Finite Group Databasebeta

← C47×#19726 #26059424

Subgroups — C47×#19726 #26059424

Order 12032.

724 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3226C211yesmaximal, characteristic, complemented
2C47×#3210C211yesmaximal, characteristic, complemented
3C47×#3210C211yesmaximal, characteristic, complemented
4C47×#3206C211yesmaximal, characteristic, complemented
5C47×#3184C211yesmaximal, characteristic
6C47×#3165C211yesmaximal, characteristic, complemented
7C47×#1723C211yesmaximal, characteristic, complemented
8C47×#1722C211yesmaximal, characteristic, complemented
9C47×#1720C211yesmaximal, characteristic, complemented
10C47×#1719C211yesmaximal, characteristic, complemented
11C47×#1715C211yesmaximal, characteristic, complemented
12C47×#1714C211yesmaximal, characteristic, complemented
13C47×#1707C211yesmaximal, characteristic, complemented
14C47×#1706C211yesmaximal, characteristic, complemented
15C47×#1453C211yesmaximal, characteristic, complemented
16C47×#533C2211yescharacteristic
17C47×#532C2211yescharacteristic
18C47×#532C2211yescharacteristic
19C2×C4⋊Q8×C47C2211yescharacteristic
20C47×#501—22no—
21C47×#500C2211yescharacteristic
22C47×#500C2211yescharacteristic
23C47×#500C2211yescharacteristic
24C47×#500C2211yescharacteristic
25C47×#498C2211yescharacteristic
26C47×#498C2211yescharacteristic
27C47×#498C2211yescharacteristic
28C47×#494C2211yescharacteristic
29C47×#494C2211yescharacteristic
30C47×#493C2211yescharacteristic
31C47×#492C2211yescharacteristic
32C47×#492C2211yescharacteristic
33C47×#492C2211yescharacteristic
34C47×#492C2211yescharacteristic
35C47×#487C2211yescharacteristic
36C47×#487C2211yescharacteristic
37C47×#487C2211yescharacteristic
38C47×#487C2211yescharacteristic
39C47×#486C2211yescharacteristic
40C47×#486C2211yescharacteristic
41C47×#486C2211yescharacteristic
42C47×#486C2211yescharacteristic
43C47×#486C2211yescharacteristic
44C47×#486C2211yescharacteristic
45C47×#480—22no—
46C47×#474—22no—
47C47×#469—22no—
48C47×#464—22no—
49C47×#464—22no—
50C47×#461—22no—
51C47×#452—22no—
52C47×#452—22no—
53C47×#448—22no—
54C47×#442—22no—
55C47×#431C2211yescharacteristic
56C47×#431C2211yescharacteristic
57C47×#428—22no—
58C4×M16×C47C2211yescharacteristic
59C47×#322C2211yescharacteristic
60C47×#322C2211yescharacteristic
61C47×#322C2211yescharacteristic
62C82×C47C2211yescharacteristic
63C2×#41×C47—21no—
64C2×#41×C47—21no—
65C22×Q8×C47—21no—
66C2×Q16×C47—22no—
67C2×Q16×C47—22no—
68C2×SD16×C47—22no—
69C2×SD16×C47—22no—
70C2×SD16×C47—22no—
71C2×SD16×C47—22no—
72C2×D8×C47—22no—
73C2×M16×C47D412yes—
74C4⋊Q8×C47—21no—
75C4⋊Q8×C47—21no—
76C4⋊Q8×C47—21no—
77C4⋊Q8×C47C2311yescharacteristic
78C4⋊Q8×C47C2311yescharacteristic
79C4⋊Q8×C47C2311yescharacteristic
80C4⋊Q8×C47C2311yescharacteristic
81C4⋊Q8×C47C2311yescharacteristic
82C4⋊Q8×C47C2311yescharacteristic
83#127×C47C2311yescharacteristic
84#127×C47C2311yescharacteristic
85#125×C47—21no—
86#124×C47—21no—
87#124×C47—21no—
88C22⋊Q8×C47—21no—
89C22⋊Q8×C47—21no—
90#121×C47—21no—
91#121×C47—21no—
92#121×C47—21no—
93#121×C47—21no—
94C4×Q8×C47—21no—
95C4×Q8×C47—21no—
96C4×D4×C47—21no—
97C4×D4×C47—21no—
98C4×D4×C47—21no—
99C4×D4×C47—21no—
100#117×C47—21no—
101C2×C4⋊C4×C47—21no—
102C2×C4⋊C4×C47—21no—
103C2×C42×C47C2311yescharacteristic
104#107×C47—22no—
105#107×C47—22no—
106#107×C47—22no—
107#107×C47—22no—
108#106×C47—22no—
109#106×C47—22no—
110#106×C47—22no—
111C4⋊C8×C47D412yes—
112C4⋊C8×C47D412yes—
113#103×C47—22no—
114#103×C47—22no—
115#103×C47—22no—
116#103×C47—22no—
117#102×C47—22no—
118#102×C47—22no—
119#102×C47—22no—
120#102×C47—22no—
121#102×C47—22no—
122#102×C47—22no—
123C22⋊C8×C47D412yes—
124C22⋊C8×C47D412yes—
125#97×C47D412yes—
126C4×C8×C47C2311yescharacteristic
127C4×C8×C47C2311yescharacteristic
128C4×C8×C47C2311yescharacteristic
129C4×C8×C47C2311yescharacteristic
130C4×C8×C47C2311yescharacteristic
131C4×C8×C47C2311yescharacteristic
132#41×C47—82no—
133#41×C47—82no—
134C2×Q8×C47—21no—
135C2×Q8×C47—21no—
136C2×Q8×C47—21no—
137C2×Q8×C47—21no—
138C2×Q8×C47—21no—
139C2×Q8×C47—21no—
140C2×Q8×C47—41no—
141C2×Q8×C47—82no—
142C2×D4×C47—21no—
143C2×D4×C47—21no—
144C2×D4×C47—21no—
145C2×D4×C47—21no—
146C2×D4×C47—21no—
147C2×D4×C47—21no—
148C2×D4×C47—41no—
149C2×D4×C47—41no—
150C22×C4×C47—41no—
151C22×C4×C47—41no—
152C22×C4×C47—41no—
153C22×C4×C47C2×D411yescharacteristic
154C22×C4×C47C2×D411yescharacteristic
155C22×C4×C47C2×D411yescharacteristic
156Q16×C47—82no—
157Q16×C47—82no—
158SD16×C47—82no—
159SD16×C47—82no—
160SD16×C47—82no—
161SD16×C47—82no—
162D8×C47—44no—
163M16×C47—24no—
164C2×C8×C47C2×D412yes—
165C2×C8×C47C2×D412yes—
166C2×C8×C47C2×D412yes—
167C2×C8×C47C2×D412yes—
168C2×C8×C47C2×D412yes—
169C2×C8×C47C2×D412yes—
170C4⋊C4×C47—21no—
171C4⋊C4×C47—21no—
172C4⋊C4×C47—21no—
173C4⋊C4×C47—21no—
174C4⋊C4×C47—21no—
175C4⋊C4×C47—21no—
176C4⋊C4×C47—21no—
177C4⋊C4×C47—21no—
178C4⋊C4×C47—21no—
179C4⋊C4×C47—21no—
180C4⋊C4×C47—21no—
181C4⋊C4×C47—21no—
182C4⋊C4×C47—41no—
183C4⋊C4×C47—41no—
184C4⋊C4×C47—41no—
185C4⋊C4×C47—41no—
186C22⋊C4×C47—41no—
187C22⋊C4×C47—41no—
188C22⋊C4×C47—41no—
189C22⋊C4×C47—41no—
190C22⋊C4×C47—41no—
191C42×C47—41no—
192C42×C47C2×D411yescharacteristic
193C42×C47C2×D411yescharacteristic
194C42×C47C2×D411yescharacteristic
195C42×C47C2411yescharacteristic
196C23×C47—41no—
197C23×C47—41no—
198C23×C47#12711yescharacteristic
199Q8×C47—42no—
200Q8×C47—42no—
201Q8×C47—42no—
202Q8×C47—42no—
203Q8×C47—42no—
204Q8×C47—42no—
205Q8×C47—82no—
206D4×C47—42no—
207D4×C47—42no—
208D4×C47—42no—
209D4×C47—42no—
210D4×C47—42no—
211D4×C47—42no—
212D4×C47—82no—
213D4×C47—82no—
214C2×C4×C47—22no—
215C2×C4×C47—22no—
216C2×C4×C47—22no—
217C2×C4×C47—41no—
218C2×C4×C47—41no—
219C2×C4×C47—41no—
220C2×C4×C47—41no—
221C2×C4×C47—41no—
222C2×C4×C47—41no—
223C2×C4×C47—82no—
224C2×C4×C47—82no—
225C2×C4×C47—82no—
226C2×C4×C47#12711yescharacteristic
227C2×C4×C47#12711yescharacteristic
228C2×C4×C47#12711yescharacteristic
229C2×C4×C47C22×D411yescharacteristic
230C2×C4×C47C22×D411yescharacteristic
231C2×C4×C47C22×D411yescharacteristic
232C8×C47—22no—
233C8×C47—22no—
234C8×C47—22no—
235C8×C47—22no—
236C8×C47—22no—
237C8×C47#13714yes—
238#19726C4711yesmaximal, characteristic, direct product factor, Sylow
239C22×C47—21no—
240C22×C47—21no—
241C22×C47—21no—
242C22×C47—81no—
243C22×C47—81no—
244C22×C47—81no—
245C22×C47—81no—
246C22×C47—81no—
247C22×C47—81no—
248C22×C47C2×#12711yescharacteristic
249C4×C47—21no—
250C4×C47—21no—
251C4×C47—21no—
252C4×C47—81no—
253C4×C47—81no—
254C4×C47—81no—
255C4×C47—81no—
256C4×C47—81no—
257C4×C47—81no—
258C4×C47C2×#13712yes—
259C4×C47#57612yes—
260C4×C47#57712yes—
261#3226C2×C4711yescharacteristic, complemented
262#3210C2×C4711yescharacteristic, complemented
263#3210C2×C4711yescharacteristic, complemented
264#3206C2×C4711yescharacteristic, complemented
265#3184C2×C4711yescharacteristic
266#3165C2×C4711yescharacteristic, complemented
267#1723C2×C4711yescharacteristic, complemented
268#1722C2×C4711yescharacteristic, complemented
269#1720C2×C4711yescharacteristic, complemented
270#1719C2×C4711yescharacteristic, complemented
271#1715C2×C4711yescharacteristic, complemented
272#1714C2×C4711yescharacteristic, complemented
273#1707C2×C4711yescharacteristic, complemented
274#1706C2×C4711yescharacteristic, complemented
275#1453C2×C4711yescharacteristic, complemented
276C2×C47—41no—
277C2×C47—161no—
278C2×C47—161no—
279C2×C47#315211yescharacteristic
280C2×C47#315411yescharacteristic
281C2×C47#315511yescharacteristic
282#533C22×C4711yescharacteristic
283#532C22×C4711yescharacteristic
284#532C22×C4711yescharacteristic
285C2×C4⋊Q8C22×C4711yescharacteristic
286#501—22no—
287#500C22×C4711yescharacteristic
288#500C22×C4711yescharacteristic
289#500C22×C4711yescharacteristic
290#500C22×C4711yescharacteristic
291#498C22×C4711yescharacteristic
292#498C22×C4711yescharacteristic
293#498C22×C4711yescharacteristic
294#494C22×C4711yescharacteristic
295#494C22×C4711yescharacteristic
296#493C22×C4711yescharacteristic
297#492C22×C4711yescharacteristic
298#492C22×C4711yescharacteristic
299#492C22×C4711yescharacteristic
300#492C22×C4711yescharacteristic
301#487C22×C4711yescharacteristic
302#487C22×C4711yescharacteristic
303#487C22×C4711yescharacteristic
304#487C22×C4711yescharacteristic
305#486C22×C4711yescharacteristic
306#486C22×C4711yescharacteristic
307#486C22×C4711yescharacteristic
308#486C22×C4711yescharacteristic
309#486C22×C4711yescharacteristic
310#486C22×C4711yescharacteristic
311#480—22no—
312#474—22no—
313#469—22no—
314#464—22no—
315#464—22no—
316#461—22no—
317#452—22no—
318#452—22no—
319#448—22no—
320#442—22no—
321#431C22×C4711yescharacteristic
322#431C22×C4711yescharacteristic
323#428—22no—
324C4×M16C22×C4711yescharacteristic
325#322C22×C4711yescharacteristic
326#322C22×C4711yescharacteristic
327#322C22×C4711yescharacteristic
328C82C22×C4711yescharacteristic
329C47#1972611yescharacteristic, direct product factor, Sylow
330C2×#41—21no—
331C2×#41—21no—
332C22×Q8—21no—
333C2×Q16—22no—
334C2×Q16—22no—
335C2×SD16—22no—
336C2×SD16—22no—
337C2×SD16—22no—
338C2×SD16—22no—
339C2×D8—22no—
340C2×M16D4×C4712yes—
341C4⋊Q8—21no—
342C4⋊Q8—21no—
343C4⋊Q8—21no—
344C4⋊Q8C23×C4711yescharacteristic
345C4⋊Q8C23×C4711yescharacteristic
346C4⋊Q8C23×C4711yescharacteristic
347C4⋊Q8C23×C4711yescharacteristic
348C4⋊Q8C23×C4711yescharacteristic
349C4⋊Q8C23×C4711yescharacteristic
350#127C23×C4711yescharacteristic
351#127C23×C4711yescharacteristic
352#125—21no—
353#124—21no—
354#124—21no—
355C22⋊Q8—21no—
356C22⋊Q8—21no—
357#121—21no—
358#121—21no—
359#121—21no—
360#121—21no—
361C4×Q8—21no—
362C4×Q8—21no—
363C4×D4—21no—
364C4×D4—21no—
365C4×D4—21no—
366C4×D4—21no—
367#117—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C42C23×C4711yescharacteristic
371#107—22no—
372#107—22no—
373#107—22no—
374#107—22no—
375#106—22no—
376#106—22no—
377#106—22no—
378C4⋊C8D4×C4712yes—
379C4⋊C8D4×C4712yes—
380#103—22no—
381#103—22no—
382#103—22no—
383#103—22no—
384#102—22no—
385#102—22no—
386#102—22no—
387#102—22no—
388#102—22no—
389#102—22no—
390C22⋊C8D4×C4712yes—
391C22⋊C8D4×C4712yes—
392#97D4×C4712yes—
393C4×C8C23×C4711yescharacteristic
394C4×C8C23×C4711yescharacteristic
395C4×C8C23×C4711yescharacteristic
396C4×C8C23×C4711yescharacteristic
397C4×C8C23×C4711yescharacteristic
398C4×C8C23×C4711yescharacteristic
399#41—82no—
400#41—82no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—41no—
408C2×Q8—82no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—41no—
416C2×D4—41no—
417C22×C4—41no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4C2×D4×C4711yescharacteristic
421C22×C4C2×D4×C4711yescharacteristic
422C22×C4C2×D4×C4711yescharacteristic
423Q16—82no—
424Q16—82no—
425SD16—82no—
426SD16—82no—
427SD16—82no—
428SD16—82no—
429D8—44no—
430M16—24no—
431C2×C8C2×D4×C4712yes—
432C2×C8C2×D4×C4712yes—
433C2×C8C2×D4×C4712yes—
434C2×C8C2×D4×C4712yes—
435C2×C8C2×D4×C4712yes—
436C2×C8C2×D4×C4712yes—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—41no—
450C4⋊C4—41no—
451C4⋊C4—41no—
452C4⋊C4—41no—
453C22⋊C4—41no—
454C22⋊C4—41no—
455C22⋊C4—41no—
456C22⋊C4—41no—
457C22⋊C4—41no—
458C42—41no—
459C42C2×D4×C4711yescharacteristic
460C42C2×D4×C4711yescharacteristic
461C42C2×D4×C4711yescharacteristic
462C42C24×C4711yescharacteristic
463C23—41no—
464C23—41no—
465C23#127×C4711yescharacteristic
466Q8—42no—
467Q8—42no—
468Q8—42no—
469Q8—42no—
470Q8—42no—
471Q8—42no—
472Q8—82no—
473D4—42no—
474D4—42no—
475D4—42no—
476D4—42no—
477D4—42no—
478D4—42no—
479D4—82no—
480D4—82no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—82no—
491C2×C4—82no—
492C2×C4—82no—
493C2×C4#127×C4711yescharacteristic
494C2×C4#127×C4711yescharacteristic
495C2×C4#127×C4711yescharacteristic
496C2×C4C22×D4×C4711yescharacteristic
497C2×C4C22×D4×C4711yescharacteristic
498C2×C4C22×D4×C4711yescharacteristic
499C8—22no—
500C8—22no—
501C8—22no—
502C8—22no—
503C8—22no—
504C8#137×C4714yes—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—81no—
509C22—81no—
510C22—81no—
511C22—81no—
512C22—81no—
513C22—81no—
514C22C2×#127×C4711yescharacteristic
515C4—21no—
516C4—21no—
517C4—21no—
518C4—81no—
519C4—81no—
520C4—81no—
521C4—81no—
522C4—81no—
523C4—81no—
524C4C2×#137×C4712yes—
525C4C47×#57612yes—
526C4C47×#57712yes—
527C2—41no—
528C2—161no—
529C2—161no—
530C2C47×#315211yescharacteristic
531C2C47×#315411yescharacteristic
532C2C47×#315511yescharacteristic
subgroupG/H
center, socleC22×C47C2×#127
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#3184C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3226C2semidirect
2. C47×#3210C2semidirect
3. C47×#3210C2semidirect
4. C47×#3206C2semidirect
6. C47×#3165C2semidirect
7. C47×#1723C2semidirect
8. C47×#1722C2semidirect
9. C47×#1720C2semidirect
10. C47×#1719C2semidirect
11. C47×#1715C2semidirect
12. C47×#1714C2semidirect
13. C47×#1707C2semidirect
14. C47×#1706C2semidirect
15. C47×#1453C2semidirect
238. #19726C47direct (N × H)
261. #3226C2×C47semidirect
262. #3210C2×C47semidirect
263. #3210C2×C47semidirect
264. #3206C2×C47semidirect
266. #3165C2×C47semidirect
267. #1723C2×C47semidirect
268. #1722C2×C47semidirect
269. #1720C2×C47semidirect
270. #1719C2×C47semidirect
271. #1715C2×C47semidirect
272. #1714C2×C47semidirect
273. #1707C2×C47semidirect
274. #1706C2×C47semidirect
275. #1453C2×C47semidirect
329. C47#19726direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#32262
C47×#32102
C47×#32062
C47×#31842
C47×#31652
C47×#17232
C47×#17222
C47×#17202
C47×#17192
C47×#17152
C47×#17142
C47×#17072
C47×#17062
C47×#14532
#1972647