Finite Group Databasebeta

← #25968316

Subgroups — #25968316

Order 11008.

2058 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148493C211yesmaximal, characteristic, complemented
2#19148382C211yesmaximal, characteristic, complemented
3#19145707C214yesmaximal, complemented
4#19145692C214yesmaximal, complemented
5#19145572C214yesmaximal, complemented
6#19145561C214yesmaximal, complemented
7#19145063C211yesmaximal, characteristic, complemented
8C2×#14583283C211yesmaximal, characteristic, complemented
9#19144984C211yesmaximal, characteristic, complemented
10#19144128C211yesmaximal, characteristic, complemented
11#19144119C211yesmaximal, characteristic, complemented
12#19144110C211yesmaximal, characteristic, complemented
13#19144101C211yesmaximal, characteristic, complemented
14#19143893C211yesmaximal, characteristic, complemented
15#19143884C211yesmaximal, characteristic, complemented
16#19143875C211yesmaximal, characteristic, complemented
17#19143866C211yesmaximal, characteristic, complemented
18#19143237C211yesmaximal, characteristic, complemented
19C43×#3131C211yesmaximal, characteristic, complemented
20C2×#13063372C2211yescharacteristic
21C2×#13063371C2211yescharacteristic
22C2×#13063355C2211yescharacteristic
23C2×#13063355C2211yescharacteristic, complemented
24C2×#13063350C2211yescharacteristic
25C2×#13063350C2211yescharacteristic, complemented
26C22×Dic172C2211yescharacteristic, complemented
27C22×#10621873C2211yescharacteristic
28C22×#10621873C2211yescharacteristic, complemented
29C22×D344C2211yescharacteristic
30#14583634—22no—
31#14583622—22no—
32#14583576—24no—
33#14583558—22no—
34#14583545—22no—
35#14583538—24no—
36#14583523C2214yescomplemented
37#14583475C2211yescharacteristic
38#14583474C2212yescomplemented
39#14583470C2211yescharacteristic
40#14583468C2211yescharacteristic
41#14583463C2211yescharacteristic
42#14583462C2212yescomplemented
43#14583448C2212yescomplemented
44#14583434C2214yescomplemented
45C2×#13063313C2211yescharacteristic
46C2×#13063313C2211yescharacteristic, complemented
47#124×D43C2212yescomplemented
48#14583376C2211yescharacteristic, complemented
49#14583373C2211yescharacteristic, complemented
50C4×#10621898C2211yescharacteristic
51#14583291C2212yescomplemented
52#14583286C2212yescomplemented
53#14583283C2214yescomplemented
54#14583283C2214yescomplemented
55#14583281C2212yescomplemented
56#14583281C2212yescomplemented
57#14583261C2214yescomplemented
58#14583256C2214yescomplemented
59#14583124C2214yescomplemented
60#14583120C2214yescomplemented
61#14583117C2214yescomplemented
62#14583113C2214yescomplemented
63#14583108C2214yescomplemented
64#14583103C2214yescomplemented
65#14583098C2214yescomplemented
66#14583093C2214yescomplemented
67#14583064C2214yescomplemented
68#14583062C2214yescomplemented
69#14583056C2214yescomplemented
70#14583051C2214yescomplemented
71#14583047C2214yes—
72#14583045C2214yescomplemented
73#14583039C2214yescomplemented
74#14583034C2214yes—
75#14582958C2214yescomplemented
76#14582950C2214yescomplemented
77#14582925C2211yescharacteristic, complemented
78#14582925C2211yescharacteristic, complemented
79#14582907C2211yescharacteristic, complemented
80#14582907C2211yescharacteristic, complemented
81#14582903C2211yescharacteristic
82#14582903C2211yescharacteristic
83#14582865C2211yescharacteristic
84#14582865C2211yescharacteristic
85C4×#10621877C2211yescharacteristic, complemented
86C43×#533C2211yescharacteristic, complemented
87C43×#532C2211yescharacteristic
88C43×#488C2212yescomplemented
89C43×#488C2212yescomplemented
90C43×#487C2212yescomplemented
91C43×#486C2212yescomplemented
92C43×#416C2211yescharacteristic
93C43×#416C2211yescharacteristic
94C43×#416C2211yescharacteristic, complemented
95C43×#416C2211yescharacteristic, complemented
96C2×C4×C8×C43C2211yescharacteristic, complemented
97#13063372—42no—
98#13063372—42no—
99#13063371—42no—
100#13063371—42no—
101C2×#10621902C2312yes—
102C2×#10621898—21no—
103C2×#10621898—21no—
104C2×#10621898C2311yescharacteristic
105C2×#10621900—22no—
106C2×#10621900C2312yes—
107C22×Dic86—21no—
108C22×Dic86C2311yescharacteristic
109C22×Dic86C2311yescharacteristic
110C2×Q8×D43C2312yes—
111C22×D172—21no—
112C22×D172C2311yescharacteristic
113C22×D172C2311yescharacteristic
114C2×D4×D43—22no—
115C2×D4×D43C2312yes—
116#13063355—42no—
117#13063355—42no—
118#13063350—42no—
119#13063350—42no—
120C2×Dic172—42no—
121C2×Dic172C2314yes—
122C2×#10621885C2312yes—
123C2×#10621885C2312yes—
124C2×#10621873—42no—
125C2×#10621873—42no—
126C2×#10621873C2314yes—
127C2×#10621873C2314yes—
128C2×#10621883C2312yes—
129C2×#10621883C2312yes—
130C2×#10621884C2312yes—
131C2×#10621884C2312yes—
132C2×D344—42no—
133C2×D344C2314yes—
134C2×#10621882C2312yes—
135C2×#10621882C2312yes—
136C2×#10621877C2311yescharacteristic
137C2×#10621877C2311yescharacteristic
138#13063325—21no—
139#13063323C2312yes—
140#13063322—21no—
141#13063321C2312yes—
142#13063320—24no—
143#13063320—24no—
144#13063314—24no—
145#13063314C2312yes—
146#13063313—21no—
147#13063313—21no—
148#13063313—22no—
149#13063313—22no—
150#13063313C2312yes—
151#13063313C2312yes—
152#13063313C2312yes—
153#13063313C2312yes—
154#13063312C2312yes—
155#13063311—24no—
156#13063310—24no—
157#13063310—24no—
158#13063310—24no—
159#13063309—22no—
160#13063306—22no—
161#13063305C2314yes—
162#13063304—22no—
163#13063303—24no—
164#13063301—24no—
165#13063300C2314yes—
166#13063299—22no—
167#13063298—24no—
168#13063297—24no—
169#13063295—22no—
170#13063293—22no—
171#13063293—24no—
172C4×Dic86—22no—
173C4×Dic86D412yes—
174#13063290C2314yes—
175C4×D172—22no—
176C4×D172D412yes—
177#13063287—24no—
178#13063287C2314yes—
179C4×C22⋊D43D414yes—
180(C22⋊D43)⋊C4—24no—
181#13063284C2311yescharacteristic
182#13063283—24no—
183#13063282C2312yes—
184#13063281—22no—
185C2×(C2×D43)⋊C4—22no—
186C2×(C2×D43)⋊C4—22no—
187C22⋊C4×D43—24no—
188C22⋊C4×D43—22no—
189C42×D43C2312yes—
190Dic43⋊C8C2314yes—
191Dic43⋊C8C2314yes—
192#13063248C2314yes—
193#13063248C2314yes—
194#13063245C2314yes—
195#13063245C2314yes—
196(C2×D43)⋊C8C2314yes—
197(C2×D43)⋊C8C2314yes—
198#13063236C2312yes—
199C4×C43⋊C8C2312yes—
200C2×#41×C43C2311yescharacteristic
201C2×#41×C43C2311yescharacteristic
202C22×C8×C43C2311yescharacteristic
203C22×C8×C43C2311yescharacteristic
204C4⋊Q8×C43C2311yescharacteristic
205C4⋊Q8×C43C2312yes—
206#127×C43C2311yescharacteristic
207#125×C43C2312yes—
208#124×C43C2311yescharacteristic
209#124×C43C2311yescharacteristic
210C22⋊Q8×C43—22no—
211#121×C43—22no—
212C4×Q8×C43—22no—
213C4×D4×C43—22no—
214#117×C43C2311yescharacteristic
215#117×C43C2311yescharacteristic
216C2×C42×C43C2311yescharacteristic
217#103×C43C2312yes—
218#103×C43C2312yes—
219#103×C43C2312yes—
220#103×C43C2312yes—
221#102×C43C2312yes—
222#102×C43C2312yes—
223#102×C43C2312yes—
224#102×C43C2312yes—
225C4×C8×C43C2312yes—
226C4×C8×C43C2312yes—
227C23×D43—21no—
228C23×D43—21no—
229C23×D43—22no—
230#41×C43—22no—
231#41×C43—22no—
232#41×C43—22no—
233#41×C43—22no—
234C2×Q8×C43—22no—
235C2×Q8×C43C2411yescharacteristic
236C2×Q8×C43C2411yescharacteristic
237C2×D4×C43—22no—
238C2×D4×C43—21no—
239C2×D4×C43—21no—
240C2×D4×C43C2411yescharacteristic
241C2×D4×C43C2411yescharacteristic
242C22×C4×C43—21no—
243C22×C4×C43—21no—
244C22×C4×C43C2×D412yes—
245C22×C4×C43C2411yescharacteristic
246C2×C22⋊D43—22no—
247C2×C22⋊D43—24no—
248C2×C22⋊D43—22no—
249C2×C22⋊D43C2×D412yes—
250C22×Dic43—22no—
251C22×Dic43—21no—
252C22×Dic43—21no—
253#10621902—42no—
254#10621902—42no—
255Q8×D43—42no—
256Q8×D43—42no—
257#10621900—42no—
258#10621900—42no—
259#10621900—48no—
260D4×D43—42no—
261D4×D43—42no—
262D4×D43—48no—
263#10621898—22no—
264#10621898—22no—
265#10621898—44no—
266#10621898—44no—
267C2×D172—21no—
268C2×D172—21no—
269C2×D172—22no—
270C2×D172—24no—
271C2×D172—22no—
272C2×D172—22no—
273C2×D172—22no—
274C2×D172—22no—
275C2×D172—44no—
276C2×D172C2×D411yescharacteristic
277C2×D172C2412yes—
278C2×D172C2412yes—
279C2×C4×D43—22no—
280C2×C4×D43—24no—
281C2×C4×D43—22no—
282C2×C4×D43C2×D414yes—
283C2×C4×D43C2412yes—
284C2×Dic86—22no—
285C2×Dic86—22no—
286C2×Dic86—22no—
287C2×Dic86—22no—
288C2×Dic86—21no—
289C2×Dic86—21no—
290C2×Dic86—22no—
291C2×Dic86—44no—
292C2×Dic86C2×D411yescharacteristic
293C2×Dic86C2412yes—
294C2×Dic86C2412yes—
295C2×C8×C43—22no—
296C2×C8×C43—22no—
297C2×C8×C43C2412yes—
298C2×C8×C43C2412yes—
299C4⋊C4×C43—22no—
300C4⋊C4×C43—22no—
301C4⋊C4×C43—22no—
302C4⋊C4×C43—22no—
303C4⋊C4×C43C2412yes—
304C4⋊C4×C43C2412yes—
305C22⋊C4×C43—22no—
306C22⋊C4×C43—22no—
307C22⋊C4×C43—21no—
308C22⋊C4×C43—21no—
309C42×C43—21no—
310C42×C43—21no—
311C42×C43C2×D412yes—
312C42×C43C2411yescharacteristic
313C42×C43C2411yescharacteristic
314C22⋊Dic43—24no—
315C22⋊Dic43C2×D412yes—
316#10621885—42no—
317#10621885—42no—
318#10621884—42no—
319#10621884—42no—
320#10621883—42no—
321#10621883—42no—
322#10621882—42no—
323#10621882—42no—
324(C2×D43)⋊C4—24no—
325(C2×D43)⋊C4—24no—
326(C2×D43)⋊C4—24no—
327(C2×D43)⋊C4—24no—
328(C2×D43)⋊C4—24no—
329(C2×D43)⋊C4—24no—
330(C2×D43)⋊C4—24no—
331(C2×D43)⋊C4—24no—
332(C2×D43)⋊C4C2×D414yes—
333C4⋊Dic43—24no—
334C4⋊Dic43C2×D412yes—
335Dic43⋊C4—24no—
336Dic43⋊C4—24no—
337Dic43⋊C4C2×D414yes—
338C4×Dic43—24no—
339C4×Dic43C2×D414yes—
340C4×Dic43C2412yes—
341#10621877—22no—
342#10621877—22no—
343C2×C43⋊C8C2412yes—
344C2×C43⋊C8C2412yes—
345Dic172—44no—
346D344—44no—
347#10621873—44no—
348#10621873—44no—
349C23×C43—21no—
350C23×C43—21no—
351C23×C43C22×D411yescharacteristic
352C22×D43—22no—
353C22×D43—22no—
354C22×D43—44no—
355C22×D43—42no—
356C22×D43—42no—
357C22×D43—84no—
358C22×D43—82no—
359C22×D43—82no—
360C22×D43C22×D412yes—
361Q8×C43—21no—
362Q8×C43—21no—
363Q8×C43—21no—
364Q8×C43—21no—
365Q8×C43—82no—
366D4×C43—21no—
367D4×C43—21no—
368D4×C43—21no—
369D4×C43—21no—
370D4×C43—42no—
371D4×C43—42no—
372D4×C43—82no—
373C2×C4×C43—22no—
374C2×C4×C43—21no—
375C2×C4×C43—22no—
376C2×C4×C43—21no—
377C2×C4×C43—42no—
378C2×C4×C43—42no—
379C2×C4×C43—42no—
380C2×C4×C43C22×D412yes—
381C2×C4×C43C22×D412yes—
382C2×C4×C43C22×D411yescharacteristic
383C2×C4×C43H(5,𝔽2)12yes—
384C2×C4×C43H(5,𝔽2)12yes—
385C2×C4×C43C2511yescharacteristic
386C22⋊D43—24no—
387C22⋊D43—44no—
388C22⋊D43—44no—
389C22⋊D43—84no—
390C2×Dic43—22no—
391C2×Dic43—22no—
392C2×Dic43—44no—
393C2×Dic43—42no—
394C2×Dic43—42no—
395C2×Dic43C22×D414yes—
396C2×Dic43C22×D412yes—
397D172—22no—
398D172—22no—
399D172—22no—
400D172—22no—
401D172—22no—
402D172—44no—
403D172—42no—
404D172—42no—
405D172—84no—
406C4×D43—22no—
407C4×D43—22no—
408C4×D43—44no—
409C4×D43—44no—
410C4×D43—44no—
411C4×D43—84no—
412Dic86—22no—
413Dic86—22no—
414Dic86—22no—
415Dic86—22no—
416Dic86—22no—
417Dic86—44no—
418Dic86—42no—
419Dic86—42no—
420C8×C43—22no—
421C8×C43—22no—
422C43⋊C8—22no—
423C43⋊C8—22no—
424#60819—431nomaximal, Sylow
425C22×C43—22no—
426C22×C43—42no—
427C22×C43—42no—
428C22×C43—41no—
429C22×C43—41no—
430C22×C43#53512yes—
431C22×C43C23×D411yescharacteristic
432C2×D43—24no—
433C2×D43—22no—
434C2×D43—44no—
435C2×D43—44no—
436C2×D43—42no—
437C2×D43—42no—
438C2×D43—164no—
439C2×D43—162no—
440C2×D43—162no—
441C4×C43—22no—
442C4×C43—22no—
443C4×C43—42no—
444C4×C43—42no—
445C4×C43—41no—
446C4×C43—41no—
447C4×C43#53512yes—
448C4×C43C2×H(5,𝔽2)11yescharacteristic
449C4×C43C2×H(5,𝔽2)11yescharacteristic
450Dic43—24no—
451Dic43—22no—
452Dic43—42no—
453Dic43—42no—
454#3510—431no—
455#3500—431no—
456#3225—434no—
457#3224—434no—
458#3212—434no—
459#3211—434no—
460#3153—431no—
461C2×#495—431no—
462#3140—431no—
463#3131D4311yescharacteristic, complemented
464#3044—431no—
465#3043—431no—
466#3042—431no—
467#3041—431no—
468#3011—431no—
469#3010—431no—
470#3009—431no—
471#3008—431no—
472#2922—431no—
473C2×C43—22no—
474C2×C43—81no—
475C2×C43—81no—
476C2×C43C2×#53511yescharacteristic
477C2×C43#358412yes—
478D43—42no—
479D43—82no—
480D43—82no—
481C2×2−1+4—431no—
482C2×H(5,𝔽2)—431no—
483C2×#137—431no—
484C2×#137—431no—
485C2×AGL(1,ℤ/8)—431no—
486C2×AGL(1,ℤ/8)—431no—
487C22×Q16—431no—
488C22×SD16—431no—
489C22×SD16—431no—
490C22×D8—431no—
491#559—862no—
492#556—862no—
493#551—864no—
494#548—862no—
495#546—862no—
496#546—864no—
497#542—434no—
498#536—431no—
499#536—432no—
500#536—431no—
501#535—431no—
502#535—432no—
503#535—431no—
504#533C2×D4311yescharacteristic, complemented
505#532—432no—
506#532C2×D4311yescharacteristic
507#529—434no—
508C2×#124—432no—
509C2×#124—431no—
510C2×#124—431no—
511#519—431no—
512#518—431no—
513C4×#41—431no—
514#497—432no—
515#496—432no—
516#495—432no—
517#495—432no—
518#495—434no—
519#495—434no—
520#489—434no—
521#488—434no—
522#488C2×D4312yescomplemented
523#488C2×D4312yescomplemented
524#487C2×D4312yescomplemented
525#486C2×D4312yescomplemented
526#464—434no—
527#464—434no—
528#463—434no—
529#463—434no—
530#462—434no—
531#461—434no—
532#460—434no—
533#459—434no—
534#452—434no—
535#452—434no—
536#451—434no—
537#450—434no—
538#449—434no—
539#449—434no—
540#448—434no—
541#447—434no—
542#433—434no—
543#431—434no—
544#424—431no—
545#424—431no—
546#419—431no—
547#419—431no—
548#418—431no—
549#418—431no—
550#416C2×D4311yescharacteristic
551#416C2×D4311yescharacteristic
552#416C2×D4311yescharacteristic, complemented
553#416C2×D4311yescharacteristic, complemented
554#408—431no—
555#408—431no—
556C4×M16—431no—
557C2×C4×C8C2×D4311yescharacteristic, complemented
558C43#6081911yescharacteristic, complemented, Sylow
5592−1+4—1722no—
5602−1+4—1722no—
561H(5,𝔽2)—1722no—
562H(5,𝔽2)—1722no—
563C2×#41—431no—
564C2×#41—432no—
565C2×#41—432no—
566C2×#41—861no—
567C2×#41—861no—
568C2×#41—862no—
569C2×#41C22×D4311yescharacteristic
570C2×#41C22×D4311yescharacteristic
571C22×Q8—432no—
572C22×Q8—431no—
573C22×Q8—431no—
574C22×Q8—861no—
575C22×D4—432no—
576C22×D4—431no—
577C22×D4—431no—
578C22×D4—861no—
579C22×D4—862no—
580#137—1722no—
581#137—1722no—
582AGL(1,ℤ/8)—1722no—
583AGL(1,ℤ/8)—1722no—
584C2×Q16—432no—
585C2×Q16—432no—
586C2×Q16—434no—
587C2×Q16—1722no—
588C2×SD16—432no—
589C2×SD16—432no—
590C2×SD16—432no—
591C2×SD16—432no—
592C2×SD16—434no—
593C2×SD16—434no—
594C2×SD16—1722no—
595C2×SD16—1722no—
596C2×D8—432no—
597C2×D8—432no—
598C2×D8—434no—
599C2×D8—1722no—
600C2×M16—431no—
601C2×M16—431no—
602C22×C8C22×D4311yescharacteristic
603C22×C8C22×D4311yescharacteristic
604C4⋊Q8—432no—
605C4⋊Q8—861no—
606C4⋊Q8C22×D4311yescharacteristic
607C4⋊Q8C22×D4312yes—
608#127—432no—
609#127—861no—
610#127C22×D4311yescharacteristic
611#126—864no—
612#126—864no—
613#125C22×D4312yes—
614#124—432no—
615#124—432no—
616#124—432no—
617#124—432no—
618#124—432no—
619#124—432no—
620#124—861no—
621#124—861no—
622#124—864no—
623#124—864no—
624#124—862no—
625#124—862no—
626#124C22×D4311yescharacteristic
627#124C22×D4311yescharacteristic
628#123—862no—
629#123—864no—
630#123—864no—
631#123—862no—
632#123—864no—
633C22⋊Q8—22no—
634C22⋊Q8—434no—
635C22⋊Q8—864no—
636C22⋊Q8—862no—
637C22⋊Q8—864no—
638#121—22no—
639#121—434no—
640#121—864no—
641#121—862no—
642#121—864no—
643#120—862no—
644#120—862no—
645#120—864no—
646C4×Q8—22no—
647C4×Q8—432no—
648C4×Q8—434no—
649C4×Q8—862no—
650C4×D4—22no—
651C4×D4—434no—
652C4×D4—434no—
653C4×D4—432no—
654C4×D4—862no—
655C4×D4—864no—
656C4×D4—864no—
657#117—431no—
658#117—432no—
659#117—864no—
660#117—862no—
661#117C22×D4311yescharacteristic
662#117C22×D4311yescharacteristic
663C2×C22⋊C4—862no—
664C2×C22⋊C4—864no—
665C2×C22⋊C4—862no—
666C2×C22⋊C4—862no—
667C2×C42—432no—
668C2×C42C22×D4311yescharacteristic
669C4⋊C8—434no—
670C4⋊C8—434no—
671#103—434no—
672#103—434no—
673#103C22×D4312yes—
674#103C22×D4312yes—
675#103C22×D4312yes—
676#103C22×D4312yes—
677#102—434no—
678#102—434no—
679#102C22×D4312yes—
680#102C22×D4312yes—
681#102C22×D4312yes—
682#102C22×D4312yes—
683C22⋊C8—434no—
684C22⋊C8—434no—
685#97—432no—
686C4×C8—432no—
687C4×C8C22×D4312yes—
688C4×C8C22×D4312yes—
689C24—862no—
690C24—861no—
691C24—861no—
692#41—22no—
693#41—22no—
694#41—22no—
695#41—22no—
696#41—862no—
697#41—862no—
698#41—1724no—
699#41—1724no—
700#41—1722no—
701#41—1722no—
702#41—1722no—
703#41—1722no—
704#41—1728no—
705C2×Q8—22no—
706C2×Q8—431no—
707C2×Q8—432no—
708C2×Q8—432no—
709C2×Q8—862no—
710C2×Q8—861no—
711C2×Q8—861no—
712C2×Q8—862no—
713C2×Q8—862no—
714C2×Q8—862no—
715C2×Q8—862no—
716C2×Q8—1724no—
717C2×Q8—1722no—
718C2×Q8—1722no—
719C2×Q8C23×D4311yescharacteristic
720C2×Q8C23×D4311yescharacteristic
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—22no—
724C2×D4—432no—
725C2×D4—431no—
726C2×D4—432no—
727C2×D4—432no—
728C2×D4—864no—
729C2×D4—862no—
730C2×D4—864no—
731C2×D4—862no—
732C2×D4—862no—
733C2×D4—861no—
734C2×D4—861no—
735C2×D4—862no—
736C2×D4—862no—
737C2×D4—862no—
738C2×D4—862no—
739C2×D4—1724no—
740C2×D4—1722no—
741C2×D4—1722no—
742C2×D4—1728no—
743C2×D4C23×D4311yescharacteristic
744C2×D4C23×D4311yescharacteristic
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—432no—
748C22×C4—434no—
749C22×C4—864no—
750C22×C4—862no—
751C22×C4—862no—
752C22×C4—862no—
753C22×C4—861no—
754C22×C4—861no—
755C22×C4D4×D4312yes—
756C22×C4C23×D4311yescharacteristic
757Q16—1724no—
758Q16—1722no—
759Q16—1722no—
760SD16—1724no—
761SD16—1724no—
762SD16—1722no—
763SD16—1722no—
764SD16—1722no—
765SD16—1722no—
766D8—1724no—
767D8—1722no—
768D8—1722no—
769M16—862no—
770M16—862no—
771C2×C8—22no—
772C2×C8—22no—
773C2×C8—432no—
774C2×C8—432no—
775C2×C8C23×D4312yes—
776C2×C8C23×D4312yes—
777C4⋊C4—22no—
778C4⋊C4—22no—
779C4⋊C4—22no—
780C4⋊C4—22no—
781C4⋊C4—432no—
782C4⋊C4—434no—
783C4⋊C4—864no—
784C4⋊C4—864no—
785C4⋊C4—864no—
786C4⋊C4C23×D4312yes—
787C4⋊C4C23×D4312yes—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—22no—
791C22⋊C4—22no—
792C22⋊C4—432no—
793C22⋊C4—434no—
794C22⋊C4—864no—
795C22⋊C4—864no—
796C22⋊C4—864no—
797C22⋊C4—864no—
798C22⋊C4—864no—
799C22⋊C4—864no—
800C22⋊C4—864no—
801C22⋊C4—864no—
802C22⋊C4—864no—
803C42—21no—
804C42—21no—
805C42—434no—
806C42—432no—
807C42—864no—
808C42D4×D4312yes—
809C42C23×D4311yescharacteristic
810C42C23×D4311yescharacteristic
811C23—21no—
812C23—21no—
813C23—432no—
814C23—862no—
815C23—862no—
816C23—3442no—
817C23—3442no—
818C23—3444no—
819C23—1724no—
820C23—1722no—
821C23—1722no—
822C23C2×D4×D4311yescharacteristic
823Q8—21no—
824Q8—21no—
825Q8—21no—
826Q8—21no—
827Q8—82no—
828Q8—862no—
829Q8—862no—
830Q8—862no—
831Q8—862no—
832Q8—862no—
833Q8—1724no—
834Q8—1722no—
835Q8—1722no—
836D4—21no—
837D4—21no—
838D4—21no—
839D4—21no—
840D4—42no—
841D4—42no—
842D4—82no—
843D4—864no—
844D4—862no—
845D4—862no—
846D4—862no—
847D4—862no—
848D4—862no—
849D4—3444no—
850D4—3444no—
851D4—1724no—
852D4—1724no—
853D4—1724no—
854D4—1722no—
855D4—1722no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—434no—
864C2×C4—432no—
865C2×C4—862no—
866C2×C4—862no—
867C2×C4—862no—
868C2×C4—862no—
869C2×C4—3444no—
870C2×C4—1724no—
871C2×C4—1724no—
872C2×C4—1724no—
873C2×C4—1724no—
874C2×C4—1722no—
875C2×C4—1722no—
876C2×C4C2×D4×D4312yes—
877C2×C4C2×D4×D4312yes—
878C2×C4C2×D4×D4311yescharacteristic
879C2×C4#1306337112yes—
880C2×C4#1306337112yes—
881C2×C4C24×D4311yescharacteristic
882C8—22no—
883C8—22no—
884C8—862no—
885C8—862no—
886C22—22no—
887C22—42no—
888C22—42no—
889C22—41no—
890C22—41no—
891C22—864no—
892C22—862no—
893C22—1724no—
894C22—1724no—
895C22—1722no—
896C22—1722no—
897C22—6882no—
898C22—6882no—
899C22—6884no—
900C22#1458346712yes—
901C22C22×D4×D4311yescharacteristic
902C4—22no—
903C4—22no—
904C4—42no—
905C4—42no—
906C4—41no—
907C4—41no—
908C4—864no—
909C4—862no—
910C4—1722no—
911C4—1722no—
912C4#1458346712yes—
913C4C2×#1306337111yescharacteristic
914C4C2×#1306337111yescharacteristic
915C2—22no—
916C2—81no—
917C2—81no—
918C2—3442no—
919C2—3442no—
920C2—1722no—
921C2C2×#1458346711yescharacteristic
922C2#1914936412yes—
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3131C2
socleC22×C43C23×D4
hypercenter#3131D43
hypocenterC43#60819
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3131

Complements

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

NH ≅ G/Ntype
1. #19148493C2semidirect
2. #19148382C2semidirect
3. #19145707C2semidirect
4. #19145692C2semidirect
5. #19145572C2semidirect
6. #19145561C2semidirect
7. #19145063C2semidirect
8. C2×#14583283C2semidirect
9. #19144984C2semidirect
10. #19144128C2semidirect
11. #19144119C2semidirect
12. #19144110C2semidirect
13. #19144101C2semidirect
14. #19143893C2semidirect
15. #19143884C2semidirect
16. #19143875C2semidirect
17. #19143866C2semidirect
18. #19143237C2semidirect
19. C43×#3131C2semidirect
23. C2×#13063355C22semidirect
25. C2×#13063350C22semidirect
26. C22×Dic172C22semidirect
28. C22×#10621873C22semidirect
36. #14583523C22semidirect
38. #14583474C22semidirect
42. #14583462C22semidirect
43. #14583448C22semidirect
44. #14583434C22semidirect
46. C2×#13063313C22semidirect
47. #124×D43C22semidirect
48. #14583376C22semidirect
49. #14583373C22semidirect
51. #14583291C22semidirect
52. #14583286C22semidirect
53. #14583283C22semidirect
54. #14583283C22semidirect
55. #14583281C22semidirect
56. #14583281C22semidirect
57. #14583261C22semidirect
58. #14583256C22semidirect
59. #14583124C22semidirect
60. #14583120C22semidirect
61. #14583117C22semidirect
62. #14583113C22semidirect
63. #14583108C22semidirect
64. #14583103C22semidirect
65. #14583098C22semidirect
66. #14583093C22semidirect
67. #14583064C22semidirect
68. #14583062C22semidirect
69. #14583056C22semidirect
70. #14583051C22semidirect
72. #14583045C22semidirect
73. #14583039C22semidirect
75. #14582958C22semidirect
76. #14582950C22semidirect
77. #14582925C22semidirect
78. #14582925C22semidirect
79. #14582907C22semidirect
80. #14582907C22semidirect
85. C4×#10621877C22semidirect
86. C43×#533C22semidirect
88. C43×#488C22semidirect
89. C43×#488C22semidirect
90. C43×#487C22semidirect
91. C43×#486C22semidirect
94. C43×#416C22semidirect
95. C43×#416C22semidirect
96. C2×C4×C8×C43C22semidirect
463. #3131D43semidirect
504. #533C2×D43semidirect
522. #488C2×D43semidirect
523. #488C2×D43semidirect
524. #487C2×D43semidirect
525. #486C2×D43semidirect
552. #416C2×D43semidirect
553. #416C2×D43semidirect
557. C2×C4×C8C2×D43semidirect
558. C43#60819semidirect

Maximal subgroups

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

subgroupindex
#191484932
#191483822
#191457072
#191456922
#191455722
#191455612
#191450632
C2×#145832832
#191449842
#191441282
#191441192
#191441102
#191441012
#191438932
#191438842
#191438752
#191438662
#191432372
C43×#31312
#6081943