Finite Group Databasebeta

← C47×#14878 #26054576

Subgroups — C47×#14878 #26054576

Order 12032.

1634 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Q8×C47C211yesmaximal, characteristic
2C2×C47×#398C212yesmaximal
3C2×C47×#387C211yesmaximal, characteristic
4C47×#1446C211yesmaximal, characteristic
5C47×#1446C211yesmaximal, characteristic
6C47×#1444C211yesmaximal, characteristic
7C47×#1442C211yesmaximal, characteristic
8C47×#1441C212yesmaximal
9C47×#1436C212yesmaximal
10C47×#1436C212yesmaximal
11C47×C4⋊#95C211yesmaximal, characteristic
12C23×Q8×C47C2211yescharacteristic
13C2×C4×Q8×C47—28no—
14C2×C4×Q8×C47—24no—
15C22×C4⋊C4×C47C2211yescharacteristic
16C22×C4⋊C4×C47C2211yescharacteristic
17C22×C4⋊C4×C47C2212yes—
18C22×C4⋊C4×C47C2212yes—
19C22×C4⋊C4×C47C2212yes—
20C22×C4⋊C4×C47C2211yescharacteristic
21C22×C42×C47C2212yes—
22C22×C42×C47C2211yescharacteristic
23C47×#398—28no—
24C47×#387—24no—
25C2×#95×C47C2211yescharacteristic
26C2×#95×C47C2211yescharacteristic
27C2×#95×C47C2211yescharacteristic
28C2×#95×C47C2211yescharacteristic
29C2×#95×C47C2212yes—
30C2×#95×C47C2212yes—
31C2×#95×C47C2212yes—
32C2×#95×C47C2212yes—
33C2×#95×C47C2211yescharacteristic
34C2×#95×C47C2211yescharacteristic
35C2×#95×C47C2212yes—
36C2×#95×C47C2212yes—
37C2×#95×C47C2212yes—
38C2×#95×C47C2212yes—
39C22×Q8×C47—24no—
40C22×Q8×C47—22no—
41C22×Q8×C47—24no—
42C22×Q8×C47—22no—
43C22×Q8×C47Q814yes—
44C23×C4×C47C2311yescharacteristic
45C23×C4×C47C2312yes—
46C23×C4×C47C2311yescharacteristic
47C23×C4×C47C2312yes—
48C23×C4×C47C2311yescharacteristic
49C23×C4×C47C2311yescharacteristic
50C23×C4×C47C2312yes—
51C23×C4×C47C2311yescharacteristic
52C23×C4×C47C2311yescharacteristic
53C23×C4×C47C2312yes—
54C23×C4×C47C2311yescharacteristic
55C4×Q8×C47—232no—
56C2×C4⋊C4×C47—24no—
57C2×C4⋊C4×C47—22no—
58C2×C4⋊C4×C47—24no—
59C2×C4⋊C4×C47—24no—
60C2×C4⋊C4×C47—22no—
61C2×C4⋊C4×C47—22no—
62C2×C4⋊C4×C47—22no—
63C2×C4⋊C4×C47—24no—
64C2×C4⋊C4×C47—24no—
65C2×C4⋊C4×C47—24no—
66C2×C4⋊C4×C47—24no—
67C2×C4⋊C4×C47—24no—
68C2×C4⋊C4×C47—42no—
69C2×C4⋊C4×C47—42no—
70C2×C4⋊C4×C47D418yes—
71C2×C4⋊C4×C47Q814yescomplemented
72C2×C42×C47—24no—
73C2×C42×C47—24no—
74C2×C42×C47—24no—
75C2×C42×C47—24no—
76C2×C42×C47D414yes—
77#95×C47—22no—
78#95×C47—22no—
79#95×C47—22no—
80#95×C47—22no—
81#95×C47—24no—
82#95×C47—24no—
83#95×C47—24no—
84#95×C47—24no—
85#95×C47—22no—
86#95×C47—24no—
87#95×C47—24no—
88#95×C47—24no—
89#95×C47—22no—
90#95×C47—42no—
91C24×C47C2411yescharacteristic
92C2×Q8×C47—28no—
93C2×Q8×C47—28no—
94C2×Q8×C47—216no—
95C2×Q8×C47—28no—
96C2×Q8×C47—216no—
97C22×C4×C47—22no—
98C22×C4×C47—22no—
99C22×C4×C47—22no—
100C22×C4×C47—22no—
101C22×C4×C47—22no—
102C22×C4×C47—22no—
103C22×C4×C47—22no—
104C22×C4×C47—22no—
105C22×C4×C47—21no—
106C22×C4×C47—22no—
107C22×C4×C47—21no—
108C22×C4×C47—22no—
109C22×C4×C47—22no—
110C22×C4×C47—21no—
111C22×C4×C47—22no—
112C22×C4×C47—21no—
113C22×C4×C47—22no—
114C22×C4×C47—21no—
115C22×C4×C47—21no—
116C22×C4×C47—22no—
117C22×C4×C47—22no—
118C22×C4×C47—22no—
119C22×C4×C47—22no—
120C22×C4×C47—22no—
121C22×C4×C47—22no—
122C22×C4×C47—22no—
123C22×C4×C47—22no—
124C22×C4×C47—22no—
125C22×C4×C47—22no—
126C22×C4×C47—22no—
127C22×C4×C47—22no—
128C22×C4×C47—22no—
129C22×C4×C47—21no—
130C22×C4×C47—22no—
131C22×C4×C47—21no—
132C22×C4×C47—22no—
133C22×C4×C47—22no—
134C22×C4×C47—22no—
135C22×C4×C47—22no—
136C22×C4×C47—22no—
137C22×C4×C47—22no—
138C22×C4×C47—21no—
139C22×C4×C47—22no—
140C22×C4×C47—21no—
141C22×C4×C47—22no—
142C22×C4×C47—21no—
143C22×C4×C47—21no—
144C22×C4×C47—22no—
145C22×C4×C47C2×D414yes—
146C22×C4×C47C2×D414yes—
147C22×C4×C47C2×D412yes—
148C22×C4×C47C2×D412yes—
149C22×C4×C47C2×D414yes—
150C22×C4×C47C2×D412yes—
151C22×C4×C47C2×Q812yes—
152C22×C4×C47C2×Q812yes—
153C22×C4×C47C2×Q812yes—
154C22×C4×C47C2×Q814yes—
155C22×C4×C47C2×Q812yes—
156C22×C4×C47#4114yes—
157C22×C4×C47#4112yes—
158C22×C4×C47#4114yes—
159C22×C4×C47#4112yes—
160C4⋊C4×C47—28no—
161C4⋊C4×C47—216no—
162C4⋊C4×C47—28no—
163C4⋊C4×C47—48no—
164C4⋊C4×C47—48no—
165C4⋊C4×C47—44no—
166C42×C47—216no—
167C42×C47—28no—
168C23×C47C22×D411yescharacteristic
169C23×C47C22×D412yes—
170C23×C47C22×Q811yescharacteristic
171C23×C47C22×Q811yescharacteristic
172C23×C47C2×#4112yes—
173C23×C47C2×#4111yescharacteristic
174C23×C47C2×#4111yescharacteristic
175C23×C47C2×#4112yes—
176C23×C47H(5,𝔽2)11yescharacteristic
177C23×C472−1+412yes—
178C23×C472−1+411yescharacteristic
179Q8×C47—232no—
180C2×C4×C47—22no—
181C2×C4×C47—24no—
182C2×C4×C47—22no—
183C2×C4×C47—24no—
184C2×C4×C47—24no—
185C2×C4×C47—24no—
186C2×C4×C47—22no—
187C2×C4×C47—24no—
188C2×C4×C47—24no—
189C2×C4×C47—24no—
190C2×C4×C47—24no—
191C2×C4×C47—22no—
192C2×C4×C47—22no—
193C2×C4×C47—22no—
194C2×C4×C47—24no—
195C2×C4×C47—24no—
196C2×C4×C47—24no—
197C2×C4×C47—24no—
198C2×C4×C47—24no—
199C2×C4×C47—22no—
200C2×C4×C47—22no—
201C2×C4×C47—24no—
202C2×C4×C47—24no—
203C2×C4×C47—24no—
204C2×C4×C47—24no—
205C2×C4×C47—24no—
206C2×C4×C47—24no—
207C2×C4×C47—24no—
208C2×C4×C47—41no—
209C2×C4×C47—41no—
210C2×C4×C47—42no—
211C2×C4×C47—42no—
212C2×C4×C47—41no—
213C2×C4×C47—42no—
214C2×C4×C47—41no—
215C2×C4×C47—42no—
216C2×C4×C47—42no—
217C2×C4×C47—42no—
218C2×C4×C47—42no—
219C2×C4×C47—42no—
220C2×C4×C47—42no—
221C2×C4×C47—42no—
222C2×C4×C47—41no—
223C2×C4×C47—41no—
224C2×C4×C47—42no—
225C2×C4×C47—42no—
226C2×C4×C47—41no—
227C2×C4×C47—41no—
228C2×C4×C47—41no—
229C2×C4×C47—41no—
230C2×C4×C47—42no—
231C2×C4×C47—42no—
232C2×C4×C47—42no—
233C2×C4×C47—42no—
234C2×C4×C47—42no—
235C2×C4×C47—42no—
236C2×C4×C47—42no—
237C2×C4×C47—42no—
238C2×C4×C47—42no—
239C2×C4×C47#12014yes—
240C2×C4×C47C22⋊Q814yes—
241C2×C4×C47C22⋊Q814yes—
242C2×C4×C47C22⋊Q818yes—
243#14878C4711yesmaximal, characteristic, direct product factor, Sylow
244C22×C47C2×#12011yescharacteristic
245C22×C47C2×C22⋊Q811yescharacteristic
246C22×C47C2×C22⋊Q811yescharacteristic
247C22×C47C2×C22⋊Q812yes—
248C22×C47#52511yescharacteristic
249C22×C47#52512yes—
250C22×C47#52912yes—
251C22×C47#53211yescharacteristic
252C22×C47#53312yes—
253C22×C47#53611yescharacteristic
254C22×C47#53711yescharacteristic
255C22×C47#54112yes—
256C22×C47#54212yes—
257C22×C47#54612yes—
258C22×C47#54712yes—
259C22×C47#54812yes—
260C22×C47D4×Q812yes—
261C22×C47#55212yes—
262C22×C47#55712yes—
263C22×C47#55711yescharacteristic
264C22×C47#55711yescharacteristic
265C22×C47Q8211yescharacteristic
266C22×C47#55911yescharacteristic
267C4×C47—28no—
268C4×C47—24no—
269C4×C47—24no—
270C4×C47—24no—
271C4×C47—42no—
272C4×C47—42no—
273C4×C47—44no—
274C4×C47—44no—
275C4×C47—81no—
276C4×C47—81no—
277C4×C47—82no—
278C22×C4×Q8C2×C4711yescharacteristic
279C2×#398C2×C4712yes—
280C2×#387C2×C4711yescharacteristic
281#1446C2×C4711yescharacteristic
282#1446C2×C4711yescharacteristic
283#1444C2×C4711yescharacteristic
284#1442C2×C4711yescharacteristic
285#1441C2×C4712yes—
286#1436C2×C4712yes—
287#1436C2×C4712yes—
288C4⋊#95C2×C4711yescharacteristic
289C2×C47#239611yescharacteristic
290C2×C47#240911yescharacteristic
291C2×C47#243011yescharacteristic
292C2×C47#245112yes—
293C2×C47#245312yes—
294C2×C47#245812yes—
295C2×C47#246212yes—
296C2×C47#256511yescharacteristic
297C2×C47#258211yescharacteristic
298C2×C47#263711yescharacteristic
299C2×C47#284811yescharacteristic
300C23×Q8C22×C4711yescharacteristic
301C2×C4×Q8—28no—
302C2×C4×Q8—24no—
303C22×C4⋊C4C22×C4711yescharacteristic
304C22×C4⋊C4C22×C4711yescharacteristic
305C22×C4⋊C4C22×C4712yes—
306C22×C4⋊C4C22×C4712yes—
307C22×C4⋊C4C22×C4712yes—
308C22×C4⋊C4C22×C4711yescharacteristic
309C22×C42C22×C4712yes—
310C22×C42C22×C4711yescharacteristic
311#398—28no—
312#387—24no—
313C2×#95C22×C4712yes—
314C2×#95C22×C4712yes—
315C2×#95C22×C4712yes—
316C2×#95C22×C4712yes—
317C2×#95C22×C4711yescharacteristic
318C2×#95C22×C4711yescharacteristic
319C2×#95C22×C4711yescharacteristic
320C2×#95C22×C4712yes—
321C2×#95C22×C4712yes—
322C2×#95C22×C4712yes—
323C2×#95C22×C4711yescharacteristic
324C2×#95C22×C4711yescharacteristic
325C2×#95C22×C4711yescharacteristic
326C2×#95C22×C4712yes—
327C47#1487811yescharacteristic, direct product factor, Sylow
328C22×Q8—24no—
329C22×Q8—22no—
330C22×Q8—24no—
331C22×Q8—22no—
332C22×Q8Q8×C4714yes—
333C23×C4C23×C4711yescharacteristic
334C23×C4C23×C4712yes—
335C23×C4C23×C4711yescharacteristic
336C23×C4C23×C4712yes—
337C23×C4C23×C4711yescharacteristic
338C23×C4C23×C4711yescharacteristic
339C23×C4C23×C4712yes—
340C23×C4C23×C4711yescharacteristic
341C23×C4C23×C4712yes—
342C23×C4C23×C4711yescharacteristic
343C23×C4C23×C4711yescharacteristic
344C4×Q8—232no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4D4×C4718yes—
360C2×C4⋊C4Q8×C4714yescomplemented
361C2×C42—24no—
362C2×C42—24no—
363C2×C42—24no—
364C2×C42—24no—
365C2×C42D4×C4714yes—
366#95—22no—
367#95—22no—
368#95—22no—
369#95—22no—
370#95—24no—
371#95—24no—
372#95—24no—
373#95—24no—
374#95—22no—
375#95—24no—
376#95—24no—
377#95—24no—
378#95—22no—
379#95—42no—
380C24C24×C4711yescharacteristic
381C2×Q8—28no—
382C2×Q8—28no—
383C2×Q8—216no—
384C2×Q8—28no—
385C2×Q8—216no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4C2×D4×C4714yes—
435C22×C4C2×D4×C4712yes—
436C22×C4C2×D4×C4714yes—
437C22×C4C2×D4×C4714yes—
438C22×C4C2×D4×C4712yes—
439C22×C4C2×D4×C4712yes—
440C22×C4C2×Q8×C4712yes—
441C22×C4C2×Q8×C4712yes—
442C22×C4C2×Q8×C4712yes—
443C22×C4C2×Q8×C4714yes—
444C22×C4C2×Q8×C4712yes—
445C22×C4#41×C4714yes—
446C22×C4#41×C4712yes—
447C22×C4#41×C4714yes—
448C22×C4#41×C4712yes—
449C4⋊C4—28no—
450C4⋊C4—216no—
451C4⋊C4—28no—
452C4⋊C4—48no—
453C4⋊C4—48no—
454C4⋊C4—44no—
455C42—216no—
456C42—28no—
457C23C22×D4×C4711yescharacteristic
458C23C22×D4×C4712yes—
459C23C22×Q8×C4711yescharacteristic
460C23C22×Q8×C4711yescharacteristic
461C23C2×#41×C4712yes—
462C23C2×#41×C4711yescharacteristic
463C23C2×#41×C4711yescharacteristic
464C23C2×#41×C4712yes—
465C23H(5,𝔽2)×C4711yescharacteristic
466C232−1+4×C4712yes—
467C232−1+4×C4711yescharacteristic
468Q8—232no—
469C2×C4—22no—
470C2×C4—24no—
471C2×C4—22no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—22no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4#120×C4714yes—
529C2×C4C22⋊Q8×C4714yes—
530C2×C4C22⋊Q8×C4714yes—
531C2×C4C22⋊Q8×C4718yes—
532C22C2×#120×C4711yescharacteristic
533C22C2×C22⋊Q8×C4711yescharacteristic
534C22C2×C22⋊Q8×C4711yescharacteristic
535C22C2×C22⋊Q8×C4712yes—
536C22C47×#52511yescharacteristic
537C22C47×#52512yes—
538C22C47×#52912yes—
539C22C47×#53211yescharacteristic
540C22C47×#53312yes—
541C22C47×#53611yescharacteristic
542C22C47×#53711yescharacteristic
543C22C47×#54112yes—
544C22C47×#54212yes—
545C22C47×#54612yes—
546C22C47×#54712yes—
547C22C47×#54812yes—
548C22D4×Q8×C4712yes—
549C22C47×#55212yes—
550C22C47×#55712yes—
551C22C47×#55711yescharacteristic
552C22C47×#55711yescharacteristic
553C22Q82×C4711yescharacteristic
554C22C47×#55911yescharacteristic
555C4—28no—
556C4—24no—
557C4—24no—
558C4—24no—
559C4—42no—
560C4—42no—
561C4—44no—
562C4—44no—
563C4—81no—
564C4—81no—
565C4—82no—
566C2C47×#239611yescharacteristic
567C2C47×#240911yescharacteristic
568C2C47×#243011yescharacteristic
569C2C47×#245112yes—
570C2C47×#245312yes—
571C2C47×#245812yes—
572C2C47×#246212yes—
573C2C47×#256511yescharacteristic
574C2C47×#258211yescharacteristic
575C2C47×#263711yescharacteristic
576C2C47×#284811yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C47C24
commutator, Frattini, cosocleC24C24×C47
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C47 ◁ G

Complements

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

NH ≅ G/Ntype
71. C2×C4⋊C4×C47Q8semidirect
243. #14878C47direct (N × H)
327. C47#14878direct (N × H)
360. C2×C4⋊C4Q8×C47semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Q8×C472
C2×C47×#3982
C2×C47×#3872
C47×#14462
C47×#14442
C47×#14422
C47×#14412
C47×#14362
C47×C4⋊#952
#1487847