Finite Group Databasebeta

← C47×#29375 #26069073

Subgroups — C47×#29375 #26069073

Order 12032.

778 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#124×C47C211yesmaximal, characteristic
2C47×#2295C211yesmaximal, characteristic, complemented
3C47×#2101C211yesmaximal, characteristic, complemented
4C47×#2097C211yesmaximal, characteristic, complemented
5C47×#2042C211yesmaximal, characteristic
6C47×#2015C211yesmaximal, characteristic
7C47×#1928C211yesmaximal, characteristic, complemented
8C47×#1926C211yesmaximal, characteristic
9C47×#1880C211yesmaximal, characteristic
10C47×#1878C211yesmaximal, characteristic, complemented
11C47×#1878C211yesmaximal, characteristic, complemented
12C47×#1877C211yesmaximal, characteristic
13C47×#1865C211yesmaximal, characteristic, complemented
14C47×#1862C211yesmaximal, characteristic
15C47×#1839C211yesmaximal, characteristic, complemented
16C22×Q16×C47C2211yescharacteristic
17C22×SD16×C47C2211yescharacteristic
18C2×#124×C47C2211yescharacteristic
19C2×C4×Q8×C47C2211yescharacteristic
20C2×C4×Q8×C47C2211yescharacteristic
21C2×C4×D4×C47C2211yescharacteristic
22C2×#107×C47C2211yescharacteristic
23C2×#106×C47C2211yescharacteristic
24C2×#103×C47C2211yescharacteristic
25C2×#103×C47C2211yescharacteristic
26C2×#103×C47C2211yescharacteristic
27C2×#103×C47C2211yescharacteristic
28C2×#103×C47C2211yescharacteristic
29C2×#102×C47C2211yescharacteristic
30C2×#102×C47C2211yescharacteristic
31C2×#102×C47C2211yescharacteristic
32C47×#391C2211yescharacteristic
33C47×#391C2211yescharacteristic
34C47×#391C2211yescharacteristic
35C47×#390C2211yescharacteristic
36C47×#389C2211yescharacteristic
37C47×#389C2211yescharacteristic
38C47×#388—21no—
39C47×#388—21no—
40C47×#387—21no—
41C47×#387—21no—
42C47×#382C2211yescharacteristic
43C4×C4⋊C4×C47—21no—
44C4×C4⋊C4×C47C2211yescharacteristic
45C4×C22⋊C4×C47—21no—
46C4×C22⋊C4×C47—21no—
47C47×#376—21no—
48C43×C47C2211yescharacteristic
49C47×#340C2211yescharacteristic
50C47×#340C2211yescharacteristic
51C47×#340C2211yescharacteristic
52C47×#340C2211yescharacteristic
53C47×#336C2211yescharacteristic
54C47×#336C2211yescharacteristic
55C47×#336C2211yescharacteristic
56C47×#336C2211yescharacteristic
57C47×#336C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C22×Q8×C47C2311yescharacteristic
60C22×Q8×C47C2311yescharacteristic
61C22×D4×C47C2311yescharacteristic
62C23×C4×C47—21no—
63C2×Q16×C47—22no—
64C2×Q16×C47—22no—
65C2×Q16×C47—41no—
66C2×SD16×C47—22no—
67C2×SD16×C47—22no—
68C2×SD16×C47—41no—
69C22×C8×C47C2311yescharacteristic
70C22×C8×C47C2311yescharacteristic
71C22×C8×C47C2311yescharacteristic
72C22×C8×C47C2311yescharacteristic
73#124×C47—22no—
74#124×C47—22no—
75C4×Q8×C47—22no—
76C4×Q8×C47—22no—
77C4×Q8×C47—41no—
78C4×Q8×C47—41no—
79C4×D4×C47—41no—
80C4×D4×C47—41no—
81C2×C4⋊C4×C47—21no—
82C2×C4⋊C4×C47—21no—
83C2×C4⋊C4×C47—21no—
84C2×C4⋊C4×C47—21no—
85C2×C4⋊C4×C47C2311yescharacteristic
86C2×C4⋊C4×C47C2311yescharacteristic
87C2×C4⋊C4×C47C2311yescharacteristic
88C2×C4⋊C4×C47C2311yescharacteristic
89C2×C4⋊C4×C47C2311yescharacteristic
90C2×C22⋊C4×C47—21no—
91C2×C22⋊C4×C47—21no—
92C2×C22⋊C4×C47—21no—
93C2×C22⋊C4×C47—21no—
94C2×C22⋊C4×C47—21no—
95C2×C42×C47—21no—
96C2×C42×C47—21no—
97C2×C42×C47—21no—
98C2×C42×C47D411yescharacteristic
99C2×C42×C47D411yescharacteristic
100C2×C42×C47D411yescharacteristic
101C2×C42×C47D411yescharacteristic
102C2×C42×C47C2311yescharacteristic
103C2×C42×C47C2311yescharacteristic
104C2×C42×C47C2311yescharacteristic
105#107×C47—41no—
106#106×C47—41no—
107#103×C47—22no—
108#103×C47—22no—
109#103×C47—41no—
110#103×C47—41no—
111#103×C47—41no—
112#102×C47—22no—
113#102×C47—22no—
114#102×C47—41no—
115#95×C47—21no—
116#95×C47—21no—
117#95×C47—21no—
118#95×C47—21no—
119#95×C47—21no—
120#95×C47—21no—
121#95×C47—21no—
122#95×C47—21no—
123#95×C47—21no—
124#95×C47—21no—
125#95×C47—21no—
126C24×C47—21no—
127C2×Q8×C47—21no—
128C2×Q8×C47—21no—
129C2×Q8×C47—21no—
130C2×Q8×C47—21no—
131C2×Q8×C47—21no—
132C2×Q8×C47—21no—
133C2×Q8×C47—21no—
134C2×Q8×C47—21no—
135C2×Q8×C47—21no—
136C2×Q8×C47—21no—
137C2×Q8×C47#4112yes—
138C2×Q8×C47#4112yes—
139C2×D4×C47—21no—
140C2×D4×C47—21no—
141C2×D4×C47—21no—
142C2×D4×C47—21no—
143C2×D4×C47—21no—
144C2×D4×C47#4112yes—
145C22×C4×C47—21no—
146C22×C4×C47—21no—
147C22×C4×C47—21no—
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—21no—
152C22×C4×C47—42no—
153C22×C4×C47—42no—
154C22×C4×C47—42no—
155C22×C4×C47C2×D411yescharacteristic
156C22×C4×C47C2×D411yescharacteristic
157C22×C4×C47C2×D411yescharacteristic
158C22×C4×C47C2×D411yescharacteristic
159C22×C4×C47C2×D411yescharacteristic
160C22×C4×C47C2×D411yescharacteristic
161C22×C4×C47C2411yescharacteristic
162Q16×C47—44no—
163SD16×C47—44no—
164C2×C8×C47—21no—
165C2×C8×C47—21no—
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47—21no—
169C2×C8×C47—21no—
170C2×C8×C47—21no—
171C2×C8×C47—21no—
172C2×C8×C47—21no—
173C2×C8×C47—21no—
174C2×C8×C47—21no—
175C2×C8×C47—21no—
176C4⋊C4×C47—24no—
177C4⋊C4×C47—21no—
178C4⋊C4×C47—21no—
179C4⋊C4×C47—21no—
180C4⋊C4×C47—21no—
181C4⋊C4×C47—21no—
182C4⋊C4×C47—21no—
183C4⋊C4×C47—21no—
184C4⋊C4×C47—21no—
185C4⋊C4×C47—21no—
186C4⋊C4×C47—42no—
187C4⋊C4×C47—42no—
188C4⋊C4×C47—42no—
189C4⋊C4×C47#4112yes—
190C22⋊C4×C47—24no—
191C22⋊C4×C47—24no—
192C22⋊C4×C47—42no—
193C22⋊C4×C47—42no—
194C22⋊C4×C47—42no—
195C42×C47—24no—
196C42×C47—22no—
197C42×C47—22no—
198C42×C47—21no—
199C42×C47—21no—
200C42×C47—21no—
201C42×C47—21no—
202C42×C47—21no—
203C42×C47—21no—
204C42×C47—41no—
205C42×C47—41no—
206C42×C47—42no—
207C42×C47—42no—
208C23×C47—22no—
209C23×C47—41no—
210C23×C47—41no—
211C23×C47—41no—
212C23×C47—41no—
213C23×C47—41no—
214C23×C47—41no—
215C23×C47C22×D411yescharacteristic
216Q8×C47—22no—
217Q8×C47—22no—
218Q8×C47—22no—
219Q8×C47—22no—
220Q8×C47—41no—
221Q8×C47—41no—
222Q8×C47—41no—
223Q8×C47—41no—
224D4×C47—22no—
225D4×C47—22no—
226D4×C47—41no—
227D4×C47—41no—
228C2×C4×C47—21no—
229C2×C4×C47—21no—
230C2×C4×C47—21no—
231C2×C4×C47—21no—
232C2×C4×C47—21no—
233C2×C4×C47—21no—
234C2×C4×C47—21no—
235C2×C4×C47—22no—
236C2×C4×C47—22no—
237C2×C4×C47—22no—
238C2×C4×C47—21no—
239C2×C4×C47—21no—
240C2×C4×C47—21no—
241C2×C4×C47—21no—
242C2×C4×C47—21no—
243C2×C4×C47—21no—
244C2×C4×C47—21no—
245C2×C4×C47—21no—
246C2×C4×C47—21no—
247C2×C4×C47—41no—
248C2×C4×C47—41no—
249C2×C4×C47—41no—
250C2×C4×C47—41no—
251C2×C4×C47—41no—
252C2×C4×C47—41no—
253C2×C4×C47—41no—
254C2×C4×C47—41no—
255C2×C4×C47—41no—
256C2×C4×C47—41no—
257C2×C4×C47—41no—
258C2×C4×C47—41no—
259C2×C4×C47—41no—
260C2×C4×C47—41no—
261C2×C4×C47—41no—
262C2×C4×C47—41no—
263C2×C4×C47—41no—
264C2×C4×C47—41no—
265C2×C4×C47—84no—
266C2×C4×C47#13512yes—
267C2×C4×C47#13712yes—
268C2×C4×C47C2×#4111yescharacteristic
269C2×C4×C47C2×#4111yescharacteristic
270C2×C4×C47C2×#4111yescharacteristic
271C2×C4×C47C2×#4111yescharacteristic
272C2×C4×C47H(5,𝔽2)11yescharacteristic
273C2×C4×C47H(5,𝔽2)11yescharacteristic
274C8×C47—41no—
275C8×C47—41no—
276C8×C47—41no—
277C8×C47—41no—
278#29375C4711yesmaximal, characteristic, direct product factor, Sylow
279C22×C47—42no—
280C22×C47—42no—
281C22×C47—42no—
282C22×C47—81no—
283C22×C47—81no—
284C22×C47—81no—
285C22×C47—81no—
286C22×C47#52511yescharacteristic
287C22×C47#52511yescharacteristic
288C22×C47#53511yescharacteristic
289C22×C47C2×#13511yescharacteristic
290C22×C47C2×#13711yescharacteristic
291C22×C47#57511yescharacteristic
292C22×C47#57511yescharacteristic
293C4×C47—22no—
294C4×C47—22no—
295C4×C47—41no—
296C4×C47—42no—
297C4×C47—41no—
298C4×C47—42no—
299C4×C47—42no—
300C4×C47—41no—
301C4×C47—41no—
302C4×C47—81no—
303C4×C47—81no—
304C4×C47—81no—
305C4×C47—81no—
306C4×C47#55111yescharacteristic
307C4×C47#55111yescharacteristic
308C4×C47#55311yescharacteristic
309C4×C47#55311yescharacteristic
310C4×#124C2×C4711yescharacteristic
311#2295C2×C4711yescharacteristic, complemented
312#2101C2×C4711yescharacteristic, complemented
313#2097C2×C4711yescharacteristic, complemented
314#2042C2×C4711yescharacteristic
315#2015C2×C4711yescharacteristic
316#1928C2×C4711yescharacteristic, complemented
317#1926C2×C4711yescharacteristic
318#1880C2×C4711yescharacteristic
319#1878C2×C4711yescharacteristic, complemented
320#1878C2×C4711yescharacteristic, complemented
321#1877C2×C4711yescharacteristic
322#1865C2×C4711yescharacteristic, complemented
323#1862C2×C4711yescharacteristic
324#1839C2×C4711yescharacteristic, complemented
325C2×C47—82no—
326C2×C47#259811yescharacteristic
327C2×C47#310211yescharacteristic
328C2×C47#310711yescharacteristic
329C2×C47#311111yescharacteristic
330C2×C47#311711yescharacteristic
331C2×C47#321111yescharacteristic
332C2×C47#321611yescharacteristic
333C22×Q16C22×C4711yescharacteristic
334C22×SD16C22×C4711yescharacteristic
335C2×#124C22×C4711yescharacteristic
336C2×C4×Q8C22×C4711yescharacteristic
337C2×C4×Q8C22×C4711yescharacteristic
338C2×C4×D4C22×C4711yescharacteristic
339C2×#107C22×C4711yescharacteristic
340C2×#106C22×C4711yescharacteristic
341C2×#103C22×C4711yescharacteristic
342C2×#103C22×C4711yescharacteristic
343C2×#103C22×C4711yescharacteristic
344C2×#103C22×C4711yescharacteristic
345C2×#103C22×C4711yescharacteristic
346C2×#102C22×C4711yescharacteristic
347C2×#102C22×C4711yescharacteristic
348C2×#102C22×C4711yescharacteristic
349#391C22×C4711yescharacteristic
350#391C22×C4711yescharacteristic
351#391C22×C4711yescharacteristic
352#390C22×C4711yescharacteristic
353#389C22×C4711yescharacteristic
354#389C22×C4711yescharacteristic
355#388—21no—
356#388—21no—
357#387—21no—
358#387—21no—
359#382C22×C4711yescharacteristic
360C4×C4⋊C4—21no—
361C4×C4⋊C4C22×C4711yescharacteristic
362C4×C22⋊C4—21no—
363C4×C22⋊C4—21no—
364#376—21no—
365C43C22×C4711yescharacteristic
366#340C22×C4711yescharacteristic
367#340C22×C4711yescharacteristic
368#340C22×C4711yescharacteristic
369#340C22×C4711yescharacteristic
370#336C22×C4711yescharacteristic
371#336C22×C4711yescharacteristic
372#336C22×C4711yescharacteristic
373#336C22×C4711yescharacteristic
374#336C22×C4711yescharacteristic
375#336C22×C4711yescharacteristic
376C47#2937511yescharacteristic, direct product factor, Sylow
377C22×Q8C23×C4711yescharacteristic
378C22×Q8C23×C4711yescharacteristic
379C22×D4C23×C4711yescharacteristic
380C23×C4—21no—
381C2×Q16—22no—
382C2×Q16—22no—
383C2×Q16—41no—
384C2×SD16—22no—
385C2×SD16—22no—
386C2×SD16—41no—
387C22×C8C23×C4711yescharacteristic
388C22×C8C23×C4711yescharacteristic
389C22×C8C23×C4711yescharacteristic
390C22×C8C23×C4711yescharacteristic
391#124—22no—
392#124—22no—
393C4×Q8—22no—
394C4×Q8—22no—
395C4×Q8—41no—
396C4×Q8—41no—
397C4×D4—41no—
398C4×D4—41no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4C23×C4711yescharacteristic
404C2×C4⋊C4C23×C4711yescharacteristic
405C2×C4⋊C4C23×C4711yescharacteristic
406C2×C4⋊C4C23×C4711yescharacteristic
407C2×C4⋊C4C23×C4711yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C42—21no—
414C2×C42—21no—
415C2×C42—21no—
416C2×C42D4×C4711yescharacteristic
417C2×C42D4×C4711yescharacteristic
418C2×C42D4×C4711yescharacteristic
419C2×C42D4×C4711yescharacteristic
420C2×C42C23×C4711yescharacteristic
421C2×C42C23×C4711yescharacteristic
422C2×C42C23×C4711yescharacteristic
423#107—41no—
424#106—41no—
425#103—22no—
426#103—22no—
427#103—41no—
428#103—41no—
429#103—41no—
430#102—22no—
431#102—22no—
432#102—41no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—21no—
440#95—21no—
441#95—21no—
442#95—21no—
443#95—21no—
444C24—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8#41×C4712yes—
456C2×Q8#41×C4712yes—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4#41×C4712yes—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4C2×D4×C4711yescharacteristic
474C22×C4C2×D4×C4711yescharacteristic
475C22×C4C2×D4×C4711yescharacteristic
476C22×C4C2×D4×C4711yescharacteristic
477C22×C4C2×D4×C4711yescharacteristic
478C22×C4C2×D4×C4711yescharacteristic
479C22×C4C24×C4711yescharacteristic
480Q16—44no—
481SD16—44no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C4⋊C4—24no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—42no—
505C4⋊C4—42no—
506C4⋊C4—42no—
507C4⋊C4#41×C4712yes—
508C22⋊C4—24no—
509C22⋊C4—24no—
510C22⋊C4—42no—
511C22⋊C4—42no—
512C22⋊C4—42no—
513C42—24no—
514C42—22no—
515C42—22no—
516C42—21no—
517C42—21no—
518C42—21no—
519C42—21no—
520C42—21no—
521C42—21no—
522C42—41no—
523C42—41no—
524C42—42no—
525C42—42no—
526C23—22no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23C22×D4×C4711yescharacteristic
534Q8—22no—
535Q8—22no—
536Q8—22no—
537Q8—22no—
538Q8—41no—
539Q8—41no—
540Q8—41no—
541Q8—41no—
542D4—22no—
543D4—22no—
544D4—41no—
545D4—41no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—84no—
584C2×C4#135×C4712yes—
585C2×C4#137×C4712yes—
586C2×C4C2×#41×C4711yescharacteristic
587C2×C4C2×#41×C4711yescharacteristic
588C2×C4C2×#41×C4711yescharacteristic
589C2×C4C2×#41×C4711yescharacteristic
590C2×C4H(5,𝔽2)×C4711yescharacteristic
591C2×C4H(5,𝔽2)×C4711yescharacteristic
592C8—41no—
593C8—41no—
594C8—41no—
595C8—41no—
596C22—42no—
597C22—42no—
598C22—42no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22C47×#52511yescharacteristic
604C22C47×#52511yescharacteristic
605C22C47×#53511yescharacteristic
606C22C2×#135×C4711yescharacteristic
607C22C2×#137×C4711yescharacteristic
608C22C47×#57511yescharacteristic
609C22C47×#57511yescharacteristic
610C4—22no—
611C4—22no—
612C4—41no—
613C4—42no—
614C4—41no—
615C4—42no—
616C4—42no—
617C4—41no—
618C4—41no—
619C4—81no—
620C4—81no—
621C4—81no—
622C4—81no—
623C4C47×#55111yescharacteristic
624C4C47×#55111yescharacteristic
625C4C47×#55311yescharacteristic
626C4C47×#55311yescharacteristic
627C2—82no—
628C2C47×#259811yescharacteristic
629C2C47×#310211yescharacteristic
630C2C47×#310711yescharacteristic
631C2C47×#311111yescharacteristic
632C2C47×#311711yescharacteristic
633C2C47×#321111yescharacteristic
634C2C47×#321611yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC22×D4×C47C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C43×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2295C2semidirect
3. C47×#2101C2semidirect
4. C47×#2097C2semidirect
7. C47×#1928C2semidirect
10. C47×#1878C2semidirect
11. C47×#1878C2semidirect
13. C47×#1865C2semidirect
15. C47×#1839C2semidirect
278. #29375C47direct (N × H)
311. #2295C2×C47semidirect
312. #2101C2×C47semidirect
313. #2097C2×C47semidirect
316. #1928C2×C47semidirect
319. #1878C2×C47semidirect
320. #1878C2×C47semidirect
322. #1865C2×C47semidirect
324. #1839C2×C47semidirect
376. C47#29375direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#124×C472
C47×#22952
C47×#21012
C47×#20972
C47×#20422
C47×#20152
C47×#19282
C47×#19262
C47×#18802
C47×#18782
C47×#18772
C47×#18652
C47×#18622
C47×#18392
#2937547