Finite Group Databasebeta

← D43×#3207 #25967791

Subgroups — D43×#3207 #25967791

Order 11008.

2466 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#532×D43C211yesmaximal, characteristic, complemented
2#532×D43C211yesmaximal, characteristic, complemented
3#19145531C211yesmaximal, characteristic, complemented
4#19145530C211yesmaximal, characteristic, complemented
5#19145529C211yesmaximal, characteristic, complemented
6#19145528C211yesmaximal, characteristic, complemented
7#19145527C214yesmaximal, complemented
8#19145526C214yesmaximal, complemented
9#19145525C211yesmaximal, characteristic, complemented
10#19145524C211yesmaximal, characteristic, complemented
11#19145523C211yesmaximal, characteristic, complemented
12#493×D43C211yesmaximal, characteristic, complemented
13#492×D43C211yesmaximal, characteristic, complemented
14#487×D43C211yesmaximal, characteristic, complemented
15#486×D43C211yesmaximal, characteristic, complemented
16#463×D43C214yesmaximal, complemented
17#449×D43C214yesmaximal, complemented
18#431×D43C211yesmaximal, characteristic, complemented
19C43×#3207C211yesmaximal, characteristic, complemented
20C2×#41×D43—21no—
21C2×#41×D43C2212yes—
22C2×SD16×D43C2214yes—
23C2×D8×D43C2214yes—
24#14583450C2211yescharacteristic, complemented
25#14583450C2211yescharacteristic, complemented
26#14583449C2211yescharacteristic, complemented
27#14583449C2211yescharacteristic, complemented
28#14583448—21no—
29#14583448C2212yescomplemented
30#14583447C2211yescharacteristic, complemented
31#14583447C2211yescharacteristic, complemented
32#14583446—21no—
33#14583446—21no—
34#14583446—21no—
35#14583446C2212yescomplemented
36#14583445—21no—
37#14583445C2212yescomplemented
38#14583444—21no—
39#14583444—21no—
40#14583444—21no—
41#14583444C2212yescomplemented
42C4⋊Q8×D43C2211yescharacteristic
43C4⋊Q8×D43C2211yescharacteristic
44#127×D43C2211yescharacteristic
45#127×D43C2211yescharacteristic
46#124×D43—21no—
47#124×D43C2212yes—
48#121×D43—21no—
49#121×D43—21no—
50#121×D43—21no—
51#121×D43C2212yes—
52C4×D4×D43—21no—
53C4×D4×D43—21no—
54C4×D4×D43—21no—
55C4×D4×D43C2212yes—
56C2×C42×D43C2211yescharacteristic
57#14583276C2211yescharacteristic, complemented
58#14583275C2211yescharacteristic, complemented
59#14583275C2211yescharacteristic, complemented
60#14583274C2214yescomplemented
61#14583273C2211yescharacteristic, complemented
62#14583272C2211yescharacteristic, complemented
63#14583271C2211yescharacteristic, complemented
64#14583270C2214yescomplemented
65#14583251C2211yescharacteristic, complemented
66#14583250C2211yescharacteristic, complemented
67#14583249C2211yescharacteristic, complemented
68#14583248C2214yescomplemented
69#14583247C2211yescharacteristic, complemented
70#14583246C2211yescharacteristic, complemented
71#14583245C2211yescharacteristic, complemented
72#14583244C2214yescomplemented
73#14583117C2214yescomplemented
74#14583116C2214yescomplemented
75#14583115C2214yescomplemented
76#14583114C2214yescomplemented
77#14583113C2214yescomplemented
78#14583112C2214yescomplemented
79#14583111C2214yescomplemented
80#14583047C2214yescomplemented
81#14583046C2214yescomplemented
82#14583045C2214yescomplemented
83#14583044C2214yescomplemented
84#14583043C2214yescomplemented
85#14583042C2214yescomplemented
86#14583041C2214yescomplemented
87#14582952C2211yescharacteristic, complemented
88#14582951C2212yescomplemented
89#14582950C2211yescharacteristic, complemented
90#14582950C2211yescharacteristic, complemented
91#14582949C2212yescomplemented
92C4⋊C8×D43C2212yes—
93#103×D43C2214yes—
94#102×D43C2214yes—
95C22⋊C8×D43C2212yes—
96C4×C8×D43C2211yescharacteristic
97C4×C8×D43C2211yescharacteristic
98C43×#532C2211yescharacteristic, complemented
99C43×#532C2211yescharacteristic, complemented
100C43×#493C2211yescharacteristic, complemented
101C43×#492C2211yescharacteristic, complemented
102C43×#487C2211yescharacteristic, complemented
103C43×#486C2211yescharacteristic, complemented
104C43×#463C2214yescomplemented
105C43×#449C2214yescomplemented
106C43×#431C2211yescharacteristic, complemented
107C2×#10621902—21no—
108C2×#10621902C2312yes—
109C2×#10621898—21no—
110C2×#10621898—22no—
111C2×#10621898—22no—
112C2×#10621898C2312yes—
113C2×#10621900—22no—
114C2×#10621900—22no—
115C2×#10621900—21no—
116C2×#10621900C2312yes—
117#41×D43—48no—
118#41×D43—48no—
119C2×Q8×D43—21no—
120C2×Q8×D43C2312yes—
121C2×D4×D43—22no—
122C2×D4×D43—22no—
123C2×D4×D43—21no—
124C2×D4×D43—21no—
125C2×D4×D43—21no—
126C2×D4×D43—21no—
127C2×D4×D43C2312yes—
128C2×D4×D43C2312yes—
129C22×C4×D43—22no—
130C22×C4×D43—22no—
131C22×C4×D43D411yescharacteristic
132C22×C4×D43D411yescharacteristic
133C22×C4×D43C2311yescharacteristic
134C2×#10621873C2314yes—
135C2×#10621883C2314yes—
136C2×#10621884C2314yes—
137SD16×D43—48no—
138C2×D344C2314yes—
139C2×#10621882C2314yes—
140C2×#10621882C2314yes—
141D8×D43—48no—
142C2×C8×D43C2312yes—
143C2×C8×D43C2312yes—
144#13063325C2311yescharacteristic
145#13063325C2311yescharacteristic
146#13063324—21no—
147#13063324—21no—
148#13063324—21no—
149#13063324C2312yes—
150#13063323—21no—
151#13063323C2312yes—
152#13063322C2311yescharacteristic
153#13063322C2311yescharacteristic
154#13063321—21no—
155#13063321—21no—
156#13063321—21no—
157#13063321—21no—
158#13063321C2312yes—
159#13063321C2312yes—
160#13063314—21no—
161#13063314C2312yes—
162#13063313—21no—
163#13063313C2312yes—
164#13063312—21no—
165#13063312C2312yes—
166#13063311—22no—
167#13063311—22no—
168#13063311—22no—
169#13063311—22no—
170#13063300—21no—
171#13063300—21no—
172#13063300—21no—
173#13063300C2312yes—
174#13063299—21no—
175#13063299—21no—
176#13063299—21no—
177#13063299C2312yes—
178#13063298—22no—
179#13063298—22no—
180#13063298—22no—
181#13063298—22no—
182#13063297—22no—
183#13063297—22no—
184#13063297—22no—
185#13063297—22no—
186#13063296—21no—
187#13063296—21no—
188#13063296—21no—
189#13063296C2312yes—
190C4×D172—21no—
191C4×D172—21no—
192C4×D172—21no—
193C4×D172C2312yes—
194D4×Dic43—21no—
195D4×Dic43—21no—
196D4×Dic43—21no—
197D4×Dic43C2312yes—
198#13063287—21no—
199#13063287—21no—
200#13063287—21no—
201#13063287C2312yes—
202C4×C22⋊D43—22no—
203C4×C22⋊D43—22no—
204C4×C22⋊D43—22no—
205C4×C22⋊D43—22no—
206(C22⋊D43)⋊C4—22no—
207(C22⋊D43)⋊C4—22no—
208(C22⋊D43)⋊C4—22no—
209(C22⋊D43)⋊C4—22no—
210C4⋊C4×D43—21no—
211C4⋊C4×D43—21no—
212C4⋊C4×D43—21no—
213C4⋊C4×D43C2312yes—
214C22⋊C4×D43—22no—
215C22⋊C4×D43—22no—
216C22⋊C4×D43—22no—
217C22⋊C4×D43—22no—
218C2×C4×Dic43D411yescharacteristic
219C2×C4×Dic43D411yescharacteristic
220C2×C4×Dic43C2311yescharacteristic
221C42×D43D411yescharacteristic
222C42×D43D411yescharacteristic
223C42×D43D411yescharacteristic
224C42×D43D411yescharacteristic
225C42×D43C2311yescharacteristic
226C42×D43C2311yescharacteristic
227C42×D43C2311yescharacteristic
228C42×D43C2311yescharacteristic
229C4⋊(C43⋊C8)C2312yes—
230Dic43⋊C8C2312yes—
231Dic43⋊C8C2312yes—
232#13063250C2314yes—
233#13063249C2314yes—
234#13063248C2314yes—
235#13063247C2314yes—
236#13063246C2314yes—
237#13063245C2314yes—
238C22⋊(C43⋊C8)C2312yes—
239(C2×D43)⋊C8C2312yes—
240(C2×D43)⋊C8C2312yes—
241C4×C43⋊C8C2311yescharacteristic
242C4×C43⋊C8C2311yescharacteristic
243C8×Dic43C2312yes—
244C8×Dic43C2312yes—
245C2×#41×C43—21no—
246C2×#41×C43C2312yes—
247C2×SD16×C43C2314yes—
248C2×D8×C43C2314yes—
249C4⋊Q8×C43C2311yescharacteristic
250C4⋊Q8×C43C2311yescharacteristic
251#127×C43C2311yescharacteristic
252#127×C43C2311yescharacteristic
253#124×C43—21no—
254#124×C43C2312yes—
255#121×C43—21no—
256#121×C43—21no—
257#121×C43—21no—
258#121×C43C2312yes—
259C4×D4×C43—21no—
260C4×D4×C43—21no—
261C4×D4×C43—21no—
262C4×D4×C43C2312yes—
263C2×C42×C43C2311yescharacteristic
264C4⋊C8×C43C2312yes—
265#103×C43C2314yes—
266#102×C43C2314yes—
267C22⋊C8×C43C2312yes—
268C4×C8×C43C2311yescharacteristic
269C4×C8×C43C2311yescharacteristic
270C23×D43—22no—
271C23×D43—22no—
272C23×D43C2×D411yescharacteristic
273#41×C43—44no—
274#41×C43—44no—
275C2×Q8×C43—21no—
276C2×Q8×C43C2412yes—
277C2×D4×C43—21no—
278C2×D4×C43—21no—
279C2×D4×C43—21no—
280C2×D4×C43—21no—
281C2×D4×C43—22no—
282C2×D4×C43—22no—
283C2×D4×C43C2412yes—
284C2×D4×C43C2412yes—
285C22×C4×C43—22no—
286C22×C4×C43—22no—
287C22×C4×C43C2×D411yescharacteristic
288C22×C4×C43C2×D411yescharacteristic
289C22×C4×C43C2411yescharacteristic
290C2×C22⋊D43—22no—
291C2×C22⋊D43—22no—
292C2×C22⋊D43—22no—
293C2×C22⋊D43—22no—
294C2×C22⋊D43—22no—
295C2×C22⋊D43—22no—
296C2×C22⋊D43—22no—
297C2×C22⋊D43—22no—
298C2×C22⋊D43—22no—
299C2×C22⋊D43—22no—
300C22×Dic43—22no—
301C22×Dic43—22no—
302C22×Dic43C2×D411yescharacteristic
303C22×Dic43C2×D411yescharacteristic
304C22×Dic43C2×D411yescharacteristic
305#10621902—44no—
306#10621902—44no—
307Q8×D43—28no—
308Q8×D43—44no—
309#10621900—44no—
310#10621900—44no—
311#10621900—48no—
312#10621900—48no—
313D4×D43—28no—
314D4×D43—28no—
315D4×D43—48no—
316D4×D43—48no—
317D4×D43—44no—
318D4×D43—44no—
319D4×D43—44no—
320D4×D43—44no—
321#10621898—44no—
322#10621898—48no—
323#10621898—48no—
324#10621898—44no—
325C2×D172—21no—
326C2×D172—21no—
327C2×D172—21no—
328C2×D172—21no—
329C2×D172—22no—
330C2×D172—22no—
331C2×D172C2412yes—
332C2×D172C2412yes—
333C2×C4×D43—24no—
334C2×C4×D43—24no—
335C2×C4×D43—24no—
336C2×C4×D43—22no—
337C2×C4×D43—22no—
338C2×C4×D43—22no—
339C2×C4×D43—22no—
340C2×C4×D43—22no—
341C2×C4×D43—22no—
342C2×C4×D43—48no—
343C2×C4×D43—48no—
344C2×C4×D43C2×D411yescharacteristic
345C2×C4×D43C2×D411yescharacteristic
346C2×C4×D43C2×D411yescharacteristic
347C2×C4×D43C2×D411yescharacteristic
348C2×C4×D43C2×D411yescharacteristic
349C2×C4×D43C2×D411yescharacteristic
350C2×C4×D43C2×D411yescharacteristic
351C2×C4×D43C2×D411yescharacteristic
352C2×C4×D43C2×D411yescharacteristic
353C2×C4×D43C2×D411yescharacteristic
354C2×C4×D43C2411yescharacteristic
355C2×C4×D43C2411yescharacteristic
356C2×Dic86—21no—
357C2×Dic86—22no—
358C2×Dic86—22no—
359C2×Dic86C2412yes—
360SD16×C43—44no—
361D8×C43—44no—
362C2×C8×C43C2412yes—
363C2×C8×C43C2412yes—
364C4⋊C4×C43—21no—
365C4⋊C4×C43—21no—
366C4⋊C4×C43—21no—
367C4⋊C4×C43C2412yes—
368C22⋊C4×C43—22no—
369C22⋊C4×C43—22no—
370C22⋊C4×C43—22no—
371C22⋊C4×C43—22no—
372C42×C43C2×D411yescharacteristic
373C42×C43C2×D411yescharacteristic
374C42×C43C2411yescharacteristic
375C42×C43C2411yescharacteristic
376C22⋊Dic43—22no—
377C22⋊Dic43—22no—
378C22⋊Dic43—22no—
379C22⋊Dic43—22no—
380#10621884—44no—
381#10621883—44no—
382#10621882—44no—
383#10621882—44no—
384(C2×D43)⋊C4—22no—
385(C2×D43)⋊C4—22no—
386(C2×D43)⋊C4—22no—
387(C2×D43)⋊C4—22no—
388(C2×D43)⋊C4—22no—
389(C2×D43)⋊C4—22no—
390(C2×D43)⋊C4—22no—
391(C2×D43)⋊C4—22no—
392C4⋊Dic43—21no—
393C4⋊Dic43—21no—
394C4⋊Dic43—21no—
395C4⋊Dic43C2412yes—
396Dic43⋊C4—22no—
397Dic43⋊C4—22no—
398Dic43⋊C4—22no—
399Dic43⋊C4—22no—
400C4×Dic43C2×D411yescharacteristic
401C4×Dic43C2×D411yescharacteristic
402C4×Dic43C2×D411yescharacteristic
403C4×Dic43C2×D411yescharacteristic
404C4×Dic43C2×D411yescharacteristic
405C4×Dic43C2×D411yescharacteristic
406C4×Dic43C2×D411yescharacteristic
407C4×Dic43C2×D411yescharacteristic
408C4×Dic43C2×D411yescharacteristic
409C4×Dic43C2×D411yescharacteristic
410C4×Dic43C2411yescharacteristic
411C4×Dic43C2411yescharacteristic
412C2×C43⋊C8C2412yes—
413C2×C43⋊C8C2412yes—
414D344—44no—
415#10621873—44no—
416C8×D43—24no—
417C8×D43—24no—
418C23×C43—22no—
419C23×C43—22no—
420C23×C43C22×D411yescharacteristic
421C22×D43—22no—
422C22×D43—22no—
423C22×D43—22no—
424C22×D43—22no—
425C22×D43—22no—
426C22×D43—44no—
427C22×D43—44no—
428C22×D43—44no—
429C22×D43—44no—
430C22×D43—44no—
431C22×D43—44no—
432C22×D43C22×D411yescharacteristic
433C22×D43C22×D411yescharacteristic
434Q8×C43—24no—
435Q8×C43—42no—
436D4×C43—24no—
437D4×C43—24no—
438D4×C43—44no—
439D4×C43—44no—
440D4×C43—42no—
441D4×C43—42no—
442D4×C43—42no—
443D4×C43—42no—
444C2×C4×C43—22no—
445C2×C4×C43—22no—
446C2×C4×C43—22no—
447C2×C4×C43—22no—
448C2×C4×C43—22no—
449C2×C4×C43—44no—
450C2×C4×C43—44no—
451C2×C4×C43C22×D411yescharacteristic
452C2×C4×C43C22×D411yescharacteristic
453C2×C4×C43C22×D411yescharacteristic
454C2×C4×C43C22×D411yescharacteristic
455C2×C4×C43C22×D411yescharacteristic
456C2×C4×C43C2511yescharacteristic
457C22⋊D43—44no—
458C22⋊D43—44no—
459C22⋊D43—44no—
460C22⋊D43—44no—
461C22⋊D43—44no—
462C22⋊D43—44no—
463C22⋊D43—44no—
464C22⋊D43—44no—
465C22⋊D43—44no—
466C22⋊D43—44no—
467C2×Dic43—22no—
468C2×Dic43—22no—
469C2×Dic43—22no—
470C2×Dic43—22no—
471C2×Dic43—22no—
472C2×Dic43—44no—
473C2×Dic43—44no—
474C2×Dic43C22×D411yescharacteristic
475C2×Dic43C22×D411yescharacteristic
476C2×Dic43C22×D411yescharacteristic
477C2×Dic43C22×D411yescharacteristic
478C2×Dic43C22×D411yescharacteristic
479C2×Dic43C22×D411yescharacteristic
480D172—24no—
481D172—24no—
482D172—44no—
483D172—44no—
484D172—42no—
485D172—42no—
486D172—42no—
487D172—42no—
488C4×D43—22no—
489C4×D43—22no—
490C4×D43—22no—
491C4×D43—22no—
492C4×D43—22no—
493C4×D43—22no—
494C4×D43—22no—
495C4×D43—22no—
496C4×D43—22no—
497C4×D43—44no—
498C4×D43—44no—
499C4×D43—44no—
500C4×D43—44no—
501C4×D43—44no—
502C4×D43—44no—
503C4×D43#13514yes—
504C4×D43AGL(1,ℤ/8)14yes—
505C4×D43H(5,𝔽2)14yes—
506Dic86—24no—
507Dic86—42no—
508Dic86—44no—
509Dic86—44no—
510C8×C43—22no—
511C8×C43—22no—
512C43⋊C8—22no—
513C43⋊C8—22no—
514C2×#3207—431nomaximal, Sylow
515C22×C43—21no—
516C22×C43—21no—
517C22×C43—21no—
518C22×C43—42no—
519C22×C43—42no—
520C22×C43—42no—
521C22×C43—42no—
522C22×C43—42no—
523C22×C43—42no—
524C22×C43C23×D411yescharacteristic
525C2×D43—21no—
526C2×D43—21no—
527C2×D43—21no—
528C2×D43—44no—
529C2×D43—42no—
530C2×D43—42no—
531C2×D43—42no—
532C2×D43—42no—
533C2×D43—42no—
534C2×D43—42no—
535C2×D43—88no—
536C2×D43—88no—
537C2×D43#53512yes—
538C2×D43C2×#13512yes—
539C2×D43C2×AGL(1,ℤ/8)12yes—
540C4×C43—21no—
541C4×C43—21no—
542C4×C43—21no—
543C4×C43—42no—
544C4×C43—42no—
545C4×C43C2×#13512yes—
546C4×C43C2×AGL(1,ℤ/8)12yes—
547C4×C43C2×H(5,𝔽2)12yes—
548Dic43—21no—
549Dic43—21no—
550Dic43—21no—
551Dic43—42no—
552Dic43—42no—
553Dic43#53512yes—
554Dic43C2×#13512yes—
555Dic43C2×AGL(1,ℤ/8)12yes—
556C2×#532—431no—
557C2×#532—431no—
558#3207—431no—
559#3207—431no—
560#3207—431no—
561#3207—431no—
562#3207—434no—
563#3207—434no—
564#3207—431no—
565#3207—431no—
566#3207—431no—
567#3207D4311yescharacteristic, direct product factor
568C2×#493—431no—
569C2×#492—431no—
570C2×#487—431no—
571C2×#486—431no—
572C2×#463—434no—
573C2×#449—434no—
574C2×#431—431no—
575C2×C43—41no—
576C2×C43—82no—
577C2×C43—82no—
578C2×C43C2×#53511yescharacteristic
579C2×C43C22×#13511yescharacteristic
580C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
581D43—41no—
582D43—82no—
583D43—82no—
584D43#320714yesdirect product factor
585C22×#41—432no—
586C22×#41—861no—
587C22×SD16—434no—
588C22×D8—434no—
589#532—431no—
590#532—431no—
591#532—432no—
592#532—432no—
593#532—432no—
594#532—431no—
595#532—431no—
596#532—432no—
597#532—431no—
598#532—431no—
599#532—861no—
600#532—861no—
601#532—861no—
602#532—861no—
603#532—861no—
604#532—861no—
605#532—861no—
606#532—861no—
607#532C2×D4311yescharacteristic, complemented
608#532C2×D4311yescharacteristic, complemented
609C2×C4⋊Q8—431no—
610C2×C4⋊Q8—431no—
611C2×#127—431no—
612C2×#127—431no—
613C2×#124—432no—
614C2×#124—861no—
615C2×#121—432no—
616C2×#121—861no—
617C2×#121—861no—
618C2×#121—861no—
619C2×C4×D4—432no—
620C2×C4×D4—861no—
621C2×C4×D4—861no—
622C2×C4×D4—861no—
623C22×C42—431no—
624#493—434no—
625#493—431no—
626#493—431no—
627#493—431no—
628#493C2×D4311yescharacteristic, complemented
629#492—434no—
630#492—431no—
631#492—431no—
632#492—431no—
633#492C2×D4311yescharacteristic, complemented
634#487—431no—
635#487—431no—
636#487—434no—
637#487—431no—
638#487C2×D4311yescharacteristic, complemented
639#486—431no—
640#486—431no—
641#486—434no—
642#486—431no—
643#486C2×D4311yescharacteristic, complemented
644#463—434no—
645#463—434no—
646#463—434no—
647#463—434no—
648#463—434no—
649#463—434no—
650#463—434no—
651#463C2×D4314yescomplemented
652#449—434no—
653#449—434no—
654#449—434no—
655#449—434no—
656#449—434no—
657#449—434no—
658#449—434no—
659#449C2×D4314yescomplemented
660#431—431no—
661#431—432no—
662#431—432no—
663#431—431no—
664#431—431no—
665#431C2×D4311yescharacteristic, complemented
666C2×C4⋊C8—432no—
667C2×#103—434no—
668C2×#102—434no—
669C2×C22⋊C8—432no—
670C2×C4×C8—431no—
671C2×C4×C8—431no—
672C43C2×#320711yescharacteristic, complemented, Sylow
673C2×#41—21no—
674C2×#41—432no—
675C2×#41—432no—
676C2×#41—432no—
677C2×#41—862no—
678C2×#41—862no—
679C2×#41—862no—
680C2×#41—861no—
681C2×#41—862no—
682C2×#41—861no—
683C2×#41—861no—
684C2×#41—1728no—
685C2×#41—1728no—
686C2×#41C22×D4312yes—
687C22×Q8—432no—
688C22×Q8—861no—
689C22×D4—432no—
690C22×D4—432no—
691C22×D4—861no—
692C22×D4—861no—
693C22×D4—861no—
694C22×D4—861no—
695C22×D4—862no—
696C22×D4—862no—
697C23×C4—431no—
698C23×C4—431no—
699C23×C4—431no—
700C23×C4—862no—
701C23×C4—862no—
702C2×SD16—434no—
703C2×SD16—434no—
704C2×SD16—434no—
705C2×SD16—1728no—
706C2×SD16C22×D4314yes—
707C2×D8—434no—
708C2×D8—434no—
709C2×D8—434no—
710C2×D8—1728no—
711C2×D8C22×D4314yes—
712C22×C8—432no—
713C22×C8—432no—
714C4⋊Q8—432no—
715C4⋊Q8—432no—
716C4⋊Q8—431no—
717C4⋊Q8—431no—
718C4⋊Q8—861no—
719C4⋊Q8—861no—
720C4⋊Q8—861no—
721C4⋊Q8—861no—
722C4⋊Q8C22×D4311yescharacteristic
723C4⋊Q8C22×D4311yescharacteristic
724#127—432no—
725#127—432no—
726#127—431no—
727#127—431no—
728#127—861no—
729#127—861no—
730#127—861no—
731#127—861no—
732#127C22×D4311yescharacteristic
733#127C22×D4311yescharacteristic
734#124—21no—
735#124—432no—
736#124—432no—
737#124—432no—
738#124—862no—
739#124—862no—
740#124—862no—
741#124—862no—
742#124—861no—
743#124—861no—
744#124—861no—
745#124C22×D4312yes—
746#121—21no—
747#121—21no—
748#121—21no—
749#121—432no—
750#121—432no—
751#121—432no—
752#121—862no—
753#121—862no—
754#121—862no—
755#121—862no—
756#121—861no—
757#121—861no—
758#121—861no—
759#121—862no—
760#121—861no—
761#121—861no—
762#121—861no—
763#121—862no—
764#121—862no—
765#121—862no—
766#121—861no—
767#121—861no—
768#121—861no—
769#121C22×D4312yes—
770C4×D4—21no—
771C4×D4—21no—
772C4×D4—21no—
773C4×D4—432no—
774C4×D4—432no—
775C4×D4—432no—
776C4×D4—862no—
777C4×D4—862no—
778C4×D4—862no—
779C4×D4—862no—
780C4×D4—861no—
781C4×D4—861no—
782C4×D4—861no—
783C4×D4—862no—
784C4×D4—862no—
785C4×D4—862no—
786C4×D4—862no—
787C4×D4—861no—
788C4×D4—861no—
789C4×D4—861no—
790C4×D4—861no—
791C4×D4—861no—
792C4×D4—861no—
793C4×D4C22×D4312yes—
794C2×C4⋊C4—432no—
795C2×C4⋊C4—861no—
796C2×C4⋊C4—861no—
797C2×C4⋊C4—861no—
798C2×C22⋊C4—862no—
799C2×C22⋊C4—862no—
800C2×C22⋊C4—862no—
801C2×C22⋊C4—862no—
802C2×C42—431no—
803C2×C42—431no—
804C2×C42—431no—
805C2×C42—431no—
806C2×C42—431no—
807C2×C42—431no—
808C2×C42—431no—
809C2×C42—431no—
810C2×C42—431no—
811C2×C42—431no—
812C2×C42—431no—
813C2×C42C22×D4311yescharacteristic
814C4⋊C8—432no—
815C4⋊C8—432no—
816C4⋊C8—432no—
817C4⋊C8C22×D4312yes—
818#103—434no—
819#103—434no—
820#103—434no—
821#103C22×D4314yes—
822#102—434no—
823#102—434no—
824#102—434no—
825#102C22×D4314yes—
826C22⋊C8—432no—
827C22⋊C8—432no—
828C22⋊C8—432no—
829C22⋊C8C22×D4312yes—
830C4×C8—432no—
831C4×C8—432no—
832C4×C8—431no—
833C4×C8—431no—
834C4×C8C22×D4311yescharacteristic
835C4×C8C22×D4311yescharacteristic
836C24—431no—
837C24—862no—
838C24—862no—
839#41—44no—
840#41—44no—
841#41—1724no—
842#41—1724no—
843#41—1728no—
844#41—1728no—
845#41—1724no—
846#41—1728no—
847#41—1728no—
848#41—1724no—
849#41—1724no—
850#41—1724no—
851C2×Q8—21no—
852C2×Q8—432no—
853C2×Q8—862no—
854C2×Q8—862no—
855C2×Q8—868no—
856C2×Q8—861no—
857C2×Q8—1724no—
858C2×Q8C23×D4312yes—
859C2×D4—22no—
860C2×D4—22no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—432no—
866C2×D4—432no—
867C2×D4—862no—
868C2×D4—862no—
869C2×D4—868no—
870C2×D4—868no—
871C2×D4—862no—
872C2×D4—862no—
873C2×D4—862no—
874C2×D4—862no—
875C2×D4—862no—
876C2×D4—862no—
877C2×D4—862no—
878C2×D4—862no—
879C2×D4—862no—
880C2×D4—862no—
881C2×D4—861no—
882C2×D4—861no—
883C2×D4—861no—
884C2×D4—861no—
885C2×D4—1724no—
886C2×D4—1724no—
887C2×D4—1724no—
888C2×D4—1724no—
889C2×D4—1728no—
890C2×D4—1728no—
891C2×D4C23×D4312yes—
892C2×D4C23×D4312yes—
893C22×C4—22no—
894C22×C4—22no—
895C22×C4—431no—
896C22×C4—431no—
897C22×C4—431no—
898C22×C4—431no—
899C22×C4—431no—
900C22×C4—431no—
901C22×C4—431no—
902C22×C4—431no—
903C22×C4—431no—
904C22×C4—431no—
905C22×C4—431no—
906C22×C4—431no—
907C22×C4—431no—
908C22×C4—431no—
909C22×C4—431no—
910C22×C4—864no—
911C22×C4—864no—
912C22×C4—864no—
913C22×C4—862no—
914C22×C4—862no—
915C22×C4—862no—
916C22×C4—862no—
917C22×C4—862no—
918C22×C4—862no—
919C22×C4—862no—
920C22×C4—862no—
921C22×C4—1728no—
922C22×C4—1728no—
923C22×C4D4×D4311yescharacteristic
924C22×C4D4×D4311yescharacteristic
925C22×C4C23×D4311yescharacteristic
926SD16—44no—
927SD16—1724no—
928SD16—1724no—
929SD16—1724no—
930D8—44no—
931D8—1724no—
932D8—1724no—
933D8—1724no—
934C2×C8—432no—
935C2×C8—432no—
936C2×C8—864no—
937C2×C8—864no—
938C2×C8C23×D4312yes—
939C2×C8C23×D4312yes—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—432no—
944C4⋊C4—862no—
945C4⋊C4—862no—
946C4⋊C4—862no—
947C4⋊C4—862no—
948C4⋊C4—861no—
949C4⋊C4—861no—
950C4⋊C4—861no—
951C4⋊C4C23×D4312yes—
952C22⋊C4—22no—
953C22⋊C4—22no—
954C22⋊C4—22no—
955C22⋊C4—22no—
956C22⋊C4—862no—
957C22⋊C4—862no—
958C22⋊C4—862no—
959C22⋊C4—862no—
960C22⋊C4—862no—
961C22⋊C4—862no—
962C22⋊C4—862no—
963C22⋊C4—862no—
964C22⋊C4—862no—
965C22⋊C4—862no—
966C22⋊C4—862no—
967C22⋊C4—862no—
968C42—431no—
969C42—431no—
970C42—431no—
971C42—431no—
972C42—431no—
973C42—431no—
974C42—431no—
975C42—431no—
976C42—431no—
977C42—431no—
978C42—431no—
979C42—431no—
980C42D4×D4311yescharacteristic
981C42D4×D4311yescharacteristic
982C42C23×D4311yescharacteristic
983C42C23×D4311yescharacteristic
984C23—22no—
985C23—22no—
986C23—431no—
987C23—431no—
988C23—862no—
989C23—862no—
990C23—862no—
991C23—862no—
992C23—862no—
993C23—1724no—
994C23—1724no—
995C23—1724no—
996C23—1724no—
997C23—1724no—
998C23—1724no—
999C23C2×D4×D4311yescharacteristic
1000Q8—24no—
1001Q8—42no—
1002Q8—864no—
1003Q8—1724no—
1004Q8—1724no—
1005Q8—1722no—
1006D4—24no—
1007D4—24no—
1008D4—44no—
1009D4—44no—
1010D4—42no—
1011D4—42no—
1012D4—42no—
1013D4—42no—
1014D4—864no—
1015D4—864no—
1016D4—1724no—
1017D4—1724no—
1018D4—1724no—
1019D4—1724no—
1020D4—1724no—
1021D4—1724no—
1022D4—1724no—
1023D4—1724no—
1024D4—1724no—
1025D4—1724no—
1026D4—1724no—
1027D4—1724no—
1028D4—1722no—
1029D4—1722no—
1030D4—1722no—
1031D4—1722no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—44no—
1038C2×C4—44no—
1039C2×C4—431no—
1040C2×C4—431no—
1041C2×C4—431no—
1042C2×C4—434no—
1043C2×C4—434no—
1044C2×C4—434no—
1045C2×C4—431no—
1046C2×C4—431no—
1047C2×C4—431no—
1048C2×C4—862no—
1049C2×C4—862no—
1050C2×C4—862no—
1051C2×C4—862no—
1052C2×C4—862no—
1053C2×C4—862no—
1054C2×C4—862no—
1055C2×C4—862no—
1056C2×C4—862no—
1057C2×C4—862no—
1058C2×C4—862no—
1059C2×C4—862no—
1060C2×C4—862no—
1061C2×C4—862no—
1062C2×C4—1724no—
1063C2×C4—1724no—
1064C2×C4—1724no—
1065C2×C4—1724no—
1066C2×C4—1724no—
1067C2×C4—1724no—
1068C2×C4—1724no—
1069C2×C4—1724no—
1070C2×C4C2×D4×D4311yescharacteristic
1071C2×C4C2×D4×D4311yescharacteristic
1072C2×C4C2×D4×D4311yescharacteristic
1073C2×C4C2×D4×D4311yescharacteristic
1074C2×C4C2×D4×D4311yescharacteristic
1075C2×C4C24×D4311yescharacteristic
1076C8—22no—
1077C8—22no—
1078C8—862no—
1079C8—862no—
1080C22—21no—
1081C22—21no—
1082C22—21no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—432no—
1090C22—432no—
1091C22—432no—
1092C22—861no—
1093C22—861no—
1094C22—861no—
1095C22—3448no—
1096C22—3448no—
1097C22—1724no—
1098C22—1722no—
1099C22—1722no—
1100C22—1722no—
1101C22—1722no—
1102C22—1722no—
1103C22—1722no—
1104C22C22×D4×D4311yescharacteristic
1105C4—21no—
1106C4—21no—
1107C4—21no—
1108C4—42no—
1109C4—42no—
1110C4—432no—
1111C4—432no—
1112C4—432no—
1113C4—861no—
1114C4—861no—
1115C4—861no—
1116C4—1722no—
1117C4—1722no—
1118C4#135×D4312yes—
1119C4AGL(1,ℤ/8)×D4312yes—
1120C4H(5,𝔽2)×D4312yes—
1121C2—41no—
1122C2—82no—
1123C2—82no—
1124C2—434no—
1125C2—3442no—
1126C2—3442no—
1127C2—1721no—
1128C2#535×D4311yescharacteristic
1129C2C2×#135×D4311yescharacteristic
1130C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3207C2
socleC22×C43C23×D4
hypercenter#3207D43
hypocenterC43C2×#3207
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3207

Complements

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

NH ≅ G/Ntype
1. #532×D43C2semidirect
2. #532×D43C2semidirect
3. #19145531C2semidirect
4. #19145530C2semidirect
5. #19145529C2semidirect
6. #19145528C2semidirect
7. #19145527C2semidirect
8. #19145526C2semidirect
9. #19145525C2semidirect
10. #19145524C2semidirect
11. #19145523C2semidirect
12. #493×D43C2semidirect
13. #492×D43C2semidirect
14. #487×D43C2semidirect
15. #486×D43C2semidirect
16. #463×D43C2semidirect
17. #449×D43C2semidirect
18. #431×D43C2semidirect
19. C43×#3207C2semidirect
24. #14583450C22semidirect
25. #14583450C22semidirect
26. #14583449C22semidirect
27. #14583449C22semidirect
29. #14583448C22semidirect
30. #14583447C22semidirect
31. #14583447C22semidirect
35. #14583446C22semidirect
37. #14583445C22semidirect
41. #14583444C22semidirect
57. #14583276C22semidirect
58. #14583275C22semidirect
59. #14583275C22semidirect
60. #14583274C22semidirect
61. #14583273C22semidirect
62. #14583272C22semidirect
63. #14583271C22semidirect
64. #14583270C22semidirect
65. #14583251C22semidirect
66. #14583250C22semidirect
67. #14583249C22semidirect
68. #14583248C22semidirect
69. #14583247C22semidirect
70. #14583246C22semidirect
71. #14583245C22semidirect
72. #14583244C22semidirect
73. #14583117C22semidirect
74. #14583116C22semidirect
75. #14583115C22semidirect
76. #14583114C22semidirect
77. #14583113C22semidirect
78. #14583112C22semidirect
79. #14583111C22semidirect
80. #14583047C22semidirect
81. #14583046C22semidirect
82. #14583045C22semidirect
83. #14583044C22semidirect
84. #14583043C22semidirect
85. #14583042C22semidirect
86. #14583041C22semidirect
87. #14582952C22semidirect
88. #14582951C22semidirect
89. #14582950C22semidirect
90. #14582950C22semidirect
91. #14582949C22semidirect
98. C43×#532C22semidirect
99. C43×#532C22semidirect
100. C43×#493C22semidirect
101. C43×#492C22semidirect
102. C43×#487C22semidirect
103. C43×#486C22semidirect
104. C43×#463C22semidirect
105. C43×#449C22semidirect
106. C43×#431C22semidirect
567. #3207D43direct (N × H)
584. D43#3207direct (N × H)
607. #532C2×D43semidirect
608. #532C2×D43semidirect
628. #493C2×D43semidirect
633. #492C2×D43semidirect
638. #487C2×D43semidirect
643. #486C2×D43semidirect
651. #463C2×D43semidirect
659. #449C2×D43semidirect
665. #431C2×D43semidirect
672. C43C2×#3207semidirect

Maximal subgroups

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

subgroupindex
#532×D432
#191455312
#191455302
#191455292
#191455282
#191455272
#191455262
#191455252
#191455242
#191455232
#493×D432
#492×D432
#487×D432
#486×D432
#463×D432
#449×D432
#431×D432
C43×#32072
C2×#320743