Finite Group Databasebeta

← C47×#18841 #26058539

Subgroups — C47×#18841 #26058539

Order 12032.

892 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3507C211yesmaximal, characteristic, complemented
2C47×#3253C211yesmaximal, characteristic
3C47×#3210C211yesmaximal, characteristic, complemented
4C47×#3112C211yesmaximal, characteristic, complemented
5C47×#1638C212yesmaximal, complemented
6C47×#1632C212yesmaximal, complemented
7C47×#1628C212yesmaximal, complemented
8C47×#1622C212yesmaximal, complemented
9C47×#1559C211yesmaximal, characteristic, complemented
10C47×#1496C211yesmaximal, characteristic, complemented
11C47×#1487C211yesmaximal, characteristic, complemented
12C47×#559—21no—
13C47×#557—21no—
14C47×#556—22no—
15C47×#556C2212yes—
16C47×#554C2212yes—
17C47×#552—22no—
18C47×#539—22no—
19C47×#536—21no—
20C47×#533C2211yescharacteristic
21C47×#532C2211yescharacteristic
22C47×#532C2211yescharacteristic
23C47×#529—22no—
24C47×#520—21no—
25C2×C4×Q8×C47C2211yescharacteristic
26C47×#494C2211yescharacteristic
27C47×#492C2211yescharacteristic
28C47×#487C2211yescharacteristic
29C47×#486C2211yescharacteristic
30C47×#480—21no—
31C47×#477C2212yes—
32C47×#476—21no—
33C47×#476C2212yes—
34C47×#469—22no—
35C47×#464—22no—
36C47×#460C2212yes—
37C47×#459—21no—
38C47×#459C2212yes—
39C47×#452—22no—
40C47×#448—21no—
41C47×#440—22no—
42C47×#432C2211yescharacteristic
43C47×#431C2211yescharacteristic
44C47×#423C2211yescharacteristic
45C47×#333C2212yes—
46C47×#332C2212yes—
47C47×Q8⋊C8C2212yes—
48C47×Q8⋊C8C2212yes—
49C47×D4⋊C8C2212yes—
50C47×D4⋊C8C2212yes—
51C2×#41×C47—21no—
52C2×#41×C47—21no—
53C22×Q8×C47D411yescharacteristic
54C2×Q16×C47—22no—
55C2×SD16×C47—22no—
56C2×SD16×C47—22no—
57C2×D8×C47—22no—
58C2×M16×C47—21no—
59C4⋊Q8×C47—22no—
60C4⋊Q8×C47D411yescharacteristic
61C4⋊Q8×C47C2311yescharacteristic
62C4⋊Q8×C47C2311yescharacteristic
63C4⋊Q8×C47C2311yescharacteristic
64#127×C47D411yescharacteristic
65#127×C47C2311yescharacteristic
66#126×C47—24no—
67#126×C47—24no—
68#125×C47—24no—
69#125×C47—22no—
70#125×C47—21no—
71#124×C47—22no—
72#124×C47—22no—
73#124×C47—21no—
74#124×C47—21no—
75#123×C47—24no—
76#123×C47—24no—
77C22⋊Q8×C47—22no—
78C22⋊Q8×C47—22no—
79C22⋊Q8×C47—24no—
80C22⋊Q8×C47—21no—
81C22⋊Q8×C47D412yes—
82#121×C47—21no—
83#121×C47—21no—
84#121×C47—21no—
85#121×C47D412yes—
86C4×Q8×C47—22no—
87C4×Q8×C47—22no—
88C4×Q8×C47—21no—
89C4×Q8×C47—21no—
90C4×Q8×C47—21no—
91C4×Q8×C47D412yes—
92C4×Q8×C47D412yes—
93C4×Q8×C47C2312yes—
94C4×D4×C47—24no—
95C4×D4×C47—22no—
96C4×D4×C47—22no—
97C4×D4×C47—21no—
98C4×D4×C47—21no—
99C4×D4×C47—21no—
100C4×D4×C47C2312yes—
101#117×C47—24no—
102#117×C47—21no—
103#117×C47—22no—
104C2×C4⋊C4×C47—21no—
105C2×C4⋊C4×C47—22no—
106C2×C4⋊C4×C47D411yescharacteristic
107C2×C42×C47—21no—
108C2×C42×C47C2311yescharacteristic
109#107×C47—22no—
110#106×C47—22no—
111C4⋊C8×C47—21no—
112C4⋊C8×C47—21no—
113C4⋊C8×C47C2312yes—
114C4⋊C8×C47C2312yes—
115#103×C47—22no—
116#103×C47—22no—
117#102×C47—22no—
118#102×C47—22no—
119#102×C47—22no—
120#102×C47—22no—
121C22⋊C8×C47—21no—
122C22⋊C8×C47—21no—
123#97×C47—21no—
124C4×C8×C47C2311yescharacteristic
125C4×C8×C47C2311yescharacteristic
126#41×C47—44no—
127#41×C47—82no—
128C2×Q8×C47—21no—
129C2×Q8×C47—21no—
130C2×Q8×C47—21no—
131C2×Q8×C47—21no—
132C2×Q8×C47—42no—
133C2×Q8×C47C2×D412yes—
134C2×Q8×C47C2×D412yes—
135C2×D4×C47—22no—
136C2×D4×C47—21no—
137C2×D4×C47—21no—
138C2×D4×C47—21no—
139C2×D4×C47—21no—
140C2×D4×C47—21no—
141C2×D4×C47—41no—
142C2×D4×C47C2×D412yes—
143C22×C4×C47—21no—
144C22×C4×C47—24no—
145C22×C4×C47—21no—
146C22×C4×C47—22no—
147C22×C4×C47—41no—
148C22×C4×C47C2×D411yescharacteristic
149C22×C4×C47C2×D411yescharacteristic
150C22×C4×C47C2×D411yescharacteristic
151Q16×C47—82no—
152SD16×C47—44no—
153SD16×C47—82no—
154D8×C47—82no—
155M16×C47—81no—
156C2×C8×C47—21no—
157C2×C8×C47—22no—
158C2×C8×C47—22no—
159C2×C8×C47—21no—
160C4⋊C4×C47—24no—
161C4⋊C4×C47—24no—
162C4⋊C4×C47—24no—
163C4⋊C4×C47—22no—
164C4⋊C4×C47—21no—
165C4⋊C4×C47—22no—
166C4⋊C4×C47—21no—
167C4⋊C4×C47—22no—
168C4⋊C4×C47—21no—
169C4⋊C4×C47—22no—
170C4⋊C4×C47—21no—
171C4⋊C4×C47—21no—
172C4⋊C4×C47—21no—
173C4⋊C4×C47—21no—
174C4⋊C4×C47C2×D412yes—
175C4⋊C4×C47C2×D412yes—
176C4⋊C4×C47C2×D412yes—
177C22⋊C4×C47—24no—
178C22⋊C4×C47—24no—
179C22⋊C4×C47—24no—
180C22⋊C4×C47—22no—
181C22⋊C4×C47—22no—
182C22⋊C4×C47—22no—
183C22⋊C4×C47—41no—
184C22⋊C4×C47—41no—
185C42×C47—24no—
186C42×C47—22no—
187C42×C47—22no—
188C42×C47—22no—
189C42×C47C2×D411yescharacteristic
190C42×C47C2×D411yescharacteristic
191C42×C47C2×D411yescharacteristic
192C42×C47C2411yescharacteristic
193C23×C47—22no—
194C23×C47—41no—
195C23×C47#12011yescharacteristic
196Q8×C47—22no—
197Q8×C47—22no—
198Q8×C47—42no—
199Q8×C47—42no—
200Q8×C47—42no—
201Q8×C47—42no—
202Q8×C47—41no—
203Q8×C47—41no—
204D4×C47—22no—
205D4×C47—22no—
206D4×C47—42no—
207D4×C47—42no—
208D4×C47—44no—
209D4×C47—42no—
210D4×C47—41no—
211D4×C47—41no—
212D4×C47—81no—
213D4×C47—82no—
214C2×C4×C47—22no—
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—22no—
218C2×C4×C47—22no—
219C2×C4×C47—22no—
220C2×C4×C47—22no—
221C2×C4×C47—22no—
222C2×C4×C47—41no—
223C2×C4×C47—42no—
224C2×C4×C47—44no—
225C2×C4×C47—41no—
226C2×C4×C47—82no—
227C2×C4×C47—81no—
228C2×C4×C47—84no—
229C2×C4×C47#12011yescharacteristic
230C2×C4×C47#12011yescharacteristic
231C2×C4×C47#12011yescharacteristic
232C2×C4×C47C22×D411yescharacteristic
233C2×C4×C47C22×D411yescharacteristic
234C2×C4×C47C22×D411yescharacteristic
235C8×C47—41no—
236C8×C47—41no—
237C8×C47—42no—
238C8×C47—42no—
239#18841C4711yesmaximal, characteristic, direct product factor, Sylow
240C22×C47—21no—
241C22×C47—21no—
242C22×C47—21no—
243C22×C47—42no—
244C22×C47—42no—
245C22×C47—42no—
246C22×C47—81no—
247C22×C47—81no—
248C22×C47—81no—
249C22×C47C2×#12011yescharacteristic
250C4×C47—21no—
251C4×C47—21no—
252C4×C47—21no—
253C4×C47—21no—
254C4×C47—42no—
255C4×C47—42no—
256C4×C47—42no—
257C4×C47—42no—
258C4×C47—42no—
259C4×C47—81no—
260C4×C47#57512yes—
261C4×C47#57711yescharacteristic
262C4×C47#57811yescharacteristic
263#3507C2×C4711yescharacteristic, complemented
264#3253C2×C4711yescharacteristic
265#3210C2×C4711yescharacteristic, complemented
266#3112C2×C4711yescharacteristic, complemented
267#1638C2×C4712yescomplemented
268#1632C2×C4712yescomplemented
269#1628C2×C4712yescomplemented
270#1622C2×C4712yescomplemented
271#1559C2×C4711yescharacteristic, complemented
272#1496C2×C4711yescharacteristic, complemented
273#1487C2×C4711yescharacteristic, complemented
274C2×C47—41no—
275C2×C47—82no—
276C2×C47—161no—
277C2×C47#300511yescharacteristic
278C2×C47#301311yescharacteristic
279C2×C47#302111yescharacteristic
280#559—21no—
281#557—21no—
282#556—22no—
283#556C22×C4712yes—
284#554C22×C4712yes—
285#552—22no—
286#539—22no—
287#536—21no—
288#533C22×C4711yescharacteristic
289#532C22×C4711yescharacteristic
290#532C22×C4711yescharacteristic
291#529—22no—
292#520—21no—
293C2×C4×Q8C22×C4711yescharacteristic
294#494C22×C4711yescharacteristic
295#492C22×C4711yescharacteristic
296#487C22×C4711yescharacteristic
297#486C22×C4711yescharacteristic
298#480—21no—
299#477C22×C4712yes—
300#476—21no—
301#476C22×C4712yes—
302#469—22no—
303#464—22no—
304#460C22×C4712yes—
305#459—21no—
306#459C22×C4712yes—
307#452—22no—
308#448—21no—
309#440—22no—
310#432C22×C4711yescharacteristic
311#431C22×C4711yescharacteristic
312#423C22×C4711yescharacteristic
313#333C22×C4712yes—
314#332C22×C4712yes—
315Q8⋊C8C22×C4712yes—
316Q8⋊C8C22×C4712yes—
317D4⋊C8C22×C4712yes—
318D4⋊C8C22×C4712yes—
319C47#1884111yescharacteristic, direct product factor, Sylow
320C2×#41—21no—
321C2×#41—21no—
322C22×Q8D4×C4711yescharacteristic
323C2×Q16—22no—
324C2×SD16—22no—
325C2×SD16—22no—
326C2×D8—22no—
327C2×M16—21no—
328C4⋊Q8—22no—
329C4⋊Q8D4×C4711yescharacteristic
330C4⋊Q8C23×C4711yescharacteristic
331C4⋊Q8C23×C4711yescharacteristic
332C4⋊Q8C23×C4711yescharacteristic
333#127D4×C4711yescharacteristic
334#127C23×C4711yescharacteristic
335#126—24no—
336#126—24no—
337#125—24no—
338#125—22no—
339#125—21no—
340#124—22no—
341#124—22no—
342#124—21no—
343#124—21no—
344#123—24no—
345#123—24no—
346C22⋊Q8—22no—
347C22⋊Q8—22no—
348C22⋊Q8—24no—
349C22⋊Q8—21no—
350C22⋊Q8D4×C4712yes—
351#121—21no—
352#121—21no—
353#121—21no—
354#121D4×C4712yes—
355C4×Q8—22no—
356C4×Q8—22no—
357C4×Q8—21no—
358C4×Q8—21no—
359C4×Q8—21no—
360C4×Q8D4×C4712yes—
361C4×Q8D4×C4712yes—
362C4×Q8C23×C4712yes—
363C4×D4—24no—
364C4×D4—22no—
365C4×D4—22no—
366C4×D4—21no—
367C4×D4—21no—
368C4×D4—21no—
369C4×D4C23×C4712yes—
370#117—24no—
371#117—21no—
372#117—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4D4×C4711yescharacteristic
376C2×C42—21no—
377C2×C42C23×C4711yescharacteristic
378#107—22no—
379#106—22no—
380C4⋊C8—21no—
381C4⋊C8—21no—
382C4⋊C8C23×C4712yes—
383C4⋊C8C23×C4712yes—
384#103—22no—
385#103—22no—
386#102—22no—
387#102—22no—
388#102—22no—
389#102—22no—
390C22⋊C8—21no—
391C22⋊C8—21no—
392#97—21no—
393C4×C8C23×C4711yescharacteristic
394C4×C8C23×C4711yescharacteristic
395#41—44no—
396#41—82no—
397C2×Q8—21no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—42no—
402C2×Q8C2×D4×C4712yes—
403C2×Q8C2×D4×C4712yes—
404C2×D4—22no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—41no—
411C2×D4C2×D4×C4712yes—
412C22×C4—21no—
413C22×C4—24no—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—41no—
417C22×C4C2×D4×C4711yescharacteristic
418C22×C4C2×D4×C4711yescharacteristic
419C22×C4C2×D4×C4711yescharacteristic
420Q16—82no—
421SD16—44no—
422SD16—82no—
423D8—82no—
424M16—81no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8—22no—
428C2×C8—22no—
429C4⋊C4—24no—
430C4⋊C4—24no—
431C4⋊C4—24no—
432C4⋊C4—22no—
433C4⋊C4—21no—
434C4⋊C4—22no—
435C4⋊C4—21no—
436C4⋊C4—22no—
437C4⋊C4—21no—
438C4⋊C4—22no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4C2×D4×C4712yes—
444C4⋊C4C2×D4×C4712yes—
445C4⋊C4C2×D4×C4712yes—
446C22⋊C4—24no—
447C22⋊C4—24no—
448C22⋊C4—24no—
449C22⋊C4—22no—
450C22⋊C4—22no—
451C22⋊C4—22no—
452C22⋊C4—41no—
453C22⋊C4—41no—
454C42—24no—
455C42—22no—
456C42—22no—
457C42—22no—
458C42C2×D4×C4711yescharacteristic
459C42C2×D4×C4711yescharacteristic
460C42C2×D4×C4711yescharacteristic
461C42C24×C4711yescharacteristic
462C23—22no—
463C23—41no—
464C23#120×C4711yescharacteristic
465Q8—22no—
466Q8—22no—
467Q8—42no—
468Q8—42no—
469Q8—42no—
470Q8—42no—
471Q8—41no—
472Q8—41no—
473D4—22no—
474D4—22no—
475D4—42no—
476D4—42no—
477D4—44no—
478D4—42no—
479D4—41no—
480D4—41no—
481D4—81no—
482D4—82no—
483C2×C4—22no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—44no—
494C2×C4—41no—
495C2×C4—82no—
496C2×C4—81no—
497C2×C4—84no—
498C2×C4#120×C4711yescharacteristic
499C2×C4#120×C4711yescharacteristic
500C2×C4#120×C4711yescharacteristic
501C2×C4C22×D4×C4711yescharacteristic
502C2×C4C22×D4×C4711yescharacteristic
503C2×C4C22×D4×C4711yescharacteristic
504C8—41no—
505C8—41no—
506C8—42no—
507C8—42no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—42no—
512C22—42no—
513C22—42no—
514C22—81no—
515C22—81no—
516C22—81no—
517C22C2×#120×C4711yescharacteristic
518C4—21no—
519C4—21no—
520C4—21no—
521C4—21no—
522C4—42no—
523C4—42no—
524C4—42no—
525C4—42no—
526C4—42no—
527C4—81no—
528C4C47×#57512yes—
529C4C47×#57711yescharacteristic
530C4C47×#57811yescharacteristic
531C2—41no—
532C2—82no—
533C2—161no—
534C2C47×#300511yescharacteristic
535C2C47×#301311yescharacteristic
536C2C47×#302111yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#3253C2
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×#3507C2semidirect
3. C47×#3210C2semidirect
4. C47×#3112C2semidirect
5. C47×#1638C2semidirect
6. C47×#1632C2semidirect
7. C47×#1628C2semidirect
8. C47×#1622C2semidirect
9. C47×#1559C2semidirect
10. C47×#1496C2semidirect
11. C47×#1487C2semidirect
239. #18841C47direct (N × H)
263. #3507C2×C47semidirect
265. #3210C2×C47semidirect
266. #3112C2×C47semidirect
267. #1638C2×C47semidirect
268. #1632C2×C47semidirect
269. #1628C2×C47semidirect
270. #1622C2×C47semidirect
271. #1559C2×C47semidirect
272. #1496C2×C47semidirect
273. #1487C2×C47semidirect
319. C47#18841direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35072
C47×#32532
C47×#32102
C47×#31122
C47×#16382
C47×#16322
C47×#16282
C47×#16222
C47×#15592
C47×#14962
C47×#14872
#1884147