Finite Group Databasebeta

← C47×#26852 #26066550

Subgroups — C47×#26852 #26066550

Order 12032.

698 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3137C211yesmaximal, characteristic
2C47×#3097C211yesmaximal, characteristic
3C47×#3082C211yesmaximal, characteristic, complemented
4C47×#2947C211yesmaximal, characteristic
5C47×#2064C211yesmaximal, characteristic, complemented
6C47×#2061C211yesmaximal, characteristic, complemented
7C47×#2052C211yesmaximal, characteristic
8C47×#2005C211yesmaximal, characteristic
9C47×#1960C211yesmaximal, characteristic, complemented
10C47×#1938C211yesmaximal, characteristic
11C47×#1930C211yesmaximal, characteristic, complemented
12C47×#1930C211yesmaximal, characteristic, complemented
13C47×#1886C211yesmaximal, characteristic, complemented
14C47×#1860C211yesmaximal, characteristic
15C47×#1773C211yesmaximal, characteristic, complemented
16C2×#137×C47C2211yescharacteristic
17C47×#544C2211yescharacteristic
18C47×#536C2211yescharacteristic
19C2×C4⋊Q8×C47C2211yescharacteristic
20C47×#520C2211yescharacteristic
21C47×#519C2211yescharacteristic
22C47×#491—21no—
23C47×#489—21no—
24C47×#488—21no—
25C47×#487—21no—
26C47×#485—21no—
27C47×#485—21no—
28C47×#484—21no—
29C47×#483—21no—
30C47×#479—21no—
31C47×#479—21no—
32C47×#477—21no—
33C47×#475—21no—
34C47×#441—21no—
35C47×#440—21no—
36C4×Q16×C47—21no—
37C4×SD16×C47—21no—
38C2×#108×C47C2211yescharacteristic
39C47×#428C2211yescharacteristic
40C47×#428C2211yescharacteristic
41C47×#428C2211yescharacteristic
42C47×#427C2211yescharacteristic
43C47×#424C2211yescharacteristic
44C2×#104×C47C2211yescharacteristic
45C47×#419C2211yescharacteristic
46C47×#419C2211yescharacteristic
47C47×#419C2211yescharacteristic
48C47×#417C2211yescharacteristic
49C47×#416C2211yescharacteristic
50C2×#103×C47C2211yescharacteristic
51C2×#103×C47C2211yescharacteristic
52C2×#103×C47C2211yescharacteristic
53C2×#103×C47C2211yescharacteristic
54C2×#101×C47C2211yescharacteristic
55C2×#101×C47C2211yescharacteristic
56C47×#408C2211yescharacteristic
57C47×#405C2211yescharacteristic
58C47×#405C2211yescharacteristic
59C2×#97×C47C2211yescharacteristic
60C47×#382C2211yescharacteristic
61C47×#343C2211yescharacteristic
62C47×#343C2211yescharacteristic
63C47×#341C2211yescharacteristic
64C47×#339C2211yescharacteristic
65C47×#339C2211yescharacteristic
66C47×#339C2211yescharacteristic
67C2×#41×C47C2311yescharacteristic
68C22×Q8×C47C2311yescharacteristic
69C22×Q8×C47C2311yescharacteristic
70#137×C47—22no—
71#137×C47—22no—
72C2×Q16×C47—21no—
73C2×SD16×C47—21no—
74C2×M16×C47C2311yescharacteristic
75C2×M16×C47C2311yescharacteristic
76C2×M16×C47C2311yescharacteristic
77C2×M16×C47C2311yescharacteristic
78C22×C8×C47C2311yescharacteristic
79C22×C8×C47C2311yescharacteristic
80C4⋊Q8×C47—21no—
81C4⋊Q8×C47—21no—
82C4⋊Q8×C47—21no—
83C4⋊Q8×C47—22no—
84C4⋊Q8×C47—22no—
85#125×C47—21no—
86#125×C47—21no—
87#124×C47—21no—
88#123×C47—41no—
89C22⋊Q8×C47—21no—
90C22⋊Q8×C47—21no—
91C22⋊Q8×C47—41no—
92C4×Q8×C47—21no—
93C4×Q8×C47—21no—
94C4×Q8×C47—21no—
95C4×Q8×C47—21no—
96C4×Q8×C47—21no—
97C4×D4×C47—21no—
98C4×D4×C47—41no—
99#117×C47—21no—
100#117×C47—41no—
101#117×C47C2311yescharacteristic
102#117×C47C2311yescharacteristic
103#117×C47C2311yescharacteristic
104C2×C4⋊C4×C47—21no—
105C2×C4⋊C4×C47—41no—
106C2×C4⋊C4×C47C2311yescharacteristic
107C2×C4⋊C4×C47C2311yescharacteristic
108C2×C42×C47C2311yescharacteristic
109#108×C47—22no—
110#107×C47—21no—
111#107×C47—21no—
112#107×C47—21no—
113#107×C47D411yescharacteristic
114#107×C47D411yescharacteristic
115#106×C47—21no—
116#106×C47—21no—
117#106×C47—21no—
118#106×C47D411yescharacteristic
119#106×C47D411yescharacteristic
120C4⋊C8×C47—21no—
121C4⋊C8×C47—21no—
122#104×C47—22no—
123#103×C47—21no—
124#103×C47—21no—
125#103×C47—21no—
126#103×C47—21no—
127#103×C47—21no—
128#103×C47—21no—
129#103×C47—21no—
130#103×C47—21no—
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×C47D411yescharacteristic
139#103×C47D411yescharacteristic
140#102×C47—21no—
141#102×C47D411yescharacteristic
142#102×C47D411yescharacteristic
143#101×C47—22no—
144#101×C47—22no—
145C22⋊C8×C47—21no—
146C22⋊C8×C47—21no—
147#97×C47—21no—
148#97×C47—21no—
149#97×C47—22no—
150C4×C8×C47—21no—
151C4×C8×C47—21no—
152#95×C47—41no—
153#41×C47—21no—
154#41×C47—21no—
155#41×C47—21no—
156#41×C47—21no—
157C2×Q8×C47—21no—
158C2×Q8×C47—21no—
159C2×Q8×C47—21no—
160C2×Q8×C47—21no—
161C2×Q8×C47—21no—
162C2×Q8×C47—21no—
163C2×Q8×C47—21no—
164C2×Q8×C47—21no—
165C2×Q8×C47—21no—
166C2×Q8×C47—21no—
167C2×Q8×C47—21no—
168C2×Q8×C47—41no—
169C2×Q8×C47C2×D411yescharacteristic
170C2×Q8×C47#4112yes—
171C2×D4×C47—21no—
172C2×D4×C47C2×D411yescharacteristic
173C22×C4×C47—21no—
174C22×C4×C47—21no—
175C22×C4×C47—21no—
176C22×C4×C47—21no—
177C22×C4×C47—21no—
178C22×C4×C47—21no—
179C22×C4×C47—41no—
180C22×C4×C47C2411yescharacteristic
181Q16×C47—24no—
182SD16×C47—24no—
183M16×C47—21no—
184M16×C47—21no—
185M16×C47—21no—
186M16×C47—21no—
187M16×C47—21no—
188M16×C47—21no—
189M16×C47—21no—
190M16×C47#4112yes—
191C2×C8×C47—21no—
192C2×C8×C47—21no—
193C2×C8×C47—21no—
194C2×C8×C47—21no—
195C2×C8×C47—21no—
196C2×C8×C47—21no—
197C2×C8×C47—21no—
198C2×C8×C47—21no—
199C2×C8×C47C2×D411yescharacteristic
200C2×C8×C47C2×D411yescharacteristic
201C2×C8×C47C2×D411yescharacteristic
202C2×C8×C47C2×D411yescharacteristic
203C4⋊C4×C47—21no—
204C4⋊C4×C47—21no—
205C4⋊C4×C47—21no—
206C4⋊C4×C47—21no—
207C4⋊C4×C47—41no—
208C4⋊C4×C47—44no—
209C4⋊C4×C47—41no—
210C4⋊C4×C47—41no—
211C4⋊C4×C47—41no—
212C4⋊C4×C47—41no—
213C4⋊C4×C47—41no—
214C4⋊C4×C47—41no—
215C4⋊C4×C47—41no—
216C4⋊C4×C47C2×D411yescharacteristic
217C4⋊C4×C47C2×D411yescharacteristic
218C4⋊C4×C47C2×D411yescharacteristic
219C4⋊C4×C47C2×D411yescharacteristic
220C4⋊C4×C47C2×D411yescharacteristic
221C4⋊C4×C47C2×D411yescharacteristic
222C22⋊C4×C47—21no—
223C22⋊C4×C47—21no—
224C22⋊C4×C47—21no—
225C22⋊C4×C47—41no—
226C22⋊C4×C47—41no—
227C22⋊C4×C47—41no—
228C42×C47—21no—
229C42×C47—21no—
230C42×C47—21no—
231C42×C47—21no—
232C42×C47—41no—
233C42×C47—41no—
234C42×C47—41no—
235C42×C47#4112yes—
236C23×C47—21no—
237C23×C47H(5,𝔽2)11yescharacteristic
238Q8×C47—22no—
239Q8×C47—21no—
240Q8×C47—21no—
241Q8×C47—22no—
242Q8×C47—41no—
243Q8×C47—41no—
244Q8×C47—41no—
245Q8×C47—41no—
246Q8×C47—41no—
247Q8×C47—41no—
248Q8×C47—161no—
249D4×C47—21no—
250D4×C47—21no—
251D4×C47—41no—
252D4×C47—41no—
253C2×C4×C47—21no—
254C2×C4×C47—21no—
255C2×C4×C47—21no—
256C2×C4×C47—21no—
257C2×C4×C47—21no—
258C2×C4×C47—21no—
259C2×C4×C47—21no—
260C2×C4×C47—22no—
261C2×C4×C47—22no—
262C2×C4×C47—41no—
263C2×C4×C47—41no—
264C2×C4×C47—41no—
265C2×C4×C47—41no—
266C2×C4×C47—41no—
267C2×C4×C47—41no—
268C2×C4×C47—41no—
269C2×C4×C47—41no—
270C2×C4×C47—41no—
271C2×C4×C47—41no—
272C2×C4×C47—41no—
273C2×C4×C47—81no—
274C2×C4×C47—81no—
275C2×C4×C47—161no—
276C2×C4×C47C22×D411yescharacteristic
277C2×C4×C47C22×D411yescharacteristic
278C2×C4×C47C2×#4111yescharacteristic
279C2×C4×C47C2×#4111yescharacteristic
280C2×C4×C47C2×#4111yescharacteristic
281C2×C4×C472−1+411yescharacteristic
282C8×C47—22no—
283C8×C47—21no—
284C8×C47—21no—
285C8×C47—21no—
286C8×C47—21no—
287C8×C47—41no—
288C8×C47—41no—
289C8×C47—41no—
290#26852C4711yesmaximal, characteristic, direct product factor, Sylow
291C22×C47—21no—
292C22×C47—21no—
293C22×C47—41no—
294C22×C47—41no—
295C22×C47—41no—
296C22×C47#54211yescharacteristic
297C22×C47D4211yescharacteristic
298C22×C47#55111yescharacteristic
299C4×C47—42no—
300C4×C47—41no—
301C4×C47—42no—
302C4×C47—41no—
303C4×C47—41no—
304C4×C47—41no—
305C4×C47—41no—
306C4×C47—41no—
307C4×C47—41no—
308C4×C47—81no—
309C4×C47—81no—
310C4×C47—81no—
311C4×C47#52511yescharacteristic
312C4×C47#53211yescharacteristic
313C4×C47#54711yescharacteristic
314C4×C47#54811yescharacteristic
315#3137C2×C4711yescharacteristic
316#3097C2×C4711yescharacteristic
317#3082C2×C4711yescharacteristic, complemented
318#2947C2×C4711yescharacteristic
319#2064C2×C4711yescharacteristic, complemented
320#2061C2×C4711yescharacteristic, complemented
321#2052C2×C4711yescharacteristic
322#2005C2×C4711yescharacteristic
323#1960C2×C4711yescharacteristic, complemented
324#1938C2×C4711yescharacteristic
325#1930C2×C4711yescharacteristic, complemented
326#1930C2×C4711yescharacteristic, complemented
327#1886C2×C4711yescharacteristic, complemented
328#1860C2×C4711yescharacteristic
329#1773C2×C4711yescharacteristic, complemented
330C2×C47—21no—
331C2×C47—21no—
332C2×C47—81no—
333C2×C47#246111yescharacteristic
334C2×C47#328911yescharacteristic
335C2×C47#328911yescharacteristic
336C2×#137C22×C4711yescharacteristic
337#544C22×C4711yescharacteristic
338#536C22×C4711yescharacteristic
339C2×C4⋊Q8C22×C4711yescharacteristic
340#520C22×C4711yescharacteristic
341#519C22×C4711yescharacteristic
342#491—21no—
343#489—21no—
344#488—21no—
345#487—21no—
346#485—21no—
347#485—21no—
348#484—21no—
349#483—21no—
350#479—21no—
351#479—21no—
352#477—21no—
353#475—21no—
354#441—21no—
355#440—21no—
356C4×Q16—21no—
357C4×SD16—21no—
358C2×#108C22×C4711yescharacteristic
359#428C22×C4711yescharacteristic
360#428C22×C4711yescharacteristic
361#428C22×C4711yescharacteristic
362#427C22×C4711yescharacteristic
363#424C22×C4711yescharacteristic
364C2×#104C22×C4711yescharacteristic
365#419C22×C4711yescharacteristic
366#419C22×C4711yescharacteristic
367#419C22×C4711yescharacteristic
368#417C22×C4711yescharacteristic
369#416C22×C4711yescharacteristic
370C2×#103C22×C4711yescharacteristic
371C2×#103C22×C4711yescharacteristic
372C2×#103C22×C4711yescharacteristic
373C2×#103C22×C4711yescharacteristic
374C2×#101C22×C4711yescharacteristic
375C2×#101C22×C4711yescharacteristic
376#408C22×C4711yescharacteristic
377#405C22×C4711yescharacteristic
378#405C22×C4711yescharacteristic
379C2×#97C22×C4711yescharacteristic
380#382C22×C4711yescharacteristic
381#343C22×C4711yescharacteristic
382#343C22×C4711yescharacteristic
383#341C22×C4711yescharacteristic
384#339C22×C4711yescharacteristic
385#339C22×C4711yescharacteristic
386#339C22×C4711yescharacteristic
387C47#2685211yescharacteristic, direct product factor, Sylow
388C2×#41C23×C4711yescharacteristic
389C22×Q8C23×C4711yescharacteristic
390C22×Q8C23×C4711yescharacteristic
391#137—22no—
392#137—22no—
393C2×Q16—21no—
394C2×SD16—21no—
395C2×M16C23×C4711yescharacteristic
396C2×M16C23×C4711yescharacteristic
397C2×M16C23×C4711yescharacteristic
398C2×M16C23×C4711yescharacteristic
399C22×C8C23×C4711yescharacteristic
400C22×C8C23×C4711yescharacteristic
401C4⋊Q8—21no—
402C4⋊Q8—21no—
403C4⋊Q8—21no—
404C4⋊Q8—22no—
405C4⋊Q8—22no—
406#125—21no—
407#125—21no—
408#124—21no—
409#123—41no—
410C22⋊Q8—21no—
411C22⋊Q8—21no—
412C22⋊Q8—41no—
413C4×Q8—21no—
414C4×Q8—21no—
415C4×Q8—21no—
416C4×Q8—21no—
417C4×Q8—21no—
418C4×D4—21no—
419C4×D4—41no—
420#117—21no—
421#117—41no—
422#117C23×C4711yescharacteristic
423#117C23×C4711yescharacteristic
424#117C23×C4711yescharacteristic
425C2×C4⋊C4—21no—
426C2×C4⋊C4—41no—
427C2×C4⋊C4C23×C4711yescharacteristic
428C2×C4⋊C4C23×C4711yescharacteristic
429C2×C42C23×C4711yescharacteristic
430#108—22no—
431#107—21no—
432#107—21no—
433#107—21no—
434#107D4×C4711yescharacteristic
435#107D4×C4711yescharacteristic
436#106—21no—
437#106—21no—
438#106—21no—
439#106D4×C4711yescharacteristic
440#106D4×C4711yescharacteristic
441C4⋊C8—21no—
442C4⋊C8—21no—
443#104—22no—
444#103—21no—
445#103—21no—
446#103—21no—
447#103—21no—
448#103—21no—
449#103—21no—
450#103—21no—
451#103—21no—
452#103—21no—
453#103—21no—
454#103—21no—
455#103—21no—
456#103—21no—
457#103—21no—
458#103—21no—
459#103D4×C4711yescharacteristic
460#103D4×C4711yescharacteristic
461#102—21no—
462#102D4×C4711yescharacteristic
463#102D4×C4711yescharacteristic
464#101—22no—
465#101—22no—
466C22⋊C8—21no—
467C22⋊C8—21no—
468#97—21no—
469#97—21no—
470#97—22no—
471C4×C8—21no—
472C4×C8—21no—
473#95—41no—
474#41—21no—
475#41—21no—
476#41—21no—
477#41—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—41no—
490C2×Q8C2×D4×C4711yescharacteristic
491C2×Q8#41×C4712yes—
492C2×D4—21no—
493C2×D4C2×D4×C4711yescharacteristic
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—41no—
501C22×C4C24×C4711yescharacteristic
502Q16—24no—
503SD16—24no—
504M16—21no—
505M16—21no—
506M16—21no—
507M16—21no—
508M16—21no—
509M16—21no—
510M16—21no—
511M16#41×C4712yes—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8C2×D4×C4711yescharacteristic
521C2×C8C2×D4×C4711yescharacteristic
522C2×C8C2×D4×C4711yescharacteristic
523C2×C8C2×D4×C4711yescharacteristic
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—41no—
529C4⋊C4—44no—
530C4⋊C4—41no—
531C4⋊C4—41no—
532C4⋊C4—41no—
533C4⋊C4—41no—
534C4⋊C4—41no—
535C4⋊C4—41no—
536C4⋊C4—41no—
537C4⋊C4C2×D4×C4711yescharacteristic
538C4⋊C4C2×D4×C4711yescharacteristic
539C4⋊C4C2×D4×C4711yescharacteristic
540C4⋊C4C2×D4×C4711yescharacteristic
541C4⋊C4C2×D4×C4711yescharacteristic
542C4⋊C4C2×D4×C4711yescharacteristic
543C22⋊C4—21no—
544C22⋊C4—21no—
545C22⋊C4—21no—
546C22⋊C4—41no—
547C22⋊C4—41no—
548C22⋊C4—41no—
549C42—21no—
550C42—21no—
551C42—21no—
552C42—21no—
553C42—41no—
554C42—41no—
555C42—41no—
556C42#41×C4712yes—
557C23—21no—
558C23H(5,𝔽2)×C4711yescharacteristic
559Q8—22no—
560Q8—21no—
561Q8—21no—
562Q8—22no—
563Q8—41no—
564Q8—41no—
565Q8—41no—
566Q8—41no—
567Q8—41no—
568Q8—41no—
569Q8—161no—
570D4—21no—
571D4—21no—
572D4—41no—
573D4—41no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—81no—
595C2×C4—81no—
596C2×C4—161no—
597C2×C4C22×D4×C4711yescharacteristic
598C2×C4C22×D4×C4711yescharacteristic
599C2×C4C2×#41×C4711yescharacteristic
600C2×C4C2×#41×C4711yescharacteristic
601C2×C4C2×#41×C4711yescharacteristic
602C2×C42−1+4×C4711yescharacteristic
603C8—22no—
604C8—21no—
605C8—21no—
606C8—21no—
607C8—21no—
608C8—41no—
609C8—41no—
610C8—41no—
611C22—21no—
612C22—21no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22C47×#54211yescharacteristic
617C22D42×C4711yescharacteristic
618C22C47×#55111yescharacteristic
619C4—42no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—41no—
624C4—41no—
625C4—41no—
626C4—41no—
627C4—42no—
628C4—81no—
629C4—81no—
630C4—81no—
631C4C47×#52511yescharacteristic
632C4C47×#53211yescharacteristic
633C4C47×#54711yescharacteristic
634C4C47×#54811yescharacteristic
635C2—21no—
636C2—21no—
637C2—81no—
638C2C47×#246111yescharacteristic
639C2C47×#328911yescharacteristic
640C2C47×#328911yescharacteristic
subgroupG/H
center, socleC22×C47D42
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC2×#41×C47C23
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
3. C47×#3082C2semidirect
5. C47×#2064C2semidirect
6. C47×#2061C2semidirect
9. C47×#1960C2semidirect
11. C47×#1930C2semidirect
12. C47×#1930C2semidirect
13. C47×#1886C2semidirect
15. C47×#1773C2semidirect
290. #26852C47direct (N × H)
317. #3082C2×C47semidirect
319. #2064C2×C47semidirect
320. #2061C2×C47semidirect
323. #1960C2×C47semidirect
325. #1930C2×C47semidirect
326. #1930C2×C47semidirect
327. #1886C2×C47semidirect
329. #1773C2×C47semidirect
387. C47#26852direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#31372
C47×#30972
C47×#30822
C47×#29472
C47×#20642
C47×#20612
C47×#20522
C47×#20052
C47×#19602
C47×#19382
C47×#19302
C47×#18862
C47×#18602
C47×#17732
#2685247