Finite Group Databasebeta

← C47×#24283 #26063981

Subgroups — C47×#24283 #26063981

Order 12032.

1304 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#137×C47C211yesmaximal, characteristic, complemented
2C2×C47×#473C211yesmaximal, characteristic, complemented
3C2×C47×#471C211yesmaximal, characteristic, complemented
4C47×#3005C211yesmaximal, characteristic
5C47×#3004C211yesmaximal, characteristic, complemented
6C47×#2930C211yesmaximal, characteristic, complemented
7C47×#2047C211yesmaximal, characteristic, complemented
8C47×#2046C211yesmaximal, characteristic, complemented
9C47×#2020C211yesmaximal, characteristic, complemented
10C47×#2019C211yesmaximal, characteristic, complemented
11C47×#1979C211yesmaximal, characteristic, complemented
12C47×#1977C211yesmaximal, characteristic, complemented
13C47×#1811C211yesmaximal, characteristic, complemented
14C47×#1785C211yesmaximal, characteristic, complemented
15C47×#1784C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C23×Q8×C47C2211yescharacteristic
18C2×#137×C47—24no—
19C2×#137×C47—24no—
20C2×#137×C47—22no—
21C2×#137×C47—22no—
22C2×#137×C47C2211yescharacteristic
23C2×#137×C47C2211yescharacteristic
24C2×#137×C47C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
26C22×Q16×C47C2211yescharacteristic
27C22×Q16×C47C2211yescharacteristic
28C22×SD16×C47C2211yescharacteristic
29C22×SD16×C47C2211yescharacteristic
30C2×#131×C47C2211yescharacteristic
31C22×M16×C47C2211yescharacteristic
32C47×#525C2211yescharacteristic
33C47×#473—24no—
34C47×#471—24no—
35C47×#452—22no—
36C47×#451—22no—
37C47×#449—22no—
38C47×#448—22no—
39C47×#436—22no—
40C47×#435—22no—
41C2×#108×C47C2211yescharacteristic
42C2×#108×C47C2211yescharacteristic
43C47×#424C2211yescharacteristic
44C47×#419C2211yescharacteristic
45C47×#419C2211yescharacteristic
46C47×#419C2211yescharacteristic
47C47×#418C2211yescharacteristic
48C2×#101×C47C2211yescharacteristic
49C2×#101×C47C2211yescharacteristic
50C2×#101×C47C2211yescharacteristic
51C2×#101×C47C2211yescharacteristic
52C2×#101×C47C2211yescharacteristic
53C2×#101×C47C2211yescharacteristic
54C2×#100×C47C2211yescharacteristic
55C2×#100×C47C2211yescharacteristic
56C47×#408C2211yescharacteristic
57C47×#407C2211yescharacteristic
58C47×#407C2211yescharacteristic
59C47×#407C2211yescharacteristic
60C47×#405C2211yescharacteristic
61C47×#341C2211yescharacteristic
62C47×#341C2211yescharacteristic
63C2×#41×C47—22no—
64C2×#41×C47—22no—
65C2×#41×C47—22no—
66C2×#41×C47—22no—
67C2×#41×C47—41no—
68C2×#41×C47—41no—
69C2×#41×C47C2311yescharacteristic
70C22×Q8×C47—21no—
71C22×Q8×C47—22no—
72C22×Q8×C47—22no—
73C22×Q8×C47—22no—
74C22×Q8×C47—22no—
75C22×Q8×C47—41no—
76C22×Q8×C47—41no—
77C22×Q8×C47C2311yescharacteristic
78C22×Q8×C47C2311yescharacteristic
79C22×Q8×C47C2311yescharacteristic
80C22×D4×C47—21no—
81C22×D4×C47C2311yescharacteristic
82C23×C4×C47—21no—
83C23×C4×C47—21no—
84C23×C4×C47C2311yescharacteristic
85#137×C47—216no—
86#137×C47—216no—
87#137×C47—22no—
88#137×C47—22no—
89#137×C47—22no—
90#137×C47—41no—
91#137×C47—41no—
92#137×C47—41no—
93AGL(1,ℤ/8)×C47—22no—
94AGL(1,ℤ/8)×C47—41no—
95C2×Q16×C47—22no—
96C2×Q16×C47—22no—
97C2×Q16×C47—21no—
98C2×Q16×C47—21no—
99C2×Q16×C47—21no—
100C2×Q16×C47—22no—
101C2×Q16×C47—22no—
102C2×Q16×C47—21no—
103C2×Q16×C47—21no—
104C2×Q16×C47D414yescomplemented
105C2×SD16×C47—22no—
106C2×SD16×C47—22no—
107C2×SD16×C47—21no—
108C2×SD16×C47—21no—
109C2×SD16×C47—21no—
110C2×SD16×C47—21no—
111C2×SD16×C47—22no—
112C2×SD16×C47—22no—
113C2×SD16×C47—21no—
114C2×SD16×C47—21no—
115C2×SD16×C47D414yescomplemented
116C2×D8×C47—21no—
117#131×C47—22no—
118#131×C47—22no—
119C2×M16×C47—22no—
120C2×M16×C47—22no—
121C2×M16×C47—21no—
122C2×M16×C47D412yes—
123C2×M16×C47D412yes—
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
132C22×C8×C47C2311yescharacteristic
133#123×C47—21no—
134C22⋊Q8×C47D412yes—
135#121×C47D412yes—
136#120×C47—21no—
137C4×D4×C47—22no—
138#117×C47C2311yescharacteristic
139#108×C47—22no—
140#108×C47—22no—
141C4⋊C8×C47—22no—
142#103×C47—22no—
143#103×C47—22no—
144#103×C47—22no—
145#102×C47—22no—
146#101×C47—22no—
147#101×C47—22no—
148#101×C47—22no—
149#101×C47—41no—
150#101×C47—41no—
151#101×C47—41no—
152#100×C47—22no—
153#100×C47—41no—
154C22⋊C8×C47—22no—
155C22⋊C8×C47—22no—
156C22⋊C8×C47—22no—
157C22⋊C8×C47—22no—
158#97×C47—21no—
159C4×C8×C47—21no—
160C24×C47—21no—
161C24×C47#4111yescharacteristic
162#41×C47—28no—
163#41×C47—21no—
164#41×C47—21no—
165#41×C47—21no—
166#41×C47—21no—
167#41×C47—44no—
168#41×C47—44no—
169#41×C47—44no—
170C2×Q8×C47—21no—
171C2×Q8×C47—21no—
172C2×Q8×C47—21no—
173C2×Q8×C47—28no—
174C2×Q8×C47—21no—
175C2×Q8×C47—21no—
176C2×Q8×C47—21no—
177C2×Q8×C47—21no—
178C2×Q8×C47—21no—
179C2×Q8×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×C47—42no—
187C2×Q8×C47—42no—
188C2×Q8×C47—44no—
189C2×Q8×C47—44no—
190C2×Q8×C47—44no—
191C2×Q8×C47—42no—
192C2×Q8×C47C2×D411yescharacteristic
193C2×Q8×C47C2×D412yes—
194C2×Q8×C47C2×D412yes—
195C2×Q8×C47C2×D412yes—
196C2×D4×C47—21no—
197C2×D4×C47—22no—
198C2×D4×C47—21no—
199C2×D4×C47—21no—
200C2×D4×C47—21no—
201C2×D4×C47—21no—
202C2×D4×C47—21no—
203C2×D4×C47—42no—
204C2×D4×C47—42no—
205C2×D4×C47—42no—
206C2×D4×C47C2×D411yescharacteristic
207C2×D4×C47C2×D412yes—
208C22×C4×C47—21no—
209C22×C4×C47—21no—
210C22×C4×C47—21no—
211C22×C4×C47—21no—
212C22×C4×C47—21no—
213C22×C4×C47—21no—
214C22×C4×C47—21no—
215C22×C4×C47—21no—
216C22×C4×C47—42no—
217C22×C4×C47—42no—
218C22×C4×C47—42no—
219C22×C4×C47—42no—
220C22×C4×C47—42no—
221C22×C4×C47—42no—
222C22×C4×C47C2×D412yes—
223C22×C4×C47C2×D412yes—
224C22×C4×C47#4111yescharacteristic
225C22×C4×C47C2411yescharacteristic
226Q16×C47—28no—
227Q16×C47—24no—
228Q16×C47—24no—
229Q16×C47—42no—
230Q16×C47—42no—
231Q16×C47—42no—
232SD16×C47—28no—
233SD16×C47—24no—
234SD16×C47—24no—
235SD16×C47—42no—
236SD16×C47—42no—
237SD16×C47—42no—
238SD16×C47—42no—
239D8×C47—42no—
240M16×C47—24no—
241M16×C47—24no—
242M16×C47—21no—
243M16×C47—21no—
244M16×C47—21no—
245M16×C47—21no—
246M16×C47—21no—
247M16×C47—21no—
248M16×C47—21no—
249M16×C47—21no—
250M16×C47—21no—
251M16×C47—21no—
252M16×C47—21no—
253M16×C47—21no—
254M16×C47—42no—
255C2×C8×C47—21no—
256C2×C8×C47—21no—
257C2×C8×C47—21no—
258C2×C8×C47—21no—
259C2×C8×C47—21no—
260C2×C8×C47—21no—
261C2×C8×C47—21no—
262C2×C8×C47—21no—
263C2×C8×C47—42no—
264C2×C8×C47C2×D412yes—
265C2×C8×C47C2×D412yes—
266C2×C8×C47C2×D412yes—
267C2×C8×C47C2×D411yescharacteristic
268C2×C8×C47C2×D411yescharacteristic
269C4⋊C4×C47—22no—
270C4⋊C4×C47C2×D412yes—
271C22⋊C4×C47—22no—
272C22⋊C4×C47—21no—
273C22⋊C4×C47—22no—
274C42×C47—21no—
275C23×C47—21no—
276C23×C47—21no—
277C23×C47—21no—
278C23×C47—22no—
279C23×C47—42no—
280C23×C47—41no—
281C23×C47—41no—
282C23×C47—82no—
283C23×C47#12112yes—
284C23×C47C2×#4111yescharacteristic
285Q8×C47—22no—
286Q8×C47—22no—
287Q8×C47—22no—
288Q8×C47—21no—
289Q8×C47—22no—
290Q8×C47—22no—
291Q8×C47—22no—
292Q8×C47—21no—
293Q8×C47—48no—
294Q8×C47—41no—
295Q8×C47—41no—
296Q8×C47—41no—
297Q8×C47—41no—
298Q8×C47—41no—
299Q8×C47—41no—
300D4×C47—22no—
301D4×C47—21no—
302D4×C47—22no—
303D4×C47—21no—
304D4×C47—48no—
305D4×C47—41no—
306D4×C47—41no—
307D4×C47—41no—
308D4×C47—41no—
309D4×C47—82no—
310C2×C4×C47—21no—
311C2×C4×C47—21no—
312C2×C4×C47—22no—
313C2×C4×C47—22no—
314C2×C4×C47—22no—
315C2×C4×C47—22no—
316C2×C4×C47—22no—
317C2×C4×C47—21no—
318C2×C4×C47—22no—
319C2×C4×C47—22no—
320C2×C4×C47—22no—
321C2×C4×C47—48no—
322C2×C4×C47—48no—
323C2×C4×C47—41no—
324C2×C4×C47—41no—
325C2×C4×C47—41no—
326C2×C4×C47—41no—
327C2×C4×C47—41no—
328C2×C4×C47—41no—
329C2×C4×C47—41no—
330C2×C4×C47—41no—
331C2×C4×C47#12112yes—
332C2×C4×C47C22×D411yescharacteristic
333C2×C4×C47C22×D411yescharacteristic
334C2×C4×C47C22×D411yescharacteristic
335C2×C4×C47C22×D411yescharacteristic
336C2×C4×C47H(5,𝔽2)11yescharacteristic
337C2×C4×C47H(5,𝔽2)11yescharacteristic
338C8×C47—22no—
339C8×C47—41no—
340C8×C47—41no—
341C8×C47—41no—
342C8×C47—41no—
343C8×C47—41no—
344C8×C47—41no—
345C8×C47#12012yes—
346C8×C47#12012yes—
347#24283C4711yesmaximal, characteristic, direct product factor, Sylow
348C22×C47—22no—
349C22×C47—22no—
350C22×C47—22no—
351C22×C47—22no—
352C22×C47—42no—
353C22×C47—42no—
354C22×C47—42no—
355C22×C47—41no—
356C22×C47—42no—
357C22×C47—82no—
358C22×C47—82no—
359C22×C47—82no—
360C22×C47C2×#12111yescharacteristic
361C22×C47#54611yescharacteristic
362C22×C47#54611yescharacteristic
363C4×C47—22no—
364C4×C47—42no—
365C4×C47—42no—
366C4×C47—42no—
367C4×C47—41no—
368C4×C47—42no—
369C4×C47C2×#12011yescharacteristic
370C4×C47#53511yescharacteristic
371C4×C47D4211yescharacteristic
372C4×C47D4211yescharacteristic
373C22×#137C2×C4711yescharacteristic, complemented
374C2×#473C2×C4711yescharacteristic, complemented
375C2×#471C2×C4711yescharacteristic, complemented
376#3005C2×C4711yescharacteristic
377#3004C2×C4711yescharacteristic, complemented
378#2930C2×C4711yescharacteristic, complemented
379#2047C2×C4711yescharacteristic, complemented
380#2046C2×C4711yescharacteristic, complemented
381#2020C2×C4711yescharacteristic, complemented
382#2019C2×C4711yescharacteristic, complemented
383#1979C2×C4711yescharacteristic, complemented
384#1977C2×C4711yescharacteristic, complemented
385#1811C2×C4711yescharacteristic, complemented
386#1785C2×C4711yescharacteristic, complemented
387#1784C2×C4711yescharacteristic, complemented
388C2×C47—21no—
389C2×C47—21no—
390C2×C47—42no—
391C2×C47—81no—
392C2×C47—82no—
393C2×C47#240811yescharacteristic
394C2×C47#306912yes—
395C22×#41C22×C4711yescharacteristic
396C23×Q8C22×C4711yescharacteristic
397C2×#137—24no—
398C2×#137—24no—
399C2×#137—22no—
400C2×#137—22no—
401C2×#137C22×C4711yescharacteristic
402C2×#137C22×C4711yescharacteristic
403C2×#137C22×C4711yescharacteristic
404C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
405C22×Q16C22×C4711yescharacteristic
406C22×Q16C22×C4711yescharacteristic
407C22×SD16C22×C4711yescharacteristic
408C22×SD16C22×C4711yescharacteristic
409C2×#131C22×C4711yescharacteristic
410C22×M16C22×C4711yescharacteristic
411#525C22×C4711yescharacteristic
412#473—24no—
413#471—24no—
414#452—22no—
415#451—22no—
416#449—22no—
417#448—22no—
418#436—22no—
419#435—22no—
420C2×#108C22×C4711yescharacteristic
421C2×#108C22×C4711yescharacteristic
422#424C22×C4711yescharacteristic
423#419C22×C4711yescharacteristic
424#419C22×C4711yescharacteristic
425#419C22×C4711yescharacteristic
426#418C22×C4711yescharacteristic
427C2×#101C22×C4711yescharacteristic
428C2×#101C22×C4711yescharacteristic
429C2×#101C22×C4711yescharacteristic
430C2×#101C22×C4711yescharacteristic
431C2×#101C22×C4711yescharacteristic
432C2×#101C22×C4711yescharacteristic
433C2×#100C22×C4711yescharacteristic
434C2×#100C22×C4711yescharacteristic
435#408C22×C4711yescharacteristic
436#407C22×C4711yescharacteristic
437#407C22×C4711yescharacteristic
438#407C22×C4711yescharacteristic
439#405C22×C4711yescharacteristic
440#341C22×C4711yescharacteristic
441#341C22×C4711yescharacteristic
442C47#2428311yescharacteristic, direct product factor, Sylow
443C2×#41—22no—
444C2×#41—22no—
445C2×#41—22no—
446C2×#41—22no—
447C2×#41—41no—
448C2×#41—41no—
449C2×#41C23×C4711yescharacteristic
450C22×Q8—21no—
451C22×Q8—22no—
452C22×Q8—22no—
453C22×Q8—22no—
454C22×Q8—22no—
455C22×Q8—41no—
456C22×Q8—41no—
457C22×Q8C23×C4711yescharacteristic
458C22×Q8C23×C4711yescharacteristic
459C22×Q8C23×C4711yescharacteristic
460C22×D4—21no—
461C22×D4C23×C4711yescharacteristic
462C23×C4—21no—
463C23×C4—21no—
464C23×C4C23×C4711yescharacteristic
465#137—216no—
466#137—216no—
467#137—22no—
468#137—22no—
469#137—22no—
470#137—41no—
471#137—41no—
472#137—41no—
473AGL(1,ℤ/8)—22no—
474AGL(1,ℤ/8)—41no—
475C2×Q16—22no—
476C2×Q16—22no—
477C2×Q16—21no—
478C2×Q16—21no—
479C2×Q16—21no—
480C2×Q16—22no—
481C2×Q16—21no—
482C2×Q16—21no—
483C2×Q16—22no—
484C2×Q16D4×C4714yescomplemented
485C2×SD16—22no—
486C2×SD16—22no—
487C2×SD16—21no—
488C2×SD16—21no—
489C2×SD16—21no—
490C2×SD16—21no—
491C2×SD16—22no—
492C2×SD16—21no—
493C2×SD16—21no—
494C2×SD16—22no—
495C2×SD16D4×C4714yescomplemented
496C2×D8—21no—
497#131—22no—
498#131—22no—
499C2×M16—22no—
500C2×M16—22no—
501C2×M16—21no—
502C2×M16D4×C4712yes—
503C2×M16D4×C4712yes—
504C2×M16C23×C4711yescharacteristic
505C2×M16C23×C4711yescharacteristic
506C2×M16C23×C4711yescharacteristic
507C2×M16C23×C4711yescharacteristic
508C2×M16C23×C4711yescharacteristic
509C2×M16C23×C4711yescharacteristic
510C22×C8—21no—
511C22×C8C23×C4711yescharacteristic
512C22×C8C23×C4711yescharacteristic
513#123—21no—
514C22⋊Q8D4×C4712yes—
515#121D4×C4712yes—
516#120—21no—
517C4×D4—22no—
518#117C23×C4711yescharacteristic
519#108—22no—
520#108—22no—
521C4⋊C8—22no—
522#103—22no—
523#103—22no—
524#103—22no—
525#102—22no—
526#101—22no—
527#101—22no—
528#101—22no—
529#101—41no—
530#101—41no—
531#101—41no—
532#100—22no—
533#100—41no—
534C22⋊C8—22no—
535C22⋊C8—22no—
536C22⋊C8—22no—
537C22⋊C8—22no—
538#97—21no—
539C4×C8—21no—
540C24—21no—
541C24#41×C4711yescharacteristic
542#41—28no—
543#41—21no—
544#41—21no—
545#41—21no—
546#41—21no—
547#41—44no—
548#41—44no—
549#41—44no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—28no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—42no—
567C2×Q8—42no—
568C2×Q8—44no—
569C2×Q8—44no—
570C2×Q8—44no—
571C2×Q8—42no—
572C2×Q8C2×D4×C4712yes—
573C2×Q8C2×D4×C4712yes—
574C2×Q8C2×D4×C4712yes—
575C2×Q8C2×D4×C4711yescharacteristic
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4C2×D4×C4712yes—
587C2×D4C2×D4×C4711yescharacteristic
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4C2×D4×C4712yes—
603C22×C4C2×D4×C4712yes—
604C22×C4#41×C4711yescharacteristic
605C22×C4C24×C4711yescharacteristic
606Q16—28no—
607Q16—24no—
608Q16—24no—
609Q16—42no—
610Q16—42no—
611Q16—42no—
612SD16—28no—
613SD16—24no—
614SD16—24no—
615SD16—42no—
616SD16—42no—
617SD16—42no—
618SD16—42no—
619D8—42no—
620M16—24no—
621M16—24no—
622M16—21no—
623M16—21no—
624M16—21no—
625M16—21no—
626M16—21no—
627M16—21no—
628M16—21no—
629M16—21no—
630M16—21no—
631M16—21no—
632M16—21no—
633M16—21no—
634M16—42no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—42no—
644C2×C8C2×D4×C4712yes—
645C2×C8C2×D4×C4711yescharacteristic
646C2×C8C2×D4×C4711yescharacteristic
647C2×C8C2×D4×C4712yes—
648C2×C8C2×D4×C4712yes—
649C4⋊C4—22no—
650C4⋊C4C2×D4×C4712yes—
651C22⋊C4—22no—
652C22⋊C4—21no—
653C22⋊C4—22no—
654C42—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—22no—
659C23—42no—
660C23—41no—
661C23—41no—
662C23—82no—
663C23#121×C4712yes—
664C23C2×#41×C4711yescharacteristic
665Q8—22no—
666Q8—22no—
667Q8—22no—
668Q8—21no—
669Q8—22no—
670Q8—22no—
671Q8—22no—
672Q8—21no—
673Q8—48no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678Q8—41no—
679Q8—41no—
680D4—22no—
681D4—21no—
682D4—22no—
683D4—21no—
684D4—48no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—82no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—48no—
702C2×C4—48no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4#121×C4712yes—
712C2×C4C22×D4×C4711yescharacteristic
713C2×C4C22×D4×C4711yescharacteristic
714C2×C4C22×D4×C4711yescharacteristic
715C2×C4C22×D4×C4711yescharacteristic
716C2×C4H(5,𝔽2)×C4711yescharacteristic
717C2×C4H(5,𝔽2)×C4711yescharacteristic
718C8—22no—
719C8—41no—
720C8—41no—
721C8—41no—
722C8—41no—
723C8—41no—
724C8—41no—
725C8#120×C4712yes—
726C8#120×C4712yes—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—41no—
736C22—82no—
737C22—82no—
738C22—82no—
739C22C2×#121×C4711yescharacteristic
740C22C47×#54611yescharacteristic
741C22C47×#54611yescharacteristic
742C4—22no—
743C4—42no—
744C4—42no—
745C4—42no—
746C4—42no—
747C4—41no—
748C4C2×#120×C4711yescharacteristic
749C4C47×#53511yescharacteristic
750C4D42×C4711yescharacteristic
751C4D42×C4711yescharacteristic
752C2—21no—
753C2—21no—
754C2—42no—
755C2—81no—
756C2—82no—
757C2C47×#240811yescharacteristic
758C2C47×#306912yes—
subgroupG/H
center, socleC22×C47C2×#121
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC47×#3005C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C23×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#137×C47C2semidirect
2. C2×C47×#473C2semidirect
3. C2×C47×#471C2semidirect
5. C47×#3004C2semidirect
6. C47×#2930C2semidirect
7. C47×#2047C2semidirect
8. C47×#2046C2semidirect
9. C47×#2020C2semidirect
10. C47×#2019C2semidirect
11. C47×#1979C2semidirect
12. C47×#1977C2semidirect
13. C47×#1811C2semidirect
14. C47×#1785C2semidirect
15. C47×#1784C2semidirect
104. C2×Q16×C47D4semidirect
115. C2×SD16×C47D4semidirect
347. #24283C47direct (N × H)
373. C22×#137C2×C47semidirect
374. C2×#473C2×C47semidirect
375. C2×#471C2×C47semidirect
377. #3004C2×C47semidirect
378. #2930C2×C47semidirect
379. #2047C2×C47semidirect
380. #2046C2×C47semidirect
381. #2020C2×C47semidirect
382. #2019C2×C47semidirect
383. #1979C2×C47semidirect
384. #1977C2×C47semidirect
385. #1811C2×C47semidirect
386. #1785C2×C47semidirect
387. #1784C2×C47semidirect
442. C47#24283direct (N × H)
484. C2×Q16D4×C47semidirect
495. C2×SD16D4×C47semidirect

Maximal subgroups

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

subgroupindex
C22×#137×C472
C2×C47×#4732
C2×C47×#4712
C47×#30052
C47×#30042
C47×#29302
C47×#20472
C47×#20462
C47×#20202
C47×#20192
C47×#19792
C47×#19772
C47×#18112
C47×#17852
C47×#17842
#2428347