Finite Group Databasebeta

← C47×#24671 #26064369

Subgroups — C47×#24671 #26064369

Order 12032.

786 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3039C211yesmaximal, characteristic, complemented
2C2×C47×#461C211yesmaximal, characteristic, complemented
3C4×AGL(1,ℤ/8)×C47C211yesmaximal, characteristic
4C47×#2925C211yesmaximal, characteristic, complemented
5C47×#2052C212yesmaximal, complemented
6C47×#2019C212yesmaximal
7C47×#1977C212yesmaximal, complemented
8C47×#1966C211yesmaximal, characteristic, complemented
9C47×#1950C211yesmaximal, characteristic, complemented
10C47×#1930C212yesmaximal, complemented
11C47×#1800C211yesmaximal, characteristic, complemented
12C2×#137×C47C2212yes—
13C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
14C22×SD16×C47C2212yes—
15C2×C4⋊Q8×C47C2211yescharacteristic
16C4×#41×C47C2211yescharacteristic
17C2×C4×D4×C47C2211yescharacteristic
18C47×#462—21no—
19C47×#462—21no—
20C47×#461—21no—
21C47×#461—21no—
22C47×#461—21no—
23C47×#461—21no—
24C47×#461—22no—
25C47×#442—21no—
26C47×#440—21no—
27C4×SD16×C47—21no—
28C4×D8×C47—21no—
29C47×#433—22no—
30C47×#432—21no—
31C47×#431—21no—
32C2×#108×C47C2212yes—
33C47×#428C2211yescharacteristic
34C47×#423C2211yescharacteristic
35C47×#423C2211yescharacteristic
36C2×C4⋊C8×C47C2211yescharacteristic
37C47×#419C2212yes—
38C47×#418C2211yescharacteristic
39C47×#417C2211yescharacteristic
40C2×#103×C47C2212yes—
41C2×#101×C47C2212yes—
42C2×#101×C47C2212yes—
43C2×#100×C47C2212yes—
44C47×#408C2212yes—
45C47×#405C2212yes—
46C4×M16×C47C2211yescharacteristic
47C47×#343C2212yes—
48C47×#341C2212yes—
49C2×#41×C47C2311yescharacteristic
50C22×Q8×C47C2312yes—
51C22×D4×C47C2311yescharacteristic
52C23×C4×C47—21no—
53#137×C47—42no—
54#137×C47—42no—
55AGL(1,ℤ/8)×C47—22no—
56AGL(1,ℤ/8)×C47—22no—
57C2×Q16×C47—22no—
58C2×SD16×C47—21no—
59C2×SD16×C47—22no—
60C2×SD16×C47—24no—
61C2×SD16×C47—22no—
62C2×SD16×C47—22no—
63C2×SD16×C47—42no—
64C2×D8×C47—21no—
65C2×M16×C47C2312yes—
66C2×M16×C47C2312yes—
67C2×M16×C47C2311yescharacteristic
68C2×M16×C47C2311yescharacteristic
69C22×C8×C47C2312yes—
70C4⋊Q8×C47—21no—
71C4⋊Q8×C47—21no—
72C4⋊Q8×C47—21no—
73C4⋊Q8×C47—21no—
74C4×Q8×C47D411yescharacteristic
75C4×Q8×C47D411yescharacteristic
76C4×D4×C47—21no—
77C4×D4×C47—21no—
78C4×D4×C47—21no—
79C4×D4×C47—21no—
80C4×D4×C47—21no—
81C4×D4×C47—21no—
82C4×D4×C47D411yescharacteristic
83C4×D4×C47D411yescharacteristic
84#117×C47—21no—
85#117×C47C2311yescharacteristic
86C2×C4⋊C4×C47—21no—
87C2×C4⋊C4×C47—21no—
88C2×C4⋊C4×C47C2311yescharacteristic
89C2×C22⋊C4×C47—21no—
90C2×C42×C47—21no—
91C2×C42×C47C2311yescharacteristic
92#108×C47—42no—
93#107×C47—21no—
94#106×C47—21no—
95C4⋊C8×C47—21no—
96C4⋊C8×C47—21no—
97C4⋊C8×C47—21no—
98C4⋊C8×C47—21no—
99C4⋊C8×C47D411yescharacteristic
100C4⋊C8×C47D411yescharacteristic
101C4⋊C8×C47D412yes—
102#103×C47—21no—
103#103×C47—22no—
104#103×C47—22no—
105#103×C47—22no—
106#103×C47—22no—
107#102×C47—21no—
108#102×C47—21no—
109#102×C47—21no—
110#101×C47—24no—
111#101×C47—42no—
112#100×C47—42no—
113C22⋊C8×C47—22no—
114C22⋊C8×C47—22no—
115#97×C47—22no—
116#97×C47—21no—
117C4×C8×C47—22no—
118C4×C8×C47—21no—
119C24×C47—21no—
120#41×C47—21no—
121#41×C47—21no—
122#41×C47—21no—
123#41×C47—21no—
124C2×Q8×C47—22no—
125C2×Q8×C47—22no—
126C2×Q8×C47—22no—
127C2×Q8×C47—22no—
128C2×Q8×C47—22no—
129C2×Q8×C47—22no—
130C2×Q8×C47C2×D411yescharacteristic
131C2×D4×C47—21no—
132C2×D4×C47—21no—
133C2×D4×C47—21no—
134C2×D4×C47—21no—
135C2×D4×C47—21no—
136C2×D4×C47—21no—
137C2×D4×C47C2×D411yescharacteristic
138C2×D4×C47#4112yes—
139C22×C4×C47—21no—
140C22×C4×C47—21no—
141C22×C4×C47—21no—
142C22×C4×C47—22no—
143C22×C4×C47—21no—
144C22×C4×C47—41no—
145C22×C4×C47—41no—
146C22×C4×C47—82no—
147C22×C4×C47#4111yescharacteristic
148C22×C4×C47#4111yescharacteristic
149C22×C4×C47C2411yescharacteristic
150Q16×C47—44no—
151SD16×C47—24no—
152SD16×C47—44no—
153SD16×C47—44no—
154SD16×C47—44no—
155D8×C47—24no—
156M16×C47—21no—
157M16×C47—22no—
158M16×C47—21no—
159M16×C47—22no—
160M16×C47—22no—
161M16×C47—22no—
162M16×C47—21no—
163M16×C47#4112yes—
164C2×C8×C47—21no—
165C2×C8×C47—22no—
166C2×C8×C47—22no—
167C2×C8×C47—22no—
168C2×C8×C47—21no—
169C2×C8×C47—22no—
170C2×C8×C47C2×D412yes—
171C2×C8×C47C2×D412yes—
172C4⋊C4×C47—21no—
173C4⋊C4×C47—21no—
174C4⋊C4×C47—21no—
175C4⋊C4×C47—21no—
176C4⋊C4×C47—41no—
177C4⋊C4×C47—41no—
178C4⋊C4×C47—41no—
179C4⋊C4×C47—41no—
180C4⋊C4×C47C2×D411yescharacteristic
181C4⋊C4×C47C2×D411yescharacteristic
182C22⋊C4×C47—21no—
183C22⋊C4×C47—21no—
184C22⋊C4×C47—21no—
185C22⋊C4×C47—41no—
186C22⋊C4×C47—41no—
187C42×C47—21no—
188C42×C47—21no—
189C42×C47—21no—
190C42×C47C2×D411yescharacteristic
191C42×C47C2×D411yescharacteristic
192C42×C47C2×D411yescharacteristic
193C42×C47C2×D411yescharacteristic
194C23×C47—21no—
195C23×C47—22no—
196C23×C47—41no—
197C23×C47—41no—
198C23×C47—81no—
199C23×C47—81no—
200C23×C47C2×#4111yescharacteristic
201Q8×C47—21no—
202Q8×C47—21no—
203Q8×C47—42no—
204Q8×C47—42no—
205Q8×C47—42no—
206Q8×C47—42no—
207D4×C47—21no—
208D4×C47—22no—
209D4×C47—21no—
210D4×C47—22no—
211D4×C47—41no—
212D4×C47—41no—
213D4×C47—41no—
214D4×C47—41no—
215C2×C4×C47—22no—
216C2×C4×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—21no—
219C2×C4×C47—41no—
220C2×C4×C47—41no—
221C2×C4×C47—41no—
222C2×C4×C47—42no—
223C2×C4×C47—41no—
224C2×C4×C47—42no—
225C2×C4×C47—42no—
226C2×C4×C47—42no—
227C2×C4×C47—81no—
228C2×C4×C47—82no—
229C2×C4×C47—82no—
230C2×C4×C47—81no—
231C2×C4×C47#12111yescharacteristic
232C2×C4×C47#12111yescharacteristic
233C2×C4×C47#12111yescharacteristic
234C2×C4×C47#12111yescharacteristic
235C2×C4×C47C22×D411yescharacteristic
236C2×C4×C47C22×D411yescharacteristic
237C2×C4×C47C2×#4111yescharacteristic
238C2×C4×C47C2×#4111yescharacteristic
239C2×C4×C47H(5,𝔽2)11yescharacteristic
240C2×C4×C47H(5,𝔽2)11yescharacteristic
241C8×C47—22no—
242C8×C47—22no—
243C8×C47—22no—
244C8×C47—41no—
245C8×C47—42no—
246C8×C47—42no—
247#24671C4711yesmaximal, characteristic, direct product factor, Sylow
248C22×C47—21no—
249C22×C47—21no—
250C22×C47—41no—
251C22×C47—42no—
252C22×C47—41no—
253C22×C47—41no—
254C22×C47—82no—
255C22×C47—82no—
256C22×C47—81no—
257C22×C47—81no—
258C22×C47C2×#12111yescharacteristic
259C22×C47#55311yescharacteristic
260C22×C47#55511yescharacteristic
261C4×C47—21no—
262C4×C47—21no—
263C4×C47—21no—
264C4×C47—41no—
265C4×C47—41no—
266C4×C47—41no—
267C4×C47—82no—
268C4×C47—81no—
269C4×C47#47112yes—
270C4×C47#52511yescharacteristic
271C4×C47#53511yescharacteristic
272C4×C47#54611yescharacteristic
273C4×C47#55011yescharacteristic
274#3039C2×C4711yescharacteristic, complemented
275C2×#461C2×C4711yescharacteristic, complemented
276C4×AGL(1,ℤ/8)C2×C4711yescharacteristic
277#2925C2×C4711yescharacteristic, complemented
278#2052C2×C4712yescomplemented
279#2019C2×C4712yes—
280#1977C2×C4712yescomplemented
281#1966C2×C4711yescharacteristic, complemented
282#1950C2×C4711yescharacteristic, complemented
283#1930C2×C4712yescomplemented
284#1800C2×C4711yescharacteristic, complemented
285C2×C47—21no—
286C2×C47—21no—
287C2×C47—81no—
288C2×C47—82no—
289C2×C47#241411yescharacteristic
290C2×C47C2×#47111yescharacteristic
291C2×C47#306911yescharacteristic
292C2×#137C22×C4712yes—
293C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
294C22×SD16C22×C4712yes—
295C2×C4⋊Q8C22×C4711yescharacteristic
296C4×#41C22×C4711yescharacteristic
297C2×C4×D4C22×C4711yescharacteristic
298#462—21no—
299#462—21no—
300#461—21no—
301#461—21no—
302#461—21no—
303#461—21no—
304#461—22no—
305#442—21no—
306#440—21no—
307C4×SD16—21no—
308C4×D8—21no—
309#433—22no—
310#432—21no—
311#431—21no—
312C2×#108C22×C4712yes—
313#428C22×C4711yescharacteristic
314#423C22×C4711yescharacteristic
315#423C22×C4711yescharacteristic
316C2×C4⋊C8C22×C4711yescharacteristic
317#419C22×C4712yes—
318#418C22×C4711yescharacteristic
319#417C22×C4711yescharacteristic
320C2×#103C22×C4712yes—
321C2×#101C22×C4712yes—
322C2×#101C22×C4712yes—
323C2×#100C22×C4712yes—
324#408C22×C4712yes—
325#405C22×C4712yes—
326C4×M16C22×C4711yescharacteristic
327#343C22×C4712yes—
328#341C22×C4712yes—
329C47#2467111yescharacteristic, direct product factor, Sylow
330C2×#41C23×C4711yescharacteristic
331C22×Q8C23×C4712yes—
332C22×D4C23×C4711yescharacteristic
333C23×C4—21no—
334#137—42no—
335#137—42no—
336AGL(1,ℤ/8)—22no—
337AGL(1,ℤ/8)—22no—
338C2×Q16—22no—
339C2×SD16—21no—
340C2×SD16—22no—
341C2×SD16—24no—
342C2×SD16—22no—
343C2×SD16—22no—
344C2×SD16—42no—
345C2×D8—21no—
346C2×M16C23×C4712yes—
347C2×M16C23×C4712yes—
348C2×M16C23×C4711yescharacteristic
349C2×M16C23×C4711yescharacteristic
350C22×C8C23×C4712yes—
351C4⋊Q8—21no—
352C4⋊Q8—21no—
353C4⋊Q8—21no—
354C4⋊Q8—21no—
355C4×Q8D4×C4711yescharacteristic
356C4×Q8D4×C4711yescharacteristic
357C4×D4—21no—
358C4×D4—21no—
359C4×D4—21no—
360C4×D4—21no—
361C4×D4—21no—
362C4×D4—21no—
363C4×D4D4×C4711yescharacteristic
364C4×D4D4×C4711yescharacteristic
365#117—21no—
366#117C23×C4711yescharacteristic
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4C23×C4711yescharacteristic
370C2×C22⋊C4—21no—
371C2×C42—21no—
372C2×C42C23×C4711yescharacteristic
373#108—42no—
374#107—21no—
375#106—21no—
376C4⋊C8—21no—
377C4⋊C8—21no—
378C4⋊C8—21no—
379C4⋊C8—21no—
380C4⋊C8D4×C4711yescharacteristic
381C4⋊C8D4×C4711yescharacteristic
382C4⋊C8D4×C4712yes—
383#103—21no—
384#103—22no—
385#103—22no—
386#103—22no—
387#103—22no—
388#102—21no—
389#102—21no—
390#102—21no—
391#101—24no—
392#101—42no—
393#100—42no—
394C22⋊C8—22no—
395C22⋊C8—22no—
396#97—22no—
397#97—21no—
398C4×C8—22no—
399C4×C8—21no—
400C24—21no—
401#41—21no—
402#41—21no—
403#41—21no—
404#41—21no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—22no—
411C2×Q8C2×D4×C4711yescharacteristic
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4C2×D4×C4711yescharacteristic
419C2×D4#41×C4712yes—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—82no—
428C22×C4#41×C4711yescharacteristic
429C22×C4#41×C4711yescharacteristic
430C22×C4C24×C4711yescharacteristic
431Q16—44no—
432SD16—24no—
433SD16—44no—
434SD16—44no—
435SD16—44no—
436D8—24no—
437M16—21no—
438M16—22no—
439M16—22no—
440M16—22no—
441M16—21no—
442M16—21no—
443M16—22no—
444M16#41×C4712yes—
445C2×C8—21no—
446C2×C8—22no—
447C2×C8—22no—
448C2×C8—22no—
449C2×C8—21no—
450C2×C8—22no—
451C2×C8C2×D4×C4712yes—
452C2×C8C2×D4×C4712yes—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—41no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4C2×D4×C4711yescharacteristic
462C4⋊C4C2×D4×C4711yescharacteristic
463C22⋊C4—21no—
464C22⋊C4—21no—
465C22⋊C4—21no—
466C22⋊C4—41no—
467C22⋊C4—41no—
468C42—21no—
469C42—21no—
470C42—21no—
471C42C2×D4×C4711yescharacteristic
472C42C2×D4×C4711yescharacteristic
473C42C2×D4×C4711yescharacteristic
474C42C2×D4×C4711yescharacteristic
475C23—21no—
476C23—22no—
477C23—41no—
478C23—41no—
479C23—81no—
480C23—81no—
481C23C2×#41×C4711yescharacteristic
482Q8—21no—
483Q8—21no—
484Q8—42no—
485Q8—42no—
486Q8—42no—
487Q8—42no—
488D4—21no—
489D4—22no—
490D4—21no—
491D4—22no—
492D4—41no—
493D4—41no—
494D4—41no—
495D4—41no—
496C2×C4—22no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—41no—
501C2×C4—42no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—81no—
509C2×C4—82no—
510C2×C4—82no—
511C2×C4—81no—
512C2×C4#121×C4711yescharacteristic
513C2×C4#121×C4711yescharacteristic
514C2×C4#121×C4711yescharacteristic
515C2×C4#121×C4711yescharacteristic
516C2×C4C22×D4×C4711yescharacteristic
517C2×C4C22×D4×C4711yescharacteristic
518C2×C4C2×#41×C4711yescharacteristic
519C2×C4C2×#41×C4711yescharacteristic
520C2×C4H(5,𝔽2)×C4711yescharacteristic
521C2×C4H(5,𝔽2)×C4711yescharacteristic
522C8—22no—
523C8—22no—
524C8—22no—
525C8—41no—
526C8—42no—
527C8—42no—
528C22—21no—
529C22—21no—
530C22—41no—
531C22—41no—
532C22—41no—
533C22—42no—
534C22—82no—
535C22—82no—
536C22—81no—
537C22—81no—
538C22C2×#121×C4711yescharacteristic
539C22C47×#55311yescharacteristic
540C22C47×#55511yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—81no—
548C4—82no—
549C4C47×#47112yes—
550C4C47×#52511yescharacteristic
551C4C47×#53511yescharacteristic
552C4C47×#54611yescharacteristic
553C4C47×#55011yescharacteristic
554C2—21no—
555C2—21no—
556C2—81no—
557C2—82no—
558C2C47×#241411yescharacteristic
559C2C2×C47×#47111yescharacteristic
560C2C47×#306911yescharacteristic
subgroupG/H
center, socleC22×C47C2×#121
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC2×AGL(1,ℤ/8)×C47C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3039C2semidirect
2. C2×C47×#461C2semidirect
4. C47×#2925C2semidirect
5. C47×#2052C2semidirect
7. C47×#1977C2semidirect
8. C47×#1966C2semidirect
9. C47×#1950C2semidirect
10. C47×#1930C2semidirect
11. C47×#1800C2semidirect
247. #24671C47direct (N × H)
274. #3039C2×C47semidirect
275. C2×#461C2×C47semidirect
277. #2925C2×C47semidirect
278. #2052C2×C47semidirect
280. #1977C2×C47semidirect
281. #1966C2×C47semidirect
282. #1950C2×C47semidirect
283. #1930C2×C47semidirect
284. #1800C2×C47semidirect
329. C47#24671direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#30392
C2×C47×#4612
C4×AGL(1,ℤ/8)×C472
C47×#29252
C47×#20522
C47×#20192
C47×#19772
C47×#19662
C47×#19502
C47×#19302
C47×#18002
#2467147