Finite Group Databasebeta

← #577×Dic47 #27080514

Subgroups — #577×Dic47 #27080514

Order 12032.

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×Dic47C211yesmaximal, characteristic, complemented
2H(5,𝔽2)×Dic47C211yesmaximal, characteristic, complemented
3#20252272C213yesmaximal, complemented
4#20252248C213yesmaximal, complemented
5#20252232C213yesmaximal, complemented
6#20252221C213yesmaximal, complemented
7#137×Dic47C213yesmaximal, complemented
8AGL(1,ℤ/8)×Dic47C213yesmaximal, complemented
9#135×Dic47C213yesmaximal, complemented
10C2×SD16×Dic47C213yesmaximal, complemented
11#20251983C211yesmaximal, characteristic, complemented
12#20251921C211yesmaximal, characteristic, complemented
13#20251914C211yesmaximal, characteristic, complemented
14#131×Dic47C211yesmaximal, characteristic, complemented
15C2×C47×#577C211yesmaximal, characteristic
16C2×#13094031C2211yescharacteristic
17#15689606—21no—
18#15689606—23no—
19#15689606C2213yes—
20#15689606C2211yescharacteristic
21#15689606C2211yescharacteristic
22#15689606C2213yescomplemented
23#15689601—21no—
24#15689601C2213yescomplemented
25#15689598—23no—
26#15689598C2213yes—
27#41×Dic47—21no—
28#41×Dic47—23no—
29#41×Dic47C2213yes—
30#41×Dic47C2211yescharacteristic
31#41×Dic47C2213yescomplemented
32C2×Q8×Dic47—21no—
33C2×Q8×Dic47C2213yescomplemented
34C2×D4×Dic47—23no—
35C2×D4×Dic47C2213yes—
36#15689235C2216yescomplemented
37#15689230C2216yescomplemented
38#15689224C2216yescomplemented
39#15689224C2216yescomplemented
40Q16×Dic47C2213yescomplemented
41Q16×Dic47C2213yescomplemented
42SD16×Dic47C2211yescharacteristic, complemented
43SD16×Dic47C2213yescomplemented
44SD16×Dic47C2213yescomplemented
45SD16×Dic47C2213yescomplemented
46SD16×Dic47C2216yescomplemented
47SD16×Dic47C2216yescomplemented
48SD16×Dic47C2216yescomplemented
49D8×Dic47C2213yescomplemented
50D8×Dic47C2213yescomplemented
51#15689165C2213yescomplemented
52#15689165C2213yescomplemented
53#15689161C2213yescomplemented
54C2×#13093956C2213yescomplemented
55#15689132C2213yescomplemented
56#15689128C2213yes—
57#15689124C2213yes—
58#15689124C2213yescomplemented
59#15689119C2213yes—
60#15689119C2213yescomplemented
61C2×#13093948C2213yescomplemented
62C2×#13093945C2213yes—
63#15689081C2213yescomplemented
64#15689078C2213yescomplemented
65M16×Dic47C2213yescomplemented
66C2×C8×Dic47C2213yescomplemented
67C2×2−1+4×C47C2211yescharacteristic
68C2×H(5,𝔽2)×C47C2211yescharacteristic
69C47×#577C4116yescomplemented
70C2×#137×C47C2213yes—
71C2×AGL(1,ℤ/8)×C47C2213yes—
72C2×#135×C47C2213yes—
73C22×SD16×C47C2213yes—
74C2×#131×C47C2211yescharacteristic
75C23×Dic47—23no—
76#13094031—24no—
77C2×#10625329C2313yes—
78C22×C47⋊C8C2313yes—
79Q8×Dic47—21no—
80Q8×Dic47—21no—
81Q8×Dic47—23no—
82Q8×Dic47—23no—
83Q8×Dic47—23no—
84Q8×Dic47—23no—
85Q8×Dic47D411yescharacteristic
86Q8×Dic47D411yescharacteristic
87Q8×Dic47C2311yescharacteristic
88Q8×Dic47C2313yes—
89Q8×Dic47C2313yes—
90Q8×Dic47C2313yes—
91Q8×Dic47C2316yes—
92D4×Dic47—23no—
93D4×Dic47—23no—
94D4×Dic47—23no—
95D4×Dic47—23no—
96D4×Dic47—23no—
97D4×Dic47—23no—
98D4×Dic47—26no—
99D4×Dic47—26no—
100D4×Dic47—23no—
101D4×Dic47—23no—
102D4×Dic47—23no—
103D4×Dic47—23no—
104D4×Dic47D413yes—
105D4×Dic47D413yes—
106D4×Dic47C2313yes—
107D4×Dic47C2316yes—
108D4×Dic47C2313yes—
109D4×Dic47C2313yes—
110D4×Dic47C2311yescharacteristic
111#13093983—26no—
112#13093983—23no—
113#13093983—23no—
114#13093983—23no—
115#13093983—23no—
116#13093983C2313yes—
117#13093983C2313yes—
118#13093983C2313yes—
119C2×C4⋊Dic47—23no—
120C2×C4⋊Dic47—23no—
121C2×C4⋊Dic47—23no—
122C2×C4⋊Dic47C2313yes—
123C2×C4⋊Dic47C2313yes—
124C2×C22⋊Dic47—23no—
125C2×C22⋊Dic47—26no—
126C2×C4×Dic47—23no—
127C2×C4×Dic47—23no—
128C2×C4×Dic47—23no—
129C2×C4×Dic47C2313yes—
130#13093958C2313yes—
131#13093958C2313yes—
132#13093956C2316yes—
133#13093956C2313yes—
134#13093956C2311yescharacteristic
135#13093948C2311yescharacteristic
136#13093948C2313yes—
137#13093948C2313yes—
138#13093948C2313yes—
139#13093948C2316yes—
140#13093945C2313yes—
141#13093945C2316yes—
142#13093945C2313yes—
143#13093945C2313yes—
144#13093945C2311yescharacteristic
145#13093934C2316yes—
146C8×Dic47C2313yes—
147C8×Dic47C2313yes—
148C8×Dic47C2311yescharacteristic
149C8×Dic47C2313yes—
1502−1+4×C47—24no—
1512−1+4×C47C2×C418yescomplemented
152H(5,𝔽2)×C47—24no—
153H(5,𝔽2)×C47C2×C418yescomplemented
154C2×#41×C47—21no—
155C2×#41×C47—23no—
156C2×#41×C47C2313yes—
157C2×#41×C47C2313yes—
158C2×#41×C47C2311yescharacteristic
159C22×Q8×C47—21no—
160C22×Q8×C47C2313yes—
161C22×D4×C47—23no—
162C22×D4×C47C2313yes—
163#137×C47C2×C4124yescomplemented
164AGL(1,ℤ/8)×C47C2×C4124yescomplemented
165#135×C47C2×C4124yescomplemented
166C2×Q16×C47C2313yes—
167C2×SD16×C47C2×C4124yescomplemented
168C2×SD16×C47C2316yes—
169C2×SD16×C47C2313yes—
170C2×SD16×C47C2311yescharacteristic
171C2×D8×C47C2313yes—
172#131×C47C2×C418yescomplemented
173C2×M16×C47C2313yes—
174C22×C8×C47C2313yes—
175C24×C47—23no—
176#41×C47—28no—
177#41×C47—224no—
178#41×C47—26no—
179#41×C47—26no—
180#41×C47C22×C4112yes—
181#41×C47C22×C414yes—
182#41×C47C22×C4112yescomplemented
183#41×C47#4114yes—
184C2×Q8×C47—28no—
185C2×Q8×C47—23no—
186C2×Q8×C47—26no—
187C2×Q8×C47C22×C4112yescomplemented
188C2×Q8×C47C2×D411yescharacteristic
189C2×Q8×C47C2413yes—
190C2×Q8×C47C2411yescharacteristic
191C2×D4×C47—23no—
192C2×D4×C47—23no—
193C2×D4×C47—224no—
194C2×D4×C47—23no—
195C2×D4×C47—26no—
196C2×D4×C47C22×C4112yes—
197C2×D4×C47C2×D413yes—
198C2×D4×C47C2411yescharacteristic
199C2×D4×C47C2413yes—
200C22×C4×C47—23no—
201C22×C4×C47—23no—
202C22×C4×C47—23no—
203C22×C4×C47C2413yes—
204C22×Dic47—23no—
205C22×Dic47—23no—
206C22×Dic47—21no—
207C22×Dic47—23no—
208C22×Dic47—23no—
209C22×Dic47—23no—
210C22×Dic47—26no—
211C22×Dic47—86no—
212C22×Dic47C2×D413yes—
213C22×Dic47C2×D413yes—
214Q16×C47C22×C4112yescomplemented
215SD16×C47C22×C4112yescomplemented
216SD16×C47C22×C4124yescomplemented
217SD16×C47C22×C414yescomplemented
218D8×C47C22×C4112yescomplemented
219M16×C47C22×C4112yescomplemented
220C2×C8×C47C22×C4112yescomplemented
221C2×C8×C47C2411yescharacteristic
222C2×C8×C47C2413yes—
223C22⋊Dic47—23no—
224C22⋊Dic47—23no—
225C22⋊Dic47—23no—
226C22⋊Dic47—26no—
227C22⋊Dic47—23no—
228C22⋊Dic47—21no—
229C22⋊Dic47—23no—
230C22⋊Dic47C2×D416yes—
231C4⋊Dic47—23no—
232C4⋊Dic47—23no—
233C4⋊Dic47—23no—
234C4⋊Dic47—26no—
235C4⋊Dic47—23no—
236C4⋊Dic47—21no—
237C4⋊Dic47—23no—
238C4⋊Dic47C2×D413yes—
239C4⋊Dic47C2×D413yes—
240C4⋊Dic47C2413yes—
241C4⋊Dic47C2411yescharacteristic
242C4⋊Dic47C2413yes—
243C4⋊Dic47C2411yescharacteristic
244C4×Dic47—23no—
245C4×Dic47—23no—
246C4×Dic47—21no—
247C4×Dic47—23no—
248C4×Dic47—23no—
249C4×Dic47—23no—
250C4×Dic47—26no—
251C4×Dic47C2×D413yes—
252C4×Dic47C2×D413yes—
253C4×Dic47C2411yescharacteristic
254C4×Dic47C2413yes—
255#10625329—26no—
256C2×C47⋊C8—26no—
257C2×C47⋊C8C2411yescharacteristic
258C2×C47⋊C8C2413yes—
259C23×C47—21no—
260C23×C47—23no—
261C23×C47—212no—
262C23×C47—83no—
263C23×C47—83no—
264C23×C47C22×D413yes—
265Q8×C47—212no—
266Q8×C47—23no—
267Q8×C47—21no—
268Q8×C47C4×D414yes—
269Q8×C47C23×C416yes—
270Q8×C47C23×C412yes—
271D4×C47—212no—
272D4×C47—212no—
273D4×C47—212no—
274D4×C47—23no—
275D4×C47—21no—
276D4×C47C4×D4112yes—
277D4×C47C23×C412yes—
278D4×C47C23×C416yes—
279C2×C4×C47—212no—
280C2×C4×C47—21no—
281C2×C4×C47—23no—
282C2×C4×C47—212no—
283C2×C4×C47—212no—
284C2×C4×C47C23×C416yes—
285C2×C4×C47C22×D413yes—
286C2×C4×C47C2×#4116yes—
287C2×C4×C47C2511yescharacteristic
288C2×Dic47—26no—
289C2×Dic47—21no—
290C2×Dic47—23no—
291C2×Dic47—21no—
292C2×Dic47—23no—
293C2×Dic47—43no—
294C2×Dic47—42no—
295C2×Dic47—46no—
296C2×Dic47—83no—
297C2×Dic47—83no—
298C2×Dic47—86no—
299C2×Dic47—83no—
300C2×Dic47—83no—
301C2×Dic47C22×D413yes—
302C2×Dic47C22×D413yes—
303C2×Dic47C22×D411yescharacteristic
304C2×Dic47C22×D411yescharacteristic
305C8×C47C23×C412yes—
306C8×C47C23×C416yes—
307C47⋊C8—21no—
308C47⋊C8—23no—
309C4×#577—471nomaximal, Sylow
310C22×C47—23no—
311C22×C47—23no—
312C22×C47—22no—
313C22×C47—26no—
314C22×C47—41no—
315C22×C47—43no—
316C22×C47—43no—
317C22×C47—41no—
318C22×C47—812no—
319C22×C47C2×C4×D416yes—
320C22×C47C23×D411yescharacteristic
321C4×C47—22no—
322C4×C47—26no—
323C4×C47C2×C4×D416yes—
324C4×C47C24×C411yescharacteristic
325C4×C47C22×#4111yescharacteristic
326Dic47—21no—
327Dic47—23no—
328Dic47—23no—
329Dic47—43no—
330Dic47—41no—
331Dic47—41no—
332Dic47—43no—
333Dic47#57712yesdirect product factor
334C2×#577D4711yescharacteristic
335C4×2−1+4—471no—
336C4×H(5,𝔽2)—471no—
337#2952—473no—
338#2949—473no—
339#2947—473no—
340#2946—473no—
341C4×#137—473no—
342C4×AGL(1,ℤ/8)—473no—
343C4×#135—473no—
344C2×C4×SD16—473no—
345#2912—471no—
346#2898—471no—
347#2897—471no—
348C4×#131—471no—
349C2×C47—26no—
350C2×C47—42no—
351C2×C47—46no—
352C2×C47C22×C4×D411yescharacteristic
353C2×C47C2×#57711yescharacteristic
354C2×C47#358411yescharacteristic
355C2×2−1+4C2×D4711yescharacteristic
356C2×H(5,𝔽2)C2×D4711yescharacteristic
357#577Dic47116yesdirect product factor
358C2×#137C2×D4713yes—
359C2×AGL(1,ℤ/8)C2×D4713yes—
360C2×#135C2×D4713yes—
361C22×SD16C2×D4713yes—
362C2×#131—471no—
363C2×#131C2×D4711yescharacteristic
364#520—471no—
365#520—471no—
366#520—473no—
367#520—473no—
368#520—943no—
369#520—941no—
370#519—473no—
371#519—941no—
372#518—473no—
373#518—943no—
374C4×#41—471no—
375C4×#41—473no—
376C4×#41—473no—
377C4×#41—943no—
378C4×#41—941no—
379C2×C4×Q8—473no—
380C2×C4×Q8—941no—
381C2×C4×D4—473no—
382C2×C4×D4—943no—
383#442—476no—
384#441—476no—
385#440—476no—
386#440—476no—
387C4×Q16—473no—
388C4×Q16—473no—
389C4×SD16—473no—
390C4×SD16—476no—
391C4×SD16—476no—
392C4×SD16—476no—
393C4×SD16—471no—
394C4×SD16—473no—
395C4×SD16—473no—
396C4×D8—473no—
397C4×D8—473no—
398#428—473no—
399#428—473no—
400#427—473no—
401C2×#106—473no—
402#419—473no—
403#418—473no—
404#417—473no—
405#417—473no—
406#416—473no—
407#416—473no—
408C2×#103—473no—
409C2×#102—473no—
410#405—473no—
411#405—473no—
412C4×M16—473no—
413C2×C4×C8—473no—
414C47C4×#57711yescharacteristic, complemented, Sylow
4152−1+4—24no—
4162−1+4C2×Dic4718yescomplemented
417H(5,𝔽2)—24no—
418H(5,𝔽2)C2×Dic4718yescomplemented
419C2×#41—21no—
420C2×#41—23no—
421C2×#41C22×D4713yes—
422C2×#41C22×D4713yes—
423C2×#41C22×D4711yescharacteristic
424C22×Q8—21no—
425C22×Q8C22×D4713yes—
426C22×D4—23no—
427C22×D4C22×D4713yes—
428C23×C4—943no—
429#137C2×Dic47124yescomplemented
430AGL(1,ℤ/8)C2×Dic47124yescomplemented
431#135C2×Dic47124yescomplemented
432C2×Q16C22×D4713yes—
433C2×SD16C2×Dic47124yescomplemented
434C2×SD16C22×D4713yes—
435C2×SD16C22×D4716yes—
436C2×SD16C22×D4711yescharacteristic
437C2×D8C22×D4713yes—
438#131—944no—
439#131C2×Dic4718yescomplemented
440C2×M16—473no—
441C2×M16C22×D4713yes—
442C22×C8—473no—
443C22×C8C22×D4713yes—
444C4×Q8—471no—
445C4×Q8—471no—
446C4×Q8—473no—
447C4×Q8—476no—
448C4×Q8—471no—
449C4×Q8—473no—
450C4×Q8—473no—
451C4×Q8—943no—
452C4×Q8—943no—
453C4×Q8—943no—
454C4×Q8—943no—
455C4×Q8—941no—
456C4×Q8—941no—
457C4×D4—473no—
458C4×D4—473no—
459C4×D4—473no—
460C4×D4—476no—
461C4×D4—471no—
462C4×D4—473no—
463C4×D4—473no—
464C4×D4—943no—
465C4×D4—943no—
466C4×D4—946no—
467C4×D4—946no—
468C4×D4—943no—
469C4×D4—943no—
470C4×D4—943no—
471C4×D4—943no—
472C4×D4—943no—
473C4×D4—943no—
474C4×D4—943no—
475C4×D4—943no—
476#117—473no—
477#117—473no—
478#117—473no—
479#117—943no—
480#117—943no—
481#117—946no—
482#117—943no—
483#117—943no—
484C2×C4⋊C4—473no—
485C2×C4⋊C4—473no—
486C2×C4⋊C4—943no—
487C2×C4⋊C4—943no—
488C2×C4⋊C4—943no—
489C2×C22⋊C4—946no—
490C2×C22⋊C4—943no—
491C2×C42—473no—
492C2×C42—943no—
493C2×C42—943no—
494C2×C42—943no—
495#107—473no—
496#107—473no—
497#106—473no—
498#106—476no—
499#106—471no—
500#103—473no—
501#103—476no—
502#103—471no—
503#103—473no—
504#103—473no—
505#102—473no—
506#102—476no—
507#102—471no—
508#102—473no—
509#102—473no—
510#97—476no—
511C4×C8—471no—
512C4×C8—473no—
513C4×C8—473no—
514C4×C8—473no—
515C24—23no—
516#41—28no—
517#41—224no—
518#41—26no—
519#41—26no—
520#41#1062535214yes—
521#41C22×Dic47112yes—
522#41C22×Dic4714yes—
523#41C22×Dic47112yescomplemented
524C2×Q8—28no—
525C2×Q8—23no—
526C2×Q8—26no—
527C2×Q8D4×D4711yescharacteristic
528C2×Q8C22×Dic47112yescomplemented
529C2×Q8C23×D4713yes—
530C2×Q8C23×D4711yescharacteristic
531C2×D4—23no—
532C2×D4—23no—
533C2×D4—224no—
534C2×D4—23no—
535C2×D4—26no—
536C2×D4D4×D4713yes—
537C2×D4C22×Dic47112yes—
538C2×D4C23×D4711yescharacteristic
539C2×D4C23×D4713yes—
540C22×C4—23no—
541C22×C4—23no—
542C22×C4—23no—
543C22×C4—473no—
544C22×C4—473no—
545C22×C4—943no—
546C22×C4—943no—
547C22×C4—946no—
548C22×C4—941no—
549C22×C4—943no—
550C22×C4—943no—
551C22×C4—943no—
552C22×C4—3766no—
553C22×C4C23×D4713yes—
554Q16C22×Dic47112yescomplemented
555SD16C22×Dic47112yescomplemented
556SD16C22×Dic47124yescomplemented
557SD16C22×Dic4714yescomplemented
558D8C22×Dic47112yescomplemented
559M16—946no—
560M16C22×Dic47112yescomplemented
561C2×C8—471no—
562C2×C8—473no—
563C2×C8—946no—
564C2×C8C22×Dic47112yescomplemented
565C2×C8C23×D4711yescharacteristic
566C2×C8C23×D4713yes—
567C4⋊C4—473no—
568C4⋊C4—473no—
569C4⋊C4—473no—
570C4⋊C4—471no—
571C4⋊C4—473no—
572C4⋊C4—471no—
573C4⋊C4—943no—
574C4⋊C4—943no—
575C4⋊C4—946no—
576C4⋊C4—941no—
577C4⋊C4—943no—
578C4⋊C4—943no—
579C4⋊C4—943no—
580C22⋊C4—476no—
581C22⋊C4—943no—
582C22⋊C4—943no—
583C22⋊C4—946no—
584C22⋊C4—941no—
585C22⋊C4—943no—
586C22⋊C4—943no—
587C22⋊C4—943no—
588C42—473no—
589C42—473no—
590C42—471no—
591C42—473no—
592C42—941no—
593C42—943no—
594C42—943no—
595C42—943no—
596C42—946no—
597C42—943no—
598C42—943no—
599C23—21no—
600C23—23no—
601C23—212no—
602C23—83no—
603C23—83no—
604C23C2×D4×D4713yes—
605Q8—212no—
606Q8—23no—
607Q8—21no—
608Q8D4×Dic4714yes—
609Q8C23×Dic4716yes—
610Q8C23×Dic4712yes—
611D4—212no—
612D4—212no—
613D4—212no—
614D4—23no—
615D4—21no—
616D4D4×Dic47112yes—
617D4C23×Dic4712yes—
618D4C23×Dic4716yes—
619C2×C4—212no—
620C2×C4—21no—
621C2×C4—23no—
622C2×C4—212no—
623C2×C4—212no—
624C2×C4—471no—
625C2×C4—471no—
626C2×C4—473no—
627C2×C4—473no—
628C2×C4—946no—
629C2×C4—941no—
630C2×C4—941no—
631C2×C4—943no—
632C2×C4—943no—
633C2×C4—3763no—
634C2×C4—3763no—
635C2×C4—3766no—
636C2×C4—3763no—
637C2×C4—3763no—
638C2×C4—1882no—
639C2×C4—1886no—
640C2×C4—1883no—
641C2×C4C23×Dic4716yes—
642C2×C4C2×D4×D4713yes—
643C2×C4C2×#1062535216yes—
644C2×C4C24×D4711yescharacteristic
645C8—941no—
646C8—943no—
647C8C23×Dic4712yes—
648C8C23×Dic4716yes—
649C22—23no—
650C22—23no—
651C22—22no—
652C22—26no—
653C22—43no—
654C22—41no—
655C22—41no—
656C22—43no—
657C22—812no—
658C22C2×D4×Dic4716yes—
659C22C22×D4×D4711yescharacteristic
660C4—22no—
661C4—26no—
662C4—472no—
663C4—943no—
664C4—943no—
665C4—941no—
666C4—1883no—
667C4—1881no—
668C4—1881no—
669C4—1883no—
670C4C2×D4×Dic4716yes—
671C4C24×Dic4711yescharacteristic
672C4C22×#1062535211yescharacteristic
673C2—26no—
674C2—46no—
675C2—42no—
676C2C22×D4×Dic4711yescharacteristic
677C2#577×D4711yescharacteristic
678C2#2025816011yescharacteristic
subgroupG/H
centerC22C22×D4×D47
commutatorC4×C47C24×C4
FrattiniC2×C4C24×D47
Fitting, prime radicalC2×C47×#577C2
socleC22×C47C23×D4
cosocleC2×C4×C47C25
hypercenterC2×#577D47
hypocenterC47C4×#577
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#577

Complements

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

NH ≅ G/Ntype
1. 2−1+4×Dic47C2semidirect
2. H(5,𝔽2)×Dic47C2semidirect
3. #20252272C2semidirect
4. #20252248C2semidirect
5. #20252232C2semidirect
6. #20252221C2semidirect
7. #137×Dic47C2semidirect
8. AGL(1,ℤ/8)×Dic47C2semidirect
9. #135×Dic47C2semidirect
10. C2×SD16×Dic47C2semidirect
11. #20251983C2semidirect
12. #20251921C2semidirect
13. #20251914C2semidirect
14. #131×Dic47C2semidirect
22. #15689606C22semidirect
24. #15689601C22semidirect
31. #41×Dic47C22semidirect
33. C2×Q8×Dic47C22semidirect
36. #15689235C22semidirect
37. #15689230C22semidirect
38. #15689224C22semidirect
39. #15689224C22semidirect
40. Q16×Dic47C22semidirect
41. Q16×Dic47C22semidirect
42. SD16×Dic47C22semidirect
43. SD16×Dic47C22semidirect
44. SD16×Dic47C22semidirect
45. SD16×Dic47C22semidirect
46. SD16×Dic47C22semidirect
47. SD16×Dic47C22semidirect
48. SD16×Dic47C22semidirect
49. D8×Dic47C22semidirect
50. D8×Dic47C22semidirect
51. #15689165C22semidirect
52. #15689165C22semidirect
53. #15689161C22semidirect
54. C2×#13093956C22semidirect
55. #15689132C22semidirect
58. #15689124C22semidirect
60. #15689119C22semidirect
61. C2×#13093948C22semidirect
63. #15689081C22semidirect
64. #15689078C22semidirect
65. M16×Dic47C22semidirect
66. C2×C8×Dic47C22semidirect
69. C47×#577C4semidirect
151. 2−1+4×C47C2×C4semidirect
153. H(5,𝔽2)×C47C2×C4semidirect
163. #137×C47C2×C4semidirect
164. AGL(1,ℤ/8)×C47C2×C4semidirect
165. #135×C47C2×C4semidirect
167. C2×SD16×C47C2×C4semidirect
172. #131×C47C2×C4semidirect
182. #41×C47C22×C4semidirect
187. C2×Q8×C47C22×C4semidirect
214. Q16×C47C22×C4semidirect
215. SD16×C47C22×C4semidirect
216. SD16×C47C22×C4semidirect
217. SD16×C47C22×C4semidirect
218. D8×C47C22×C4semidirect
219. M16×C47C22×C4semidirect
220. C2×C8×C47C22×C4semidirect
333. Dic47#577direct (N × H)
357. #577Dic47direct (N × H)
414. C47C4×#577semidirect
416. 2−1+4C2×Dic47semidirect
418. H(5,𝔽2)C2×Dic47semidirect
429. #137C2×Dic47semidirect
430. AGL(1,ℤ/8)C2×Dic47semidirect
431. #135C2×Dic47semidirect
433. C2×SD16C2×Dic47semidirect
439. #131C2×Dic47semidirect
523. #41C22×Dic47semidirect
528. C2×Q8C22×Dic47semidirect
554. Q16C22×Dic47semidirect
555. SD16C22×Dic47semidirect
556. SD16C22×Dic47semidirect
557. SD16C22×Dic47semidirect
558. D8C22×Dic47semidirect
560. M16C22×Dic47semidirect
564. C2×C8C22×Dic47semidirect

Maximal subgroups

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

subgroupindex
2−1+4×Dic472
H(5,𝔽2)×Dic472
#202522722
#202522482
#202522322
#202522212
#137×Dic472
AGL(1,ℤ/8)×Dic472
#135×Dic472
C2×SD16×Dic472
#202519832
#202519212
#202519142
#131×Dic472
C2×C47×#5772
C4×#57747