Finite Group Databasebeta

← C47×#18833 #26058531

Subgroups — C47×#18833 #26058531

Order 12032.

894 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×#3511C211yesmaximal, characteristic
2C47×#3235C211yesmaximal, characteristic, complemented
3C47×#3229C211yesmaximal, characteristic, complemented
4C47×#3116C211yesmaximal, characteristic, complemented
5C47×#1654C212yesmaximal, complemented
6C47×#1652C212yesmaximal, complemented
7C47×#1638C212yesmaximal, complemented
8C47×#1635C212yesmaximal, complemented
9C47×#1556C211yesmaximal, characteristic, complemented
10C47×#1496C211yesmaximal, characteristic, complemented
11C47×#1488C211yesmaximal, characteristic, complemented
12C47×#556C2212yes—
13C47×#555—21no—
14C47×#554—21no—
15C47×#553—22no—
16C47×#548—22no—
17C47×#547C2212yes—
18C47×#542—22no—
19C47×#537—21no—
20C47×#533—21no—
21C47×#533C2211yescharacteristic
22C47×#532—21no—
23C47×#532C2211yescharacteristic
24C2×C4⋊Q8×C47C2211yescharacteristic
25C47×#520—21no—
26C4×#41×C47C2211yescharacteristic
27C47×#501—21no—
28C47×#498C2212yes—
29C47×#490—21no—
30C47×#487C2212yes—
31C47×#485—21no—
32C47×#483—22no—
33C47×#482—22no—
34C47×#477C2211yescharacteristic
35C47×#476C2211yescharacteristic
36C47×#476C2212yes—
37C47×#475—22no—
38C47×#474C2212yes—
39C47×#462C2211yescharacteristic
40C47×#461C2211yescharacteristic
41C47×#452—21no—
42C47×#441—21no—
43C47×#440—21no—
44C47×#432C2211yescharacteristic
45C47×#432C2211yescharacteristic
46C47×#431C2211yescharacteristic
47C47×#332C2212yes—
48C47×#332C2212yes—
49C47×Q8⋊C8C2212yes—
50C47×D4⋊C8C2212yes—
51C47×D4⋊C8C2212yes—
52C47×D4⋊C8C2212yes—
53C2×#41×C47—22no—
54C2×#41×C47—21no—
55C2×#41×C47D411yescharacteristic
56C22×Q8×C47—21no—
57C2×Q16×C47—21no—
58C2×SD16×C47—21no—
59C4⋊Q8×C47—21no—
60C4⋊Q8×C47—21no—
61C4⋊Q8×C47D412yes—
62C4⋊Q8×C47D411yescharacteristic
63C4⋊Q8×C47C2311yescharacteristic
64C4⋊Q8×C47C2311yescharacteristic
65C4⋊Q8×C47C2312yes—
66#127×C47D411yescharacteristic
67#126×C47—24no—
68#125×C47—22no—
69#125×C47—21no—
70#124×C47—24no—
71#124×C47—22no—
72#124×C47—21no—
73#123×C47—24no—
74C22⋊Q8×C47—22no—
75C22⋊Q8×C47—24no—
76C22⋊Q8×C47—22no—
77C22⋊Q8×C47—22no—
78C22⋊Q8×C47—21no—
79C22⋊Q8×C47—21no—
80#121×C47—22no—
81#121×C47—22no—
82#121×C47—24no—
83#121×C47—22no—
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×C47D411yescharacteristic
91C4×Q8×C47C2311yescharacteristic
92C4×D4×C47—22no—
93C4×D4×C47—24no—
94C4×D4×C47—22no—
95C4×D4×C47—21no—
96C4×D4×C47—21no—
97C4×D4×C47—21no—
98C4×D4×C47D411yescharacteristic
99C4×D4×C47C2311yescharacteristic
100C4×D4×C47C2312yes—
101#117×C47—22no—
102#117×C47—22no—
103#117×C47—21no—
104#117×C47—21no—
105#117×C47D411yescharacteristic
106C2×C4⋊C4×C47—21no—
107C2×C4⋊C4×C47—22no—
108C2×C4⋊C4×C47D412yes—
109C2×C42×C47—21no—
110C2×C42×C47C2311yescharacteristic
111#107×C47—22no—
112#107×C47—21no—
113#106×C47—24no—
114#106×C47—22no—
115#106×C47—21no—
116C4⋊C8×C47—21no—
117C4⋊C8×C47C2311yescharacteristic
118C4⋊C8×C47C2311yescharacteristic
119C4⋊C8×C47C2312yes—
120#103×C47—21no—
121#103×C47—21no—
122#103×C47—21no—
123#103×C47—24no—
124#102×C47—21no—
125#102×C47—22no—
126#102×C47—22no—
127C22⋊C8×C47—21no—
128C22⋊C8×C47—21no—
129C22⋊C8×C47—21no—
130#97×C47—21no—
131#97×C47—21no—
132C4×C8×C47C2312yes—
133#41×C47—41no—
134#41×C47—41no—
135#41×C47—42no—
136#41×C47—42no—
137#41×C47—84no—
138C2×Q8×C47—21no—
139C2×Q8×C47—22no—
140C2×Q8×C47—22no—
141C2×Q8×C47—21no—
142C2×Q8×C47—21no—
143C2×Q8×C47—82no—
144C2×Q8×C47C2×D411yescharacteristic
145C2×D4×C47—21no—
146C2×D4×C47—22no—
147C2×D4×C47—24no—
148C2×D4×C47—21no—
149C2×D4×C47—21no—
150C2×D4×C47C2×D411yescharacteristic
151C2×D4×C47C2×D412yes—
152C22×C4×C47—24no—
153C22×C4×C47—22no—
154C22×C4×C47—21no—
155C22×C4×C47—21no—
156C22×C4×C47—21no—
157C22×C4×C47—22no—
158C22×C4×C47C2×D411yescharacteristic
159C22×C4×C47C2×D411yescharacteristic
160C22×C4×C47C2×D411yescharacteristic
161Q16×C47—42no—
162SD16×C47—42no—
163C2×C8×C47—22no—
164C2×C8×C47—21no—
165C2×C8×C47—21no—
166C2×C8×C47—22no—
167C4⋊C4×C47—24no—
168C4⋊C4×C47—24no—
169C4⋊C4×C47—22no—
170C4⋊C4×C47—22no—
171C4⋊C4×C47—21no—
172C4⋊C4×C47—21no—
173C4⋊C4×C47—22no—
174C4⋊C4×C47—21no—
175C4⋊C4×C47—21no—
176C4⋊C4×C47—21no—
177C4⋊C4×C47—21no—
178C4⋊C4×C47—21no—
179C4⋊C4×C47—41no—
180C4⋊C4×C47—41no—
181C4⋊C4×C47C2×D411yescharacteristic
182C4⋊C4×C47C2×D414yes—
183C4⋊C4×C47C2×D411yescharacteristic
184C4⋊C4×C47C2×D412yes—
185C22⋊C4×C47—24no—
186C22⋊C4×C47—24no—
187C22⋊C4×C47—24no—
188C22⋊C4×C47—21no—
189C22⋊C4×C47—21no—
190C22⋊C4×C47—22no—
191C22⋊C4×C47—21no—
192C22⋊C4×C47—22no—
193C22⋊C4×C47—41no—
194C42×C47—24no—
195C42×C47—21no—
196C42×C47—21no—
197C42×C47—21no—
198C42×C47—41no—
199C42×C47C2×D411yescharacteristic
200C42×C47C2×D411yescharacteristic
201C42×C47C2×D411yescharacteristic
202C42×C47C2411yescharacteristic
203C23×C47—21no—
204C23×C47—22no—
205C23×C47#12011yescharacteristic
206Q8×C47—21no—
207Q8×C47—21no—
208Q8×C47—42no—
209Q8×C47—42no—
210Q8×C47—44no—
211Q8×C47—41no—
212Q8×C47—41no—
213Q8×C47—82no—
214D4×C47—21no—
215D4×C47—21no—
216D4×C47—24no—
217D4×C47—42no—
218D4×C47—42no—
219D4×C47—42no—
220D4×C47—44no—
221D4×C47—84no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—22no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—22no—
228C2×C4×C47—21no—
229C2×C4×C47—24no—
230C2×C4×C47—41no—
231C2×C4×C47—42no—
232C2×C4×C47—42no—
233C2×C4×C47—42no—
234C2×C4×C47—42no—
235C2×C4×C47—42no—
236C2×C4×C47—41no—
237C2×C4×C47—41no—
238C2×C4×C47—82no—
239C2×C4×C47—84no—
240C2×C4×C47#12011yescharacteristic
241C2×C4×C47#12011yescharacteristic
242C2×C4×C47#12011yescharacteristic
243C2×C4×C47C22×D411yescharacteristic
244C2×C4×C47C22×D411yescharacteristic
245C2×C4×C47C22×D411yescharacteristic
246C8×C47—42no—
247C8×C47—41no—
248C8×C47—41no—
249C8×C47—42no—
250#18833C4711yesmaximal, characteristic, direct product factor, Sylow
251C22×C47—21no—
252C22×C47—21no—
253C22×C47—21no—
254C22×C47—41no—
255C22×C47—42no—
256C22×C47—41no—
257C22×C47—42no—
258C22×C47—41no—
259C22×C47—42no—
260C22×C47C2×#12011yescharacteristic
261C4×C47—21no—
262C4×C47—21no—
263C4×C47—21no—
264C4×C47—21no—
265C4×C47—41no—
266C4×C47—42no—
267C4×C47—41no—
268C4×C47—44no—
269C4×C47—41no—
270C4×C47—81no—
271C4×C47—81no—
272C4×C47#57511yescharacteristic
273C4×C47#57511yescharacteristic
274C4×C47#57712yes—
275#3511C2×C4711yescharacteristic
276#3235C2×C4711yescharacteristic, complemented
277#3229C2×C4711yescharacteristic, complemented
278#3116C2×C4711yescharacteristic, complemented
279#1654C2×C4712yescomplemented
280#1652C2×C4712yescomplemented
281#1638C2×C4712yescomplemented
282#1635C2×C4712yescomplemented
283#1556C2×C4711yescharacteristic, complemented
284#1496C2×C4711yescharacteristic, complemented
285#1488C2×C4711yescharacteristic, complemented
286C2×C47—41no—
287C2×C47—81no—
288C2×C47—82no—
289C2×C47#300511yescharacteristic
290C2×C47#300911yescharacteristic
291C2×C47#302011yescharacteristic
292#556C22×C4712yes—
293#555—21no—
294#554—21no—
295#553—22no—
296#548—22no—
297#547C22×C4712yes—
298#542—22no—
299#537—21no—
300#533—21no—
301#533C22×C4711yescharacteristic
302#532—21no—
303#532C22×C4711yescharacteristic
304C2×C4⋊Q8C22×C4711yescharacteristic
305#520—21no—
306C4×#41C22×C4711yescharacteristic
307#501—21no—
308#498C22×C4712yes—
309#490—21no—
310#487C22×C4712yes—
311#485—21no—
312#483—22no—
313#482—22no—
314#477C22×C4711yescharacteristic
315#476C22×C4711yescharacteristic
316#476C22×C4712yes—
317#475—22no—
318#474C22×C4712yes—
319#462C22×C4711yescharacteristic
320#461C22×C4711yescharacteristic
321#452—21no—
322#441—21no—
323#440—21no—
324#432C22×C4711yescharacteristic
325#432C22×C4711yescharacteristic
326#431C22×C4711yescharacteristic
327#332C22×C4712yes—
328#332C22×C4712yes—
329Q8⋊C8C22×C4712yes—
330D4⋊C8C22×C4712yes—
331D4⋊C8C22×C4712yes—
332D4⋊C8C22×C4712yes—
333C47#1883311yescharacteristic, direct product factor, Sylow
334C2×#41—22no—
335C2×#41—21no—
336C2×#41D4×C4711yescharacteristic
337C22×Q8—21no—
338C2×Q16—21no—
339C2×SD16—21no—
340C4⋊Q8—21no—
341C4⋊Q8—21no—
342C4⋊Q8D4×C4712yes—
343C4⋊Q8D4×C4711yescharacteristic
344C4⋊Q8C23×C4711yescharacteristic
345C4⋊Q8C23×C4711yescharacteristic
346C4⋊Q8C23×C4712yes—
347#127D4×C4711yescharacteristic
348#126—24no—
349#125—22no—
350#125—21no—
351#124—24no—
352#124—22no—
353#124—21no—
354#123—24no—
355C22⋊Q8—22no—
356C22⋊Q8—24no—
357C22⋊Q8—22no—
358C22⋊Q8—22no—
359C22⋊Q8—21no—
360C22⋊Q8—21no—
361#121—22no—
362#121—22no—
363#121—24no—
364#121—22no—
365#121—21no—
366#121D4×C4712yes—
367C4×Q8—22no—
368C4×Q8—22no—
369C4×Q8—21no—
370C4×Q8—21no—
371C4×Q8D4×C4711yescharacteristic
372C4×Q8C23×C4711yescharacteristic
373C4×D4—22no—
374C4×D4—24no—
375C4×D4—22no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4D4×C4711yescharacteristic
380C4×D4C23×C4711yescharacteristic
381C4×D4C23×C4712yes—
382#117—22no—
383#117—22no—
384#117—21no—
385#117—21no—
386#117D4×C4711yescharacteristic
387C2×C4⋊C4—21no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4D4×C4712yes—
390C2×C42—21no—
391C2×C42C23×C4711yescharacteristic
392#107—21no—
393#107—22no—
394#106—21no—
395#106—24no—
396#106—22no—
397C4⋊C8—21no—
398C4⋊C8C23×C4711yescharacteristic
399C4⋊C8C23×C4711yescharacteristic
400C4⋊C8C23×C4712yes—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—24no—
405#102—21no—
406#102—22no—
407#102—22no—
408C22⋊C8—21no—
409C22⋊C8—21no—
410C22⋊C8—21no—
411#97—21no—
412#97—21no—
413C4×C8C23×C4712yes—
414#41—41no—
415#41—41no—
416#41—42no—
417#41—42no—
418#41—84no—
419C2×Q8—21no—
420C2×Q8—22no—
421C2×Q8—22no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—82no—
425C2×Q8C2×D4×C4711yescharacteristic
426C2×D4—21no—
427C2×D4—22no—
428C2×D4—24no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4C2×D4×C4712yes—
432C2×D4C2×D4×C4711yescharacteristic
433C22×C4—24no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4C2×D4×C4711yescharacteristic
440C22×C4C2×D4×C4711yescharacteristic
441C22×C4C2×D4×C4711yescharacteristic
442Q16—42no—
443SD16—42no—
444C2×C8—22no—
445C2×C8—22no—
446C2×C8—21no—
447C2×C8—21no—
448C4⋊C4—24no—
449C4⋊C4—24no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—22no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4C2×D4×C4711yescharacteristic
463C4⋊C4C2×D4×C4714yes—
464C4⋊C4C2×D4×C4711yescharacteristic
465C4⋊C4C2×D4×C4712yes—
466C22⋊C4—24no—
467C22⋊C4—24no—
468C22⋊C4—24no—
469C22⋊C4—21no—
470C22⋊C4—21no—
471C22⋊C4—22no—
472C22⋊C4—21no—
473C22⋊C4—22no—
474C22⋊C4—41no—
475C42—24no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—41no—
480C42C2×D4×C4711yescharacteristic
481C42C2×D4×C4711yescharacteristic
482C42C2×D4×C4711yescharacteristic
483C42C24×C4711yescharacteristic
484C23—21no—
485C23—22no—
486C23#120×C4711yescharacteristic
487Q8—21no—
488Q8—21no—
489Q8—42no—
490Q8—42no—
491Q8—44no—
492Q8—41no—
493Q8—41no—
494Q8—82no—
495D4—21no—
496D4—21no—
497D4—24no—
498D4—42no—
499D4—42no—
500D4—42no—
501D4—44no—
502D4—84no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—22no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—24no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—82no—
520C2×C4—84no—
521C2×C4#120×C4711yescharacteristic
522C2×C4#120×C4711yescharacteristic
523C2×C4#120×C4711yescharacteristic
524C2×C4C22×D4×C4711yescharacteristic
525C2×C4C22×D4×C4711yescharacteristic
526C2×C4C22×D4×C4711yescharacteristic
527C8—42no—
528C8—41no—
529C8—41no—
530C8—42no—
531C22—21no—
532C22—21no—
533C22—21no—
534C22—41no—
535C22—42no—
536C22—41no—
537C22—42no—
538C22—41no—
539C22—42no—
540C22C2×#120×C4711yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—41no—
546C4—42no—
547C4—41no—
548C4—44no—
549C4—41no—
550C4—81no—
551C4—81no—
552C4C47×#57511yescharacteristic
553C4C47×#57511yescharacteristic
554C4C47×#57712yes—
555C2—41no—
556C2—81no—
557C2—82no—
558C2C47×#300511yescharacteristic
559C2C47×#300911yescharacteristic
560C2C47×#302011yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#3511C2
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
2. C47×#3235C2semidirect
3. C47×#3229C2semidirect
4. C47×#3116C2semidirect
5. C47×#1654C2semidirect
6. C47×#1652C2semidirect
7. C47×#1638C2semidirect
8. C47×#1635C2semidirect
9. C47×#1556C2semidirect
10. C47×#1496C2semidirect
11. C47×#1488C2semidirect
250. #18833C47direct (N × H)
276. #3235C2×C47semidirect
277. #3229C2×C47semidirect
278. #3116C2×C47semidirect
279. #1654C2×C47semidirect
280. #1652C2×C47semidirect
281. #1638C2×C47semidirect
282. #1635C2×C47semidirect
283. #1556C2×C47semidirect
284. #1496C2×C47semidirect
285. #1488C2×C47semidirect
333. C47#18833direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35112
C47×#32352
C47×#32292
C47×#31162
C47×#16542
C47×#16522
C47×#16382
C47×#16352
C47×#15562
C47×#14962
C47×#14882
#1883347