Finite Group Databasebeta

← #25968290

Subgroups — #25968290

Order 11008.

2138 conjugacy classes of subgroups.

The subgroup lattice has 1074 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148474C211yesmaximal, characteristic, complemented
2#19148371C211yesmaximal, characteristic
3#19145666C214yesmaximal, complemented
4#19145663C214yesmaximal, complemented
5#19145553C211yesmaximal, characteristic, complemented
6#19145552C211yesmaximal, characteristic, complemented
7#19145547C211yesmaximal, characteristic, complemented
8#19145546C211yesmaximal, characteristic, complemented
9#19145537C211yesmaximal, characteristic, complemented
10#19145536C211yesmaximal, characteristic, complemented
11#19145532C211yesmaximal, characteristic, complemented
12#19145049C211yesmaximal, characteristic, complemented
13#492×D43C211yesmaximal, characteristic, complemented
14#19144966C211yesmaximal, characteristic, complemented
15#19144914C211yesmaximal, characteristic, complemented
16#19144111C214yesmaximal, complemented
17#19143867C214yesmaximal, complemented
18#19143234C211yesmaximal, characteristic, complemented
19C43×#3208C211yesmaximal, characteristic, complemented
20C2×#13063370C2212yes—
21C2×#13063354C2214yescomplemented
22C2×SD16×D43C2214yescomplemented
23#14583626—21no—
24#14583625—21no—
25#14583620—21no—
26#14583617—21no—
27#14583590—21no—
28#14583588—21no—
29#14583587—21no—
30#14583583—21no—
31#14583569—21no—
32#14583569—21no—
33#14583534—21no—
34#14583534—21no—
35D4×C22⋊D43—21no—
36D4×C22⋊D43—21no—
37D4×C22⋊D43—21no—
38D4×C22⋊D43—21no—
39#14583509C2212yescomplemented
40#14583507C2212yescomplemented
41#14583472C2212yes—
42#14583466C2212yes—
43#14583462C2212yes—
44#14583462C2212yes—
45#14583456C2211yescharacteristic, complemented
46#14583454C2211yescharacteristic, complemented
47#14583454C2211yescharacteristic, complemented
48#14583454C2211yescharacteristic, complemented
49#14583449C2211yescharacteristic
50#14583447C2211yescharacteristic
51#14583447C2211yescharacteristic
52C4⋊Q8×D43C2211yescharacteristic, complemented
53#127×D43C2211yescharacteristic
54#127×D43C2211yescharacteristic
55#14583375C2212yescomplemented
56C4×#10621898C2211yescharacteristic
57#14583290C2214yescomplemented
58#14583279C2211yescharacteristic, complemented
59#14583278C2211yescharacteristic, complemented
60#14583273C2211yescharacteristic, complemented
61#14583272C2211yescharacteristic, complemented
62#14583271C2211yescharacteristic, complemented
63#14583271C2211yescharacteristic, complemented
64#14583270C2214yescomplemented
65#14583262C2214yescomplemented
66#14583252C2214yescomplemented
67#14583251C2211yescharacteristic, complemented
68#14583250C2211yescharacteristic, complemented
69#14583247C2211yescharacteristic, complemented
70#14583246C2211yescharacteristic, complemented
71#14583245C2211yescharacteristic, complemented
72#14583245C2211yescharacteristic, complemented
73#14583122C2214yescomplemented
74#14583121C2214yescomplemented
75#14583120C2214yescomplemented
76#14583119C2214yescomplemented
77#14583098C2214yescomplemented
78#14583097C2214yescomplemented
79#14583096C2214yescomplemented
80#14583063C2214yescomplemented
81#14583062C2214yescomplemented
82#14583059C2214yescomplemented
83#14583058C2214yescomplemented
84#14583051C2214yescomplemented
85#14583050C2214yescomplemented
86#14583048C2214yescomplemented
87#14582959C2212yescomplemented
88#14582957C2212yescomplemented
89#14582952C2211yescharacteristic, complemented
90#14582950C2211yescharacteristic, complemented
91#14582950C2211yescharacteristic, complemented
92#14582924C2212yescomplemented
93#14582902C2214yescomplemented
94#14582892C2214yescomplemented
95#14582864C2212yes—
96C4×#10621872C2211yescharacteristic, complemented
97C4×C8×D43C2211yescharacteristic, complemented
98C43×#533C2211yescharacteristic, complemented
99C2×#127×C43C2211yescharacteristic
100C43×#492C2211yescharacteristic, complemented
101C43×#492C2211yescharacteristic, complemented
102C43×#486C2211yescharacteristic, complemented
103C43×#486C2211yescharacteristic, complemented
104C43×#460C2214yescomplemented
105C43×#450C2214yescomplemented
106C43×#431C2211yescharacteristic, complemented
107#13063370—48no—
108C2×#10621898C2311yescharacteristic
109C2×#10621898C2312yes—
110C2×#10621900—22no—
111C2×#10621900C2312yes—
112C2×#10621900C2312yes—
113C2×Q8×D43C2312yes—
114C22×C22⋊D43—22no—
115C22×C22⋊D43—22no—
116C2×D4×D43—22no—
117C2×D4×D43—21no—
118C2×D4×D43—21no—
119C2×D4×D43—21no—
120C2×D4×D43—21no—
121C2×D4×D43C2312yes—
122C2×D4×D43C2312yes—
123#13063354—48no—
124C2×Dic172C2314yes—
125C2×#10621885C2314yes—
126C2×#10621873C2314yes—
127C2×#10621883C2314yes—
128C2×#10621883C2314yes—
129C2×#10621884C2314yes—
130SD16×D43—48no—
131C2×#10621872C2312yes—
132C2×C8×D43C2312yes—
133#13063325C2311yescharacteristic
134#13063325C2311yescharacteristic
135#13063325C2311yescharacteristic
136#13063324—22no—
137#13063324—21no—
138#13063324—21no—
139#13063323C2312yes—
140#13063322C2311yescharacteristic
141#13063321—21no—
142#13063321—21no—
143#13063321—21no—
144#13063321—21no—
145#13063321C2312yes—
146#13063321C2312yes—
147#13063320—22no—
148#13063319—22no—
149#13063318—22no—
150#13063318—22no—
151#13063317—21no—
152#13063317—22no—
153#13063316—22no—
154#13063316—21no—
155#13063316—21no—
156#13063316C2312yes—
157#13063315—22no—
158#13063315—22no—
159#13063313C2312yes—
160#13063312C2312yes—
161#13063312C2312yes—
162#13063311—22no—
163#13063310—22no—
164#13063307—22no—
165#13063305—21no—
166#13063305—21no—
167#13063305C2312yes—
168#13063304—21no—
169#13063304C2312yes—
170#13063301—21no—
171#13063301—21no—
172#13063301C2312yes—
173#13063299—21no—
174#13063299—21no—
175#13063297—22no—
176#13063297—22no—
177#13063297—22no—
178#13063297—22no—
179#13063296—21no—
180#13063296—21no—
181#13063296—21no—
182#13063296—21no—
183#13063296—22no—
184#13063296—22no—
185#13063294—22no—
186#13063294—22no—
187#13063293—22no—
188#13063293—22no—
189#13063293—22no—
190#13063293—22no—
191Q8×Dic43—21no—
192Q8×Dic43—21no—
193Q8×Dic43C2312yes—
194C4×Dic86—21no—
195C4×Dic86—22no—
196C4×Dic86D411yescharacteristic
197C4×Dic86D411yescharacteristic
198C4×Dic86C2312yes—
199#13063290—22no—
200#13063290—21no—
201#13063290—21no—
202#13063290C2312yes—
203C4×D172—21no—
204C4×D172—21no—
205C4×D172D411yescharacteristic
206C4×D172D411yescharacteristic
207D4×Dic43—21no—
208D4×Dic43—21no—
209D4×Dic43—21no—
210D4×Dic43—21no—
211C4×C22⋊D43D411yescharacteristic
212C4×C22⋊D43D411yescharacteristic
213C4×C22⋊D43D411yescharacteristic
214C4×C22⋊D43D411yescharacteristic
215#13063284—21no—
216#13063284C2311yescharacteristic
217#13063283—21no—
218#13063283—21no—
219#13063283—22no—
220#13063283C2312yes—
221#13063282—22no—
222#13063282C2311yescharacteristic
223#13063282C2311yescharacteristic
224C4⋊C4×D43—21no—
225C4⋊C4×D43—21no—
226C42×D43C2311yescharacteristic
227C42×D43C2311yescharacteristic
228C4⋊(C43⋊C8)C2312yes—
229Dic43⋊C8C2312yes—
230Dic43⋊C8C2312yes—
231#13063250C2314yes—
232#13063248C2314yes—
233#13063247C2314yes—
234#13063246C2314yes—
235#13063246C2314yes—
236#13063245C2314yes—
237C22⋊(C43⋊C8)C2312yes—
238(C2×D43)⋊C8C2312yes—
239(C2×D43)⋊C8C2312yes—
240#13063235C2312yes—
241C4×C43⋊C8C2311yescharacteristic
242C4×C43⋊C8C2311yescharacteristic
243C8×Dic43C2312yes—
244C22×D4×C43—21no—
245C22×D4×C43—21no—
246C22×D4×C43C2312yes—
247C2×SD16×C43C2314yes—
248C2×SD16×C43C2314yes—
249C4⋊Q8×C43C2311yescharacteristic
250C4⋊Q8×C43C2311yescharacteristic
251#127×C43—21no—
252#127×C43—21no—
253#127×C43C2312yes—
254#127×C43C2311yescharacteristic
255#127×C43C2311yescharacteristic
256#125×C43—21no—
257C22⋊Q8×C43—21no—
258C22⋊Q8×C43C2312yes—
259C4×Q8×C43—21no—
260C4×Q8×C43C2312yes—
261#117×C43—21no—
262C2×C42×C43C2311yescharacteristic
263C4⋊C8×C43C2312yes—
264#102×C43C2314yes—
265#102×C43C2314yes—
266C22⋊C8×C43C2312yes—
267C4×C8×C43C2311yescharacteristic
268C4×C8×C43C2311yescharacteristic
269C24×C43—22no—
270C23×D43—22no—
271C23×D43—22no—
272C2×Q8×C43—21no—
273C2×Q8×C43C2412yes—
274C2×D4×C43—22no—
275C2×D4×C43—21no—
276C2×D4×C43—21no—
277C2×D4×C43—21no—
278C2×D4×C43—21no—
279C2×D4×C43—22no—
280C2×D4×C43—22no—
281C2×D4×C43—44no—
282C2×D4×C43—82no—
283C2×D4×C43—82no—
284C2×D4×C43C2412yes—
285C2×D4×C43C2412yes—
286C22×C4×C43C2×D411yescharacteristic
287C22×C4×C43C2×D411yescharacteristic
288C22×C4×C43C2411yescharacteristic
289C2×C22⋊D43—22no—
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—48no—
299C2×C22⋊D43—48no—
300C2×C22⋊D43C2×D411yescharacteristic
301C2×C22⋊D43C2×D411yescharacteristic
302C22×Dic43—22no—
303C22×Dic43—22no—
304Q8×D43—28no—
305#10621900—28no—
306#10621900—44no—
307#10621900—48no—
308D4×D43—28no—
309D4×D43—44no—
310D4×D43—48no—
311D4×D43—82no—
312D4×D43—82no—
313D4×D43—82no—
314D4×D43—82no—
315#10621898—24no—
316#10621898—44no—
317C2×D172—21no—
318C2×D172—21no—
319C2×D172C2×D411yescharacteristic
320C2×D172C2412yes—
321C2×C4×D43—22no—
322C2×C4×D43—22no—
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—22no—
331C2×Dic86C2×D411yescharacteristic
332C2×Dic86C2412yes—
333C2×Dic86C2412yes—
334SD16×C43—44no—
335SD16×C43—44no—
336C2×C8×C43C2412yes—
337C2×C8×C43C2412yes—
338C4⋊C4×C43—21no—
339C4⋊C4×C43—21no—
340C4⋊C4×C43—21no—
341C4⋊C4×C43—22no—
342C4⋊C4×C43—22no—
343C4⋊C4×C43C2412yes—
344C22⋊C4×C43—22no—
345C42×C43—22no—
346C42×C43C2×D411yescharacteristic
347C42×C43C2×D411yescharacteristic
348C42×C43C2411yescharacteristic
349C42×C43C2411yescharacteristic
350C22⋊Dic43—22no—
351C22⋊Dic43—22no—
352C22⋊Dic43—22no—
353C22⋊Dic43—22no—
354C22⋊Dic43—22no—
355C22⋊Dic43C2×D411yescharacteristic
356C22⋊Dic43C2×D411yescharacteristic
357#10621885—44no—
358#10621884—44no—
359#10621883—44no—
360#10621883—44no—
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—
366(C2×D43)⋊C4C2×D411yescharacteristic
367(C2×D43)⋊C4C2×D411yescharacteristic
368(C2×D43)⋊C4C2×D411yescharacteristic
369(C2×D43)⋊C4C2×D411yescharacteristic
370C4⋊Dic43—21no—
371C4⋊Dic43—21no—
372C4⋊Dic43—21no—
373C4⋊Dic43—21no—
374C4⋊Dic43—21no—
375C4⋊Dic43—22no—
376C4⋊Dic43—22no—
377C4⋊Dic43—22no—
378C4⋊Dic43C2×D411yescharacteristic
379C4⋊Dic43C2×D411yescharacteristic
380C4⋊Dic43C2412yes—
381Dic43⋊C4—22no—
382Dic43⋊C4—22no—
383Dic43⋊C4—22no—
384Dic43⋊C4—22no—
385Dic43⋊C4—22no—
386Dic43⋊C4—22no—
387Dic43⋊C4—22no—
388Dic43⋊C4C2×D411yescharacteristic
389Dic43⋊C4C2×D411yescharacteristic
390Dic43⋊C4C2×D411yescharacteristic
391Dic43⋊C4C2×D411yescharacteristic
392C4×Dic43—22no—
393C4×Dic43—22no—
394C4×Dic43—22no—
395C4×Dic43—22no—
396C4×Dic43C2×D411yescharacteristic
397C4×Dic43C2×D411yescharacteristic
398C4×Dic43C2×D411yescharacteristic
399C4×Dic43C2×D411yescharacteristic
400C4×Dic43C2411yescharacteristic
401C4×Dic43C2411yescharacteristic
402C2×C43⋊C8C2412yes—
403C2×C43⋊C8C2412yes—
404Dic172—44no—
405#10621873—44no—
406#10621872—24no—
407C8×D43—24no—
408C23×C43—22no—
409C23×C43—22no—
410C23×C43—44no—
411C23×C43—82no—
412C23×C43—82no—
413C23×C43C22×D411yescharacteristic
414C22×D43—22no—
415C22×D43—44no—
416C22×D43—44no—
417C22×D43—82no—
418C22×D43—82no—
419C22×D43—82no—
420C22×D43—82no—
421C22×D43C22×D411yescharacteristic
422C22×D43C22×D411yescharacteristic
423Q8×C43—24no—
424Q8×C43—42no—
425D4×C43—24no—
426D4×C43—24no—
427D4×C43—44no—
428D4×C43—42no—
429D4×C43—42no—
430D4×C43—42no—
431D4×C43—42no—
432D4×C43—82no—
433D4×C43—82no—
434C2×C4×C43—22no—
435C2×C4×C43—22no—
436C2×C4×C43—22no—
437C2×C4×C43—22no—
438C2×C4×C43—22no—
439C2×C4×C43C22×D411yescharacteristic
440C2×C4×C43C22×D411yescharacteristic
441C2×C4×C43C22×D411yescharacteristic
442C2×C4×C43C22×D411yescharacteristic
443C2×C4×C43C22×D411yescharacteristic
444C2×C4×C43C2511yescharacteristic
445C22⋊D43—22no—
446C22⋊D43—22no—
447C22⋊D43—44no—
448C22⋊D43—44no—
449C22⋊D43—44no—
450C22⋊D43—44no—
451C22⋊D43—44no—
452C22⋊D43—82no—
453C22⋊D43—82no—
454C22⋊D43—82no—
455C22⋊D43—82no—
456C2×Dic43—22no—
457C2×Dic43—22no—
458C2×Dic43—22no—
459C2×Dic43—44no—
460C2×Dic43—44no—
461C2×Dic43C22×D411yescharacteristic
462C2×Dic43C22×D411yescharacteristic
463C2×Dic43C22×D411yescharacteristic
464C2×Dic43C22×D411yescharacteristic
465C2×Dic43C22×D411yescharacteristic
466C2×Dic43C22×D411yescharacteristic
467D172—22no—
468D172—24no—
469D172—42no—
470D172—42no—
471C4×D43—22no—
472C4×D43—22no—
473C4×D43—22no—
474C4×D43—22no—
475C4×D43—22no—
476C4×D43—44no—
477C4×D43—44no—
478C4×D43H(5,𝔽2)14yes—
479Dic86—22no—
480Dic86—24no—
481Dic86—24no—
482Dic86—42no—
483Dic86—44no—
484C8×C43—22no—
485C8×C43—22no—
486C43⋊C8—22no—
487C43⋊C8—22no—
488#60818—431nomaximal, Sylow
489C22×C43—21no—
490C22×C43—21no—
491C22×C43—21no—
492C22×C43—42no—
493C22×C43—42no—
494C22×C43—42no—
495C22×C43—42no—
496C22×C43—42no—
497C22×C43—42no—
498C22×C43—164no—
499C22×C43C23×D411yescharacteristic
500C2×D43—21no—
501C2×D43—21no—
502C2×D43—21no—
503C2×D43—21no—
504C2×D43—21no—
505C2×D43—42no—
506C2×D43—42no—
507C2×D43—42no—
508C2×D43—164no—
509C2×D43—164no—
510C2×D43#53512yes—
511C4×C43—21no—
512C4×C43—21no—
513C4×C43—21no—
514C4×C43—42no—
515C4×C43—42no—
516C4×C43#57712yes—
517C4×C43#57712yes—
518C4×C43C2×H(5,𝔽2)12yes—
519Dic43—21no—
520Dic43—21no—
521Dic43—21no—
522Dic43—21no—
523Dic43—21no—
524Dic43—42no—
525Dic43—42no—
526Dic43—42no—
527Dic43#53512yes—
528#3509—431no—
529#3498—431no—
530#3222—434no—
531#3222—434no—
532#3210—431no—
533#3210—431no—
534#3210—431no—
535#3210—431no—
536#3208—431no—
537#3208—431no—
538#3208—431no—
539#3208D4311yescharacteristic, complemented
540#3152—431no—
541C2×#492—431no—
542#3138—431no—
543#3131—431no—
544#3043—434no—
545#3009—434no—
546#2922—431no—
547C2×C43—41no—
548C2×C43—82no—
549C2×C43—82no—
550C2×C43C2×#53511yescharacteristic
551C2×C43C2×#57711yescharacteristic
552C2×C43C2×#57711yescharacteristic
553D43—22no—
554D43—41no—
555D43—82no—
556C2×H(5,𝔽2)—432no—
557C2×#137—434no—
558C22×SD16—434no—
559#557—861no—
560#557—861no—
561#556—861no—
562#556—861no—
563#552—861no—
564#552—861no—
565#552—861no—
566#552—861no—
567#550—861no—
568#550—861no—
569D42—861no—
570D42—861no—
571D42—861no—
572D42—861no—
573D42—861no—
574D42—861no—
575#541—432no—
576#541—432no—
577#536—432no—
578#535—432no—
579#535—432no—
580#535—432no—
581#533—431no—
582#533—431no—
583#533—431no—
584#533—431no—
585#533C2×D4311yescharacteristic, complemented
586#532—431no—
587#532—431no—
588#532—431no—
589C2×C4⋊Q8—431no—
590C2×#127—431no—
591C2×#127—431no—
592C2×#127C2×D4311yescharacteristic
593#519—432no—
594C4×#41—431no—
595#497—434no—
596#494—431no—
597#494—431no—
598#492—434no—
599#492—431no—
600#492—431no—
601#492—431no—
602#492—431no—
603#492C2×D4311yescharacteristic, complemented
604#492C2×D4311yescharacteristic, complemented
605#490—434no—
606#488—434no—
607#487—431no—
608#487—431no—
609#486—431no—
610#486—431no—
611#486—431no—
612#486—431no—
613#486C2×D4311yescharacteristic, complemented
614#486C2×D4311yescharacteristic, complemented
615#464—434no—
616#464—434no—
617#464—434no—
618#464—434no—
619#460—434no—
620#460—434no—
621#460—434no—
622#460C2×D4314yescomplemented
623#452—434no—
624#452—434no—
625#452—434no—
626#452—434no—
627#450—434no—
628#450—434no—
629#450—434no—
630#450C2×D4314yescomplemented
631#433—432no—
632#433—432no—
633#431—431no—
634#431—431no—
635#431—431no—
636#431C2×D4311yescharacteristic, complemented
637#424—432no—
638#418—434no—
639#416—434no—
640#408—432no—
641C4×M16—431no—
642C2×C4×C8—431no—
643C43#6081811yescharacteristic, complemented, Sylow
644H(5,𝔽2)—1728no—
645C2×#41—431no—
646C2×#41—432no—
647C2×#41—432no—
648C2×#41—432no—
649C2×#41—862no—
650C22×Q8—432no—
651C22×D4—21no—
652C22×D4—21no—
653C22×D4—432no—
654C22×D4—432no—
655C22×D4—861no—
656C22×D4—861no—
657C22×D4—861no—
658C22×D4—861no—
659C22×D4—862no—
660C22×D4—862no—
661C22×D4—862no—
662C22×D4C22×D4312yes—
663#137—1728no—
664C2×Q16—434no—
665C2×Q16—434no—
666C2×SD16—434no—
667C2×SD16—434no—
668C2×SD16—434no—
669C2×SD16—434no—
670C2×SD16—1728no—
671C2×SD16C22×D4314yes—
672C2×SD16C22×D4314yes—
673C2×M16—432no—
674C22×C8—432no—
675C4⋊Q8—432no—
676C4⋊Q8—431no—
677C4⋊Q8—431no—
678C4⋊Q8—431no—
679C4⋊Q8—861no—
680C4⋊Q8—861no—
681C4⋊Q8—862no—
682C4⋊Q8C22×D4311yescharacteristic
683C4⋊Q8C22×D4311yescharacteristic
684#127—21no—
685#127—21no—
686#127—432no—
687#127—432no—
688#127—431no—
689#127—861no—
690#127—861no—
691#127—861no—
692#127—861no—
693#127C22×D4311yescharacteristic
694#127C22×D4311yescharacteristic
695#127C22×D4312yes—
696#126—862no—
697#126—862no—
698#126—862no—
699#126—862no—
700#125—21no—
701#125—432no—
702#125—862no—
703#125—861no—
704#125—861no—
705#125—862no—
706#125—862no—
707#125—862no—
708#125—861no—
709#124—432no—
710#124—432no—
711#124—432no—
712#124—862no—
713#123—862no—
714#123—862no—
715C22⋊Q8—21no—
716C22⋊Q8—432no—
717C22⋊Q8—432no—
718C22⋊Q8—432no—
719C22⋊Q8—861no—
720C22⋊Q8—861no—
721C22⋊Q8—861no—
722C22⋊Q8—861no—
723C22⋊Q8—861no—
724C22⋊Q8C22×D4312yes—
725#121—862no—
726#121—862no—
727#121—862no—
728#121—862no—
729#121—862no—
730#121—862no—
731#121—861no—
732#121—861no—
733#121—861no—
734#121—861no—
735#121—861no—
736#121—861no—
737#120—862no—
738#120—862no—
739#120—862no—
740#120—862no—
741#120—862no—
742#120—862no—
743C4×Q8—21no—
744C4×Q8—431no—
745C4×Q8—431no—
746C4×Q8—432no—
747C4×Q8—432no—
748C4×Q8—432no—
749C4×Q8—862no—
750C4×Q8—861no—
751C4×Q8—861no—
752C4×Q8—861no—
753C4×Q8—861no—
754C4×Q8—862no—
755C4×Q8—861no—
756C4×Q8C22×D4312yes—
757C4×D4—431no—
758C4×D4—431no—
759C4×D4—431no—
760C4×D4—431no—
761C4×D4—431no—
762C4×D4—431no—
763C4×D4—861no—
764C4×D4—861no—
765C4×D4—861no—
766C4×D4—861no—
767C4×D4—861no—
768C4×D4—861no—
769#117—21no—
770#117—431no—
771#117—431no—
772#117—431no—
773#117—432no—
774#117—862no—
775#117—862no—
776#117—861no—
777#117—861no—
778#117—861no—
779C2×C4⋊C4—861no—
780C2×C4⋊C4—861no—
781C2×C42—431no—
782C2×C42—431no—
783C2×C42C22×D4311yescharacteristic
784C4⋊C8—432no—
785C4⋊C8—432no—
786C4⋊C8—432no—
787C4⋊C8C22×D4312yes—
788#103—434no—
789#103—434no—
790#102—434no—
791#102—434no—
792#102—434no—
793#102—434no—
794#102C22×D4314yes—
795#102C22×D4314yes—
796C22⋊C8—432no—
797C22⋊C8—432no—
798C22⋊C8—432no—
799C22⋊C8C22×D4312yes—
800#97—432no—
801C4×C8—432no—
802C4×C8—431no—
803C4×C8—431no—
804C4×C8C22×D4311yescharacteristic
805C4×C8C22×D4311yescharacteristic
806C24—22no—
807C24—862no—
808C24—862no—
809#41—864no—
810#41—868no—
811#41—1724no—
812#41—1724no—
813#41—1728no—
814C2×Q8—21no—
815C2×Q8—431no—
816C2×Q8—432no—
817C2×Q8—432no—
818C2×Q8—862no—
819C2×Q8—868no—
820C2×Q8—861no—
821C2×Q8C23×D4312yes—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—22no—
827C2×D4—22no—
828C2×D4—22no—
829C2×D4—44no—
830C2×D4—82no—
831C2×D4—82no—
832C2×D4—431no—
833C2×D4—431no—
834C2×D4—431no—
835C2×D4—432no—
836C2×D4—868no—
837C2×D4—862no—
838C2×D4—862no—
839C2×D4—862no—
840C2×D4—862no—
841C2×D4—862no—
842C2×D4—862no—
843C2×D4—862no—
844C2×D4—862no—
845C2×D4—862no—
846C2×D4—861no—
847C2×D4—861no—
848C2×D4—3442no—
849C2×D4—3442no—
850C2×D4—3442no—
851C2×D4—3442no—
852C2×D4—1724no—
853C2×D4—1728no—
854C2×D4—1728no—
855C2×D4—1728no—
856C2×D4C23×D4312yes—
857C2×D4C23×D4312yes—
858C22×C4—431no—
859C22×C4—431no—
860C22×C4—431no—
861C22×C4—431no—
862C22×C4—431no—
863C22×C4—431no—
864C22×C4—862no—
865C22×C4—862no—
866C22×C4—862no—
867C22×C4—862no—
868C22×C4D4×D4311yescharacteristic
869C22×C4D4×D4311yescharacteristic
870C22×C4C23×D4311yescharacteristic
871Q16—1724no—
872Q16—1724no—
873SD16—44no—
874SD16—44no—
875SD16—1724no—
876SD16—1724no—
877SD16—1724no—
878SD16—1724no—
879M16—864no—
880C2×C8—432no—
881C2×C8—432no—
882C2×C8—864no—
883C2×C8C23×D4312yes—
884C2×C8C23×D4312yes—
885C4⋊C4—21no—
886C4⋊C4—21no—
887C4⋊C4—21no—
888C4⋊C4—22no—
889C4⋊C4—22no—
890C4⋊C4—431no—
891C4⋊C4—431no—
892C4⋊C4—431no—
893C4⋊C4—431no—
894C4⋊C4—431no—
895C4⋊C4—431no—
896C4⋊C4—432no—
897C4⋊C4—862no—
898C4⋊C4—862no—
899C4⋊C4—862no—
900C4⋊C4—862no—
901C4⋊C4—862no—
902C4⋊C4—862no—
903C4⋊C4—862no—
904C4⋊C4—862no—
905C4⋊C4—861no—
906C4⋊C4—861no—
907C4⋊C4—861no—
908C4⋊C4—862no—
909C4⋊C4—861no—
910C4⋊C4—861no—
911C4⋊C4—862no—
912C4⋊C4C23×D4312yes—
913C22⋊C4—22no—
914C22⋊C4—431no—
915C22⋊C4—431no—
916C22⋊C4—431no—
917C22⋊C4—431no—
918C22⋊C4—431no—
919C22⋊C4—431no—
920C22⋊C4—862no—
921C22⋊C4—862no—
922C22⋊C4—862no—
923C22⋊C4—862no—
924C22⋊C4—862no—
925C22⋊C4—862no—
926C22⋊C4—862no—
927C22⋊C4—862no—
928C22⋊C4—862no—
929C22⋊C4—862no—
930C42—22no—
931C42—431no—
932C42—431no—
933C42—431no—
934C42—431no—
935C42—431no—
936C42—431no—
937C42—862no—
938C42—862no—
939C42—862no—
940C42—862no—
941C42D4×D4311yescharacteristic
942C42D4×D4311yescharacteristic
943C42C23×D4311yescharacteristic
944C42C23×D4311yescharacteristic
945C23—22no—
946C23—22no—
947C23—44no—
948C23—82no—
949C23—82no—
950C23—431no—
951C23—431no—
952C23—862no—
953C23—3442no—
954C23—3442no—
955C23—3442no—
956C23—3442no—
957C23—1724no—
958C23—1724no—
959C23C2×D4×D4311yescharacteristic
960Q8—24no—
961Q8—42no—
962Q8—862no—
963Q8—864no—
964Q8—864no—
965Q8—1724no—
966Q8—1722no—
967D4—24no—
968D4—24no—
969D4—44no—
970D4—42no—
971D4—42no—
972D4—42no—
973D4—42no—
974D4—82no—
975D4—82no—
976D4—862no—
977D4—862no—
978D4—862no—
979D4—864no—
980D4—3442no—
981D4—3442no—
982D4—3442no—
983D4—3442no—
984D4—1724no—
985D4—1724no—
986D4—1724no—
987D4—1724no—
988D4—1724no—
989D4—1722no—
990D4—1722no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—431no—
997C2×C4—434no—
998C2×C4—431no—
999C2×C4—431no—
1000C2×C4—431no—
1001C2×C4—431no—
1002C2×C4—431no—
1003C2×C4—862no—
1004C2×C4—862no—
1005C2×C4—862no—
1006C2×C4—862no—
1007C2×C4—862no—
1008C2×C4—862no—
1009C2×C4—862no—
1010C2×C4—862no—
1011C2×C4—1724no—
1012C2×C4—1724no—
1013C2×C4—1724no—
1014C2×C4—1724no—
1015C2×C4C2×D4×D4311yescharacteristic
1016C2×C4C2×D4×D4311yescharacteristic
1017C2×C4C2×D4×D4311yescharacteristic
1018C2×C4C2×D4×D4311yescharacteristic
1019C2×C4C2×D4×D4311yescharacteristic
1020C2×C4C24×D4311yescharacteristic
1021C8—22no—
1022C8—22no—
1023C8—862no—
1024C8—862no—
1025C22—21no—
1026C22—21no—
1027C22—21no—
1028C22—42no—
1029C22—42no—
1030C22—42no—
1031C22—42no—
1032C22—42no—
1033C22—42no—
1034C22—164no—
1035C22—432no—
1036C22—861no—
1037C22—861no—
1038C22—861no—
1039C22—861no—
1040C22—861no—
1041C22—1722no—
1042C22—1722no—
1043C22—1722no—
1044C22—6884no—
1045C22—6884no—
1046C22C22×D4×D4311yescharacteristic
1047C4—21no—
1048C4—21no—
1049C4—21no—
1050C4—42no—
1051C4—42no—
1052C4—432no—
1053C4—861no—
1054C4—861no—
1055C4—861no—
1056C4—861no—
1057C4—861no—
1058C4—1722no—
1059C4—1722no—
1060C4—1722no—
1061C4#1458370512yes—
1062C4#1458370912yes—
1063C4H(5,𝔽2)×D4312yes—
1064C2—41no—
1065C2—82no—
1066C2—82no—
1067C2—862no—
1068C2—3442no—
1069C2—1721no—
1070C2#535×D4311yescharacteristic
1071C2C2×#1458370511yescharacteristic
1072C2C2×#1458370911yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3208C2
socleC22×C43C23×D4
prime radical#19148371C2
hypercenter#3208D43
hypocenterC43#60818
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3208

Complements

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

NH ≅ G/Ntype
1. #19148474C2semidirect
3. #19145666C2semidirect
4. #19145663C2semidirect
5. #19145553C2semidirect
6. #19145552C2semidirect
7. #19145547C2semidirect
8. #19145546C2semidirect
9. #19145537C2semidirect
10. #19145536C2semidirect
11. #19145532C2semidirect
12. #19145049C2semidirect
13. #492×D43C2semidirect
14. #19144966C2semidirect
15. #19144914C2semidirect
16. #19144111C2semidirect
17. #19143867C2semidirect
18. #19143234C2semidirect
19. C43×#3208C2semidirect
21. C2×#13063354C22semidirect
22. C2×SD16×D43C22semidirect
39. #14583509C22semidirect
40. #14583507C22semidirect
45. #14583456C22semidirect
46. #14583454C22semidirect
47. #14583454C22semidirect
48. #14583454C22semidirect
52. C4⋊Q8×D43C22semidirect
55. #14583375C22semidirect
57. #14583290C22semidirect
58. #14583279C22semidirect
59. #14583278C22semidirect
60. #14583273C22semidirect
61. #14583272C22semidirect
62. #14583271C22semidirect
63. #14583271C22semidirect
64. #14583270C22semidirect
65. #14583262C22semidirect
66. #14583252C22semidirect
67. #14583251C22semidirect
68. #14583250C22semidirect
69. #14583247C22semidirect
70. #14583246C22semidirect
71. #14583245C22semidirect
72. #14583245C22semidirect
73. #14583122C22semidirect
74. #14583121C22semidirect
75. #14583120C22semidirect
76. #14583119C22semidirect
77. #14583098C22semidirect
78. #14583097C22semidirect
79. #14583096C22semidirect
80. #14583063C22semidirect
81. #14583062C22semidirect
82. #14583059C22semidirect
83. #14583058C22semidirect
84. #14583051C22semidirect
85. #14583050C22semidirect
86. #14583048C22semidirect
87. #14582959C22semidirect
88. #14582957C22semidirect
89. #14582952C22semidirect
90. #14582950C22semidirect
91. #14582950C22semidirect
92. #14582924C22semidirect
93. #14582902C22semidirect
94. #14582892C22semidirect
96. C4×#10621872C22semidirect
97. C4×C8×D43C22semidirect
98. C43×#533C22semidirect
100. C43×#492C22semidirect
101. C43×#492C22semidirect
102. C43×#486C22semidirect
103. C43×#486C22semidirect
104. C43×#460C22semidirect
105. C43×#450C22semidirect
106. C43×#431C22semidirect
539. #3208D43semidirect
585. #533C2×D43semidirect
603. #492C2×D43semidirect
604. #492C2×D43semidirect
613. #486C2×D43semidirect
614. #486C2×D43semidirect
622. #460C2×D43semidirect
630. #450C2×D43semidirect
636. #431C2×D43semidirect
643. C43#60818semidirect

Maximal subgroups

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

subgroupindex
#191484742
#191483712
#191456662
#191456632
#191455532
#191455522
#191455472
#191455462
#191455372
#191455362
#191455322
#191450492
#492×D432
#191449662
#191449142
#191441112
#191438672
#191432342
C43×#32082
#6081843