Finite Group Databasebeta

← C47×#25196 #26064894

Subgroups — C47×#25196 #26064894

Order 12032.

1032 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3068C211yesmaximal, characteristic, complemented
2C47×#3068C211yesmaximal, characteristic, complemented
3C47×#3019C211yesmaximal, characteristic, complemented
4C2×C47×#453C211yesmaximal, characteristic, complemented
5C47×#2956C211yesmaximal, characteristic, complemented
6C47×#2888C211yesmaximal, characteristic, complemented
7C47×#2069C211yesmaximal, characteristic, complemented
8C47×#2050C211yesmaximal, characteristic, complemented
9C47×#2048C211yesmaximal, characteristic, complemented
10C47×#2002C211yesmaximal, characteristic, complemented
11C47×#1965C211yesmaximal, characteristic, complemented
12C47×#1932C211yesmaximal, characteristic, complemented
13C47×#1914C211yesmaximal, characteristic, complemented
14C47×#1903C211yesmaximal, characteristic, complemented
15C47×#1861C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C47C2211yescharacteristic
17C47×#575C2211yescharacteristic
18C47×#575C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
21C2×AGL(1,ℤ/8)×C47C2211yescharacteristic, complemented
22C47×#568C2211yescharacteristic
23C47×#568C2211yescharacteristic
24C47×#568C2211yescharacteristic, complemented
25C47×#535C2211yescharacteristic
26C2×#127×C47C2211yescharacteristic
27C47×#472—22no—
28C47×#472—22no—
29C47×#471—22no—
30C47×#471—22no—
31C47×#455—22no—
32C47×#453—22no—
33C47×#453—22no—
34C47×#453—22no—
35C47×#444—22no—
36C47×#443—22no—
37C47×#430C2211yescharacteristic, complemented
38C47×#430C2211yescharacteristic, complemented
39C47×#430C2211yescharacteristic, complemented
40C47×#423C2211yescharacteristic, complemented
41C47×#421C2211yescharacteristic
42C47×#421C2211yescharacteristic
43C2×#104×C47C2211yescharacteristic
44C2×#104×C47C2211yescharacteristic
45C2×#104×C47C2211yescharacteristic, complemented
46C47×#418C2211yescharacteristic, complemented
47C47×#413—22no—
48C47×#413C2211yescharacteristic
49C47×#413C2211yescharacteristic
50C47×#413C2211yescharacteristic, complemented
51C2×#100×C47—22no—
52C2×#100×C47C2211yescharacteristic
53C2×#100×C47C2211yescharacteristic
54C2×#100×C47C2211yescharacteristic
55C2×#100×C47C2211yescharacteristic
56C2×#100×C47C2211yescharacteristic, complemented
57C2×#100×C47C2211yescharacteristic, complemented
58C4×M16×C47C2211yescharacteristic, complemented
59C47×#344C2211yescharacteristic, complemented
60C47×#344C2211yescharacteristic, complemented
61C47×#339C2211yescharacteristic, complemented
62C47×#338C2211yescharacteristic, complemented
63H(5,𝔽2)×C47—22no—
64H(5,𝔽2)×C47—22no—
65H(5,𝔽2)×C47—41no—
66H(5,𝔽2)×C47—41no—
67C2×#41×C47—21no—
68C2×#41×C47—21no—
69C2×#41×C47C2311yescharacteristic
70C2×#41×C47C2311yescharacteristic
71C2×#41×C47C2311yescharacteristic
72C22×D4×C47—22no—
73C22×D4×C47—21no—
74C22×D4×C47—21no—
75C22×D4×C47—22no—
76C22×D4×C47C2311yescharacteristic
77C22×D4×C47C2311yescharacteristic
78#137×C47—21no—
79#137×C47—21no—
80#137×C47—21no—
81#137×C47D412yescomplemented
82AGL(1,ℤ/8)×C47—21no—
83AGL(1,ℤ/8)×C47—22no—
84AGL(1,ℤ/8)×C47—22no—
85AGL(1,ℤ/8)×C47—21no—
86AGL(1,ℤ/8)×C47—21no—
87AGL(1,ℤ/8)×C47—22no—
88AGL(1,ℤ/8)×C47—22no—
89AGL(1,ℤ/8)×C47—41no—
90AGL(1,ℤ/8)×C47—41no—
91AGL(1,ℤ/8)×C47D412yescomplemented
92#135×C47—22no—
93#135×C47—41no—
94C2×SD16×C47—21no—
95C2×SD16×C47—21no—
96C2×SD16×C47—21no—
97C2×D8×C47—21no—
98C2×D8×C47—21no—
99C2×D8×C47—21no—
100#131×C47—22no—
101#131×C47—22no—
102#131×C47—22no—
103#131×C47—22no—
104#131×C47—41no—
105#131×C47—41no—
106C2×M16×C47—22no—
107C2×M16×C47—22no—
108C2×M16×C47—41no—
109C2×M16×C47C2311yescharacteristic
110C2×M16×C47C2311yescharacteristic
111C2×M16×C47C2311yescharacteristic
112C2×M16×C47C2311yescharacteristic
113C2×M16×C47C2311yescharacteristic
114C2×M16×C47C2311yescharacteristic
115C2×M16×C47C2311yescharacteristic
116C2×M16×C47C2311yescharacteristic
117#127×C47—21no—
118#127×C47—21no—
119#127×C47—21no—
120#127×C47—41no—
121#124×C47—21no—
122#121×C47—41no—
123#120×C47—22no—
124#117×C47C2311yescharacteristic
125C2×C42×C47C2311yescharacteristic
126#108×C47—22no—
127#108×C47—22no—
128#108×C47—22no—
129C4⋊C8×C47—41no—
130#104×C47—22no—
131#104×C47—22no—
132#104×C47—21no—
133#104×C47—21no—
134#104×C47—21no—
135#104×C47—21no—
136#104×C47D412yescomplemented
137#104×C47D412yescomplemented
138#102×C47—41no—
139#101×C47—21no—
140#101×C47—21no—
141#101×C47D412yescomplemented
142#100×C47—21no—
143#100×C47—21no—
144#100×C47—22no—
145#100×C47—22no—
146#100×C47—22no—
147#100×C47—22no—
148#100×C47—22no—
149#100×C47—22no—
150#100×C47D412yescomplemented
151#97×C47—21no—
152C4×C8×C47—21no—
153C24×C47—22no—
154C24×C47—21no—
155C24×C47#4112yes—
156#41×C47—21no—
157#41×C47—21no—
158#41×C47—21no—
159#41×C47—21no—
160#41×C47—21no—
161#41×C47—21no—
162#41×C47—21no—
163#41×C47—21no—
164#41×C47—21no—
165#41×C47—21no—
166#41×C47—42no—
167#41×C47—42no—
168#41×C47—42no—
169#41×C47—42no—
170#41×C47C2×D412yes—
171#41×C47C2×D412yes—
172C2×Q8×C47C2×D411yescharacteristic
173C2×Q8×C47C2×D411yescharacteristic
174C2×Q8×C47#4111yescharacteristic
175C2×D4×C47—21no—
176C2×D4×C47—22no—
177C2×D4×C47—22no—
178C2×D4×C47—21no—
179C2×D4×C47—21no—
180C2×D4×C47—21no—
181C2×D4×C47—21no—
182C2×D4×C47—21no—
183C2×D4×C47—21no—
184C2×D4×C47—21no—
185C2×D4×C47—21no—
186C2×D4×C47—21no—
187C2×D4×C47—21no—
188C2×D4×C47—21no—
189C2×D4×C47—21no—
190C2×D4×C47—21no—
191C2×D4×C47—21no—
192C2×D4×C47—42no—
193C2×D4×C47—42no—
194C2×D4×C47—42no—
195C2×D4×C47—42no—
196C2×D4×C47—44no—
197C2×D4×C47—44no—
198C2×D4×C47—42no—
199C2×D4×C47—42no—
200C2×D4×C47—42no—
201C2×D4×C47—84no—
202C2×D4×C47C2×D411yescharacteristic
203C2×D4×C47C2×D411yescharacteristic
204C2×D4×C47#4111yescharacteristic
205C22×C4×C47—21no—
206C22×C4×C47—22no—
207C22×C4×C47—21no—
208C22×C4×C47—21no—
209C22×C4×C47—21no—
210C22×C4×C47C2411yescharacteristic
211Q16×C47—22no—
212Q16×C47—41no—
213SD16×C47—22no—
214SD16×C47—22no—
215SD16×C47—42no—
216SD16×C47—42no—
217SD16×C47—41no—
218SD16×C47—41no—
219SD16×C47—42no—
220D8×C47—22no—
221D8×C47—42no—
222D8×C47—42no—
223D8×C47—41no—
224D8×C47—42no—
225M16×C47—21no—
226M16×C47—21no—
227M16×C47—21no—
228M16×C47—21no—
229M16×C47—21no—
230M16×C47—21no—
231M16×C47—21no—
232M16×C47—21no—
233M16×C47—21no—
234M16×C47—21no—
235M16×C47—21no—
236M16×C47—21no—
237M16×C47—42no—
238M16×C47—42no—
239M16×C47—42no—
240M16×C47C2×D412yes—
241M16×C47C2×D412yes—
242M16×C47C2×D412yes—
243M16×C47C2×D412yes—
244C2×C8×C47—21no—
245C2×C8×C47—21no—
246C2×C8×C47—21no—
247C2×C8×C47—21no—
248C2×C8×C47—21no—
249C2×C8×C47—21no—
250C2×C8×C47—21no—
251C2×C8×C47—21no—
252C2×C8×C47—42no—
253C2×C8×C47—42no—
254C2×C8×C47—42no—
255C4⋊C4×C47—21no—
256C22⋊C4×C47—21no—
257C22⋊C4×C47—42no—
258C42×C47—21no—
259C42×C47—21no—
260C42×C47C2×D411yescharacteristic
261C42×C47C2×D411yescharacteristic
262C23×C47—21no—
263C23×C47—22no—
264C23×C47—21no—
265C23×C47—22no—
266C23×C47—21no—
267C23×C47—22no—
268C23×C47—44no—
269C23×C47—41no—
270C23×C47—41no—
271C23×C47—41no—
272C23×C47—82no—
273C23×C47—82no—
274C23×C47—162no—
275C23×C47C2×#4111yescharacteristic
276Q8×C47—21no—
277Q8×C47—21no—
278Q8×C47—21no—
279Q8×C47—21no—
280Q8×C47—21no—
281Q8×C47#12112yes—
282D4×C47—22no—
283D4×C47—22no—
284D4×C47—21no—
285D4×C47—21no—
286D4×C47—21no—
287D4×C47—21no—
288D4×C47—21no—
289D4×C47—44no—
290D4×C47—44no—
291D4×C47—41no—
292D4×C47—41no—
293D4×C47—41no—
294D4×C47—41no—
295D4×C47—41no—
296D4×C47—41no—
297D4×C47—41no—
298D4×C47—41no—
299D4×C47—41no—
300D4×C47—41no—
301D4×C47—41no—
302D4×C47—41no—
303D4×C47—84no—
304D4×C47—84no—
305D4×C47—162no—
306D4×C47#12112yes—
307C2×C4×C47—21no—
308C2×C4×C47—21no—
309C2×C4×C47—22no—
310C2×C4×C47—22no—
311C2×C4×C47—21no—
312C2×C4×C47—21no—
313C2×C4×C47—21no—
314C2×C4×C47—44no—
315C2×C4×C47—42no—
316C2×C4×C47—41no—
317C2×C4×C47—41no—
318C2×C4×C47—41no—
319C2×C4×C47—41no—
320C2×C4×C47—41no—
321C2×C4×C47C22×D411yescharacteristic
322C2×C4×C47C22×D411yescharacteristic
323C2×C4×C47C22×D411yescharacteristic
324C2×C4×C47C2×#4111yescharacteristic
325C2×C4×C47H(5,𝔽2)11yescharacteristic
326C2×C4×C47H(5,𝔽2)11yescharacteristic
327C8×C47—22no—
328C8×C47—22no—
329C8×C47—22no—
330C8×C47—22no—
331C8×C47—41no—
332C8×C47—41no—
333C8×C47—41no—
334C8×C47—41no—
335#25196C4711yesmaximal, characteristic, direct product factor, Sylow
336C22×C47—22no—
337C22×C47—41no—
338C22×C47—41no—
339C22×C47—41no—
340C22×C47—42no—
341C22×C47—81no—
342C22×C47—82no—
343C22×C47—81no—
344C22×C47—82no—
345C22×C47—82no—
346C22×C47—81no—
347C22×C47—82no—
348C22×C47—81no—
349C22×C47—161no—
350C22×C47—161no—
351C22×C47—164no—
352C22×C47#52511yescharacteristic
353C22×C47#54611yescharacteristic
354C22×C47#54611yescharacteristic
355C4×C47—22no—
356C4×C47—22no—
357C4×C47—41no—
358C4×C47—41no—
359C4×C47—41no—
360C4×C47—81no—
361C4×C47C2×#12111yescharacteristic
362C4×C47#53811yescharacteristic
363C4×C47D4211yescharacteristic
364C4×C47D4211yescharacteristic
365#3068C2×C4711yescharacteristic, complemented
366#3068C2×C4711yescharacteristic, complemented
367#3019C2×C4711yescharacteristic, complemented
368C2×#453C2×C4711yescharacteristic, complemented
369#2956C2×C4711yescharacteristic, complemented
370#2888C2×C4711yescharacteristic, complemented
371#2069C2×C4711yescharacteristic, complemented
372#2050C2×C4711yescharacteristic, complemented
373#2048C2×C4711yescharacteristic, complemented
374#2002C2×C4711yescharacteristic, complemented
375#1965C2×C4711yescharacteristic, complemented
376#1932C2×C4711yescharacteristic, complemented
377#1914C2×C4711yescharacteristic, complemented
378#1903C2×C4711yescharacteristic, complemented
379#1861C2×C4711yescharacteristic, complemented
380C2×C47—21no—
381C2×C47—21no—
382C2×C47—21no—
383C2×C47—42no—
384C2×C47—81no—
385C2×C47—82no—
386C2×C47—81no—
387C2×C47—161no—
388C2×C47#242411yescharacteristic
389C2×H(5,𝔽2)C22×C4711yescharacteristic
390#575C22×C4711yescharacteristic
391#575C22×C4711yescharacteristic
392C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
393C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
394C2×AGL(1,ℤ/8)C22×C4711yescharacteristic, complemented
395#568C22×C4711yescharacteristic
396#568C22×C4711yescharacteristic
397#568C22×C4711yescharacteristic, complemented
398#535C22×C4711yescharacteristic
399C2×#127C22×C4711yescharacteristic
400#472—22no—
401#472—22no—
402#471—22no—
403#471—22no—
404#455—22no—
405#453—22no—
406#453—22no—
407#453—22no—
408#444—22no—
409#443—22no—
410#430C22×C4711yescharacteristic, complemented
411#430C22×C4711yescharacteristic, complemented
412#430C22×C4711yescharacteristic, complemented
413#423C22×C4711yescharacteristic, complemented
414#421C22×C4711yescharacteristic
415#421C22×C4711yescharacteristic
416C2×#104C22×C4711yescharacteristic
417C2×#104C22×C4711yescharacteristic
418C2×#104C22×C4711yescharacteristic, complemented
419#418C22×C4711yescharacteristic, complemented
420#413—22no—
421#413C22×C4711yescharacteristic
422#413C22×C4711yescharacteristic
423#413C22×C4711yescharacteristic, complemented
424C2×#100—22no—
425C2×#100C22×C4711yescharacteristic
426C2×#100C22×C4711yescharacteristic
427C2×#100C22×C4711yescharacteristic
428C2×#100C22×C4711yescharacteristic
429C2×#100C22×C4711yescharacteristic, complemented
430C2×#100C22×C4711yescharacteristic, complemented
431C4×M16C22×C4711yescharacteristic, complemented
432#344C22×C4711yescharacteristic, complemented
433#344C22×C4711yescharacteristic, complemented
434#339C22×C4711yescharacteristic, complemented
435#338C22×C4711yescharacteristic, complemented
436C47#2519611yescharacteristic, direct product factor, Sylow
437H(5,𝔽2)—22no—
438H(5,𝔽2)—22no—
439H(5,𝔽2)—41no—
440H(5,𝔽2)—41no—
441C2×#41—21no—
442C2×#41—21no—
443C2×#41C23×C4711yescharacteristic
444C2×#41C23×C4711yescharacteristic
445C2×#41C23×C4711yescharacteristic
446C22×D4—22no—
447C22×D4—21no—
448C22×D4—21no—
449C22×D4—22no—
450C22×D4C23×C4711yescharacteristic
451C22×D4C23×C4711yescharacteristic
452#137—21no—
453#137—21no—
454#137—21no—
455#137D4×C4712yescomplemented
456AGL(1,ℤ/8)—21no—
457AGL(1,ℤ/8)—22no—
458AGL(1,ℤ/8)—22no—
459AGL(1,ℤ/8)—21no—
460AGL(1,ℤ/8)—21no—
461AGL(1,ℤ/8)—22no—
462AGL(1,ℤ/8)—22no—
463AGL(1,ℤ/8)—41no—
464AGL(1,ℤ/8)—41no—
465AGL(1,ℤ/8)D4×C4712yescomplemented
466#135—22no—
467#135—41no—
468C2×SD16—21no—
469C2×SD16—21no—
470C2×SD16—21no—
471C2×D8—21no—
472C2×D8—21no—
473C2×D8—21no—
474#131—22no—
475#131—22no—
476#131—22no—
477#131—22no—
478#131—41no—
479#131—41no—
480C2×M16—22no—
481C2×M16—22no—
482C2×M16—41no—
483C2×M16C23×C4711yescharacteristic
484C2×M16C23×C4711yescharacteristic
485C2×M16C23×C4711yescharacteristic
486C2×M16C23×C4711yescharacteristic
487C2×M16C23×C4711yescharacteristic
488C2×M16C23×C4711yescharacteristic
489C2×M16C23×C4711yescharacteristic
490C2×M16C23×C4711yescharacteristic
491#127—21no—
492#127—21no—
493#127—21no—
494#127—41no—
495#124—21no—
496#121—41no—
497#120—22no—
498#117C23×C4711yescharacteristic
499C2×C42C23×C4711yescharacteristic
500#108—22no—
501#108—22no—
502#108—22no—
503C4⋊C8—41no—
504#104—22no—
505#104—22no—
506#104—21no—
507#104—21no—
508#104—21no—
509#104—21no—
510#104D4×C4712yescomplemented
511#104D4×C4712yescomplemented
512#102—41no—
513#101—21no—
514#101—21no—
515#101D4×C4712yescomplemented
516#100—21no—
517#100—21no—
518#100—22no—
519#100—22no—
520#100—22no—
521#100—22no—
522#100—22no—
523#100—22no—
524#100D4×C4712yescomplemented
525#97—21no—
526C4×C8—21no—
527C24—22no—
528C24—21no—
529C24#41×C4712yes—
530#41—21no—
531#41—21no—
532#41—21no—
533#41—21no—
534#41—21no—
535#41—21no—
536#41—21no—
537#41—21no—
538#41—21no—
539#41—21no—
540#41—42no—
541#41—42no—
542#41—42no—
543#41—42no—
544#41C2×D4×C4712yes—
545#41C2×D4×C4712yes—
546C2×Q8C2×D4×C4711yescharacteristic
547C2×Q8C2×D4×C4711yescharacteristic
548C2×Q8#41×C4711yescharacteristic
549C2×D4—21no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—44no—
571C2×D4—44no—
572C2×D4—42no—
573C2×D4—42no—
574C2×D4—42no—
575C2×D4—84no—
576C2×D4C2×D4×C4711yescharacteristic
577C2×D4C2×D4×C4711yescharacteristic
578C2×D4#41×C4711yescharacteristic
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4C24×C4711yescharacteristic
585Q16—22no—
586Q16—41no—
587SD16—22no—
588SD16—22no—
589SD16—42no—
590SD16—42no—
591SD16—41no—
592SD16—41no—
593SD16—42no—
594D8—22no—
595D8—42no—
596D8—42no—
597D8—41no—
598D8—42no—
599M16—21no—
600M16—21no—
601M16—21no—
602M16—21no—
603M16—21no—
604M16—21no—
605M16—21no—
606M16—21no—
607M16—21no—
608M16—21no—
609M16—21no—
610M16—21no—
611M16—42no—
612M16—42no—
613M16—42no—
614M16C2×D4×C4712yes—
615M16C2×D4×C4712yes—
616M16C2×D4×C4712yes—
617M16C2×D4×C4712yes—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—42no—
627C2×C8—42no—
628C2×C8—42no—
629C4⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—42no—
632C42—21no—
633C42—21no—
634C42C2×D4×C4711yescharacteristic
635C42C2×D4×C4711yescharacteristic
636C23—21no—
637C23—22no—
638C23—21no—
639C23—22no—
640C23—21no—
641C23—22no—
642C23—44no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—82no—
647C23—82no—
648C23—162no—
649C23C2×#41×C4711yescharacteristic
650Q8—21no—
651Q8—21no—
652Q8—21no—
653Q8—21no—
654Q8—21no—
655Q8#121×C4712yes—
656D4—22no—
657D4—22no—
658D4—21no—
659D4—21no—
660D4—21no—
661D4—21no—
662D4—21no—
663D4—44no—
664D4—44no—
665D4—41no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—84no—
678D4—84no—
679D4—162no—
680D4#121×C4712yes—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—44no—
689C2×C4—42no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4C22×D4×C4711yescharacteristic
696C2×C4C22×D4×C4711yescharacteristic
697C2×C4C22×D4×C4711yescharacteristic
698C2×C4C2×#41×C4711yescharacteristic
699C2×C4H(5,𝔽2)×C4711yescharacteristic
700C2×C4H(5,𝔽2)×C4711yescharacteristic
701C8—22no—
702C8—22no—
703C8—22no—
704C8—22no—
705C8—41no—
706C8—41no—
707C8—41no—
708C8—41no—
709C22—22no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—42no—
714C22—81no—
715C22—82no—
716C22—81no—
717C22—82no—
718C22—82no—
719C22—81no—
720C22—82no—
721C22—81no—
722C22—161no—
723C22—161no—
724C22—164no—
725C22C47×#52511yescharacteristic
726C22C47×#54611yescharacteristic
727C22C47×#54611yescharacteristic
728C4—22no—
729C4—22no—
730C4—41no—
731C4—41no—
732C4—41no—
733C4—81no—
734C4C2×#121×C4711yescharacteristic
735C4C47×#53811yescharacteristic
736C4D42×C4711yescharacteristic
737C4D42×C4711yescharacteristic
738C2—21no—
739C2—21no—
740C2—21no—
741C2—42no—
742C2—82no—
743C2—81no—
744C2—81no—
745C2—161no—
746C2C47×#242411yescharacteristic
subgroupG/H
center, socleC2×C47#2424
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×#3068C2semidirect
2. C47×#3068C2semidirect
3. C47×#3019C2semidirect
4. C2×C47×#453C2semidirect
5. C47×#2956C2semidirect
6. C47×#2888C2semidirect
7. C47×#2069C2semidirect
8. C47×#2050C2semidirect
9. C47×#2048C2semidirect
10. C47×#2002C2semidirect
11. C47×#1965C2semidirect
12. C47×#1932C2semidirect
13. C47×#1914C2semidirect
14. C47×#1903C2semidirect
15. C47×#1861C2semidirect
21. C2×AGL(1,ℤ/8)×C47C22semidirect
24. C47×#568C22semidirect
37. C47×#430C22semidirect
38. C47×#430C22semidirect
39. C47×#430C22semidirect
40. C47×#423C22semidirect
45. C2×#104×C47C22semidirect
46. C47×#418C22semidirect
50. C47×#413C22semidirect
56. C2×#100×C47C22semidirect
57. C2×#100×C47C22semidirect
58. C4×M16×C47C22semidirect
59. C47×#344C22semidirect
60. C47×#344C22semidirect
61. C47×#339C22semidirect
62. C47×#338C22semidirect
81. #137×C47D4semidirect
91. AGL(1,ℤ/8)×C47D4semidirect
136. #104×C47D4semidirect
137. #104×C47D4semidirect
141. #101×C47D4semidirect
150. #100×C47D4semidirect
335. #25196C47direct (N × H)
365. #3068C2×C47semidirect
366. #3068C2×C47semidirect
367. #3019C2×C47semidirect
368. C2×#453C2×C47semidirect
369. #2956C2×C47semidirect
370. #2888C2×C47semidirect
371. #2069C2×C47semidirect
372. #2050C2×C47semidirect
373. #2048C2×C47semidirect
374. #2002C2×C47semidirect
375. #1965C2×C47semidirect
376. #1932C2×C47semidirect
377. #1914C2×C47semidirect
378. #1903C2×C47semidirect
379. #1861C2×C47semidirect
394. C2×AGL(1,ℤ/8)C22×C47semidirect
397. #568C22×C47semidirect
410. #430C22×C47semidirect
411. #430C22×C47semidirect
412. #430C22×C47semidirect
413. #423C22×C47semidirect
418. C2×#104C22×C47semidirect
419. #418C22×C47semidirect
423. #413C22×C47semidirect
429. C2×#100C22×C47semidirect
430. C2×#100C22×C47semidirect
431. C4×M16C22×C47semidirect
432. #344C22×C47semidirect
433. #344C22×C47semidirect
434. #339C22×C47semidirect
435. #338C22×C47semidirect
436. C47#25196direct (N × H)
455. #137D4×C47semidirect
465. AGL(1,ℤ/8)D4×C47semidirect
510. #104D4×C47semidirect
511. #104D4×C47semidirect
515. #101D4×C47semidirect
524. #100D4×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#30682
C47×#30192
C2×C47×#4532
C47×#29562
C47×#28882
C47×#20692
C47×#20502
C47×#20482
C47×#20022
C47×#19652
C47×#19322
C47×#19142
C47×#19032
C47×#18612
#2519647