Finite Group Databasebeta

← C47×#18438 #26058136

Subgroups — C47×#18438 #26058136

Order 12032.

908 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×#3561C211yesmaximal, characteristic
2C47×#3238C211yesmaximal, characteristic, complemented
3C47×#3229C211yesmaximal, characteristic, complemented
4C47×#2640C211yesmaximal, characteristic, complemented
5C47×#1612C214yesmaximal, complemented
6C47×#1608C214yesmaximal, complemented
7C47×#1506C211yesmaximal, characteristic, complemented
8C47×#1500C211yesmaximal, characteristic, complemented
9C47×#1469C211yesmaximal, characteristic, complemented
10C47×#563—21no—
11C47×#562—21no—
12C47×#556—21no—
13C47×#551—22no—
14D4×Q8×C47—21no—
15C47×#548—21no—
16C47×#546—21no—
17C47×#543C2212yes—
18C47×#542—21no—
19C47×#542—22no—
20C47×#538C2212yes—
21C47×#536—21no—
22C47×#533C2211yescharacteristic
23C2×C4⋊Q8×C47C2211yescharacteristic
24C47×#529C2211yescharacteristic
25C2×#124×C47C2211yescharacteristic
26C47×#501—21no—
27C47×#498—21no—
28C47×#489—21no—
29C47×#487—21no—
30C47×#483C2212yes—
31C47×#483C2214yes—
32C47×#480C2212yes—
33C47×#477—21no—
34C47×#476—21no—
35C47×#475—22no—
36C47×#432C2211yescharacteristic
37C47×#431C2211yescharacteristic
38C47×#397C2214yes—
39C47×#393—22no—
40C47×#391—21no—
41C47×#390—21no—
42C47×#376C2211yescharacteristic
43C47×#328C2212yes—
44C47×#328C2214yes—
45C47×#327C2212yes—
46C47×#323C2214yes—
47C2×#41×C47—21no—
48C22×Q8×C47—21no—
49C22×Q8×C47—21no—
50C22×Q8×C47D411yescharacteristic
51C22×D4×C47D411yescharacteristic
52C4⋊Q8×C47—21no—
53C4⋊Q8×C47—22no—
54C4⋊Q8×C47—21no—
55C4⋊Q8×C47—21no—
56C4⋊Q8×C47—21no—
57C4⋊Q8×C47—21no—
58C4⋊Q8×C47D411yescharacteristic
59C4⋊Q8×C47D411yescharacteristic
60#126×C47—22no—
61#126×C47—22no—
62#126×C47—22no—
63#126×C47—21no—
64#125×C47—21no—
65#125×C47D411yescharacteristic
66#124×C47—21no—
67#124×C47—22no—
68#124×C47—22no—
69#124×C47—21no—
70#124×C47—21no—
71#124×C47—21no—
72#124×C47—21no—
73#124×C47D411yescharacteristic
74#123×C47—22no—
75#123×C47—22no—
76#123×C47—22no—
77#123×C47—21no—
78#123×C47—22no—
79C22⋊Q8×C47—22no—
80C22⋊Q8×C47—21no—
81C22⋊Q8×C47—22no—
82C22⋊Q8×C47—22no—
83C22⋊Q8×C47—22no—
84C22⋊Q8×C47—21no—
85C22⋊Q8×C47—22no—
86C22⋊Q8×C47—22no—
87C22⋊Q8×C47—22no—
88C22⋊Q8×C47C2311yescharacteristic
89C22⋊Q8×C47C2312yes—
90#121×C47—21no—
91#121×C47—22no—
92#121×C47—22no—
93#121×C47C2311yescharacteristic
94#120×C47—22no—
95C4×Q8×C47—21no—
96C4×Q8×C47—21no—
97C4×Q8×C47D412yes—
98C4×Q8×C47D411yescharacteristic
99C4×D4×C47—21no—
100C4×D4×C47—22no—
101C4×D4×C47—21no—
102C4×D4×C47—22no—
103C4×D4×C47D411yescharacteristic
104#117×C47—22no—
105#117×C47—21no—
106#117×C47—21no—
107C2×C4⋊C4×C47—21no—
108C2×C4⋊C4×C47C2312yes—
109C2×C22⋊C4×C47—22no—
110C2×C22⋊C4×C47—24no—
111C2×C22⋊C4×C47D412yes—
112C2×C22⋊C4×C47C2312yes—
113C2×C42×C47—21no—
114C2×C42×C47C2311yescharacteristic
115#107×C47—22no—
116#106×C47—24no—
117#106×C47—22no—
118C4⋊C8×C47—21no—
119C4⋊C8×C47—21no—
120#103×C47—24no—
121#103×C47—22no—
122#102×C47—22no—
123C22⋊C8×C47C2312yes—
124C22⋊C8×C47C2312yes—
125#97×C47—21no—
126C4×C8×C47—21no—
127#95×C47—21no—
128#95×C47—24no—
129#95×C47C2312yes—
130C24×C47C2×D412yes—
131#41×C47—82no—
132C2×Q8×C47—22no—
133C2×Q8×C47—21no—
134C2×Q8×C47—21no—
135C2×Q8×C47—21no—
136C2×Q8×C47—42no—
137C2×Q8×C47—41no—
138C2×Q8×C47—41no—
139C2×Q8×C47—82no—
140C2×Q8×C47—82no—
141C2×Q8×C47C2×D411yescharacteristic
142C2×Q8×C47C2×D412yes—
143C2×D4×C47—21no—
144C2×D4×C47—22no—
145C2×D4×C47—22no—
146C2×D4×C47—21no—
147C2×D4×C47—21no—
148C2×D4×C47—42no—
149C2×D4×C47C2×D411yescharacteristic
150C22×C4×C47—22no—
151C22×C4×C47—22no—
152C22×C4×C47—22no—
153C22×C4×C47—21no—
154C22×C4×C47—22no—
155C22×C4×C47—22no—
156C22×C4×C47C2×D411yescharacteristic
157C22×C4×C47C2×D411yescharacteristic
158C22×C4×C47C2×D412yes—
159C22×C4×C47C2411yescharacteristic
160C2×C8×C47—22no—
161C2×C8×C47—22no—
162C4⋊C4×C47—22no—
163C4⋊C4×C47—22no—
164C4⋊C4×C47—22no—
165C4⋊C4×C47—22no—
166C4⋊C4×C47—21no—
167C4⋊C4×C47—21no—
168C4⋊C4×C47—21no—
169C4⋊C4×C47—21no—
170C4⋊C4×C47—21no—
171C4⋊C4×C47—21no—
172C4⋊C4×C47—22no—
173C4⋊C4×C47—21no—
174C4⋊C4×C47—22no—
175C4⋊C4×C47—22no—
176C4⋊C4×C47—22no—
177C4⋊C4×C47—41no—
178C4⋊C4×C47—41no—
179C4⋊C4×C47C2×D411yescharacteristic
180C4⋊C4×C47C2×D412yes—
181C4⋊C4×C47C2×D411yescharacteristic
182C22⋊C4×C47—22no—
183C22⋊C4×C47—22no—
184C22⋊C4×C47—22no—
185C22⋊C4×C47—22no—
186C22⋊C4×C47—22no—
187C22⋊C4×C47—21no—
188C22⋊C4×C47—22no—
189C22⋊C4×C47—22no—
190C22⋊C4×C47—22no—
191C22⋊C4×C47—21no—
192C22⋊C4×C47—21no—
193C22⋊C4×C47—21no—
194C22⋊C4×C47—22no—
195C22⋊C4×C47—22no—
196C22⋊C4×C47—21no—
197C22⋊C4×C47—84no—
198C42×C47—22no—
199C42×C47—22no—
200C42×C47—21no—
201C42×C47—42no—
202C42×C47C2×D411yescharacteristic
203C42×C47C2×D411yescharacteristic
204C42×C47C2×D411yescharacteristic
205C42×C47C2×D411yescharacteristic
206C23×C47—22no—
207C23×C47—21no—
208C23×C47—24no—
209C23×C47—42no—
210C23×C47—42no—
211C23×C47C22×D411yescharacteristic
212Q8×C47—41no—
213Q8×C47—42no—
214Q8×C47—42no—
215Q8×C47—42no—
216Q8×C47—81no—
217Q8×C47—82no—
218Q8×C47—82no—
219Q8×C47—82no—
220D4×C47—41no—
221D4×C47—42no—
222D4×C47—42no—
223D4×C47—81no—
224D4×C47—82no—
225D4×C47—82no—
226C2×C4×C47—22no—
227C2×C4×C47—22no—
228C2×C4×C47—21no—
229C2×C4×C47—22no—
230C2×C4×C47—21no—
231C2×C4×C47—22no—
232C2×C4×C47—22no—
233C2×C4×C47—21no—
234C2×C4×C47—41no—
235C2×C4×C47—42no—
236C2×C4×C47—42no—
237C2×C4×C47—42no—
238C2×C4×C47—42no—
239C2×C4×C47—42no—
240C2×C4×C47—42no—
241C2×C4×C47—44no—
242C2×C4×C47—82no—
243C2×C4×C47—82no—
244C2×C4×C47—82no—
245C2×C4×C47#12011yescharacteristic
246C2×C4×C47#12011yescharacteristic
247C2×C4×C47#12011yescharacteristic
248C2×C4×C47#12011yescharacteristic
249C2×C4×C47C22×D411yescharacteristic
250C2×C4×C47C22×D411yescharacteristic
251C8×C47—42no—
252C8×C47—42no—
253#18438C4711yesmaximal, characteristic, direct product factor, Sylow
254C22×C47—21no—
255C22×C47—21no—
256C22×C47—41no—
257C22×C47—42no—
258C22×C47—41no—
259C22×C47—42no—
260C22×C47—42no—
261C22×C47—41no—
262C22×C47—84no—
263C22×C47C2×#12011yescharacteristic
264C22×C47#57712yes—
265C4×C47—21no—
266C4×C47—21no—
267C4×C47—21no—
268C4×C47—21no—
269C4×C47—21no—
270C4×C47—41no—
271C4×C47—41no—
272C4×C47—42no—
273C4×C47—42no—
274C4×C47—41no—
275C4×C47—42no—
276C4×C47—82no—
277C4×C47—82no—
278C4×C47#45512yes—
279#3561C2×C4711yescharacteristic
280#3238C2×C4711yescharacteristic, complemented
281#3229C2×C4711yescharacteristic, complemented
282#2640C2×C4711yescharacteristic, complemented
283#1612C2×C4714yescomplemented
284#1608C2×C4714yescomplemented
285#1506C2×C4711yescharacteristic, complemented
286#1500C2×C4711yescharacteristic, complemented
287#1469C2×C4711yescharacteristic, complemented
288C2×C47—22no—
289C2×C47—81no—
290C2×C47—82no—
291C2×C47#301011yescharacteristic
292C2×C47C2×#45511yescharacteristic
293C2×C47#302811yescharacteristic
294#563—21no—
295#562—21no—
296#556—21no—
297#551—22no—
298D4×Q8—21no—
299#548—21no—
300#546—21no—
301#543C22×C4712yes—
302#542—21no—
303#542—22no—
304#538C22×C4712yes—
305#536—21no—
306#533C22×C4711yescharacteristic
307C2×C4⋊Q8C22×C4711yescharacteristic
308#529C22×C4711yescharacteristic
309C2×#124C22×C4711yescharacteristic
310#501—21no—
311#498—21no—
312#489—21no—
313#487—21no—
314#483C22×C4712yes—
315#483C22×C4714yes—
316#480C22×C4712yes—
317#477—21no—
318#476—21no—
319#475—22no—
320#432C22×C4711yescharacteristic
321#431C22×C4711yescharacteristic
322#397C22×C4714yes—
323#393—22no—
324#391—21no—
325#390—21no—
326#376C22×C4711yescharacteristic
327#328C22×C4712yes—
328#328C22×C4714yes—
329#327C22×C4712yes—
330#323C22×C4714yes—
331C47#1843811yescharacteristic, direct product factor, Sylow
332C2×#41—21no—
333C22×Q8—21no—
334C22×Q8—21no—
335C22×Q8D4×C4711yescharacteristic
336C22×D4D4×C4711yescharacteristic
337C4⋊Q8—21no—
338C4⋊Q8—22no—
339C4⋊Q8—21no—
340C4⋊Q8—21no—
341C4⋊Q8—21no—
342C4⋊Q8—21no—
343C4⋊Q8D4×C4711yescharacteristic
344C4⋊Q8D4×C4711yescharacteristic
345#126—22no—
346#126—22no—
347#126—22no—
348#126—21no—
349#125—21no—
350#125D4×C4711yescharacteristic
351#124—21no—
352#124—22no—
353#124—22no—
354#124—21no—
355#124—21no—
356#124—21no—
357#124—21no—
358#124D4×C4711yescharacteristic
359#123—22no—
360#123—22no—
361#123—22no—
362#123—21no—
363#123—22no—
364C22⋊Q8—22no—
365C22⋊Q8—21no—
366C22⋊Q8—22no—
367C22⋊Q8—22no—
368C22⋊Q8—22no—
369C22⋊Q8—21no—
370C22⋊Q8—22no—
371C22⋊Q8—22no—
372C22⋊Q8—22no—
373C22⋊Q8C23×C4711yescharacteristic
374C22⋊Q8C23×C4712yes—
375#121—21no—
376#121—22no—
377#121—22no—
378#121C23×C4711yescharacteristic
379#120—22no—
380C4×Q8—21no—
381C4×Q8—21no—
382C4×Q8D4×C4711yescharacteristic
383C4×Q8D4×C4712yes—
384C4×D4—21no—
385C4×D4—22no—
386C4×D4—21no—
387C4×D4—22no—
388C4×D4D4×C4711yescharacteristic
389#117—22no—
390#117—21no—
391#117—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4C23×C4712yes—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4D4×C4712yes—
397C2×C22⋊C4C23×C4712yes—
398C2×C42—21no—
399C2×C42C23×C4711yescharacteristic
400#107—22no—
401#106—24no—
402#106—22no—
403C4⋊C8—21no—
404C4⋊C8—21no—
405#103—24no—
406#103—22no—
407#102—22no—
408C22⋊C8C23×C4712yes—
409C22⋊C8C23×C4712yes—
410#97—21no—
411C4×C8—21no—
412#95—21no—
413#95—24no—
414#95C23×C4712yes—
415C24C2×D4×C4712yes—
416#41—82no—
417C2×Q8—22no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—42no—
422C2×Q8—41no—
423C2×Q8—41no—
424C2×Q8—82no—
425C2×Q8—82no—
426C2×Q8C2×D4×C4711yescharacteristic
427C2×Q8C2×D4×C4712yes—
428C2×D4—21no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—42no—
434C2×D4C2×D4×C4711yescharacteristic
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4C2×D4×C4711yescharacteristic
442C22×C4C2×D4×C4711yescharacteristic
443C22×C4C2×D4×C4712yes—
444C22×C4C24×C4711yescharacteristic
445C2×C8—22no—
446C2×C8—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—22no—
458C4⋊C4—21no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4C2×D4×C4711yescharacteristic
465C4⋊C4C2×D4×C4712yes—
466C4⋊C4C2×D4×C4711yescharacteristic
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C22⋊C4—22no—
471C22⋊C4—22no—
472C22⋊C4—21no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—22no—
480C22⋊C4—22no—
481C22⋊C4—21no—
482C22⋊C4—84no—
483C42—22no—
484C42—22no—
485C42—21no—
486C42—42no—
487C42C2×D4×C4711yescharacteristic
488C42C2×D4×C4711yescharacteristic
489C42C2×D4×C4711yescharacteristic
490C42C2×D4×C4711yescharacteristic
491C23—22no—
492C23—21no—
493C23—24no—
494C23—42no—
495C23—42no—
496C23C22×D4×C4711yescharacteristic
497Q8—41no—
498Q8—42no—
499Q8—42no—
500Q8—42no—
501Q8—81no—
502Q8—82no—
503Q8—82no—
504Q8—82no—
505D4—41no—
506D4—42no—
507D4—42no—
508D4—81no—
509D4—82no—
510D4—82no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—44no—
527C2×C4—82no—
528C2×C4—82no—
529C2×C4—82no—
530C2×C4#120×C4711yescharacteristic
531C2×C4#120×C4711yescharacteristic
532C2×C4#120×C4711yescharacteristic
533C2×C4#120×C4711yescharacteristic
534C2×C4C22×D4×C4711yescharacteristic
535C2×C4C22×D4×C4711yescharacteristic
536C8—42no—
537C8—42no—
538C22—21no—
539C22—21no—
540C22—41no—
541C22—42no—
542C22—41no—
543C22—42no—
544C22—42no—
545C22—41no—
546C22—84no—
547C22C2×#120×C4711yescharacteristic
548C22C47×#57712yes—
549C4—21no—
550C4—21no—
551C4—21no—
552C4—21no—
553C4—21no—
554C4—41no—
555C4—41no—
556C4—42no—
557C4—42no—
558C4—41no—
559C4—42no—
560C4—82no—
561C4—82no—
562C4C47×#45512yes—
563C2—22no—
564C2—82no—
565C2—81no—
566C2C47×#301011yescharacteristic
567C2C2×C47×#45511yescharacteristic
568C2C47×#302811yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC47×#3561C2
LCSG ▷ C22×C4 ▷ 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×#3238C2semidirect
3. C47×#3229C2semidirect
4. C47×#2640C2semidirect
5. C47×#1612C2semidirect
6. C47×#1608C2semidirect
7. C47×#1506C2semidirect
8. C47×#1500C2semidirect
9. C47×#1469C2semidirect
253. #18438C47direct (N × H)
280. #3238C2×C47semidirect
281. #3229C2×C47semidirect
282. #2640C2×C47semidirect
283. #1612C2×C47semidirect
284. #1608C2×C47semidirect
285. #1506C2×C47semidirect
286. #1500C2×C47semidirect
287. #1469C2×C47semidirect
331. C47#18438direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35612
C47×#32382
C47×#32292
C47×#26402
C47×#16122
C47×#16082
C47×#15062
C47×#15002
C47×#14692
#1843847