Finite Group Databasebeta

← C47×#24473 #26064171

Subgroups — C47×#24473 #26064171

Order 12032.

1314 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3586C211yesmaximal, characteristic, complemented
2C47×#3068C211yesmaximal, characteristic, complemented
3C47×#3040C211yesmaximal, characteristic, complemented
4C47×#3021C211yesmaximal, characteristic, complemented
5C2×C47×#454C211yesmaximal, characteristic, complemented
6C47×#2901C211yesmaximal, characteristic, complemented
7C47×#2050C211yesmaximal, characteristic, complemented
8C47×#2049C211yesmaximal, characteristic, complemented
9C47×#2008C211yesmaximal, characteristic, complemented
10C47×#2004C211yesmaximal, characteristic, complemented
11C47×#1906C211yesmaximal, characteristic, complemented
12C47×#1903C211yesmaximal, characteristic, complemented
13C47×#1902C211yesmaximal, characteristic, complemented
14C47×#1861C211yesmaximal, characteristic, complemented
15C47×#1796C211yesmaximal, characteristic, complemented
16C47×#585C2211yescharacteristic
17C2×2−1+4×C47C2211yescharacteristic
18C47×#578—22no—
19C47×#578—22no—
20C47×#577—22no—
21C47×#577—22no—
22C47×#575—22no—
23C47×#575C2211yescharacteristic
24C47×#575C2211yescharacteristic
25C2×#137×C47—22no—
26C2×#137×C47C2211yescharacteristic
27C2×#137×C47C2211yescharacteristic
28C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
29C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
30C2×AGL(1,ℤ/8)×C47C2211yescharacteristic, complemented
31C47×#568C2211yescharacteristic
32C47×#568C2211yescharacteristic
33C47×#535C2211yescharacteristic
34C2×#124×C47C2211yescharacteristic, complemented
35C4×#41×C47C2211yescharacteristic
36C47×#472—22no—
37C47×#471—22no—
38C47×#464—22no—
39C47×#463—22no—
40C47×#454—22no—
41C47×#454—22no—
42C47×#454—22no—
43C47×#453—22no—
44C47×#430C2211yescharacteristic, complemented
45C47×#423C2211yescharacteristic, complemented
46C47×#421—22no—
47C47×#421C2211yescharacteristic
48C47×#421C2211yescharacteristic
49C47×#421C2211yescharacteristic
50C47×#421C2211yescharacteristic
51C2×#104×C47—22no—
52C2×#104×C47C2211yescharacteristic
53C2×#104×C47C2211yescharacteristic
54C2×#104×C47C2211yescharacteristic, complemented
55C47×#419C2211yescharacteristic, complemented
56C47×#419C2211yescharacteristic, complemented
57C47×#418C2211yescharacteristic, complemented
58C47×#413C2211yescharacteristic
59C47×#413C2211yescharacteristic, complemented
60C2×#101×C47C2211yescharacteristic, complemented
61C2×#100×C47C2211yescharacteristic, complemented
62C47×#410C2211yescharacteristic, complemented
63C47×#344C2211yescharacteristic, complemented
64C47×#344C2211yescharacteristic, complemented
65C47×#339C2211yescharacteristic, complemented
66C47×#338C2211yescharacteristic, complemented
672−1+4×C47—22no—
682−1+4×C47—22no—
692−1+4×C47—21no—
702−1+4×C47—21no—
712−1+4×C47—22no—
722−1+4×C47—41no—
732−1+4×C47D412yes—
74H(5,𝔽2)×C47—21no—
75H(5,𝔽2)×C47—21no—
76H(5,𝔽2)×C47—41no—
77H(5,𝔽2)×C47D412yes—
78C2×#41×C47—22no—
79C2×#41×C47—22no—
80C2×#41×C47—21no—
81C2×#41×C47—21no—
82C2×#41×C47—41no—
83C2×#41×C47—41no—
84C2×#41×C47C2311yescharacteristic
85C2×#41×C47C2311yescharacteristic
86C2×#41×C47C2311yescharacteristic
87C2×#41×C47C2311yescharacteristic
88C22×Q8×C47—21no—
89C22×Q8×C47—21no—
90C22×Q8×C47C2311yescharacteristic
91C22×D4×C47C2311yescharacteristic
92#137×C47—24no—
93#137×C47—24no—
94#137×C47—24no—
95#137×C47—22no—
96#137×C47—22no—
97#137×C47—21no—
98#137×C47—22no—
99#137×C47—21no—
100#137×C47—21no—
101#137×C47—22no—
102#137×C47D412yescomplemented
103AGL(1,ℤ/8)×C47—24no—
104AGL(1,ℤ/8)×C47—21no—
105AGL(1,ℤ/8)×C47—21no—
106AGL(1,ℤ/8)×C47—21no—
107AGL(1,ℤ/8)×C47—22no—
108AGL(1,ℤ/8)×C47—22no—
109AGL(1,ℤ/8)×C47—22no—
110AGL(1,ℤ/8)×C47—22no—
111AGL(1,ℤ/8)×C47—22no—
112AGL(1,ℤ/8)×C47—41no—
113AGL(1,ℤ/8)×C47D412yescomplemented
114#135×C47—24no—
115#135×C47—24no—
116#135×C47—22no—
117#135×C47—22no—
118C2×Q16×C47—24no—
119C2×Q16×C47—21no—
120C2×Q16×C47D412yescomplemented
121C2×SD16×C47—24no—
122C2×SD16×C47—21no—
123C2×SD16×C47—21no—
124C2×SD16×C47—21no—
125C2×SD16×C47—21no—
126C2×SD16×C47D412yescomplemented
127C2×D8×C47—21no—
128C2×D8×C47—21no—
129C2×D8×C47—21no—
130#131×C47—22no—
131#131×C47—22no—
132#131×C47—22no—
133#131×C47—41no—
134C2×M16×C47—22no—
135C2×M16×C47—22no—
136C2×M16×C47C2311yescharacteristic
137C2×M16×C47C2311yescharacteristic
138C2×M16×C47C2311yescharacteristic
139C2×M16×C47C2311yescharacteristic
140C2×M16×C47C2311yescharacteristic
141C2×M16×C47C2311yescharacteristic
142#127×C47—21no—
143#124×C47—21no—
144#124×C47—22no—
145#124×C47—21no—
146#124×C47—21no—
147#121×C47—41no—
148#120×C47—41no—
149C4×Q8×C47—21no—
150C4×D4×C47—21no—
151C4×D4×C47—41no—
152#117×C47—21no—
153#117×C47C2311yescharacteristic
154#117×C47C2311yescharacteristic
155C2×C22⋊C4×C47—41no—
156C2×C42×C47—21no—
157C2×C42×C47C2311yescharacteristic
158#108×C47—22no—
159C4⋊C8×C47—22no—
160#104×C47—22no—
161#104×C47—22no—
162#104×C47—22no—
163#104×C47—22no—
164#104×C47—21no—
165#104×C47—21no—
166#104×C47—21no—
167#104×C47—21no—
168#104×C47D412yescomplemented
169#104×C47D412yescomplemented
170#103×C47—22no—
171#103×C47—41no—
172#102×C47—22no—
173#101×C47—21no—
174#101×C47—21no—
175#101×C47—22no—
176#100×C47—21no—
177#100×C47—21no—
178#100×C47—22no—
179#99×C47—41no—
180C24×C47—21no—
181#41×C47—21no—
182#41×C47—21no—
183#41×C47—21no—
184#41×C47—21no—
185#41×C47—24no—
186#41×C47—22no—
187#41×C47—22no—
188#41×C47—22no—
189#41×C47—22no—
190#41×C47—21no—
191#41×C47—21no—
192#41×C47—21no—
193#41×C47—21no—
194#41×C47—21no—
195#41×C47—21no—
196#41×C47—21no—
197#41×C47—21no—
198#41×C47—42no—
199#41×C47—42no—
200#41×C47—42no—
201#41×C47—42no—
202#41×C47—42no—
203#41×C47—44no—
204#41×C47—42no—
205#41×C47—41no—
206#41×C47—41no—
207#41×C47—44no—
208#41×C47—42no—
209#41×C47C2×D412yes—
210#41×C47C2×D412yes—
211#41×C47C2×D412yes—
212#41×C47C2×D412yes—
213C2×Q8×C47—21no—
214C2×Q8×C47—24no—
215C2×Q8×C47—22no—
216C2×Q8×C47—22no—
217C2×Q8×C47—21no—
218C2×Q8×C47—21no—
219C2×Q8×C47—21no—
220C2×Q8×C47—21no—
221C2×Q8×C47—41no—
222C2×Q8×C47—42no—
223C2×Q8×C47—42no—
224C2×Q8×C47—41no—
225C2×Q8×C47—42no—
226C2×Q8×C47C2×D412yes—
227C2×Q8×C47C2×D411yescharacteristic
228C2×Q8×C47C2×D411yescharacteristic
229C2×Q8×C47C2×D411yescharacteristic
230C2×Q8×C47#4111yescharacteristic
231C2×D4×C47—21no—
232C2×D4×C47—21no—
233C2×D4×C47—22no—
234C2×D4×C47—22no—
235C2×D4×C47—21no—
236C2×D4×C47—21no—
237C2×D4×C47—21no—
238C2×D4×C47—21no—
239C2×D4×C47—21no—
240C2×D4×C47—21no—
241C2×D4×C47—21no—
242C2×D4×C47—21no—
243C2×D4×C47—42no—
244C2×D4×C47—41no—
245C2×D4×C47—42no—
246C2×D4×C47—42no—
247C2×D4×C47—41no—
248C2×D4×C47—42no—
249C2×D4×C47C2×D411yescharacteristic
250C2×D4×C47C2×D411yescharacteristic
251C2×D4×C47C2×D411yescharacteristic
252C2×D4×C47#4111yescharacteristic
253C22×C4×C47—21no—
254C22×C4×C47—21no—
255C22×C4×C47—21no—
256C22×C4×C47—21no—
257C22×C4×C47—21no—
258C22×C4×C47—21no—
259C22×C4×C47—42no—
260C22×C4×C47—41no—
261C22×C4×C47—41no—
262C22×C4×C47—41no—
263C22×C4×C47C2411yescharacteristic
264Q16×C47—24no—
265Q16×C47—22no—
266Q16×C47—22no—
267Q16×C47—24no—
268SD16×C47—24no—
269SD16×C47—22no—
270SD16×C47—22no—
271SD16×C47—22no—
272SD16×C47—22no—
273SD16×C47—24no—
274SD16×C47—42no—
275SD16×C47—42no—
276SD16×C47—42no—
277D8×C47—22no—
278D8×C47—22no—
279D8×C47—42no—
280D8×C47—42no—
281D8×C47—42no—
282M16×C47—24no—
283M16×C47—21no—
284M16×C47—21no—
285M16×C47—21no—
286M16×C47—21no—
287M16×C47—21no—
288M16×C47—21no—
289M16×C47—21no—
290M16×C47—21no—
291M16×C47—21no—
292M16×C47—21no—
293M16×C47—42no—
294M16×C47C2×D412yes—
295M16×C47C2×D412yes—
296C2×C8×C47—24no—
297C2×C8×C47—21no—
298C2×C8×C47—21no—
299C2×C8×C47—21no—
300C2×C8×C47—21no—
301C2×C8×C47—21no—
302C2×C8×C47—42no—
303C2×C8×C47C2×D412yes—
304C4⋊C4×C47—21no—
305C4⋊C4×C47—21no—
306C4⋊C4×C47—41no—
307C22⋊C4×C47—21no—
308C22⋊C4×C47—21no—
309C22⋊C4×C47—42no—
310C22⋊C4×C47—42no—
311C22⋊C4×C47—41no—
312C22⋊C4×C47—42no—
313C42×C47—21no—
314C42×C47—21no—
315C42×C47—21no—
316C42×C47—41no—
317C42×C47C2×D411yescharacteristic
318C42×C47C2×D411yescharacteristic
319C23×C47—21no—
320C23×C47—21no—
321C23×C47—21no—
322C23×C47—21no—
323C23×C47—42no—
324C23×C47—41no—
325C23×C47—41no—
326C23×C47—41no—
327C23×C47—82no—
328C23×C47H(5,𝔽2)11yescharacteristic
329Q8×C47—21no—
330Q8×C47—21no—
331Q8×C47—21no—
332Q8×C47—22no—
333Q8×C47—21no—
334Q8×C47—21no—
335Q8×C47—21no—
336Q8×C47—22no—
337Q8×C47—42no—
338Q8×C47—44no—
339Q8×C47—41no—
340Q8×C47—41no—
341Q8×C47#12012yes—
342Q8×C47#12112yes—
343D4×C47—22no—
344D4×C47—22no—
345D4×C47—22no—
346D4×C47—22no—
347D4×C47—21no—
348D4×C47—21no—
349D4×C47—21no—
350D4×C47—21no—
351D4×C47—21no—
352D4×C47—21no—
353D4×C47—42no—
354D4×C47—42no—
355D4×C47—42no—
356D4×C47—44no—
357D4×C47—41no—
358D4×C47—41no—
359D4×C47—41no—
360D4×C47—41no—
361D4×C47—41no—
362D4×C47—41no—
363D4×C47—41no—
364D4×C47—41no—
365D4×C47—162no—
366D4×C47#12012yes—
367D4×C47#12112yes—
368C2×C4×C47—21no—
369C2×C4×C47—21no—
370C2×C4×C47—22no—
371C2×C4×C47—22no—
372C2×C4×C47—22no—
373C2×C4×C47—22no—
374C2×C4×C47—21no—
375C2×C4×C47—21no—
376C2×C4×C47—21no—
377C2×C4×C47—22no—
378C2×C4×C47—21no—
379C2×C4×C47—42no—
380C2×C4×C47—42no—
381C2×C4×C47—42no—
382C2×C4×C47—44no—
383C2×C4×C47—44no—
384C2×C4×C47—41no—
385C2×C4×C47—41no—
386C2×C4×C47—41no—
387C2×C4×C47—41no—
388C2×C4×C47—41no—
389C2×C4×C47—41no—
390C2×C4×C47—41no—
391C2×C4×C47—41no—
392C2×C4×C47—81no—
393C2×C4×C47—82no—
394C2×C4×C47C22×D411yescharacteristic
395C2×C4×C47C22×D411yescharacteristic
396C2×C4×C47C22×D411yescharacteristic
397C2×C4×C47C22×D411yescharacteristic
398C2×C4×C47C2×#4111yescharacteristic
399C2×C4×C47H(5,𝔽2)11yescharacteristic
400C8×C47—22no—
401C8×C47—22no—
402C8×C47—22no—
403C8×C47—41no—
404C8×C47—41no—
405C8×C47—41no—
406#24473C4711yesmaximal, characteristic, direct product factor, Sylow
407C22×C47—22no—
408C22×C47—22no—
409C22×C47—41no—
410C22×C47—41no—
411C22×C47—41no—
412C22×C47—81no—
413C22×C47—81no—
414C22×C47—81no—
415C22×C47—81no—
416C22×C47—82no—
417C22×C47—82no—
418C22×C47—81no—
419C22×C47—161no—
420C22×C47—162no—
421C22×C47#53411yescharacteristic
422C22×C47D4211yescharacteristic
423C22×C47#54611yescharacteristic
424C4×C47—22no—
425C4×C47—22no—
426C4×C47—41no—
427C4×C47—41no—
428C4×C47—41no—
429C4×C47—42no—
430C4×C47—41no—
431C4×C47—81no—
432C4×C47—81no—
433C4×C47C2×#12011yescharacteristic
434C4×C47C2×#12111yescharacteristic
435C4×C47D4211yescharacteristic
436C4×C47#54611yescharacteristic
437#3586C2×C4711yescharacteristic, complemented
438#3068C2×C4711yescharacteristic, complemented
439#3040C2×C4711yescharacteristic, complemented
440#3021C2×C4711yescharacteristic, complemented
441C2×#454C2×C4711yescharacteristic, complemented
442#2901C2×C4711yescharacteristic, complemented
443#2050C2×C4711yescharacteristic, complemented
444#2049C2×C4711yescharacteristic, complemented
445#2008C2×C4711yescharacteristic, complemented
446#2004C2×C4711yescharacteristic, complemented
447#1906C2×C4711yescharacteristic, complemented
448#1903C2×C4711yescharacteristic, complemented
449#1902C2×C4711yescharacteristic, complemented
450#1861C2×C4711yescharacteristic, complemented
451#1796C2×C4711yescharacteristic, complemented
452C2×C47—21no—
453C2×C47—21no—
454C2×C47—21no—
455C2×C47—42no—
456C2×C47—42no—
457C2×C47—81no—
458C2×C47—81no—
459C2×C47—161no—
460C2×C47#241011yescharacteristic
461#585C22×C4711yescharacteristic
462C2×2−1+4C22×C4711yescharacteristic
463#578—22no—
464#578—22no—
465#577—22no—
466#577—22no—
467#575—22no—
468#575C22×C4711yescharacteristic
469#575C22×C4711yescharacteristic
470C2×#137—22no—
471C2×#137C22×C4711yescharacteristic
472C2×#137C22×C4711yescharacteristic
473C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
474C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
475C2×AGL(1,ℤ/8)C22×C4711yescharacteristic, complemented
476#568C22×C4711yescharacteristic
477#568C22×C4711yescharacteristic
478#535C22×C4711yescharacteristic
479C2×#124C22×C4711yescharacteristic, complemented
480C4×#41C22×C4711yescharacteristic
481#472—22no—
482#471—22no—
483#464—22no—
484#463—22no—
485#454—22no—
486#454—22no—
487#454—22no—
488#453—22no—
489#430C22×C4711yescharacteristic, complemented
490#423C22×C4711yescharacteristic, complemented
491#421—22no—
492#421C22×C4711yescharacteristic
493#421C22×C4711yescharacteristic
494#421C22×C4711yescharacteristic
495#421C22×C4711yescharacteristic
496C2×#104—22no—
497C2×#104C22×C4711yescharacteristic
498C2×#104C22×C4711yescharacteristic
499C2×#104C22×C4711yescharacteristic, complemented
500#419C22×C4711yescharacteristic, complemented
501#419C22×C4711yescharacteristic, complemented
502#418C22×C4711yescharacteristic, complemented
503#413C22×C4711yescharacteristic
504#413C22×C4711yescharacteristic, complemented
505C2×#101C22×C4711yescharacteristic, complemented
506C2×#100C22×C4711yescharacteristic, complemented
507#410C22×C4711yescharacteristic, complemented
508#344C22×C4711yescharacteristic, complemented
509#344C22×C4711yescharacteristic, complemented
510#339C22×C4711yescharacteristic, complemented
511#338C22×C4711yescharacteristic, complemented
512C47#2447311yescharacteristic, direct product factor, Sylow
5132−1+4—22no—
5142−1+4—22no—
5152−1+4—21no—
5162−1+4—21no—
5172−1+4—22no—
5182−1+4—41no—
5192−1+4D4×C4712yes—
520H(5,𝔽2)—21no—
521H(5,𝔽2)—21no—
522H(5,𝔽2)—41no—
523H(5,𝔽2)D4×C4712yes—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—21no—
527C2×#41—21no—
528C2×#41—41no—
529C2×#41—41no—
530C2×#41C23×C4711yescharacteristic
531C2×#41C23×C4711yescharacteristic
532C2×#41C23×C4711yescharacteristic
533C2×#41C23×C4711yescharacteristic
534C22×Q8—21no—
535C22×Q8—21no—
536C22×Q8C23×C4711yescharacteristic
537C22×D4C23×C4711yescharacteristic
538#137—24no—
539#137—24no—
540#137—24no—
541#137—22no—
542#137—22no—
543#137—21no—
544#137—22no—
545#137—21no—
546#137—21no—
547#137—22no—
548#137D4×C4712yescomplemented
549AGL(1,ℤ/8)—24no—
550AGL(1,ℤ/8)—21no—
551AGL(1,ℤ/8)—21no—
552AGL(1,ℤ/8)—21no—
553AGL(1,ℤ/8)—22no—
554AGL(1,ℤ/8)—22no—
555AGL(1,ℤ/8)—22no—
556AGL(1,ℤ/8)—22no—
557AGL(1,ℤ/8)—22no—
558AGL(1,ℤ/8)—41no—
559AGL(1,ℤ/8)D4×C4712yescomplemented
560#135—24no—
561#135—24no—
562#135—22no—
563#135—22no—
564C2×Q16—24no—
565C2×Q16—21no—
566C2×Q16D4×C4712yescomplemented
567C2×SD16—24no—
568C2×SD16—21no—
569C2×SD16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16D4×C4712yescomplemented
573C2×D8—21no—
574C2×D8—21no—
575C2×D8—21no—
576#131—22no—
577#131—22no—
578#131—22no—
579#131—41no—
580C2×M16—22no—
581C2×M16—22no—
582C2×M16C23×C4711yescharacteristic
583C2×M16C23×C4711yescharacteristic
584C2×M16C23×C4711yescharacteristic
585C2×M16C23×C4711yescharacteristic
586C2×M16C23×C4711yescharacteristic
587C2×M16C23×C4711yescharacteristic
588#127—21no—
589#124—22no—
590#124—21no—
591#124—21no—
592#124—21no—
593#121—41no—
594#120—41no—
595C4×Q8—21no—
596C4×D4—21no—
597C4×D4—41no—
598#117—21no—
599#117C23×C4711yescharacteristic
600#117C23×C4711yescharacteristic
601C2×C22⋊C4—41no—
602C2×C42—21no—
603C2×C42C23×C4711yescharacteristic
604#108—22no—
605C4⋊C8—22no—
606#104—22no—
607#104—22no—
608#104—22no—
609#104—22no—
610#104—21no—
611#104—21no—
612#104—21no—
613#104—21no—
614#104D4×C4712yescomplemented
615#104D4×C4712yescomplemented
616#103—22no—
617#103—41no—
618#102—22no—
619#101—21no—
620#101—21no—
621#101—22no—
622#100—21no—
623#100—21no—
624#100—22no—
625#99—41no—
626C24—21no—
627#41—21no—
628#41—21no—
629#41—21no—
630#41—21no—
631#41—24no—
632#41—22no—
633#41—22no—
634#41—22no—
635#41—22no—
636#41—21no—
637#41—21no—
638#41—21no—
639#41—21no—
640#41—21no—
641#41—21no—
642#41—21no—
643#41—21no—
644#41—42no—
645#41—42no—
646#41—42no—
647#41—42no—
648#41—42no—
649#41—44no—
650#41—42no—
651#41—41no—
652#41—41no—
653#41—44no—
654#41—42no—
655#41C2×D4×C4712yes—
656#41C2×D4×C4712yes—
657#41C2×D4×C4712yes—
658#41C2×D4×C4712yes—
659C2×Q8—21no—
660C2×Q8—24no—
661C2×Q8—22no—
662C2×Q8—22no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—41no—
668C2×Q8—42no—
669C2×Q8—42no—
670C2×Q8—41no—
671C2×Q8—42no—
672C2×Q8C2×D4×C4711yescharacteristic
673C2×Q8C2×D4×C4711yescharacteristic
674C2×Q8C2×D4×C4712yes—
675C2×Q8C2×D4×C4711yescharacteristic
676C2×Q8#41×C4711yescharacteristic
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—22no—
680C2×D4—22no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—42no—
690C2×D4—41no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—41no—
694C2×D4—42no—
695C2×D4C2×D4×C4711yescharacteristic
696C2×D4C2×D4×C4711yescharacteristic
697C2×D4C2×D4×C4711yescharacteristic
698C2×D4#41×C4711yescharacteristic
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—42no—
706C22×C4—41no—
707C22×C4—41no—
708C22×C4—41no—
709C22×C4C24×C4711yescharacteristic
710Q16—24no—
711Q16—22no—
712Q16—22no—
713Q16—24no—
714SD16—24no—
715SD16—22no—
716SD16—22no—
717SD16—22no—
718SD16—22no—
719SD16—24no—
720SD16—42no—
721SD16—42no—
722SD16—42no—
723D8—22no—
724D8—22no—
725D8—42no—
726D8—42no—
727D8—42no—
728M16—24no—
729M16—21no—
730M16—21no—
731M16—21no—
732M16—21no—
733M16—21no—
734M16—21no—
735M16—21no—
736M16—21no—
737M16—21no—
738M16—21no—
739M16—42no—
740M16C2×D4×C4712yes—
741M16C2×D4×C4712yes—
742C2×C8—24no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—42no—
749C2×C8C2×D4×C4712yes—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—41no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—42no—
756C22⋊C4—42no—
757C22⋊C4—41no—
758C22⋊C4—42no—
759C42—21no—
760C42—21no—
761C42—21no—
762C42—41no—
763C42C2×D4×C4711yescharacteristic
764C42C2×D4×C4711yescharacteristic
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—42no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—82no—
774C23H(5,𝔽2)×C4711yescharacteristic
775Q8—21no—
776Q8—21no—
777Q8—21no—
778Q8—22no—
779Q8—21no—
780Q8—21no—
781Q8—21no—
782Q8—22no—
783Q8—42no—
784Q8—44no—
785Q8—41no—
786Q8—41no—
787Q8#120×C4712yes—
788Q8#121×C4712yes—
789D4—22no—
790D4—22no—
791D4—22no—
792D4—22no—
793D4—21no—
794D4—21no—
795D4—21no—
796D4—21no—
797D4—21no—
798D4—21no—
799D4—42no—
800D4—42no—
801D4—42no—
802D4—44no—
803D4—41no—
804D4—41no—
805D4—41no—
806D4—41no—
807D4—41no—
808D4—41no—
809D4—41no—
810D4—41no—
811D4—162no—
812D4#120×C4712yes—
813D4#121×C4712yes—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—22no—
824C2×C4—21no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—81no—
839C2×C4—82no—
840C2×C4C22×D4×C4711yescharacteristic
841C2×C4C22×D4×C4711yescharacteristic
842C2×C4C22×D4×C4711yescharacteristic
843C2×C4C22×D4×C4711yescharacteristic
844C2×C4C2×#41×C4711yescharacteristic
845C2×C4H(5,𝔽2)×C4711yescharacteristic
846C8—22no—
847C8—22no—
848C8—22no—
849C8—41no—
850C8—41no—
851C8—41no—
852C22—22no—
853C22—22no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—82no—
862C22—82no—
863C22—81no—
864C22—161no—
865C22—162no—
866C22C47×#53411yescharacteristic
867C22D42×C4711yescharacteristic
868C22C47×#54611yescharacteristic
869C4—22no—
870C4—22no—
871C4—41no—
872C4—41no—
873C4—41no—
874C4—42no—
875C4—41no—
876C4—81no—
877C4—81no—
878C4C2×#120×C4711yescharacteristic
879C4C2×#121×C4711yescharacteristic
880C4D42×C4711yescharacteristic
881C4C47×#54611yescharacteristic
882C2—21no—
883C2—21no—
884C2—21no—
885C2—42no—
886C2—42no—
887C2—81no—
888C2—81no—
889C2—161no—
890C2C47×#241011yescharacteristic
subgroupG/H
center, socleC2×C47#2410
commutator, Frattini, cosocleC22×C4C24×C47
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C47 ◁ C22×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3586C2semidirect
2. C47×#3068C2semidirect
3. C47×#3040C2semidirect
4. C47×#3021C2semidirect
5. C2×C47×#454C2semidirect
6. C47×#2901C2semidirect
7. C47×#2050C2semidirect
8. C47×#2049C2semidirect
9. C47×#2008C2semidirect
10. C47×#2004C2semidirect
11. C47×#1906C2semidirect
12. C47×#1903C2semidirect
13. C47×#1902C2semidirect
14. C47×#1861C2semidirect
15. C47×#1796C2semidirect
30. C2×AGL(1,ℤ/8)×C47C22semidirect
34. C2×#124×C47C22semidirect
44. C47×#430C22semidirect
45. C47×#423C22semidirect
54. C2×#104×C47C22semidirect
55. C47×#419C22semidirect
56. C47×#419C22semidirect
57. C47×#418C22semidirect
59. C47×#413C22semidirect
60. C2×#101×C47C22semidirect
61. C2×#100×C47C22semidirect
62. C47×#410C22semidirect
63. C47×#344C22semidirect
64. C47×#344C22semidirect
65. C47×#339C22semidirect
66. C47×#338C22semidirect
102. #137×C47D4semidirect
113. AGL(1,ℤ/8)×C47D4semidirect
120. C2×Q16×C47D4semidirect
126. C2×SD16×C47D4semidirect
168. #104×C47D4semidirect
169. #104×C47D4semidirect
406. #24473C47direct (N × H)
437. #3586C2×C47semidirect
438. #3068C2×C47semidirect
439. #3040C2×C47semidirect
440. #3021C2×C47semidirect
441. C2×#454C2×C47semidirect
442. #2901C2×C47semidirect
443. #2050C2×C47semidirect
444. #2049C2×C47semidirect
445. #2008C2×C47semidirect
446. #2004C2×C47semidirect
447. #1906C2×C47semidirect
448. #1903C2×C47semidirect
449. #1902C2×C47semidirect
450. #1861C2×C47semidirect
451. #1796C2×C47semidirect
475. C2×AGL(1,ℤ/8)C22×C47semidirect
479. C2×#124C22×C47semidirect
489. #430C22×C47semidirect
490. #423C22×C47semidirect
499. C2×#104C22×C47semidirect
500. #419C22×C47semidirect
501. #419C22×C47semidirect
502. #418C22×C47semidirect
504. #413C22×C47semidirect
505. C2×#101C22×C47semidirect
506. C2×#100C22×C47semidirect
507. #410C22×C47semidirect
508. #344C22×C47semidirect
509. #344C22×C47semidirect
510. #339C22×C47semidirect
511. #338C22×C47semidirect
512. C47#24473direct (N × H)
548. #137D4×C47semidirect
559. AGL(1,ℤ/8)D4×C47semidirect
566. C2×Q16D4×C47semidirect
572. C2×SD16D4×C47semidirect
614. #104D4×C47semidirect
615. #104D4×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#35862
C47×#30682
C47×#30402
C47×#30212
C2×C47×#4542
C47×#29012
C47×#20502
C47×#20492
C47×#20082
C47×#20042
C47×#19062
C47×#19032
C47×#19022
C47×#18612
C47×#17962
#2447347