Finite Group Databasebeta

← D43×#3216 #25967885

Subgroups — D43×#3216 #25967885

Order 11008.

2166 conjugacy classes of subgroups.

The subgroup lattice has 1032 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#19145608C211yesmaximal, characteristic, complemented
4#19145607C212yesmaximal, complemented
5#19145606C211yesmaximal, characteristic, complemented
6#19145605C212yesmaximal, complemented
7#19145604C212yesmaximal, complemented
8#19145603C214yesmaximal, complemented
9#19145602C211yesmaximal, characteristic, complemented
10#19145601C212yesmaximal, complemented
11#497×D43C212yesmaximal, complemented
12#489×D43C212yesmaximal, complemented
13#462×D43C212yesmaximal, complemented
14#460×D43C212yesmaximal, complemented
15#452×D43C214yesmaximal, complemented
16#432×D43C211yesmaximal, characteristic, complemented
17C43×#3216C211yesmaximal, characteristic, complemented
18C2×#41×D43C2212yes—
19C2×Q16×D43C2214yes—
20C2×SD16×D43C2214yes—
21#14583456C2211yescharacteristic, complemented
22#14583455—21no—
23#14583454C2211yescharacteristic, complemented
24#14583454C2211yescharacteristic, complemented
25#14583453—21no—
26#14583453C2212yescomplemented
27#14583452—21no—
28#14583451—21no—
29#14583451C2212yescomplemented
30#14583450C2211yescharacteristic
31#14583449C2211yescharacteristic
32#14583448C2212yes—
33#14583447C2211yescharacteristic
34#14583446—21no—
35#14583446—21no—
36#14583445C2212yes—
37#14583444—21no—
38#14583444—21no—
39C4⋊Q8×D43C2211yescharacteristic
40C4⋊Q8×D43C2211yescharacteristic
41C4⋊Q8×D43C2211yescharacteristic
42#127×D43C2211yescharacteristic
43#125×D43—21no—
44#124×D43C2212yes—
45C22⋊Q8×D43—21no—
46C22⋊Q8×D43C2212yes—
47#121×D43—21no—
48#121×D43—21no—
49C4×Q8×D43—21no—
50C4×Q8×D43C2212yes—
51C4×D4×D43—21no—
52C4×D4×D43—21no—
53#117×D43—21no—
54C2×C42×D43C2211yescharacteristic
55#14583294C2212yescomplemented
56#14583293C2212yescomplemented
57#14583292C2214yescomplemented
58#14583291C2212yescomplemented
59#14583290C2214yescomplemented
60#14583261C2212yescomplemented
61#14583260C2214yescomplemented
62#14583259C2212yescomplemented
63#14583258C2212yescomplemented
64#14583257C2214yescomplemented
65#14583110C2212yescomplemented
66#14583109C2212yescomplemented
67#14583108C2214yescomplemented
68#14583107C2214yescomplemented
69#14583106C2212yescomplemented
70#14583100C2212yescomplemented
71#14583099C2212yescomplemented
72#14583098C2214yescomplemented
73#14583097C2214yescomplemented
74#14583096C2212yescomplemented
75#14583064C2214yescomplemented
76#14583063C2214yescomplemented
77#14583062C2214yescomplemented
78#14583061C2214yescomplemented
79#14583060C2214yescomplemented
80#14583059C2214yescomplemented
81#14583058C2214yescomplemented
82#14582956C2211yescharacteristic, complemented
83#14582955C2212yescomplemented
84#14582954C2212yescomplemented
85#14582953C2212yescomplemented
86C4⋊C8×D43C2212yes—
87#103×D43C2214yes—
88#102×D43C2214yes—
89C22⋊C8×D43C2212yes—
90#97×D43C2212yes—
91C43×#533C2211yescharacteristic, complemented
92C43×#532C2211yescharacteristic
93C43×#497C2212yescomplemented
94C43×#489C2212yescomplemented
95C43×#462C2212yescomplemented
96C43×#460C2212yescomplemented
97C43×#452C2214yescomplemented
98C43×#432C2211yescharacteristic, complemented
99C2×#10621902C2312yes—
100C2×#10621898—22no—
101C2×#10621898C2312yes—
102C2×#10621900—22no—
103C2×#10621900C2312yes—
104#41×D43—48no—
105C2×Q8×D43—21no—
106C2×Q8×D43C2312yes—
107C2×Q8×D43C2312yes—
108C2×D4×D43—22no—
109C2×D4×D43—21no—
110C2×D4×D43—21no—
111C2×D4×D43C2312yes—
112C22×C4×D43—22no—
113C22×C4×D43D411yescharacteristic
114C22×C4×D43D411yescharacteristic
115C22×C4×D43C2311yescharacteristic
116C2×Dic172C2314yes—
117C2×#10621885C2314yes—
118C2×#10621885C2314yes—
119Q16×D43—48no—
120C2×#10621873C2314yes—
121C2×#10621883C2314yes—
122C2×#10621884C2314yes—
123SD16×D43—48no—
124C2×C8×D43C2314yes—
125#13063325C2311yescharacteristic
126#13063325C2311yescharacteristic
127#13063325C2311yescharacteristic
128#13063324—21no—
129#13063324—21no—
130#13063324—21no—
131#13063324—21no—
132#13063324—21no—
133#13063324C2312yes—
134#13063323—21no—
135#13063323C2312yes—
136#13063323C2312yes—
137#13063322C2311yescharacteristic
138#13063321—21no—
139#13063321—21no—
140#13063321C2312yes—
141#13063317—21no—
142#13063316—21no—
143#13063316—21no—
144#13063315—22no—
145#13063315—22no—
146#13063314C2312yes—
147#13063313C2312yes—
148#13063312C2312yes—
149#13063311—22no—
150#13063311—22no—
151#13063305—21no—
152#13063305C2312yes—
153#13063304—21no—
154#13063304C2312yes—
155#13063303—22no—
156#13063303—22no—
157#13063302—22no—
158#13063302—22no—
159#13063301—21no—
160#13063301C2312yes—
161#13063300—21no—
162#13063300—21no—
163#13063299—21no—
164#13063299—21no—
165#13063298—22no—
166#13063298—22no—
167#13063297—22no—
168#13063297—22no—
169#13063296—21no—
170#13063296—21no—
171Q8×Dic43—21no—
172Q8×Dic43C2312yes—
173C4×Dic86—21no—
174C4×Dic86—22no—
175C4×Dic86—22no—
176C4×Dic86C2312yes—
177#13063290—21no—
178#13063290—22no—
179#13063290—22no—
180#13063290C2312yes—
181C4×D172—21no—
182C4×D172—21no—
183D4×Dic43—21no—
184D4×Dic43—21no—
185#13063287—21no—
186#13063287—21no—
187C4×C22⋊D43—22no—
188C4×C22⋊D43—22no—
189(C22⋊D43)⋊C4—22no—
190(C22⋊D43)⋊C4—22no—
191#13063284—21no—
192#13063283—21no—
193#13063283—21no—
194#13063282—22no—
195#13063281—22no—
196C4⋊C4×D43—21no—
197C4⋊C4×D43—21no—
198C4⋊C4×D43—21no—
199C4⋊C4×D43—21no—
200C4⋊C4×D43—21no—
201C4⋊C4×D43—22no—
202C4⋊C4×D43—22no—
203C4⋊C4×D43C2312yes—
204C22⋊C4×D43—22no—
205C22⋊C4×D43—22no—
206C22⋊C4×D43—22no—
207C2×C4×Dic43D411yescharacteristic
208C2×C4×Dic43D411yescharacteristic
209C2×C4×Dic43C2311yescharacteristic
210C42×D43—22no—
211C42×D43D411yescharacteristic
212C42×D43D411yescharacteristic
213C42×D43D411yescharacteristic
214C42×D43D411yescharacteristic
215C42×D43C2311yescharacteristic
216C42×D43C2311yescharacteristic
217C42×D43C2311yescharacteristic
218C42×D43C2311yescharacteristic
219C4⋊(C43⋊C8)C2312yes—
220Dic43⋊C8C2314yes—
221#13063250C2314yes—
222#13063249C2314yes—
223#13063248C2314yes—
224#13063247C2314yes—
225#13063246C2314yes—
226#13063245C2314yes—
227C22⋊(C43⋊C8)C2312yes—
228(C2×D43)⋊C8C2314yes—
229#13063236C2312yes—
230#13063235C2314yes—
231C2×#41×C43C2312yes—
232C2×Q16×C43C2314yes—
233C2×SD16×C43C2314yes—
234C4⋊Q8×C43C2311yescharacteristic
235C4⋊Q8×C43C2311yescharacteristic
236C4⋊Q8×C43C2311yescharacteristic
237#127×C43C2311yescharacteristic
238#125×C43—21no—
239#124×C43C2312yes—
240C22⋊Q8×C43—21no—
241C22⋊Q8×C43C2312yes—
242#121×C43—21no—
243#121×C43—21no—
244C4×Q8×C43—21no—
245C4×Q8×C43C2312yes—
246C4×D4×C43—21no—
247C4×D4×C43—21no—
248#117×C43—21no—
249C2×C42×C43C2311yescharacteristic
250C4⋊C8×C43C2312yes—
251#103×C43C2314yes—
252#102×C43C2314yes—
253C22⋊C8×C43C2312yes—
254#97×C43C2312yes—
255C23×D43—22no—
256C23×D43C2×D411yescharacteristic
257#41×C43—44no—
258C2×Q8×C43—21no—
259C2×Q8×C43C2412yes—
260C2×Q8×C43C2412yes—
261C2×D4×C43—21no—
262C2×D4×C43—21no—
263C2×D4×C43—22no—
264C2×D4×C43C2412yes—
265C22×C4×C43—22no—
266C22×C4×C43C2×D411yescharacteristic
267C22×C4×C43C2×D411yescharacteristic
268C22×C4×C43C2411yescharacteristic
269C2×C22⋊D43—22no—
270C2×C22⋊D43—22no—
271C2×C22⋊D43—22no—
272C2×C22⋊D43—22no—
273C2×C22⋊D43—22no—
274C22×Dic43—22no—
275C22×Dic43C2×D411yescharacteristic
276C22×Dic43C2×D411yescharacteristic
277C22×Dic43C2×D411yescharacteristic
278#10621902—44no—
279Q8×D43—24no—
280Q8×D43—24no—
281Q8×D43—28no—
282Q8×D43—44no—
283#10621900—44no—
284#10621900—48no—
285D4×D43—28no—
286D4×D43—48no—
287D4×D43—44no—
288D4×D43—44no—
289#10621898—44no—
290#10621898—48no—
291C2×D172—21no—
292C2×D172—21no—
293C2×D172—22no—
294C2×D172C2412yes—
295C2×C4×D43—24no—
296C2×C4×D43—24no—
297C2×C4×D43—22no—
298C2×C4×D43—22no—
299C2×C4×D43—22no—
300C2×C4×D43—22no—
301C2×C4×D43—22no—
302C2×C4×D43—42no—
303C2×C4×D43—48no—
304C2×C4×D43C2×D411yescharacteristic
305C2×C4×D43C2×D411yescharacteristic
306C2×C4×D43C2×D411yescharacteristic
307C2×C4×D43C2×D411yescharacteristic
308C2×C4×D43C2×D411yescharacteristic
309C2×C4×D43C2×D411yescharacteristic
310C2×C4×D43C2×D411yescharacteristic
311C2×C4×D43C2×D411yescharacteristic
312C2×C4×D43C2×D411yescharacteristic
313C2×C4×D43C2×D411yescharacteristic
314C2×C4×D43C2411yescharacteristic
315C2×C4×D43C2411yescharacteristic
316C2×Dic86—21no—
317C2×Dic86—22no—
318C2×Dic86—22no—
319C2×Dic86—22no—
320C2×Dic86C2412yes—
321C2×Dic86C2412yes—
322Q16×C43—44no—
323SD16×C43—44no—
324C2×C8×C43C2414yes—
325C4⋊C4×C43—21no—
326C4⋊C4×C43—21no—
327C4⋊C4×C43—21no—
328C4⋊C4×C43—21no—
329C4⋊C4×C43—21no—
330C4⋊C4×C43—22no—
331C4⋊C4×C43—22no—
332C4⋊C4×C43C2412yes—
333C22⋊C4×C43—22no—
334C22⋊C4×C43—22no—
335C22⋊C4×C43—22no—
336C42×C43—22no—
337C42×C43C2×D411yescharacteristic
338C42×C43C2×D411yescharacteristic
339C42×C43C2411yescharacteristic
340C42×C43C2411yescharacteristic
341C22⋊Dic43—22no—
342C22⋊Dic43—22no—
343C22⋊Dic43—22no—
344#10621885—44no—
345#10621885—44no—
346#10621884—44no—
347#10621883—44no—
348(C2×D43)⋊C4—22no—
349(C2×D43)⋊C4—22no—
350(C2×D43)⋊C4—22no—
351(C2×D43)⋊C4—22no—
352(C2×D43)⋊C4—22no—
353(C2×D43)⋊C4—22no—
354C4⋊Dic43—21no—
355C4⋊Dic43—21no—
356C4⋊Dic43—21no—
357C4⋊Dic43—21no—
358C4⋊Dic43—21no—
359C4⋊Dic43—22no—
360C4⋊Dic43—22no—
361C4⋊Dic43C2412yes—
362Dic43⋊C4—22no—
363Dic43⋊C4—22no—
364Dic43⋊C4—22no—
365Dic43⋊C4—22no—
366Dic43⋊C4—22no—
367Dic43⋊C4—22no—
368Dic43⋊C4—22no—
369Dic43⋊C4—22no—
370Dic43⋊C4—22no—
371Dic43⋊C4—22no—
372C4×Dic43—22no—
373C4×Dic43—22no—
374C4×Dic43—22no—
375C4×Dic43C2×D411yescharacteristic
376C4×Dic43C2×D411yescharacteristic
377C4×Dic43C2×D411yescharacteristic
378C4×Dic43C2×D411yescharacteristic
379C4×Dic43C2×D411yescharacteristic
380C4×Dic43C2×D411yescharacteristic
381C4×Dic43C2×D411yescharacteristic
382C4×Dic43C2×D411yescharacteristic
383C4×Dic43C2×D411yescharacteristic
384C4×Dic43C2×D411yescharacteristic
385C4×Dic43C2411yescharacteristic
386C4×Dic43C2411yescharacteristic
387C2×C43⋊C8C2414yes—
388Dic172—44no—
389#10621873—44no—
390C8×D43—28no—
391C23×C43—22no—
392C23×C43C22×D411yescharacteristic
393C22×D43—22no—
394C22×D43—22no—
395C22×D43—22no—
396C22×D43—22no—
397C22×D43—44no—
398C22×D43—44no—
399C22×D43—44no—
400C22×D43C22×D411yescharacteristic
401C22×D43C22×D411yescharacteristic
402Q8×C43—22no—
403Q8×C43—22no—
404Q8×C43—24no—
405Q8×C43—42no—
406D4×C43—24no—
407D4×C43—42no—
408D4×C43—44no—
409D4×C43—42no—
410C2×C4×C43—22no—
411C2×C4×C43—22no—
412C2×C4×C43—22no—
413C2×C4×C43—22no—
414C2×C4×C43—22no—
415C2×C4×C43—41no—
416C2×C4×C43—44no—
417C2×C4×C43C22×D411yescharacteristic
418C2×C4×C43C22×D411yescharacteristic
419C2×C4×C43C22×D411yescharacteristic
420C2×C4×C43C22×D411yescharacteristic
421C2×C4×C43C22×D411yescharacteristic
422C2×C4×C43C2511yescharacteristic
423C22⋊D43—44no—
424C22⋊D43—44no—
425C22⋊D43—44no—
426C22⋊D43—44no—
427C22⋊D43—44no—
428C2×Dic43—22no—
429C2×Dic43—22no—
430C2×Dic43—22no—
431C2×Dic43—22no—
432C2×Dic43—22no—
433C2×Dic43—41no—
434C2×Dic43—44no—
435C2×Dic43C22×D411yescharacteristic
436C2×Dic43C22×D411yescharacteristic
437C2×Dic43C22×D411yescharacteristic
438C2×Dic43C22×D411yescharacteristic
439C2×Dic43C22×D411yescharacteristic
440C2×Dic43C22×D411yescharacteristic
441D172—24no—
442D172—42no—
443D172—44no—
444D172—42no—
445C4×D43—22no—
446C4×D43—22no—
447C4×D43—22no—
448C4×D43—22no—
449C4×D43—22no—
450C4×D43—22no—
451C4×D43—22no—
452C4×D43—22no—
453C4×D43—41no—
454C4×D43—41no—
455C4×D43—44no—
456C4×D43—44no—
457C4×D43—44no—
458C4×D43—44no—
459C4×D43—44no—
460C4×D43#13714yes—
461C4×D43H(5,𝔽2)14yes—
462Dic86—22no—
463Dic86—22no—
464Dic86—24no—
465Dic86—44no—
466Dic86—42no—
467Dic86—44no—
468Dic86—44no—
469C8×C43—24no—
470C43⋊C8—24no—
471C2×#3216—431nomaximal, Sylow
472C22×C43—21no—
473C22×C43—21no—
474C22×C43—21no—
475C22×C43—42no—
476C22×C43—42no—
477C22×C43—42no—
478C22×C43C23×D411yescharacteristic
479C2×D43—21no—
480C2×D43—21no—
481C2×D43—21no—
482C2×D43—44no—
483C2×D43—42no—
484C2×D43—42no—
485C2×D43—42no—
486C2×D43—88no—
487C2×D43#53512yes—
488C2×D43C2×#13712yes—
489C2×D43#57512yes—
490C4×C43—21no—
491C4×C43—21no—
492C4×C43—21no—
493C4×C43—21no—
494C4×C43—42no—
495C4×C43—42no—
496C4×C43—42no—
497C4×C43C2×#13712yes—
498C4×C43C2×H(5,𝔽2)12yes—
499Dic43—21no—
500Dic43—21no—
501Dic43—21no—
502Dic43—21no—
503Dic43—42no—
504Dic43—42no—
505Dic43—42no—
506Dic43#53512yes—
507Dic43C2×#13712yes—
508C2×#533—431no—
509C2×#532—431no—
510#3216—432no—
511#3216—432no—
512#3216—432no—
513#3216—432no—
514#3216—434no—
515#3216—431no—
516#3216—431no—
517#3216—431no—
518#3216D4311yescharacteristic, direct product factor
519C2×#497—432no—
520C2×#489—432no—
521C2×#462—432no—
522C2×#460—432no—
523C2×#452—434no—
524C2×#432—431no—
525C2×C43—41no—
526C2×C43—82no—
527C2×C43C2×#53511yescharacteristic
528C2×C43C22×#13711yescharacteristic
529C2×C43C2×#57511yescharacteristic
530D43—41no—
531D43—82no—
532D43#321614yesdirect product factor
533C22×#41—432no—
534C22×Q16—434no—
535C22×SD16—434no—
536#533—431no—
537#533—431no—
538#533—432no—
539#533—432no—
540#533—431no—
541#533—861no—
542#533—861no—
543#533—861no—
544#533—861no—
545#533C2×D4311yescharacteristic, complemented
546#532—432no—
547#532—431no—
548#532—431no—
549#532—432no—
550#532—431no—
551#532—861no—
552#532—861no—
553#532—861no—
554#532—861no—
555#532C2×D4311yescharacteristic
556C2×C4⋊Q8—431no—
557C2×C4⋊Q8—431no—
558C2×C4⋊Q8—431no—
559C2×#127—431no—
560C2×#125—861no—
561C2×#124—432no—
562C2×C22⋊Q8—432no—
563C2×C22⋊Q8—861no—
564C2×#121—861no—
565C2×#121—861no—
566C2×C4×Q8—432no—
567C2×C4×Q8—861no—
568C2×C4×D4—861no—
569C2×C4×D4—861no—
570C2×#117—861no—
571C22×C42—431no—
572#497—434no—
573#497—434no—
574#497—432no—
575#497—432no—
576#497—432no—
577#497C2×D4312yescomplemented
578#489—432no—
579#489—432no—
580#489—434no—
581#489—434no—
582#489—432no—
583#489C2×D4312yescomplemented
584#462—434no—
585#462—432no—
586#462—432no—
587#462—432no—
588#462—434no—
589#462C2×D4312yescomplemented
590#460—434no—
591#460—432no—
592#460—432no—
593#460—432no—
594#460—434no—
595#460C2×D4312yescomplemented
596#452—434no—
597#452—434no—
598#452—434no—
599#452—434no—
600#452—434no—
601#452—434no—
602#452—434no—
603#452C2×D4314yescomplemented
604#432—431no—
605#432—432no—
606#432—432no—
607#432—432no—
608#432C2×D4311yescharacteristic, complemented
609C2×C4⋊C8—432no—
610C2×#103—434no—
611C2×#102—434no—
612C2×C22⋊C8—432no—
613C2×#97—432no—
614C43C2×#321611yescharacteristic, complemented, Sylow
615C2×#41—432no—
616C2×#41—432no—
617C2×#41—432no—
618C2×#41—862no—
619C2×#41—862no—
620C2×#41—1728no—
621C2×#41C22×D4312yes—
622C22×Q8—432no—
623C22×Q8—432no—
624C22×Q8—861no—
625C22×D4—432no—
626C22×D4—861no—
627C22×D4—861no—
628C22×D4—862no—
629C23×C4—431no—
630C23×C4—431no—
631C23×C4—431no—
632C23×C4—862no—
633C2×Q16—434no—
634C2×Q16—434no—
635C2×Q16—434no—
636C2×Q16—1728no—
637C2×Q16C22×D4314yes—
638C2×SD16—434no—
639C2×SD16—434no—
640C2×SD16—434no—
641C2×SD16—1728no—
642C2×SD16C22×D4314yes—
643C22×C8—434no—
644C4⋊Q8—432no—
645C4⋊Q8—432no—
646C4⋊Q8—432no—
647C4⋊Q8—431no—
648C4⋊Q8—431no—
649C4⋊Q8—431no—
650C4⋊Q8—861no—
651C4⋊Q8—861no—
652C4⋊Q8—861no—
653C4⋊Q8—861no—
654C4⋊Q8—861no—
655C4⋊Q8—861no—
656C4⋊Q8C22×D4311yescharacteristic
657C4⋊Q8C22×D4311yescharacteristic
658C4⋊Q8C22×D4311yescharacteristic
659#127—432no—
660#127—431no—
661#127—861no—
662#127—861no—
663#127C22×D4311yescharacteristic
664#125—21no—
665#125—862no—
666#125—862no—
667#125—861no—
668#125—861no—
669#125—861no—
670#124—432no—
671#124—432no—
672#124—432no—
673#124—862no—
674#124—862no—
675#124C22×D4312yes—
676C22⋊Q8—21no—
677C22⋊Q8—432no—
678C22⋊Q8—432no—
679C22⋊Q8—432no—
680C22⋊Q8—862no—
681C22⋊Q8—862no—
682C22⋊Q8—862no—
683C22⋊Q8—862no—
684C22⋊Q8—861no—
685C22⋊Q8—861no—
686C22⋊Q8—861no—
687C22⋊Q8C22×D4312yes—
688#121—21no—
689#121—21no—
690#121—862no—
691#121—862no—
692#121—861no—
693#121—861no—
694#121—861no—
695#121—861no—
696#121—862no—
697#121—862no—
698#121—861no—
699#121—861no—
700C4×Q8—21no—
701C4×Q8—432no—
702C4×Q8—432no—
703C4×Q8—432no—
704C4×Q8—862no—
705C4×Q8—862no—
706C4×Q8—862no—
707C4×Q8—861no—
708C4×Q8—862no—
709C4×Q8—861no—
710C4×Q8—861no—
711C4×Q8C22×D4312yes—
712C4×D4—21no—
713C4×D4—21no—
714C4×D4—862no—
715C4×D4—862no—
716C4×D4—861no—
717C4×D4—861no—
718C4×D4—862no—
719C4×D4—862no—
720C4×D4—861no—
721C4×D4—861no—
722C4×D4—861no—
723C4×D4—861no—
724#117—21no—
725#117—862no—
726#117—862no—
727#117—861no—
728#117—861no—
729#117—861no—
730C2×C4⋊C4—432no—
731C2×C4⋊C4—861no—
732C2×C4⋊C4—861no—
733C2×C4⋊C4—861no—
734C2×C4⋊C4—861no—
735C2×C4⋊C4—862no—
736C2×C4⋊C4—862no—
737C2×C4⋊C4—861no—
738C2×C22⋊C4—862no—
739C2×C22⋊C4—862no—
740C2×C22⋊C4—862no—
741C2×C42—431no—
742C2×C42—431no—
743C2×C42—431no—
744C2×C42—431no—
745C2×C42—431no—
746C2×C42—431no—
747C2×C42—431no—
748C2×C42—431no—
749C2×C42—431no—
750C2×C42—431no—
751C2×C42—431no—
752C2×C42—862no—
753C2×C42C22×D4311yescharacteristic
754C4⋊C8—434no—
755C4⋊C8—432no—
756C4⋊C8C22×D4312yes—
757#103—434no—
758#103—434no—
759#103—434no—
760#103C22×D4314yes—
761#102—434no—
762#102—434no—
763#102—434no—
764#102C22×D4314yes—
765C22⋊C8—432no—
766C22⋊C8—434no—
767C22⋊C8C22×D4312yes—
768#97—434no—
769#97—432no—
770#97C22×D4312yes—
771C24—431no—
772C24—862no—
773#41—44no—
774#41—1724no—
775#41—1728no—
776#41—1724no—
777#41—1728no—
778#41—1724no—
779C2×Q8—21no—
780C2×Q8—432no—
781C2×Q8—432no—
782C2×Q8—862no—
783C2×Q8—862no—
784C2×Q8—862no—
785C2×Q8—864no—
786C2×Q8—864no—
787C2×Q8—868no—
788C2×Q8—861no—
789C2×Q8—1724no—
790C2×Q8C23×D4312yes—
791C2×Q8C23×D4312yes—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—432no—
796C2×D4—862no—
797C2×D4—868no—
798C2×D4—862no—
799C2×D4—862no—
800C2×D4—862no—
801C2×D4—862no—
802C2×D4—862no—
803C2×D4—861no—
804C2×D4—861no—
805C2×D4—1724no—
806C2×D4—1724no—
807C2×D4—1728no—
808C2×D4C23×D4312yes—
809C22×C4—22no—
810C22×C4—431no—
811C22×C4—431no—
812C22×C4—431no—
813C22×C4—431no—
814C22×C4—431no—
815C22×C4—431no—
816C22×C4—431no—
817C22×C4—431no—
818C22×C4—431no—
819C22×C4—431no—
820C22×C4—431no—
821C22×C4—431no—
822C22×C4—431no—
823C22×C4—431no—
824C22×C4—431no—
825C22×C4—864no—
826C22×C4—864no—
827C22×C4—862no—
828C22×C4—862no—
829C22×C4—862no—
830C22×C4—862no—
831C22×C4—862no—
832C22×C4—862no—
833C22×C4—1722no—
834C22×C4—1728no—
835C22×C4D4×D4311yescharacteristic
836C22×C4D4×D4311yescharacteristic
837C22×C4C23×D4311yescharacteristic
838Q16—44no—
839Q16—1724no—
840Q16—1724no—
841Q16—1724no—
842SD16—44no—
843SD16—1724no—
844SD16—1724no—
845SD16—1724no—
846C2×C8—434no—
847C2×C8—868no—
848C2×C8C23×D4314yes—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—22no—
855C4⋊C4—22no—
856C4⋊C4—432no—
857C4⋊C4—862no—
858C4⋊C4—862no—
859C4⋊C4—862no—
860C4⋊C4—862no—
861C4⋊C4—862no—
862C4⋊C4—862no—
863C4⋊C4—862no—
864C4⋊C4—862no—
865C4⋊C4—862no—
866C4⋊C4—862no—
867C4⋊C4—861no—
868C4⋊C4—861no—
869C4⋊C4—861no—
870C4⋊C4—861no—
871C4⋊C4—862no—
872C4⋊C4—862no—
873C4⋊C4—861no—
874C4⋊C4C23×D4312yes—
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—862no—
879C22⋊C4—862no—
880C22⋊C4—862no—
881C22⋊C4—862no—
882C22⋊C4—862no—
883C22⋊C4—862no—
884C22⋊C4—862no—
885C22⋊C4—862no—
886C22⋊C4—862no—
887C42—22no—
888C42—431no—
889C42—431no—
890C42—431no—
891C42—431no—
892C42—431no—
893C42—431no—
894C42—431no—
895C42—431no—
896C42—431no—
897C42—431no—
898C42—431no—
899C42—431no—
900C42—862no—
901C42—862no—
902C42—862no—
903C42D4×D4311yescharacteristic
904C42D4×D4311yescharacteristic
905C42C23×D4311yescharacteristic
906C42C23×D4311yescharacteristic
907C23—22no—
908C23—431no—
909C23—431no—
910C23—862no—
911C23—862no—
912C23—862no—
913C23—862no—
914C23—1724no—
915C23—1724no—
916C23—1724no—
917C23C2×D4×D4311yescharacteristic
918Q8—22no—
919Q8—22no—
920Q8—24no—
921Q8—42no—
922Q8—862no—
923Q8—862no—
924Q8—864no—
925Q8—1722no—
926Q8—1724no—
927Q8—1724no—
928Q8—1724no—
929D4—24no—
930D4—42no—
931D4—44no—
932D4—42no—
933D4—864no—
934D4—1722no—
935D4—1724no—
936D4—1724no—
937D4—1724no—
938D4—1724no—
939D4—1724no—
940D4—1724no—
941D4—1722no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—41no—
948C2×C4—44no—
949C2×C4—431no—
950C2×C4—431no—
951C2×C4—434no—
952C2×C4—434no—
953C2×C4—431no—
954C2×C4—431no—
955C2×C4—431no—
956C2×C4—431no—
957C2×C4—862no—
958C2×C4—862no—
959C2×C4—862no—
960C2×C4—862no—
961C2×C4—862no—
962C2×C4—862no—
963C2×C4—862no—
964C2×C4—862no—
965C2×C4—862no—
966C2×C4—862no—
967C2×C4—862no—
968C2×C4—862no—
969C2×C4—862no—
970C2×C4—1721no—
971C2×C4—1721no—
972C2×C4—1724no—
973C2×C4—1724no—
974C2×C4—1724no—
975C2×C4—1724no—
976C2×C4—1724no—
977C2×C4—1721no—
978C2×C4—1724no—
979C2×C4C2×D4×D4311yescharacteristic
980C2×C4C2×D4×D4311yescharacteristic
981C2×C4C2×D4×D4311yescharacteristic
982C2×C4C2×D4×D4311yescharacteristic
983C2×C4C2×D4×D4311yescharacteristic
984C2×C4C24×D4311yescharacteristic
985C8—24no—
986C8—864no—
987C22—21no—
988C22—21no—
989C22—21no—
990C22—42no—
991C22—42no—
992C22—42no—
993C22—432no—
994C22—432no—
995C22—432no—
996C22—861no—
997C22—861no—
998C22—861no—
999C22—3448no—
1000C22—1724no—
1001C22—1722no—
1002C22—1722no—
1003C22—1722no—
1004C22C22×D4×D4311yescharacteristic
1005C4—21no—
1006C4—21no—
1007C4—21no—
1008C4—21no—
1009C4—42no—
1010C4—42no—
1011C4—42no—
1012C4—432no—
1013C4—432no—
1014C4—861no—
1015C4—861no—
1016C4—861no—
1017C4—861no—
1018C4—1722no—
1019C4—1722no—
1020C4—1722no—
1021C4#137×D4312yes—
1022C4H(5,𝔽2)×D4312yes—
1023C2—41no—
1024C2—82no—
1025C2—434no—
1026C2—3442no—
1027C2—1721no—
1028C2#535×D4311yescharacteristic
1029C2C2×#137×D4311yescharacteristic
1030C2#575×D4311yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3216C2
socleC22×C43C23×D4
prime radical#532×D43C2
hypercenter#3216D43
hypocenterC43C2×#3216
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3216

Complements

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

NH ≅ G/Ntype
1. #533×D43C2semidirect
3. #19145608C2semidirect
4. #19145607C2semidirect
5. #19145606C2semidirect
6. #19145605C2semidirect
7. #19145604C2semidirect
8. #19145603C2semidirect
9. #19145602C2semidirect
10. #19145601C2semidirect
11. #497×D43C2semidirect
12. #489×D43C2semidirect
13. #462×D43C2semidirect
14. #460×D43C2semidirect
15. #452×D43C2semidirect
16. #432×D43C2semidirect
17. C43×#3216C2semidirect
21. #14583456C22semidirect
23. #14583454C22semidirect
24. #14583454C22semidirect
26. #14583453C22semidirect
29. #14583451C22semidirect
55. #14583294C22semidirect
56. #14583293C22semidirect
57. #14583292C22semidirect
58. #14583291C22semidirect
59. #14583290C22semidirect
60. #14583261C22semidirect
61. #14583260C22semidirect
62. #14583259C22semidirect
63. #14583258C22semidirect
64. #14583257C22semidirect
65. #14583110C22semidirect
66. #14583109C22semidirect
67. #14583108C22semidirect
68. #14583107C22semidirect
69. #14583106C22semidirect
70. #14583100C22semidirect
71. #14583099C22semidirect
72. #14583098C22semidirect
73. #14583097C22semidirect
74. #14583096C22semidirect
75. #14583064C22semidirect
76. #14583063C22semidirect
77. #14583062C22semidirect
78. #14583061C22semidirect
79. #14583060C22semidirect
80. #14583059C22semidirect
81. #14583058C22semidirect
82. #14582956C22semidirect
83. #14582955C22semidirect
84. #14582954C22semidirect
85. #14582953C22semidirect
91. C43×#533C22semidirect
93. C43×#497C22semidirect
94. C43×#489C22semidirect
95. C43×#462C22semidirect
96. C43×#460C22semidirect
97. C43×#452C22semidirect
98. C43×#432C22semidirect
518. #3216D43direct (N × H)
532. D43#3216direct (N × H)
545. #533C2×D43semidirect
577. #497C2×D43semidirect
583. #489C2×D43semidirect
589. #462C2×D43semidirect
595. #460C2×D43semidirect
603. #452C2×D43semidirect
608. #432C2×D43semidirect
614. C43C2×#3216semidirect

Maximal subgroups

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

subgroupindex
#533×D432
#532×D432
#191456082
#191456072
#191456062
#191456052
#191456042
#191456032
#191456022
#191456012
#497×D432
#489×D432
#462×D432
#460×D432
#452×D432
#432×D432
C43×#32162
C2×#321643