Finite Group Databasebeta

← C47×#24796 #26064494

Subgroups — C47×#24796 #26064494

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
1C2×C47×#471C211yesmaximal, characteristic, complemented
2C47×#3057C211yesmaximal, characteristic, complemented
3C47×#3046C211yesmaximal, characteristic, complemented
4C47×#3045C211yesmaximal, characteristic
5C2×C47×#443C211yesmaximal, characteristic, complemented
6C47×#2912C211yesmaximal, characteristic, complemented
7C47×#2064C211yesmaximal, characteristic, complemented
8C47×#2063C211yesmaximal, characteristic, complemented
9C47×#2038C211yesmaximal, characteristic, complemented
10C47×#2037C211yesmaximal, characteristic, complemented
11C47×#1968C211yesmaximal, characteristic, complemented
12C47×#1945C211yesmaximal, characteristic, complemented
13C47×#1883C211yesmaximal, characteristic, complemented
14C47×#1882C211yesmaximal, characteristic, complemented
15C47×#1815C211yesmaximal, characteristic, complemented
16C2×#137×C47C2211yescharacteristic
17C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
18C2×#135×C47C2211yescharacteristic
19C22×SD16×C47C2211yescharacteristic
20C2×#131×C47C2211yescharacteristic
21C2×#131×C47C2211yescharacteristic
22C47×#536C2211yescharacteristic
23C47×#535C2211yescharacteristic
24C47×#520C2211yescharacteristic
25C47×#520C2211yescharacteristic
26C47×#471—24no—
27C47×#468—21no—
28C47×#468—21no—
29C47×#465—21no—
30C47×#465—21no—
31C47×#464—21no—
32C47×#464—21no—
33C47×#463—21no—
34C47×#463—21no—
35C47×#462—21no—
36C47×#461—21no—
37C47×#460—21no—
38C47×#459—21no—
39C47×#443—24no—
40C2×#108×C47C2211yescharacteristic
41C2×#108×C47C2211yescharacteristic
42C47×#428—21no—
43C47×#428—21no—
44C47×#428C2211yescharacteristic
45C47×#428C2211yescharacteristic
46C47×#427—21no—
47C47×#427C2211yescharacteristic
48C2×#106×C47—21no—
49C2×#106×C47C2211yescharacteristic
50C47×#424C2211yescharacteristic
51C47×#424C2211yescharacteristic
52C2×#104×C47C2211yescharacteristic
53C2×#104×C47C2211yescharacteristic
54C47×#419C2211yescharacteristic
55C47×#418C2211yescharacteristic
56C47×#417C2211yescharacteristic
57C47×#417C2211yescharacteristic
58C2×#103×C47C2211yescharacteristic
59C2×#102×C47C2211yescharacteristic
60C2×#101×C47C2211yescharacteristic
61C2×#100×C47C2211yescharacteristic
62C2×C4×C8×C47C2211yescharacteristic
63C47×#391C2211yescharacteristic
64C47×#390C2211yescharacteristic
65C47×#343C2211yescharacteristic
66C47×#343C2211yescharacteristic
67C47×#339C2211yescharacteristic
68C47×#339C2211yescharacteristic
69C2×#41×C47C2311yescharacteristic
70C2×#41×C47C2311yescharacteristic
71C22×Q8×C47C2311yescharacteristic
72C22×D4×C47C2311yescharacteristic
73#137×C47—22no—
74#137×C47—22no—
75AGL(1,ℤ/8)×C47—22no—
76AGL(1,ℤ/8)×C47—22no—
77#135×C47—22no—
78#135×C47—22no—
79C2×Q16×C47—21no—
80C2×Q16×C47D411yescharacteristic
81C2×SD16×C47—21no—
82C2×SD16×C47—21no—
83C2×SD16×C47—21no—
84C2×SD16×C47—21no—
85C2×SD16×C47—22no—
86C2×SD16×C47—22no—
87C2×SD16×C47D411yescharacteristic
88C2×SD16×C47D411yescharacteristic
89C2×D8×C47—21no—
90C2×D8×C47D411yescharacteristic
91#131×C47—22no—
92#131×C47—22no—
93#131×C47—22no—
94#131×C47D414yescomplemented
95C2×M16×C47—21no—
96C2×M16×C47—21no—
97C2×M16×C47C2311yescharacteristic
98C2×M16×C47C2311yescharacteristic
99C2×M16×C47C2311yescharacteristic
100C2×M16×C47C2311yescharacteristic
101C22×C8×C47—21no—
102C22×C8×C47—21no—
103C22×C8×C47C2311yescharacteristic
104C22×C8×C47C2311yescharacteristic
105C4⋊Q8×C47—21no—
106#127×C47—21no—
107#124×C47—21no—
108#124×C47—21no—
109#123×C47—41no—
110C22⋊Q8×C47—21no—
111C22⋊Q8×C47—21no—
112#121×C47—21no—
113#121×C47—21no—
114#120×C47—41no—
115C4×Q8×C47—21no—
116C4×Q8×C47—21no—
117C4×D4×C47—21no—
118C4×D4×C47—21no—
119C4×D4×C47—41no—
120C4×D4×C47—41no—
121#117×C47—21no—
122#117×C47—21no—
123#117×C47C2311yescharacteristic
124#117×C47C2311yescharacteristic
125C2×C4⋊C4×C47—21no—
126C2×C4⋊C4×C47—21no—
127C2×C4⋊C4×C47C2311yescharacteristic
128C2×C4⋊C4×C47C2311yescharacteristic
129C2×C22⋊C4×C47—41no—
130C2×C42×C47C2311yescharacteristic
131#108×C47—22no—
132#108×C47—22no—
133#107×C47—21no—
134#107×C47—21no—
135#107×C47D411yescharacteristic
136#107×C47D411yescharacteristic
137#106×C47—21no—
138#106×C47—21no—
139#106×C47—21no—
140#106×C47—21no—
141#106×C47D411yescharacteristic
142#106×C47D411yescharacteristic
143C4⋊C8×C47—21no—
144C4⋊C8×C47—21no—
145C4⋊C8×C47—21no—
146C4⋊C8×C47—21no—
147#104×C47—22no—
148#104×C47—22no—
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#102×C47—21no—
156#102×C47—21no—
157#102×C47—21no—
158#102×C47—21no—
159#102×C47—21no—
160#102×C47—21no—
161#101×C47—22no—
162#100×C47—22no—
163C4×C8×C47—22no—
164#95×C47—41no—
165C24×C47—21no—
166#41×C47—21no—
167#41×C47—21no—
168#41×C47—21no—
169#41×C47—21no—
170#41×C47—21no—
171#41×C47—21no—
172#41×C47C2×D412yes—
173#41×C47#4112yes—
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×Q8×C47C2×D411yescharacteristic
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×C47C2×D411yescharacteristic
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—41no—
201C22×C4×C47—41no—
202C22×C4×C47C2411yescharacteristic
203Q16×C47—22no—
204Q16×C47—42no—
205SD16×C47—22no—
206SD16×C47—22no—
207SD16×C47—42no—
208SD16×C47—42no—
209SD16×C47—42no—
210SD16×C47—42no—
211D8×C47—22no—
212D8×C47—42no—
213M16×C47—21no—
214M16×C47—24no—
215M16×C47—21no—
216M16×C47—21no—
217M16×C47—21no—
218M16×C47—21no—
219M16×C47—21no—
220M16×C47—21no—
221M16×C47—42no—
222M16×C47C2×D412yes—
223C2×C8×C47—21no—
224C2×C8×C47—21no—
225C2×C8×C47—21no—
226C2×C8×C47—24no—
227C2×C8×C47—21no—
228C2×C8×C47—21no—
229C2×C8×C47—21no—
230C2×C8×C47—42no—
231C2×C8×C47C2×D411yescharacteristic
232C2×C8×C47C2×D411yescharacteristic
233C2×C8×C47C2×D411yescharacteristic
234C2×C8×C47C2×D411yescharacteristic
235C2×C8×C47C2×D412yes—
236C2×C8×C47#4112yes—
237C4⋊C4×C47—21no—
238C4⋊C4×C47—21no—
239C4⋊C4×C47—21no—
240C4⋊C4×C47—21no—
241C4⋊C4×C47—41no—
242C4⋊C4×C47—41no—
243C4⋊C4×C47—41no—
244C4⋊C4×C47—41no—
245C4⋊C4×C47C2×D411yescharacteristic
246C4⋊C4×C47C2×D411yescharacteristic
247C4⋊C4×C47C2×D411yescharacteristic
248C4⋊C4×C47C2×D411yescharacteristic
249C22⋊C4×C47—21no—
250C22⋊C4×C47—21no—
251C22⋊C4×C47—41no—
252C22⋊C4×C47—41no—
253C22⋊C4×C47—41no—
254C22⋊C4×C47—41no—
255C22⋊C4×C47—41no—
256C22⋊C4×C47—41no—
257C22⋊C4×C47—82no—
258C42×C47—21no—
259C42×C47—21no—
260C42×C47—21no—
261C42×C47—21no—
262C42×C47—41no—
263C42×C47—41no—
264C23×C47—21no—
265C23×C47—21no—
266C23×C47—41no—
267C23×C47—41no—
268C23×C47—41no—
269C23×C47—81no—
270C23×C47—81no—
271C23×C47H(5,𝔽2)11yescharacteristic
272Q8×C47—21no—
273Q8×C47—21no—
274Q8×C47—21no—
275Q8×C47—41no—
276Q8×C47—41no—
277Q8×C47—41no—
278Q8×C47—41no—
279Q8×C47#12112yes—
280D4×C47—22no—
281D4×C47—22no—
282D4×C47—21no—
283D4×C47—21no—
284D4×C47—21no—
285D4×C47—41no—
286D4×C47—41no—
287D4×C47—41no—
288D4×C47—41no—
289D4×C47—41no—
290D4×C47—41no—
291D4×C47—161no—
292D4×C47—161no—
293D4×C47#12112yes—
294C2×C4×C47—21no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—21no—
299C2×C4×C47—21no—
300C2×C4×C47—21no—
301C2×C4×C47—21no—
302C2×C4×C47—21no—
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—81no—
313C2×C4×C47—81no—
314C2×C4×C47—161no—
315C2×C4×C47—161no—
316C2×C4×C47C22×D411yescharacteristic
317C2×C4×C47C22×D411yescharacteristic
318C2×C4×C47C22×D411yescharacteristic
319C2×C4×C47C2×#4111yescharacteristic
320C2×C4×C47C2×#4111yescharacteristic
321C2×C4×C472−1+411yescharacteristic
322C8×C47—22no—
323C8×C47—21no—
324C8×C47—21no—
325C8×C47—41no—
326C8×C47—41no—
327C8×C47—41no—
328C8×C47#12112yes—
329C8×C47#12112yes—
330#24796C4711yesmaximal, characteristic, direct product factor, Sylow
331C22×C47—21no—
332C22×C47—21no—
333C22×C47—22no—
334C22×C47—41no—
335C22×C47—41no—
336C22×C47—41no—
337C22×C47—41no—
338C22×C47—41no—
339C22×C47—82no—
340C22×C47—81no—
341C22×C47—81no—
342C22×C47—81no—
343C22×C47—161no—
344C22×C47#53711yescharacteristic
345C22×C47D4211yescharacteristic
346C22×C47#55311yescharacteristic
347C4×C47—22no—
348C4×C47—42no—
349C4×C47—41no—
350C4×C47—41no—
351C4×C47—41no—
352C4×C47—41no—
353C4×C47—41no—
354C4×C47—81no—
355C4×C47—81no—
356C4×C47—81no—
357C4×C47C2×#12111yescharacteristic
358C4×C47C2×#12111yescharacteristic
359C4×C47#54711yescharacteristic
360C4×C47#54811yescharacteristic
361C2×#471C2×C4711yescharacteristic, complemented
362#3057C2×C4711yescharacteristic, complemented
363#3046C2×C4711yescharacteristic, complemented
364#3045C2×C4711yescharacteristic
365C2×#443C2×C4711yescharacteristic, complemented
366#2912C2×C4711yescharacteristic, complemented
367#2064C2×C4711yescharacteristic, complemented
368#2063C2×C4711yescharacteristic, complemented
369#2038C2×C4711yescharacteristic, complemented
370#2037C2×C4711yescharacteristic, complemented
371#1968C2×C4711yescharacteristic, complemented
372#1945C2×C4711yescharacteristic, complemented
373#1883C2×C4711yescharacteristic, complemented
374#1882C2×C4711yescharacteristic, complemented
375#1815C2×C4711yescharacteristic, complemented
376C2×C47—21no—
377C2×C47—21no—
378C2×C47—42no—
379C2×C47—81no—
380C2×C47—161no—
381C2×C47#241611yescharacteristic
382C2×C47#329011yescharacteristic
383C2×C47#329111yescharacteristic
384C2×#137C22×C4711yescharacteristic
385C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
386C2×#135C22×C4711yescharacteristic
387C22×SD16C22×C4711yescharacteristic
388C2×#131C22×C4711yescharacteristic
389C2×#131C22×C4711yescharacteristic
390#536C22×C4711yescharacteristic
391#535C22×C4711yescharacteristic
392#520C22×C4711yescharacteristic
393#520C22×C4711yescharacteristic
394#471—24no—
395#468—21no—
396#468—21no—
397#465—21no—
398#465—21no—
399#464—21no—
400#464—21no—
401#463—21no—
402#463—21no—
403#462—21no—
404#461—21no—
405#460—21no—
406#459—21no—
407#443—24no—
408C2×#108C22×C4711yescharacteristic
409C2×#108C22×C4711yescharacteristic
410#428—21no—
411#428—21no—
412#428C22×C4711yescharacteristic
413#428C22×C4711yescharacteristic
414#427—21no—
415#427C22×C4711yescharacteristic
416C2×#106—21no—
417C2×#106C22×C4711yescharacteristic
418#424C22×C4711yescharacteristic
419#424C22×C4711yescharacteristic
420C2×#104C22×C4711yescharacteristic
421C2×#104C22×C4711yescharacteristic
422#419C22×C4711yescharacteristic
423#418C22×C4711yescharacteristic
424#417C22×C4711yescharacteristic
425#417C22×C4711yescharacteristic
426C2×#103C22×C4711yescharacteristic
427C2×#102C22×C4711yescharacteristic
428C2×#101C22×C4711yescharacteristic
429C2×#100C22×C4711yescharacteristic
430C2×C4×C8C22×C4711yescharacteristic
431#391C22×C4711yescharacteristic
432#390C22×C4711yescharacteristic
433#343C22×C4711yescharacteristic
434#343C22×C4711yescharacteristic
435#339C22×C4711yescharacteristic
436#339C22×C4711yescharacteristic
437C47#2479611yescharacteristic, direct product factor, Sylow
438C2×#41C23×C4711yescharacteristic
439C2×#41C23×C4711yescharacteristic
440C22×Q8C23×C4711yescharacteristic
441C22×D4C23×C4711yescharacteristic
442#137—22no—
443#137—22no—
444AGL(1,ℤ/8)—22no—
445AGL(1,ℤ/8)—22no—
446#135—22no—
447#135—22no—
448C2×Q16—21no—
449C2×Q16D4×C4711yescharacteristic
450C2×SD16—21no—
451C2×SD16—21no—
452C2×SD16—21no—
453C2×SD16—21no—
454C2×SD16—22no—
455C2×SD16—22no—
456C2×SD16D4×C4711yescharacteristic
457C2×SD16D4×C4711yescharacteristic
458C2×D8—21no—
459C2×D8D4×C4711yescharacteristic
460#131—22no—
461#131—22no—
462#131—22no—
463#131D4×C4714yescomplemented
464C2×M16—21no—
465C2×M16—21no—
466C2×M16C23×C4711yescharacteristic
467C2×M16C23×C4711yescharacteristic
468C2×M16C23×C4711yescharacteristic
469C2×M16C23×C4711yescharacteristic
470C22×C8—21no—
471C22×C8—21no—
472C22×C8C23×C4711yescharacteristic
473C22×C8C23×C4711yescharacteristic
474C4⋊Q8—21no—
475#127—21no—
476#124—21no—
477#124—21no—
478#123—41no—
479C22⋊Q8—21no—
480C22⋊Q8—21no—
481#121—21no—
482#121—21no—
483#120—41no—
484C4×Q8—21no—
485C4×Q8—21no—
486C4×D4—21no—
487C4×D4—21no—
488C4×D4—41no—
489C4×D4—41no—
490#117—21no—
491#117—21no—
492#117C23×C4711yescharacteristic
493#117C23×C4711yescharacteristic
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4C23×C4711yescharacteristic
497C2×C4⋊C4C23×C4711yescharacteristic
498C2×C22⋊C4—41no—
499C2×C42C23×C4711yescharacteristic
500#108—22no—
501#108—22no—
502#107—21no—
503#107—21no—
504#107D4×C4711yescharacteristic
505#107D4×C4711yescharacteristic
506#106—21no—
507#106—21no—
508#106—21no—
509#106—21no—
510#106D4×C4711yescharacteristic
511#106D4×C4711yescharacteristic
512C4⋊C8—21no—
513C4⋊C8—21no—
514C4⋊C8—21no—
515C4⋊C8—21no—
516#104—22no—
517#104—22no—
518#103—21no—
519#103—21no—
520#103—21no—
521#103—21no—
522#103—21no—
523#103—21no—
524#102—21no—
525#102—21no—
526#102—21no—
527#102—21no—
528#102—21no—
529#102—21no—
530#101—22no—
531#100—22no—
532C4×C8—22no—
533#95—41no—
534C24—21no—
535#41—21no—
536#41—21no—
537#41—21no—
538#41—21no—
539#41—21no—
540#41—21no—
541#41C2×D4×C4712yes—
542#41#41×C4712yes—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8C2×D4×C4711yescharacteristic
550C2×Q8C2×D4×C4711yescharacteristic
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—41no—
560C2×D4—41no—
561C2×D4C2×D4×C4711yescharacteristic
562C2×D4C2×D4×C4711yescharacteristic
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4C24×C4711yescharacteristic
572Q16—22no—
573Q16—42no—
574SD16—22no—
575SD16—22no—
576SD16—42no—
577SD16—42no—
578SD16—42no—
579SD16—42no—
580D8—22no—
581D8—42no—
582M16—21no—
583M16—24no—
584M16—21no—
585M16—21no—
586M16—21no—
587M16—21no—
588M16—21no—
589M16—21no—
590M16—42no—
591M16C2×D4×C4712yes—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—24no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—42no—
600C2×C8C2×D4×C4711yescharacteristic
601C2×C8C2×D4×C4711yescharacteristic
602C2×C8C2×D4×C4712yes—
603C2×C8C2×D4×C4711yescharacteristic
604C2×C8C2×D4×C4711yescharacteristic
605C2×C8#41×C4712yes—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—41no—
611C4⋊C4—41no—
612C4⋊C4—41no—
613C4⋊C4—41no—
614C4⋊C4C2×D4×C4711yescharacteristic
615C4⋊C4C2×D4×C4711yescharacteristic
616C4⋊C4C2×D4×C4711yescharacteristic
617C4⋊C4C2×D4×C4711yescharacteristic
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—41no—
621C22⋊C4—41no—
622C22⋊C4—41no—
623C22⋊C4—41no—
624C22⋊C4—41no—
625C22⋊C4—41no—
626C22⋊C4—82no—
627C42—21no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—41no—
632C42—41no—
633C23—21no—
634C23—21no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—81no—
639C23—81no—
640C23H(5,𝔽2)×C4711yescharacteristic
641Q8—21no—
642Q8—21no—
643Q8—21no—
644Q8—41no—
645Q8—41no—
646Q8—41no—
647Q8—41no—
648Q8#121×C4712yes—
649D4—22no—
650D4—22no—
651D4—21no—
652D4—21no—
653D4—21no—
654D4—41no—
655D4—41no—
656D4—41no—
657D4—41no—
658D4—41no—
659D4—41no—
660D4—161no—
661D4—161no—
662D4#121×C4712yes—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
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—81no—
682C2×C4—81no—
683C2×C4—161no—
684C2×C4—161no—
685C2×C4C22×D4×C4711yescharacteristic
686C2×C4C22×D4×C4711yescharacteristic
687C2×C4C22×D4×C4711yescharacteristic
688C2×C4C2×#41×C4711yescharacteristic
689C2×C4C2×#41×C4711yescharacteristic
690C2×C42−1+4×C4711yescharacteristic
691C8—22no—
692C8—21no—
693C8—21no—
694C8—41no—
695C8—41no—
696C8—41no—
697C8#121×C4712yes—
698C8#121×C4712yes—
699C22—21no—
700C22—21no—
701C22—22no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—82no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22—161no—
712C22C47×#53711yescharacteristic
713C22D42×C4711yescharacteristic
714C22C47×#55311yescharacteristic
715C4—22no—
716C4—42no—
717C4—41no—
718C4—41no—
719C4—41no—
720C4—41no—
721C4—41no—
722C4—81no—
723C4—81no—
724C4—81no—
725C4C2×#121×C4711yescharacteristic
726C4C2×#121×C4711yescharacteristic
727C4C47×#54711yescharacteristic
728C4C47×#54811yescharacteristic
729C2—21no—
730C2—21no—
731C2—42no—
732C2—81no—
733C2—161no—
734C2C47×#241611yescharacteristic
735C2C47×#329011yescharacteristic
736C2C47×#329111yescharacteristic
subgroupG/H
center, socleC22×C47D42
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC47×#3045C2
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. C2×C47×#471C2semidirect
2. C47×#3057C2semidirect
3. C47×#3046C2semidirect
5. C2×C47×#443C2semidirect
6. C47×#2912C2semidirect
7. C47×#2064C2semidirect
8. C47×#2063C2semidirect
9. C47×#2038C2semidirect
10. C47×#2037C2semidirect
11. C47×#1968C2semidirect
12. C47×#1945C2semidirect
13. C47×#1883C2semidirect
14. C47×#1882C2semidirect
15. C47×#1815C2semidirect
94. #131×C47D4semidirect
330. #24796C47direct (N × H)
361. C2×#471C2×C47semidirect
362. #3057C2×C47semidirect
363. #3046C2×C47semidirect
365. C2×#443C2×C47semidirect
366. #2912C2×C47semidirect
367. #2064C2×C47semidirect
368. #2063C2×C47semidirect
369. #2038C2×C47semidirect
370. #2037C2×C47semidirect
371. #1968C2×C47semidirect
372. #1945C2×C47semidirect
373. #1883C2×C47semidirect
374. #1882C2×C47semidirect
375. #1815C2×C47semidirect
437. C47#24796direct (N × H)
463. #131D4×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×#30572
C47×#30462
C47×#30452
C2×C47×#4432
C47×#29122
C47×#20642
C47×#20632
C47×#20382
C47×#20372
C47×#19682
C47×#19452
C47×#18832
C47×#18822
C47×#18152
#2479647