Finite Group Databasebeta

← C47×#33764 #26073462

Subgroups — C47×#33764 #26073462

Order 12032.

596 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3061C211yesmaximal, characteristic, complemented
2C47×#3058C211yesmaximal, characteristic, complemented
3C47×#2237C211yesmaximal, characteristic, complemented
4C47×#2234C211yesmaximal, characteristic, complemented
5C47×#2233C211yesmaximal, characteristic, complemented
6C47×#2232C211yesmaximal, characteristic, complemented
7C47×#2220C211yesmaximal, characteristic, complemented
8C47×#2218C211yesmaximal, characteristic, complemented
9C47×#2217C211yesmaximal, characteristic, complemented
10C47×#2215C211yesmaximal, characteristic, complemented
11C47×#2187C211yesmaximal, characteristic, complemented
12C47×#2186C211yesmaximal, characteristic, complemented
13C47×#2186C211yesmaximal, characteristic, complemented
14C47×#2184C211yesmaximal, characteristic, complemented
15C47×#2113C211yesmaximal, characteristic, complemented
16C2×#135×C47C2211yescharacteristic, complemented
17C22×D8×C47C2211yescharacteristic
18C2×#131×C47C2211yescharacteristic
19C47×#537—21no—
20C47×#535—21no—
21C2×SD32×C47C2211yescharacteristic
22C2×SD32×C47C2211yescharacteristic
23C2×D16×C47C2211yescharacteristic
24C2×D16×C47C2211yescharacteristic
25C2×M32×C47C2211yescharacteristic, complemented
26C22×C16×C47C2211yescharacteristic, complemented
27C47×#469—21no—
28C47×#469—21no—
29C47×#468—21no—
30C47×#468—21no—
31C47×#467C2211yescharacteristic
32C47×#467C2211yescharacteristic, complemented
33C47×#466C2211yescharacteristic
34C47×#466C2211yescharacteristic
35C47×#466C2211yescharacteristic
36C47×#466C2211yescharacteristic
37C47×#466C2211yescharacteristic
38C47×#466C2211yescharacteristic, complemented
39C47×#427C2211yescharacteristic
40C2×#107×C47C2211yescharacteristic, complemented
41C47×#418—21no—
42C47×#417—21no—
43C47×#367C2211yescharacteristic, complemented
44C47×#367C2211yescharacteristic, complemented
45C47×#366C2211yescharacteristic, complemented
46C47×#366C2211yescharacteristic, complemented
47C47×#358C2211yescharacteristic, complemented
48C47×#358C2211yescharacteristic, complemented
49C47×#357C2211yescharacteristic
50C47×#357C2211yescharacteristic
51C47×#357C2211yescharacteristic
52C47×#357C2211yescharacteristic
53C47×#357C2211yescharacteristic, complemented
54C47×#357C2211yescharacteristic, complemented
55C47×C22⋊C16C2211yescharacteristic
56C47×C22⋊C16C2211yescharacteristic
57C47×C22⋊C16C2211yescharacteristic, complemented
58C47×C22⋊C16C2211yescharacteristic, complemented
59C2×#41×C47—21no—
60C2×#41×C47D411yescharacteristic
61C22×D4×C47—21no—
62#135×C47—41no—
63#135×C47—41no—
64C2×Q16×C47C2311yescharacteristic
65C2×SD16×C47—21no—
66C2×D8×C47—21no—
67C2×D8×C47—41no—
68C2×D8×C47—41no—
69C2×D8×C47C2311yescharacteristic
70C2×D8×C47C2311yescharacteristic
71C2×D8×C47C2311yescharacteristic
72#131×C47—41no—
73#131×C47—41no—
74C2×M16×C47D411yescharacteristic
75C2×M16×C47D411yescharacteristic
76C2×M16×C47D411yescharacteristic
77C22×C8×C47C2311yescharacteristic
78C22×C8×C47C2311yescharacteristic
79C22×C8×C47C2311yescharacteristic
80#127×C47—41no—
81#124×C47—41no—
82C22⋊Q8×C47—21no—
83C22⋊Q8×C47—21no—
84C22⋊Q8×C47—41no—
85#121×C47—21no—
86#121×C47—21no—
87#121×C47—21no—
88#121×C47—21no—
89#121×C47—21no—
90#121×C47—21no—
91#121×C47—41no—
92#121×C47—41no—
93#121×C47—41no—
94#120×C47—41no—
95#120×C47—41no—
96#117×C47—21no—
97C2×C4⋊C4×C47—21no—
98SD32×C47—41no—
99SD32×C47—41no—
100D16×C47—41no—
101D16×C47—41no—
102M32×C47—41no—
103C2×C16×C47—41no—
104C2×C16×C47C2311yescharacteristic
105C2×C16×C47C2311yescharacteristic
106C2×C16×C47C2311yescharacteristic
107C2×C16×C47C2311yescharacteristic
108#107×C47—21no—
109#107×C47C2311yescharacteristic
110#107×C47C2311yescharacteristic
111#107×C47C2311yescharacteristic
112#107×C47C2311yescharacteristic
113#106×C47—21no—
114#103×C47—21no—
115#103×C47—21no—
116#102×C47—21no—
117#102×C47—21no—
118#102×C47—21no—
119#102×C47—21no—
120#102×C47—21no—
121#102×C47—21no—
122C24×C47—41no—
123#41×C47—41no—
124#41×C47—41no—
125#41×C47—42no—
126#41×C47—42no—
127C2×Q8×C47—21no—
128C2×Q8×C47D811yescharacteristic
129C2×D4×C47—21no—
130C2×D4×C47—21no—
131C2×D4×C47—21no—
132C2×D4×C47—42no—
133C2×D4×C47—42no—
134C2×D4×C47—41no—
135C2×D4×C47—41no—
136C2×D4×C47—41no—
137C2×D4×C47—41no—
138C2×D4×C47—41no—
139C2×D4×C47—41no—
140C2×D4×C47—41no—
141C2×D4×C47—41no—
142C2×D4×C47D811yescharacteristic
143C2×D4×C47D811yescharacteristic
144C2×D4×C47D811yescharacteristic
145C22×C4×C47—41no—
146C22×C4×C47—41no—
147C22×C4×C47C2×D411yescharacteristic
148C22×C4×C47C2×D411yescharacteristic
149C22×C4×C47C2×D411yescharacteristic
150Q16×C47—21no—
151Q16×C47—21no—
152SD16×C47—42no—
153D8×C47—21no—
154D8×C47—21no—
155D8×C47—21no—
156D8×C47—21no—
157D8×C47—21no—
158D8×C47—21no—
159D8×C47—42no—
160M16×C47—41no—
161M16×C47—41no—
162M16×C47—41no—
163C2×C8×C47—21no—
164C2×C8×C47—21no—
165C2×C8×C47—21no—
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47—21no—
169C2×C8×C47C2×D411yescharacteristic
170C2×C8×C47C2×D411yescharacteristic
171C2×C8×C47C2×D411yescharacteristic
172C2×C8×C47C2411yescharacteristic
173C4⋊C4×C47—21no—
174C4⋊C4×C47—21no—
175C4⋊C4×C47—21no—
176C4⋊C4×C47—21no—
177C4⋊C4×C47—41no—
178C4⋊C4×C47—41no—
179C4⋊C4×C47—41no—
180C22⋊C4×C47—41no—
181C22⋊C4×C47—41no—
182C22⋊C4×C47—41no—
183C22⋊C4×C47—41no—
184C22⋊C4×C47—41no—
185C22⋊C4×C47—41no—
186C22⋊C4×C47—41no—
187C22⋊C4×C47—41no—
188C22⋊C4×C47—41no—
189C42×C47—41no—
190C16×C47—21no—
191C16×C47—21no—
192C16×C47—21no—
193C16×C47—21no—
194C23×C47—41no—
195C23×C47—41no—
196C23×C47—41no—
197C23×C47—82no—
198C23×C47—161no—
199C23×C47—161no—
200C23×C47C2×D811yescharacteristic
201C23×C47C2×D811yescharacteristic
202C23×C47C2×D811yescharacteristic
203Q8×C47—41no—
204Q8×C47—41no—
205Q8×C47—41no—
206D4×C47—41no—
207D4×C47—41no—
208D4×C47—41no—
209D4×C47—41no—
210D4×C47—41no—
211D4×C47—41no—
212D4×C47—41no—
213D4×C47—41no—
214D4×C47—41no—
215D4×C47—82no—
216D4×C47—82no—
217D4×C47—161no—
218D4×C47—161no—
219D4×C47—161no—
220D4×C47—161no—
221D4×C47—161no—
222D4×C47—161no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—21no—
228C2×C4×C47—21no—
229C2×C4×C47—41no—
230C2×C4×C47—41no—
231C2×C4×C47—41no—
232C2×C4×C47—41no—
233C2×C4×C47—41no—
234C2×C4×C47—82no—
235C2×C4×C47—161no—
236C2×C4×C47C2×D811yescharacteristic
237C2×C4×C47C2×D811yescharacteristic
238C2×C4×C47C2×D811yescharacteristic
239C2×C4×C47C22×D411yescharacteristic
240C8×C47—21no—
241C8×C47—21no—
242C8×C47—21no—
243C8×C47H(5,𝔽2)11yescharacteristic
244C8×C47H(5,𝔽2)11yescharacteristic
245#33764C4711yesmaximal, characteristic, direct product factor, Sylow
246C22×C47—21no—
247C22×C47—21no—
248C22×C47—21no—
249C22×C47—21no—
250C22×C47—21no—
251C22×C47—21no—
252C22×C47—21no—
253C22×C47—21no—
254C22×C47—21no—
255C22×C47—81no—
256C22×C47—81no—
257C22×C47—81no—
258C22×C47—81no—
259C22×C47—81no—
260C22×C47—81no—
261C22×C47—81no—
262C22×C47—81no—
263C22×C47—81no—
264C22×C47—164no—
265C22×C47C22×D811yescharacteristic
266C4×C47—21no—
267C4×C47—21no—
268C4×C47—21no—
269C4×C47—81no—
270C4×C47—81no—
271C4×C47—81no—
272C4×C47—81no—
273C4×C47—81no—
274C4×C47#53411yescharacteristic
275C4×C47#57511yescharacteristic
276#3061C2×C4711yescharacteristic, complemented
277#3058C2×C4711yescharacteristic, complemented
278#2237C2×C4711yescharacteristic, complemented
279#2234C2×C4711yescharacteristic, complemented
280#2233C2×C4711yescharacteristic, complemented
281#2232C2×C4711yescharacteristic, complemented
282#2220C2×C4711yescharacteristic, complemented
283#2218C2×C4711yescharacteristic, complemented
284#2217C2×C4711yescharacteristic, complemented
285#2215C2×C4711yescharacteristic, complemented
286#2187C2×C4711yescharacteristic, complemented
287#2186C2×C4711yescharacteristic, complemented
288#2186C2×C4711yescharacteristic, complemented
289#2184C2×C4711yescharacteristic, complemented
290#2113C2×C4711yescharacteristic, complemented
291C2×C47—41no—
292C2×C47—41no—
293C2×C47—41no—
294C2×C47—161no—
295C2×C47—161no—
296C2×C47—161no—
297C2×C47#318611yescharacteristic
298C2×C47#341511yescharacteristic
299C2×C47#341611yescharacteristic
300C2×#135C22×C4711yescharacteristic, complemented
301C22×D8C22×C4711yescharacteristic
302C2×#131C22×C4711yescharacteristic
303#537—21no—
304#535—21no—
305C2×SD32C22×C4711yescharacteristic
306C2×SD32C22×C4711yescharacteristic
307C2×D16C22×C4711yescharacteristic
308C2×D16C22×C4711yescharacteristic
309C2×M32C22×C4711yescharacteristic, complemented
310C22×C16C22×C4711yescharacteristic, complemented
311#469—21no—
312#469—21no—
313#468—21no—
314#468—21no—
315#467C22×C4711yescharacteristic
316#467C22×C4711yescharacteristic, complemented
317#466C22×C4711yescharacteristic
318#466C22×C4711yescharacteristic
319#466C22×C4711yescharacteristic
320#466C22×C4711yescharacteristic
321#466C22×C4711yescharacteristic
322#466C22×C4711yescharacteristic, complemented
323#427C22×C4711yescharacteristic
324C2×#107C22×C4711yescharacteristic, complemented
325#418—21no—
326#417—21no—
327#367C22×C4711yescharacteristic, complemented
328#367C22×C4711yescharacteristic, complemented
329#366C22×C4711yescharacteristic, complemented
330#366C22×C4711yescharacteristic, complemented
331#358C22×C4711yescharacteristic, complemented
332#358C22×C4711yescharacteristic, complemented
333#357C22×C4711yescharacteristic
334#357C22×C4711yescharacteristic
335#357C22×C4711yescharacteristic
336#357C22×C4711yescharacteristic
337#357C22×C4711yescharacteristic, complemented
338#357C22×C4711yescharacteristic, complemented
339C22⋊C16C22×C4711yescharacteristic
340C22⋊C16C22×C4711yescharacteristic
341C22⋊C16C22×C4711yescharacteristic, complemented
342C22⋊C16C22×C4711yescharacteristic, complemented
343C47#3376411yescharacteristic, direct product factor, Sylow
344C2×#41—21no—
345C2×#41D4×C4711yescharacteristic
346C22×D4—21no—
347#135—41no—
348#135—41no—
349C2×Q16C23×C4711yescharacteristic
350C2×SD16—21no—
351C2×D8—21no—
352C2×D8—41no—
353C2×D8—41no—
354C2×D8C23×C4711yescharacteristic
355C2×D8C23×C4711yescharacteristic
356C2×D8C23×C4711yescharacteristic
357#131—41no—
358#131—41no—
359C2×M16D4×C4711yescharacteristic
360C2×M16D4×C4711yescharacteristic
361C2×M16D4×C4711yescharacteristic
362C22×C8C23×C4711yescharacteristic
363C22×C8C23×C4711yescharacteristic
364C22×C8C23×C4711yescharacteristic
365#127—41no—
366#124—41no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369C22⋊Q8—41no—
370#121—21no—
371#121—21no—
372#121—21no—
373#121—21no—
374#121—21no—
375#121—21no—
376#121—41no—
377#121—41no—
378#121—41no—
379#120—41no—
380#120—41no—
381#117—21no—
382C2×C4⋊C4—21no—
383SD32—41no—
384SD32—41no—
385D16—41no—
386D16—41no—
387M32—41no—
388C2×C16—41no—
389C2×C16C23×C4711yescharacteristic
390C2×C16C23×C4711yescharacteristic
391C2×C16C23×C4711yescharacteristic
392C2×C16C23×C4711yescharacteristic
393#107—21no—
394#107C23×C4711yescharacteristic
395#107C23×C4711yescharacteristic
396#107C23×C4711yescharacteristic
397#107C23×C4711yescharacteristic
398#106—21no—
399#103—21no—
400#103—21no—
401#102—21no—
402#102—21no—
403#102—21no—
404#102—21no—
405#102—21no—
406#102—21no—
407C24—41no—
408#41—41no—
409#41—41no—
410#41—42no—
411#41—42no—
412C2×Q8—21no—
413C2×Q8D8×C4711yescharacteristic
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—42no—
418C2×D4—42no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—41no—
426C2×D4—41no—
427C2×D4D8×C4711yescharacteristic
428C2×D4D8×C4711yescharacteristic
429C2×D4D8×C4711yescharacteristic
430C22×C4—41no—
431C22×C4—41no—
432C22×C4C2×D4×C4711yescharacteristic
433C22×C4C2×D4×C4711yescharacteristic
434C22×C4C2×D4×C4711yescharacteristic
435Q16—21no—
436Q16—21no—
437SD16—42no—
438D8—21no—
439D8—21no—
440D8—21no—
441D8—21no—
442D8—21no—
443D8—21no—
444D8—42no—
445M16—41no—
446M16—41no—
447M16—41no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8C2×D4×C4711yescharacteristic
455C2×C8C2×D4×C4711yescharacteristic
456C2×C8C2×D4×C4711yescharacteristic
457C2×C8C24×C4711yescharacteristic
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C22⋊C4—41no—
466C22⋊C4—41no—
467C22⋊C4—41no—
468C22⋊C4—41no—
469C22⋊C4—41no—
470C22⋊C4—41no—
471C22⋊C4—41no—
472C22⋊C4—41no—
473C22⋊C4—41no—
474C42—41no—
475C16—21no—
476C16—21no—
477C16—21no—
478C16—21no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23—82no—
483C23—161no—
484C23—161no—
485C23C2×D8×C4711yescharacteristic
486C23C2×D8×C4711yescharacteristic
487C23C2×D8×C4711yescharacteristic
488Q8—41no—
489Q8—41no—
490Q8—41no—
491D4—41no—
492D4—41no—
493D4—41no—
494D4—41no—
495D4—41no—
496D4—41no—
497D4—41no—
498D4—41no—
499D4—41no—
500D4—82no—
501D4—82no—
502D4—161no—
503D4—161no—
504D4—161no—
505D4—161no—
506D4—161no—
507D4—161no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—82no—
520C2×C4—161no—
521C2×C4C2×D8×C4711yescharacteristic
522C2×C4C2×D8×C4711yescharacteristic
523C2×C4C2×D8×C4711yescharacteristic
524C2×C4C22×D4×C4711yescharacteristic
525C8—21no—
526C8—21no—
527C8—21no—
528C8H(5,𝔽2)×C4711yescharacteristic
529C8H(5,𝔽2)×C4711yescharacteristic
530C22—21no—
531C22—21no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—81no—
540C22—81no—
541C22—81no—
542C22—81no—
543C22—81no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22—81no—
548C22—164no—
549C22C22×D8×C4711yescharacteristic
550C4—21no—
551C4—21no—
552C4—21no—
553C4—81no—
554C4—81no—
555C4—81no—
556C4—81no—
557C4—81no—
558C4C47×#53411yescharacteristic
559C4C47×#57511yescharacteristic
560C2—41no—
561C2—41no—
562C2—41no—
563C2—161no—
564C2—161no—
565C2—161no—
566C2C47×#318611yescharacteristic
567C2C47×#341511yescharacteristic
568C2C47×#341611yescharacteristic
subgroupG/H
center, socleC22×C47C22×D8
commutator, Frattini, cosocleC2×C8C24×C47
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C2×#41×C47 ◁ C2×#131×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3061C2semidirect
2. C47×#3058C2semidirect
3. C47×#2237C2semidirect
4. C47×#2234C2semidirect
5. C47×#2233C2semidirect
6. C47×#2232C2semidirect
7. C47×#2220C2semidirect
8. C47×#2218C2semidirect
9. C47×#2217C2semidirect
10. C47×#2215C2semidirect
11. C47×#2187C2semidirect
12. C47×#2186C2semidirect
13. C47×#2186C2semidirect
14. C47×#2184C2semidirect
15. C47×#2113C2semidirect
16. C2×#135×C47C22semidirect
25. C2×M32×C47C22semidirect
26. C22×C16×C47C22semidirect
32. C47×#467C22semidirect
38. C47×#466C22semidirect
40. C2×#107×C47C22semidirect
43. C47×#367C22semidirect
44. C47×#367C22semidirect
45. C47×#366C22semidirect
46. C47×#366C22semidirect
47. C47×#358C22semidirect
48. C47×#358C22semidirect
53. C47×#357C22semidirect
54. C47×#357C22semidirect
57. C47×C22⋊C16C22semidirect
58. C47×C22⋊C16C22semidirect
245. #33764C47direct (N × H)
276. #3061C2×C47semidirect
277. #3058C2×C47semidirect
278. #2237C2×C47semidirect
279. #2234C2×C47semidirect
280. #2233C2×C47semidirect
281. #2232C2×C47semidirect
282. #2220C2×C47semidirect
283. #2218C2×C47semidirect
284. #2217C2×C47semidirect
285. #2215C2×C47semidirect
286. #2187C2×C47semidirect
287. #2186C2×C47semidirect
288. #2186C2×C47semidirect
289. #2184C2×C47semidirect
290. #2113C2×C47semidirect
300. C2×#135C22×C47semidirect
309. C2×M32C22×C47semidirect
310. C22×C16C22×C47semidirect
316. #467C22×C47semidirect
322. #466C22×C47semidirect
324. C2×#107C22×C47semidirect
327. #367C22×C47semidirect
328. #367C22×C47semidirect
329. #366C22×C47semidirect
330. #366C22×C47semidirect
331. #358C22×C47semidirect
332. #358C22×C47semidirect
337. #357C22×C47semidirect
338. #357C22×C47semidirect
341. C22⋊C16C22×C47semidirect
342. C22⋊C16C22×C47semidirect
343. C47#33764direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#30612
C47×#30582
C47×#22372
C47×#22342
C47×#22332
C47×#22322
C47×#22202
C47×#22182
C47×#22172
C47×#22152
C47×#21872
C47×#21862
C47×#21842
C47×#21132
#3376447