Finite Group Databasebeta

← C47×#27077 #26066775

Subgroups — C47×#27077 #26066775

Order 12032.

748 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2511C211yesmaximal, characteristic, complemented
2C47×#2367C211yesmaximal, characteristic
3C47×#2096C211yesmaximal, characteristic, complemented
4C47×#2056C211yesmaximal, characteristic, complemented
5C47×#2042C211yesmaximal, characteristic
6C47×#2015C211yesmaximal, characteristic
7C47×#1968C211yesmaximal, characteristic
8C47×#1927C211yesmaximal, characteristic, complemented
9C47×#1926C211yesmaximal, characteristic
10C47×#1919C211yesmaximal, characteristic, complemented
11C47×#1916C211yesmaximal, characteristic, complemented
12C47×#1878C211yesmaximal, characteristic, complemented
13C47×#1877C211yesmaximal, characteristic
14C47×#1802C211yesmaximal, characteristic
15C4×#103×C47C211yesmaximal, characteristic, complemented
16C22×Q16×C47C2211yescharacteristic
17C22×SD16×C47C2211yescharacteristic
18C2×#124×C47C2211yescharacteristic
19C2×C4×Q8×C47C2211yescharacteristic
20C2×C4×D4×C47C2211yescharacteristic
21C2×#106×C47C2211yescharacteristic
22C2×#106×C47C2211yescharacteristic
23C2×C4⋊C8×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
32C2×C4×C8×C47C2211yescharacteristic
33C47×#400—21no—
34C47×#400—21no—
35C47×#391C2211yescharacteristic
36C47×#391C2211yescharacteristic
37C47×#391C2211yescharacteristic
38C47×#391C2211yescharacteristic
39C47×#390C2211yescharacteristic
40C47×#389C2211yescharacteristic
41C47×#388—21no—
42C47×#388—21no—
43C47×#387—21no—
44C47×#387—21no—
45C47×#385—21no—
46C47×#384C2211yescharacteristic
47C4×C4⋊C4×C47C2211yescharacteristic
48C4×C4⋊C4×C47C2211yescharacteristic
49C4×C4⋊C4×C47C2211yescharacteristic
50C4×C22⋊C4×C47—21no—
51C47×#340C2211yescharacteristic
52C47×#340C2211yescharacteristic
53C47×#340C2211yescharacteristic
54C47×#340C2211yescharacteristic
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—41no—
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—41no—
77C4×D4×C47—22no—
78C4×D4×C47—41no—
79C2×C4⋊C4×C47—21no—
80C2×C4⋊C4×C47—21no—
81C2×C4⋊C4×C47—21no—
82C2×C4⋊C4×C47—21no—
83C2×C4⋊C4×C47D411yescharacteristic
84C2×C4⋊C4×C47D411yescharacteristic
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×C47C2311yescharacteristic
99C2×C42×C47C2311yescharacteristic
100C2×C42×C47C2311yescharacteristic
101#106×C47—22no—
102#106×C47—41no—
103C4⋊C8×C47—41no—
104#103×C47—22no—
105#103×C47—22no—
106#103×C47—22no—
107#103×C47—41no—
108#103×C47—41no—
109#102×C47—22no—
110#102×C47—41no—
111#102×C47—41no—
112C4×C8×C47—41no—
113#95×C47—21no—
114#95×C47—21no—
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×C47D411yescharacteristic
125#95×C47D411yescharacteristic
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—21no—
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—81no—
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#4112yes—
176C4⋊C4×C47—22no—
177C4⋊C4×C47—22no—
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—21no—
187C4⋊C4×C47—42no—
188C4⋊C4×C47—42no—
189C4⋊C4×C47—81no—
190C4⋊C4×C47—81no—
191C4⋊C4×C47#4112yes—
192C22⋊C4×C47—24no—
193C22⋊C4×C47—24no—
194C22⋊C4×C47—42no—
195C22⋊C4×C47—42no—
196C22⋊C4×C47—81no—
197C42×C47—21no—
198C42×C47—21no—
199C42×C47—21no—
200C42×C47—21no—
201C42×C47—21no—
202C42×C47—21no—
203C42×C47—42no—
204C42×C47—81no—
205C42×C47—81no—
206C23×C47—22no—
207C23×C47—41no—
208C23×C47—41no—
209C23×C47—41no—
210C23×C47—41no—
211C23×C47—41no—
212C23×C47—41no—
213C23×C47C22×D411yescharacteristic
214Q8×C47—22no—
215Q8×C47—22no—
216Q8×C47—41no—
217Q8×C47—41no—
218Q8×C47—41no—
219Q8×C47—41no—
220Q8×C47—41no—
221Q8×C47—41no—
222D4×C47—22no—
223D4×C47—22no—
224D4×C47—41no—
225D4×C47—41no—
226C2×C4×C47—21no—
227C2×C4×C47—21no—
228C2×C4×C47—21no—
229C2×C4×C47—21no—
230C2×C4×C47—21no—
231C2×C4×C47—21no—
232C2×C4×C47—22no—
233C2×C4×C47—21no—
234C2×C4×C47—21no—
235C2×C4×C47—22no—
236C2×C4×C47—21no—
237C2×C4×C47—21no—
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—41no—
245C2×C4×C47—41no—
246C2×C4×C47—41no—
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—84no—
264C2×C4×C47#13512yes—
265C2×C4×C47#13712yes—
266C2×C4×C47C2×#4111yescharacteristic
267C2×C4×C47C2×#4111yescharacteristic
268C2×C4×C47C2×#4111yescharacteristic
269C2×C4×C47C2×#4111yescharacteristic
270C2×C4×C47H(5,𝔽2)11yescharacteristic
271C2×C4×C47H(5,𝔽2)11yescharacteristic
272C8×C47—22no—
273C8×C47—41no—
274C8×C47—41no—
275C8×C47—41no—
276#27077C4711yesmaximal, characteristic, direct product factor, Sylow
277C22×C47—42no—
278C22×C47—42no—
279C22×C47—42no—
280C22×C47—81no—
281C22×C47—81no—
282C22×C47—81no—
283C22×C47—81no—
284C22×C47#52511yescharacteristic
285C22×C47#54611yescharacteristic
286C22×C47#55011yescharacteristic
287C22×C47C2×#13511yescharacteristic
288C22×C47C2×#13711yescharacteristic
289C22×C47#57711yescharacteristic
290C22×C47#57711yescharacteristic
291C4×C47—22no—
292C4×C47—22no—
293C4×C47—41no—
294C4×C47—41no—
295C4×C47—42no—
296C4×C47—41no—
297C4×C47—42no—
298C4×C47—41no—
299C4×C47—81no—
300C4×C47—81no—
301C4×C47—81no—
302C4×C47—81no—
303C4×C47—81no—
304C4×C47#52911yescharacteristic
305C4×C47#53811yescharacteristic
306C4×C47#55111yescharacteristic
307C4×C47#55311yescharacteristic
308#2511C2×C4711yescharacteristic, complemented
309#2367C2×C4711yescharacteristic
310#2096C2×C4711yescharacteristic, complemented
311#2056C2×C4711yescharacteristic, complemented
312#2042C2×C4711yescharacteristic
313#2015C2×C4711yescharacteristic
314#1968C2×C4711yescharacteristic
315#1927C2×C4711yescharacteristic, complemented
316#1926C2×C4711yescharacteristic
317#1919C2×C4711yescharacteristic, complemented
318#1916C2×C4711yescharacteristic, complemented
319#1878C2×C4711yescharacteristic, complemented
320#1877C2×C4711yescharacteristic
321#1802C2×C4711yescharacteristic
322C4×#103C2×C4711yescharacteristic, complemented
323C2×C47—82no—
324C2×C47#246711yescharacteristic
325C2×C47#310711yescharacteristic
326C2×C47#312511yescharacteristic
327C2×C47#329611yescharacteristic
328C2×C47#331611yescharacteristic
329C2×C47#339411yescharacteristic
330C2×C47#340011yescharacteristic
331C22×Q16C22×C4711yescharacteristic
332C22×SD16C22×C4711yescharacteristic
333C2×#124C22×C4711yescharacteristic
334C2×C4×Q8C22×C4711yescharacteristic
335C2×C4×D4C22×C4711yescharacteristic
336C2×#106C22×C4711yescharacteristic
337C2×#106C22×C4711yescharacteristic
338C2×C4⋊C8C22×C4711yescharacteristic
339C2×#103C22×C4711yescharacteristic
340C2×#103C22×C4711yescharacteristic
341C2×#103C22×C4711yescharacteristic
342C2×#103C22×C4711yescharacteristic
343C2×#103C22×C4711yescharacteristic
344C2×#102C22×C4711yescharacteristic
345C2×#102C22×C4711yescharacteristic
346C2×#102C22×C4711yescharacteristic
347C2×C4×C8C22×C4711yescharacteristic
348#400—21no—
349#400—21no—
350#391C22×C4711yescharacteristic
351#391C22×C4711yescharacteristic
352#391C22×C4711yescharacteristic
353#391C22×C4711yescharacteristic
354#390C22×C4711yescharacteristic
355#389C22×C4711yescharacteristic
356#388—21no—
357#388—21no—
358#387—21no—
359#387—21no—
360#385—21no—
361#384C22×C4711yescharacteristic
362C4×C4⋊C4C22×C4711yescharacteristic
363C4×C4⋊C4C22×C4711yescharacteristic
364C4×C4⋊C4C22×C4711yescharacteristic
365C4×C22⋊C4—21no—
366#340C22×C4711yescharacteristic
367#340C22×C4711yescharacteristic
368#340C22×C4711yescharacteristic
369#340C22×C4711yescharacteristic
370#336C22×C4711yescharacteristic
371#336C22×C4711yescharacteristic
372#336C22×C4711yescharacteristic
373#336C22×C4711yescharacteristic
374C47#2707711yescharacteristic, direct product factor, Sylow
375C22×Q8C23×C4711yescharacteristic
376C22×Q8C23×C4711yescharacteristic
377C22×D4C23×C4711yescharacteristic
378C23×C4—21no—
379C2×Q16—22no—
380C2×Q16—41no—
381C2×Q16—41no—
382C2×SD16—22no—
383C2×SD16—22no—
384C2×SD16—41no—
385C22×C8C23×C4711yescharacteristic
386C22×C8C23×C4711yescharacteristic
387C22×C8C23×C4711yescharacteristic
388C22×C8C23×C4711yescharacteristic
389#124—22no—
390#124—22no—
391C4×Q8—22no—
392C4×Q8—41no—
393C4×D4—22no—
394C4×D4—41no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4D4×C4711yescharacteristic
400C2×C4⋊C4D4×C4711yescharacteristic
401C2×C4⋊C4C23×C4711yescharacteristic
402C2×C4⋊C4C23×C4711yescharacteristic
403C2×C4⋊C4C23×C4711yescharacteristic
404C2×C4⋊C4C23×C4711yescharacteristic
405C2×C4⋊C4C23×C4711yescharacteristic
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C42—21no—
412C2×C42—21no—
413C2×C42—21no—
414C2×C42C23×C4711yescharacteristic
415C2×C42C23×C4711yescharacteristic
416C2×C42C23×C4711yescharacteristic
417#106—22no—
418#106—41no—
419C4⋊C8—41no—
420#103—22no—
421#103—22no—
422#103—22no—
423#103—41no—
424#103—41no—
425#102—22no—
426#102—41no—
427#102—41no—
428C4×C8—41no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—21no—
440#95D4×C4711yescharacteristic
441#95D4×C4711yescharacteristic
442C24—21no—
443C2×Q8—21no—
444C2×Q8—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#41×C4712yes—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4#41×C4712yes—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—81no—
471C22×C4C2×D4×C4711yescharacteristic
472C22×C4C2×D4×C4711yescharacteristic
473C22×C4C2×D4×C4711yescharacteristic
474C22×C4C2×D4×C4711yescharacteristic
475C22×C4C2×D4×C4711yescharacteristic
476C22×C4C2×D4×C4711yescharacteristic
477C22×C4C24×C4711yescharacteristic
478Q16—44no—
479SD16—44no—
480C2×C8—21no—
481C2×C8—21no—
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#41×C4712yes—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—21no—
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—42no—
504C4⋊C4—42no—
505C4⋊C4—81no—
506C4⋊C4—81no—
507C4⋊C4#41×C4712yes—
508C22⋊C4—24no—
509C22⋊C4—24no—
510C22⋊C4—42no—
511C22⋊C4—42no—
512C22⋊C4—81no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—21no—
517C42—21no—
518C42—21no—
519C42—42no—
520C42—81no—
521C42—81no—
522C23—22no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23C22×D4×C4711yescharacteristic
530Q8—22no—
531Q8—22no—
532Q8—41no—
533Q8—41no—
534Q8—41no—
535Q8—41no—
536Q8—41no—
537Q8—41no—
538D4—22no—
539D4—22no—
540D4—41no—
541D4—41no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—22no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
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—84no—
580C2×C4#135×C4712yes—
581C2×C4#137×C4712yes—
582C2×C4C2×#41×C4711yescharacteristic
583C2×C4C2×#41×C4711yescharacteristic
584C2×C4C2×#41×C4711yescharacteristic
585C2×C4C2×#41×C4711yescharacteristic
586C2×C4H(5,𝔽2)×C4711yescharacteristic
587C2×C4H(5,𝔽2)×C4711yescharacteristic
588C8—22no—
589C8—41no—
590C8—41no—
591C8—41no—
592C22—42no—
593C22—42no—
594C22—42no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22C47×#52511yescharacteristic
600C22C47×#54611yescharacteristic
601C22C47×#55011yescharacteristic
602C22C2×#135×C4711yescharacteristic
603C22C2×#137×C4711yescharacteristic
604C22C47×#57711yescharacteristic
605C22C47×#57711yescharacteristic
606C4—22no—
607C4—22no—
608C4—41no—
609C4—42no—
610C4—41no—
611C4—41no—
612C4—41no—
613C4—42no—
614C4—81no—
615C4—81no—
616C4—81no—
617C4—81no—
618C4—81no—
619C4C47×#52911yescharacteristic
620C4C47×#53811yescharacteristic
621C4C47×#55111yescharacteristic
622C4C47×#55311yescharacteristic
623C2—82no—
624C2C47×#246711yescharacteristic
625C2C47×#310711yescharacteristic
626C2C47×#312511yescharacteristic
627C2C47×#329611yescharacteristic
628C2C47×#331611yescharacteristic
629C2C47×#339411yescharacteristic
630C2C47×#340011yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC22×D4×C47C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C4×C4⋊C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#2511C2semidirect
3. C47×#2096C2semidirect
4. C47×#2056C2semidirect
8. C47×#1927C2semidirect
10. C47×#1919C2semidirect
11. C47×#1916C2semidirect
12. C47×#1878C2semidirect
15. C4×#103×C47C2semidirect
276. #27077C47direct (N × H)
308. #2511C2×C47semidirect
310. #2096C2×C47semidirect
311. #2056C2×C47semidirect
315. #1927C2×C47semidirect
317. #1919C2×C47semidirect
318. #1916C2×C47semidirect
319. #1878C2×C47semidirect
322. C4×#103C2×C47semidirect
374. C47#27077direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#25112
C47×#23672
C47×#20962
C47×#20562
C47×#20422
C47×#20152
C47×#19682
C47×#19272
C47×#19262
C47×#19192
C47×#19162
C47×#18782
C47×#18772
C47×#18022
C4×#103×C472
#2707747