Finite Group Databasebeta

← C47×#24805 #26064503

Subgroups — C47×#24805 #26064503

Order 12032.

870 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#471C211yesmaximal, characteristic, complemented
2C47×#3056C211yesmaximal, characteristic, complemented
3C47×#3055C211yesmaximal, characteristic
4C2×C47×#468C211yesmaximal, characteristic, complemented
5C47×#2930C211yesmaximal, characteristic, complemented
6C2×C47×#430C211yesmaximal, characteristic, complemented
7C47×#2064C211yesmaximal, characteristic, complemented
8C47×#2063C211yesmaximal, characteristic, complemented
9C47×#2052C211yesmaximal, characteristic, complemented
10C47×#2051C211yesmaximal, characteristic, complemented
11C47×#1977C211yesmaximal, characteristic, complemented
12C47×#1952C211yesmaximal, characteristic, complemented
13C47×#1901C211yesmaximal, characteristic, complemented
14C47×#1900C211yesmaximal, characteristic, complemented
15C47×#1816C211yesmaximal, characteristic, complemented
16C2×#137×C47C2211yescharacteristic
17C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
18C22×SD16×C47C2211yescharacteristic
19C2×#131×C47C2211yescharacteristic
20C22×M16×C47C2211yescharacteristic
21C22×M16×C47C2211yescharacteristic
22C22×M16×C47C2211yescharacteristic
23C47×#525C2211yescharacteristic
24C2×C22⋊Q8×C47C2211yescharacteristic
25C2×#121×C47C2211yescharacteristic
26C47×#471—24no—
27C47×#470—21no—
28C47×#469—21no—
29C47×#468—21no—
30C47×#468—21no—
31C47×#468—21no—
32C47×#468—21no—
33C47×#468—21no—
34C47×#468—21no—
35C47×#467—21no—
36C47×#466—21no—
37C47×#465—21no—
38C47×#465—21no—
39C47×#436—21no—
40C47×#436—21no—
41C47×#435—21no—
42C47×#435—21no—
43C47×#430—24no—
44C2×#108×C47C2211yescharacteristic
45C2×#108×C47C2211yescharacteristic
46C2×#108×C47C2211yescharacteristic
47C2×#108×C47C2211yescharacteristic
48C47×#428C2211yescharacteristic
49C47×#428C2211yescharacteristic
50C2×#107×C47C2211yescharacteristic
51C47×#424C2211yescharacteristic
52C47×#419C2211yescharacteristic
53C47×#418C2211yescharacteristic
54C47×#417C2211yescharacteristic
55C47×#417C2211yescharacteristic
56C2×#103×C47C2211yescharacteristic
57C2×#102×C47C2211yescharacteristic
58C2×#101×C47C2211yescharacteristic
59C2×#101×C47C2211yescharacteristic
60C2×#100×C47C2211yescharacteristic
61C2×#100×C47C2211yescharacteristic
62C47×#408C2211yescharacteristic
63C47×#407C2211yescharacteristic
64C47×#405C2211yescharacteristic
65C47×#343C2211yescharacteristic
66C47×#343C2211yescharacteristic
67C47×#343C2211yescharacteristic
68C47×#343C2211yescharacteristic
69C2×#41×C47C2311yescharacteristic
70C22×Q8×C47C2311yescharacteristic
71C22×D4×C47—21no—
72C22×D4×C47C2311yescharacteristic
73C23×C4×C47C2311yescharacteristic
74#137×C47—22no—
75#137×C47—41no—
76AGL(1,ℤ/8)×C47—22no—
77AGL(1,ℤ/8)×C47—41no—
78C2×Q16×C47—21no—
79C2×SD16×C47—21no—
80C2×SD16×C47—21no—
81C2×SD16×C47—21no—
82C2×SD16×C47—21no—
83C2×SD16×C47—22no—
84C2×SD16×C47—22no—
85C2×D8×C47—21no—
86#131×C47—22no—
87#131×C47—22no—
88C2×M16×C47—21no—
89C2×M16×C47—21no—
90C2×M16×C47—22no—
91C2×M16×C47—21no—
92C2×M16×C47—22no—
93C2×M16×C47—22no—
94C2×M16×C47—22no—
95C2×M16×C47—41no—
96C2×M16×C47—41no—
97C2×M16×C47D411yescharacteristic
98C2×M16×C47D411yescharacteristic
99C2×M16×C47D411yescharacteristic
100C2×M16×C47D411yescharacteristic
101C2×M16×C47C2311yescharacteristic
102C2×M16×C47C2311yescharacteristic
103C2×M16×C47C2311yescharacteristic
104C2×M16×C47C2311yescharacteristic
105C2×M16×C47C2311yescharacteristic
106C2×M16×C47C2311yescharacteristic
107C22×C8×C47—21no—
108C22×C8×C47—21no—
109C22×C8×C47—21no—
110C22×C8×C47C2311yescharacteristic
111C22×C8×C47C2311yescharacteristic
112#123×C47—21no—
113C22⋊Q8×C47—21no—
114C22⋊Q8×C47—21no—
115C22⋊Q8×C47—21no—
116C22⋊Q8×C47—21no—
117C22⋊Q8×C47D411yescharacteristic
118C22⋊Q8×C47D411yescharacteristic
119#121×C47—21no—
120#121×C47—21no—
121#121×C47—21no—
122#121×C47—21no—
123#121×C47D411yescharacteristic
124#121×C47D411yescharacteristic
125#120×C47—21no—
126C4×D4×C47—21no—
127C4×D4×C47—21no—
128#117×C47C2311yescharacteristic
129C2×C4⋊C4×C47—21no—
130C2×C4⋊C4×C47C2311yescharacteristic
131C2×C4⋊C4×C47C2311yescharacteristic
132C2×C22⋊C4×C47—21no—
133C2×C22⋊C4×C47—21no—
134#108×C47—22no—
135#108×C47—22no—
136#108×C47—22no—
137#108×C47D414yescomplemented
138#107×C47—21no—
139#107×C47—21no—
140#107×C47—21no—
141#107×C47—21no—
142#106×C47—21no—
143#106×C47—21no—
144C4⋊C8×C47—21no—
145C4⋊C8×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#102×C47—21no—
153#102×C47—21no—
154#102×C47—21no—
155#102×C47—21no—
156#102×C47—21no—
157#102×C47—21no—
158#101×C47—22no—
159#101×C47—41no—
160#100×C47—22no—
161#100×C47—41no—
162C22⋊C8×C47—21no—
163C22⋊C8×C47—21no—
164C22⋊C8×C47—21no—
165C22⋊C8×C47—21no—
166#97×C47—21no—
167C4×C8×C47—21no—
168C24×C47—21no—
169C24×C47#4111yescharacteristic
170#41×C47—21no—
171#41×C47—21no—
172#41×C47—21no—
173#41×C47—21no—
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×C47C2×D411yescharacteristic
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—41no—
191C2×D4×C47—41no—
192C2×D4×C47—82no—
193C2×D4×C47C2×D411yescharacteristic
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47C2×D411yescharacteristic
203C22×C4×C47C2×D411yescharacteristic
204C22×C4×C47C2×D411yescharacteristic
205C22×C4×C47C2×D411yescharacteristic
206C22×C4×C47#4111yescharacteristic
207C22×C4×C47C2411yescharacteristic
208Q16×C47—42no—
209SD16×C47—42no—
210SD16×C47—42no—
211SD16×C47—42no—
212SD16×C47—42no—
213D8×C47—42no—
214M16×C47—21no—
215M16×C47—21no—
216M16×C47—22no—
217M16×C47—22no—
218M16×C47—22no—
219M16×C47—22no—
220M16×C47—21no—
221M16×C47—21no—
222M16×C47—21no—
223M16×C47—21no—
224M16×C47—21no—
225M16×C47—21no—
226M16×C47—21no—
227M16×C47—21no—
228M16×C47—42no—
229M16×C47—42no—
230M16×C47—42no—
231M16×C47C2×D412yes—
232M16×C47C2×D412yes—
233C2×C8×C47—21no—
234C2×C8×C47—21no—
235C2×C8×C47—21no—
236C2×C8×C47—21no—
237C2×C8×C47—21no—
238C2×C8×C47—21no—
239C2×C8×C47—21no—
240C2×C8×C47—21no—
241C2×C8×C47—42no—
242C2×C8×C47—42no—
243C2×C8×C47—42no—
244C2×C8×C47C2×D411yescharacteristic
245C2×C8×C47C2×D411yescharacteristic
246C2×C8×C47C2×D411yescharacteristic
247C2×C8×C47C2×D411yescharacteristic
248C2×C8×C47C2×D412yes—
249C2×C8×C47#4112yes—
250C4⋊C4×C47—21no—
251C4⋊C4×C47—21no—
252C4⋊C4×C47—21no—
253C4⋊C4×C47—21no—
254C4⋊C4×C47—21no—
255C4⋊C4×C47—21no—
256C4⋊C4×C47—41no—
257C4⋊C4×C47—41no—
258C4⋊C4×C47C2×D411yescharacteristic
259C4⋊C4×C47C2×D411yescharacteristic
260C22⋊C4×C47—21no—
261C22⋊C4×C47—21no—
262C22⋊C4×C47—21no—
263C22⋊C4×C47—21no—
264C22⋊C4×C47—21no—
265C22⋊C4×C47—41no—
266C22⋊C4×C47—41no—
267C22⋊C4×C47—41no—
268C22⋊C4×C47—41no—
269C42×C47—21no—
270C23×C47—21no—
271C23×C47—21no—
272C23×C47—21no—
273C23×C47—41no—
274C23×C47—41no—
275C23×C47—41no—
276C23×C47—41no—
277C23×C47—41no—
278C23×C47—81no—
279C23×C47—81no—
280C23×C47#12111yescharacteristic
281C23×C47#12111yescharacteristic
282C23×C47C2×#4111yescharacteristic
283Q8×C47—21no—
284Q8×C47—21no—
285Q8×C47—41no—
286Q8×C47—41no—
287Q8×C47—41no—
288Q8×C47—41no—
289D4×C47—21no—
290D4×C47—21no—
291D4×C47—41no—
292D4×C47—41no—
293D4×C47—41no—
294D4×C47—41no—
295D4×C47—41no—
296D4×C47—41no—
297D4×C47—81no—
298D4×C47—81no—
299D4×C47—82no—
300D4×C47—82no—
301C2×C4×C47—21no—
302C2×C4×C47—21no—
303C2×C4×C47—21no—
304C2×C4×C47—21no—
305C2×C4×C47—21no—
306C2×C4×C47—21no—
307C2×C4×C47—21no—
308C2×C4×C47—21no—
309C2×C4×C47—21no—
310C2×C4×C47—21no—
311C2×C4×C47—21no—
312C2×C4×C47—21no—
313C2×C4×C47—21no—
314C2×C4×C47—41no—
315C2×C4×C47—41no—
316C2×C4×C47—41no—
317C2×C4×C47—41no—
318C2×C4×C47—41no—
319C2×C4×C47—41no—
320C2×C4×C47—41no—
321C2×C4×C47—81no—
322C2×C4×C47—81no—
323C2×C4×C47#12111yescharacteristic
324C2×C4×C47#12111yescharacteristic
325C2×C4×C47C22×D411yescharacteristic
326C2×C4×C47C22×D411yescharacteristic
327C2×C4×C47C22×D411yescharacteristic
328C2×C4×C47C2×#4111yescharacteristic
329C2×C4×C47H(5,𝔽2)11yescharacteristic
330C2×C4×C472−1+411yescharacteristic
331C8×C47—21no—
332C8×C47—21no—
333C8×C47—22no—
334C8×C47—22no—
335C8×C47—41no—
336C8×C47—41no—
337C8×C47—41no—
338C8×C47—41no—
339C8×C47#12112yes—
340C8×C47#12112yes—
341#24805C4711yesmaximal, characteristic, direct product factor, Sylow
342C22×C47—21no—
343C22×C47—21no—
344C22×C47—21no—
345C22×C47—21no—
346C22×C47—21no—
347C22×C47—21no—
348C22×C47—21no—
349C22×C47—21no—
350C22×C47—41no—
351C22×C47—41no—
352C22×C47—41no—
353C22×C47—81no—
354C22×C47—81no—
355C22×C47—81no—
356C22×C47—81no—
357C22×C47—81no—
358C22×C47—161no—
359C22×C47—161no—
360C22×C47C2×#12111yescharacteristic
361C22×C47#54811yescharacteristic
362C22×C47#55311yescharacteristic
363C4×C47—21no—
364C4×C47—21no—
365C4×C47—41no—
366C4×C47—41no—
367C4×C47—41no—
368C4×C47—81no—
369C4×C47—81no—
370C4×C47—81no—
371C4×C47C2×#12111yescharacteristic
372C4×C47#53711yescharacteristic
373C4×C47D4211yescharacteristic
374C4×C47#54711yescharacteristic
375C2×#471C2×C4711yescharacteristic, complemented
376#3056C2×C4711yescharacteristic, complemented
377#3055C2×C4711yescharacteristic
378C2×#468C2×C4711yescharacteristic, complemented
379#2930C2×C4711yescharacteristic, complemented
380C2×#430C2×C4711yescharacteristic, complemented
381#2064C2×C4711yescharacteristic, complemented
382#2063C2×C4711yescharacteristic, complemented
383#2052C2×C4711yescharacteristic, complemented
384#2051C2×C4711yescharacteristic, complemented
385#1977C2×C4711yescharacteristic, complemented
386#1952C2×C4711yescharacteristic, complemented
387#1901C2×C4711yescharacteristic, complemented
388#1900C2×C4711yescharacteristic, complemented
389#1816C2×C4711yescharacteristic, complemented
390C2×C47—21no—
391C2×C47—21no—
392C2×C47—41no—
393C2×C47—41no—
394C2×C47—81no—
395C2×C47—161no—
396C2×C47#241611yescharacteristic
397C2×C47#306811yescharacteristic
398C2×C47#306911yescharacteristic
399C2×#137C22×C4711yescharacteristic
400C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
401C22×SD16C22×C4711yescharacteristic
402C2×#131C22×C4711yescharacteristic
403C22×M16C22×C4711yescharacteristic
404C22×M16C22×C4711yescharacteristic
405C22×M16C22×C4711yescharacteristic
406#525C22×C4711yescharacteristic
407C2×C22⋊Q8C22×C4711yescharacteristic
408C2×#121C22×C4711yescharacteristic
409#471—24no—
410#470—21no—
411#469—21no—
412#468—21no—
413#468—21no—
414#468—21no—
415#468—21no—
416#468—21no—
417#468—21no—
418#467—21no—
419#466—21no—
420#465—21no—
421#465—21no—
422#436—21no—
423#436—21no—
424#435—21no—
425#435—21no—
426#430—24no—
427C2×#108C22×C4711yescharacteristic
428C2×#108C22×C4711yescharacteristic
429C2×#108C22×C4711yescharacteristic
430C2×#108C22×C4711yescharacteristic
431#428C22×C4711yescharacteristic
432#428C22×C4711yescharacteristic
433C2×#107C22×C4711yescharacteristic
434#424C22×C4711yescharacteristic
435#419C22×C4711yescharacteristic
436#418C22×C4711yescharacteristic
437#417C22×C4711yescharacteristic
438#417C22×C4711yescharacteristic
439C2×#103C22×C4711yescharacteristic
440C2×#102C22×C4711yescharacteristic
441C2×#101C22×C4711yescharacteristic
442C2×#101C22×C4711yescharacteristic
443C2×#100C22×C4711yescharacteristic
444C2×#100C22×C4711yescharacteristic
445#408C22×C4711yescharacteristic
446#407C22×C4711yescharacteristic
447#405C22×C4711yescharacteristic
448#343C22×C4711yescharacteristic
449#343C22×C4711yescharacteristic
450#343C22×C4711yescharacteristic
451#343C22×C4711yescharacteristic
452C47#2480511yescharacteristic, direct product factor, Sylow
453C2×#41C23×C4711yescharacteristic
454C22×Q8C23×C4711yescharacteristic
455C22×D4—21no—
456C22×D4C23×C4711yescharacteristic
457C23×C4C23×C4711yescharacteristic
458#137—22no—
459#137—41no—
460AGL(1,ℤ/8)—22no—
461AGL(1,ℤ/8)—41no—
462C2×Q16—21no—
463C2×SD16—21no—
464C2×SD16—21no—
465C2×SD16—21no—
466C2×SD16—21no—
467C2×SD16—22no—
468C2×SD16—22no—
469C2×D8—21no—
470#131—22no—
471#131—22no—
472C2×M16—21no—
473C2×M16—21no—
474C2×M16—22no—
475C2×M16—21no—
476C2×M16—22no—
477C2×M16—22no—
478C2×M16—22no—
479C2×M16—41no—
480C2×M16—41no—
481C2×M16D4×C4711yescharacteristic
482C2×M16D4×C4711yescharacteristic
483C2×M16D4×C4711yescharacteristic
484C2×M16D4×C4711yescharacteristic
485C2×M16C23×C4711yescharacteristic
486C2×M16C23×C4711yescharacteristic
487C2×M16C23×C4711yescharacteristic
488C2×M16C23×C4711yescharacteristic
489C2×M16C23×C4711yescharacteristic
490C2×M16C23×C4711yescharacteristic
491C22×C8—21no—
492C22×C8—21no—
493C22×C8—21no—
494C22×C8C23×C4711yescharacteristic
495C22×C8C23×C4711yescharacteristic
496#123—21no—
497C22⋊Q8—21no—
498C22⋊Q8—21no—
499C22⋊Q8—21no—
500C22⋊Q8—21no—
501C22⋊Q8D4×C4711yescharacteristic
502C22⋊Q8D4×C4711yescharacteristic
503#121—21no—
504#121—21no—
505#121—21no—
506#121—21no—
507#121D4×C4711yescharacteristic
508#121D4×C4711yescharacteristic
509#120—21no—
510C4×D4—21no—
511C4×D4—21no—
512#117C23×C4711yescharacteristic
513C2×C4⋊C4—21no—
514C2×C4⋊C4C23×C4711yescharacteristic
515C2×C4⋊C4C23×C4711yescharacteristic
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518#108—22no—
519#108—22no—
520#108—22no—
521#108D4×C4714yescomplemented
522#107—21no—
523#107—21no—
524#107—21no—
525#107—21no—
526#106—21no—
527#106—21no—
528C4⋊C8—21no—
529C4⋊C8—21no—
530#103—21no—
531#103—21no—
532#103—21no—
533#103—21no—
534#103—21no—
535#103—21no—
536#102—21no—
537#102—21no—
538#102—21no—
539#102—21no—
540#102—21no—
541#102—21no—
542#101—22no—
543#101—41no—
544#100—22no—
545#100—41no—
546C22⋊C8—21no—
547C22⋊C8—21no—
548C22⋊C8—21no—
549C22⋊C8—21no—
550#97—21no—
551C4×C8—21no—
552C24—21no—
553C24#41×C4711yescharacteristic
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×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—82no—
577C2×D4C2×D4×C4711yescharacteristic
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4C2×D4×C4711yescharacteristic
587C22×C4C2×D4×C4711yescharacteristic
588C22×C4C2×D4×C4711yescharacteristic
589C22×C4C2×D4×C4711yescharacteristic
590C22×C4#41×C4711yescharacteristic
591C22×C4C24×C4711yescharacteristic
592Q16—42no—
593SD16—42no—
594SD16—42no—
595SD16—42no—
596SD16—42no—
597D8—42no—
598M16—21no—
599M16—21no—
600M16—22no—
601M16—22no—
602M16—22no—
603M16—22no—
604M16—21no—
605M16—21no—
606M16—21no—
607M16—21no—
608M16—21no—
609M16—21no—
610M16—21no—
611M16—21no—
612M16—42no—
613M16—42no—
614M16—42no—
615M16C2×D4×C4712yes—
616M16C2×D4×C4712yes—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—42no—
626C2×C8—42no—
627C2×C8—42no—
628C2×C8C2×D4×C4711yescharacteristic
629C2×C8C2×D4×C4711yescharacteristic
630C2×C8C2×D4×C4711yescharacteristic
631C2×C8C2×D4×C4711yescharacteristic
632C2×C8C2×D4×C4712yes—
633C2×C8#41×C4712yes—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—41no—
641C4⋊C4—41no—
642C4⋊C4C2×D4×C4711yescharacteristic
643C4⋊C4C2×D4×C4711yescharacteristic
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—41no—
650C22⋊C4—41no—
651C22⋊C4—41no—
652C22⋊C4—41no—
653C42—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—81no—
663C23—81no—
664C23#121×C4711yescharacteristic
665C23#121×C4711yescharacteristic
666C23C2×#41×C4711yescharacteristic
667Q8—21no—
668Q8—21no—
669Q8—41no—
670Q8—41no—
671Q8—41no—
672Q8—41no—
673D4—21no—
674D4—21no—
675D4—41no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—41no—
681D4—81no—
682D4—81no—
683D4—82no—
684D4—82no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—81no—
706C2×C4—81no—
707C2×C4#121×C4711yescharacteristic
708C2×C4#121×C4711yescharacteristic
709C2×C4C22×D4×C4711yescharacteristic
710C2×C4C22×D4×C4711yescharacteristic
711C2×C4C22×D4×C4711yescharacteristic
712C2×C4C2×#41×C4711yescharacteristic
713C2×C4H(5,𝔽2)×C4711yescharacteristic
714C2×C42−1+4×C4711yescharacteristic
715C8—21no—
716C8—21no—
717C8—22no—
718C8—22no—
719C8—41no—
720C8—41no—
721C8—41no—
722C8—41no—
723C8#121×C4712yes—
724C8#121×C4712yes—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—81no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—161no—
742C22—161no—
743C22C2×#121×C4711yescharacteristic
744C22C47×#54811yescharacteristic
745C22C47×#55311yescharacteristic
746C4—21no—
747C4—21no—
748C4—41no—
749C4—41no—
750C4—41no—
751C4—81no—
752C4—81no—
753C4—81no—
754C4C2×#121×C4711yescharacteristic
755C4C47×#53711yescharacteristic
756C4D42×C4711yescharacteristic
757C4C47×#54711yescharacteristic
758C2—21no—
759C2—21no—
760C2—41no—
761C2—41no—
762C2—81no—
763C2—161no—
764C2C47×#241611yescharacteristic
765C2C47×#306811yescharacteristic
766C2C47×#306911yescharacteristic
subgroupG/H
center, socleC22×C47C2×#121
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC47×#3055C2
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. C2×C47×#471C2semidirect
2. C47×#3056C2semidirect
4. C2×C47×#468C2semidirect
5. C47×#2930C2semidirect
6. C2×C47×#430C2semidirect
7. C47×#2064C2semidirect
8. C47×#2063C2semidirect
9. C47×#2052C2semidirect
10. C47×#2051C2semidirect
11. C47×#1977C2semidirect
12. C47×#1952C2semidirect
13. C47×#1901C2semidirect
14. C47×#1900C2semidirect
15. C47×#1816C2semidirect
137. #108×C47D4semidirect
341. #24805C47direct (N × H)
375. C2×#471C2×C47semidirect
376. #3056C2×C47semidirect
378. C2×#468C2×C47semidirect
379. #2930C2×C47semidirect
380. C2×#430C2×C47semidirect
381. #2064C2×C47semidirect
382. #2063C2×C47semidirect
383. #2052C2×C47semidirect
384. #2051C2×C47semidirect
385. #1977C2×C47semidirect
386. #1952C2×C47semidirect
387. #1901C2×C47semidirect
388. #1900C2×C47semidirect
389. #1816C2×C47semidirect
452. C47#24805direct (N × H)
521. #108D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4712
C47×#30562
C47×#30552
C2×C47×#4682
C47×#29302
C2×C47×#4302
C47×#20642
C47×#20632
C47×#20522
C47×#20512
C47×#19772
C47×#19522
C47×#19012
C47×#19002
C47×#18162
#2480547