Finite Group Databasebeta

← C47×#24931 #26064629

Subgroups — C47×#24931 #26064629

Order 12032.

870 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3098C211yesmaximal, characteristic, complemented
2C47×#3013C211yesmaximal, characteristic
3C47×#2951C211yesmaximal, characteristic, complemented
4C47×#2898C211yesmaximal, characteristic, complemented
5C47×#2095C211yesmaximal, characteristic, complemented
6C47×#2078C211yesmaximal, characteristic, complemented
7C47×#2052C211yesmaximal, characteristic, complemented
8C47×#2039C211yesmaximal, characteristic, complemented
9C47×#1930C211yesmaximal, characteristic, complemented
10C47×#1929C211yesmaximal, characteristic, complemented
11C47×#1882C211yesmaximal, characteristic, complemented
12C47×#1876C211yesmaximal, characteristic, complemented
13C47×#1859C211yesmaximal, characteristic, complemented
14C47×#1816C211yesmaximal, characteristic, complemented
15C47×#1793C211yesmaximal, characteristic, complemented
16C2×2−1+4×C47C2211yescharacteristic
17C2×#137×C47C2211yescharacteristic
18C2×#135×C47C2211yescharacteristic
19C2×#131×C47C2211yescharacteristic
20C47×#537C2211yescharacteristic
21C47×#520C2211yescharacteristic
22C47×#520C2211yescharacteristic
23C47×#485—21no—
24C47×#484—21no—
25C47×#482—21no—
26C47×#480—21no—
27C47×#452—21no—
28C47×#451—21no—
29C47×#449—21no—
30C47×#448—21no—
31C47×#440—21no—
32C47×#440—21no—
33C4×Q16×C47—21no—
34C4×D8×C47—21no—
35C2×#108×C47C2211yescharacteristic
36C47×#428C2211yescharacteristic
37C2×#107×C47C2211yescharacteristic
38C2×#107×C47C2211yescharacteristic
39C2×#104×C47C2211yescharacteristic
40C2×#104×C47C2211yescharacteristic
41C2×#104×C47C2211yescharacteristic
42C47×#419—21no—
43C47×#419C2211yescharacteristic
44C47×#417—21no—
45C47×#417C2211yescharacteristic
46C47×#417C2211yescharacteristic
47C47×#417C2211yescharacteristic
48C47×#417C2211yescharacteristic
49C47×#417C2211yescharacteristic
50C47×#416—21no—
51C47×#416C2211yescharacteristic
52C2×#103×C47—21no—
53C2×#103×C47C2211yescharacteristic
54C2×#103×C47C2211yescharacteristic
55C2×#101×C47C2211yescharacteristic
56C47×#408C2211yescharacteristic
57C47×#408C2211yescharacteristic
58C47×#405C2211yescharacteristic
59C47×#391C2211yescharacteristic
60C47×#384C2211yescharacteristic
61C47×#343C2211yescharacteristic
62C47×#343C2211yescharacteristic
63C47×#343C2211yescharacteristic
64C47×#341C2211yescharacteristic
65C47×#339C2211yescharacteristic
66C47×#336C2211yescharacteristic
672−1+4×C47—22no—
682−1+4×C47—22no—
692−1+4×C47—22no—
702−1+4×C47—41no—
71C2×#41×C47—21no—
72C2×#41×C47—21no—
73C2×#41×C47—41no—
74C2×#41×C47C2311yescharacteristic
75C2×#41×C47C2311yescharacteristic
76C2×#41×C47C2311yescharacteristic
77C22×Q8×C47—21no—
78C22×Q8×C47—21no—
79C22×Q8×C47C2311yescharacteristic
80#137×C47—22no—
81#137×C47—41no—
82#135×C47—22no—
83#135×C47—22no—
84C2×Q16×C47—21no—
85C2×Q16×C47D411yescharacteristic
86C2×SD16×C47—21no—
87C2×SD16×C47D411yescharacteristic
88C2×SD16×C47D411yescharacteristic
89C2×D8×C47D411yescharacteristic
90#131×C47—22no—
91#131×C47—41no—
92C2×M16×C47—21no—
93C2×M16×C47C2311yescharacteristic
94C2×M16×C47C2311yescharacteristic
95C2×M16×C47C2311yescharacteristic
96C2×M16×C47C2311yescharacteristic
97C22×C8×C47—21no—
98C22×C8×C47C2311yescharacteristic
99C22×C8×C47C2311yescharacteristic
100C22⋊Q8×C47—21no—
101C22⋊Q8×C47—21no—
102#121×C47—21no—
103#121×C47—21no—
104#121×C47—41no—
105C4×Q8×C47—21no—
106C4×Q8×C47—21no—
107C4×D4×C47—21no—
108C4×D4×C47—21no—
109C4×D4×C47—41no—
110C4×D4×C47—41no—
111#117×C47—21no—
112#117×C47—21no—
113#117×C47C2311yescharacteristic
114C2×C4⋊C4×C47—21no—
115C2×C4⋊C4×C47—21no—
116C2×C4⋊C4×C47—41no—
117C2×C4⋊C4×C47C2311yescharacteristic
118C2×C4⋊C4×C47C2311yescharacteristic
119C2×C4⋊C4×C47C2311yescharacteristic
120C2×C42×C47C2311yescharacteristic
121#108×C47—41no—
122#107×C47—21no—
123#107×C47—21no—
124#107×C47—21no—
125#107×C47—21no—
126#107×C47—21no—
127#106×C47—21no—
128#104×C47—22no—
129#104×C47—41no—
130#104×C47—41no—
131#103×C47—21no—
132#103×C47—21no—
133#103×C47—21no—
134#103×C47—21no—
135#103×C47—21no—
136#103×C47—21no—
137#103×C47—21no—
138#103×C47—21no—
139#103×C47—21no—
140#103×C47—21no—
141#103×C47—21no—
142#103×C47D411yescharacteristic
143#103×C47D411yescharacteristic
144#102×C47—21no—
145#102×C47—21no—
146#102×C47—21no—
147#102×C47—21no—
148#102×C47—21no—
149#102×C47D411yescharacteristic
150#102×C47D411yescharacteristic
151#101×C47—22no—
152C22⋊C8×C47—21no—
153C22⋊C8×C47—21no—
154C22⋊C8×C47—21no—
155C22⋊C8×C47—21no—
156#97×C47—21no—
157C4×C8×C47—21no—
158#95×C47—41no—
159#41×C47—21no—
160#41×C47—21no—
161#41×C47—24no—
162#41×C47—21no—
163#41×C47—21no—
164#41×C47—21no—
165#41×C47—21no—
166#41×C47—21no—
167#41×C47—21no—
168#41×C47—21no—
169#41×C47—21no—
170#41×C47—42no—
171#41×C47—44no—
172#41×C47—42no—
173#41×C47—44no—
174#41×C47—42no—
175#41×C47#4112yes—
176#41×C47#4112yes—
177C2×Q8×C47—21no—
178C2×Q8×C47—24no—
179C2×Q8×C47—21no—
180C2×Q8×C47—21no—
181C2×Q8×C47—21no—
182C2×Q8×C47—21no—
183C2×Q8×C47—41no—
184C2×Q8×C47—42no—
185C2×Q8×C47—42no—
186C2×Q8×C47—42no—
187C2×Q8×C47C2×D411yescharacteristic
188C2×Q8×C47C2×D411yescharacteristic
189C2×Q8×C47C2×D411yescharacteristic
190C2×Q8×C47#4112yes—
191C2×D4×C47—21no—
192C2×D4×C47—21no—
193C2×D4×C47—21no—
194C2×D4×C47—41no—
195C2×D4×C47—41no—
196C2×D4×C47C2×D411yescharacteristic
197C2×D4×C47C2×D411yescharacteristic
198C2×D4×C47C2×D411yescharacteristic
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—21no—
205C22×C4×C47—21no—
206C22×C4×C47—21no—
207C22×C4×C47—41no—
208C22×C4×C47—41no—
209C22×C4×C47—41no—
210C22×C4×C47—41no—
211C22×C4×C47C2411yescharacteristic
212Q16×C47—22no—
213Q16×C47—42no—
214SD16×C47—22no—
215SD16×C47—22no—
216SD16×C47—42no—
217D8×C47—22no—
218M16×C47—21no—
219M16×C47—21no—
220M16×C47—21no—
221M16×C47—21no—
222M16×C47—21no—
223M16×C47—21no—
224M16×C47—21no—
225M16×C47—21no—
226M16×C47—42no—
227C2×C8×C47—21no—
228C2×C8×C47—21no—
229C2×C8×C47—21no—
230C2×C8×C47—21no—
231C2×C8×C47—21no—
232C2×C8×C47—21no—
233C2×C8×C47—21no—
234C2×C8×C47—21no—
235C2×C8×C47—42no—
236C2×C8×C47C2×D411yescharacteristic
237C2×C8×C47C2×D411yescharacteristic
238C2×C8×C47C2×D411yescharacteristic
239C2×C8×C47C2×D411yescharacteristic
240C4⋊C4×C47—21no—
241C4⋊C4×C47—21no—
242C4⋊C4×C47—21no—
243C4⋊C4×C47—21no—
244C4⋊C4×C47—21no—
245C4⋊C4×C47—21no—
246C4⋊C4×C47—41no—
247C4⋊C4×C47—41no—
248C4⋊C4×C47—41no—
249C4⋊C4×C47—82no—
250C4⋊C4×C47C2×D411yescharacteristic
251C4⋊C4×C47C2×D411yescharacteristic
252C22⋊C4×C47—21no—
253C22⋊C4×C47—41no—
254C22⋊C4×C47—41no—
255C22⋊C4×C47—41no—
256C22⋊C4×C47—41no—
257C42×C47—21no—
258C42×C47—21no—
259C42×C47—21no—
260C42×C47—41no—
261C42×C47—41no—
262C23×C47—21no—
263C23×C47—21no—
264C23×C47—21no—
265C23×C47H(5,𝔽2)11yescharacteristic
266Q8×C47—21no—
267Q8×C47—21no—
268Q8×C47—21no—
269Q8×C47—22no—
270Q8×C47—22no—
271Q8×C47—21no—
272Q8×C47—21no—
273Q8×C47—44no—
274Q8×C47—41no—
275Q8×C47—41no—
276Q8×C47#12312yes—
277D4×C47—22no—
278D4×C47—22no—
279D4×C47—21no—
280D4×C47—21no—
281D4×C47—21no—
282D4×C47—21no—
283D4×C47—21no—
284D4×C47—44no—
285D4×C47—41no—
286D4×C47—41no—
287D4×C47—41no—
288D4×C47—41no—
289D4×C47—161no—
290D4×C47#12312yes—
291C2×C4×C47—21no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—21no—
296C2×C4×C47—21no—
297C2×C4×C47—21no—
298C2×C4×C47—21no—
299C2×C4×C47—22no—
300C2×C4×C47—44no—
301C2×C4×C47—41no—
302C2×C4×C47—44no—
303C2×C4×C47—41no—
304C2×C4×C47—41no—
305C2×C4×C47—41no—
306C2×C4×C47—41no—
307C2×C4×C47—41no—
308C2×C4×C47—41no—
309C2×C4×C47—41no—
310C2×C4×C47—41no—
311C2×C4×C47—41no—
312C2×C4×C47—41no—
313C2×C4×C47—81no—
314C2×C4×C47—81no—
315C2×C4×C47—81no—
316C2×C4×C47—161no—
317C2×C4×C47—161no—
318C2×C4×C47C22×D411yescharacteristic
319C2×C4×C47C22×D411yescharacteristic
320C2×C4×C47C2×#4111yescharacteristic
321C2×C4×C47C2×#4111yescharacteristic
322C2×C4×C47C2×#4111yescharacteristic
323C2×C4×C47H(5,𝔽2)11yescharacteristic
324C8×C47—21no—
325C8×C47—21no—
326C8×C47—21no—
327C8×C47—21no—
328C8×C47—41no—
329C8×C47—41no—
330C8×C47—41no—
331C8×C47—41no—
332#24931C4711yesmaximal, characteristic, direct product factor, Sylow
333C22×C47—21no—
334C22×C47—21no—
335C22×C47—22no—
336C22×C47—41no—
337C22×C47—41no—
338C22×C47—41no—
339C22×C47—41no—
340C22×C47—41no—
341C22×C47—41no—
342C22×C47—41no—
343C22×C47—41no—
344C22×C47#53811yescharacteristic
345C22×C47D4211yescharacteristic
346C22×C47#55111yescharacteristic
347C4×C47—22no—
348C4×C47—42no—
349C4×C47—41no—
350C4×C47—42no—
351C4×C47—41no—
352C4×C47—41no—
353C4×C47—41no—
354C4×C47—81no—
355C4×C47—81no—
356C4×C47—81no—
357C4×C47C2×#12311yescharacteristic
358C4×C47#52511yescharacteristic
359C4×C47#54611yescharacteristic
360C4×C47#54611yescharacteristic
361#3098C2×C4711yescharacteristic, complemented
362#3013C2×C4711yescharacteristic
363#2951C2×C4711yescharacteristic, complemented
364#2898C2×C4711yescharacteristic, complemented
365#2095C2×C4711yescharacteristic, complemented
366#2078C2×C4711yescharacteristic, complemented
367#2052C2×C4711yescharacteristic, complemented
368#2039C2×C4711yescharacteristic, complemented
369#1930C2×C4711yescharacteristic, complemented
370#1929C2×C4711yescharacteristic, complemented
371#1882C2×C4711yescharacteristic, complemented
372#1876C2×C4711yescharacteristic, complemented
373#1859C2×C4711yescharacteristic, complemented
374#1816C2×C4711yescharacteristic, complemented
375#1793C2×C4711yescharacteristic, complemented
376C2×C47—21no—
377C2×C47—21no—
378C2×C47—42no—
379C2×C47—81no—
380C2×C47—81no—
381C2×C47#241811yescharacteristic
382C2×C47#328811yescharacteristic
383C2×C47#329311yescharacteristic
384C2×2−1+4C22×C4711yescharacteristic
385C2×#137C22×C4711yescharacteristic
386C2×#135C22×C4711yescharacteristic
387C2×#131C22×C4711yescharacteristic
388#537C22×C4711yescharacteristic
389#520C22×C4711yescharacteristic
390#520C22×C4711yescharacteristic
391#485—21no—
392#484—21no—
393#482—21no—
394#480—21no—
395#452—21no—
396#451—21no—
397#449—21no—
398#448—21no—
399#440—21no—
400#440—21no—
401C4×Q16—21no—
402C4×D8—21no—
403C2×#108C22×C4711yescharacteristic
404#428C22×C4711yescharacteristic
405C2×#107C22×C4711yescharacteristic
406C2×#107C22×C4711yescharacteristic
407C2×#104C22×C4711yescharacteristic
408C2×#104C22×C4711yescharacteristic
409C2×#104C22×C4711yescharacteristic
410#419—21no—
411#419C22×C4711yescharacteristic
412#417—21no—
413#417C22×C4711yescharacteristic
414#417C22×C4711yescharacteristic
415#417C22×C4711yescharacteristic
416#417C22×C4711yescharacteristic
417#417C22×C4711yescharacteristic
418#416—21no—
419#416C22×C4711yescharacteristic
420C2×#103—21no—
421C2×#103C22×C4711yescharacteristic
422C2×#103C22×C4711yescharacteristic
423C2×#101C22×C4711yescharacteristic
424#408C22×C4711yescharacteristic
425#408C22×C4711yescharacteristic
426#405C22×C4711yescharacteristic
427#391C22×C4711yescharacteristic
428#384C22×C4711yescharacteristic
429#343C22×C4711yescharacteristic
430#343C22×C4711yescharacteristic
431#343C22×C4711yescharacteristic
432#341C22×C4711yescharacteristic
433#339C22×C4711yescharacteristic
434#336C22×C4711yescharacteristic
435C47#2493111yescharacteristic, direct product factor, Sylow
4362−1+4—22no—
4372−1+4—22no—
4382−1+4—22no—
4392−1+4—41no—
440C2×#41—21no—
441C2×#41—21no—
442C2×#41—41no—
443C2×#41C23×C4711yescharacteristic
444C2×#41C23×C4711yescharacteristic
445C2×#41C23×C4711yescharacteristic
446C22×Q8—21no—
447C22×Q8—21no—
448C22×Q8C23×C4711yescharacteristic
449#137—22no—
450#137—41no—
451#135—22no—
452#135—22no—
453C2×Q16—21no—
454C2×Q16D4×C4711yescharacteristic
455C2×SD16—21no—
456C2×SD16D4×C4711yescharacteristic
457C2×SD16D4×C4711yescharacteristic
458C2×D8D4×C4711yescharacteristic
459#131—22no—
460#131—41no—
461C2×M16—21no—
462C2×M16C23×C4711yescharacteristic
463C2×M16C23×C4711yescharacteristic
464C2×M16C23×C4711yescharacteristic
465C2×M16C23×C4711yescharacteristic
466C22×C8—21no—
467C22×C8C23×C4711yescharacteristic
468C22×C8C23×C4711yescharacteristic
469C22⋊Q8—21no—
470C22⋊Q8—21no—
471#121—21no—
472#121—21no—
473#121—41no—
474C4×Q8—21no—
475C4×Q8—21no—
476C4×D4—21no—
477C4×D4—21no—
478C4×D4—41no—
479C4×D4—41no—
480#117—21no—
481#117—21no—
482#117C23×C4711yescharacteristic
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—41no—
486C2×C4⋊C4C23×C4711yescharacteristic
487C2×C4⋊C4C23×C4711yescharacteristic
488C2×C4⋊C4C23×C4711yescharacteristic
489C2×C42C23×C4711yescharacteristic
490#108—41no—
491#107—21no—
492#107—21no—
493#107—21no—
494#107—21no—
495#107—21no—
496#106—21no—
497#104—22no—
498#104—41no—
499#104—41no—
500#103—21no—
501#103—21no—
502#103—21no—
503#103—21no—
504#103—21no—
505#103—21no—
506#103—21no—
507#103—21no—
508#103—21no—
509#103—21no—
510#103—21no—
511#103D4×C4711yescharacteristic
512#103D4×C4711yescharacteristic
513#102—21no—
514#102—21no—
515#102—21no—
516#102—21no—
517#102—21no—
518#102D4×C4711yescharacteristic
519#102D4×C4711yescharacteristic
520#101—22no—
521C22⋊C8—21no—
522C22⋊C8—21no—
523C22⋊C8—21no—
524C22⋊C8—21no—
525#97—21no—
526C4×C8—21no—
527#95—41no—
528#41—21no—
529#41—21no—
530#41—24no—
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—42no—
540#41—44no—
541#41—42no—
542#41—44no—
543#41—42no—
544#41#41×C4712yes—
545#41#41×C4712yes—
546C2×Q8—21no—
547C2×Q8—24no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—41no—
553C2×Q8—42no—
554C2×Q8—42no—
555C2×Q8—42no—
556C2×Q8C2×D4×C4711yescharacteristic
557C2×Q8C2×D4×C4711yescharacteristic
558C2×Q8C2×D4×C4711yescharacteristic
559C2×Q8#41×C4712yes—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—41no—
564C2×D4—41no—
565C2×D4C2×D4×C4711yescharacteristic
566C2×D4C2×D4×C4711yescharacteristic
567C2×D4C2×D4×C4711yescharacteristic
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4C24×C4711yescharacteristic
581Q16—22no—
582Q16—42no—
583SD16—22no—
584SD16—22no—
585SD16—42no—
586D8—22no—
587M16—21no—
588M16—21no—
589M16—21no—
590M16—21no—
591M16—21no—
592M16—21no—
593M16—21no—
594M16—21no—
595M16—42no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—42no—
605C2×C8C2×D4×C4711yescharacteristic
606C2×C8C2×D4×C4711yescharacteristic
607C2×C8C2×D4×C4711yescharacteristic
608C2×C8C2×D4×C4711yescharacteristic
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—41no—
616C4⋊C4—41no—
617C4⋊C4—41no—
618C4⋊C4—82no—
619C4⋊C4C2×D4×C4711yescharacteristic
620C4⋊C4C2×D4×C4711yescharacteristic
621C22⋊C4—21no—
622C22⋊C4—41no—
623C22⋊C4—41no—
624C22⋊C4—41no—
625C22⋊C4—41no—
626C42—21no—
627C42—21no—
628C42—21no—
629C42—41no—
630C42—41no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23H(5,𝔽2)×C4711yescharacteristic
635Q8—21no—
636Q8—21no—
637Q8—21no—
638Q8—22no—
639Q8—22no—
640Q8—21no—
641Q8—21no—
642Q8—44no—
643Q8—41no—
644Q8—41no—
645Q8#123×C4712yes—
646D4—22no—
647D4—22no—
648D4—21no—
649D4—21no—
650D4—21no—
651D4—21no—
652D4—21no—
653D4—44no—
654D4—41no—
655D4—41no—
656D4—41no—
657D4—41no—
658D4—161no—
659D4#123×C4712yes—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—22no—
669C2×C4—44no—
670C2×C4—41no—
671C2×C4—44no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—81no—
683C2×C4—81no—
684C2×C4—81no—
685C2×C4—161no—
686C2×C4—161no—
687C2×C4C22×D4×C4711yescharacteristic
688C2×C4C22×D4×C4711yescharacteristic
689C2×C4C2×#41×C4711yescharacteristic
690C2×C4C2×#41×C4711yescharacteristic
691C2×C4C2×#41×C4711yescharacteristic
692C2×C4H(5,𝔽2)×C4711yescharacteristic
693C8—21no—
694C8—21no—
695C8—21no—
696C8—21no—
697C8—41no—
698C8—41no—
699C8—41no—
700C8—41no—
701C22—21no—
702C22—21no—
703C22—22no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22C47×#53811yescharacteristic
713C22D42×C4711yescharacteristic
714C22C47×#55111yescharacteristic
715C4—22no—
716C4—42no—
717C4—41no—
718C4—41no—
719C4—41no—
720C4—42no—
721C4—41no—
722C4—81no—
723C4—81no—
724C4—81no—
725C4C2×#123×C4711yescharacteristic
726C4C47×#52511yescharacteristic
727C4C47×#54611yescharacteristic
728C4C47×#54611yescharacteristic
729C2—21no—
730C2—21no—
731C2—42no—
732C2—81no—
733C2—81no—
734C2C47×#241811yescharacteristic
735C2C47×#328811yescharacteristic
736C2C47×#329311yescharacteristic
subgroupG/H
center, socleC22×C47D42
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC47×#3013C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C22×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3098C2semidirect
3. C47×#2951C2semidirect
4. C47×#2898C2semidirect
5. C47×#2095C2semidirect
6. C47×#2078C2semidirect
7. C47×#2052C2semidirect
8. C47×#2039C2semidirect
9. C47×#1930C2semidirect
10. C47×#1929C2semidirect
11. C47×#1882C2semidirect
12. C47×#1876C2semidirect
13. C47×#1859C2semidirect
14. C47×#1816C2semidirect
15. C47×#1793C2semidirect
332. #24931C47direct (N × H)
361. #3098C2×C47semidirect
363. #2951C2×C47semidirect
364. #2898C2×C47semidirect
365. #2095C2×C47semidirect
366. #2078C2×C47semidirect
367. #2052C2×C47semidirect
368. #2039C2×C47semidirect
369. #1930C2×C47semidirect
370. #1929C2×C47semidirect
371. #1882C2×C47semidirect
372. #1876C2×C47semidirect
373. #1859C2×C47semidirect
374. #1816C2×C47semidirect
375. #1793C2×C47semidirect
435. C47#24931direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#30982
C47×#30132
C47×#29512
C47×#28982
C47×#20952
C47×#20782
C47×#20522
C47×#20392
C47×#19302
C47×#19292
C47×#18822
C47×#18762
C47×#18592
C47×#18162
C47×#17932
#2493147