Finite Group Databasebeta

← #25968292

Subgroups — #25968292

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#19148368C211yesmaximal, characteristic
3#19145665C214yesmaximal, complemented
4#19145664C214yesmaximal, complemented
5#19145554C211yesmaximal, characteristic, complemented
6#19145551C211yesmaximal, characteristic, complemented
7#19145548C211yesmaximal, characteristic, complemented
8#19145538C211yesmaximal, characteristic, complemented
9#19145537C211yesmaximal, characteristic, complemented
10#19145533C211yesmaximal, characteristic, complemented
11#19145532C211yesmaximal, characteristic, complemented
12#19145053C211yesmaximal, characteristic, complemented
13#492×D43C211yesmaximal, characteristic, complemented
14#19144966C211yesmaximal, characteristic, complemented
15#19144919C211yesmaximal, characteristic, complemented
16#19144114C214yesmaximal, complemented
17#19143869C214yesmaximal, complemented
18#19143234C211yesmaximal, characteristic, complemented
19C43×#3210C211yesmaximal, characteristic, complemented
20C2×#13063371C2212yes—
21C2×#13063357C2214yescomplemented
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#14583570—21no—
32#14583570—21no—
33D4×D172—21no—
34D4×D172—21no—
35#14583533—21no—
36#14583533—21no—
37#14583533—21no—
38#14583533—21no—
39#14583509C2212yescomplemented
40#14583507C2212yescomplemented
41#14583472C2212yes—
42#14583467C2212yes—
43#14583467C2212yes—
44#14583463C2212yes—
45#14583456C2211yescharacteristic, complemented
46#14583454C2211yescharacteristic, complemented
47#14583454C2211yescharacteristic, complemented
48#14583454C2211yescharacteristic, complemented
49#14583450C2211yescharacteristic
50#14583450C2211yescharacteristic
51C4⋊Q8×D43C2211yescharacteristic, complemented
52C2×#13063322C2211yescharacteristic
53#127×D43C2211yescharacteristic
54#127×D43C2211yescharacteristic
55#14583375C2212yescomplemented
56C4×#10621898C2211yescharacteristic
57#14583292C2214yescomplemented
58#14583278C2211yescharacteristic, complemented
59#14583273C2211yescharacteristic, complemented
60#14583273C2211yescharacteristic, complemented
61#14583272C2211yescharacteristic, complemented
62#14583272C2211yescharacteristic, complemented
63#14583271C2211yescharacteristic, complemented
64#14583270C2214yescomplemented
65#14583262C2214yescomplemented
66#14583255C2214yescomplemented
67#14583249C2211yescharacteristic, complemented
68#14583247C2211yescharacteristic, complemented
69#14583247C2211yescharacteristic, complemented
70#14583246C2211yescharacteristic, complemented
71#14583246C2211yescharacteristic, complemented
72#14583245C2211yescharacteristic, complemented
73#14583124C2214yescomplemented
74#14583123C2214yescomplemented
75#14583118C2214yescomplemented
76#14583100C2214yescomplemented
77#14583099C2214yescomplemented
78#14583098C2214yescomplemented
79#14583097C2214yescomplemented
80#14583064C2214yescomplemented
81#14583061C2214yescomplemented
82#14583060C2214yescomplemented
83#14583052C2214yescomplemented
84#14583051C2214yescomplemented
85#14583049C2214yescomplemented
86#14583048C2214yescomplemented
87#14582959C2212yescomplemented
88#14582957C2212yescomplemented
89#14582952C2211yescharacteristic, complemented
90#14582950C2211yescharacteristic, complemented
91#14582950C2211yescharacteristic, complemented
92#14582924C2212yescomplemented
93#14582902C2214yescomplemented
94#14582894C2214yescomplemented
95#14582864C2212yes—
96C4×#10621872C2211yescharacteristic, complemented
97C4×C8×D43C2211yescharacteristic, complemented
98C43×#533C2211yescharacteristic, complemented
99C43×#532C2211yescharacteristic
100C43×#494C2211yescharacteristic, complemented
101C43×#492C2211yescharacteristic, complemented
102C43×#487C2211yescharacteristic, complemented
103C43×#486C2211yescharacteristic, complemented
104C43×#464C2214yescomplemented
105C43×#452C2214yescomplemented
106C43×#431C2211yescharacteristic, complemented
107#13063371—48no—
108C2×#10621902C2312yes—
109C2×#10621902C2312yes—
110C2×#10621898—22no—
111C2×#10621898C2311yescharacteristic
112C2×Q8×D43C2312yes—
113C22×D172—21no—
114C22×D172—21no—
115C22×D172—22no—
116C22×D172C2312yes—
117C2×D4×D43—22no—
118C2×D4×D43—22no—
119C2×D4×D43—21no—
120C2×D4×D43—21no—
121C2×D4×D43—21no—
122C2×D4×D43—21no—
123C2×D4×D43C2312yes—
124C2×D4×D43C2312yes—
125#13063357—48no—
126C2×#10621885C2314yes—
127C2×#10621873C2314yes—
128C2×#10621873C2314yes—
129C2×#10621883C2314yes—
130C2×#10621884C2314yes—
131C2×#10621884C2314yes—
132SD16×D43—48no—
133C2×#10621872C2312yes—
134C2×C8×D43C2312yes—
135#13063325C2311yescharacteristic
136#13063325C2311yescharacteristic
137#13063324—22no—
138#13063324—21no—
139#13063324—21no—
140#13063323C2312yes—
141#13063322—21no—
142#13063322—21no—
143#13063322C2312yes—
144#13063322C2311yescharacteristic
145#13063322C2311yescharacteristic
146#13063321—21no—
147#13063321—21no—
148#13063321—21no—
149#13063321—21no—
150#13063321C2312yes—
151#13063321C2312yes—
152#13063320—22no—
153#13063319—22no—
154#13063318—22no—
155#13063318—22no—
156#13063317—21no—
157#13063317—22no—
158#13063316—22no—
159#13063316—21no—
160#13063316—21no—
161#13063316C2312yes—
162#13063315—22no—
163#13063315—22no—
164#13063314C2312yes—
165#13063314C2312yes—
166#13063311—22no—
167#13063310—22no—
168#13063307—22no—
169#13063305—21no—
170#13063305—21no—
171#13063305C2312yes—
172#13063304—21no—
173#13063304C2312yes—
174#13063301—21no—
175#13063301—21no—
176#13063301C2312yes—
177#13063300—21no—
178#13063300—21no—
179#13063300—21no—
180#13063300—21no—
181#13063299—22no—
182#13063299—22no—
183#13063298—22no—
184#13063298—22no—
185#13063298—22no—
186#13063298—22no—
187#13063295—22no—
188#13063295—22no—
189#13063295—22no—
190#13063295—22no—
191#13063293—22no—
192#13063293—22no—
193Q8×Dic43—21no—
194Q8×Dic43—21no—
195Q8×Dic43C2312yes—
196C4×Dic86—21no—
197C4×Dic86—22no—
198C4×Dic86D411yescharacteristic
199C4×Dic86D411yescharacteristic
200C4×Dic86C2312yes—
201#13063290—22no—
202#13063290—21no—
203#13063290—21no—
204#13063290C2312yes—
205C4×D172D411yescharacteristic
206C4×D172D411yescharacteristic
207#13063287—21no—
208#13063287—21no—
209#13063287—21no—
210#13063287—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#13063249C2314yes—
232#13063247C2314yes—
233#13063247C2314yes—
234#13063246C2314yes—
235#13063245C2314yes—
236#13063245C2314yes—
237C22⋊(C43⋊C8)C2312yes—
238(C2×D43)⋊C8C2312yes—
239(C2×D43)⋊C8C2312yes—
240#13063235C2312yes—
241C4×C43⋊C8C2311yescharacteristic
242C4×C43⋊C8C2311yescharacteristic
243C8×Dic43C2312yes—
244C2×#41×C43C2312yes—
245C2×Q16×C43C2314yes—
246C2×SD16×C43C2314yes—
247C4⋊Q8×C43C2311yescharacteristic
248C4⋊Q8×C43C2311yescharacteristic
249C4⋊Q8×C43C2311yescharacteristic
250#127×C43C2311yescharacteristic
251#125×C43—21no—
252#124×C43C2312yes—
253C22⋊Q8×C43—21no—
254C22⋊Q8×C43C2312yes—
255#121×C43—21no—
256#121×C43—21no—
257C4×Q8×C43—21no—
258C4×Q8×C43C2312yes—
259C4×D4×C43—21no—
260C4×D4×C43—21no—
261#117×C43—21no—
262C2×C42×C43C2311yescharacteristic
263C4⋊C8×C43C2312yes—
264#103×C43C2314yes—
265#102×C43C2314yes—
266C22⋊C8×C43C2312yes—
267C4×C8×C43C2311yescharacteristic
268C4×C8×C43C2311yescharacteristic
269C23×D43—22no—
270C23×D43—22no—
271C23×D43—22no—
272#41×C43—44no—
273C2×Q8×C43—21no—
274C2×Q8×C43C2412yes—
275C2×Q8×C43C2412yes—
276C2×D4×C43—21no—
277C2×D4×C43—21no—
278C2×D4×C43—22no—
279C2×D4×C43C2412yes—
280C22×C4×C43—22no—
281C22×C4×C43C2×D411yescharacteristic
282C22×C4×C43C2×D411yescharacteristic
283C22×C4×C43C2411yescharacteristic
284C2×C22⋊D43—22no—
285C2×C22⋊D43—22no—
286C2×C22⋊D43—22no—
287C2×C22⋊D43—22no—
288C2×C22⋊D43—22no—
289C2×C22⋊D43—22no—
290C2×C22⋊D43C2×D411yescharacteristic
291C2×C22⋊D43C2×D411yescharacteristic
292#10621902—28no—
293#10621902—44no—
294Q8×D43—28no—
295D4×D43—28no—
296D4×D43—44no—
297D4×D43—48no—
298D4×D43—48no—
299D4×D43—82no—
300D4×D43—82no—
301D4×D43—82no—
302D4×D43—82no—
303#10621898—24no—
304#10621898—48no—
305C2×D172—21no—
306C2×D172—21no—
307C2×D172—21no—
308C2×D172—21no—
309C2×D172—22no—
310C2×D172—22no—
311C2×D172—22no—
312C2×D172—22no—
313C2×D172—22no—
314C2×D172—44no—
315C2×D172—48no—
316C2×D172—82no—
317C2×D172—82no—
318C2×D172C2×D411yescharacteristic
319C2×D172C2412yes—
320C2×D172C2412yes—
321C2×C4×D43—22no—
322C2×C4×D43—22no—
323C2×C4×D43—22no—
324C2×C4×D43C2×D411yescharacteristic
325C2×C4×D43C2×D411yescharacteristic
326C2×C4×D43C2×D411yescharacteristic
327C2×C4×D43C2×D411yescharacteristic
328C2×C4×D43C2411yescharacteristic
329C2×C4×D43C2411yescharacteristic
330C2×Dic86—21no—
331C2×Dic86—22no—
332C2×Dic86C2×D411yescharacteristic
333C2×Dic86C2412yes—
334Q16×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—21no—
342C4⋊C4×C43—21no—
343C4⋊C4×C43—22no—
344C4⋊C4×C43—22no—
345C4⋊C4×C43C2412yes—
346C22⋊C4×C43—22no—
347C22⋊C4×C43—22no—
348C22⋊C4×C43—22no—
349C42×C43—22no—
350C42×C43C2×D411yescharacteristic
351C42×C43C2×D411yescharacteristic
352C42×C43C2411yescharacteristic
353C42×C43C2411yescharacteristic
354C22⋊Dic43—22no—
355C22⋊Dic43C2×D411yescharacteristic
356C22⋊Dic43C2×D411yescharacteristic
357#10621885—44no—
358#10621884—44no—
359#10621884—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)⋊C4—22no—
367(C2×D43)⋊C4—22no—
368(C2×D43)⋊C4C2×D411yescharacteristic
369(C2×D43)⋊C4C2×D411yescharacteristic
370(C2×D43)⋊C4C2×D411yescharacteristic
371(C2×D43)⋊C4C2×D411yescharacteristic
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—
404#10621873—44no—
405#10621873—44no—
406#10621872—24no—
407C8×D43—24no—
408C23×C43—22no—
409C23×C43C22×D411yescharacteristic
410C22×D43—22no—
411C22×D43—22no—
412C22×D43—44no—
413C22×D43—44no—
414C22×D43—44no—
415C22×D43—82no—
416C22×D43—82no—
417C22×D43—82no—
418C22×D43—82no—
419C22×D43—82no—
420C22×D43—82no—
421C22×D43C22×D411yescharacteristic
422C22×D43C22×D411yescharacteristic
423Q8×C43—24no—
424Q8×C43—24no—
425Q8×C43—42no—
426D4×C43—24no—
427D4×C43—44no—
428D4×C43—42no—
429D4×C43—42no—
430C2×C4×C43—22no—
431C2×C4×C43—22no—
432C2×C4×C43—22no—
433C2×C4×C43—22no—
434C2×C4×C43—22no—
435C2×C4×C43—22no—
436C2×C4×C43—44no—
437C2×C4×C43C22×D411yescharacteristic
438C2×C4×C43C22×D411yescharacteristic
439C2×C4×C43C22×D411yescharacteristic
440C2×C4×C43C22×D411yescharacteristic
441C2×C4×C43C22×D411yescharacteristic
442C2×C4×C43C2511yescharacteristic
443C22⋊D43—22no—
444C22⋊D43—22no—
445C22⋊D43—44no—
446C22⋊D43—44no—
447C22⋊D43—82no—
448C22⋊D43—82no—
449C22⋊D43—82no—
450C22⋊D43—82no—
451C2×Dic43—22no—
452C2×Dic43—22no—
453C2×Dic43C22×D411yescharacteristic
454C2×Dic43C22×D411yescharacteristic
455C2×Dic43C22×D411yescharacteristic
456C2×Dic43C22×D411yescharacteristic
457C2×Dic43C22×D411yescharacteristic
458C2×Dic43C22×D411yescharacteristic
459D172—22no—
460D172—24no—
461D172—24no—
462D172—44no—
463D172—44no—
464D172—44no—
465D172—42no—
466D172—42no—
467D172—42no—
468D172—42no—
469D172—82no—
470D172—82no—
471C4×D43—22no—
472C4×D43—22no—
473C4×D43—22no—
474C4×D43—22no—
475C4×D43—22no—
476C4×D43—44no—
477C4×D43—44no—
478C4×D43—44no—
479C4×D43H(5,𝔽2)14yes—
480Dic86—22no—
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×C43C23×D411yescharacteristic
496C2×D43—21no—
497C2×D43—21no—
498C2×D43—21no—
499C2×D43—21no—
500C2×D43—21no—
501C2×D43—42no—
502C2×D43—42no—
503C2×D43—42no—
504C2×D43—42no—
505C2×D43—42no—
506C2×D43—42no—
507C2×D43—164no—
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—42no—
517C4×C43#57712yes—
518C4×C43#57712yes—
519C4×C43C2×H(5,𝔽2)12yes—
520Dic43—21no—
521Dic43—21no—
522Dic43—21no—
523Dic43—21no—
524Dic43—21no—
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#3210D4311yescharacteristic, complemented
536#3208—431no—
537#3208—431no—
538#3208—431no—
539#3208—431no—
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×C43C2×#53511yescharacteristic
550C2×C43C2×#57711yescharacteristic
551C2×C43C2×#57711yescharacteristic
552D43—22no—
553D43—41no—
554D43—82no—
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#532C2×D4311yescharacteristic
589C2×C4⋊Q8—431no—
590C2×#127—431no—
591C2×#127—431no—
592C2×#127—431no—
593#519—432no—
594C4×#41—431no—
595#497—434no—
596#494—431no—
597#494C2×D4311yescharacteristic, complemented
598#492—434no—
599#492—431no—
600#492—431no—
601#492—431no—
602#492—431no—
603#492—431no—
604#492C2×D4311yescharacteristic, complemented
605#490—434no—
606#488—434no—
607#487—431no—
608#487C2×D4311yescharacteristic, complemented
609#486—431no—
610#486—431no—
611#486—431no—
612#486—431no—
613#486—431no—
614#486C2×D4311yescharacteristic, complemented
615#464—434no—
616#464—434no—
617#464—434no—
618#464C2×D4314yescomplemented
619#460—434no—
620#460—434no—
621#460—434no—
622#460—434no—
623#452—434no—
624#452—434no—
625#452—434no—
626#452C2×D4314yescomplemented
627#450—434no—
628#450—434no—
629#450—434no—
630#450—434no—
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—862no—
649C2×#41C22×D4312yes—
650C22×Q8—432no—
651C22×D4—432no—
652C22×D4—432no—
653C22×D4—432no—
654C22×D4—862no—
655C22×D4—861no—
656C22×D4—861no—
657C22×D4—861no—
658C22×D4—861no—
659C22×D4—862no—
660C22×D4—862no—
661C22×D4—861no—
662C22×D4—861no—
663#137—1728no—
664C2×Q16—434no—
665C2×Q16C22×D4314yes—
666C2×SD16—434no—
667C2×SD16—434no—
668C2×SD16—434no—
669C2×SD16—434no—
670C2×SD16—434no—
671C2×SD16—1728no—
672C2×SD16C22×D4314yes—
673C2×M16—432no—
674C22×C8—432no—
675C4⋊Q8—432no—
676C4⋊Q8—431no—
677C4⋊Q8—431no—
678C4⋊Q8—861no—
679C4⋊Q8—861no—
680C4⋊Q8—862no—
681C4⋊Q8C22×D4311yescharacteristic
682C4⋊Q8C22×D4311yescharacteristic
683C4⋊Q8C22×D4311yescharacteristic
684#127—432no—
685#127—432no—
686#127—431no—
687#127—431no—
688#127—432no—
689#127—861no—
690#127—861no—
691#127—861no—
692#127—861no—
693#127—861no—
694#127—861no—
695#127C22×D4311yescharacteristic
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—862no—
712#124C22×D4312yes—
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—21no—
726#121—21no—
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—862no—
736#121—862no—
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—21no—
758C4×D4—21no—
759C4×D4—431no—
760C4×D4—431no—
761C4×D4—431no—
762C4×D4—431no—
763C4×D4—431no—
764C4×D4—431no—
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#103C22×D4314yes—
790#102—434no—
791#102—434no—
792#102—434no—
793#102—434no—
794#102—434no—
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—862no—
807C24—862no—
808C24—862no—
809#41—44no—
810#41—864no—
811#41—868no—
812#41—1728no—
813#41—1724no—
814C2×Q8—21no—
815C2×Q8—431no—
816C2×Q8—432no—
817C2×Q8—862no—
818C2×Q8—868no—
819C2×Q8—861no—
820C2×Q8C23×D4312yes—
821C2×Q8C23×D4312yes—
822C2×D4—22no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—431no—
826C2×D4—431no—
827C2×D4—431no—
828C2×D4—432no—
829C2×D4—432no—
830C2×D4—862no—
831C2×D4—862no—
832C2×D4—868no—
833C2×D4—862no—
834C2×D4—862no—
835C2×D4—862no—
836C2×D4—862no—
837C2×D4—862no—
838C2×D4—862no—
839C2×D4—862no—
840C2×D4—862no—
841C2×D4—861no—
842C2×D4—861no—
843C2×D4—861no—
844C2×D4—861no—
845C2×D4—862no—
846C2×D4—3442no—
847C2×D4—3442no—
848C2×D4—3442no—
849C2×D4—3442no—
850C2×D4—3442no—
851C2×D4—3442no—
852C2×D4—1724no—
853C2×D4—1728no—
854C2×D4—1724no—
855C2×D4—1728no—
856C2×D4—1728no—
857C2×D4C23×D4312yes—
858C22×C4—22no—
859C22×C4—431no—
860C22×C4—431no—
861C22×C4—431no—
862C22×C4—431no—
863C22×C4—431no—
864C22×C4—431no—
865C22×C4—862no—
866C22×C4—862no—
867C22×C4—862no—
868C22×C4D4×D4311yescharacteristic
869C22×C4D4×D4311yescharacteristic
870C22×C4C23×D4311yescharacteristic
871Q16—44no—
872Q16—1724no—
873SD16—44no—
874SD16—1724no—
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—21no—
890C4⋊C4—21no—
891C4⋊C4—22no—
892C4⋊C4—431no—
893C4⋊C4—431no—
894C4⋊C4—431no—
895C4⋊C4—431no—
896C4⋊C4—431no—
897C4⋊C4—431no—
898C4⋊C4—432no—
899C4⋊C4—862no—
900C4⋊C4—862no—
901C4⋊C4—862no—
902C4⋊C4—862no—
903C4⋊C4—862no—
904C4⋊C4—862no—
905C4⋊C4—862no—
906C4⋊C4—862no—
907C4⋊C4—861no—
908C4⋊C4—861no—
909C4⋊C4—861no—
910C4⋊C4—862no—
911C4⋊C4—862no—
912C4⋊C4C23×D4312yes—
913C22⋊C4—22no—
914C22⋊C4—22no—
915C22⋊C4—22no—
916C22⋊C4—431no—
917C22⋊C4—431no—
918C22⋊C4—431no—
919C22⋊C4—431no—
920C22⋊C4—431no—
921C22⋊C4—431no—
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—431no—
947C23—431no—
948C23—862no—
949C23—862no—
950C23—3442no—
951C23—3442no—
952C23—3442no—
953C23—3442no—
954C23—3442no—
955C23—3442no—
956C23—1724no—
957C23—1724no—
958C23—1724no—
959C23C2×D4×D4311yescharacteristic
960Q8—24no—
961Q8—24no—
962Q8—42no—
963Q8—862no—
964Q8—864no—
965Q8—1724no—
966Q8—1722no—
967D4—24no—
968D4—44no—
969D4—42no—
970D4—42no—
971D4—862no—
972D4—862no—
973D4—862no—
974D4—864no—
975D4—864no—
976D4—3442no—
977D4—3442no—
978D4—3442no—
979D4—3442no—
980D4—3442no—
981D4—3442no—
982D4—1724no—
983D4—1724no—
984D4—1724no—
985D4—1724no—
986D4—1724no—
987D4—1722no—
988D4—1722no—
989D4—1722no—
990D4—1722no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—44no—
998C2×C4—431no—
999C2×C4—434no—
1000C2×C4—431no—
1001C2×C4—431no—
1002C2×C4—431no—
1003C2×C4—431no—
1004C2×C4—431no—
1005C2×C4—862no—
1006C2×C4—862no—
1007C2×C4—862no—
1008C2×C4—862no—
1009C2×C4—862no—
1010C2×C4—862no—
1011C2×C4—862no—
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—432no—
1032C22—861no—
1033C22—861no—
1034C22—861no—
1035C22—861no—
1036C22—861no—
1037C22—1722no—
1038C22—1722no—
1039C22—1722no—
1040C22—1722no—
1041C22—1722no—
1042C22—1722no—
1043C22—6884no—
1044C22—6884no—
1045C22—6884no—
1046C22C22×D4×D4311yescharacteristic
1047C4—21no—
1048C4—21no—
1049C4—21no—
1050C4—42no—
1051C4—42no—
1052C4—42no—
1053C4—432no—
1054C4—861no—
1055C4—861no—
1056C4—861no—
1057C4—861no—
1058C4—861no—
1059C4—1722no—
1060C4—1722no—
1061C4#1458370612yes—
1062C4#1458370812yes—
1063C4H(5,𝔽2)×D4312yes—
1064C2—41no—
1065C2—82no—
1066C2—862no—
1067C2—3442no—
1068C2—3442no—
1069C2—1721no—
1070C2#535×D4311yescharacteristic
1071C2C2×#1458370611yescharacteristic
1072C2C2×#1458370811yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3210C2
socleC22×C43C23×D4
prime radical#19148368C2
hypercenter#3210D43
hypocenterC43#60818
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3210

Complements

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

NH ≅ G/Ntype
1. #19148474C2semidirect
3. #19145665C2semidirect
4. #19145664C2semidirect
5. #19145554C2semidirect
6. #19145551C2semidirect
7. #19145548C2semidirect
8. #19145538C2semidirect
9. #19145537C2semidirect
10. #19145533C2semidirect
11. #19145532C2semidirect
12. #19145053C2semidirect
13. #492×D43C2semidirect
14. #19144966C2semidirect
15. #19144919C2semidirect
16. #19144114C2semidirect
17. #19143869C2semidirect
18. #19143234C2semidirect
19. C43×#3210C2semidirect
21. C2×#13063357C22semidirect
22. C2×SD16×D43C22semidirect
39. #14583509C22semidirect
40. #14583507C22semidirect
45. #14583456C22semidirect
46. #14583454C22semidirect
47. #14583454C22semidirect
48. #14583454C22semidirect
51. C4⋊Q8×D43C22semidirect
55. #14583375C22semidirect
57. #14583292C22semidirect
58. #14583278C22semidirect
59. #14583273C22semidirect
60. #14583273C22semidirect
61. #14583272C22semidirect
62. #14583272C22semidirect
63. #14583271C22semidirect
64. #14583270C22semidirect
65. #14583262C22semidirect
66. #14583255C22semidirect
67. #14583249C22semidirect
68. #14583247C22semidirect
69. #14583247C22semidirect
70. #14583246C22semidirect
71. #14583246C22semidirect
72. #14583245C22semidirect
73. #14583124C22semidirect
74. #14583123C22semidirect
75. #14583118C22semidirect
76. #14583100C22semidirect
77. #14583099C22semidirect
78. #14583098C22semidirect
79. #14583097C22semidirect
80. #14583064C22semidirect
81. #14583061C22semidirect
82. #14583060C22semidirect
83. #14583052C22semidirect
84. #14583051C22semidirect
85. #14583049C22semidirect
86. #14583048C22semidirect
87. #14582959C22semidirect
88. #14582957C22semidirect
89. #14582952C22semidirect
90. #14582950C22semidirect
91. #14582950C22semidirect
92. #14582924C22semidirect
93. #14582902C22semidirect
94. #14582894C22semidirect
96. C4×#10621872C22semidirect
97. C4×C8×D43C22semidirect
98. C43×#533C22semidirect
100. C43×#494C22semidirect
101. C43×#492C22semidirect
102. C43×#487C22semidirect
103. C43×#486C22semidirect
104. C43×#464C22semidirect
105. C43×#452C22semidirect
106. C43×#431C22semidirect
535. #3210D43semidirect
585. #533C2×D43semidirect
597. #494C2×D43semidirect
604. #492C2×D43semidirect
608. #487C2×D43semidirect
614. #486C2×D43semidirect
618. #464C2×D43semidirect
626. #452C2×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
#191483682
#191456652
#191456642
#191455542
#191455512
#191455482
#191455382
#191455372
#191455332
#191455322
#191450532
#492×D432
#191449662
#191449192
#191441142
#191438692
#191432342
C43×#32102
#6081843