Finite Group Databasebeta

← C47×#25446 #26065144

Subgroups — C47×#25446 #26065144

Order 12032.

876 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3154C211yesmaximal, characteristic, complemented
2C47×#3069C211yesmaximal, characteristic, complemented
3C47×#3068C211yesmaximal, characteristic, complemented
4C47×#3067C211yesmaximal, characteristic, complemented
5C2×C47×#471C211yesmaximal, characteristic, complemented
6C47×#2957C211yesmaximal, characteristic, complemented
7C47×#2049C211yesmaximal, characteristic, complemented
8C47×#2048C211yesmaximal, characteristic, complemented
9C47×#2009C211yesmaximal, characteristic, complemented
10C47×#2008C211yesmaximal, characteristic, complemented
11C47×#1977C211yesmaximal, characteristic, complemented
12C47×#1953C211yesmaximal, characteristic, complemented
13C47×#1915C211yesmaximal, characteristic, complemented
14C47×#1914C211yesmaximal, characteristic, complemented
15C47×#1757C211yesmaximal, characteristic, complemented
16C47×#575C2211yescharacteristic
17C47×#575C2211yescharacteristic
18C2×#137×C47C2211yescharacteristic
19C2×#137×C47C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
21C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
22C2×#135×C47C2211yescharacteristic
23C22×SD16×C47C2211yescharacteristic
24C47×#568C2211yescharacteristic
25C47×#568C2211yescharacteristic
26C2×#131×C47C2211yescharacteristic
27C47×#536C2211yescharacteristic
28C47×#535C2211yescharacteristic
29C47×#497—21no—
30C47×#496—21no—
31C47×#495—21no—
32C47×#492—21no—
33C47×#473—22no—
34C47×#473—21no—
35C47×#472—22no—
36C47×#472—21no—
37C47×#471—22no—
38C47×#471—22no—
39C47×#471—21no—
40C47×#471—21no—
41C47×#471—22no—
42C47×#471—22no—
43C47×#444—22no—
44C47×#443—22no—
45C47×#430C2211yescharacteristic
46C47×#430C2211yescharacteristic
47C2×#108×C47C2211yescharacteristic
48C2×#108×C47C2211yescharacteristic
49C47×#421C2211yescharacteristic
50C47×#421C2211yescharacteristic
51C47×#419C2211yescharacteristic
52C47×#418C2211yescharacteristic
53C47×#413C2211yescharacteristic
54C47×#413C2211yescharacteristic
55C47×#413C2211yescharacteristic
56C2×#101×C47C2211yescharacteristic
57C2×#101×C47C2211yescharacteristic
58C2×#100×C47C2211yescharacteristic
59C2×#100×C47C2211yescharacteristic
60C47×#410C2211yescharacteristic
61C47×#405C2211yescharacteristic
62C47×#405C2211yescharacteristic
63C47×#344C2211yescharacteristic
64C47×#344C2211yescharacteristic
65C47×#344C2211yescharacteristic
66C47×#344C2211yescharacteristic
67C2×#41×C47C2311yescharacteristic
68C2×#41×C47C2311yescharacteristic
69C2×#41×C47C2311yescharacteristic
70C22×Q8×C47C2311yescharacteristic
71C22×D4×C47C2311yescharacteristic
72#137×C47—21no—
73#137×C47—21no—
74#137×C47—21no—
75#137×C47—21no—
76#137×C47—22no—
77#137×C47—22no—
78#137×C47—41no—
79#137×C47—41no—
80AGL(1,ℤ/8)×C47—21no—
81AGL(1,ℤ/8)×C47—21no—
82AGL(1,ℤ/8)×C47—21no—
83AGL(1,ℤ/8)×C47—21no—
84AGL(1,ℤ/8)×C47—22no—
85AGL(1,ℤ/8)×C47—22no—
86AGL(1,ℤ/8)×C47—41no—
87AGL(1,ℤ/8)×C47—41no—
88#135×C47—21no—
89#135×C47—21no—
90#135×C47—21no—
91#135×C47—21no—
92#135×C47—41no—
93#135×C47—41no—
94C2×Q16×C47—21no—
95C2×Q16×C47—21no—
96C2×Q16×C47D411yescharacteristic
97C2×SD16×C47—21no—
98C2×SD16×C47—21no—
99C2×SD16×C47—21no—
100C2×SD16×C47—21no—
101C2×SD16×C47—21no—
102C2×SD16×C47—21no—
103C2×SD16×C47—21no—
104C2×SD16×C47—21no—
105C2×SD16×C47—21no—
106C2×SD16×C47—21no—
107C2×SD16×C47D411yescharacteristic
108C2×SD16×C47D411yescharacteristic
109C2×D8×C47—21no—
110C2×D8×C47—21no—
111C2×D8×C47D411yescharacteristic
112#131×C47—22no—
113#131×C47—22no—
114#131×C47—22no—
115#131×C47—22no—
116#131×C47—21no—
117#131×C47—21no—
118#131×C47—21no—
119#131×C47—21no—
120C2×M16×C47—21no—
121C2×M16×C47—41no—
122C2×M16×C47—41no—
123C2×M16×C47C2311yescharacteristic
124C2×M16×C47C2311yescharacteristic
125C2×M16×C47C2311yescharacteristic
126C2×M16×C47C2311yescharacteristic
127C2×M16×C47C2311yescharacteristic
128C2×M16×C47C2311yescharacteristic
129C2×M16×C47C2311yescharacteristic
130C22×C8×C47—21no—
131C22×C8×C47C2311yescharacteristic
132C4⋊Q8×C47—21no—
133#127×C47—21no—
134#124×C47—21no—
135#124×C47—21no—
136#123×C47—22no—
137C22⋊Q8×C47—41no—
138#121×C47—41no—
139#120×C47—22no—
140#117×C47C2311yescharacteristic
141#117×C47C2311yescharacteristic
142#108×C47—22no—
143#108×C47—22no—
144#108×C47—21no—
145#108×C47—21no—
146#108×C47D412yescomplemented
147#108×C47D412yescomplemented
148#104×C47—22no—
149#104×C47—22no—
150#103×C47—41no—
151#102×C47—41no—
152#101×C47—21no—
153#101×C47—21no—
154#101×C47—22no—
155#101×C47—22no—
156#101×C47D412yescomplemented
157#100×C47—21no—
158#100×C47—21no—
159#100×C47—22no—
160#100×C47—22no—
161#100×C47D412yescomplemented
162#99×C47—22no—
163#97×C47—21no—
164#97×C47—21no—
165C4×C8×C47—21no—
166C4×C8×C47—21no—
167C24×C47—21no—
168#41×C47—21no—
169#41×C47—21no—
170#41×C47—21no—
171#41×C47—21no—
172#41×C47—21no—
173#41×C47—21no—
174#41×C47—21no—
175#41×C47—21no—
176#41×C47—21no—
177#41×C47—21no—
178#41×C47—21no—
179#41×C47—21no—
180C2×Q8×C47—21no—
181C2×Q8×C47—21no—
182C2×Q8×C47—21no—
183C2×Q8×C47—21no—
184C2×Q8×C47—21no—
185C2×Q8×C47—21no—
186C2×Q8×C47C2×D411yescharacteristic
187C2×Q8×C47C2×D411yescharacteristic
188C2×Q8×C47C2×D411yescharacteristic
189C2×D4×C47—21no—
190C2×D4×C47—21no—
191C2×D4×C47—21no—
192C2×D4×C47—21no—
193C2×D4×C47—21no—
194C2×D4×C47—21no—
195C2×D4×C47—21no—
196C2×D4×C47—21no—
197C2×D4×C47—21no—
198C2×D4×C47—42no—
199C2×D4×C47C2×D411yescharacteristic
200C2×D4×C47C2×D411yescharacteristic
201C2×D4×C47C2×D411yescharacteristic
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—21no—
205C22×C4×C47—21no—
206C22×C4×C47C2411yescharacteristic
207Q16×C47—21no—
208Q16×C47—21no—
209Q16×C47—42no—
210Q16×C47—42no—
211Q16×C47—41no—
212Q16×C47—41no—
213SD16×C47—21no—
214SD16×C47—21no—
215SD16×C47—21no—
216SD16×C47—21no—
217SD16×C47—42no—
218SD16×C47—42no—
219SD16×C47—42no—
220SD16×C47—42no—
221SD16×C47—41no—
222SD16×C47—41no—
223SD16×C47—41no—
224SD16×C47—41no—
225SD16×C47—41no—
226SD16×C47—41no—
227SD16×C47—41no—
228SD16×C47—41no—
229D8×C47—21no—
230D8×C47—21no—
231D8×C47—42no—
232D8×C47—42no—
233D8×C47—41no—
234D8×C47—41no—
235M16×C47—21no—
236M16×C47—21no—
237M16×C47—21no—
238M16×C47—21no—
239M16×C47—21no—
240M16×C47—21no—
241M16×C47—21no—
242M16×C47—21no—
243M16×C47—21no—
244M16×C47—21no—
245M16×C47—42no—
246M16×C47—42no—
247M16×C47—41no—
248M16×C47—41no—
249M16×C47C2×D412yes—
250M16×C47C2×D412yes—
251M16×C47C2×D412yes—
252M16×C47C2×D412yes—
253C2×C8×C47—21no—
254C2×C8×C47—21no—
255C2×C8×C47—21no—
256C2×C8×C47—21no—
257C2×C8×C47—21no—
258C2×C8×C47—21no—
259C2×C8×C47—21no—
260C2×C8×C47—42no—
261C2×C8×C47—42no—
262C2×C8×C47—41no—
263C2×C8×C47—41no—
264C2×C8×C47C2×D411yescharacteristic
265C2×C8×C47C2×D411yescharacteristic
266C2×C8×C47C2×D411yescharacteristic
267C2×C8×C47C2×D411yescharacteristic
268C2×C8×C47#4111yescharacteristic
269C2×C8×C47#4111yescharacteristic
270C4⋊C4×C47—21no—
271C4⋊C4×C47—21no—
272C4⋊C4×C47—42no—
273C22⋊C4×C47—21no—
274C22⋊C4×C47—42no—
275C22⋊C4×C47—42no—
276C22⋊C4×C47#4112yes—
277C42×C47—21no—
278C42×C47—21no—
279C23×C47—21no—
280C23×C47—21no—
281C23×C47—21no—
282C23×C47—41no—
283C23×C47—41no—
284C23×C47—41no—
285C23×C47—161no—
286C23×C47C2×#4111yescharacteristic
287Q8×C47—21no—
288Q8×C47—21no—
289Q8×C47—21no—
290Q8×C47—21no—
291Q8×C47—21no—
292Q8×C47—21no—
293Q8×C47—41no—
294Q8×C47—41no—
295Q8×C47—41no—
296Q8×C47—41no—
297D4×C47—21no—
298D4×C47—21no—
299D4×C47—21no—
300D4×C47—21no—
301D4×C47—21no—
302D4×C47—21no—
303D4×C47—41no—
304D4×C47—41no—
305D4×C47—41no—
306D4×C47—41no—
307D4×C47—41no—
308D4×C47—41no—
309D4×C47—41no—
310D4×C47—41no—
311D4×C47—41no—
312D4×C47—41no—
313D4×C47—162no—
314C2×C4×C47—21no—
315C2×C4×C47—22no—
316C2×C4×C47—21no—
317C2×C4×C47—21no—
318C2×C4×C47—41no—
319C2×C4×C47—41no—
320C2×C4×C47—41no—
321C2×C4×C47—41no—
322C2×C4×C47—41no—
323C2×C4×C47—41no—
324C2×C4×C47—41no—
325C2×C4×C47—41no—
326C2×C4×C47—41no—
327C2×C4×C47—41no—
328C2×C4×C47C22×D411yescharacteristic
329C2×C4×C47C22×D411yescharacteristic
330C2×C4×C47C22×D411yescharacteristic
331C2×C4×C47C2×#4111yescharacteristic
332C2×C4×C47H(5,𝔽2)11yescharacteristic
333C2×C4×C47H(5,𝔽2)11yescharacteristic
334C8×C47—22no—
335C8×C47—22no—
336C8×C47—22no—
337C8×C47—22no—
338C8×C47—41no—
339C8×C47—41no—
340C8×C47—41no—
341C8×C47#12111yescharacteristic
342C8×C47#12111yescharacteristic
343C8×C47#12111yescharacteristic
344C8×C47#12111yescharacteristic
345#25446C4711yesmaximal, characteristic, direct product factor, Sylow
346C22×C47—41no—
347C22×C47—41no—
348C22×C47—41no—
349C22×C47—41no—
350C22×C47—81no—
351C22×C47—81no—
352C22×C47—81no—
353C22×C47—82no—
354C22×C47—81no—
355C22×C47—161no—
356C22×C47—161no—
357C22×C47#53211yescharacteristic
358C22×C47#54611yescharacteristic
359C22×C47#55011yescharacteristic
360C4×C47—42no—
361C4×C47—41no—
362C4×C47—41no—
363C4×C47—41no—
364C4×C47—81no—
365C4×C47—81no—
366C4×C47C2×#12111yescharacteristic
367C4×C47#54011yescharacteristic
368C4×C47D4211yescharacteristic
369C4×C47D4211yescharacteristic
370#3154C2×C4711yescharacteristic, complemented
371#3069C2×C4711yescharacteristic, complemented
372#3068C2×C4711yescharacteristic, complemented
373#3067C2×C4711yescharacteristic, complemented
374C2×#471C2×C4711yescharacteristic, complemented
375#2957C2×C4711yescharacteristic, complemented
376#2049C2×C4711yescharacteristic, complemented
377#2048C2×C4711yescharacteristic, complemented
378#2009C2×C4711yescharacteristic, complemented
379#2008C2×C4711yescharacteristic, complemented
380#1977C2×C4711yescharacteristic, complemented
381#1953C2×C4711yescharacteristic, complemented
382#1915C2×C4711yescharacteristic, complemented
383#1914C2×C4711yescharacteristic, complemented
384#1757C2×C4711yescharacteristic, complemented
385C2×C47—21no—
386C2×C47—21no—
387C2×C47—21no—
388C2×C47—81no—
389C2×C47—81no—
390C2×C47—81no—
391C2×C47—161no—
392C2×C47#242811yescharacteristic
393#575C22×C4711yescharacteristic
394#575C22×C4711yescharacteristic
395C2×#137C22×C4711yescharacteristic
396C2×#137C22×C4711yescharacteristic
397C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
398C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
399C2×#135C22×C4711yescharacteristic
400C22×SD16C22×C4711yescharacteristic
401#568C22×C4711yescharacteristic
402#568C22×C4711yescharacteristic
403C2×#131C22×C4711yescharacteristic
404#536C22×C4711yescharacteristic
405#535C22×C4711yescharacteristic
406#497—21no—
407#496—21no—
408#495—21no—
409#492—21no—
410#473—21no—
411#473—22no—
412#472—21no—
413#472—22no—
414#471—21no—
415#471—21no—
416#471—22no—
417#471—22no—
418#471—22no—
419#471—22no—
420#444—22no—
421#443—22no—
422#430C22×C4711yescharacteristic
423#430C22×C4711yescharacteristic
424C2×#108C22×C4711yescharacteristic
425C2×#108C22×C4711yescharacteristic
426#421C22×C4711yescharacteristic
427#421C22×C4711yescharacteristic
428#419C22×C4711yescharacteristic
429#418C22×C4711yescharacteristic
430#413C22×C4711yescharacteristic
431#413C22×C4711yescharacteristic
432#413C22×C4711yescharacteristic
433C2×#101C22×C4711yescharacteristic
434C2×#101C22×C4711yescharacteristic
435C2×#100C22×C4711yescharacteristic
436C2×#100C22×C4711yescharacteristic
437#410C22×C4711yescharacteristic
438#405C22×C4711yescharacteristic
439#405C22×C4711yescharacteristic
440#344C22×C4711yescharacteristic
441#344C22×C4711yescharacteristic
442#344C22×C4711yescharacteristic
443#344C22×C4711yescharacteristic
444C47#2544611yescharacteristic, direct product factor, Sylow
445C2×#41C23×C4711yescharacteristic
446C2×#41C23×C4711yescharacteristic
447C2×#41C23×C4711yescharacteristic
448C22×Q8C23×C4711yescharacteristic
449C22×D4C23×C4711yescharacteristic
450#137—21no—
451#137—21no—
452#137—21no—
453#137—21no—
454#137—22no—
455#137—22no—
456#137—41no—
457#137—41no—
458AGL(1,ℤ/8)—21no—
459AGL(1,ℤ/8)—21no—
460AGL(1,ℤ/8)—21no—
461AGL(1,ℤ/8)—21no—
462AGL(1,ℤ/8)—22no—
463AGL(1,ℤ/8)—22no—
464AGL(1,ℤ/8)—41no—
465AGL(1,ℤ/8)—41no—
466#135—21no—
467#135—21no—
468#135—21no—
469#135—21no—
470#135—41no—
471#135—41no—
472C2×Q16—21no—
473C2×Q16—21no—
474C2×Q16D4×C4711yescharacteristic
475C2×SD16—21no—
476C2×SD16—21no—
477C2×SD16—21no—
478C2×SD16—21no—
479C2×SD16—21no—
480C2×SD16—21no—
481C2×SD16—21no—
482C2×SD16—21no—
483C2×SD16—21no—
484C2×SD16—21no—
485C2×SD16D4×C4711yescharacteristic
486C2×SD16D4×C4711yescharacteristic
487C2×D8—21no—
488C2×D8—21no—
489C2×D8D4×C4711yescharacteristic
490#131—22no—
491#131—22no—
492#131—22no—
493#131—22no—
494#131—21no—
495#131—21no—
496#131—21no—
497#131—21no—
498C2×M16—21no—
499C2×M16—41no—
500C2×M16—41no—
501C2×M16C23×C4711yescharacteristic
502C2×M16C23×C4711yescharacteristic
503C2×M16C23×C4711yescharacteristic
504C2×M16C23×C4711yescharacteristic
505C2×M16C23×C4711yescharacteristic
506C2×M16C23×C4711yescharacteristic
507C2×M16C23×C4711yescharacteristic
508C22×C8—21no—
509C22×C8C23×C4711yescharacteristic
510C4⋊Q8—21no—
511#127—21no—
512#124—21no—
513#124—21no—
514#123—22no—
515C22⋊Q8—41no—
516#121—41no—
517#120—22no—
518#117C23×C4711yescharacteristic
519#117C23×C4711yescharacteristic
520#108—22no—
521#108—22no—
522#108—21no—
523#108—21no—
524#108D4×C4712yescomplemented
525#108D4×C4712yescomplemented
526#104—22no—
527#104—22no—
528#103—41no—
529#102—41no—
530#101—21no—
531#101—21no—
532#101—22no—
533#101—22no—
534#101D4×C4712yescomplemented
535#100—21no—
536#100—21no—
537#100—22no—
538#100—22no—
539#100D4×C4712yescomplemented
540#99—22no—
541#97—21no—
542#97—21no—
543C4×C8—21no—
544C4×C8—21no—
545C24—21no—
546#41—21no—
547#41—21no—
548#41—21no—
549#41—21no—
550#41—21no—
551#41—21no—
552#41—21no—
553#41—21no—
554#41—21no—
555#41—21no—
556#41—21no—
557#41—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8C2×D4×C4711yescharacteristic
565C2×Q8C2×D4×C4711yescharacteristic
566C2×Q8C2×D4×C4711yescharacteristic
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—42no—
577C2×D4C2×D4×C4711yescharacteristic
578C2×D4C2×D4×C4711yescharacteristic
579C2×D4C2×D4×C4711yescharacteristic
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4C24×C4711yescharacteristic
585Q16—21no—
586Q16—21no—
587Q16—42no—
588Q16—42no—
589Q16—41no—
590Q16—41no—
591SD16—21no—
592SD16—21no—
593SD16—21no—
594SD16—21no—
595SD16—42no—
596SD16—42no—
597SD16—42no—
598SD16—42no—
599SD16—41no—
600SD16—41no—
601SD16—41no—
602SD16—41no—
603SD16—41no—
604SD16—41no—
605SD16—41no—
606SD16—41no—
607D8—21no—
608D8—21no—
609D8—42no—
610D8—42no—
611D8—41no—
612D8—41no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—21no—
617M16—21no—
618M16—21no—
619M16—21no—
620M16—21no—
621M16—21no—
622M16—21no—
623M16—42no—
624M16—42no—
625M16—41no—
626M16—41no—
627M16C2×D4×C4712yes—
628M16C2×D4×C4712yes—
629M16C2×D4×C4712yes—
630M16C2×D4×C4712yes—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—42no—
639C2×C8—42no—
640C2×C8—41no—
641C2×C8—41no—
642C2×C8C2×D4×C4711yescharacteristic
643C2×C8C2×D4×C4711yescharacteristic
644C2×C8C2×D4×C4711yescharacteristic
645C2×C8C2×D4×C4711yescharacteristic
646C2×C8#41×C4711yescharacteristic
647C2×C8#41×C4711yescharacteristic
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—42no—
651C22⋊C4—21no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4#41×C4712yes—
655C42—21no—
656C42—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—161no—
664C23C2×#41×C4711yescharacteristic
665Q8—21no—
666Q8—21no—
667Q8—21no—
668Q8—21no—
669Q8—21no—
670Q8—21no—
671Q8—41no—
672Q8—41no—
673Q8—41no—
674Q8—41no—
675D4—21no—
676D4—21no—
677D4—21no—
678D4—21no—
679D4—21no—
680D4—21no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—41no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—41no—
690D4—41no—
691D4—162no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4C22×D4×C4711yescharacteristic
707C2×C4C22×D4×C4711yescharacteristic
708C2×C4C22×D4×C4711yescharacteristic
709C2×C4C2×#41×C4711yescharacteristic
710C2×C4H(5,𝔽2)×C4711yescharacteristic
711C2×C4H(5,𝔽2)×C4711yescharacteristic
712C8—22no—
713C8—22no—
714C8—22no—
715C8—22no—
716C8—41no—
717C8—41no—
718C8—41no—
719C8#121×C4711yescharacteristic
720C8#121×C4711yescharacteristic
721C8#121×C4711yescharacteristic
722C8#121×C4711yescharacteristic
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—82no—
731C22—81no—
732C22—161no—
733C22—161no—
734C22C47×#53211yescharacteristic
735C22C47×#54611yescharacteristic
736C22C47×#55011yescharacteristic
737C4—42no—
738C4—41no—
739C4—41no—
740C4—41no—
741C4—81no—
742C4—81no—
743C4C2×#121×C4711yescharacteristic
744C4C47×#54011yescharacteristic
745C4D42×C4711yescharacteristic
746C4D42×C4711yescharacteristic
747C2—21no—
748C2—21no—
749C2—21no—
750C2—81no—
751C2—81no—
752C2—81no—
753C2—161no—
754C2C47×#242811yescharacteristic
subgroupG/H
center, socleC2×C47#2428
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×#3154C2semidirect
2. C47×#3069C2semidirect
3. C47×#3068C2semidirect
4. C47×#3067C2semidirect
5. C2×C47×#471C2semidirect
6. C47×#2957C2semidirect
7. C47×#2049C2semidirect
8. C47×#2048C2semidirect
9. C47×#2009C2semidirect
10. C47×#2008C2semidirect
11. C47×#1977C2semidirect
12. C47×#1953C2semidirect
13. C47×#1915C2semidirect
14. C47×#1914C2semidirect
15. C47×#1757C2semidirect
146. #108×C47D4semidirect
147. #108×C47D4semidirect
156. #101×C47D4semidirect
161. #100×C47D4semidirect
345. #25446C47direct (N × H)
370. #3154C2×C47semidirect
371. #3069C2×C47semidirect
372. #3068C2×C47semidirect
373. #3067C2×C47semidirect
374. C2×#471C2×C47semidirect
375. #2957C2×C47semidirect
376. #2049C2×C47semidirect
377. #2048C2×C47semidirect
378. #2009C2×C47semidirect
379. #2008C2×C47semidirect
380. #1977C2×C47semidirect
381. #1953C2×C47semidirect
382. #1915C2×C47semidirect
383. #1914C2×C47semidirect
384. #1757C2×C47semidirect
444. C47#25446direct (N × H)
524. #108D4×C47semidirect
525. #108D4×C47semidirect
534. #101D4×C47semidirect
539. #100D4×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#31542
C47×#30692
C47×#30682
C47×#30672
C2×C47×#4712
C47×#29572
C47×#20492
C47×#20482
C47×#20092
C47×#20082
C47×#19772
C47×#19532
C47×#19152
C47×#19142
C47×#17572
#2544647