Finite Group Databasebeta

← D43×#3228 #25968649

Subgroups — D43×#3228 #25968649

Order 11008.

2058 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D43C211yesmaximal, characteristic, complemented
2#532×D43C211yesmaximal, characteristic
3#19145734C211yesmaximal, characteristic, complemented
4#19145733C211yesmaximal, characteristic, complemented
5#19145732C211yesmaximal, characteristic, complemented
6#19145731C211yesmaximal, characteristic, complemented
7#19145730C214yesmaximal, complemented
8#19145729C214yesmaximal, complemented
9#19145728C211yesmaximal, characteristic, complemented
10#19145727C211yesmaximal, characteristic, complemented
11#19145726C211yesmaximal, characteristic, complemented
12#500×D43C211yesmaximal, characteristic, complemented
13#498×D43C211yesmaximal, characteristic, complemented
14#486×D43C211yesmaximal, characteristic, complemented
15#486×D43C211yesmaximal, characteristic, complemented
16#482×D43C214yesmaximal, complemented
17#478×D43C214yesmaximal, complemented
18#431×D43C211yesmaximal, characteristic, complemented
19C43×#3228C211yesmaximal, characteristic, complemented
20C2×#41×D43—21no—
21#14583456C2211yescharacteristic, complemented
22#14583455C2212yescomplemented
23#14583454C2211yescharacteristic, complemented
24#14583454C2211yescharacteristic, complemented
25#14583453—21no—
26#14583453—21no—
27#14583452C2212yescomplemented
28#14583451—21no—
29#14583451—21no—
30#14583450C2211yescharacteristic
31#14583449C2211yescharacteristic
32#14583448—21no—
33#14583447C2211yescharacteristic
34#14583446—21no—
35#14583446C2212yes—
36#14583445—21no—
37#14583444—21no—
38#14583444C2212yes—
39C4⋊Q8×D43C2211yescharacteristic
40C4⋊Q8×D43C2211yescharacteristic
41C4⋊Q8×D43C2211yescharacteristic
42#127×D43C2211yescharacteristic
43#125×D43C2212yes—
44#124×D43—21no—
45C22⋊Q8×D43—21no—
46C22⋊Q8×D43—21no—
47#121×D43—21no—
48#121×D43C2212yes—
49C4×Q8×D43—21no—
50C4×Q8×D43—21no—
51C4×D4×D43—21no—
52C4×D4×D43C2212yes—
53#117×D43C2212yes—
54C2×C42×D43C2211yescharacteristic
55#14583304C2211yescharacteristic, complemented
56#14583303C2214yescomplemented
57#14583302C2211yescharacteristic, complemented
58#14583302C2211yescharacteristic, complemented
59#14583297C2211yescharacteristic, complemented
60#14583296C2214yescomplemented
61#14583295C2211yescharacteristic, complemented
62#14583295C2211yescharacteristic, complemented
63#14583247C2211yescharacteristic, complemented
64#14583247C2211yescharacteristic, complemented
65#14583246C2211yescharacteristic, complemented
66#14583246C2211yescharacteristic, complemented
67#14583245C2211yescharacteristic, complemented
68#14583245C2211yescharacteristic, complemented
69#14583244C2214yescomplemented
70#14583244C2214yescomplemented
71#14583226C2214yescomplemented
72#14583225C2214yescomplemented
73#14583224C2214yescomplemented
74#14583223C2214yescomplemented
75#14583222C2214yescomplemented
76#14583221C2214yescomplemented
77#14583220C2214yescomplemented
78#14583202C2214yescomplemented
79#14583201C2214yescomplemented
80#14583200C2214yescomplemented
81#14583199C2214yescomplemented
82#14583198C2214yescomplemented
83#14583197C2214yescomplemented
84#14583196C2214yescomplemented
85#14582952C2211yescharacteristic, complemented
86#14582951C2212yescomplemented
87#14582950C2211yescharacteristic, complemented
88#14582950C2211yescharacteristic, complemented
89#14582949C2212yescomplemented
90#107×D43C2214yes—
91#106×D43C2214yes—
92C4⋊C8×D43C2212yes—
93#102×D43C2214yes—
94#102×D43C2214yes—
95C22⋊C8×D43C2212yes—
96C4×C8×D43C2211yescharacteristic
97C4×C8×D43C2211yescharacteristic
98C43×#533C2211yescharacteristic, complemented
99C43×#532C2211yescharacteristic
100C43×#500C2211yescharacteristic, complemented
101C43×#498C2211yescharacteristic, complemented
102C43×#486C2211yescharacteristic, complemented
103C43×#486C2211yescharacteristic, complemented
104C43×#482C2214yescomplemented
105C43×#478C2214yescomplemented
106C43×#431C2211yescharacteristic, complemented
107C2×#10621902—21no—
108C2×#10621898—21no—
109C2×#10621898—22no—
110C2×#10621900—22no—
111C2×#10621900—21no—
112#41×D43—48no—
113C2×Q8×D43—21no—
114C2×Q8×D43—21no—
115C2×Q8×D43—21no—
116C2×D4×D43—22no—
117C2×D4×D43—21no—
118C2×D4×D43—21no—
119C2×D4×D43C2312yes—
120C22×C4×D43—22no—
121C22×C4×D43D411yescharacteristic
122C22×C4×D43D411yescharacteristic
123C22×C4×D43C2311yescharacteristic
124C2×C8×D43C2312yes—
125C2×C8×D43C2312yes—
126#13063325C2311yescharacteristic
127#13063325C2311yescharacteristic
128#13063325C2311yescharacteristic
129#13063324—21no—
130#13063324—21no—
131#13063324—21no—
132#13063324C2312yes—
133#13063324C2312yes—
134#13063324C2312yes—
135#13063323—21no—
136#13063323—21no—
137#13063323—21no—
138#13063322C2311yescharacteristic
139#13063321—21no—
140#13063321—21no—
141#13063321C2312yes—
142#13063317C2312yes—
143#13063316C2312yes—
144#13063316C2312yes—
145#13063315—22no—
146#13063315—22no—
147#13063314—21no—
148#13063313—21no—
149#13063312—21no—
150#13063311—22no—
151#13063311—22no—
152#13063305—21no—
153#13063305—21no—
154#13063304—21no—
155#13063304—21no—
156#13063303—22no—
157#13063303—22no—
158#13063302—22no—
159#13063302—22no—
160#13063301—21no—
161#13063301—21no—
162#13063300—21no—
163#13063300C2312yes—
164#13063299—21no—
165#13063299C2312yes—
166#13063298—22no—
167#13063298—22no—
168#13063297—22no—
169#13063297—22no—
170#13063296—21no—
171#13063296C2312yes—
172Q8×Dic43—21no—
173Q8×Dic43—21no—
174C4×Dic86—21no—
175C4×Dic86—21no—
176C4×Dic86—22no—
177C4×Dic86—22no—
178#13063290—21no—
179#13063290—21no—
180#13063290—22no—
181#13063290—22no—
182C4×D172—21no—
183C4×D172C2312yes—
184D4×Dic43—21no—
185D4×Dic43C2312yes—
186#13063287—21no—
187#13063287C2312yes—
188C4×C22⋊D43—22no—
189C4×C22⋊D43—22no—
190(C22⋊D43)⋊C4—22no—
191(C22⋊D43)⋊C4—22no—
192#13063284C2312yes—
193#13063283C2312yes—
194#13063283C2312yes—
195#13063282—22no—
196#13063281—22no—
197C4⋊C4×D43—21no—
198C4⋊C4×D43—22no—
199C4⋊C4×D43—22no—
200C4⋊C4×D43—21no—
201C4⋊C4×D43—21no—
202C4⋊C4×D43C2312yes—
203C4⋊C4×D43C2312yes—
204C4⋊C4×D43C2312yes—
205C22⋊C4×D43—22no—
206C22⋊C4×D43—22no—
207C22⋊C4×D43—22no—
208C2×C4×Dic43D411yescharacteristic
209C2×C4×Dic43D411yescharacteristic
210C2×C4×Dic43C2311yescharacteristic
211C42×D43—22no—
212C42×D43D411yescharacteristic
213C42×D43D411yescharacteristic
214C42×D43D411yescharacteristic
215C42×D43D411yescharacteristic
216C42×D43C2311yescharacteristic
217C42×D43C2311yescharacteristic
218C42×D43C2311yescharacteristic
219C42×D43C2311yescharacteristic
220#13063259C2314yes—
221#13063258C2314yes—
222#13063258C2314yes—
223#13063257C2314yes—
224#13063256C2314yes—
225#13063256C2314yes—
226C4⋊(C43⋊C8)C2312yes—
227Dic43⋊C8C2312yes—
228Dic43⋊C8C2312yes—
229#13063247C2314yes—
230#13063247C2314yes—
231#13063246C2314yes—
232#13063246C2314yes—
233#13063245C2314yes—
234#13063245C2314yes—
235C22⋊(C43⋊C8)C2312yes—
236(C2×D43)⋊C8C2312yes—
237(C2×D43)⋊C8C2312yes—
238C4×C43⋊C8C2311yescharacteristic
239C4×C43⋊C8C2311yescharacteristic
240C8×Dic43C2312yes—
241C8×Dic43C2312yes—
242C2×#41×C43—21no—
243C4⋊Q8×C43C2311yescharacteristic
244C4⋊Q8×C43C2311yescharacteristic
245C4⋊Q8×C43C2311yescharacteristic
246#127×C43C2311yescharacteristic
247#125×C43C2312yes—
248#124×C43—21no—
249C22⋊Q8×C43—21no—
250C22⋊Q8×C43—21no—
251#121×C43—21no—
252#121×C43C2312yes—
253C4×Q8×C43—21no—
254C4×Q8×C43—21no—
255C4×D4×C43—21no—
256C4×D4×C43C2312yes—
257#117×C43C2312yes—
258C2×C42×C43C2311yescharacteristic
259#107×C43C2314yes—
260#106×C43C2314yes—
261C4⋊C8×C43C2312yes—
262#102×C43C2314yes—
263#102×C43C2314yes—
264C22⋊C8×C43C2312yes—
265C4×C8×C43C2311yescharacteristic
266C4×C8×C43C2311yescharacteristic
267C23×D43—22no—
268C23×D43C2×D411yescharacteristic
269#41×C43—44no—
270C2×Q8×C43—21no—
271C2×Q8×C43—21no—
272C2×Q8×C43—21no—
273C2×D4×C43—21no—
274C2×D4×C43—21no—
275C2×D4×C43—22no—
276C2×D4×C43C2412yes—
277C22×C4×C43—22no—
278C22×C4×C43C2×D411yescharacteristic
279C22×C4×C43C2×D411yescharacteristic
280C22×C4×C43C2411yescharacteristic
281C2×C22⋊D43—22no—
282C2×C22⋊D43—22no—
283C2×C22⋊D43—22no—
284C2×C22⋊D43—22no—
285C2×C22⋊D43—22no—
286C22×Dic43—22no—
287C22×Dic43C2×D411yescharacteristic
288C22×Dic43C2×D411yescharacteristic
289C22×Dic43C2×D411yescharacteristic
290#10621902—44no—
291Q8×D43—44no—
292Q8×D43—44no—
293Q8×D43—44no—
294#10621900—44no—
295#10621900—48no—
296D4×D43—28no—
297D4×D43—48no—
298D4×D43—44no—
299D4×D43—44no—
300#10621898—48no—
301#10621898—44no—
302C2×D172—21no—
303C2×D172—21no—
304C2×D172—22no—
305C2×D172C2412yes—
306C2×C4×D43—24no—
307C2×C4×D43—24no—
308C2×C4×D43—24no—
309C2×C4×D43—22no—
310C2×C4×D43—22no—
311C2×C4×D43—22no—
312C2×C4×D43—22no—
313C2×C4×D43—22no—
314C2×C4×D43—48no—
315C2×C4×D43C2×D411yescharacteristic
316C2×C4×D43C2×D411yescharacteristic
317C2×C4×D43C2×D411yescharacteristic
318C2×C4×D43C2×D411yescharacteristic
319C2×C4×D43C2×D411yescharacteristic
320C2×C4×D43C2×D411yescharacteristic
321C2×C4×D43C2×D411yescharacteristic
322C2×C4×D43C2×D411yescharacteristic
323C2×C4×D43C2×D411yescharacteristic
324C2×C4×D43C2×D411yescharacteristic
325C2×C4×D43C2411yescharacteristic
326C2×C4×D43C2411yescharacteristic
327C2×Dic86—21no—
328C2×Dic86—21no—
329C2×Dic86—21no—
330C2×Dic86—22no—
331C2×Dic86—22no—
332C2×Dic86—22no—
333C2×C8×C43C2412yes—
334C2×C8×C43C2412yes—
335C4⋊C4×C43—21no—
336C4⋊C4×C43—22no—
337C4⋊C4×C43—22no—
338C4⋊C4×C43—21no—
339C4⋊C4×C43—21no—
340C4⋊C4×C43C2412yes—
341C4⋊C4×C43C2412yes—
342C4⋊C4×C43C2412yes—
343C22⋊C4×C43—22no—
344C22⋊C4×C43—22no—
345C22⋊C4×C43—22no—
346C42×C43—22no—
347C42×C43C2×D411yescharacteristic
348C42×C43C2×D411yescharacteristic
349C42×C43C2411yescharacteristic
350C42×C43C2411yescharacteristic
351C22⋊Dic43—22no—
352C22⋊Dic43—22no—
353C22⋊Dic43—22no—
354(C2×D43)⋊C4—22no—
355(C2×D43)⋊C4—22no—
356(C2×D43)⋊C4—22no—
357(C2×D43)⋊C4—22no—
358(C2×D43)⋊C4—22no—
359(C2×D43)⋊C4—22no—
360C4⋊Dic43—21no—
361C4⋊Dic43—21no—
362C4⋊Dic43—21no—
363C4⋊Dic43—22no—
364C4⋊Dic43—22no—
365C4⋊Dic43C2412yes—
366C4⋊Dic43C2412yes—
367C4⋊Dic43C2412yes—
368Dic43⋊C4—22no—
369Dic43⋊C4—22no—
370Dic43⋊C4—22no—
371Dic43⋊C4—22no—
372Dic43⋊C4—22no—
373Dic43⋊C4—22no—
374Dic43⋊C4—22no—
375Dic43⋊C4—22no—
376Dic43⋊C4—22no—
377Dic43⋊C4—22no—
378C4×Dic43—22no—
379C4×Dic43—22no—
380C4×Dic43—22no—
381C4×Dic43C2×D411yescharacteristic
382C4×Dic43C2×D411yescharacteristic
383C4×Dic43C2×D411yescharacteristic
384C4×Dic43C2×D411yescharacteristic
385C4×Dic43C2×D411yescharacteristic
386C4×Dic43C2×D411yescharacteristic
387C4×Dic43C2×D411yescharacteristic
388C4×Dic43C2×D411yescharacteristic
389C4×Dic43C2×D411yescharacteristic
390C4×Dic43C2×D411yescharacteristic
391C4×Dic43C2411yescharacteristic
392C4×Dic43C2411yescharacteristic
393C2×C43⋊C8C2412yes—
394C2×C43⋊C8C2412yes—
395C8×D43—24no—
396C8×D43—24no—
397C23×C43—22no—
398C23×C43C22×D411yescharacteristic
399C22×D43—22no—
400C22×D43—22no—
401C22×D43—22no—
402C22×D43—22no—
403C22×D43—44no—
404C22×D43—44no—
405C22×D43—44no—
406C22×D43C22×D411yescharacteristic
407C22×D43C22×D411yescharacteristic
408Q8×C43—42no—
409Q8×C43—42no—
410Q8×C43—42no—
411D4×C43—24no—
412D4×C43—44no—
413D4×C43—42no—
414D4×C43—42no—
415C2×C4×C43—22no—
416C2×C4×C43—22no—
417C2×C4×C43—22no—
418C2×C4×C43—22no—
419C2×C4×C43—22no—
420C2×C4×C43—22no—
421C2×C4×C43—44no—
422C2×C4×C43C22×D411yescharacteristic
423C2×C4×C43C22×D411yescharacteristic
424C2×C4×C43C22×D411yescharacteristic
425C2×C4×C43C22×D411yescharacteristic
426C2×C4×C43C22×D411yescharacteristic
427C2×C4×C43C2511yescharacteristic
428C22⋊D43—44no—
429C22⋊D43—44no—
430C22⋊D43—44no—
431C22⋊D43—44no—
432C22⋊D43—44no—
433C2×Dic43—22no—
434C2×Dic43—22no—
435C2×Dic43—22no—
436C2×Dic43—22no—
437C2×Dic43—22no—
438C2×Dic43—22no—
439C2×Dic43—44no—
440C2×Dic43C22×D411yescharacteristic
441C2×Dic43C22×D411yescharacteristic
442C2×Dic43C22×D411yescharacteristic
443C2×Dic43C22×D411yescharacteristic
444C2×Dic43C22×D411yescharacteristic
445C2×Dic43C22×D411yescharacteristic
446D172—24no—
447D172—44no—
448D172—42no—
449D172—42no—
450C4×D43—22no—
451C4×D43—22no—
452C4×D43—22no—
453C4×D43—22no—
454C4×D43—22no—
455C4×D43—22no—
456C4×D43—22no—
457C4×D43—22no—
458C4×D43—22no—
459C4×D43—44no—
460C4×D43—44no—
461C4×D43—44no—
462C4×D43—44no—
463C4×D43—44no—
464C4×D43#13514yes—
465C4×D43AGL(1,ℤ/8)14yes—
466C4×D432−1+414yes—
467Dic86—42no—
468Dic86—42no—
469Dic86—42no—
470Dic86—44no—
471Dic86—44no—
472Dic86—44no—
473C8×C43—22no—
474C8×C43—22no—
475C43⋊C8—22no—
476C43⋊C8—22no—
477C2×#3228—431nomaximal, Sylow
478C22×C43—21no—
479C22×C43—21no—
480C22×C43—21no—
481C22×C43—42no—
482C22×C43—42no—
483C22×C43—42no—
484C22×C43C23×D411yescharacteristic
485C2×D43—21no—
486C2×D43—21no—
487C2×D43—21no—
488C2×D43—44no—
489C2×D43—42no—
490C2×D43—42no—
491C2×D43—42no—
492C2×D43—88no—
493C2×D43#53612yes—
494C2×D43C2×#13512yes—
495C2×D43C2×AGL(1,ℤ/8)12yes—
496C4×C43—21no—
497C4×C43—21no—
498C4×C43—21no—
499C4×C43—42no—
500C4×C43—42no—
501C4×C43—42no—
502C4×C43C2×#13512yes—
503C4×C43C2×AGL(1,ℤ/8)12yes—
504C4×C43C2×2−1+412yes—
505Dic43—21no—
506Dic43—21no—
507Dic43—21no—
508Dic43—42no—
509Dic43—42no—
510Dic43—42no—
511Dic43#53612yes—
512Dic43C2×#13512yes—
513Dic43C2×AGL(1,ℤ/8)12yes—
514C2×#533—431no—
515C2×#532—431no—
516#3228—431no—
517#3228—431no—
518#3228—431no—
519#3228—431no—
520#3228—434no—
521#3228—434no—
522#3228—431no—
523#3228—431no—
524#3228—431no—
525#3228D4311yescharacteristic, direct product factor
526C2×#500—431no—
527C2×#498—431no—
528C2×#486—431no—
529C2×#486—431no—
530C2×#482—434no—
531C2×#478—434no—
532C2×#431—431no—
533C2×C43—41no—
534C2×C43—82no—
535C2×C43C2×#53611yescharacteristic
536C2×C43C22×#13511yescharacteristic
537C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
538D43—41no—
539D43—82no—
540D43#322814yesdirect product factor
541C22×#41—861no—
542#533—431no—
543#533—431no—
544#533—432no—
545#533—432no—
546#533—431no—
547#533—861no—
548#533—861no—
549#533—861no—
550#533—861no—
551#533C2×D4311yescharacteristic, complemented
552#532—431no—
553#532—431no—
554#532—432no—
555#532—432no—
556#532—431no—
557#532—861no—
558#532—861no—
559#532—861no—
560#532—861no—
561#532C2×D4311yescharacteristic
562C2×C4⋊Q8—431no—
563C2×C4⋊Q8—431no—
564C2×C4⋊Q8—431no—
565C2×#127—431no—
566C2×#125—432no—
567C2×#124—861no—
568C2×C22⋊Q8—861no—
569C2×C22⋊Q8—861no—
570C2×#121—432no—
571C2×#121—861no—
572C2×C4×Q8—861no—
573C2×C4×Q8—861no—
574C2×C4×D4—432no—
575C2×C4×D4—861no—
576C2×#117—432no—
577C22×C42—431no—
578#500—431no—
579#500—431no—
580#500—434no—
581#500—431no—
582#500C2×D4311yescharacteristic, complemented
583#498—431no—
584#498—431no—
585#498—434no—
586#498—431no—
587#498C2×D4311yescharacteristic, complemented
588#486—431no—
589#486—431no—
590#486—431no—
591#486—431no—
592#486—434no—
593#486—434no—
594#486—431no—
595#486—431no—
596#486C2×D4311yescharacteristic, complemented
597#486C2×D4311yescharacteristic, complemented
598#482—434no—
599#482—434no—
600#482—434no—
601#482—434no—
602#482—434no—
603#482—434no—
604#482—434no—
605#482C2×D4314yescomplemented
606#478—434no—
607#478—434no—
608#478—434no—
609#478—434no—
610#478—434no—
611#478—434no—
612#478—434no—
613#478C2×D4314yescomplemented
614#431—431no—
615#431—432no—
616#431—432no—
617#431—431no—
618#431—431no—
619#431C2×D4311yescharacteristic, complemented
620C2×#107—434no—
621C2×#106—434no—
622C2×C4⋊C8—432no—
623C2×#102—434no—
624C2×#102—434no—
625C2×C22⋊C8—432no—
626C2×C4×C8—431no—
627C2×C4×C8—431no—
628C43C2×#322811yescharacteristic, complemented, Sylow
629C2×#41—21no—
630C2×#41—862no—
631C2×#41—862no—
632C2×#41—861no—
633C2×#41—861no—
634C2×#41—861no—
635C2×#41—1728no—
636C22×Q8—861no—
637C22×Q8—861no—
638C22×Q8—861no—
639C22×D4—432no—
640C22×D4—861no—
641C22×D4—861no—
642C22×D4—862no—
643C23×C4—431no—
644C23×C4—431no—
645C23×C4—431no—
646C23×C4—862no—
647C22×C8—432no—
648C22×C8—432no—
649C4⋊Q8—432no—
650C4⋊Q8—432no—
651C4⋊Q8—432no—
652C4⋊Q8—431no—
653C4⋊Q8—431no—
654C4⋊Q8—431no—
655C4⋊Q8—861no—
656C4⋊Q8—861no—
657C4⋊Q8—861no—
658C4⋊Q8—861no—
659C4⋊Q8—861no—
660C4⋊Q8—861no—
661C4⋊Q8C22×D4311yescharacteristic
662C4⋊Q8C22×D4311yescharacteristic
663C4⋊Q8C22×D4311yescharacteristic
664#127—432no—
665#127—431no—
666#127—861no—
667#127—861no—
668#127C22×D4311yescharacteristic
669#125—432no—
670#125—432no—
671#125—432no—
672#125—862no—
673#125—862no—
674#125C22×D4312yes—
675#124—21no—
676#124—862no—
677#124—862no—
678#124—861no—
679#124—861no—
680#124—861no—
681C22⋊Q8—21no—
682C22⋊Q8—21no—
683C22⋊Q8—862no—
684C22⋊Q8—862no—
685C22⋊Q8—862no—
686C22⋊Q8—862no—
687C22⋊Q8—861no—
688C22⋊Q8—861no—
689C22⋊Q8—861no—
690C22⋊Q8—861no—
691C22⋊Q8—861no—
692C22⋊Q8—861no—
693#121—21no—
694#121—432no—
695#121—432no—
696#121—432no—
697#121—862no—
698#121—862no—
699#121—861no—
700#121—862no—
701#121—861no—
702#121—862no—
703#121—861no—
704#121C22×D4312yes—
705C4×Q8—21no—
706C4×Q8—21no—
707C4×Q8—862no—
708C4×Q8—862no—
709C4×Q8—862no—
710C4×Q8—861no—
711C4×Q8—862no—
712C4×Q8—861no—
713C4×Q8—861no—
714C4×Q8—861no—
715C4×Q8—861no—
716C4×Q8—861no—
717C4×D4—21no—
718C4×D4—432no—
719C4×D4—432no—
720C4×D4—432no—
721C4×D4—862no—
722C4×D4—862no—
723C4×D4—861no—
724C4×D4—862no—
725C4×D4—862no—
726C4×D4—861no—
727C4×D4—861no—
728C4×D4C22×D4312yes—
729#117—432no—
730#117—432no—
731#117—432no—
732#117—862no—
733#117—862no—
734#117C22×D4312yes—
735C2×C4⋊C4—432no—
736C2×C4⋊C4—432no—
737C2×C4⋊C4—432no—
738C2×C4⋊C4—861no—
739C2×C4⋊C4—862no—
740C2×C4⋊C4—862no—
741C2×C4⋊C4—861no—
742C2×C4⋊C4—861no—
743C2×C22⋊C4—862no—
744C2×C22⋊C4—862no—
745C2×C22⋊C4—862no—
746C2×C42—431no—
747C2×C42—431no—
748C2×C42—431no—
749C2×C42—431no—
750C2×C42—431no—
751C2×C42—431no—
752C2×C42—431no—
753C2×C42—431no—
754C2×C42—431no—
755C2×C42—431no—
756C2×C42—431no—
757C2×C42—862no—
758C2×C42C22×D4311yescharacteristic
759#107—434no—
760#107—434no—
761#107—434no—
762#107C22×D4314yes—
763#106—434no—
764#106—434no—
765#106—434no—
766#106C22×D4314yes—
767C4⋊C8—432no—
768C4⋊C8—432no—
769C4⋊C8—432no—
770C4⋊C8C22×D4312yes—
771#102—434no—
772#102—434no—
773#102—434no—
774#102—434no—
775#102—434no—
776#102—434no—
777#102C22×D4314yes—
778#102C22×D4314yes—
779C22⋊C8—432no—
780C22⋊C8—432no—
781C22⋊C8—432no—
782C22⋊C8C22×D4312yes—
783C4×C8—432no—
784C4×C8—432no—
785C4×C8—431no—
786C4×C8—431no—
787C4×C8C22×D4311yescharacteristic
788C4×C8C22×D4311yescharacteristic
789C24—431no—
790C24—862no—
791#41—44no—
792#41—1724no—
793#41—1728no—
794#41—1728no—
795#41—1724no—
796#41—1724no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—862no—
801C2×Q8—862no—
802C2×Q8—862no—
803C2×Q8—861no—
804C2×Q8—861no—
805C2×Q8—861no—
806C2×Q8—1724no—
807C2×Q8—1724no—
808C2×Q8—1724no—
809C2×D4—22no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—432no—
813C2×D4—862no—
814C2×D4—868no—
815C2×D4—862no—
816C2×D4—862no—
817C2×D4—862no—
818C2×D4—862no—
819C2×D4—862no—
820C2×D4—861no—
821C2×D4—861no—
822C2×D4—1724no—
823C2×D4—1724no—
824C2×D4—1728no—
825C2×D4C23×D4312yes—
826C22×C4—22no—
827C22×C4—431no—
828C22×C4—431no—
829C22×C4—431no—
830C22×C4—431no—
831C22×C4—431no—
832C22×C4—431no—
833C22×C4—431no—
834C22×C4—431no—
835C22×C4—431no—
836C22×C4—431no—
837C22×C4—431no—
838C22×C4—431no—
839C22×C4—431no—
840C22×C4—431no—
841C22×C4—431no—
842C22×C4—864no—
843C22×C4—864no—
844C22×C4—864no—
845C22×C4—862no—
846C22×C4—862no—
847C22×C4—862no—
848C22×C4—862no—
849C22×C4—862no—
850C22×C4—862no—
851C22×C4—1728no—
852C22×C4D4×D4311yescharacteristic
853C22×C4D4×D4311yescharacteristic
854C22×C4C23×D4311yescharacteristic
855C2×C8—432no—
856C2×C8—432no—
857C2×C8—864no—
858C2×C8—864no—
859C2×C8C23×D4312yes—
860C2×C8C23×D4312yes—
861C4⋊C4—21no—
862C4⋊C4—22no—
863C4⋊C4—22no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—432no—
867C4⋊C4—432no—
868C4⋊C4—432no—
869C4⋊C4—862no—
870C4⋊C4—862no—
871C4⋊C4—862no—
872C4⋊C4—862no—
873C4⋊C4—862no—
874C4⋊C4—862no—
875C4⋊C4—862no—
876C4⋊C4—862no—
877C4⋊C4—862no—
878C4⋊C4—862no—
879C4⋊C4—861no—
880C4⋊C4—862no—
881C4⋊C4—862no—
882C4⋊C4—861no—
883C4⋊C4—861no—
884C4⋊C4C23×D4312yes—
885C4⋊C4C23×D4312yes—
886C4⋊C4C23×D4312yes—
887C22⋊C4—22no—
888C22⋊C4—22no—
889C22⋊C4—22no—
890C22⋊C4—862no—
891C22⋊C4—862no—
892C22⋊C4—862no—
893C22⋊C4—862no—
894C22⋊C4—862no—
895C22⋊C4—862no—
896C22⋊C4—862no—
897C22⋊C4—862no—
898C22⋊C4—862no—
899C42—22no—
900C42—431no—
901C42—431no—
902C42—431no—
903C42—431no—
904C42—431no—
905C42—431no—
906C42—431no—
907C42—431no—
908C42—431no—
909C42—431no—
910C42—431no—
911C42—431no—
912C42—862no—
913C42—862no—
914C42—862no—
915C42D4×D4311yescharacteristic
916C42D4×D4311yescharacteristic
917C42C23×D4311yescharacteristic
918C42C23×D4311yescharacteristic
919C23—22no—
920C23—431no—
921C23—431no—
922C23—862no—
923C23—862no—
924C23—862no—
925C23—862no—
926C23—1724no—
927C23—1724no—
928C23—1724no—
929C23C2×D4×D4311yescharacteristic
930Q8—42no—
931Q8—42no—
932Q8—42no—
933Q8—1724no—
934Q8—1724no—
935Q8—1724no—
936Q8—1722no—
937Q8—1722no—
938Q8—1722no—
939D4—24no—
940D4—44no—
941D4—42no—
942D4—42no—
943D4—864no—
944D4—1724no—
945D4—1724no—
946D4—1724no—
947D4—1724no—
948D4—1724no—
949D4—1724no—
950D4—1722no—
951D4—1722no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—44no—
959C2×C4—431no—
960C2×C4—431no—
961C2×C4—431no—
962C2×C4—434no—
963C2×C4—434no—
964C2×C4—434no—
965C2×C4—431no—
966C2×C4—431no—
967C2×C4—431no—
968C2×C4—862no—
969C2×C4—862no—
970C2×C4—862no—
971C2×C4—862no—
972C2×C4—862no—
973C2×C4—862no—
974C2×C4—862no—
975C2×C4—862no—
976C2×C4—862no—
977C2×C4—862no—
978C2×C4—862no—
979C2×C4—862no—
980C2×C4—862no—
981C2×C4—862no—
982C2×C4—862no—
983C2×C4—1724no—
984C2×C4—1724no—
985C2×C4—1724no—
986C2×C4—1724no—
987C2×C4—1724no—
988C2×C4—1724no—
989C2×C4C2×D4×D4311yescharacteristic
990C2×C4C2×D4×D4311yescharacteristic
991C2×C4C2×D4×D4311yescharacteristic
992C2×C4C2×D4×D4311yescharacteristic
993C2×C4C2×D4×D4311yescharacteristic
994C2×C4C24×D4311yescharacteristic
995C8—22no—
996C8—22no—
997C8—862no—
998C8—862no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—42no—
1003C22—42no—
1004C22—42no—
1005C22—432no—
1006C22—432no—
1007C22—432no—
1008C22—861no—
1009C22—861no—
1010C22—861no—
1011C22—3448no—
1012C22—1724no—
1013C22—1722no—
1014C22—1722no—
1015C22—1722no—
1016C22C22×D4×D4311yescharacteristic
1017C4—21no—
1018C4—21no—
1019C4—21no—
1020C4—42no—
1021C4—42no—
1022C4—42no—
1023C4—432no—
1024C4—432no—
1025C4—432no—
1026C4—861no—
1027C4—861no—
1028C4—861no—
1029C4—1722no—
1030C4—1722no—
1031C4—1722no—
1032C4#135×D4312yes—
1033C4AGL(1,ℤ/8)×D4312yes—
1034C42−1+4×D4312yes—
1035C2—41no—
1036C2—82no—
1037C2—434no—
1038C2—3442no—
1039C2—1721no—
1040C2#536×D4311yescharacteristic
1041C2C2×#135×D4311yescharacteristic
1042C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3228C2
socleC22×C43C23×D4
prime radical#532×D43C2
hypercenter#3228D43
hypocenterC43C2×#3228
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3228

Complements

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

NH ≅ G/Ntype
1. #533×D43C2semidirect
3. #19145734C2semidirect
4. #19145733C2semidirect
5. #19145732C2semidirect
6. #19145731C2semidirect
7. #19145730C2semidirect
8. #19145729C2semidirect
9. #19145728C2semidirect
10. #19145727C2semidirect
11. #19145726C2semidirect
12. #500×D43C2semidirect
13. #498×D43C2semidirect
14. #486×D43C2semidirect
15. #486×D43C2semidirect
16. #482×D43C2semidirect
17. #478×D43C2semidirect
18. #431×D43C2semidirect
19. C43×#3228C2semidirect
21. #14583456C22semidirect
22. #14583455C22semidirect
23. #14583454C22semidirect
24. #14583454C22semidirect
27. #14583452C22semidirect
55. #14583304C22semidirect
56. #14583303C22semidirect
57. #14583302C22semidirect
58. #14583302C22semidirect
59. #14583297C22semidirect
60. #14583296C22semidirect
61. #14583295C22semidirect
62. #14583295C22semidirect
63. #14583247C22semidirect
64. #14583247C22semidirect
65. #14583246C22semidirect
66. #14583246C22semidirect
67. #14583245C22semidirect
68. #14583245C22semidirect
69. #14583244C22semidirect
70. #14583244C22semidirect
71. #14583226C22semidirect
72. #14583225C22semidirect
73. #14583224C22semidirect
74. #14583223C22semidirect
75. #14583222C22semidirect
76. #14583221C22semidirect
77. #14583220C22semidirect
78. #14583202C22semidirect
79. #14583201C22semidirect
80. #14583200C22semidirect
81. #14583199C22semidirect
82. #14583198C22semidirect
83. #14583197C22semidirect
84. #14583196C22semidirect
85. #14582952C22semidirect
86. #14582951C22semidirect
87. #14582950C22semidirect
88. #14582950C22semidirect
89. #14582949C22semidirect
98. C43×#533C22semidirect
100. C43×#500C22semidirect
101. C43×#498C22semidirect
102. C43×#486C22semidirect
103. C43×#486C22semidirect
104. C43×#482C22semidirect
105. C43×#478C22semidirect
106. C43×#431C22semidirect
525. #3228D43direct (N × H)
540. D43#3228direct (N × H)
551. #533C2×D43semidirect
582. #500C2×D43semidirect
587. #498C2×D43semidirect
596. #486C2×D43semidirect
597. #486C2×D43semidirect
605. #482C2×D43semidirect
613. #478C2×D43semidirect
619. #431C2×D43semidirect
628. C43C2×#3228semidirect

Maximal subgroups

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

subgroupindex
#533×D432
#532×D432
#191457342
#191457332
#191457322
#191457312
#191457302
#191457292
#191457282
#191457272
#191457262
#500×D432
#498×D432
#486×D432
#482×D432
#478×D432
#431×D432
C43×#32282
C2×#322843