Finite Group Databasebeta

← C47×#26921 #26066619

Subgroups — C47×#26921 #26066619

Order 12032.

758 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3082C211yesmaximal, characteristic, complemented
2C47×#3081C211yesmaximal, characteristic, complemented
3C47×#2949C211yesmaximal, characteristic, complemented
4C47×#2948C211yesmaximal, characteristic
5C47×#2046C211yesmaximal, characteristic, complemented
6C47×#2045C211yesmaximal, characteristic
7C47×#2027C211yesmaximal, characteristic, complemented
8C47×#2012C211yesmaximal, characteristic
9C47×#1931C211yesmaximal, characteristic, complemented
10C47×#1930C211yesmaximal, characteristic, complemented
11C47×#1922C211yesmaximal, characteristic, complemented
12C47×#1922C211yesmaximal, characteristic, complemented
13C47×#1888C211yesmaximal, characteristic, complemented
14C47×#1885C211yesmaximal, characteristic, complemented
15C47×#1856C211yesmaximal, characteristic, complemented
16C22×SD16×C47C2211yescharacteristic
17C22×D8×C47C2211yescharacteristic
18C47×#544C2211yescharacteristic
19C2×#124×C47C2211yescharacteristic
20C47×#519C2211yescharacteristic
21C47×#518C2211yescharacteristic
22C47×#518C2211yescharacteristic
23C47×#479—21no—
24C47×#479—21no—
25C47×#478—21no—
26C47×#478—21no—
27C47×#477—21no—
28C47×#476—21no—
29C47×#475—21no—
30C47×#474—21no—
31C47×#442—21no—
32C47×#442—21no—
33C47×#440—21no—
34C47×#440—21no—
35C4×SD16×C47—21no—
36C4×SD16×C47—21no—
37C4×D8×C47—21no—
38C4×D8×C47—21no—
39C47×#428C2211yescharacteristic
40C47×#428C2211yescharacteristic
41C47×#427C2211yescharacteristic
42C47×#427C2211yescharacteristic
43C47×#424C2211yescharacteristic
44C47×#424C2211yescharacteristic
45C47×#419C2211yescharacteristic
46C47×#419C2211yescharacteristic
47C47×#418C2211yescharacteristic
48C47×#418C2211yescharacteristic
49C47×#418C2211yescharacteristic
50C47×#418C2211yescharacteristic
51C2×#103×C47C2211yescharacteristic
52C2×#102×C47C2211yescharacteristic
53C2×#101×C47C2211yescharacteristic
54C2×#100×C47C2211yescharacteristic
55C2×#100×C47C2211yescharacteristic
56C47×#405C2211yescharacteristic
57C47×#405C2211yescharacteristic
58C47×#390C2211yescharacteristic
59C47×#343C2211yescharacteristic
60C47×#341C2211yescharacteristic
61C47×#341C2211yescharacteristic
62C47×#339C2211yescharacteristic
63C47×#339C2211yescharacteristic
64C47×#339C2211yescharacteristic
65C47×#339C2211yescharacteristic
66C47×#336C2211yescharacteristic
67C22×Q8×C47C2311yescharacteristic
68C22×D4×C47C2311yescharacteristic
69C22×D4×C47C2311yescharacteristic
70C2×SD16×C47—22no—
71C2×SD16×C47—22no—
72C2×SD16×C47—21no—
73C2×SD16×C47—21no—
74C2×D8×C47—22no—
75C2×D8×C47—22no—
76C2×D8×C47—21no—
77C2×D8×C47—21no—
78C2×M16×C47C2311yescharacteristic
79C2×M16×C47C2311yescharacteristic
80C2×M16×C47C2311yescharacteristic
81C2×M16×C47C2311yescharacteristic
82C22×C8×C47C2311yescharacteristic
83C22×C8×C47C2311yescharacteristic
84C4⋊Q8×C47—21no—
85C4⋊Q8×C47—21no—
86#125×C47—21no—
87#125×C47—21no—
88#124×C47—22no—
89#124×C47—22no—
90C22⋊Q8×C47—41no—
91C4×Q8×C47—21no—
92C4×Q8×C47—21no—
93C4×Q8×C47—21no—
94C4×Q8×C47—21no—
95C4×D4×C47—21no—
96C4×D4×C47—21no—
97C4×D4×C47—21no—
98C4×D4×C47—21no—
99C4×D4×C47—21no—
100C4×D4×C47—21no—
101C4×D4×C47—21no—
102C4×D4×C47—21no—
103#117×C47—41no—
104#117×C47C2311yescharacteristic
105#117×C47C2311yescharacteristic
106#117×C47C2311yescharacteristic
107#117×C47C2311yescharacteristic
108C2×C4⋊C4×C47C2311yescharacteristic
109C2×C22⋊C4×C47—41no—
110C2×C22⋊C4×C47—41no—
111C2×C22⋊C4×C47—41no—
112C2×C22⋊C4×C47—41no—
113C2×C42×C47C2311yescharacteristic
114#107×C47—21no—
115#107×C47—21no—
116#107×C47D411yescharacteristic
117#107×C47D411yescharacteristic
118#107×C47D411yescharacteristic
119#107×C47D411yescharacteristic
120#106×C47—21no—
121#106×C47—21no—
122#106×C47D411yescharacteristic
123#106×C47D411yescharacteristic
124#106×C47D411yescharacteristic
125#106×C47D411yescharacteristic
126C4⋊C8×C47—21no—
127C4⋊C8×C47—21no—
128C4⋊C8×C47—21no—
129C4⋊C8×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#102×C47—21no—
137#102×C47—21no—
138#102×C47—21no—
139#102×C47—21no—
140#102×C47—21no—
141#102×C47—21no—
142#102×C47—21no—
143#102×C47—21no—
144#102×C47—21no—
145#102×C47—21no—
146#101×C47—22no—
147#100×C47—22no—
148#100×C47—22no—
149#97×C47—21no—
150#97×C47—21no—
151C4×C8×C47—21no—
152C4×C8×C47—21no—
153C24×C47—21no—
154C24×C47—21no—
155C2×Q8×C47—21no—
156C2×Q8×C47—21no—
157C2×Q8×C47—21no—
158C2×Q8×C47—21no—
159C2×Q8×C47—21no—
160C2×Q8×C47—41no—
161C2×Q8×C47#4112yes—
162C2×D4×C47—21no—
163C2×D4×C47—21no—
164C2×D4×C47—21no—
165C2×D4×C47—21no—
166C2×D4×C47—21no—
167C2×D4×C47—21no—
168C2×D4×C47—21no—
169C2×D4×C47—21no—
170C2×D4×C47—21no—
171C2×D4×C47—21no—
172C2×D4×C47#4112yes—
173C2×D4×C47#4112yes—
174C22×C4×C47—21no—
175C22×C4×C47—21no—
176C22×C4×C47—21no—
177C22×C4×C47—41no—
178C22×C4×C47—41no—
179C22×C4×C47—41no—
180C22×C4×C47—41no—
181C22×C4×C47C2411yescharacteristic
182SD16×C47—24no—
183SD16×C47—24no—
184D8×C47—24no—
185D8×C47—24no—
186M16×C47—21no—
187M16×C47—21no—
188M16×C47—21no—
189M16×C47—21no—
190M16×C47—21no—
191M16×C47—21no—
192M16×C47—21no—
193M16×C47—21no—
194C2×C8×C47—21no—
195C2×C8×C47—21no—
196C2×C8×C47—21no—
197C2×C8×C47—21no—
198C2×C8×C47—21no—
199C2×C8×C47—21no—
200C2×C8×C47—21no—
201C2×C8×C47—21no—
202C2×C8×C47C2×D411yescharacteristic
203C2×C8×C47C2×D411yescharacteristic
204C2×C8×C47C2×D411yescharacteristic
205C2×C8×C47C2×D411yescharacteristic
206C4⋊C4×C47—21no—
207C4⋊C4×C47—21no—
208C4⋊C4×C47—41no—
209C4⋊C4×C47—41no—
210C4⋊C4×C47—41no—
211C4⋊C4×C47—41no—
212C4⋊C4×C47—41no—
213C4⋊C4×C47C2×D411yescharacteristic
214C4⋊C4×C47C2×D411yescharacteristic
215C4⋊C4×C47C2×D411yescharacteristic
216C4⋊C4×C47C2×D411yescharacteristic
217C4⋊C4×C47C2×D411yescharacteristic
218C4⋊C4×C47C2×D411yescharacteristic
219C4⋊C4×C47C2×D411yescharacteristic
220C4⋊C4×C47C2×D411yescharacteristic
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×C47—41no—
229C22⋊C4×C47—44no—
230C22⋊C4×C47—82no—
231C42×C47—21no—
232C42×C47—21no—
233C42×C47—21no—
234C42×C47—21no—
235C42×C47—21no—
236C42×C47—21no—
237C42×C47—41no—
238C42×C47—41no—
239C23×C47—22no—
240C23×C47—22no—
241C23×C47—41no—
242C23×C47—41no—
243C23×C47—41no—
244C23×C47—41no—
245C23×C47—81no—
246C23×C47—81no—
247C23×C47—81no—
248C23×C47—81no—
249C23×C47H(5,𝔽2)11yescharacteristic
250Q8×C47—22no—
251Q8×C47—22no—
252Q8×C47—41no—
253Q8×C47—41no—
254Q8×C47—161no—
255D4×C47—22no—
256D4×C47—22no—
257D4×C47—22no—
258D4×C47—22no—
259D4×C47—41no—
260D4×C47—41no—
261D4×C47—41no—
262D4×C47—41no—
263C2×C4×C47—21no—
264C2×C4×C47—21no—
265C2×C4×C47—21no—
266C2×C4×C47—21no—
267C2×C4×C47—21no—
268C2×C4×C47—21no—
269C2×C4×C47—21no—
270C2×C4×C47—21no—
271C2×C4×C47—22no—
272C2×C4×C47—41no—
273C2×C4×C47—41no—
274C2×C4×C47—41no—
275C2×C4×C47—41no—
276C2×C4×C47—41no—
277C2×C4×C47—41no—
278C2×C4×C47—81no—
279C2×C4×C47—161no—
280C2×C4×C47—161no—
281C2×C4×C47—161no—
282C2×C4×C47—161no—
283C2×C4×C47C22×D411yescharacteristic
284C2×C4×C47C22×D411yescharacteristic
285C2×C4×C47C2×#4111yescharacteristic
286C2×C4×C47C2×#4111yescharacteristic
287C2×C4×C47C2×#4111yescharacteristic
288C2×C4×C472−1+411yescharacteristic
289C8×C47—21no—
290C8×C47—21no—
291C8×C47—21no—
292C8×C47—21no—
293C8×C47—41no—
294C8×C47—41no—
295C8×C47—41no—
296C8×C47—41no—
297#26921C4711yesmaximal, characteristic, direct product factor, Sylow
298C22×C47—21no—
299C22×C47—21no—
300C22×C47—42no—
301C22×C47—42no—
302C22×C47—82no—
303C22×C47—82no—
304C22×C47—81no—
305C22×C47—81no—
306C22×C47—81no—
307C22×C47—81no—
308C22×C47—161no—
309C22×C47—161no—
310C22×C47#53911yescharacteristic
311C22×C47D4211yescharacteristic
312C22×C47#55111yescharacteristic
313C4×C47—42no—
314C4×C47—41no—
315C4×C47—41no—
316C4×C47—41no—
317C4×C47—41no—
318C4×C47—41no—
319C4×C47—41no—
320C4×C47—41no—
321C4×C47—41no—
322C4×C47—81no—
323C4×C47—81no—
324C4×C47#52511yescharacteristic
325C4×C47#52511yescharacteristic
326C4×C47#54811yescharacteristic
327C4×C47#54811yescharacteristic
328#3082C2×C4711yescharacteristic, complemented
329#3081C2×C4711yescharacteristic, complemented
330#2949C2×C4711yescharacteristic, complemented
331#2948C2×C4711yescharacteristic
332#2046C2×C4711yescharacteristic, complemented
333#2045C2×C4711yescharacteristic
334#2027C2×C4711yescharacteristic, complemented
335#2012C2×C4711yescharacteristic
336#1931C2×C4711yescharacteristic, complemented
337#1930C2×C4711yescharacteristic, complemented
338#1922C2×C4711yescharacteristic, complemented
339#1922C2×C4711yescharacteristic, complemented
340#1888C2×C4711yescharacteristic, complemented
341#1885C2×C4711yescharacteristic, complemented
342#1856C2×C4711yescharacteristic, complemented
343C2×C47—21no—
344C2×C47—21no—
345C2×C47—82no—
346C2×C47—82no—
347C2×C47#246311yescharacteristic
348C2×C47#328811yescharacteristic
349C2×C47#329011yescharacteristic
350C22×SD16C22×C4711yescharacteristic
351C22×D8C22×C4711yescharacteristic
352#544C22×C4711yescharacteristic
353C2×#124C22×C4711yescharacteristic
354#519C22×C4711yescharacteristic
355#518C22×C4711yescharacteristic
356#518C22×C4711yescharacteristic
357#479—21no—
358#479—21no—
359#478—21no—
360#478—21no—
361#477—21no—
362#476—21no—
363#475—21no—
364#474—21no—
365#442—21no—
366#442—21no—
367#440—21no—
368#440—21no—
369C4×SD16—21no—
370C4×SD16—21no—
371C4×D8—21no—
372C4×D8—21no—
373#428C22×C4711yescharacteristic
374#428C22×C4711yescharacteristic
375#427C22×C4711yescharacteristic
376#427C22×C4711yescharacteristic
377#424C22×C4711yescharacteristic
378#424C22×C4711yescharacteristic
379#419C22×C4711yescharacteristic
380#419C22×C4711yescharacteristic
381#418C22×C4711yescharacteristic
382#418C22×C4711yescharacteristic
383#418C22×C4711yescharacteristic
384#418C22×C4711yescharacteristic
385C2×#103C22×C4711yescharacteristic
386C2×#102C22×C4711yescharacteristic
387C2×#101C22×C4711yescharacteristic
388C2×#100C22×C4711yescharacteristic
389C2×#100C22×C4711yescharacteristic
390#405C22×C4711yescharacteristic
391#405C22×C4711yescharacteristic
392#390C22×C4711yescharacteristic
393#343C22×C4711yescharacteristic
394#341C22×C4711yescharacteristic
395#341C22×C4711yescharacteristic
396#339C22×C4711yescharacteristic
397#339C22×C4711yescharacteristic
398#339C22×C4711yescharacteristic
399#339C22×C4711yescharacteristic
400#336C22×C4711yescharacteristic
401C47#2692111yescharacteristic, direct product factor, Sylow
402C22×Q8C23×C4711yescharacteristic
403C22×D4C23×C4711yescharacteristic
404C22×D4C23×C4711yescharacteristic
405C2×SD16—22no—
406C2×SD16—22no—
407C2×SD16—21no—
408C2×SD16—21no—
409C2×D8—22no—
410C2×D8—22no—
411C2×D8—21no—
412C2×D8—21no—
413C2×M16C23×C4711yescharacteristic
414C2×M16C23×C4711yescharacteristic
415C2×M16C23×C4711yescharacteristic
416C2×M16C23×C4711yescharacteristic
417C22×C8C23×C4711yescharacteristic
418C22×C8C23×C4711yescharacteristic
419C4⋊Q8—21no—
420C4⋊Q8—21no—
421#125—21no—
422#125—21no—
423#124—22no—
424#124—22no—
425C22⋊Q8—41no—
426C4×Q8—21no—
427C4×Q8—21no—
428C4×Q8—21no—
429C4×Q8—21no—
430C4×D4—21no—
431C4×D4—21no—
432C4×D4—21no—
433C4×D4—21no—
434C4×D4—21no—
435C4×D4—21no—
436C4×D4—21no—
437C4×D4—21no—
438#117—41no—
439#117C23×C4711yescharacteristic
440#117C23×C4711yescharacteristic
441#117C23×C4711yescharacteristic
442#117C23×C4711yescharacteristic
443C2×C4⋊C4C23×C4711yescharacteristic
444C2×C22⋊C4—41no—
445C2×C22⋊C4—41no—
446C2×C22⋊C4—41no—
447C2×C22⋊C4—41no—
448C2×C42C23×C4711yescharacteristic
449#107—21no—
450#107—21no—
451#107D4×C4711yescharacteristic
452#107D4×C4711yescharacteristic
453#107D4×C4711yescharacteristic
454#107D4×C4711yescharacteristic
455#106—21no—
456#106—21no—
457#106D4×C4711yescharacteristic
458#106D4×C4711yescharacteristic
459#106D4×C4711yescharacteristic
460#106D4×C4711yescharacteristic
461C4⋊C8—21no—
462C4⋊C8—21no—
463C4⋊C8—21no—
464C4⋊C8—21no—
465#103—21no—
466#103—21no—
467#103—21no—
468#103—21no—
469#103—21no—
470#103—21no—
471#102—21no—
472#102—21no—
473#102—21no—
474#102—21no—
475#102—21no—
476#102—21no—
477#102—21no—
478#102—21no—
479#102—21no—
480#102—21no—
481#101—22no—
482#100—22no—
483#100—22no—
484#97—21no—
485#97—21no—
486C4×C8—21no—
487C4×C8—21no—
488C24—21no—
489C24—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—41no—
496C2×Q8#41×C4712yes—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4#41×C4712yes—
508C2×D4#41×C4712yes—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4C24×C4711yescharacteristic
517SD16—24no—
518SD16—24no—
519D8—24no—
520D8—24no—
521M16—21no—
522M16—21no—
523M16—21no—
524M16—21no—
525M16—21no—
526M16—21no—
527M16—21no—
528M16—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8C2×D4×C4711yescharacteristic
538C2×C8C2×D4×C4711yescharacteristic
539C2×C8C2×D4×C4711yescharacteristic
540C2×C8C2×D4×C4711yescharacteristic
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—41no—
544C4⋊C4—41no—
545C4⋊C4—41no—
546C4⋊C4—41no—
547C4⋊C4—41no—
548C4⋊C4C2×D4×C4711yescharacteristic
549C4⋊C4C2×D4×C4711yescharacteristic
550C4⋊C4C2×D4×C4711yescharacteristic
551C4⋊C4C2×D4×C4711yescharacteristic
552C4⋊C4C2×D4×C4711yescharacteristic
553C4⋊C4C2×D4×C4711yescharacteristic
554C4⋊C4C2×D4×C4711yescharacteristic
555C4⋊C4C2×D4×C4711yescharacteristic
556C22⋊C4—21no—
557C22⋊C4—21no—
558C22⋊C4—21no—
559C22⋊C4—21no—
560C22⋊C4—41no—
561C22⋊C4—41no—
562C22⋊C4—41no—
563C22⋊C4—41no—
564C22⋊C4—44no—
565C22⋊C4—82no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—21no—
572C42—41no—
573C42—41no—
574C23—22no—
575C23—22no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—81no—
581C23—81no—
582C23—81no—
583C23—81no—
584C23H(5,𝔽2)×C4711yescharacteristic
585Q8—22no—
586Q8—22no—
587Q8—41no—
588Q8—41no—
589Q8—161no—
590D4—22no—
591D4—22no—
592D4—22no—
593D4—22no—
594D4—41no—
595D4—41no—
596D4—41no—
597D4—41no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—81no—
614C2×C4—161no—
615C2×C4—161no—
616C2×C4—161no—
617C2×C4—161no—
618C2×C4C22×D4×C4711yescharacteristic
619C2×C4C22×D4×C4711yescharacteristic
620C2×C4C2×#41×C4711yescharacteristic
621C2×C4C2×#41×C4711yescharacteristic
622C2×C4C2×#41×C4711yescharacteristic
623C2×C42−1+4×C4711yescharacteristic
624C8—21no—
625C8—21no—
626C8—21no—
627C8—21no—
628C8—41no—
629C8—41no—
630C8—41no—
631C8—41no—
632C22—21no—
633C22—21no—
634C22—42no—
635C22—42no—
636C22—82no—
637C22—82no—
638C22—81no—
639C22—81no—
640C22—81no—
641C22—81no—
642C22—161no—
643C22—161no—
644C22C47×#53911yescharacteristic
645C22D42×C4711yescharacteristic
646C22C47×#55111yescharacteristic
647C4—41no—
648C4—41no—
649C4—41no—
650C4—41no—
651C4—41no—
652C4—41no—
653C4—41no—
654C4—41no—
655C4—42no—
656C4—81no—
657C4—81no—
658C4C47×#52511yescharacteristic
659C4C47×#52511yescharacteristic
660C4C47×#54811yescharacteristic
661C4C47×#54811yescharacteristic
662C2—21no—
663C2—21no—
664C2—82no—
665C2—82no—
666C2C47×#246311yescharacteristic
667C2C47×#328811yescharacteristic
668C2C47×#329011yescharacteristic
subgroupG/H
center, socleC22×C47D42
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC22×D8×C47C22
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×#3082C2semidirect
2. C47×#3081C2semidirect
3. C47×#2949C2semidirect
5. C47×#2046C2semidirect
7. C47×#2027C2semidirect
9. C47×#1931C2semidirect
10. C47×#1930C2semidirect
11. C47×#1922C2semidirect
12. C47×#1922C2semidirect
13. C47×#1888C2semidirect
14. C47×#1885C2semidirect
15. C47×#1856C2semidirect
297. #26921C47direct (N × H)
328. #3082C2×C47semidirect
329. #3081C2×C47semidirect
330. #2949C2×C47semidirect
332. #2046C2×C47semidirect
334. #2027C2×C47semidirect
336. #1931C2×C47semidirect
337. #1930C2×C47semidirect
338. #1922C2×C47semidirect
339. #1922C2×C47semidirect
340. #1888C2×C47semidirect
341. #1885C2×C47semidirect
342. #1856C2×C47semidirect
401. C47#26921direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#30822
C47×#30812
C47×#29492
C47×#29482
C47×#20462
C47×#20452
C47×#20272
C47×#20122
C47×#19312
C47×#19302
C47×#19222
C47×#18882
C47×#18852
C47×#18562
#2692147