Finite Group Databasebeta

← #577×Dic43 #25960833

Subgroups — #577×Dic43 #25960833

Order 11008.

2742 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
12−1+4×Dic43C211yesmaximal, characteristic, complemented
2H(5,𝔽2)×Dic43C211yesmaximal, characteristic, complemented
3#19143479C213yesmaximal, complemented
4#19143455C213yesmaximal, complemented
5#19143439C213yesmaximal, complemented
6#19143428C213yesmaximal, complemented
7#137×Dic43C213yesmaximal, complemented
8AGL(1,ℤ/8)×Dic43C213yesmaximal, complemented
9#135×Dic43C213yesmaximal, complemented
10C2×SD16×Dic43C213yesmaximal, complemented
11#19143190C211yesmaximal, characteristic, complemented
12#19143128C211yesmaximal, characteristic, complemented
13#19143121C211yesmaximal, characteristic, complemented
14#131×Dic43C211yesmaximal, characteristic, complemented
15C2×C43×#577C211yesmaximal, characteristic
16C2×#13063332C2211yescharacteristic
17#14583382—21no—
18#14583382—23no—
19#14583382C2213yes—
20#14583382C2211yescharacteristic
21#14583382C2211yescharacteristic
22#14583382C2213yescomplemented
23#14583377—21no—
24#14583377C2213yescomplemented
25#14583374—23no—
26#14583374C2213yes—
27#41×Dic43—21no—
28#41×Dic43—23no—
29#41×Dic43C2213yes—
30#41×Dic43C2211yescharacteristic
31#41×Dic43C2213yescomplemented
32C2×Q8×Dic43—21no—
33C2×Q8×Dic43C2213yescomplemented
34C2×D4×Dic43—23no—
35C2×D4×Dic43C2213yes—
36#14583011C2216yescomplemented
37#14583006C2216yescomplemented
38#14583000C2216yescomplemented
39#14583000C2216yescomplemented
40Q16×Dic43C2213yescomplemented
41Q16×Dic43C2213yescomplemented
42SD16×Dic43C2216yescomplemented
43SD16×Dic43C2213yescomplemented
44SD16×Dic43C2216yescomplemented
45SD16×Dic43C2213yescomplemented
46SD16×Dic43C2213yescomplemented
47SD16×Dic43C2216yescomplemented
48SD16×Dic43C2211yescharacteristic, complemented
49D8×Dic43C2213yescomplemented
50D8×Dic43C2213yescomplemented
51#14582941C2213yescomplemented
52#14582941C2213yescomplemented
53#14582937C2213yescomplemented
54C2×#13063257C2213yescomplemented
55#14582908C2213yescomplemented
56#14582904C2213yes—
57#14582900C2213yes—
58#14582900C2213yescomplemented
59#14582895C2213yes—
60#14582895C2213yescomplemented
61C2×#13063249C2213yescomplemented
62C2×#13063246C2213yes—
63#14582857C2213yescomplemented
64#14582854C2213yescomplemented
65M16×Dic43C2213yescomplemented
66C2×C8×Dic43C2213yescomplemented
67C2×2−1+4×C43C2211yescharacteristic
68C2×H(5,𝔽2)×C43C2211yescharacteristic
69C43×#577C4116yescomplemented
70C2×#137×C43C2213yes—
71C2×AGL(1,ℤ/8)×C43C2213yes—
72C2×#135×C43C2213yes—
73C22×SD16×C43C2213yes—
74C2×#131×C43C2211yescharacteristic
75C23×Dic43—23no—
76#13063332—24no—
77C2×#10621877C2313yes—
78C22×C43⋊C8C2313yes—
79Q8×Dic43—21no—
80Q8×Dic43—21no—
81Q8×Dic43—23no—
82Q8×Dic43—23no—
83Q8×Dic43—23no—
84Q8×Dic43—23no—
85Q8×Dic43D411yescharacteristic
86Q8×Dic43D411yescharacteristic
87Q8×Dic43C2313yes—
88Q8×Dic43C2316yes—
89Q8×Dic43C2311yescharacteristic
90Q8×Dic43C2313yes—
91Q8×Dic43C2313yes—
92D4×Dic43—23no—
93D4×Dic43—23no—
94D4×Dic43—23no—
95D4×Dic43—23no—
96D4×Dic43—23no—
97D4×Dic43—23no—
98D4×Dic43—26no—
99D4×Dic43—26no—
100D4×Dic43—23no—
101D4×Dic43—23no—
102D4×Dic43—23no—
103D4×Dic43—23no—
104D4×Dic43D413yes—
105D4×Dic43D413yes—
106D4×Dic43C2313yes—
107D4×Dic43C2316yes—
108D4×Dic43C2313yes—
109D4×Dic43C2311yescharacteristic
110D4×Dic43C2313yes—
111#13063284—26no—
112#13063284—23no—
113#13063284—23no—
114#13063284—23no—
115#13063284—23no—
116#13063284C2313yes—
117#13063284C2313yes—
118#13063284C2313yes—
119C2×C4⋊Dic43—23no—
120C2×C4⋊Dic43—23no—
121C2×C4⋊Dic43—23no—
122C2×C4⋊Dic43C2313yes—
123C2×C4⋊Dic43C2313yes—
124C2×C22⋊Dic43—23no—
125C2×C22⋊Dic43—26no—
126C2×C4×Dic43—23no—
127C2×C4×Dic43—23no—
128C2×C4×Dic43—23no—
129C2×C4×Dic43C2313yes—
130#13063259C2313yes—
131#13063259C2313yes—
132#13063257C2313yes—
133#13063257C2316yes—
134#13063257C2311yescharacteristic
135#13063249C2313yes—
136#13063249C2316yes—
137#13063249C2311yescharacteristic
138#13063249C2313yes—
139#13063249C2313yes—
140#13063246C2313yes—
141#13063246C2316yes—
142#13063246C2313yes—
143#13063246C2311yescharacteristic
144#13063246C2313yes—
145#13063235C2316yes—
146C8×Dic43C2311yescharacteristic
147C8×Dic43C2313yes—
148C8×Dic43C2313yes—
149C8×Dic43C2313yes—
1502−1+4×C43—24no—
1512−1+4×C43C2×C418yescomplemented
152H(5,𝔽2)×C43—24no—
153H(5,𝔽2)×C43C2×C418yescomplemented
154C2×#41×C43—21no—
155C2×#41×C43—23no—
156C2×#41×C43C2313yes—
157C2×#41×C43C2313yes—
158C2×#41×C43C2311yescharacteristic
159C22×Q8×C43—21no—
160C22×Q8×C43C2313yes—
161C22×D4×C43—23no—
162C22×D4×C43C2313yes—
163#137×C43C2×C4124yescomplemented
164AGL(1,ℤ/8)×C43C2×C4124yescomplemented
165#135×C43C2×C4124yescomplemented
166C2×Q16×C43C2313yes—
167C2×SD16×C43C2×C4124yescomplemented
168C2×SD16×C43C2313yes—
169C2×SD16×C43C2316yes—
170C2×SD16×C43C2311yescharacteristic
171C2×D8×C43C2313yes—
172#131×C43C2×C418yescomplemented
173C2×M16×C43C2313yes—
174C22×C8×C43C2313yes—
175C24×C43—23no—
176#41×C43—28no—
177#41×C43—224no—
178#41×C43—26no—
179#41×C43—26no—
180#41×C43C22×C4112yes—
181#41×C43C22×C414yes—
182#41×C43C22×C4112yescomplemented
183#41×C43#4114yes—
184C2×Q8×C43—28no—
185C2×Q8×C43—23no—
186C2×Q8×C43—26no—
187C2×Q8×C43C22×C4112yescomplemented
188C2×Q8×C43C2×D411yescharacteristic
189C2×Q8×C43C2413yes—
190C2×Q8×C43C2411yescharacteristic
191C2×D4×C43—224no—
192C2×D4×C43—23no—
193C2×D4×C43—26no—
194C2×D4×C43—23no—
195C2×D4×C43—23no—
196C2×D4×C43C22×C4112yes—
197C2×D4×C43C2×D413yes—
198C2×D4×C43C2411yescharacteristic
199C2×D4×C43C2413yes—
200C22×C4×C43—23no—
201C22×C4×C43—23no—
202C22×C4×C43—23no—
203C22×C4×C43C2413yes—
204C22×Dic43—21no—
205C22×Dic43—23no—
206C22×Dic43—23no—
207C22×Dic43—23no—
208C22×Dic43—26no—
209C22×Dic43—23no—
210C22×Dic43—23no—
211C22×Dic43—86no—
212C22×Dic43C2×D413yes—
213C22×Dic43C2×D413yes—
214Q16×C43C22×C4112yescomplemented
215SD16×C43C22×C4112yescomplemented
216SD16×C43C22×C4124yescomplemented
217SD16×C43C22×C414yescomplemented
218D8×C43C22×C4112yescomplemented
219M16×C43C22×C4112yescomplemented
220C2×C8×C43C22×C4112yescomplemented
221C2×C8×C43C2411yescharacteristic
222C2×C8×C43C2413yes—
223C22⋊Dic43—23no—
224C22⋊Dic43—26no—
225C22⋊Dic43—23no—
226C22⋊Dic43—21no—
227C22⋊Dic43—23no—
228C22⋊Dic43—23no—
229C22⋊Dic43—23no—
230C22⋊Dic43C2×D416yes—
231C4⋊Dic43—23no—
232C4⋊Dic43—23no—
233C4⋊Dic43—23no—
234C4⋊Dic43—26no—
235C4⋊Dic43—23no—
236C4⋊Dic43—21no—
237C4⋊Dic43—23no—
238C4⋊Dic43C2×D413yes—
239C4⋊Dic43C2×D413yes—
240C4⋊Dic43C2413yes—
241C4⋊Dic43C2411yescharacteristic
242C4⋊Dic43C2413yes—
243C4⋊Dic43C2411yescharacteristic
244C4×Dic43—23no—
245C4×Dic43—23no—
246C4×Dic43—21no—
247C4×Dic43—23no—
248C4×Dic43—23no—
249C4×Dic43—23no—
250C4×Dic43—26no—
251C4×Dic43C2×D413yes—
252C4×Dic43C2×D413yes—
253C4×Dic43C2411yescharacteristic
254C4×Dic43C2413yes—
255#10621877—26no—
256C2×C43⋊C8—26no—
257C2×C43⋊C8C2411yescharacteristic
258C2×C43⋊C8C2413yes—
259C23×C43—21no—
260C23×C43—23no—
261C23×C43—212no—
262C23×C43—83no—
263C23×C43—83no—
264C23×C43C22×D413yes—
265Q8×C43—212no—
266Q8×C43—23no—
267Q8×C43—21no—
268Q8×C43C4×D414yes—
269Q8×C43C23×C416yes—
270Q8×C43C23×C412yes—
271D4×C43—212no—
272D4×C43—212no—
273D4×C43—212no—
274D4×C43—23no—
275D4×C43—21no—
276D4×C43C4×D4112yes—
277D4×C43C23×C412yes—
278D4×C43C23×C416yes—
279C2×C4×C43—212no—
280C2×C4×C43—21no—
281C2×C4×C43—23no—
282C2×C4×C43—212no—
283C2×C4×C43—212no—
284C2×C4×C43C23×C416yes—
285C2×C4×C43C22×D413yes—
286C2×C4×C43C2×#4116yes—
287C2×C4×C43C2511yescharacteristic
288C2×Dic43—26no—
289C2×Dic43—21no—
290C2×Dic43—23no—
291C2×Dic43—21no—
292C2×Dic43—23no—
293C2×Dic43—43no—
294C2×Dic43—42no—
295C2×Dic43—46no—
296C2×Dic43—83no—
297C2×Dic43—83no—
298C2×Dic43—86no—
299C2×Dic43—83no—
300C2×Dic43—83no—
301C2×Dic43C22×D413yes—
302C2×Dic43C22×D413yes—
303C2×Dic43C22×D411yescharacteristic
304C2×Dic43C22×D411yescharacteristic
305C8×C43C23×C412yes—
306C8×C43C23×C416yes—
307C43⋊C8—21no—
308C43⋊C8—23no—
309C4×#577—431nomaximal, Sylow
310C22×C43—23no—
311C22×C43—23no—
312C22×C43—26no—
313C22×C43—22no—
314C22×C43—43no—
315C22×C43—41no—
316C22×C43—43no—
317C22×C43—41no—
318C22×C43—812no—
319C22×C43C2×C4×D416yes—
320C22×C43C23×D411yescharacteristic
321C4×C43—22no—
322C4×C43—26no—
323C4×C43C2×C4×D416yes—
324C4×C43C24×C411yescharacteristic
325C4×C43C22×#4111yescharacteristic
326Dic43—21no—
327Dic43—23no—
328Dic43—23no—
329Dic43—43no—
330Dic43—41no—
331Dic43—41no—
332Dic43—43no—
333Dic43#57712yesdirect product factor
334C2×#577D4311yescharacteristic
335C4×2−1+4—431no—
336C4×H(5,𝔽2)—431no—
337#2952—433no—
338#2949—433no—
339#2947—433no—
340#2946—433no—
341C4×#137—433no—
342C4×AGL(1,ℤ/8)—433no—
343C4×#135—433no—
344C2×C4×SD16—433no—
345#2912—431no—
346#2898—431no—
347#2897—431no—
348C4×#131—431no—
349C2×C43—26no—
350C2×C43—42no—
351C2×C43—46no—
352C2×C43C22×C4×D411yescharacteristic
353C2×C43C2×#57711yescharacteristic
354C2×C43#358411yescharacteristic
355C2×2−1+4C2×D4311yescharacteristic
356C2×H(5,𝔽2)C2×D4311yescharacteristic
357#577Dic43116yesdirect product factor
358C2×#137C2×D4313yes—
359C2×AGL(1,ℤ/8)C2×D4313yes—
360C2×#135C2×D4313yes—
361C22×SD16C2×D4313yes—
362C2×#131—431no—
363C2×#131C2×D4311yescharacteristic
364#520—431no—
365#520—431no—
366#520—433no—
367#520—433no—
368#520—863no—
369#520—861no—
370#519—433no—
371#519—861no—
372#518—433no—
373#518—863no—
374C4×#41—431no—
375C4×#41—433no—
376C4×#41—433no—
377C4×#41—863no—
378C4×#41—861no—
379C2×C4×Q8—433no—
380C2×C4×Q8—861no—
381C2×C4×D4—433no—
382C2×C4×D4—863no—
383#442—436no—
384#441—436no—
385#440—436no—
386#440—436no—
387C4×Q16—433no—
388C4×Q16—433no—
389C4×SD16—433no—
390C4×SD16—436no—
391C4×SD16—436no—
392C4×SD16—436no—
393C4×SD16—431no—
394C4×SD16—433no—
395C4×SD16—433no—
396C4×D8—433no—
397C4×D8—433no—
398#428—433no—
399#428—433no—
400#427—433no—
401C2×#106—433no—
402#419—433no—
403#418—433no—
404#417—433no—
405#417—433no—
406#416—433no—
407#416—433no—
408C2×#103—433no—
409C2×#102—433no—
410#405—433no—
411#405—433no—
412C4×M16—433no—
413C2×C4×C8—433no—
414C43C4×#57711yescharacteristic, complemented, Sylow
4152−1+4—24no—
4162−1+4C2×Dic4318yescomplemented
417H(5,𝔽2)—24no—
418H(5,𝔽2)C2×Dic4318yescomplemented
419C2×#41—21no—
420C2×#41—23no—
421C2×#41C22×D4313yes—
422C2×#41C22×D4313yes—
423C2×#41C22×D4311yescharacteristic
424C22×Q8—21no—
425C22×Q8C22×D4313yes—
426C22×D4—23no—
427C22×D4C22×D4313yes—
428C23×C4—863no—
429#137C2×Dic43124yescomplemented
430AGL(1,ℤ/8)C2×Dic43124yescomplemented
431#135C2×Dic43124yescomplemented
432C2×Q16C22×D4313yes—
433C2×SD16C2×Dic43124yescomplemented
434C2×SD16C22×D4313yes—
435C2×SD16C22×D4316yes—
436C2×SD16C22×D4311yescharacteristic
437C2×D8C22×D4313yes—
438#131—864no—
439#131C2×Dic4318yescomplemented
440C2×M16—433no—
441C2×M16C22×D4313yes—
442C22×C8—433no—
443C22×C8C22×D4313yes—
444C4×Q8—431no—
445C4×Q8—431no—
446C4×Q8—433no—
447C4×Q8—436no—
448C4×Q8—431no—
449C4×Q8—433no—
450C4×Q8—433no—
451C4×Q8—863no—
452C4×Q8—863no—
453C4×Q8—863no—
454C4×Q8—863no—
455C4×Q8—861no—
456C4×Q8—861no—
457C4×D4—433no—
458C4×D4—433no—
459C4×D4—433no—
460C4×D4—436no—
461C4×D4—431no—
462C4×D4—433no—
463C4×D4—433no—
464C4×D4—863no—
465C4×D4—863no—
466C4×D4—866no—
467C4×D4—866no—
468C4×D4—863no—
469C4×D4—863no—
470C4×D4—863no—
471C4×D4—863no—
472C4×D4—863no—
473C4×D4—863no—
474C4×D4—863no—
475C4×D4—863no—
476#117—433no—
477#117—433no—
478#117—433no—
479#117—863no—
480#117—863no—
481#117—866no—
482#117—863no—
483#117—863no—
484C2×C4⋊C4—433no—
485C2×C4⋊C4—433no—
486C2×C4⋊C4—863no—
487C2×C4⋊C4—863no—
488C2×C4⋊C4—863no—
489C2×C22⋊C4—866no—
490C2×C22⋊C4—863no—
491C2×C42—433no—
492C2×C42—863no—
493C2×C42—863no—
494C2×C42—863no—
495#107—433no—
496#107—433no—
497#106—433no—
498#106—436no—
499#106—431no—
500#103—433no—
501#103—436no—
502#103—431no—
503#103—433no—
504#103—433no—
505#102—433no—
506#102—436no—
507#102—431no—
508#102—433no—
509#102—433no—
510#97—436no—
511C4×C8—431no—
512C4×C8—433no—
513C4×C8—433no—
514C4×C8—433no—
515C24—23no—
516#41—28no—
517#41—224no—
518#41—26no—
519#41—26no—
520#41#1062190014yes—
521#41C22×Dic43112yes—
522#41C22×Dic4314yes—
523#41C22×Dic43112yescomplemented
524C2×Q8—28no—
525C2×Q8—23no—
526C2×Q8—26no—
527C2×Q8D4×D4311yescharacteristic
528C2×Q8C22×Dic43112yescomplemented
529C2×Q8C23×D4313yes—
530C2×Q8C23×D4311yescharacteristic
531C2×D4—23no—
532C2×D4—23no—
533C2×D4—224no—
534C2×D4—23no—
535C2×D4—26no—
536C2×D4D4×D4313yes—
537C2×D4C22×Dic43112yes—
538C2×D4C23×D4311yescharacteristic
539C2×D4C23×D4313yes—
540C22×C4—23no—
541C22×C4—23no—
542C22×C4—23no—
543C22×C4—433no—
544C22×C4—433no—
545C22×C4—863no—
546C22×C4—863no—
547C22×C4—866no—
548C22×C4—861no—
549C22×C4—863no—
550C22×C4—863no—
551C22×C4—863no—
552C22×C4—3446no—
553C22×C4C23×D4313yes—
554Q16C22×Dic43112yescomplemented
555SD16C22×Dic43112yescomplemented
556SD16C22×Dic43124yescomplemented
557SD16C22×Dic4314yescomplemented
558D8C22×Dic43112yescomplemented
559M16—866no—
560M16C22×Dic43112yescomplemented
561C2×C8—431no—
562C2×C8—433no—
563C2×C8—866no—
564C2×C8C22×Dic43112yescomplemented
565C2×C8C23×D4311yescharacteristic
566C2×C8C23×D4313yes—
567C4⋊C4—433no—
568C4⋊C4—433no—
569C4⋊C4—433no—
570C4⋊C4—431no—
571C4⋊C4—433no—
572C4⋊C4—431no—
573C4⋊C4—863no—
574C4⋊C4—863no—
575C4⋊C4—866no—
576C4⋊C4—861no—
577C4⋊C4—863no—
578C4⋊C4—863no—
579C4⋊C4—863no—
580C22⋊C4—436no—
581C22⋊C4—863no—
582C22⋊C4—863no—
583C22⋊C4—866no—
584C22⋊C4—861no—
585C22⋊C4—863no—
586C22⋊C4—863no—
587C22⋊C4—863no—
588C42—433no—
589C42—433no—
590C42—431no—
591C42—433no—
592C42—861no—
593C42—863no—
594C42—863no—
595C42—863no—
596C42—866no—
597C42—863no—
598C42—863no—
599C23—21no—
600C23—23no—
601C23—212no—
602C23—83no—
603C23—83no—
604C23C2×D4×D4313yes—
605Q8—212no—
606Q8—23no—
607Q8—21no—
608Q8D4×Dic4314yes—
609Q8C23×Dic4316yes—
610Q8C23×Dic4312yes—
611D4—212no—
612D4—212no—
613D4—212no—
614D4—23no—
615D4—21no—
616D4D4×Dic43112yes—
617D4C23×Dic4312yes—
618D4C23×Dic4316yes—
619C2×C4—212no—
620C2×C4—21no—
621C2×C4—23no—
622C2×C4—212no—
623C2×C4—212no—
624C2×C4—431no—
625C2×C4—431no—
626C2×C4—433no—
627C2×C4—433no—
628C2×C4—866no—
629C2×C4—861no—
630C2×C4—861no—
631C2×C4—863no—
632C2×C4—863no—
633C2×C4—3446no—
634C2×C4—3443no—
635C2×C4—3443no—
636C2×C4—3443no—
637C2×C4—3443no—
638C2×C4—1726no—
639C2×C4—1722no—
640C2×C4—1723no—
641C2×C4C23×Dic4316yes—
642C2×C4C2×D4×D4313yes—
643C2×C4C2×#1062190016yes—
644C2×C4C24×D4311yescharacteristic
645C8—861no—
646C8—863no—
647C8C23×Dic4312yes—
648C8C23×Dic4316yes—
649C22—23no—
650C22—23no—
651C22—22no—
652C22—26no—
653C22—43no—
654C22—41no—
655C22—41no—
656C22—43no—
657C22—812no—
658C22C2×D4×Dic4316yes—
659C22C22×D4×D4311yescharacteristic
660C4—22no—
661C4—26no—
662C4—432no—
663C4—863no—
664C4—863no—
665C4—861no—
666C4—1723no—
667C4—1721no—
668C4—1721no—
669C4—1723no—
670C4C2×D4×Dic4316yes—
671C4C24×Dic4311yescharacteristic
672C4C22×#1062190011yescharacteristic
673C2—26no—
674C2—46no—
675C2—42no—
676C2C22×D4×Dic4311yescharacteristic
677C2#577×D4311yescharacteristic
678C2#1914936711yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutatorC4×C43C24×C4
FrattiniC2×C4C24×D43
Fitting, prime radicalC2×C43×#577C2
socleC22×C43C23×D4
cosocleC2×C4×C43C25
hypercenterC2×#577D43
hypocenterC43C4×#577
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#577

Complements

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

NH ≅ G/Ntype
1. 2−1+4×Dic43C2semidirect
2. H(5,𝔽2)×Dic43C2semidirect
3. #19143479C2semidirect
4. #19143455C2semidirect
5. #19143439C2semidirect
6. #19143428C2semidirect
7. #137×Dic43C2semidirect
8. AGL(1,ℤ/8)×Dic43C2semidirect
9. #135×Dic43C2semidirect
10. C2×SD16×Dic43C2semidirect
11. #19143190C2semidirect
12. #19143128C2semidirect
13. #19143121C2semidirect
14. #131×Dic43C2semidirect
22. #14583382C22semidirect
24. #14583377C22semidirect
31. #41×Dic43C22semidirect
33. C2×Q8×Dic43C22semidirect
36. #14583011C22semidirect
37. #14583006C22semidirect
38. #14583000C22semidirect
39. #14583000C22semidirect
40. Q16×Dic43C22semidirect
41. Q16×Dic43C22semidirect
42. SD16×Dic43C22semidirect
43. SD16×Dic43C22semidirect
44. SD16×Dic43C22semidirect
45. SD16×Dic43C22semidirect
46. SD16×Dic43C22semidirect
47. SD16×Dic43C22semidirect
48. SD16×Dic43C22semidirect
49. D8×Dic43C22semidirect
50. D8×Dic43C22semidirect
51. #14582941C22semidirect
52. #14582941C22semidirect
53. #14582937C22semidirect
54. C2×#13063257C22semidirect
55. #14582908C22semidirect
58. #14582900C22semidirect
60. #14582895C22semidirect
61. C2×#13063249C22semidirect
63. #14582857C22semidirect
64. #14582854C22semidirect
65. M16×Dic43C22semidirect
66. C2×C8×Dic43C22semidirect
69. C43×#577C4semidirect
151. 2−1+4×C43C2×C4semidirect
153. H(5,𝔽2)×C43C2×C4semidirect
163. #137×C43C2×C4semidirect
164. AGL(1,ℤ/8)×C43C2×C4semidirect
165. #135×C43C2×C4semidirect
167. C2×SD16×C43C2×C4semidirect
172. #131×C43C2×C4semidirect
182. #41×C43C22×C4semidirect
187. C2×Q8×C43C22×C4semidirect
214. Q16×C43C22×C4semidirect
215. SD16×C43C22×C4semidirect
216. SD16×C43C22×C4semidirect
217. SD16×C43C22×C4semidirect
218. D8×C43C22×C4semidirect
219. M16×C43C22×C4semidirect
220. C2×C8×C43C22×C4semidirect
333. Dic43#577direct (N × H)
357. #577Dic43direct (N × H)
414. C43C4×#577semidirect
416. 2−1+4C2×Dic43semidirect
418. H(5,𝔽2)C2×Dic43semidirect
429. #137C2×Dic43semidirect
430. AGL(1,ℤ/8)C2×Dic43semidirect
431. #135C2×Dic43semidirect
433. C2×SD16C2×Dic43semidirect
439. #131C2×Dic43semidirect
523. #41C22×Dic43semidirect
528. C2×Q8C22×Dic43semidirect
554. Q16C22×Dic43semidirect
555. SD16C22×Dic43semidirect
556. SD16C22×Dic43semidirect
557. SD16C22×Dic43semidirect
558. D8C22×Dic43semidirect
560. M16C22×Dic43semidirect
564. C2×C8C22×Dic43semidirect

Maximal subgroups

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

subgroupindex
2−1+4×Dic432
H(5,𝔽2)×Dic432
#191434792
#191434552
#191434392
#191434282
#137×Dic432
AGL(1,ℤ/8)×Dic432
#135×Dic432
C2×SD16×Dic432
#191431902
#191431282
#191431212
#131×Dic432
C2×C43×#5772
C4×#57743