Finite Group Databasebeta

← C47×#25430 #26065128

Subgroups — C47×#25430 #26065128

Order 12032.

914 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#495C211yesmaximal, characteristic, complemented
2C2×C47×#471C211yesmaximal, characteristic, complemented
3C47×#3057C211yesmaximal, characteristic, complemented
4C47×#3044C211yesmaximal, characteristic, complemented
5C47×#3041C211yesmaximal, characteristic
6C47×#2949C211yesmaximal, characteristic, complemented
7C47×#2047C211yesmaximal, characteristic, complemented
8C47×#2045C211yesmaximal, characteristic, complemented
9C47×#2004C211yesmaximal, characteristic, complemented
10C47×#2003C211yesmaximal, characteristic, complemented
11C47×#1977C211yesmaximal, characteristic, complemented
12C47×#1945C211yesmaximal, characteristic, complemented
13C47×#1888C211yesmaximal, characteristic, complemented
14C47×#1885C211yesmaximal, characteristic, complemented
15C47×#1764C211yesmaximal, characteristic, complemented
16C2×#137×C47C2211yescharacteristic
17C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
18C22×Q16×C47C2211yescharacteristic
19C22×SD16×C47C2211yescharacteristic
20C22×SD16×C47C2211yescharacteristic
21C22×D8×C47C2211yescharacteristic
22C2×#131×C47C2211yescharacteristic
23C47×#536C2211yescharacteristic
24C47×#535C2211yescharacteristic
25C2×#124×C47C2211yescharacteristic
26C2×#124×C47C2211yescharacteristic
27C47×#519C2211yescharacteristic
28C47×#518C2211yescharacteristic
29C47×#495—24no—
30C47×#471—24no—
31C47×#468—22no—
32C47×#465—22no—
33C47×#464—22no—
34C47×#463—22no—
35C47×#462—22no—
36C47×#459—22no—
37C47×#440—22no—
38C4×SD16×C47—22no—
39C2×#108×C47C2211yescharacteristic
40C47×#427C2211yescharacteristic
41C47×#424C2211yescharacteristic
42C47×#424C2211yescharacteristic
43C2×#104×C47C2211yescharacteristic
44C47×#419C2211yescharacteristic
45C47×#419C2211yescharacteristic
46C47×#419C2211yescharacteristic
47C47×#418C2211yescharacteristic
48C47×#418C2211yescharacteristic
49C47×#418C2211yescharacteristic
50C47×#416C2211yescharacteristic
51C2×#101×C47C2211yescharacteristic
52C2×#101×C47C2211yescharacteristic
53C2×#100×C47C2211yescharacteristic
54C2×#100×C47C2211yescharacteristic
55C47×#405C2211yescharacteristic
56C2×C4×C8×C47C2211yescharacteristic
57C47×#341C2211yescharacteristic
58C47×#339C2211yescharacteristic
59C47×#339C2211yescharacteristic
60C47×#339C2211yescharacteristic
61C2×#41×C47C2311yescharacteristic
62C22×Q8×C47C2311yescharacteristic
63C22×Q8×C47C2311yescharacteristic
64C22×D4×C47C2311yescharacteristic
65C22×D4×C47C2311yescharacteristic
66#137×C47—22no—
67#137×C47—41no—
68AGL(1,ℤ/8)×C47—22no—
69AGL(1,ℤ/8)×C47—41no—
70C2×Q16×C47—21no—
71C2×Q16×C47—22no—
72C2×Q16×C47—22no—
73C2×Q16×C47—41no—
74C2×SD16×C47—21no—
75C2×SD16×C47—21no—
76C2×SD16×C47—21no—
77C2×SD16×C47—21no—
78C2×SD16×C47—21no—
79C2×SD16×C47—21no—
80C2×SD16×C47—22no—
81C2×SD16×C47—22no—
82C2×SD16×C47—22no—
83C2×SD16×C47D414yescomplemented
84C2×D8×C47—21no—
85C2×D8×C47—22no—
86C2×D8×C47—22no—
87C2×D8×C47—41no—
88#131×C47—22no—
89#131×C47—22no—
90C2×M16×C47—21no—
91C2×M16×C47C2311yescharacteristic
92C2×M16×C47C2311yescharacteristic
93C2×M16×C47C2311yescharacteristic
94C2×M16×C47C2311yescharacteristic
95C22×C8×C47—21no—
96C22×C8×C47C2311yescharacteristic
97C22×C8×C47C2311yescharacteristic
98C4⋊Q8×C47—21no—
99#127×C47—21no—
100#124×C47—21no—
101#124×C47—22no—
102#124×C47—21no—
103#124×C47—22no—
104#124×C47—22no—
105#124×C47—22no—
106#123×C47—41no—
107C22⋊Q8×C47—22no—
108#121×C47—22no—
109#120×C47—41no—
110C4×Q8×C47—22no—
111C4×Q8×C47—22no—
112C4×D4×C47—22no—
113C4×D4×C47—22no—
114#117×C47—41no—
115#117×C47C2311yescharacteristic
116#117×C47C2311yescharacteristic
117#117×C47C2311yescharacteristic
118C2×C22⋊C4×C47—41no—
119C2×C22⋊C4×C47—41no—
120C2×C22⋊C4×C47—41no—
121C2×C42×C47C2311yescharacteristic
122#108×C47—22no—
123#107×C47D412yes—
124#106×C47D412yes—
125C4⋊C8×C47—22no—
126C4⋊C8×C47—22no—
127#104×C47—22no—
128#103×C47—22no—
129#103×C47—22no—
130#103×C47—22no—
131#103×C47D412yes—
132#102×C47—22no—
133#102×C47—22no—
134#102×C47—22no—
135#102×C47D412yes—
136#101×C47—22no—
137#101×C47—41no—
138#100×C47—22no—
139#100×C47—41no—
140#97×C47—21no—
141C4×C8×C47—22no—
142C4×C8×C47—21no—
143C24×C47—21no—
144C24×C47—21no—
145#41×C47—21no—
146#41×C47—21no—
147#41×C47—21no—
148#41×C47—21no—
149C2×Q8×C47—21no—
150C2×Q8×C47—21no—
151C2×Q8×C47—21no—
152C2×Q8×C47—21no—
153C2×Q8×C47—21no—
154C2×Q8×C47—21no—
155C2×Q8×C47—21no—
156C2×Q8×C47—21no—
157C2×Q8×C47—21no—
158C2×Q8×C47—21no—
159C2×Q8×C47—21no—
160C2×Q8×C47C2×D411yescharacteristic
161C2×Q8×C47C2×D412yes—
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—21no—
173C2×D4×C47—21no—
174C2×D4×C47—42no—
175C2×D4×C47C2×D411yescharacteristic
176C2×D4×C47C2×D412yes—
177C22×C4×C47—21no—
178C22×C4×C47—21no—
179C22×C4×C47—21no—
180C22×C4×C47—21no—
181C22×C4×C47—42no—
182C22×C4×C47C2411yescharacteristic
183Q16×C47—44no—
184Q16×C47—42no—
185SD16×C47—24no—
186SD16×C47—24no—
187SD16×C47—42no—
188SD16×C47—42no—
189SD16×C47—42no—
190SD16×C47—42no—
191D8×C47—44no—
192D8×C47—42no—
193M16×C47—21no—
194M16×C47—21no—
195M16×C47—21no—
196M16×C47—21no—
197M16×C47—21no—
198M16×C47—21no—
199M16×C47—21no—
200M16×C47—21no—
201M16×C47—42no—
202C2×C8×C47—21no—
203C2×C8×C47—21no—
204C2×C8×C47—21no—
205C2×C8×C47—21no—
206C2×C8×C47—21no—
207C2×C8×C47—21no—
208C2×C8×C47—42no—
209C2×C8×C47C2×D412yes—
210C2×C8×C47C2×D411yescharacteristic
211C2×C8×C47C2×D411yescharacteristic
212C2×C8×C47C2×D412yes—
213C2×C8×C47#4112yes—
214C4⋊C4×C47—42no—
215C4⋊C4×C47—42no—
216C4⋊C4×C47C2×D412yes—
217C4⋊C4×C47C2×D412yes—
218C4⋊C4×C47C2×D412yes—
219C22⋊C4×C47—21no—
220C22⋊C4×C47—21no—
221C22⋊C4×C47—21no—
222C22⋊C4×C47—42no—
223C22⋊C4×C47—44no—
224C22⋊C4×C47—42no—
225C22⋊C4×C47—44no—
226C22⋊C4×C47—42no—
227C42×C47—21no—
228C42×C47—21no—
229C42×C47—21no—
230C42×C47—21no—
231C42×C47—42no—
232C42×C47#4112yes—
233C23×C47—21no—
234C23×C47—22no—
235C23×C47—41no—
236C23×C47—41no—
237C23×C47—41no—
238C23×C47—41no—
239C23×C47—41no—
240C23×C47—82no—
241C23×C47—82no—
242C23×C47H(5,𝔽2)11yescharacteristic
243Q8×C47—22no—
244Q8×C47—21no—
245Q8×C47—21no—
246Q8×C47—22no—
247Q8×C47—41no—
248Q8×C47—41no—
249Q8×C47—41no—
250Q8×C47—41no—
251Q8×C47—41no—
252Q8×C47—41no—
253D4×C47—22no—
254D4×C47—21no—
255D4×C47—22no—
256D4×C47—21no—
257D4×C47—41no—
258D4×C47—41no—
259D4×C47—41no—
260D4×C47—41no—
261D4×C47—41no—
262D4×C47—41no—
263D4×C47—41no—
264D4×C47—41no—
265D4×C47—162no—
266C2×C4×C47—22no—
267C2×C4×C47—22no—
268C2×C4×C47—22no—
269C2×C4×C47—21no—
270C2×C4×C47—22no—
271C2×C4×C47—22no—
272C2×C4×C47—42no—
273C2×C4×C47—41no—
274C2×C4×C47—41no—
275C2×C4×C47—41no—
276C2×C4×C47—41no—
277C2×C4×C47—41no—
278C2×C4×C47—41no—
279C2×C4×C47—41no—
280C2×C4×C47—162no—
281C2×C4×C47C22×D411yescharacteristic
282C2×C4×C47C22×D411yescharacteristic
283C2×C4×C47C22×D411yescharacteristic
284C2×C4×C47C2×#4111yescharacteristic
285C2×C4×C47C2×#4111yescharacteristic
286C2×C4×C47H(5,𝔽2)11yescharacteristic
287C8×C47—22no—
288C8×C47—41no—
289C8×C47—41no—
290C8×C47—41no—
291C8×C47—41no—
292C8×C47#12112yes—
293C8×C47#12112yes—
294#25430C4711yesmaximal, characteristic, direct product factor, Sylow
295C22×C47—22no—
296C22×C47—41no—
297C22×C47—42no—
298C22×C47—42no—
299C22×C47—82no—
300C22×C47—82no—
301C22×C47—82no—
302C22×C47—81no—
303C22×C47—82no—
304C22×C47—161no—
305C22×C47—161no—
306C22×C47#54011yescharacteristic
307C22×C47D4211yescharacteristic
308C22×C47#54611yescharacteristic
309C4×C47—42no—
310C4×C47—41no—
311C4×C47—42no—
312C4×C47—42no—
313C4×C47—42no—
314C4×C47—42no—
315C4×C47—81no—
316C4×C47C2×#12111yescharacteristic
317C4×C47#53211yescharacteristic
318C4×C47D4211yescharacteristic
319C4×C47#55011yescharacteristic
320C2×#495C2×C4711yescharacteristic, complemented
321C2×#471C2×C4711yescharacteristic, complemented
322#3057C2×C4711yescharacteristic, complemented
323#3044C2×C4711yescharacteristic, complemented
324#3041C2×C4711yescharacteristic
325#2949C2×C4711yescharacteristic, complemented
326#2047C2×C4711yescharacteristic, complemented
327#2045C2×C4711yescharacteristic, complemented
328#2004C2×C4711yescharacteristic, complemented
329#2003C2×C4711yescharacteristic, complemented
330#1977C2×C4711yescharacteristic, complemented
331#1945C2×C4711yescharacteristic, complemented
332#1888C2×C4711yescharacteristic, complemented
333#1885C2×C4711yescharacteristic, complemented
334#1764C2×C4711yescharacteristic, complemented
335C2×C47—21no—
336C2×C47—21no—
337C2×C47—81no—
338C2×C47—82no—
339C2×C47—161no—
340C2×C47#242811yescharacteristic
341C2×C47#329012yes—
342C2×#137C22×C4711yescharacteristic
343C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
344C22×Q16C22×C4711yescharacteristic
345C22×SD16C22×C4711yescharacteristic
346C22×SD16C22×C4711yescharacteristic
347C22×D8C22×C4711yescharacteristic
348C2×#131C22×C4711yescharacteristic
349#536C22×C4711yescharacteristic
350#535C22×C4711yescharacteristic
351C2×#124C22×C4711yescharacteristic
352C2×#124C22×C4711yescharacteristic
353#519C22×C4711yescharacteristic
354#518C22×C4711yescharacteristic
355#495—24no—
356#471—24no—
357#468—22no—
358#465—22no—
359#464—22no—
360#463—22no—
361#462—22no—
362#459—22no—
363#440—22no—
364C4×SD16—22no—
365C2×#108C22×C4711yescharacteristic
366#427C22×C4711yescharacteristic
367#424C22×C4711yescharacteristic
368#424C22×C4711yescharacteristic
369C2×#104C22×C4711yescharacteristic
370#419C22×C4711yescharacteristic
371#419C22×C4711yescharacteristic
372#419C22×C4711yescharacteristic
373#418C22×C4711yescharacteristic
374#418C22×C4711yescharacteristic
375#418C22×C4711yescharacteristic
376#416C22×C4711yescharacteristic
377C2×#101C22×C4711yescharacteristic
378C2×#101C22×C4711yescharacteristic
379C2×#100C22×C4711yescharacteristic
380C2×#100C22×C4711yescharacteristic
381#405C22×C4711yescharacteristic
382C2×C4×C8C22×C4711yescharacteristic
383#341C22×C4711yescharacteristic
384#339C22×C4711yescharacteristic
385#339C22×C4711yescharacteristic
386#339C22×C4711yescharacteristic
387C47#2543011yescharacteristic, direct product factor, Sylow
388C2×#41C23×C4711yescharacteristic
389C22×Q8C23×C4711yescharacteristic
390C22×Q8C23×C4711yescharacteristic
391C22×D4C23×C4711yescharacteristic
392C22×D4C23×C4711yescharacteristic
393#137—22no—
394#137—41no—
395AGL(1,ℤ/8)—22no—
396AGL(1,ℤ/8)—41no—
397C2×Q16—22no—
398C2×Q16—21no—
399C2×Q16—22no—
400C2×Q16—41no—
401C2×SD16—21no—
402C2×SD16—21no—
403C2×SD16—21no—
404C2×SD16—21no—
405C2×SD16—21no—
406C2×SD16—21no—
407C2×SD16—22no—
408C2×SD16—22no—
409C2×SD16—22no—
410C2×SD16D4×C4714yescomplemented
411C2×D8—22no—
412C2×D8—21no—
413C2×D8—22no—
414C2×D8—41no—
415#131—22no—
416#131—22no—
417C2×M16—21no—
418C2×M16C23×C4711yescharacteristic
419C2×M16C23×C4711yescharacteristic
420C2×M16C23×C4711yescharacteristic
421C2×M16C23×C4711yescharacteristic
422C22×C8—21no—
423C22×C8C23×C4711yescharacteristic
424C22×C8C23×C4711yescharacteristic
425C4⋊Q8—21no—
426#127—21no—
427#124—22no—
428#124—21no—
429#124—22no—
430#124—21no—
431#124—22no—
432#124—22no—
433#123—41no—
434C22⋊Q8—22no—
435#121—22no—
436#120—41no—
437C4×Q8—22no—
438C4×Q8—22no—
439C4×D4—22no—
440C4×D4—22no—
441#117—41no—
442#117C23×C4711yescharacteristic
443#117C23×C4711yescharacteristic
444#117C23×C4711yescharacteristic
445C2×C22⋊C4—41no—
446C2×C22⋊C4—41no—
447C2×C22⋊C4—41no—
448C2×C42C23×C4711yescharacteristic
449#108—22no—
450#107D4×C4712yes—
451#106D4×C4712yes—
452C4⋊C8—22no—
453C4⋊C8—22no—
454#104—22no—
455#103—22no—
456#103—22no—
457#103—22no—
458#103D4×C4712yes—
459#102—22no—
460#102—22no—
461#102—22no—
462#102D4×C4712yes—
463#101—22no—
464#101—41no—
465#100—22no—
466#100—41no—
467#97—21no—
468C4×C8—22no—
469C4×C8—21no—
470C24—21no—
471C24—21no—
472#41—21no—
473#41—21no—
474#41—21no—
475#41—21no—
476C2×Q8—21no—
477C2×Q8—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×Q8C2×D4×C4712yes—
488C2×Q8C2×D4×C4711yescharacteristic
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—42no—
502C2×D4C2×D4×C4712yes—
503C2×D4C2×D4×C4711yescharacteristic
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—42no—
509C22×C4C24×C4711yescharacteristic
510Q16—44no—
511Q16—42no—
512SD16—24no—
513SD16—24no—
514SD16—42no—
515SD16—42no—
516SD16—42no—
517SD16—42no—
518D8—44no—
519D8—42no—
520M16—21no—
521M16—21no—
522M16—21no—
523M16—21no—
524M16—21no—
525M16—21no—
526M16—21no—
527M16—21no—
528M16—42no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—42no—
536C2×C8C2×D4×C4712yes—
537C2×C8C2×D4×C4711yescharacteristic
538C2×C8C2×D4×C4712yes—
539C2×C8C2×D4×C4711yescharacteristic
540C2×C8#41×C4712yes—
541C4⋊C4—42no—
542C4⋊C4—42no—
543C4⋊C4C2×D4×C4712yes—
544C4⋊C4C2×D4×C4712yes—
545C4⋊C4C2×D4×C4712yes—
546C22⋊C4—21no—
547C22⋊C4—21no—
548C22⋊C4—21no—
549C22⋊C4—42no—
550C22⋊C4—44no—
551C22⋊C4—42no—
552C22⋊C4—44no—
553C22⋊C4—42no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—21no—
558C42—42no—
559C42#41×C4712yes—
560C23—21no—
561C23—22no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—82no—
568C23—82no—
569C23H(5,𝔽2)×C4711yescharacteristic
570Q8—22no—
571Q8—21no—
572Q8—21no—
573Q8—22no—
574Q8—41no—
575Q8—41no—
576Q8—41no—
577Q8—41no—
578Q8—41no—
579Q8—41no—
580D4—22no—
581D4—21no—
582D4—22no—
583D4—21no—
584D4—41no—
585D4—41no—
586D4—41no—
587D4—41no—
588D4—41no—
589D4—41no—
590D4—41no—
591D4—41no—
592D4—162no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—42no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—162no—
608C2×C4C22×D4×C4711yescharacteristic
609C2×C4C22×D4×C4711yescharacteristic
610C2×C4C22×D4×C4711yescharacteristic
611C2×C4C2×#41×C4711yescharacteristic
612C2×C4C2×#41×C4711yescharacteristic
613C2×C4H(5,𝔽2)×C4711yescharacteristic
614C8—22no—
615C8—41no—
616C8—41no—
617C8—41no—
618C8—41no—
619C8#121×C4712yes—
620C8#121×C4712yes—
621C22—22no—
622C22—42no—
623C22—41no—
624C22—42no—
625C22—82no—
626C22—82no—
627C22—82no—
628C22—82no—
629C22—81no—
630C22—161no—
631C22—161no—
632C22C47×#54011yescharacteristic
633C22D42×C4711yescharacteristic
634C22C47×#54611yescharacteristic
635C4—42no—
636C4—42no—
637C4—42no—
638C4—42no—
639C4—41no—
640C4—42no—
641C4—81no—
642C4C2×#121×C4711yescharacteristic
643C4C47×#53211yescharacteristic
644C4D42×C4711yescharacteristic
645C4C47×#55011yescharacteristic
646C2—21no—
647C2—21no—
648C2—81no—
649C2—82no—
650C2—161no—
651C2C47×#242811yescharacteristic
652C2C47×#329012yes—
subgroupG/H
center, socleC22×C47D42
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC47×#3041C2
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×#495C2semidirect
2. C2×C47×#471C2semidirect
3. C47×#3057C2semidirect
4. C47×#3044C2semidirect
6. C47×#2949C2semidirect
7. C47×#2047C2semidirect
8. C47×#2045C2semidirect
9. C47×#2004C2semidirect
10. C47×#2003C2semidirect
11. C47×#1977C2semidirect
12. C47×#1945C2semidirect
13. C47×#1888C2semidirect
14. C47×#1885C2semidirect
15. C47×#1764C2semidirect
83. C2×SD16×C47D4semidirect
294. #25430C47direct (N × H)
320. C2×#495C2×C47semidirect
321. C2×#471C2×C47semidirect
322. #3057C2×C47semidirect
323. #3044C2×C47semidirect
325. #2949C2×C47semidirect
326. #2047C2×C47semidirect
327. #2045C2×C47semidirect
328. #2004C2×C47semidirect
329. #2003C2×C47semidirect
330. #1977C2×C47semidirect
331. #1945C2×C47semidirect
332. #1888C2×C47semidirect
333. #1885C2×C47semidirect
334. #1764C2×C47semidirect
387. C47#25430direct (N × H)
410. C2×SD16D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4952
C2×C47×#4712
C47×#30572
C47×#30442
C47×#30412
C47×#29492
C47×#20472
C47×#20452
C47×#20042
C47×#20032
C47×#19772
C47×#19452
C47×#18882
C47×#18852
C47×#17642
#2543047