Finite Group Databasebeta

← C47×#25194 #26064892

Subgroups — C47×#25194 #26064892

Order 12032.

980 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3063C211yesmaximal, characteristic, complemented
2C47×#3046C211yesmaximal, characteristic, complemented
3C2×C47×#456C211yesmaximal, characteristic, complemented
4C47×#3013C211yesmaximal, characteristic
5C2×C47×#444C211yesmaximal, characteristic, complemented
6C47×#2898C211yesmaximal, characteristic, complemented
7C47×#2064C211yesmaximal, characteristic, complemented
8C47×#2052C211yesmaximal, characteristic, complemented
9C47×#2040C211yesmaximal, characteristic, complemented
10C47×#2005C211yesmaximal, characteristic, complemented
11C47×#1960C211yesmaximal, characteristic, complemented
12C47×#1938C211yesmaximal, characteristic, complemented
13C47×#1908C211yesmaximal, characteristic, complemented
14C47×#1908C211yesmaximal, characteristic, complemented
15C47×#1860C211yesmaximal, characteristic, complemented
16C2×2−1+4×C47C2211yescharacteristic
17C2×#137×C47C2211yescharacteristic
18C2×#137×C47C2211yescharacteristic
19C2×#137×C47C2211yescharacteristic
20C2×#135×C47C2211yescharacteristic
21C2×#131×C47C2211yescharacteristic
22C2×#131×C47C2211yescharacteristic
23C47×#537C2211yescharacteristic
24C47×#536C2211yescharacteristic
25C2×C4⋊Q8×C47C2211yescharacteristic
26C47×#520C2211yescharacteristic
27C47×#470—21no—
28C47×#468—21no—
29C47×#467—21no—
30C47×#465—21no—
31C47×#464—21no—
32C47×#463—21no—
33C47×#462—21no—
34C47×#461—21no—
35C47×#456—24no—
36C47×#452—21no—
37C47×#451—21no—
38C47×#449—21no—
39C47×#448—21no—
40C47×#444—24no—
41C2×#108×C47C2211yescharacteristic
42C47×#428C2211yescharacteristic
43C47×#424C2211yescharacteristic
44C2×#104×C47C2211yescharacteristic
45C2×#104×C47C2211yescharacteristic
46C2×#104×C47C2211yescharacteristic
47C47×#419—21no—
48C47×#419C2211yescharacteristic
49C47×#417—21no—
50C47×#417C2211yescharacteristic
51C47×#417C2211yescharacteristic
52C47×#417C2211yescharacteristic
53C47×#416—21no—
54C47×#416C2211yescharacteristic
55C2×#103×C47—21no—
56C2×#103×C47C2211yescharacteristic
57C2×#103×C47C2211yescharacteristic
58C2×#103×C47C2211yescharacteristic
59C2×#103×C47C2211yescharacteristic
60C2×#101×C47C2211yescharacteristic
61C2×#101×C47C2211yescharacteristic
62C47×#408C2211yescharacteristic
63C2×#97×C47C2211yescharacteristic
64C47×#382C2211yescharacteristic
65C47×#343C2211yescharacteristic
66C47×#343C2211yescharacteristic
67C47×#341C2211yescharacteristic
68C47×#339C2211yescharacteristic
692−1+4×C47—22no—
702−1+4×C47—22no—
712−1+4×C47—22no—
722−1+4×C47—41no—
73C2×#41×C47—21no—
74C2×#41×C47—21no—
75C2×#41×C47—41no—
76C2×#41×C47C2311yescharacteristic
77C2×#41×C47C2311yescharacteristic
78C2×#41×C47C2311yescharacteristic
79C22×Q8×C47—21no—
80C22×Q8×C47—21no—
81C22×Q8×C47C2311yescharacteristic
82C22×Q8×C47C2311yescharacteristic
83#137×C47—22no—
84#137×C47—22no—
85#137×C47—22no—
86#137×C47—22no—
87#137×C47—41no—
88#137×C47—41no—
89#135×C47—22no—
90#135×C47—22no—
91C2×Q16×C47—21no—
92C2×Q16×C47—21no—
93C2×Q16×C47—21no—
94C2×Q16×C47D411yescharacteristic
95C2×SD16×C47—21no—
96C2×SD16×C47—21no—
97C2×SD16×C47—21no—
98C2×SD16×C47D411yescharacteristic
99C2×SD16×C47D411yescharacteristic
100C2×D8×C47D411yescharacteristic
101#131×C47—22no—
102#131×C47—22no—
103#131×C47—41no—
104#131×C47—41no—
105C2×M16×C47—21no—
106C2×M16×C47—21no—
107C2×M16×C47C2311yescharacteristic
108C2×M16×C47C2311yescharacteristic
109C2×M16×C47C2311yescharacteristic
110C2×M16×C47C2311yescharacteristic
111C22×C8×C47—21no—
112C22×C8×C47—21no—
113C22×C8×C47C2311yescharacteristic
114C22×C8×C47C2311yescharacteristic
115C4⋊Q8×C47—21no—
116C4⋊Q8×C47—22no—
117C4⋊Q8×C47—22no—
118#124×C47—21no—
119#123×C47—41no—
120C22⋊Q8×C47—21no—
121C22⋊Q8×C47—21no—
122C22⋊Q8×C47—21no—
123C22⋊Q8×C47—21no—
124#121×C47—21no—
125#121×C47—21no—
126#121×C47—41no—
127C4×Q8×C47—21no—
128C4×D4×C47—21no—
129C4×D4×C47—41no—
130#117×C47—21no—
131#117×C47C2311yescharacteristic
132C2×C4⋊C4×C47—21no—
133C2×C4⋊C4×C47—41no—
134C2×C4⋊C4×C47C2311yescharacteristic
135C2×C4⋊C4×C47C2311yescharacteristic
136C2×C42×C47C2311yescharacteristic
137#108×C47—22no—
138#107×C47—21no—
139#106×C47—21no—
140C4⋊C8×C47—21no—
141C4⋊C8×C47—21no—
142#104×C47—22no—
143#104×C47—22no—
144#104×C47D414yescomplemented
145#103×C47—21no—
146#103×C47—21no—
147#103×C47—21no—
148#103×C47—21no—
149#103×C47—21no—
150#103×C47—21no—
151#103×C47—21no—
152#103×C47—21no—
153#103×C47—21no—
154#103×C47—21no—
155#103×C47—21no—
156#103×C47—21no—
157#103×C47—21no—
158#103×C47D411yescharacteristic
159#103×C47D411yescharacteristic
160#102×C47—21no—
161#102×C47—21no—
162#102×C47—21no—
163#102×C47D411yescharacteristic
164#102×C47D411yescharacteristic
165#101×C47—22no—
166#101×C47—41no—
167C22⋊C8×C47—21no—
168C22⋊C8×C47—21no—
169#97×C47—22no—
170#95×C47—41no—
171#41×C47—21no—
172#41×C47—21no—
173#41×C47—24no—
174#41×C47—21no—
175#41×C47—21no—
176#41×C47—21no—
177#41×C47—21no—
178#41×C47—21no—
179#41×C47—21no—
180#41×C47—21no—
181#41×C47—21no—
182#41×C47—42no—
183#41×C47—44no—
184#41×C47—42no—
185#41×C47—44no—
186#41×C47—42no—
187#41×C47C2×D412yes—
188#41×C47#4112yes—
189C2×Q8×C47—21no—
190C2×Q8×C47—24no—
191C2×Q8×C47—21no—
192C2×Q8×C47—21no—
193C2×Q8×C47—21no—
194C2×Q8×C47—21no—
195C2×Q8×C47—21no—
196C2×Q8×C47—21no—
197C2×Q8×C47—21no—
198C2×Q8×C47—21no—
199C2×Q8×C47—21no—
200C2×Q8×C47—21no—
201C2×Q8×C47—41no—
202C2×Q8×C47—42no—
203C2×Q8×C47—42no—
204C2×Q8×C47—42no—
205C2×Q8×C47C2×D411yescharacteristic
206C2×Q8×C47C2×D411yescharacteristic
207C2×Q8×C47C2×D411yescharacteristic
208C2×Q8×C47#4112yes—
209C2×D4×C47—21no—
210C2×D4×C47—21no—
211C2×D4×C47—21no—
212C2×D4×C47—41no—
213C2×D4×C47—41no—
214C2×D4×C47C2×D411yescharacteristic
215C2×D4×C47C2×D411yescharacteristic
216C2×D4×C47C2×D411yescharacteristic
217C22×C4×C47—21no—
218C22×C4×C47—21no—
219C22×C4×C47—21no—
220C22×C4×C47—21no—
221C22×C4×C47—21no—
222C22×C4×C47—21no—
223C22×C4×C47—21no—
224C22×C4×C47—21no—
225C22×C4×C47—41no—
226C22×C4×C47—41no—
227C22×C4×C47—41no—
228C22×C4×C47C2411yescharacteristic
229Q16×C47—22no—
230Q16×C47—42no—
231Q16×C47—42no—
232Q16×C47—42no—
233SD16×C47—22no—
234SD16×C47—22no—
235SD16×C47—42no—
236SD16×C47—42no—
237SD16×C47—42no—
238D8×C47—22no—
239M16×C47—21no—
240M16×C47—21no—
241M16×C47—21no—
242M16×C47—21no—
243M16×C47—21no—
244M16×C47—21no—
245M16×C47—21no—
246M16×C47—42no—
247M16×C47—42no—
248M16×C47C2×D412yes—
249C2×C8×C47—21no—
250C2×C8×C47—21no—
251C2×C8×C47—21no—
252C2×C8×C47—21no—
253C2×C8×C47—21no—
254C2×C8×C47—21no—
255C2×C8×C47—21no—
256C2×C8×C47—21no—
257C2×C8×C47—42no—
258C2×C8×C47—42no—
259C2×C8×C47C2×D411yescharacteristic
260C2×C8×C47C2×D411yescharacteristic
261C2×C8×C47C2×D411yescharacteristic
262C2×C8×C47C2×D411yescharacteristic
263C4⋊C4×C47—21no—
264C4⋊C4×C47—21no—
265C4⋊C4×C47—21no—
266C4⋊C4×C47—21no—
267C4⋊C4×C47—41no—
268C4⋊C4×C47—44no—
269C4⋊C4×C47—41no—
270C4⋊C4×C47—41no—
271C4⋊C4×C47—41no—
272C4⋊C4×C47C2×D411yescharacteristic
273C4⋊C4×C47C2×D411yescharacteristic
274C22⋊C4×C47—21no—
275C22⋊C4×C47—41no—
276C22⋊C4×C47—41no—
277C22⋊C4×C47—41no—
278C22⋊C4×C47—41no—
279C22⋊C4×C47—41no—
280C42×C47—21no—
281C42×C47—21no—
282C42×C47—41no—
283C42×C47C2×D412yes—
284C23×C47—21no—
285C23×C47—21no—
286C23×C47—21no—
287C23×C47H(5,𝔽2)11yescharacteristic
288Q8×C47—21no—
289Q8×C47—21no—
290Q8×C47—21no—
291Q8×C47—22no—
292Q8×C47—21no—
293Q8×C47—22no—
294Q8×C47—21no—
295Q8×C47—44no—
296Q8×C47—41no—
297Q8×C47—41no—
298Q8×C47—41no—
299Q8×C47—41no—
300Q8×C47—41no—
301Q8×C47—41no—
302Q8×C47#12112yes—
303D4×C47—22no—
304D4×C47—22no—
305D4×C47—21no—
306D4×C47—21no—
307D4×C47—21no—
308D4×C47—21no—
309D4×C47—21no—
310D4×C47—44no—
311D4×C47—41no—
312D4×C47—41no—
313D4×C47—41no—
314D4×C47—41no—
315D4×C47—161no—
316D4×C47#12112yes—
317C2×C4×C47—21no—
318C2×C4×C47—22no—
319C2×C4×C47—22no—
320C2×C4×C47—21no—
321C2×C4×C47—21no—
322C2×C4×C47—21no—
323C2×C4×C47—21no—
324C2×C4×C47—22no—
325C2×C4×C47—22no—
326C2×C4×C47—44no—
327C2×C4×C47—41no—
328C2×C4×C47—41no—
329C2×C4×C47—44no—
330C2×C4×C47—41no—
331C2×C4×C47—41no—
332C2×C4×C47—41no—
333C2×C4×C47—41no—
334C2×C4×C47—41no—
335C2×C4×C47—41no—
336C2×C4×C47—41no—
337C2×C4×C47—41no—
338C2×C4×C47—41no—
339C2×C4×C47—41no—
340C2×C4×C47—41no—
341C2×C4×C47—81no—
342C2×C4×C47—81no—
343C2×C4×C47—161no—
344C2×C4×C47C22×D411yescharacteristic
345C2×C4×C47C22×D411yescharacteristic
346C2×C4×C47C22×D411yescharacteristic
347C2×C4×C47C2×#4111yescharacteristic
348C2×C4×C47C2×#4111yescharacteristic
349C2×C4×C47H(5,𝔽2)11yescharacteristic
350C8×C47—21no—
351C8×C47—21no—
352C8×C47—21no—
353C8×C47—21no—
354C8×C47—22no—
355C8×C47—41no—
356C8×C47—41no—
357C8×C47—41no—
358#25194C4711yesmaximal, characteristic, direct product factor, Sylow
359C22×C47—21no—
360C22×C47—21no—
361C22×C47—22no—
362C22×C47—41no—
363C22×C47—41no—
364C22×C47—41no—
365C22×C47—41no—
366C22×C47—41no—
367C22×C47—41no—
368C22×C47—41no—
369C22×C47—41no—
370C22×C47#53811yescharacteristic
371C22×C47D4211yescharacteristic
372C22×C47#54611yescharacteristic
373C4×C47—22no—
374C4×C47—42no—
375C4×C47—41no—
376C4×C47—42no—
377C4×C47—41no—
378C4×C47—41no—
379C4×C47—41no—
380C4×C47—81no—
381C4×C47—81no—
382C4×C47—81no—
383C4×C47C2×#12111yescharacteristic
384C4×C47#52511yescharacteristic
385C4×C47D4211yescharacteristic
386C4×C47#54611yescharacteristic
387#3063C2×C4711yescharacteristic, complemented
388#3046C2×C4711yescharacteristic, complemented
389C2×#456C2×C4711yescharacteristic, complemented
390#3013C2×C4711yescharacteristic
391C2×#444C2×C4711yescharacteristic, complemented
392#2898C2×C4711yescharacteristic, complemented
393#2064C2×C4711yescharacteristic, complemented
394#2052C2×C4711yescharacteristic, complemented
395#2040C2×C4711yescharacteristic, complemented
396#2005C2×C4711yescharacteristic, complemented
397#1960C2×C4711yescharacteristic, complemented
398#1938C2×C4711yescharacteristic, complemented
399#1908C2×C4711yescharacteristic, complemented
400#1908C2×C4711yescharacteristic, complemented
401#1860C2×C4711yescharacteristic, complemented
402C2×C47—21no—
403C2×C47—21no—
404C2×C47—42no—
405C2×C47—81no—
406C2×C47—81no—
407C2×C47#242411yescharacteristic
408C2×C47#328911yescharacteristic
409C2×C47#328911yescharacteristic
410C2×2−1+4C22×C4711yescharacteristic
411C2×#137C22×C4711yescharacteristic
412C2×#137C22×C4711yescharacteristic
413C2×#137C22×C4711yescharacteristic
414C2×#135C22×C4711yescharacteristic
415C2×#131C22×C4711yescharacteristic
416C2×#131C22×C4711yescharacteristic
417#537C22×C4711yescharacteristic
418#536C22×C4711yescharacteristic
419C2×C4⋊Q8C22×C4711yescharacteristic
420#520C22×C4711yescharacteristic
421#470—21no—
422#468—21no—
423#467—21no—
424#465—21no—
425#464—21no—
426#463—21no—
427#462—21no—
428#461—21no—
429#456—24no—
430#452—21no—
431#451—21no—
432#449—21no—
433#448—21no—
434#444—24no—
435C2×#108C22×C4711yescharacteristic
436#428C22×C4711yescharacteristic
437#424C22×C4711yescharacteristic
438C2×#104C22×C4711yescharacteristic
439C2×#104C22×C4711yescharacteristic
440C2×#104C22×C4711yescharacteristic
441#419—21no—
442#419C22×C4711yescharacteristic
443#417—21no—
444#417C22×C4711yescharacteristic
445#417C22×C4711yescharacteristic
446#417C22×C4711yescharacteristic
447#416—21no—
448#416C22×C4711yescharacteristic
449C2×#103—21no—
450C2×#103C22×C4711yescharacteristic
451C2×#103C22×C4711yescharacteristic
452C2×#103C22×C4711yescharacteristic
453C2×#103C22×C4711yescharacteristic
454C2×#101C22×C4711yescharacteristic
455C2×#101C22×C4711yescharacteristic
456#408C22×C4711yescharacteristic
457C2×#97C22×C4711yescharacteristic
458#382C22×C4711yescharacteristic
459#343C22×C4711yescharacteristic
460#343C22×C4711yescharacteristic
461#341C22×C4711yescharacteristic
462#339C22×C4711yescharacteristic
463C47#2519411yescharacteristic, direct product factor, Sylow
4642−1+4—22no—
4652−1+4—22no—
4662−1+4—22no—
4672−1+4—41no—
468C2×#41—21no—
469C2×#41—21no—
470C2×#41—41no—
471C2×#41C23×C4711yescharacteristic
472C2×#41C23×C4711yescharacteristic
473C2×#41C23×C4711yescharacteristic
474C22×Q8—21no—
475C22×Q8—21no—
476C22×Q8C23×C4711yescharacteristic
477C22×Q8C23×C4711yescharacteristic
478#137—22no—
479#137—22no—
480#137—22no—
481#137—22no—
482#137—41no—
483#137—41no—
484#135—22no—
485#135—22no—
486C2×Q16—21no—
487C2×Q16—21no—
488C2×Q16—21no—
489C2×Q16D4×C4711yescharacteristic
490C2×SD16—21no—
491C2×SD16—21no—
492C2×SD16—21no—
493C2×SD16D4×C4711yescharacteristic
494C2×SD16D4×C4711yescharacteristic
495C2×D8D4×C4711yescharacteristic
496#131—22no—
497#131—22no—
498#131—41no—
499#131—41no—
500C2×M16—21no—
501C2×M16—21no—
502C2×M16C23×C4711yescharacteristic
503C2×M16C23×C4711yescharacteristic
504C2×M16C23×C4711yescharacteristic
505C2×M16C23×C4711yescharacteristic
506C22×C8—21no—
507C22×C8—21no—
508C22×C8C23×C4711yescharacteristic
509C22×C8C23×C4711yescharacteristic
510C4⋊Q8—21no—
511C4⋊Q8—22no—
512C4⋊Q8—22no—
513#124—21no—
514#123—41no—
515C22⋊Q8—21no—
516C22⋊Q8—21no—
517C22⋊Q8—21no—
518C22⋊Q8—21no—
519#121—21no—
520#121—21no—
521#121—41no—
522C4×Q8—21no—
523C4×D4—21no—
524C4×D4—41no—
525#117—21no—
526#117C23×C4711yescharacteristic
527C2×C4⋊C4—21no—
528C2×C4⋊C4—41no—
529C2×C4⋊C4C23×C4711yescharacteristic
530C2×C4⋊C4C23×C4711yescharacteristic
531C2×C42C23×C4711yescharacteristic
532#108—22no—
533#107—21no—
534#106—21no—
535C4⋊C8—21no—
536C4⋊C8—21no—
537#104—22no—
538#104—22no—
539#104D4×C4714yescomplemented
540#103—21no—
541#103—21no—
542#103—21no—
543#103—21no—
544#103—21no—
545#103—21no—
546#103—21no—
547#103—21no—
548#103—21no—
549#103—21no—
550#103—21no—
551#103—21no—
552#103—21no—
553#103D4×C4711yescharacteristic
554#103D4×C4711yescharacteristic
555#102—21no—
556#102—21no—
557#102—21no—
558#102D4×C4711yescharacteristic
559#102D4×C4711yescharacteristic
560#101—22no—
561#101—41no—
562C22⋊C8—21no—
563C22⋊C8—21no—
564#97—22no—
565#95—41no—
566#41—21no—
567#41—21no—
568#41—24no—
569#41—21no—
570#41—21no—
571#41—21no—
572#41—21no—
573#41—21no—
574#41—21no—
575#41—21no—
576#41—21no—
577#41—42no—
578#41—44no—
579#41—42no—
580#41—44no—
581#41—42no—
582#41C2×D4×C4712yes—
583#41#41×C4712yes—
584C2×Q8—21no—
585C2×Q8—24no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—41no—
597C2×Q8—42no—
598C2×Q8—42no—
599C2×Q8—42no—
600C2×Q8C2×D4×C4711yescharacteristic
601C2×Q8C2×D4×C4711yescharacteristic
602C2×Q8C2×D4×C4711yescharacteristic
603C2×Q8#41×C4712yes—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—41no—
608C2×D4—41no—
609C2×D4C2×D4×C4711yescharacteristic
610C2×D4C2×D4×C4711yescharacteristic
611C2×D4C2×D4×C4711yescharacteristic
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—41no—
621C22×C4—41no—
622C22×C4—41no—
623C22×C4C24×C4711yescharacteristic
624Q16—22no—
625Q16—42no—
626Q16—42no—
627Q16—42no—
628SD16—22no—
629SD16—22no—
630SD16—42no—
631SD16—42no—
632SD16—42no—
633D8—22no—
634M16—21no—
635M16—21no—
636M16—21no—
637M16—21no—
638M16—21no—
639M16—21no—
640M16—21no—
641M16—42no—
642M16—42no—
643M16C2×D4×C4712yes—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—42no—
653C2×C8—42no—
654C2×C8C2×D4×C4711yescharacteristic
655C2×C8C2×D4×C4711yescharacteristic
656C2×C8C2×D4×C4711yescharacteristic
657C2×C8C2×D4×C4711yescharacteristic
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—41no—
663C4⋊C4—44no—
664C4⋊C4—41no—
665C4⋊C4—41no—
666C4⋊C4—41no—
667C4⋊C4C2×D4×C4711yescharacteristic
668C4⋊C4C2×D4×C4711yescharacteristic
669C22⋊C4—21no—
670C22⋊C4—41no—
671C22⋊C4—41no—
672C22⋊C4—41no—
673C22⋊C4—41no—
674C22⋊C4—41no—
675C42—21no—
676C42—21no—
677C42—41no—
678C42C2×D4×C4712yes—
679C23—21no—
680C23—21no—
681C23—21no—
682C23H(5,𝔽2)×C4711yescharacteristic
683Q8—21no—
684Q8—21no—
685Q8—21no—
686Q8—22no—
687Q8—21no—
688Q8—22no—
689Q8—21no—
690Q8—44no—
691Q8—41no—
692Q8—41no—
693Q8—41no—
694Q8—41no—
695Q8—41no—
696Q8—41no—
697Q8#121×C4712yes—
698D4—22no—
699D4—22no—
700D4—21no—
701D4—21no—
702D4—21no—
703D4—21no—
704D4—21no—
705D4—44no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—161no—
711D4#121×C4712yes—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—44no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—44no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—81no—
737C2×C4—81no—
738C2×C4—161no—
739C2×C4C22×D4×C4711yescharacteristic
740C2×C4C22×D4×C4711yescharacteristic
741C2×C4C22×D4×C4711yescharacteristic
742C2×C4C2×#41×C4711yescharacteristic
743C2×C4C2×#41×C4711yescharacteristic
744C2×C4H(5,𝔽2)×C4711yescharacteristic
745C8—21no—
746C8—21no—
747C8—21no—
748C8—21no—
749C8—22no—
750C8—41no—
751C8—41no—
752C8—41no—
753C22—21no—
754C22—21no—
755C22—22no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22C47×#53811yescharacteristic
765C22D42×C4711yescharacteristic
766C22C47×#54611yescharacteristic
767C4—22no—
768C4—42no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—42no—
773C4—41no—
774C4—81no—
775C4—81no—
776C4—81no—
777C4C2×#121×C4711yescharacteristic
778C4C47×#52511yescharacteristic
779C4D42×C4711yescharacteristic
780C4C47×#54611yescharacteristic
781C2—21no—
782C2—21no—
783C2—42no—
784C2—81no—
785C2—81no—
786C2C47×#242411yescharacteristic
787C2C47×#328911yescharacteristic
788C2C47×#328911yescharacteristic
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×#3063C2semidirect
2. C47×#3046C2semidirect
3. C2×C47×#456C2semidirect
5. C2×C47×#444C2semidirect
6. C47×#2898C2semidirect
7. C47×#2064C2semidirect
8. C47×#2052C2semidirect
9. C47×#2040C2semidirect
10. C47×#2005C2semidirect
11. C47×#1960C2semidirect
12. C47×#1938C2semidirect
13. C47×#1908C2semidirect
14. C47×#1908C2semidirect
15. C47×#1860C2semidirect
144. #104×C47D4semidirect
358. #25194C47direct (N × H)
387. #3063C2×C47semidirect
388. #3046C2×C47semidirect
389. C2×#456C2×C47semidirect
391. C2×#444C2×C47semidirect
392. #2898C2×C47semidirect
393. #2064C2×C47semidirect
394. #2052C2×C47semidirect
395. #2040C2×C47semidirect
396. #2005C2×C47semidirect
397. #1960C2×C47semidirect
398. #1938C2×C47semidirect
399. #1908C2×C47semidirect
400. #1908C2×C47semidirect
401. #1860C2×C47semidirect
463. C47#25194direct (N × H)
539. #104D4×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#30632
C47×#30462
C2×C47×#4562
C47×#30132
C2×C47×#4442
C47×#28982
C47×#20642
C47×#20522
C47×#20402
C47×#20052
C47×#19602
C47×#19382
C47×#19082
C47×#18602
#2519447