Finite Group Databasebeta

← D43×#3182 #25966533

Subgroups — D43×#3182 #25966533

Order 11008.

2234 conjugacy classes of subgroups.

The subgroup lattice has 1064 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#19145316C211yesmaximal, characteristic, complemented
4#19145315C211yesmaximal, characteristic, complemented
5#19145314C211yesmaximal, characteristic, complemented
6#19145313C211yesmaximal, characteristic, complemented
7#19145312C211yesmaximal, characteristic, complemented
8#19145311C211yesmaximal, characteristic, complemented
9#19145310C214yesmaximal, complemented
10#19145309C211yesmaximal, characteristic, complemented
11#19145308C214yesmaximal, complemented
12#500×D43C211yesmaximal, characteristic, complemented
13#492×D43C211yesmaximal, characteristic, complemented
14#487×D43C211yesmaximal, characteristic, complemented
15#486×D43C211yesmaximal, characteristic, complemented
16#468×D43C214yesmaximal, complemented
17#440×D43C214yesmaximal, complemented
18C4×M16×D43C211yesmaximal, characteristic, complemented
19C43×#3182C211yesmaximal, characteristic, complemented
20C2×#41×D43—21no—
21C2×SD16×D43C2214yes—
22C2×M16×D43C2212yes—
23#14583456C2211yescharacteristic, complemented
24#14583455—21no—
25#14583454C2211yescharacteristic, complemented
26#14583454C2211yescharacteristic, complemented
27#14583453—21no—
28#14583453C2212yescomplemented
29#14583452—21no—
30#14583451—21no—
31#14583451C2212yescomplemented
32#14583450C2211yescharacteristic
33#14583449C2211yescharacteristic
34#14583448—21no—
35#14583447C2211yescharacteristic
36#14583446—21no—
37#14583446C2212yes—
38#14583445—21no—
39#14583444—21no—
40#14583444C2212yes—
41C4⋊Q8×D43C2211yescharacteristic
42C4⋊Q8×D43C2211yescharacteristic
43C4⋊Q8×D43C2211yescharacteristic
44#127×D43C2211yescharacteristic
45#125×D43—21no—
46#124×D43—21no—
47C22⋊Q8×D43—21no—
48C22⋊Q8×D43C2212yes—
49#121×D43—21no—
50#121×D43C2212yes—
51C4×Q8×D43—21no—
52C4×Q8×D43C2212yes—
53C4×D4×D43—21no—
54C4×D4×D43C2212yes—
55#117×D43—21no—
56C2×C42×D43C2211yescharacteristic
57#14583304C2211yescharacteristic, complemented
58#14583303C2214yescomplemented
59#14583302C2211yescharacteristic, complemented
60#14583302C2211yescharacteristic, complemented
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#14583148C2214yescomplemented
74#14583147C2214yescomplemented
75#14583146C2214yescomplemented
76#14583145C2214yescomplemented
77#14583144C2214yescomplemented
78#14583143C2214yescomplemented
79#14583142C2214yescomplemented
80#14583002C2214yescomplemented
81#14583001C2214yescomplemented
82#14583000C2214yescomplemented
83#14582999C2214yescomplemented
84#14582998C2214yescomplemented
85#14582997C2214yescomplemented
86#14582996C2214yescomplemented
87#107×D43C2214yes—
88#103×D43C2214yes—
89#102×D43C2214yes—
90C4×#10621877C2211yescharacteristic, complemented
91#14582851C2212yescomplemented
92M16×Dic43C2212yescomplemented
93C4×#10621872C2211yescharacteristic, complemented
94C4×#10621872C2211yescharacteristic, complemented
95#97×D43C2212yes—
96C4×C8×D43C2211yescharacteristic
97C4×C8×D43C2211yescharacteristic
98C43×#533C2211yescharacteristic, complemented
99C43×#532C2211yescharacteristic
100C43×#500C2211yescharacteristic, complemented
101C43×#492C2211yescharacteristic, complemented
102C43×#487C2211yescharacteristic, complemented
103C43×#486C2211yescharacteristic, complemented
104C43×#468C2214yescomplemented
105C43×#440C2214yescomplemented
106C4×M16×C43C2211yescharacteristic, 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×D43C2312yes—
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×#10621873C2314yes—
125C2×#10621883C2314yes—
126C2×#10621884C2314yes—
127SD16×D43—216no—
128C2×#10621877C2312yes—
129C2×#10621872C2312yes—
130C2×#10621872C2312yes—
131M16×D43—28no—
132C2×C8×D43C2312yes—
133C2×C8×D43C2312yes—
134#13063325C2311yescharacteristic
135#13063325C2311yescharacteristic
136#13063325C2311yescharacteristic
137#13063324—21no—
138#13063324—21no—
139#13063324—21no—
140#13063324—21no—
141#13063324C2312yes—
142#13063324C2312yes—
143#13063323—21no—
144#13063323—21no—
145#13063323C2312yes—
146#13063322C2311yescharacteristic
147#13063321—21no—
148#13063321—21no—
149#13063321C2312yes—
150#13063317—21no—
151#13063316—21no—
152#13063316—21no—
153#13063315—22no—
154#13063315—22no—
155#13063314—21no—
156#13063313—21no—
157#13063312—21no—
158#13063311—22no—
159#13063311—22no—
160#13063305—21no—
161#13063305C2312yes—
162#13063304—21no—
163#13063304C2312yes—
164#13063303—22no—
165#13063303—22no—
166#13063302—22no—
167#13063302—22no—
168#13063301—21no—
169#13063301C2312yes—
170#13063300—21no—
171#13063300C2312yes—
172#13063299—21no—
173#13063299C2312yes—
174#13063298—22no—
175#13063298—22no—
176#13063297—22no—
177#13063297—22no—
178#13063296—21no—
179#13063296C2312yes—
180Q8×Dic43—21no—
181Q8×Dic43C2312yes—
182C4×Dic86—21no—
183C4×Dic86—22no—
184C4×Dic86—22no—
185C4×Dic86C2312yes—
186#13063290—21no—
187#13063290—22no—
188#13063290—22no—
189#13063290C2312yes—
190C4×D172—21no—
191C4×D172C2312yes—
192D4×Dic43—21no—
193D4×Dic43C2312yes—
194#13063287—21no—
195#13063287C2312yes—
196C4×C22⋊D43—22no—
197C4×C22⋊D43—22no—
198(C22⋊D43)⋊C4—22no—
199(C22⋊D43)⋊C4—22no—
200#13063284—21no—
201#13063283—21no—
202#13063283—21no—
203#13063282—22no—
204#13063281—22no—
205C4⋊C4×D43—21no—
206C4⋊C4×D43—21no—
207C4⋊C4×D43—21no—
208C4⋊C4×D43—21no—
209C4⋊C4×D43—22no—
210C4⋊C4×D43—22no—
211C4⋊C4×D43C2312yes—
212C4⋊C4×D43C2312yes—
213C22⋊C4×D43—22no—
214C22⋊C4×D43—22no—
215C22⋊C4×D43—22no—
216C2×C4×Dic43D411yescharacteristic
217C2×C4×Dic43D411yescharacteristic
218C2×C4×Dic43C2311yescharacteristic
219C42×D43—22no—
220C42×D43D411yescharacteristic
221C42×D43D411yescharacteristic
222C42×D43D411yescharacteristic
223C42×D43D411yescharacteristic
224C42×D43C2311yescharacteristic
225C42×D43C2311yescharacteristic
226C42×D43C2311yescharacteristic
227C42×D43C2311yescharacteristic
228#13063259C2314yes—
229#13063258C2314yes—
230#13063258C2314yes—
231#13063250C2314yes—
232#13063249C2314yes—
233#13063248C2314yes—
234#13063247C2314yes—
235#13063246C2314yes—
236#13063245C2314yes—
237#13063236C2312yes—
238#13063235C2312yes—
239#13063235C2312yes—
240C4×C43⋊C8C2311yescharacteristic
241C4×C43⋊C8C2311yescharacteristic
242C8×Dic43C2312yes—
243C8×Dic43C2312yes—
244C2×#41×C43—21no—
245C2×SD16×C43C2314yes—
246C2×M16×C43C2312yes—
247C4⋊Q8×C43C2311yescharacteristic
248C4⋊Q8×C43C2311yescharacteristic
249C4⋊Q8×C43C2311yescharacteristic
250#127×C43C2311yescharacteristic
251#125×C43—21no—
252#124×C43—21no—
253C22⋊Q8×C43—21no—
254C22⋊Q8×C43C2312yes—
255#121×C43—21no—
256#121×C43C2312yes—
257C4×Q8×C43—21no—
258C4×Q8×C43C2312yes—
259C4×D4×C43—21no—
260C4×D4×C43C2312yes—
261#117×C43—21no—
262C2×C42×C43C2311yescharacteristic
263#107×C43C2314yes—
264#103×C43C2314yes—
265#102×C43C2314yes—
266#97×C43C2312yes—
267C4×C8×C43C2311yescharacteristic
268C4×C8×C43C2311yescharacteristic
269C23×D43—22no—
270C23×D43C2×D411yescharacteristic
271#41×C43—44no—
272C2×Q8×C43—21no—
273C2×Q8×C43—21no—
274C2×Q8×C43C2412yes—
275C2×D4×C43—21no—
276C2×D4×C43—21no—
277C2×D4×C43—22no—
278C2×D4×C43C2412yes—
279C22×C4×C43—22no—
280C22×C4×C43C2×D411yescharacteristic
281C22×C4×C43C2×D411yescharacteristic
282C22×C4×C43C2411yescharacteristic
283C2×C22⋊D43—22no—
284C2×C22⋊D43—22no—
285C2×C22⋊D43—22no—
286C2×C22⋊D43—22no—
287C2×C22⋊D43—22no—
288C22×Dic43—22no—
289C22×Dic43C2×D411yescharacteristic
290C22×Dic43C2×D411yescharacteristic
291C22×Dic43C2×D411yescharacteristic
292#10621902—44no—
293Q8×D43—28no—
294Q8×D43—44no—
295Q8×D43—44no—
296#10621900—44no—
297#10621900—48no—
298D4×D43—28no—
299D4×D43—48no—
300D4×D43—44no—
301D4×D43—44no—
302#10621898—48no—
303#10621898—44no—
304C2×D172—21no—
305C2×D172—21no—
306C2×D172—22no—
307C2×D172C2412yes—
308C2×C4×D43—24no—
309C2×C4×D43—24no—
310C2×C4×D43—24no—
311C2×C4×D43—22no—
312C2×C4×D43—22no—
313C2×C4×D43—22no—
314C2×C4×D43—22no—
315C2×C4×D43—22no—
316C2×C4×D43—48no—
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×D43C2×D411yescharacteristic
326C2×C4×D43C2×D411yescharacteristic
327C2×C4×D43C2411yescharacteristic
328C2×C4×D43C2411yescharacteristic
329C2×Dic86—21no—
330C2×Dic86—21no—
331C2×Dic86—22no—
332C2×Dic86—22no—
333C2×Dic86—22no—
334C2×Dic86C2412yes—
335SD16×C43—28no—
336M16×C43—24no—
337C2×C8×C43C2412yes—
338C2×C8×C43C2412yes—
339C4⋊C4×C43—21no—
340C4⋊C4×C43—21no—
341C4⋊C4×C43—21no—
342C4⋊C4×C43—21no—
343C4⋊C4×C43—22no—
344C4⋊C4×C43—22no—
345C4⋊C4×C43C2412yes—
346C4⋊C4×C43C2412yes—
347C22⋊C4×C43—22no—
348C22⋊C4×C43—22no—
349C22⋊C4×C43—22no—
350C42×C43—22no—
351C42×C43C2×D411yescharacteristic
352C42×C43C2×D411yescharacteristic
353C42×C43C2411yescharacteristic
354C42×C43C2411yescharacteristic
355C22⋊Dic43—22no—
356C22⋊Dic43—22no—
357C22⋊Dic43—22no—
358#10621884—28no—
359#10621883—28no—
360(C2×D43)⋊C4—22no—
361(C2×D43)⋊C4—22no—
362(C2×D43)⋊C4—22no—
363(C2×D43)⋊C4—22no—
364(C2×D43)⋊C4—22no—
365(C2×D43)⋊C4—22no—
366C4⋊Dic43—21no—
367C4⋊Dic43—21no—
368C4⋊Dic43—21no—
369C4⋊Dic43—21no—
370C4⋊Dic43—22no—
371C4⋊Dic43—22no—
372C4⋊Dic43C2412yes—
373C4⋊Dic43C2412yes—
374Dic43⋊C4—22no—
375Dic43⋊C4—22no—
376Dic43⋊C4—22no—
377Dic43⋊C4—22no—
378Dic43⋊C4—22no—
379Dic43⋊C4—22no—
380Dic43⋊C4—22no—
381Dic43⋊C4—22no—
382Dic43⋊C4—22no—
383Dic43⋊C4—22no—
384C4×Dic43—22no—
385C4×Dic43—22no—
386C4×Dic43—22no—
387C4×Dic43C2×D411yescharacteristic
388C4×Dic43C2×D411yescharacteristic
389C4×Dic43C2×D411yescharacteristic
390C4×Dic43C2×D411yescharacteristic
391C4×Dic43C2×D411yescharacteristic
392C4×Dic43C2×D411yescharacteristic
393C4×Dic43C2×D411yescharacteristic
394C4×Dic43C2×D411yescharacteristic
395C4×Dic43C2×D411yescharacteristic
396C4×Dic43C2×D411yescharacteristic
397C4×Dic43C2411yescharacteristic
398C4×Dic43C2411yescharacteristic
399#10621877—24no—
400C2×C43⋊C8C2412yes—
401C2×C43⋊C8C2412yes—
402#10621873—28no—
403#10621872—24no—
404#10621872—24no—
405C8×D43—24no—
406C8×D43#4118yescomplemented
407C23×C43—22no—
408C23×C43C22×D411yescharacteristic
409C22×D43—22no—
410C22×D43—22no—
411C22×D43—22no—
412C22×D43—22no—
413C22×D43—44no—
414C22×D43—44no—
415C22×D43—44no—
416C22×D43C22×D411yescharacteristic
417C22×D43C22×D411yescharacteristic
418Q8×C43—24no—
419Q8×C43—42no—
420Q8×C43—42no—
421D4×C43—24no—
422D4×C43—44no—
423D4×C43—42no—
424D4×C43—42no—
425C2×C4×C43—22no—
426C2×C4×C43—22no—
427C2×C4×C43—22no—
428C2×C4×C43—22no—
429C2×C4×C43—22no—
430C2×C4×C43—22no—
431C2×C4×C43—44no—
432C2×C4×C43C22×D411yescharacteristic
433C2×C4×C43C22×D411yescharacteristic
434C2×C4×C43C22×D411yescharacteristic
435C2×C4×C43C22×D411yescharacteristic
436C2×C4×C43C22×D411yescharacteristic
437C2×C4×C43C2511yescharacteristic
438C22⋊D43—44no—
439C22⋊D43—44no—
440C22⋊D43—44no—
441C22⋊D43—44no—
442C22⋊D43—44no—
443C2×Dic43—22no—
444C2×Dic43—22no—
445C2×Dic43—22no—
446C2×Dic43—22no—
447C2×Dic43—22no—
448C2×Dic43—22no—
449C2×Dic43—44no—
450C2×Dic43C22×D411yescharacteristic
451C2×Dic43C22×D411yescharacteristic
452C2×Dic43C22×D411yescharacteristic
453C2×Dic43C22×D411yescharacteristic
454C2×Dic43C22×D411yescharacteristic
455C2×Dic43C22×D411yescharacteristic
456D172—24no—
457D172—44no—
458D172—42no—
459D172—42no—
460C4×D43—22no—
461C4×D43—22no—
462C4×D43—22no—
463C4×D43—22no—
464C4×D43—22no—
465C4×D43—22no—
466C4×D43—22no—
467C4×D43—22no—
468C4×D43—22no—
469C4×D43—44no—
470C4×D43—44no—
471C4×D43—44no—
472C4×D43—44no—
473C4×D43—44no—
474C4×D43AGL(1,ℤ/8)14yes—
475C4×D43#13714yes—
476C4×D43C2×#4114yes—
477Dic86—24no—
478Dic86—42no—
479Dic86—42no—
480Dic86—44no—
481Dic86—44no—
482Dic86—44no—
483C8×C43—22no—
484C8×C43C2×#4114yescomplemented
485C43⋊C8—22no—
486C43⋊C8C2×#4114yescomplemented
487C2×#3182—431nomaximal, Sylow
488C22×C43—21no—
489C22×C43—21no—
490C22×C43—21no—
491C22×C43—42no—
492C22×C43—42no—
493C22×C43—42no—
494C22×C43C23×D411yescharacteristic
495C2×D43—21no—
496C2×D43—21no—
497C2×D43—21no—
498C2×D43—44no—
499C2×D43—42no—
500C2×D43—42no—
501C2×D43—42no—
502C2×D43—88no—
503C2×D43#53212yes—
504C2×D43C2×AGL(1,ℤ/8)12yes—
505C2×D43C2×#13712yes—
506C4×C43—21no—
507C4×C43—21no—
508C4×C43—21no—
509C4×C43—42no—
510C4×C43—42no—
511C4×C43—42no—
512C4×C43C2×AGL(1,ℤ/8)12yes—
513C4×C43C2×#13712yes—
514C4×C43C22×#4112yes—
515Dic43—21no—
516Dic43—21no—
517Dic43—21no—
518Dic43—42no—
519Dic43—42no—
520Dic43—42no—
521Dic43#53212yes—
522Dic43C2×AGL(1,ℤ/8)12yes—
523Dic43C2×#13712yes—
524C2×#533—431no—
525C2×#532—431no—
526#3182—431no—
527#3182—431no—
528#3182—431no—
529#3182—431no—
530#3182—434no—
531#3182—434no—
532#3182—431no—
533#3182—431no—
534#3182—431no—
535#3182D4311yescharacteristic, direct product factor
536C2×#500—431no—
537C2×#492—431no—
538C2×#487—431no—
539C2×#486—431no—
540C2×#468—434no—
541C2×#440—434no—
542C2×C4×M16—431no—
543C2×C43—41no—
544C2×C43—82no—
545C2×C43C2×#53211yescharacteristic
546C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
547C2×C43C22×#13711yescharacteristic
548D43—41no—
549D43—82no—
550D43#318214yesdirect product factor
551C22×#41—861no—
552C22×SD16—434no—
553C22×M16—432no—
554#533—431no—
555#533—431no—
556#533—432no—
557#533—432no—
558#533—431no—
559#533—861no—
560#533—861no—
561#533—861no—
562#533—861no—
563#533C2×D4311yescharacteristic, complemented
564#532—431no—
565#532—431no—
566#532—432no—
567#532—432no—
568#532—431no—
569#532—861no—
570#532—861no—
571#532—861no—
572#532—861no—
573#532C2×D4311yescharacteristic
574C2×C4⋊Q8—431no—
575C2×C4⋊Q8—431no—
576C2×C4⋊Q8—431no—
577C2×#127—431no—
578C2×#125—861no—
579C2×#124—861no—
580C2×C22⋊Q8—432no—
581C2×C22⋊Q8—861no—
582C2×#121—432no—
583C2×#121—861no—
584C2×C4×Q8—432no—
585C2×C4×Q8—861no—
586C2×C4×D4—432no—
587C2×C4×D4—861no—
588C2×#117—861no—
589C22×C42—431no—
590#500—431no—
591#500—431no—
592#500—434no—
593#500—431no—
594#500C2×D4311yescharacteristic, complemented
595#492—434no—
596#492—431no—
597#492—431no—
598#492—431no—
599#492C2×D4311yescharacteristic, complemented
600#487—431no—
601#487—431no—
602#487—434no—
603#487—431no—
604#487C2×D4311yescharacteristic, complemented
605#486—431no—
606#486—431no—
607#486—434no—
608#486—431no—
609#486C2×D4311yescharacteristic, complemented
610#468—434no—
611#468—434no—
612#468—434no—
613#468—434no—
614#468—434no—
615#468—434no—
616#468—434no—
617#468C2×D4314yescomplemented
618#440—434no—
619#440—434no—
620#440—434no—
621#440—434no—
622#440—434no—
623#440—434no—
624#440—434no—
625#440C2×D4314yescomplemented
626C2×#107—434no—
627C2×#103—434no—
628C2×#102—434no—
629C4×M16—432no—
630C4×M16—431no—
631C4×M16—432no—
632C4×M16—431no—
633C4×M16—431no—
634C4×M16C2×D4311yescharacteristic, complemented
635C2×#97—432no—
636C2×C4×C8—431no—
637C2×C4×C8—431no—
638C43C2×#318211yescharacteristic, complemented, Sylow
639C2×#41—21no—
640C2×#41—862no—
641C2×#41—862no—
642C2×#41—861no—
643C2×#41—861no—
644C2×#41—861no—
645C2×#41—1728no—
646C22×Q8—432no—
647C22×Q8—861no—
648C22×Q8—861no—
649C22×D4—432no—
650C22×D4—861no—
651C22×D4—861no—
652C22×D4—862no—
653C23×C4—431no—
654C23×C4—431no—
655C23×C4—431no—
656C23×C4—862no—
657C2×SD16—434no—
658C2×SD16—434no—
659C2×SD16—434no—
660C2×SD16—8616no—
661C2×SD16C22×D4314yes—
662C2×M16—432no—
663C2×M16—432no—
664C2×M16—432no—
665C2×M16—868no—
666C2×M16C22×D4312yes—
667C22×C8—432no—
668C22×C8—432no—
669C4⋊Q8—432no—
670C4⋊Q8—432no—
671C4⋊Q8—432no—
672C4⋊Q8—431no—
673C4⋊Q8—431no—
674C4⋊Q8—431no—
675C4⋊Q8—861no—
676C4⋊Q8—861no—
677C4⋊Q8—861no—
678C4⋊Q8—861no—
679C4⋊Q8—861no—
680C4⋊Q8—861no—
681C4⋊Q8C22×D4311yescharacteristic
682C4⋊Q8C22×D4311yescharacteristic
683C4⋊Q8C22×D4311yescharacteristic
684#127—432no—
685#127—431no—
686#127—861no—
687#127—861no—
688#127C22×D4311yescharacteristic
689#125—21no—
690#125—862no—
691#125—862no—
692#125—861no—
693#125—861no—
694#125—861no—
695#124—21no—
696#124—862no—
697#124—862no—
698#124—861no—
699#124—861no—
700#124—861no—
701C22⋊Q8—21no—
702C22⋊Q8—432no—
703C22⋊Q8—432no—
704C22⋊Q8—432no—
705C22⋊Q8—862no—
706C22⋊Q8—862no—
707C22⋊Q8—862no—
708C22⋊Q8—862no—
709C22⋊Q8—861no—
710C22⋊Q8—861no—
711C22⋊Q8—861no—
712C22⋊Q8C22×D4312yes—
713#121—21no—
714#121—432no—
715#121—432no—
716#121—432no—
717#121—862no—
718#121—862no—
719#121—861no—
720#121—862no—
721#121—861no—
722#121—862no—
723#121—861no—
724#121C22×D4312yes—
725C4×Q8—21no—
726C4×Q8—432no—
727C4×Q8—432no—
728C4×Q8—432no—
729C4×Q8—862no—
730C4×Q8—862no—
731C4×Q8—862no—
732C4×Q8—861no—
733C4×Q8—862no—
734C4×Q8—861no—
735C4×Q8—861no—
736C4×Q8C22×D4312yes—
737C4×D4—21no—
738C4×D4—432no—
739C4×D4—432no—
740C4×D4—432no—
741C4×D4—862no—
742C4×D4—862no—
743C4×D4—861no—
744C4×D4—862no—
745C4×D4—862no—
746C4×D4—861no—
747C4×D4—861no—
748C4×D4C22×D4312yes—
749#117—21no—
750#117—862no—
751#117—862no—
752#117—861no—
753#117—861no—
754#117—861no—
755C2×C4⋊C4—432no—
756C2×C4⋊C4—432no—
757C2×C4⋊C4—861no—
758C2×C4⋊C4—861no—
759C2×C4⋊C4—861no—
760C2×C4⋊C4—862no—
761C2×C4⋊C4—862no—
762C2×C4⋊C4—861no—
763C2×C22⋊C4—862no—
764C2×C22⋊C4—862no—
765C2×C22⋊C4—862no—
766C2×C42—431no—
767C2×C42—431no—
768C2×C42—431no—
769C2×C42—431no—
770C2×C42—431no—
771C2×C42—431no—
772C2×C42—431no—
773C2×C42—431no—
774C2×C42—431no—
775C2×C42—431no—
776C2×C42—431no—
777C2×C42—862no—
778C2×C42C22×D4311yescharacteristic
779#107—434no—
780#107—434no—
781#107—434no—
782#107C22×D4314yes—
783#103—434no—
784#103—434no—
785#103—434no—
786#103C22×D4314yes—
787#102—434no—
788#102—434no—
789#102—434no—
790#102C22×D4314yes—
791#97—432no—
792#97—432no—
793#97—432no—
794#97C22×D4312yes—
795C4×C8—432no—
796C4×C8—432no—
797C4×C8—431no—
798C4×C8—431no—
799C4×C8C22×D4311yescharacteristic
800C4×C8C22×D4311yescharacteristic
801C24—431no—
802C24—862no—
803#41—44no—
804#41—1724no—
805#41—1728no—
806#41—1728no—
807#41—1724no—
808#41—1724no—
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—432no—
812C2×Q8—862no—
813C2×Q8—862no—
814C2×Q8—862no—
815C2×Q8—868no—
816C2×Q8—861no—
817C2×Q8—861no—
818C2×Q8—1724no—
819C2×Q8—1724no—
820C2×Q8C23×D4312yes—
821C2×D4—22no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—432no—
825C2×D4—862no—
826C2×D4—868no—
827C2×D4—862no—
828C2×D4—862no—
829C2×D4—862no—
830C2×D4—862no—
831C2×D4—862no—
832C2×D4—861no—
833C2×D4—861no—
834C2×D4—1724no—
835C2×D4—1724no—
836C2×D4—1728no—
837C2×D4C23×D4312yes—
838C22×C4—22no—
839C22×C4—431no—
840C22×C4—431no—
841C22×C4—431no—
842C22×C4—431no—
843C22×C4—431no—
844C22×C4—431no—
845C22×C4—431no—
846C22×C4—431no—
847C22×C4—431no—
848C22×C4—431no—
849C22×C4—431no—
850C22×C4—431no—
851C22×C4—431no—
852C22×C4—431no—
853C22×C4—431no—
854C22×C4—864no—
855C22×C4—864no—
856C22×C4—864no—
857C22×C4—862no—
858C22×C4—862no—
859C22×C4—862no—
860C22×C4—862no—
861C22×C4—862no—
862C22×C4—862no—
863C22×C4—1728no—
864C22×C4D4×D4311yescharacteristic
865C22×C4D4×D4311yescharacteristic
866C22×C4C23×D4311yescharacteristic
867SD16—28no—
868SD16—868no—
869SD16—868no—
870SD16—868no—
871M16—24no—
872M16—864no—
873M16—864no—
874M16—864no—
875C2×C8—432no—
876C2×C8—438no—
877C2×C8—432no—
878C2×C8—864no—
879C2×C8C23×D4312yes—
880C2×C8C23×D4312yes—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—22no—
886C4⋊C4—22no—
887C4⋊C4—432no—
888C4⋊C4—432no—
889C4⋊C4—862no—
890C4⋊C4—862no—
891C4⋊C4—862no—
892C4⋊C4—862no—
893C4⋊C4—862no—
894C4⋊C4—862no—
895C4⋊C4—862no—
896C4⋊C4—862no—
897C4⋊C4—862no—
898C4⋊C4—862no—
899C4⋊C4—861no—
900C4⋊C4—861no—
901C4⋊C4—861no—
902C4⋊C4—862no—
903C4⋊C4—862no—
904C4⋊C4—861no—
905C4⋊C4C23×D4312yes—
906C4⋊C4C23×D4312yes—
907C22⋊C4—22no—
908C22⋊C4—22no—
909C22⋊C4—22no—
910C22⋊C4—862no—
911C22⋊C4—862no—
912C22⋊C4—862no—
913C22⋊C4—862no—
914C22⋊C4—862no—
915C22⋊C4—862no—
916C22⋊C4—862no—
917C22⋊C4—862no—
918C22⋊C4—862no—
919C42—22no—
920C42—431no—
921C42—431no—
922C42—431no—
923C42—431no—
924C42—431no—
925C42—431no—
926C42—431no—
927C42—431no—
928C42—431no—
929C42—431no—
930C42—431no—
931C42—431no—
932C42—862no—
933C42—862no—
934C42—862no—
935C42D4×D4311yescharacteristic
936C42D4×D4311yescharacteristic
937C42C23×D4311yescharacteristic
938C42C23×D4311yescharacteristic
939C23—22no—
940C23—431no—
941C23—431no—
942C23—862no—
943C23—862no—
944C23—862no—
945C23—862no—
946C23—1724no—
947C23—1724no—
948C23—1724no—
949C23C2×D4×D4311yescharacteristic
950Q8—24no—
951Q8—42no—
952Q8—42no—
953Q8—864no—
954Q8—1724no—
955Q8—1724no—
956Q8—1724no—
957Q8—1722no—
958Q8—1722no—
959D4—24no—
960D4—44no—
961D4—42no—
962D4—42no—
963D4—864no—
964D4—1724no—
965D4—1724no—
966D4—1724no—
967D4—1724no—
968D4—1724no—
969D4—1724no—
970D4—1722no—
971D4—1722no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—44no—
979C2×C4—431no—
980C2×C4—431no—
981C2×C4—431no—
982C2×C4—434no—
983C2×C4—434no—
984C2×C4—434no—
985C2×C4—431no—
986C2×C4—431no—
987C2×C4—431no—
988C2×C4—862no—
989C2×C4—862no—
990C2×C4—862no—
991C2×C4—862no—
992C2×C4—862no—
993C2×C4—862no—
994C2×C4—862no—
995C2×C4—862no—
996C2×C4—862no—
997C2×C4—862no—
998C2×C4—862no—
999C2×C4—862no—
1000C2×C4—862no—
1001C2×C4—862no—
1002C2×C4—862no—
1003C2×C4—1724no—
1004C2×C4—1724no—
1005C2×C4—1724no—
1006C2×C4—1724no—
1007C2×C4—1724no—
1008C2×C4—1724no—
1009C2×C4C2×D4×D4311yescharacteristic
1010C2×C4C2×D4×D4311yescharacteristic
1011C2×C4C2×D4×D4311yescharacteristic
1012C2×C4C2×D4×D4311yescharacteristic
1013C2×C4C2×D4×D4311yescharacteristic
1014C2×C4C24×D4311yescharacteristic
1015C8—22no—
1016C8—434no—
1017C8—862no—
1018C8#41×D4314yescomplemented
1019C22—21no—
1020C22—21no—
1021C22—21no—
1022C22—42no—
1023C22—42no—
1024C22—42no—
1025C22—432no—
1026C22—432no—
1027C22—432no—
1028C22—861no—
1029C22—861no—
1030C22—861no—
1031C22—3448no—
1032C22—1724no—
1033C22—1722no—
1034C22—1722no—
1035C22—1722no—
1036C22C22×D4×D4311yescharacteristic
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—42no—
1041C4—42no—
1042C4—42no—
1043C4—432no—
1044C4—432no—
1045C4—432no—
1046C4—861no—
1047C4—861no—
1048C4—861no—
1049C4—1722no—
1050C4—1722no—
1051C4—1722no—
1052C4AGL(1,ℤ/8)×D4312yes—
1053C4#137×D4312yes—
1054C4C2×#41×D4312yes—
1055C2—41no—
1056C2—82no—
1057C2—434no—
1058C2—3442no—
1059C2—1721no—
1060C2#532×D4311yescharacteristic
1061C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
1062C2C2×#137×D4311yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3182C2
socleC22×C43C23×D4
prime radical#532×D43C2
hypercenter#3182D43
hypocenterC43C2×#3182
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3182

Complements

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

NH ≅ G/Ntype
1. #533×D43C2semidirect
3. #19145316C2semidirect
4. #19145315C2semidirect
5. #19145314C2semidirect
6. #19145313C2semidirect
7. #19145312C2semidirect
8. #19145311C2semidirect
9. #19145310C2semidirect
10. #19145309C2semidirect
11. #19145308C2semidirect
12. #500×D43C2semidirect
13. #492×D43C2semidirect
14. #487×D43C2semidirect
15. #486×D43C2semidirect
16. #468×D43C2semidirect
17. #440×D43C2semidirect
18. C4×M16×D43C2semidirect
19. C43×#3182C2semidirect
23. #14583456C22semidirect
25. #14583454C22semidirect
26. #14583454C22semidirect
28. #14583453C22semidirect
31. #14583451C22semidirect
57. #14583304C22semidirect
58. #14583303C22semidirect
59. #14583302C22semidirect
60. #14583302C22semidirect
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. #14583148C22semidirect
74. #14583147C22semidirect
75. #14583146C22semidirect
76. #14583145C22semidirect
77. #14583144C22semidirect
78. #14583143C22semidirect
79. #14583142C22semidirect
80. #14583002C22semidirect
81. #14583001C22semidirect
82. #14583000C22semidirect
83. #14582999C22semidirect
84. #14582998C22semidirect
85. #14582997C22semidirect
86. #14582996C22semidirect
90. C4×#10621877C22semidirect
91. #14582851C22semidirect
92. M16×Dic43C22semidirect
93. C4×#10621872C22semidirect
94. C4×#10621872C22semidirect
98. C43×#533C22semidirect
100. C43×#500C22semidirect
101. C43×#492C22semidirect
102. C43×#487C22semidirect
103. C43×#486C22semidirect
104. C43×#468C22semidirect
105. C43×#440C22semidirect
106. C4×M16×C43C22semidirect
406. C8×D43#41semidirect
484. C8×C43C2×#41semidirect
486. C43⋊C8C2×#41semidirect
535. #3182D43direct (N × H)
550. D43#3182direct (N × H)
563. #533C2×D43semidirect
594. #500C2×D43semidirect
599. #492C2×D43semidirect
604. #487C2×D43semidirect
609. #486C2×D43semidirect
617. #468C2×D43semidirect
625. #440C2×D43semidirect
634. C4×M16C2×D43semidirect
638. C43C2×#3182semidirect
1018. C8#41×D43semidirect

Maximal subgroups

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

subgroupindex
#533×D432
#532×D432
#191453162
#191453152
#191453142
#191453132
#191453122
#191453112
#191453102
#191453092
#191453082
#500×D432
#492×D432
#487×D432
#486×D432
#468×D432
#440×D432
C4×M16×D432
C43×#31822
C2×#318243