Finite Group Databasebeta

← C2×#24907966 #35406313

Subgroups — C2×#24907966 #35406313

Order 21248.

1798 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×Dic83C211yesmaximal, characteristic, complemented
2C2×#19127718C211yesmaximal, characteristic, complemented
3C22×#14581719C211yesmaximal, characteristic, complemented
4C2×#19127675C211yesmaximal, characteristic, complemented
5#24907966C218yesmaximal, direct product factor
6C2×#19127473C211yesmaximal, characteristic, complemented
7C2×#19127462C211yesmaximal, characteristic, complemented
8C2×#575×C83C211yesmaximal, characteristic
9C22×#13050574C2211yescharacteristic
10#41×Dic83—22no—
11#41×Dic83—22no—
12#41×Dic83—22no—
13#41×Dic83C2214yescomplemented
14C2×Q8×Dic83—21no—
15C2×D4×Dic83—22no—
16C2×D4×Dic83—21no—
17C2×#14581751—21no—
18C2×#14581751C2211yescharacteristic
19C2×#14581751C2211yescharacteristic
20C22×C4×Dic83—21no—
21C22×C4×Dic83C2211yescharacteristic
22#19127718—22no—
23#19127718C2214yescomplemented
24C2×#14581719—21no—
25C2×#14581719—21no—
26C2×#14581719—22no—
27C2×#14581719—22no—
28C2×#14581719C2214yescomplemented
29#19127675—22no—
30#19127675C2214yescomplemented
31C2×#14581707—22no—
32#19127473C2214yescomplemented
33#19127462C2214yescomplemented
34C22×#41×C83C2211yescharacteristic
35C22×#41×C83C2211yescharacteristic
36#575×C83—22no—
37#575×C83—22no—
38#575×C83C414yescomplemented
39#575×C83C2214yes—
40C2×#137×C83—21no—
41C2×#137×C83C412yescomplemented
42C2×AGL(1,ℤ/8)×C83—21no—
43C2×AGL(1,ℤ/8)×C83C412yescomplemented
44C2×#135×C83—22no—
45C22×M16×C83C2211yescharacteristic
46C23×Dic83—22no—
47C23×Dic83—21no—
48C2×#13050574—21no—
49C2×#13050574—21no—
50C2×#13050574—21no—
51C2×#13050574—21no—
52C2×#13050574—21no—
53C2×#13050574C2312yes—
54C22×C83⋊C8—21no—
55Q8×Dic83—24no—
56Q8×Dic83—24no—
57D4×Dic83—28no—
58D4×Dic83—24no—
59D4×Dic83—28no—
60D4×Dic83—24no—
61#14581751—24no—
62#14581751—24no—
63#14581751—21no—
64#14581751—21no—
65#14581751—21no—
66#14581751—21no—
67#14581751—21no—
68#14581751D412yes—
69#14581751C2312yes—
70#14581751C2312yes—
71C2×C4⋊Dic83—22no—
72C2×C4⋊Dic83—21no—
73C2×C4⋊Dic83—21no—
74C2×C22⋊Dic83—22no—
75C2×C22⋊Dic83—21no—
76C2×C22⋊Dic83D412yes—
77C2×C4×Dic83—22no—
78C2×C4×Dic83—24no—
79C2×C4×Dic83—24no—
80C2×C4×Dic83—21no—
81C2×C4×Dic83—21no—
82C2×C4×Dic83—21no—
83C2×C4×Dic83—21no—
84C2×C4×Dic83—21no—
85C2×C4×Dic83D411yescharacteristic
86C2×C4×Dic83D411yescharacteristic
87C2×C4×Dic83D412yes—
88C2×C4×Dic83C2312yes—
89#14581719—24no—
90#14581719—24no—
91#14581719—28no—
92#14581707—28no—
93C2×#41×C83—21no—
94C2×#41×C83—21no—
95C2×#41×C83—21no—
96C2×#41×C83—21no—
97C2×#41×C83—21no—
98C2×#41×C83—21no—
99C2×#41×C83—21no—
100C2×#41×C83—21no—
101C2×#41×C83—21no—
102C2×#41×C83—21no—
103C2×#41×C83—21no—
104C2×#41×C83—21no—
105C2×#41×C83—21no—
106C2×#41×C83—21no—
107C2×#41×C83—21no—
108C2×#41×C83—21no—
109C2×#41×C83C2×C412yes—
110C2×#41×C83C2×C412yes—
111C2×#41×C83C2×C412yescomplemented
112C2×#41×C83D412yes—
113C2×#41×C83D412yes—
114C2×#41×C83D412yes—
115C2×#41×C83C2312yes—
116C2×#41×C83C2312yes—
117C22×Q8×C83C2×C411yescharacteristic, complemented
118C22×Q8×C83D411yescharacteristic
119C22×D4×C83—21no—
120C22×D4×C83—21no—
121C22×D4×C83C2×C411yescharacteristic, complemented
122C22×D4×C83D411yescharacteristic
123C23×C4×C83—21no—
124C23×C4×C83—21no—
125C23×C4×C83C2311yescharacteristic
126#137×C83—24no—
127#137×C83—24no—
128#137×C83—24no—
129#137×C83C2×C418yescomplemented
130AGL(1,ℤ/8)×C83—24no—
131AGL(1,ℤ/8)×C83—24no—
132AGL(1,ℤ/8)×C83—24no—
133AGL(1,ℤ/8)×C83C2×C418yescomplemented
134#135×C83—28no—
135#135×C83—28no—
136C2×Q16×C83—22no—
137C2×SD16×C83—22no—
138C2×SD16×C83—22no—
139C2×D8×C83—22no—
140C2×M16×C83—21no—
141C2×M16×C83—21no—
142C2×M16×C83—21no—
143C2×M16×C83C2×C412yescomplemented
144C2×M16×C83C2×C412yescomplemented
145C2×M16×C83C2312yes—
146C22×C8×C83—21no—
147C22×Dic83—21no—
148C22×Dic83—28no—
149C22×Dic83—22no—
150C22×Dic83—21no—
151C22×Dic83—22no—
152C22×Dic83—22no—
153C22×Dic83—44no—
154C22×Dic83—48no—
155C22×Dic83—41no—
156#13050574—22no—
157#13050574—22no—
158#13050574—41no—
159#13050574—41no—
160C2×C83⋊C8—22no—
161C2×C83⋊C8—41no—
162C2×C83⋊C8—41no—
163C4⋊Dic83—28no—
164C4⋊Dic83—22no—
165C4⋊Dic83—22no—
166C4⋊Dic83—22no—
167C4⋊Dic83—41no—
168C22⋊Dic83—28no—
169C22⋊Dic83—22no—
170C22⋊Dic83—22no—
171C22⋊Dic83—41no—
172C22⋊Dic83C2×D414yes—
173C4×Dic83—28no—
174C4×Dic83—21no—
175C4×Dic83—22no—
176C4×Dic83—21no—
177C4×Dic83—22no—
178C4×Dic83—22no—
179C4×Dic83—22no—
180C4×Dic83—22no—
181C4×Dic83—41no—
182C4×Dic83C2×D412yes—
183C4×Dic83C2×D412yes—
184C24×C83—21no—
185C24×C83—21no—
186C24×C83C2×D411yescharacteristic
187#41×C83—22no—
188#41×C83—22no—
189#41×C83—22no—
190#41×C83—22no—
191#41×C83—22no—
192#41×C83—22no—
193#41×C83—22no—
194#41×C83—22no—
195#41×C83—22no—
196#41×C83—22no—
197#41×C83—22no—
198#41×C83—22no—
199#41×C83—22no—
200#41×C83—22no—
201#41×C83—22no—
202#41×C83—22no—
203#41×C83—22no—
204#41×C83—22no—
205#41×C83—22no—
206#41×C83—22no—
207#41×C83—41no—
208#41×C83—41no—
209#41×C83—41no—
210#41×C83—41no—
211#41×C83—41no—
212#41×C83—41no—
213#41×C83—41no—
214#41×C83—41no—
215#41×C83C22⋊C414yes—
216#41×C83C22⋊C414yes—
217#41×C83C22×C414yes—
218#41×C83C2×D414yes—
219C2×Q8×C83—21no—
220C2×Q8×C83—21no—
221C2×Q8×C83—21no—
222C2×Q8×C83—21no—
223C2×Q8×C83—21no—
224C2×Q8×C83—21no—
225C2×Q8×C83—21no—
226C2×Q8×C83—21no—
227C2×Q8×C83C22⋊C412yes—
228C2×Q8×C83C22⋊C412yes—
229C2×Q8×C83C22×C412yescomplemented
230C2×Q8×C83C2×D412yes—
231C2×D4×C83—22no—
232C2×D4×C83—22no—
233C2×D4×C83—22no—
234C2×D4×C83—22no—
235C2×D4×C83—22no—
236C2×D4×C83—22no—
237C2×D4×C83—22no—
238C2×D4×C83—22no—
239C2×D4×C83—21no—
240C2×D4×C83—21no—
241C2×D4×C83—21no—
242C2×D4×C83—21no—
243C2×D4×C83—21no—
244C2×D4×C83—21no—
245C2×D4×C83—21no—
246C2×D4×C83—21no—
247C2×D4×C83—41no—
248C2×D4×C83—41no—
249C2×D4×C83—41no—
250C2×D4×C83—41no—
251C2×D4×C83C22⋊C412yes—
252C2×D4×C83C22⋊C412yes—
253C2×D4×C83C22×C412yescomplemented
254C2×D4×C83C2×D412yes—
255C22×C4×C83—21no—
256C22×C4×C83—22no—
257C22×C4×C83—22no—
258C22×C4×C83—22no—
259C22×C4×C83—22no—
260C22×C4×C83—22no—
261C22×C4×C83—22no—
262C22×C4×C83—21no—
263C22×C4×C83—22no—
264C22×C4×C83—22no—
265C22×C4×C83—41no—
266C22×C4×C83—41no—
267C22×C4×C83—41no—
268C22×C4×C83—41no—
269C22×C4×C83C22×C411yescharacteristic
270C22×C4×C83C22×C411yescharacteristic
271C22×C4×C83C2×D411yescharacteristic
272C22×C4×C83C2×D411yescharacteristic
273C22×C4×C83C2×D411yescharacteristic
274C22×C4×C83C2×D411yescharacteristic
275C22×C4×C83C2×D411yescharacteristic
276C22×C4×C83C2×D411yescharacteristic
277C22×C4×C83C2×D411yescharacteristic
278C22×C4×C83#4111yescharacteristic
279C22×C4×C83#4111yescharacteristic
280C22×C4×C83#4111yescharacteristic
281C22×C4×C83#4111yescharacteristic
282C22×C4×C83C2411yescharacteristic
283Q16×C83—28no—
284SD16×C83—28no—
285SD16×C83—28no—
286D8×C83—28no—
287M16×C83—22no—
288M16×C83—22no—
289M16×C83—22no—
290M16×C83C22×C414yescomplemented
291C2×C8×C83—22no—
292C2×C8×C83—22no—
293C2×C8×C83—22no—
294C23×C83—22no—
295C23×C83—22no—
296C23×C83—22no—
297C23×C83—22no—
298C23×C83—42no—
299C23×C83—44no—
300C23×C83—41no—
301C23×C83—41no—
302C23×C83—82no—
303C23×C83C4×D411yescharacteristic
304C23×C83C4×D411yescharacteristic
305C23×C83#12011yescharacteristic
306C23×C83#12011yescharacteristic
307C23×C83#12111yescharacteristic
308C23×C83#12111yescharacteristic
309C23×C83C22×D411yescharacteristic
310Q8×C83—22no—
311Q8×C83—22no—
312Q8×C83—22no—
313Q8×C83—22no—
314Q8×C83—22no—
315Q8×C83—41no—
316Q8×C83—41no—
317Q8×C83C2×C22⋊C414yes—
318D4×C83—24no—
319D4×C83—24no—
320D4×C83—24no—
321D4×C83—24no—
322D4×C83—22no—
323D4×C83—22no—
324D4×C83—22no—
325D4×C83—22no—
326D4×C83—22no—
327D4×C83—42no—
328D4×C83—42no—
329D4×C83—42no—
330D4×C83—42no—
331D4×C83—41no—
332D4×C83—41no—
333D4×C83C2×C22⋊C414yes—
334C2×C4×C83—22no—
335C2×C4×C83—22no—
336C2×C4×C83—22no—
337C2×C4×C83—24no—
338C2×C4×C83—24no—
339C2×C4×C83—24no—
340C2×C4×C83—24no—
341C2×C4×C83—22no—
342C2×C4×C83—41no—
343C2×C4×C83—41no—
344C2×C4×C83—42no—
345C2×C4×C83—42no—
346C2×C4×C83—42no—
347C2×C4×C83—42no—
348C2×C4×C83C2×C22⋊C411yescharacteristic
349C2×C4×C83C2×C22⋊C411yescharacteristic
350C2×C4×C83C2×C22⋊C411yescharacteristic
351C2×C4×C83C2×C22⋊C411yescharacteristic
352C2×C4×C83C4×D411yescharacteristic
353C2×C4×C83C4×D411yescharacteristic
354C2×C4×C83C4×D411yescharacteristic
355C2×C4×C83C4×D411yescharacteristic
356C2×C4×C83C4×D411yescharacteristic
357C2×C4×C83C4×D411yescharacteristic
358C2×C4×C83#12011yescharacteristic
359C2×C4×C83#12011yescharacteristic
360C2×C4×C83#12111yescharacteristic
361C2×C4×C83#12111yescharacteristic
362C2×C4×C83#12111yescharacteristic
363C2×C4×C83#12111yescharacteristic
364C2×C4×C83#12111yescharacteristic
365C2×C4×C83#12111yescharacteristic
366C2×C4×C83#12311yescharacteristic
367C2×C4×C83#12311yescharacteristic
368C2×C4×C83#12311yescharacteristic
369C2×C4×C83#12311yescharacteristic
370C2×C4×C83C23×C411yescharacteristic
371C2×C4×C83C22×D411yescharacteristic
372C2×C4×C83C22×D411yescharacteristic
373C2×C4×C83C22×D411yescharacteristic
374C2×C4×C83C2×#4111yescharacteristic
375C2×C4×C83C2×#4111yescharacteristic
376C2×Dic83—24no—
377C2×Dic83—22no—
378C2×Dic83—24no—
379C2×Dic83—22no—
380C2×Dic83—44no—
381C2×Dic83—44no—
382C2×Dic83—416no—
383C2×Dic83—44no—
384C2×Dic83—42no—
385C2×Dic83—42no—
386C2×Dic83—82no—
387C8×C83—24no—
388C83⋊C8—42no—
389C22×C83—22no—
390C22×C83—22no—
391C22×C83—22no—
392C22×C83—24no—
393C22×C83—41no—
394C22×C83—41no—
395C22×C83—41no—
396C22×C83—41no—
397C22×C83—44no—
398C22×C83—44no—
399C22×C83—44no—
400C22×C83—42no—
401C22×C83—82no—
402C22×C83—82no—
403C22×C83—82no—
404C22×C83#38611yescharacteristic
405C22×C83#38611yescharacteristic
406C22×C83#38611yescharacteristic
407C22×C83#38611yescharacteristic
408C22×C83C2×C4×D411yescharacteristic
409C22×C83C2×#12011yescharacteristic
410C22×C83C2×#12111yescharacteristic
411C4×C83—24no—
412C4×C83—42no—
413C4×C83#38611yescharacteristic
414C4×C83#38611yescharacteristic
415C4×C83#38611yescharacteristic
416C4×C83#38611yescharacteristic
417C4×C83C22×C22⋊C411yescharacteristic
418C4×C83C2×C4×D411yescharacteristic
419C4×C83C2×#12111yescharacteristic
420C4×C83C2×#12311yescharacteristic
421Dic83—24no—
422Dic83—44no—
423Dic83—42no—
424Dic83—82no—
425C2×#1906—831nomaximal, Sylow
426C2×C83—21no—
427C2×C83—21no—
428C2×C83—21no—
429C2×C83—21no—
430C2×C83—21no—
431C2×C83—21no—
432C2×C83—44no—
433C2×C83—82no—
434C2×C83#190612yescomplemented
435C2×C83C2×#38611yescharacteristic
436C2×#575D8311yescharacteristic
437C2×C4×#41—831no—
438C2×#421—831no—
439C22×#104—831no—
440C2×#410—831no—
441#1906—838no—
442C2×#344—831no—
443C2×#339—831no—
444C83C2×#190611yescharacteristic, complemented, Sylow
445C22×#41C2×D8311yescharacteristic
446C22×#41C2×D8311yescharacteristic
447#575—22no—
448#575—22no—
449#575Dic8314yescomplemented
450#575C2×D8314yes—
451C2×#137—21no—
452C2×#137Dic8312yescomplemented
453C2×AGL(1,ℤ/8)—21no—
454C2×AGL(1,ℤ/8)Dic8312yescomplemented
455C2×#135—22no—
456C22×M16—831no—
457C22×M16C2×D8311yescharacteristic
458C4×#41—834no—
459C4×#41—1662no—
460C4×#41—1662no—
461C4×#41—1662no—
462C2×C4×Q8—1661no—
463C2×C4×D4—1662no—
464C2×C4×D4—1661no—
465C2×#117—831no—
466C2×#117—831no—
467C2×#117—1661no—
468C22×C42—831no—
469C22×C42—1661no—
470#421—834no—
471#421—1662no—
472C2×#104—834no—
473C2×#104—1661no—
474C2×#104—1662no—
475C2×#104—1661no—
476C2×#104—1662no—
477#410—834no—
478#410—1662no—
479C2×#99—1662no—
480#344—834no—
481#339—834no—
482C2×#41—21no—
483C2×#41—21no—
484C2×#41—21no—
485C2×#41—21no—
486C2×#41—21no—
487C2×#41—21no—
488C2×#41—21no—
489C2×#41—21no—
490C2×#41—21no—
491C2×#41—21no—
492C2×#41—21no—
493C2×#41—21no—
494C2×#41—21no—
495C2×#41—21no—
496C2×#41—21no—
497C2×#41—21no—
498C2×#41C2×Dic8312yes—
499C2×#41C2×Dic8312yes—
500C2×#41C2×Dic8312yescomplemented
501C2×#41C22⋊D8312yes—
502C2×#41C22⋊D8312yes—
503C2×#41C22⋊D8312yes—
504C2×#41C22×D8312yes—
505C2×#41C22×D8312yes—
506C22×Q8C2×Dic8311yescharacteristic, complemented
507C22×Q8C22⋊D8311yescharacteristic
508C22×D4—21no—
509C22×D4—21no—
510C22×D4C2×Dic8311yescharacteristic, complemented
511C22×D4C22⋊D8311yescharacteristic
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—1662no—
515C23×C4—1661no—
516C23×C4C22×D8311yescharacteristic
517#137—24no—
518#137—24no—
519#137—24no—
520#137C2×Dic8318yescomplemented
521AGL(1,ℤ/8)—24no—
522AGL(1,ℤ/8)—24no—
523AGL(1,ℤ/8)—24no—
524AGL(1,ℤ/8)C2×Dic8318yescomplemented
525#135—28no—
526#135—28no—
527C2×Q16—22no—
528C2×SD16—22no—
529C2×SD16—22no—
530C2×D8—22no—
531C2×M16—21no—
532C2×M16—21no—
533C2×M16—21no—
534C2×M16—832no—
535C2×M16—1661no—
536C2×M16—1661no—
537C2×M16—1661no—
538C2×M16—1661no—
539C2×M16—1661no—
540C2×M16C2×Dic8312yescomplemented
541C2×M16C2×Dic8312yescomplemented
542C2×M16C22×D8312yes—
543C22×C8—21no—
544C22×C8—1661no—
545C4×Q8—1664no—
546C4×Q8—1664no—
547C4×D4—1668no—
548C4×D4—1668no—
549C4×D4—1664no—
550C4×D4—1664no—
551#117—832no—
552#117—832no—
553#117—832no—
554#117—1661no—
555#117—1661no—
556#117—1664no—
557#117—1661no—
558#117—1664no—
559#117—1661no—
560#117—1661no—
561C2×C4⋊C4—1661no—
562C2×C4⋊C4—1662no—
563C2×C4⋊C4—1661no—
564C2×C22⋊C4—832no—
565C2×C22⋊C4—1661no—
566C2×C22⋊C4—1662no—
567C2×C42—831no—
568C2×C42—832no—
569C2×C42—831no—
570C2×C42—832no—
571C2×C42—1661no—
572C2×C42—1664no—
573C2×C42—1662no—
574C2×C42—1664no—
575C2×C42—1661no—
576C2×C42—1661no—
577C2×C42—1661no—
578C2×C42—1661no—
579#104—1664no—
580#104—1664no—
581#104—1668no—
582#99—1668no—
583C24—21no—
584C24—21no—
585C24D4×D8311yescharacteristic
586#41—22no—
587#41—22no—
588#41—22no—
589#41—22no—
590#41—22no—
591#41—22no—
592#41—22no—
593#41—22no—
594#41—22no—
595#41—22no—
596#41—22no—
597#41—22no—
598#41—22no—
599#41—22no—
600#41—22no—
601#41—22no—
602#41—22no—
603#41—22no—
604#41—22no—
605#41—22no—
606#41—41no—
607#41—41no—
608#41—41no—
609#41—41no—
610#41—41no—
611#41—41no—
612#41—41no—
613#41—41no—
614#41C22⋊Dic8314yes—
615#41C22⋊Dic8314yes—
616#41C22×Dic8314yes—
617#41C2×C22⋊D8314yes—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8—21no—
626C2×Q8C22⋊Dic8312yes—
627C2×Q8C22⋊Dic8312yes—
628C2×Q8C22×Dic8312yescomplemented
629C2×Q8C2×C22⋊D8312yes—
630C2×D4—22no—
631C2×D4—22no—
632C2×D4—22no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—22no—
636C2×D4—22no—
637C2×D4—22no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—41no—
647C2×D4—41no—
648C2×D4—41no—
649C2×D4—41no—
650C2×D4C22⋊Dic8312yes—
651C2×D4C22⋊Dic8312yes—
652C2×D4C22×Dic8312yescomplemented
653C2×D4C2×C22⋊D8312yes—
654C22×C4—21no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—21no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—41no—
665C22×C4—41no—
666C22×C4—41no—
667C22×C4—41no—
668C22×C4—3324no—
669C22×C4—3328no—
670C22×C4—3321no—
671C22×C4—1668no—
672C22×C4—1661no—
673C22×C4—1662no—
674C22×C4—1662no—
675C22×C4—1662no—
676C22×C4—1661no—
677C22×C4C22×Dic8311yescharacteristic
678C22×C4C22×Dic8311yescharacteristic
679C22×C4D4×D8311yescharacteristic
680C22×C4D4×D8311yescharacteristic
681C22×C4D4×D8311yescharacteristic
682C22×C4C2×C22⋊D8311yescharacteristic
683C22×C4C2×C22⋊D8311yescharacteristic
684C22×C4C2×C22⋊D8311yescharacteristic
685C22×C4C2×C22⋊D8311yescharacteristic
686C22×C4#1305058911yescharacteristic
687C22×C4#1305058911yescharacteristic
688C22×C4#1305058911yescharacteristic
689C22×C4#1305058911yescharacteristic
690C22×C4C23×D8311yescharacteristic
691Q16—28no—
692SD16—28no—
693SD16—28no—
694D8—28no—
695M16—22no—
696M16—22no—
697M16—22no—
698M16—3321no—
699M16—3321no—
700M16—1662no—
701M16—1662no—
702M16C22×Dic8314yescomplemented
703C2×C8—22no—
704C2×C8—22no—
705C2×C8—22no—
706C2×C8—3321no—
707C2×C8—3321no—
708C2×C8—1662no—
709C4⋊C4—3321no—
710C4⋊C4—1668no—
711C4⋊C4—1662no—
712C4⋊C4—1662no—
713C4⋊C4—1662no—
714C22⋊C4—3321no—
715C22⋊C4—834no—
716C22⋊C4—1662no—
717C22⋊C4—1668no—
718C22⋊C4—1662no—
719C42—3321no—
720C42—832no—
721C42—832no—
722C42—1668no—
723C42—1662no—
724C42—1661no—
725C42—1661no—
726C42—1662no—
727C42—1662no—
728C42—1662no—
729C42—1662no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—42no—
735C23—44no—
736C23—41no—
737C23—41no—
738C23—82no—
739C23D4×Dic8311yescharacteristic
740C23D4×Dic8311yescharacteristic
741C23#1458176011yescharacteristic
742C23#1458176011yescharacteristic
743C23#1458176411yescharacteristic
744C23#1458176411yescharacteristic
745C23C2×D4×D8311yescharacteristic
746Q8—22no—
747Q8—22no—
748Q8—22no—
749Q8—22no—
750Q8—22no—
751Q8—41no—
752Q8—41no—
753Q8C2×C22⋊Dic8314yes—
754D4—24no—
755D4—24no—
756D4—24no—
757D4—24no—
758D4—22no—
759D4—22no—
760D4—22no—
761D4—22no—
762D4—22no—
763D4—42no—
764D4—42no—
765D4—42no—
766D4—42no—
767D4—41no—
768D4—41no—
769D4C2×C22⋊Dic8314yes—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—3322no—
785C2×C4—3324no—
786C2×C4—3324no—
787C2×C4—3324no—
788C2×C4—33216no—
789C2×C4—3322no—
790C2×C4—6642no—
791C2×C4—1662no—
792C2×C4—1664no—
793C2×C4—1664no—
794C2×C4—1662no—
795C2×C4C2×C22⋊Dic8311yescharacteristic
796C2×C4C2×C22⋊Dic8311yescharacteristic
797C2×C4C2×C22⋊Dic8311yescharacteristic
798C2×C4C2×C22⋊Dic8311yescharacteristic
799C2×C4D4×Dic8311yescharacteristic
800C2×C4D4×Dic8311yescharacteristic
801C2×C4D4×Dic8311yescharacteristic
802C2×C4D4×Dic8311yescharacteristic
803C2×C4D4×Dic8311yescharacteristic
804C2×C4D4×Dic8311yescharacteristic
805C2×C4#1458176011yescharacteristic
806C2×C4#1458176011yescharacteristic
807C2×C4#1458176411yescharacteristic
808C2×C4#1458176411yescharacteristic
809C2×C4#1458176411yescharacteristic
810C2×C4#1458176411yescharacteristic
811C2×C4#1458176411yescharacteristic
812C2×C4#1458176411yescharacteristic
813C2×C4#1458177311yescharacteristic
814C2×C4#1458177311yescharacteristic
815C2×C4#1458177311yescharacteristic
816C2×C4#1458177311yescharacteristic
817C2×C4C23×Dic8311yescharacteristic
818C2×C4C2×D4×D8311yescharacteristic
819C2×C4C22×C22⋊D8311yescharacteristic
820C2×C4C22×C22⋊D8311yescharacteristic
821C2×C4C2×#1305058911yescharacteristic
822C2×C4C2×#1305058911yescharacteristic
823C8—24no—
824C8—3322no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—24no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—44no—
834C22—44no—
835C22—44no—
836C22—42no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22#1912758111yescharacteristic
841C22#1912758111yescharacteristic
842C22#1912758111yescharacteristic
843C22#1912758111yescharacteristic
844C22C2×D4×Dic8311yescharacteristic
845C22C2×#1458176011yescharacteristic
846C22C2×#1458176411yescharacteristic
847C4—24no—
848C4—42no—
849C4—3322no—
850C4—3324no—
851C4—6642no—
852C4—1664no—
853C4#1912758111yescharacteristic
854C4#1912758111yescharacteristic
855C4#1912758111yescharacteristic
856C4#1912758111yescharacteristic
857C4C22×C22⋊Dic8311yescharacteristic
858C4C2×D4×Dic8311yescharacteristic
859C4C2×#1458176411yescharacteristic
860C4C2×#1458177311yescharacteristic
861C2—21no—
862C2—21no—
863C2—21no—
864C2—21no—
865C2—21no—
866C2—21no—
867C2—44no—
868C2—82no—
869C2#2490796612yesdirect product factor
870C2C2×#1912758111yescharacteristic
subgroupG/H
centerC2×C4#14581764
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
Fitting, prime radicalC2×#575×C83C2
socleC22×C83#386
cosocleC22×C4×C83C24
hypercenterC2×#575D83
hypocenterC83C2×#1906
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
1. C2×#41×Dic83C2semidirect
2. C2×#19127718C2semidirect
3. C22×#14581719C2semidirect
4. C2×#19127675C2semidirect
5. #24907966C2direct (N × H)
6. C2×#19127473C2semidirect
7. C2×#19127462C2semidirect
13. #41×Dic83C22semidirect
23. #19127718C22semidirect
28. C2×#14581719C22semidirect
30. #19127675C22semidirect
32. #19127473C22semidirect
33. #19127462C22semidirect
38. #575×C83C4semidirect
41. C2×#137×C83C4semidirect
43. C2×AGL(1,ℤ/8)×C83C4semidirect
111. C2×#41×C83C2×C4semidirect
117. C22×Q8×C83C2×C4semidirect
121. C22×D4×C83C2×C4semidirect
129. #137×C83C2×C4semidirect
133. AGL(1,ℤ/8)×C83C2×C4semidirect
143. C2×M16×C83C2×C4semidirect
144. C2×M16×C83C2×C4semidirect
229. C2×Q8×C83C22×C4semidirect
253. C2×D4×C83C22×C4semidirect
290. M16×C83C22×C4semidirect
434. C2×C83#1906semidirect
444. C83C2×#1906semidirect
449. #575Dic83semidirect
452. C2×#137Dic83semidirect
454. C2×AGL(1,ℤ/8)Dic83semidirect
500. C2×#41C2×Dic83semidirect
506. C22×Q8C2×Dic83semidirect
510. C22×D4C2×Dic83semidirect
520. #137C2×Dic83semidirect
524. AGL(1,ℤ/8)C2×Dic83semidirect
540. C2×M16C2×Dic83semidirect
541. C2×M16C2×Dic83semidirect
628. C2×Q8C22×Dic83semidirect
652. C2×D4C22×Dic83semidirect
702. M16C22×Dic83semidirect
869. C2#24907966direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#41×Dic832
C2×#191277182
C22×#145817192
C2×#191276752
#249079662
C2×#191274732
C2×#191274622
C2×#575×C832
C2×#190683