Finite Group Databasebeta

← C47×#24808 #26064506

Subgroups — C47×#24808 #26064506

Order 12032.

820 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3069C211yesmaximal, characteristic, complemented
2C47×#3068C211yesmaximal, characteristic
3C2×C47×#471C211yesmaximal, characteristic, complemented
4C2×C47×#471C211yesmaximal, characteristic, complemented
5C47×#2955C211yesmaximal, characteristic, complemented
6C47×#2916C211yesmaximal, characteristic, complemented
7C47×#2070C211yesmaximal, characteristic, complemented
8C47×#2069C211yesmaximal, characteristic, complemented
9C47×#2049C211yesmaximal, characteristic, complemented
10C47×#2048C211yesmaximal, characteristic, complemented
11C47×#1977C211yesmaximal, characteristic, complemented
12C47×#1953C211yesmaximal, characteristic, complemented
13C47×#1903C211yesmaximal, characteristic, complemented
14C47×#1902C211yesmaximal, characteristic, complemented
15C47×#1813C211yesmaximal, characteristic, complemented
16C47×#575C2211yescharacteristic
17C2×#137×C47C2211yescharacteristic
18C2×#137×C47C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
21C22×SD16×C47C2211yescharacteristic
22C47×#568C2211yescharacteristic
23C47×#568C2211yescharacteristic
24C2×#131×C47C2211yescharacteristic
25C2×#131×C47C2211yescharacteristic
26C47×#473—22no—
27C47×#472—22no—
28C47×#471—22no—
29C47×#471—22no—
30C47×#471—22no—
31C47×#471—22no—
32C47×#471—22no—
33C47×#471—22no—
34C47×#444—22no—
35C47×#443—22no—
36C47×#430—22no—
37C47×#430C2211yescharacteristic
38C47×#430C2211yescharacteristic
39C47×#430C2211yescharacteristic
40C47×#430C2211yescharacteristic
41C47×#430C2211yescharacteristic
42C2×#108×C47—22no—
43C2×#108×C47C2211yescharacteristic
44C2×#108×C47C2211yescharacteristic
45C2×#108×C47C2211yescharacteristic
46C47×#421C2211yescharacteristic
47C47×#421C2211yescharacteristic
48C47×#419C2211yescharacteristic
49C47×#418C2211yescharacteristic
50C47×#413C2211yescharacteristic
51C47×#413C2211yescharacteristic
52C2×#101×C47C2211yescharacteristic
53C2×#101×C47C2211yescharacteristic
54C2×#101×C47C2211yescharacteristic
55C2×#100×C47C2211yescharacteristic
56C2×#100×C47C2211yescharacteristic
57C2×#100×C47C2211yescharacteristic
58C47×#405C2211yescharacteristic
59C47×#344C2211yescharacteristic
60C47×#344C2211yescharacteristic
61C47×#338C2211yescharacteristic
62C47×#338C2211yescharacteristic
63C2×#41×C47C2311yescharacteristic
64C2×#41×C47C2311yescharacteristic
65C22×Q8×C47C2311yescharacteristic
66C22×D4×C47C2311yescharacteristic
67#137×C47—21no—
68#137×C47—22no—
69#137×C47—22no—
70#137×C47—22no—
71#137×C47—41no—
72#137×C47D412yes—
73AGL(1,ℤ/8)×C47—21no—
74AGL(1,ℤ/8)×C47—22no—
75AGL(1,ℤ/8)×C47—22no—
76AGL(1,ℤ/8)×C47—22no—
77AGL(1,ℤ/8)×C47—41no—
78AGL(1,ℤ/8)×C47D412yes—
79#135×C47—22no—
80C2×Q16×C47—21no—
81C2×Q16×C47—21no—
82C2×SD16×C47—21no—
83C2×SD16×C47—21no—
84C2×SD16×C47—21no—
85C2×SD16×C47—21no—
86C2×SD16×C47—21no—
87C2×SD16×C47—21no—
88C2×SD16×C47—21no—
89C2×SD16×C47—21no—
90C2×SD16×C47—21no—
91C2×SD16×C47—21no—
92C2×D8×C47—21no—
93C2×D8×C47—21no—
94#131×C47—21no—
95#131×C47—21no—
96#131×C47—22no—
97#131×C47—22no—
98#131×C47—21no—
99#131×C47—21no—
100#131×C47—21no—
101#131×C47—21no—
102#131×C47—41no—
103#131×C47—41no—
104#131×C47D412yes—
105#131×C47D412yes—
106C2×M16×C47—21no—
107C2×M16×C47—21no—
108C2×M16×C47—22no—
109C2×M16×C47—22no—
110C2×M16×C47C2311yescharacteristic
111C2×M16×C47C2311yescharacteristic
112C2×M16×C47C2311yescharacteristic
113C2×M16×C47C2311yescharacteristic
114C2×M16×C47C2311yescharacteristic
115C2×M16×C47C2311yescharacteristic
116C2×M16×C47C2311yescharacteristic
117C2×M16×C47C2311yescharacteristic
118C2×M16×C47C2311yescharacteristic
119C22×C8×C47—21no—
120C22×C8×C47—21no—
121C22×C8×C47C2311yescharacteristic
122#117×C47C2311yescharacteristic
123#108×C47—22no—
124#108×C47—22no—
125#108×C47—22no—
126#108×C47—22no—
127#108×C47—22no—
128#108×C47—21no—
129#108×C47—21no—
130#108×C47—21no—
131#108×C47—21no—
132#108×C47D412yes—
133#108×C47D412yes—
134#104×C47—22no—
135#104×C47—22no—
136#103×C47—41no—
137#102×C47—41no—
138#101×C47—21no—
139#101×C47—21no—
140#101×C47—22no—
141#101×C47—22no—
142#101×C47—22no—
143#100×C47—21no—
144#100×C47—21no—
145#100×C47—22no—
146#100×C47—22no—
147#100×C47—22no—
148#97×C47—21no—
149C4×C8×C47—21no—
150C24×C47—21no—
151#41×C47—21no—
152#41×C47—21no—
153#41×C47—21no—
154#41×C47—21no—
155#41×C47—21no—
156#41×C47—21no—
157#41×C47C2×D412yes—
158#41×C47C2×D412yes—
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×C47C2×D411yescharacteristic
166C2×Q8×C47#4111yescharacteristic
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—21no—
175C2×D4×C47C2×D411yescharacteristic
176C2×D4×C47#4111yescharacteristic
177C22×C4×C47—21no—
178C22×C4×C47—21no—
179C22×C4×C47—21no—
180C22×C4×C47C2411yescharacteristic
181Q16×C47—22no—
182Q16×C47—42no—
183Q16×C47—42no—
184SD16×C47—22no—
185SD16×C47—22no—
186SD16×C47—42no—
187SD16×C47—42no—
188SD16×C47—42no—
189SD16×C47—42no—
190SD16×C47—41no—
191SD16×C47—41no—
192SD16×C47—41no—
193SD16×C47—41no—
194D8×C47—22no—
195D8×C47—42no—
196D8×C47—42no—
197M16×C47—21no—
198M16×C47—21no—
199M16×C47—21no—
200M16×C47—21no—
201M16×C47—22no—
202M16×C47—22no—
203M16×C47—21no—
204M16×C47—21no—
205M16×C47—21no—
206M16×C47—21no—
207M16×C47—21no—
208M16×C47—21no—
209M16×C47—21no—
210M16×C47—21no—
211M16×C47—21no—
212M16×C47—21no—
213M16×C47—42no—
214M16×C47—42no—
215M16×C47—41no—
216M16×C47—41no—
217M16×C47C2×D412yes—
218M16×C47C2×D412yes—
219M16×C47C2×D412yes—
220M16×C47C2×D412yes—
221C2×C8×C47—21no—
222C2×C8×C47—21no—
223C2×C8×C47—21no—
224C2×C8×C47—21no—
225C2×C8×C47—22no—
226C2×C8×C47—22no—
227C2×C8×C47—21no—
228C2×C8×C47—21no—
229C2×C8×C47—21no—
230C2×C8×C47—21no—
231C2×C8×C47—21no—
232C2×C8×C47—42no—
233C2×C8×C47—42no—
234C2×C8×C47—41no—
235C2×C8×C47—41no—
236C2×C8×C47C2×D411yescharacteristic
237C2×C8×C47C2×D411yescharacteristic
238C2×C8×C47C2×D411yescharacteristic
239C2×C8×C47C2×D411yescharacteristic
240C2×C8×C47#4111yescharacteristic
241C2×C8×C47#4111yescharacteristic
242C4⋊C4×C47—21no—
243C22⋊C4×C47—21no—
244C42×C47—21no—
245C23×C47—21no—
246C23×C47—21no—
247C23×C47—41no—
248C23×C47—41no—
249C23×C47—41no—
250C23×C47—161no—
251C23×C472−1+411yescharacteristic
252Q8×C47—21no—
253Q8×C47—21no—
254Q8×C47—21no—
255Q8×C47—41no—
256Q8×C47—41no—
257Q8×C47—41no—
258Q8×C47—41no—
259Q8×C47#12112yes—
260D4×C47—22no—
261D4×C47—22no—
262D4×C47—21no—
263D4×C47—21no—
264D4×C47—21no—
265D4×C47—41no—
266D4×C47—41no—
267D4×C47—41no—
268D4×C47—41no—
269D4×C47—41no—
270D4×C47—41no—
271D4×C47#12112yes—
272C2×C4×C47—21no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—21no—
276C2×C4×C47—41no—
277C2×C4×C47—41no—
278C2×C4×C47—41no—
279C2×C4×C47—41no—
280C2×C4×C47—41no—
281C2×C4×C47—41no—
282C2×C4×C47C22×D411yescharacteristic
283C2×C4×C47C22×D411yescharacteristic
284C2×C4×C47C22×D411yescharacteristic
285C2×C4×C47C2×#4111yescharacteristic
286C2×C4×C47C2×#4111yescharacteristic
287C2×C4×C47H(5,𝔽2)11yescharacteristic
288C8×C47—22no—
289C8×C47—22no—
290C8×C47—22no—
291C8×C47—22no—
292C8×C47—41no—
293C8×C47—41no—
294C8×C47—41no—
295C8×C47—41no—
296C8×C47—41no—
297C8×C47#12111yescharacteristic
298C8×C47#12111yescharacteristic
299C8×C47#12111yescharacteristic
300C8×C47#12111yescharacteristic
301#24808C4711yesmaximal, characteristic, direct product factor, Sylow
302C22×C47—22no—
303C22×C47—41no—
304C22×C47—41no—
305C22×C47—81no—
306C22×C47—81no—
307C22×C47—81no—
308C22×C47—161no—
309C22×C47—161no—
310C22×C47—161no—
311C22×C47#53711yescharacteristic
312C22×C47#54711yescharacteristic
313C22×C47#54811yescharacteristic
314C4×C47—22no—
315C4×C47—41no—
316C4×C47—81no—
317C4×C47—81no—
318C4×C47C2×#12111yescharacteristic
319C4×C47C2×#12111yescharacteristic
320C4×C47D4211yescharacteristic
321C4×C47#55311yescharacteristic
322#3069C2×C4711yescharacteristic, complemented
323#3068C2×C4711yescharacteristic
324C2×#471C2×C4711yescharacteristic, complemented
325C2×#471C2×C4711yescharacteristic, complemented
326#2955C2×C4711yescharacteristic, complemented
327#2916C2×C4711yescharacteristic, complemented
328#2070C2×C4711yescharacteristic, complemented
329#2069C2×C4711yescharacteristic, complemented
330#2049C2×C4711yescharacteristic, complemented
331#2048C2×C4711yescharacteristic, complemented
332#1977C2×C4711yescharacteristic, complemented
333#1953C2×C4711yescharacteristic, complemented
334#1903C2×C4711yescharacteristic, complemented
335#1902C2×C4711yescharacteristic, complemented
336#1813C2×C4711yescharacteristic, complemented
337C2×C47—21no—
338C2×C47—21no—
339C2×C47—21no—
340C2×C47—42no—
341C2×C47—81no—
342C2×C47—161no—
343C2×C47#241611yescharacteristic
344#575C22×C4711yescharacteristic
345C2×#137C22×C4711yescharacteristic
346C2×#137C22×C4711yescharacteristic
347C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
348C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
349C22×SD16C22×C4711yescharacteristic
350#568C22×C4711yescharacteristic
351#568C22×C4711yescharacteristic
352C2×#131C22×C4711yescharacteristic
353C2×#131C22×C4711yescharacteristic
354#473—22no—
355#472—22no—
356#471—22no—
357#471—22no—
358#471—22no—
359#471—22no—
360#471—22no—
361#471—22no—
362#444—22no—
363#443—22no—
364#430—22no—
365#430C22×C4711yescharacteristic
366#430C22×C4711yescharacteristic
367#430C22×C4711yescharacteristic
368#430C22×C4711yescharacteristic
369#430C22×C4711yescharacteristic
370C2×#108—22no—
371C2×#108C22×C4711yescharacteristic
372C2×#108C22×C4711yescharacteristic
373C2×#108C22×C4711yescharacteristic
374#421C22×C4711yescharacteristic
375#421C22×C4711yescharacteristic
376#419C22×C4711yescharacteristic
377#418C22×C4711yescharacteristic
378#413C22×C4711yescharacteristic
379#413C22×C4711yescharacteristic
380C2×#101C22×C4711yescharacteristic
381C2×#101C22×C4711yescharacteristic
382C2×#101C22×C4711yescharacteristic
383C2×#100C22×C4711yescharacteristic
384C2×#100C22×C4711yescharacteristic
385C2×#100C22×C4711yescharacteristic
386#405C22×C4711yescharacteristic
387#344C22×C4711yescharacteristic
388#344C22×C4711yescharacteristic
389#338C22×C4711yescharacteristic
390#338C22×C4711yescharacteristic
391C47#2480811yescharacteristic, direct product factor, Sylow
392C2×#41C23×C4711yescharacteristic
393C2×#41C23×C4711yescharacteristic
394C22×Q8C23×C4711yescharacteristic
395C22×D4C23×C4711yescharacteristic
396#137—21no—
397#137—22no—
398#137—22no—
399#137—22no—
400#137—41no—
401#137D4×C4712yes—
402AGL(1,ℤ/8)—21no—
403AGL(1,ℤ/8)—22no—
404AGL(1,ℤ/8)—22no—
405AGL(1,ℤ/8)—22no—
406AGL(1,ℤ/8)—41no—
407AGL(1,ℤ/8)D4×C4712yes—
408#135—22no—
409C2×Q16—21no—
410C2×Q16—21no—
411C2×SD16—21no—
412C2×SD16—21no—
413C2×SD16—21no—
414C2×SD16—21no—
415C2×SD16—21no—
416C2×SD16—21no—
417C2×SD16—21no—
418C2×SD16—21no—
419C2×SD16—21no—
420C2×SD16—21no—
421C2×D8—21no—
422C2×D8—21no—
423#131—21no—
424#131—21no—
425#131—22no—
426#131—22no—
427#131—21no—
428#131—21no—
429#131—21no—
430#131—21no—
431#131—41no—
432#131—41no—
433#131D4×C4712yes—
434#131D4×C4712yes—
435C2×M16—21no—
436C2×M16—21no—
437C2×M16—22no—
438C2×M16—22no—
439C2×M16C23×C4711yescharacteristic
440C2×M16C23×C4711yescharacteristic
441C2×M16C23×C4711yescharacteristic
442C2×M16C23×C4711yescharacteristic
443C2×M16C23×C4711yescharacteristic
444C2×M16C23×C4711yescharacteristic
445C2×M16C23×C4711yescharacteristic
446C2×M16C23×C4711yescharacteristic
447C2×M16C23×C4711yescharacteristic
448C22×C8—21no—
449C22×C8—21no—
450C22×C8C23×C4711yescharacteristic
451#117C23×C4711yescharacteristic
452#108—22no—
453#108—22no—
454#108—22no—
455#108—22no—
456#108—22no—
457#108—21no—
458#108—21no—
459#108—21no—
460#108—21no—
461#108D4×C4712yes—
462#108D4×C4712yes—
463#104—22no—
464#104—22no—
465#103—41no—
466#102—41no—
467#101—21no—
468#101—21no—
469#101—22no—
470#101—22no—
471#101—22no—
472#100—21no—
473#100—21no—
474#100—22no—
475#100—22no—
476#100—22no—
477#97—21no—
478C4×C8—21no—
479C24—21no—
480#41—21no—
481#41—21no—
482#41—21no—
483#41—21no—
484#41—21no—
485#41—21no—
486#41C2×D4×C4712yes—
487#41C2×D4×C4712yes—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8C2×D4×C4711yescharacteristic
495C2×Q8#41×C4711yescharacteristic
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4C2×D4×C4711yescharacteristic
505C2×D4#41×C4711yescharacteristic
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4C24×C4711yescharacteristic
510Q16—22no—
511Q16—42no—
512Q16—42no—
513SD16—22no—
514SD16—22no—
515SD16—42no—
516SD16—42no—
517SD16—42no—
518SD16—42no—
519SD16—41no—
520SD16—41no—
521SD16—41no—
522SD16—41no—
523D8—22no—
524D8—42no—
525D8—42no—
526M16—21no—
527M16—21no—
528M16—21no—
529M16—21no—
530M16—22no—
531M16—22no—
532M16—21no—
533M16—21no—
534M16—21no—
535M16—21no—
536M16—21no—
537M16—21no—
538M16—21no—
539M16—21no—
540M16—21no—
541M16—21no—
542M16—42no—
543M16—42no—
544M16—41no—
545M16—41no—
546M16C2×D4×C4712yes—
547M16C2×D4×C4712yes—
548M16C2×D4×C4712yes—
549M16C2×D4×C4712yes—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—42no—
562C2×C8—42no—
563C2×C8—41no—
564C2×C8—41no—
565C2×C8C2×D4×C4711yescharacteristic
566C2×C8C2×D4×C4711yescharacteristic
567C2×C8C2×D4×C4711yescharacteristic
568C2×C8C2×D4×C4711yescharacteristic
569C2×C8#41×C4711yescharacteristic
570C2×C8#41×C4711yescharacteristic
571C4⋊C4—21no—
572C22⋊C4—21no—
573C42—21no—
574C23—21no—
575C23—21no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—161no—
580C232−1+4×C4711yescharacteristic
581Q8—21no—
582Q8—21no—
583Q8—21no—
584Q8—41no—
585Q8—41no—
586Q8—41no—
587Q8—41no—
588Q8#121×C4712yes—
589D4—22no—
590D4—22no—
591D4—21no—
592D4—21no—
593D4—21no—
594D4—41no—
595D4—41no—
596D4—41no—
597D4—41no—
598D4—41no—
599D4—41no—
600D4#121×C4712yes—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—21no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4C22×D4×C4711yescharacteristic
612C2×C4C22×D4×C4711yescharacteristic
613C2×C4C22×D4×C4711yescharacteristic
614C2×C4C2×#41×C4711yescharacteristic
615C2×C4C2×#41×C4711yescharacteristic
616C2×C4H(5,𝔽2)×C4711yescharacteristic
617C8—22no—
618C8—22no—
619C8—22no—
620C8—22no—
621C8—41no—
622C8—41no—
623C8—41no—
624C8—41no—
625C8—41no—
626C8#121×C4711yescharacteristic
627C8#121×C4711yescharacteristic
628C8#121×C4711yescharacteristic
629C8#121×C4711yescharacteristic
630C22—22no—
631C22—41no—
632C22—41no—
633C22—81no—
634C22—81no—
635C22—81no—
636C22—161no—
637C22—161no—
638C22—161no—
639C22C47×#53711yescharacteristic
640C22C47×#54711yescharacteristic
641C22C47×#54811yescharacteristic
642C4—22no—
643C4—41no—
644C4—81no—
645C4—81no—
646C4C2×#121×C4711yescharacteristic
647C4C2×#121×C4711yescharacteristic
648C4D42×C4711yescharacteristic
649C4C47×#55311yescharacteristic
650C2—21no—
651C2—21no—
652C2—21no—
653C2—42no—
654C2—81no—
655C2—161no—
656C2C47×#241611yescharacteristic
subgroupG/H
center, socleC2×C47#2416
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC47×#3068C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C47 ◁ C22×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3069C2semidirect
3. C2×C47×#471C2semidirect
4. C2×C47×#471C2semidirect
5. C47×#2955C2semidirect
6. C47×#2916C2semidirect
7. C47×#2070C2semidirect
8. C47×#2069C2semidirect
9. C47×#2049C2semidirect
10. C47×#2048C2semidirect
11. C47×#1977C2semidirect
12. C47×#1953C2semidirect
13. C47×#1903C2semidirect
14. C47×#1902C2semidirect
15. C47×#1813C2semidirect
301. #24808C47direct (N × H)
322. #3069C2×C47semidirect
324. C2×#471C2×C47semidirect
325. C2×#471C2×C47semidirect
326. #2955C2×C47semidirect
327. #2916C2×C47semidirect
328. #2070C2×C47semidirect
329. #2069C2×C47semidirect
330. #2049C2×C47semidirect
331. #2048C2×C47semidirect
332. #1977C2×C47semidirect
333. #1953C2×C47semidirect
334. #1903C2×C47semidirect
335. #1902C2×C47semidirect
336. #1813C2×C47semidirect
391. C47#24808direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#30692
C47×#30682
C2×C47×#4712
C47×#29552
C47×#29162
C47×#20702
C47×#20692
C47×#20492
C47×#20482
C47×#19772
C47×#19532
C47×#19032
C47×#19022
C47×#18132
#2480847