Finite Group Databasebeta

← C47×#18775 #26058473

Subgroups — C47×#18775 #26058473

Order 12032.

968 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3483C211yesmaximal, characteristic
2C47×#3210C211yesmaximal, characteristic, complemented
3C47×#3116C211yesmaximal, characteristic, complemented
4C47×#3076C211yesmaximal, characteristic, complemented
5C47×#1646C211yesmaximal, characteristic, complemented
6C47×#1645C211yesmaximal, characteristic, complemented
7C47×#1642C211yesmaximal, characteristic, complemented
8C47×#1641C211yesmaximal, characteristic, complemented
9C47×#1634C211yesmaximal, characteristic, complemented
10C47×#1633C211yesmaximal, characteristic, complemented
11C47×#1631C211yesmaximal, characteristic, complemented
12C47×#1631C211yesmaximal, characteristic, complemented
13C47×#1551C211yesmaximal, characteristic, complemented
14C47×#1488C211yesmaximal, characteristic, complemented
15C47×#1477C211yesmaximal, characteristic, complemented
16Q82×C47C2211yescharacteristic
17C47×#555—22no—
18C47×#555—21no—
19C47×#555—21no—
20C47×#555C2211yescharacteristic
21C47×#550—21no—
22C47×#550—21no—
23C47×#550C2211yescharacteristic
24C47×#550C2211yescharacteristic
25C47×#533C2211yescharacteristic
26C47×#532—22no—
27C47×#532—21no—
28C47×#532—21no—
29C47×#532C2211yescharacteristic
30C4×#41×C47—21no—
31C4×#41×C47—21no—
32C4×#41×C47C2211yescharacteristic
33C4×#41×C47C2211yescharacteristic
34C47×#494C2211yescharacteristic
35C47×#492C2211yescharacteristic
36C47×#487C2211yescharacteristic
37C47×#486C2211yescharacteristic
38C47×#485—21no—
39C47×#479—21no—
40C47×#478—21no—
41C47×#477C2211yescharacteristic
42C47×#477C2211yescharacteristic
43C47×#476C2211yescharacteristic
44C47×#476C2211yescharacteristic
45C47×#475C2211yescharacteristic
46C47×#474C2211yescharacteristic
47C47×#464—22no—
48C47×#462C2211yescharacteristic
49C47×#461C2211yescharacteristic
50C47×#452—21no—
51C47×#452—22no—
52C47×#441—21no—
53C47×#440—21no—
54C47×#432C2211yescharacteristic
55C47×#431C2211yescharacteristic
56C47×#427—21no—
57C2×C4⋊C8×C47C2211yescharacteristic
58C47×#416—21no—
59C47×#333C2211yescharacteristic
60C47×#333C2211yescharacteristic
61C47×#331C2211yescharacteristic
62C47×#331C2211yescharacteristic
63C47×Q8⋊C8C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×Q8⋊C8C2211yescharacteristic
66C47×Q8⋊C8C2211yescharacteristic
67C47×D4⋊C8C2211yescharacteristic
68C47×D4⋊C8C2211yescharacteristic
69C47×D4⋊C8C2211yescharacteristic
70C47×D4⋊C8C2211yescharacteristic
71C2×#41×C47—22no—
72C2×#41×C47—21no—
73C2×#41×C47—21no—
74C2×#41×C47D411yescharacteristic
75C2×#41×C47D411yescharacteristic
76C2×#41×C47D412yes—
77C2×Q16×C47—21no—
78C2×Q16×C47—22no—
79C2×SD16×C47—21no—
80C2×SD16×C47—22no—
81C22×C8×C47—21no—
82C4⋊Q8×C47—22no—
83C4⋊Q8×C47—21no—
84C4⋊Q8×C47—21no—
85C4⋊Q8×C47C2311yescharacteristic
86C4⋊Q8×C47C2311yescharacteristic
87C4⋊Q8×C47C2311yescharacteristic
88#127×C47—22no—
89#127×C47—21no—
90#127×C47—21no—
91#127×C47C2311yescharacteristic
92#125×C47—21no—
93#124×C47—22no—
94#124×C47—22no—
95#124×C47—22no—
96#124×C47—22no—
97#124×C47D412yes—
98C22⋊Q8×C47—21no—
99C22⋊Q8×C47—21no—
100#121×C47—22no—
101#121×C47—22no—
102#121×C47—22no—
103#121×C47—22no—
104#121×C47—21no—
105#121×C47—21no—
106#121×C47—22no—
107#121×C47—22no—
108#121×C47—21no—
109#121×C47—21no—
110#121×C47—21no—
111#121×C47—21no—
112C4×Q8×C47—21no—
113C4×Q8×C47—21no—
114C4×Q8×C47—21no—
115C4×Q8×C47—21no—
116C4×Q8×C47D411yescharacteristic
117C4×Q8×C47D411yescharacteristic
118C4×Q8×C47C2311yescharacteristic
119C4×Q8×C47C2311yescharacteristic
120C4×D4×C47—22no—
121C4×D4×C47—22no—
122C4×D4×C47—22no—
123C4×D4×C47—22no—
124C4×D4×C47—21no—
125C4×D4×C47—21no—
126C4×D4×C47—21no—
127C4×D4×C47—21no—
128C4×D4×C47—21no—
129C4×D4×C47—21no—
130C4×D4×C47—21no—
131C4×D4×C47—21no—
132C4×D4×C47D411yescharacteristic
133C4×D4×C47D411yescharacteristic
134C4×D4×C47C2311yescharacteristic
135C4×D4×C47C2311yescharacteristic
136#117×C47—22no—
137#117×C47—22no—
138#117×C47—21no—
139#117×C47—21no—
140#117×C47—21no—
141#117×C47—21no—
142#117×C47—21no—
143#117×C47D411yescharacteristic
144#117×C47D411yescharacteristic
145C2×C42×C47—22no—
146C2×C42×C47—21no—
147C2×C42×C47—21no—
148C2×C42×C47C2311yescharacteristic
149#107×C47—21no—
150#107×C47—21no—
151#107×C47—21no—
152#106×C47—21no—
153#106×C47—21no—
154#106×C47—21no—
155C4⋊C8×C47—21no—
156C4⋊C8×C47—21no—
157C4⋊C8×C47C2311yescharacteristic
158C4⋊C8×C47C2311yescharacteristic
159C4⋊C8×C47C2311yescharacteristic
160C4⋊C8×C47C2311yescharacteristic
161#103×C47—22no—
162#103×C47—21no—
163#103×C47—21no—
164#103×C47—21no—
165#103×C47—21no—
166#103×C47—21no—
167#102×C47—22no—
168#102×C47—21no—
169#102×C47—21no—
170#102×C47—21no—
171C22⋊C8×C47—21no—
172C22⋊C8×C47—21no—
173#97×C47—21no—
174C4×C8×C47C2311yescharacteristic
175C4×C8×C47C2311yescharacteristic
176#41×C47—22no—
177#41×C47—22no—
178#41×C47—41no—
179#41×C47—41no—
180#41×C47—42no—
181#41×C47—42no—
182#41×C47—42no—
183#41×C47—42no—
184#41×C47—82no—
185#41×C47—84no—
186C2×Q8×C47—22no—
187C2×Q8×C47—21no—
188C2×Q8×C47—21no—
189C2×Q8×C47C2×D411yescharacteristic
190C2×Q8×C47C2×D411yescharacteristic
191C2×Q8×C47C2×D412yes—
192C2×D4×C47—22no—
193C2×D4×C47—22no—
194C2×D4×C47—21no—
195C2×D4×C47—21no—
196C2×D4×C47—22no—
197C2×D4×C47—22no—
198C2×D4×C47—22no—
199C2×D4×C47—22no—
200C2×D4×C47—21no—
201C2×D4×C47—21no—
202C2×D4×C47C2×D411yescharacteristic
203C2×D4×C47C2×D411yescharacteristic
204C2×D4×C47C2×D412yes—
205C22×C4×C47—22no—
206C22×C4×C47—22no—
207C22×C4×C47—21no—
208C22×C4×C47—21no—
209C22×C4×C47—22no—
210C22×C4×C47—21no—
211C22×C4×C47—21no—
212C22×C4×C47—21no—
213C22×C4×C47—21no—
214C22×C4×C47C2×D411yescharacteristic
215C22×C4×C47C2×D411yescharacteristic
216C22×C4×C47C2×D411yescharacteristic
217Q16×C47—42no—
218Q16×C47—82no—
219SD16×C47—42no—
220SD16×C47—82no—
221C2×C8×C47—21no—
222C2×C8×C47—21no—
223C2×C8×C47—21no—
224C2×C8×C47—21no—
225C2×C8×C47—21no—
226C2×C8×C47—21no—
227C2×C8×C47—42no—
228C4⋊C4×C47—22no—
229C4⋊C4×C47—22no—
230C4⋊C4×C47—21no—
231C4⋊C4×C47—21no—
232C4⋊C4×C47—21no—
233C4⋊C4×C47—21no—
234C4⋊C4×C47—21no—
235C4⋊C4×C47—21no—
236C4⋊C4×C47—21no—
237C4⋊C4×C47—21no—
238C4⋊C4×C47—21no—
239C4⋊C4×C47—21no—
240C4⋊C4×C47—41no—
241C4⋊C4×C47—41no—
242C4⋊C4×C47C2×D411yescharacteristic
243C4⋊C4×C47C2×D411yescharacteristic
244C4⋊C4×C47C2×D411yescharacteristic
245C4⋊C4×C47C2×D411yescharacteristic
246C22⋊C4×C47—22no—
247C22⋊C4×C47—22no—
248C22⋊C4×C47—22no—
249C22⋊C4×C47—22no—
250C22⋊C4×C47—21no—
251C22⋊C4×C47—21no—
252C22⋊C4×C47—22no—
253C22⋊C4×C47—22no—
254C22⋊C4×C47—21no—
255C22⋊C4×C47—21no—
256C22⋊C4×C47—21no—
257C22⋊C4×C47—21no—
258C22⋊C4×C47—41no—
259C42×C47—22no—
260C42×C47—22no—
261C42×C47—21no—
262C42×C47—21no—
263C42×C47—21no—
264C42×C47—21no—
265C42×C47—21no—
266C42×C47—21no—
267C42×C47—41no—
268C42×C47C2×D411yescharacteristic
269C42×C47C2×D411yescharacteristic
270C42×C47C2×D411yescharacteristic
271C42×C47C2411yescharacteristic
272C23×C47—21no—
273C23×C47—21no—
274C23×C47—22no—
275C23×C47#12011yescharacteristic
276Q8×C47—21no—
277Q8×C47—21no—
278Q8×C47—42no—
279Q8×C47—42no—
280Q8×C47—41no—
281Q8×C47—41no—
282Q8×C47—82no—
283Q8×C47#13512yes—
284Q8×C47#13712yes—
285D4×C47—21no—
286D4×C47—21no—
287D4×C47—21no—
288D4×C47—21no—
289D4×C47—42no—
290D4×C47—42no—
291D4×C47—42no—
292D4×C47—44no—
293D4×C47—44no—
294D4×C47—41no—
295D4×C47—41no—
296D4×C47—41no—
297D4×C47—41no—
298D4×C47—82no—
299D4×C47—82no—
300D4×C47—82no—
301D4×C47—82no—
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—22no—
311C2×C4×C47—21no—
312C2×C4×C47—21no—
313C2×C4×C47—41no—
314C2×C4×C47—42no—
315C2×C4×C47—42no—
316C2×C4×C47—44no—
317C2×C4×C47—44no—
318C2×C4×C47—44no—
319C2×C4×C47—42no—
320C2×C4×C47—42no—
321C2×C4×C47—41no—
322C2×C4×C47—41no—
323C2×C4×C47—41no—
324C2×C4×C47—41no—
325C2×C4×C47—41no—
326C2×C4×C47—41no—
327C2×C4×C47#12011yescharacteristic
328C2×C4×C47#12011yescharacteristic
329C2×C4×C47#12011yescharacteristic
330C2×C4×C47C22×D411yescharacteristic
331C2×C4×C47C22×D411yescharacteristic
332C2×C4×C47C22×D411yescharacteristic
333C8×C47—41no—
334C8×C47—41no—
335C8×C47—41no—
336C8×C47—41no—
337C8×C47—41no—
338C8×C47—41no—
339#18775C4711yesmaximal, characteristic, direct product factor, Sylow
340C22×C47—21no—
341C22×C47—21no—
342C22×C47—21no—
343C22×C47—41no—
344C22×C47—42no—
345C22×C47—41no—
346C22×C47—41no—
347C22×C47—42no—
348C22×C47—41no—
349C22×C47—42no—
350C22×C47—41no—
351C22×C47—41no—
352C22×C47C2×#12011yescharacteristic
353C4×C47—21no—
354C4×C47—22no—
355C4×C47—21no—
356C4×C47—22no—
357C4×C47—21no—
358C4×C47—21no—
359C4×C47—41no—
360C4×C47—41no—
361C4×C47—42no—
362C4×C47—41no—
363C4×C47—41no—
364C4×C47—81no—
365C4×C47—81no—
366C4×C47C2×#13511yescharacteristic
367C4×C47C2×#13711yescharacteristic
368C4×C47#57511yescharacteristic
369C4×C47#57511yescharacteristic
370#3483C2×C4711yescharacteristic
371#3210C2×C4711yescharacteristic, complemented
372#3116C2×C4711yescharacteristic, complemented
373#3076C2×C4711yescharacteristic, complemented
374#1646C2×C4711yescharacteristic, complemented
375#1645C2×C4711yescharacteristic, complemented
376#1642C2×C4711yescharacteristic, complemented
377#1641C2×C4711yescharacteristic, complemented
378#1634C2×C4711yescharacteristic, complemented
379#1633C2×C4711yescharacteristic, complemented
380#1631C2×C4711yescharacteristic, complemented
381#1631C2×C4711yescharacteristic, complemented
382#1551C2×C4711yescharacteristic, complemented
383#1488C2×C4711yescharacteristic, complemented
384#1477C2×C4711yescharacteristic, complemented
385C2×C47—41no—
386C2×C47—81no—
387C2×C47—81no—
388C2×C47—82no—
389C2×C47#300211yescharacteristic
390C2×C47#300711yescharacteristic
391C2×C47#301911yescharacteristic
392Q82C22×C4711yescharacteristic
393#555—22no—
394#555—21no—
395#555—21no—
396#555C22×C4711yescharacteristic
397#550—21no—
398#550—21no—
399#550C22×C4711yescharacteristic
400#550C22×C4711yescharacteristic
401#533C22×C4711yescharacteristic
402#532—22no—
403#532—21no—
404#532—21no—
405#532C22×C4711yescharacteristic
406C4×#41—21no—
407C4×#41—21no—
408C4×#41C22×C4711yescharacteristic
409C4×#41C22×C4711yescharacteristic
410#494C22×C4711yescharacteristic
411#492C22×C4711yescharacteristic
412#487C22×C4711yescharacteristic
413#486C22×C4711yescharacteristic
414#485—21no—
415#479—21no—
416#478—21no—
417#477C22×C4711yescharacteristic
418#477C22×C4711yescharacteristic
419#476C22×C4711yescharacteristic
420#476C22×C4711yescharacteristic
421#475C22×C4711yescharacteristic
422#474C22×C4711yescharacteristic
423#464—22no—
424#462C22×C4711yescharacteristic
425#461C22×C4711yescharacteristic
426#452—21no—
427#452—22no—
428#441—21no—
429#440—21no—
430#432C22×C4711yescharacteristic
431#431C22×C4711yescharacteristic
432#427—21no—
433C2×C4⋊C8C22×C4711yescharacteristic
434#416—21no—
435#333C22×C4711yescharacteristic
436#333C22×C4711yescharacteristic
437#331C22×C4711yescharacteristic
438#331C22×C4711yescharacteristic
439Q8⋊C8C22×C4711yescharacteristic
440Q8⋊C8C22×C4711yescharacteristic
441Q8⋊C8C22×C4711yescharacteristic
442Q8⋊C8C22×C4711yescharacteristic
443D4⋊C8C22×C4711yescharacteristic
444D4⋊C8C22×C4711yescharacteristic
445D4⋊C8C22×C4711yescharacteristic
446D4⋊C8C22×C4711yescharacteristic
447C47#1877511yescharacteristic, direct product factor, Sylow
448C2×#41—22no—
449C2×#41—21no—
450C2×#41—21no—
451C2×#41D4×C4711yescharacteristic
452C2×#41D4×C4711yescharacteristic
453C2×#41D4×C4712yes—
454C2×Q16—21no—
455C2×Q16—22no—
456C2×SD16—21no—
457C2×SD16—22no—
458C22×C8—21no—
459C4⋊Q8—22no—
460C4⋊Q8—21no—
461C4⋊Q8—21no—
462C4⋊Q8C23×C4711yescharacteristic
463C4⋊Q8C23×C4711yescharacteristic
464C4⋊Q8C23×C4711yescharacteristic
465#127—22no—
466#127—21no—
467#127—21no—
468#127C23×C4711yescharacteristic
469#125—21no—
470#124—22no—
471#124—22no—
472#124—22no—
473#124—22no—
474#124D4×C4712yes—
475C22⋊Q8—21no—
476C22⋊Q8—21no—
477#121—22no—
478#121—22no—
479#121—22no—
480#121—22no—
481#121—21no—
482#121—21no—
483#121—22no—
484#121—22no—
485#121—21no—
486#121—21no—
487#121—21no—
488#121—21no—
489C4×Q8—21no—
490C4×Q8—21no—
491C4×Q8—21no—
492C4×Q8—21no—
493C4×Q8D4×C4711yescharacteristic
494C4×Q8D4×C4711yescharacteristic
495C4×Q8C23×C4711yescharacteristic
496C4×Q8C23×C4711yescharacteristic
497C4×D4—22no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—21no—
502C4×D4—21no—
503C4×D4—21no—
504C4×D4—21no—
505C4×D4—21no—
506C4×D4—21no—
507C4×D4—21no—
508C4×D4—21no—
509C4×D4D4×C4711yescharacteristic
510C4×D4D4×C4711yescharacteristic
511C4×D4C23×C4711yescharacteristic
512C4×D4C23×C4711yescharacteristic
513#117—22no—
514#117—22no—
515#117—21no—
516#117—21no—
517#117—21no—
518#117—21no—
519#117—21no—
520#117D4×C4711yescharacteristic
521#117D4×C4711yescharacteristic
522C2×C42—22no—
523C2×C42—21no—
524C2×C42—21no—
525C2×C42C23×C4711yescharacteristic
526#107—21no—
527#107—21no—
528#107—21no—
529#106—21no—
530#106—21no—
531#106—21no—
532C4⋊C8—21no—
533C4⋊C8—21no—
534C4⋊C8C23×C4711yescharacteristic
535C4⋊C8C23×C4711yescharacteristic
536C4⋊C8C23×C4711yescharacteristic
537C4⋊C8C23×C4711yescharacteristic
538#103—21no—
539#103—21no—
540#103—21no—
541#103—22no—
542#103—21no—
543#103—21no—
544#102—21no—
545#102—21no—
546#102—21no—
547#102—22no—
548C22⋊C8—21no—
549C22⋊C8—21no—
550#97—21no—
551C4×C8C23×C4711yescharacteristic
552C4×C8C23×C4711yescharacteristic
553#41—22no—
554#41—22no—
555#41—41no—
556#41—41no—
557#41—42no—
558#41—42no—
559#41—42no—
560#41—42no—
561#41—82no—
562#41—84no—
563C2×Q8—22no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8C2×D4×C4711yescharacteristic
567C2×Q8C2×D4×C4711yescharacteristic
568C2×Q8C2×D4×C4712yes—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4C2×D4×C4711yescharacteristic
580C2×D4C2×D4×C4711yescharacteristic
581C2×D4C2×D4×C4712yes—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4C2×D4×C4711yescharacteristic
592C22×C4C2×D4×C4711yescharacteristic
593C22×C4C2×D4×C4711yescharacteristic
594Q16—42no—
595Q16—82no—
596SD16—42no—
597SD16—82no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—42no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—41no—
618C4⋊C4—41no—
619C4⋊C4C2×D4×C4711yescharacteristic
620C4⋊C4C2×D4×C4711yescharacteristic
621C4⋊C4C2×D4×C4711yescharacteristic
622C4⋊C4C2×D4×C4711yescharacteristic
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—41no—
636C42—22no—
637C42—22no—
638C42—21no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—41no—
645C42C2×D4×C4711yescharacteristic
646C42C2×D4×C4711yescharacteristic
647C42C2×D4×C4711yescharacteristic
648C42C24×C4711yescharacteristic
649C23—21no—
650C23—21no—
651C23—22no—
652C23#120×C4711yescharacteristic
653Q8—21no—
654Q8—21no—
655Q8—42no—
656Q8—42no—
657Q8—41no—
658Q8—41no—
659Q8—82no—
660Q8#135×C4712yes—
661Q8#137×C4712yes—
662D4—21no—
663D4—21no—
664D4—21no—
665D4—21no—
666D4—42no—
667D4—42no—
668D4—42no—
669D4—44no—
670D4—44no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—82no—
676D4—82no—
677D4—82no—
678D4—82no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4#120×C4711yescharacteristic
705C2×C4#120×C4711yescharacteristic
706C2×C4#120×C4711yescharacteristic
707C2×C4C22×D4×C4711yescharacteristic
708C2×C4C22×D4×C4711yescharacteristic
709C2×C4C22×D4×C4711yescharacteristic
710C8—41no—
711C8—41no—
712C8—41no—
713C8—41no—
714C8—41no—
715C8—41no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—41no—
720C22—42no—
721C22—41no—
722C22—41no—
723C22—42no—
724C22—41no—
725C22—42no—
726C22—41no—
727C22—41no—
728C22C2×#120×C4711yescharacteristic
729C4—21no—
730C4—22no—
731C4—21no—
732C4—22no—
733C4—21no—
734C4—21no—
735C4—41no—
736C4—41no—
737C4—42no—
738C4—41no—
739C4—41no—
740C4—81no—
741C4—81no—
742C4C2×#135×C4711yescharacteristic
743C4C2×#137×C4711yescharacteristic
744C4C47×#57511yescharacteristic
745C4C47×#57511yescharacteristic
746C2—41no—
747C2—81no—
748C2—81no—
749C2—82no—
750C2C47×#300211yescharacteristic
751C2C47×#300711yescharacteristic
752C2C47×#301911yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#3483C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#3210C2semidirect
3. C47×#3116C2semidirect
4. C47×#3076C2semidirect
5. C47×#1646C2semidirect
6. C47×#1645C2semidirect
7. C47×#1642C2semidirect
8. C47×#1641C2semidirect
9. C47×#1634C2semidirect
10. C47×#1633C2semidirect
11. C47×#1631C2semidirect
12. C47×#1631C2semidirect
13. C47×#1551C2semidirect
14. C47×#1488C2semidirect
15. C47×#1477C2semidirect
339. #18775C47direct (N × H)
371. #3210C2×C47semidirect
372. #3116C2×C47semidirect
373. #3076C2×C47semidirect
374. #1646C2×C47semidirect
375. #1645C2×C47semidirect
376. #1642C2×C47semidirect
377. #1641C2×C47semidirect
378. #1634C2×C47semidirect
379. #1633C2×C47semidirect
380. #1631C2×C47semidirect
381. #1631C2×C47semidirect
382. #1551C2×C47semidirect
383. #1488C2×C47semidirect
384. #1477C2×C47semidirect
447. C47#18775direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#34832
C47×#32102
C47×#31162
C47×#30762
C47×#16462
C47×#16452
C47×#16422
C47×#16412
C47×#16342
C47×#16332
C47×#16312
C47×#15512
C47×#14882
C47×#14772
#1877547