×Dic86C23semidirect
148. C2×Q8×D43C23semidirect
168. C2×D4×D43C23semidirect
169. C2×D4×D43C23semidirect
174. #13063358C23semidirect
175. #13063357C23semidirect
176. #13063357C23semidirect
177. #13063355C23semidirect
178. #13063354C23semidirect
179. #13063354C23semidirect
180. #13063353C23semidirect
181. #13063352C23semidirect
182. #13063352C23semidirect
183. #13063351C23semidirect
184. #13063351C23semidirect
185. #13063350C23semidirect
186. #13063349C23semidirect
187. #13063349C23semidirect
188. #13063349C23semidirect
189. #13063349C23semidirect
190. #13063349C23semidirect
191. #13063347C23semidirect
192. #13063346C23semidirect
193. #13063345C23semidirect
194. #13063345C23semidirect
195. #13063344C23semidirect
196. C2×Dic172C23semidirect
197. C2×#10621885C23semidirect
198. C2×#10621885C23semidirect
199. C2×#10621873C23semidirect
200. C2×#10621873C23semidirect
201. C2×#10621873C23semidirect
202. C2×#10621873C23semidirect
203. C2×#10621883C23semidirect
204. C2×#10621883C23semidirect
205. C2×#10621883C23semidirect
206. C2×#10621883C23semidirect
207. C2×#10621884C23semidirect
208. C2×#10621884C23semidirect
209. SD16×D43C23semidirect
210. C2×D344C23semidirect
211. C2×#10621882C23semidirect
212. C2×#10621882C23semidirect
213. C2×#10621882C23semidirect
214. C2×#10621882C23semidirect
215. D8×D43C23semidirect
216. #13063333C23semidirect
217. #13063332C23semidirect
218. #13063331C23semidirect
219. C2×#10621877C23semidirect
222. C2×#10621872C23semidirect
223. C2×#10621872C23semidirect
224. C2×#10621872C23semidirect
225. M16×D43C23semidirect
226. C22×C43⋊C8C23semidirect
227. C2×C8×D43C23semidirect
230. H(5,𝔽2)×C43C23semidirect
231. H(5,𝔽2)×C43C23semidirect
236. C2×#41×C43C23semidirect
240. C22×D4×C43C23semidirect
241. AGL(1,ℤ/8)×C43C23semidirect
242. AGL(1,ℤ/8)×C43C23semidirect
243. #135×C43C23semidirect
244. C2×Q16×C43C23semidirect
245. C2×SD16×C43C23semidirect
246. C2×SD16×C43C23semidirect
247. C2×D8×C43C23semidirect
248. C2×D8×C43C23semidirect
249. C2×D8×C43C23semidirect
250. #131×C43C23semidirect
251. C2×M16×C43C23semidirect
252. C22×C8×C43C23semidirect
269. #41×C43C24semidirect
285. C2×D4×C43C24semidirect
319. Q8×D43C24semidirect
334. #10621900C24semidirect
349. D4×D43C24semidirect
359. #10621898C24semidirect
391. C2×Dic86C24semidirect
392. Q16×C43C24semidirect
393. SD16×C43C24semidirect
394. SD16×C43C24semidirect
395. D8×C43C24semidirect
396. D8×C43C24semidirect
397. M16×C43C24semidirect
400. C2×C8×C43C24semidirect
401. #10621885C24semidirect
402. #10621885C24semidirect
403. #10621884C24semidirect
404. #10621884C24semidirect
405. #10621883C24semidirect
406. #10621883C24semidirect
407. #10621883C24semidirect
408. #10621882C24semidirect
409. #10621882C24semidirect
410. #10621882C24semidirect
411. #10621877C24semidirect
414. C2×C43⋊C8C24semidirect
415. Dic172C24semidirect
416. D344C24semidirect
417. #10621873C24semidirect
418. #10621873C24semidirect
419. #10621873C24semidirect
422. #10621872C24semidirect
423. #10621872C24semidirect
424. C8×D43C24semidirect
561. C2×#576D43semidirect
570. C2×C43#3585semidirect
590. C2×H(5,𝔽2)C2×D43semidirect
591. C2×H(5,𝔽2)C2×D43semidirect
608. #576C2×D43semidirect
630. C2×AGL(1,ℤ/8)C2×D43semidirect
631. C2×AGL(1,ℤ/8)C2×D43semidirect
637. C2×#135C2×D43semidirect
643. C22×D8C2×D43semidirect
648. C2×#131C2×D43semidirect
651. C43C2×#3585semidirect
671. H(5,𝔽2)C22×D43semidirect
672. H(5,𝔽2)C22×D43semidirect
711. C2×#41C22×D43semidirect
742. C22×D4C22×D43semidirect
764. AGL(1,ℤ/8)C22×D43semidirect
765. AGL(1,ℤ/8)C22×D43semidirect
771. #135C22×D43semidirect
775. C2×Q16C22×D43semidirect
787. C2×SD16C22×D43semidirect
788. C2×SD16C22×D43semidirect
795. C2×D8C22×D43semidirect
796. C2×D8C22×D43semidirect
797. C2×D8C22×D43semidirect
801. #131C22×D43semidirect
809. C2×M16C22×D43semidirect
812. C22×C8C22×D43semidirect
860. #41C23×D43semidirect
928. C2×D4C23×D43semidirect
955. Q16C23×D43semidirect
964. SD16C23×D43semidirect
965. SD16C23×D43semidirect
970. D8C23×D43semidirect
971. D8C23×D43semidirect
977. M16C23×D43semidirect
984. C2×C8C23×D43semidirect
1117. C2#19149370direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145837342
C2×H(5,𝔽2)×D432
#191493702
C2×#145837112
C2×#145837102
C2×#145837092
C2×#145837062
C2×#145837032
C2×#145837022
C2×#145837002
C2×#145836962
C2×#145836952
C22×#130633492
C2×AGL(1,ℤ/8)×D432
C2×#145836642
C2×C43×#5762
C2×#358543