Finite Group Databasebeta

← C47×#18927 #26058625

Subgroups — C47×#18927 #26058625

Order 12032.

946 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3506C211yesmaximal, characteristic
2C47×#3227C211yesmaximal, characteristic, complemented
3C47×#3209C211yesmaximal, characteristic, complemented
4C2×C47×#474C211yesmaximal, characteristic, complemented
5C47×#1652C214yesmaximal, complemented
6C47×#1641C214yesmaximal, complemented
7C47×#1540C211yesmaximal, characteristic, complemented
8C47×#1481C211yesmaximal, characteristic, complemented
9C47×#1478C211yesmaximal, characteristic, complemented
10C47×#559—22no—
11C47×#556C2212yes—
12C47×#555—21no—
13C47×#553—22no—
14C47×#550C2212yes—
15C47×#547—21no—
16C47×#538—22no—
17C47×#535—21no—
18C47×#533C2211yescharacteristic
19C47×#532C2211yescharacteristic
20C2×C4⋊Q8×C47C2211yescharacteristic
21C47×#525—22no—
22C47×#520—21no—
23C2×C4×D4×C47C2211yescharacteristic
24C47×#498C2212yescomplemented
25C47×#494—21no—
26C47×#487—21no—
27C47×#486C2212yescomplemented
28C47×#481—22no—
29C47×#476—22no—
30C47×#474—22no—
31C47×#474C2214yes—
32C47×#462C2214yescomplemented
33C47×#451—22no—
34C47×#431C2211yescharacteristic
35C47×#431C2211yescharacteristic
36C2×#107×C47—21no—
37C2×C4⋊C8×C47C2211yescharacteristic
38C2×#102×C47—21no—
39C47×#332C2212yescomplemented
40C47×#331C2212yescomplemented
41C47×Q8⋊C8C2214yescomplemented
42C47×D4⋊C8C2214yes—
43C2×#41×C47—22no—
44C2×#41×C47—21no—
45C22×Q8×C47—21no—
46C22×D4×C47D411yescharacteristic
47C23×C4×C47—21no—
48C2×Q16×C47—24no—
49C22×C8×C47—21no—
50C4⋊Q8×C47—21no—
51C4⋊Q8×C47—21no—
52C4⋊Q8×C47—21no—
53C4⋊Q8×C47D411yescharacteristic
54C4⋊Q8×C47D411yescharacteristic
55C4⋊Q8×C47C2312yes—
56C4⋊Q8×C47C2311yescharacteristic
57#127×C47—22no—
58#127×C47C2311yescharacteristic
59#126×C47—24no—
60#125×C47—21no—
61#124×C47—24no—
62#124×C47—22no—
63#124×C47—21no—
64#123×C47—24no—
65#123×C47—24no—
66C22⋊Q8×C47—22no—
67C22⋊Q8×C47—21no—
68C22⋊Q8×C47D412yes—
69#121×C47—22no—
70#121×C47—22no—
71#121×C47—24no—
72#121×C47—21no—
73#121×C47—22no—
74#121×C47D412yes—
75#120×C47—24no—
76C4×Q8×C47—22no—
77C4×Q8×C47—21no—
78C4×Q8×C47C2312yes—
79C4×D4×C47—24no—
80C4×D4×C47—24no—
81C4×D4×C47—22no—
82C4×D4×C47—21no—
83C4×D4×C47—21no—
84C4×D4×C47—21no—
85C4×D4×C47D412yes—
86C4×D4×C47D412yes—
87C4×D4×C47C2312yes—
88#117×C47—22no—
89#117×C47—21no—
90#117×C47—22no—
91C2×C4⋊C4×C47—22no—
92C2×C4⋊C4×C47—21no—
93C2×C4⋊C4×C47—21no—
94C2×C4⋊C4×C47D411yescharacteristic
95C2×C22⋊C4×C47—21no—
96C2×C42×C47C2311yescharacteristic
97#107×C47—24no—
98#106×C47—24no—
99C4⋊C8×C47—21no—
100C4⋊C8×C47—21no—
101C4⋊C8×C47C2312yes—
102C4⋊C8×C47C2312yes—
103#103×C47—24no—
104#102×C47—24no—
105#102×C47—24no—
106C22⋊C8×C47—21no—
107C22⋊C8×C47—21no—
108C4×C8×C47—21no—
109C4×C8×C47C2312yes—
110C24×C47—21no—
111#41×C47—42no—
112#41×C47—42no—
113#41×C47—84no—
114C2×Q8×C47—21no—
115C2×Q8×C47—21no—
116C2×Q8×C47—22no—
117C2×Q8×C47—41no—
118C2×Q8×C47—82no—
119C2×Q8×C47C2×D412yes—
120C2×D4×C47—22no—
121C2×D4×C47—24no—
122C2×D4×C47—24no—
123C2×D4×C47—21no—
124C2×D4×C47—22no—
125C2×D4×C47—22no—
126C2×D4×C47—21no—
127C2×D4×C47—21no—
128C2×D4×C47C2×D412yes—
129C2×D4×C47C2×D412yes—
130C22×C4×C47—24no—
131C22×C4×C47—21no—
132C22×C4×C47—22no—
133C22×C4×C47—22no—
134C22×C4×C47—22no—
135C22×C4×C47—41no—
136C22×C4×C47—82no—
137C22×C4×C47C2×D411yescharacteristic
138C22×C4×C47C2×D411yescharacteristic
139C22×C4×C47C2×D411yescharacteristic
140Q16×C47—84no—
141C2×C8×C47—22no—
142C2×C8×C47—22no—
143C2×C8×C47—22no—
144C2×C8×C47—42no—
145C4⋊C4×C47—24no—
146C4⋊C4×C47—21no—
147C4⋊C4×C47—21no—
148C4⋊C4×C47—21no—
149C4⋊C4×C47—22no—
150C4⋊C4×C47—21no—
151C4⋊C4×C47—21no—
152C4⋊C4×C47—22no—
153C4⋊C4×C47—22no—
154C4⋊C4×C47—22no—
155C4⋊C4×C47—41no—
156C4⋊C4×C47—41no—
157C4⋊C4×C47C2×D412yes—
158C4⋊C4×C47C2×D412yes—
159C4⋊C4×C47C2×D412yes—
160C22⋊C4×C47—24no—
161C22⋊C4×C47—24no—
162C22⋊C4×C47—24no—
163C22⋊C4×C47—22no—
164C22⋊C4×C47—22no—
165C22⋊C4×C47—22no—
166C22⋊C4×C47—22no—
167C22⋊C4×C47—22no—
168C42×C47—24no—
169C42×C47—22no—
170C42×C47C2×D411yescharacteristic
171C42×C47C2×D411yescharacteristic
172C42×C47C2×D411yescharacteristic
173C42×C47C2411yescharacteristic
174C23×C47—22no—
175C23×C47—22no—
176C23×C47—42no—
177C23×C47—81no—
178C23×C47—81no—
179C23×C47#12011yescharacteristic
180Q8×C47—24no—
181Q8×C47—41no—
182Q8×C47—41no—
183Q8×C47—44no—
184Q8×C47—81no—
185Q8×C47—82no—
186D4×C47—22no—
187D4×C47—22no—
188D4×C47—42no—
189D4×C47—44no—
190D4×C47—41no—
191D4×C47—41no—
192D4×C47—42no—
193D4×C47—42no—
194D4×C47—84no—
195D4×C47—84no—
196C2×C4×C47—22no—
197C2×C4×C47—22no—
198C2×C4×C47—22no—
199C2×C4×C47—22no—
200C2×C4×C47—22no—
201C2×C4×C47—41no—
202C2×C4×C47—44no—
203C2×C4×C47—44no—
204C2×C4×C47—42no—
205C2×C4×C47—82no—
206C2×C4×C47—81no—
207C2×C4×C47—84no—
208C2×C4×C47—82no—
209C2×C4×C47#12011yescharacteristic
210C2×C4×C47#12011yescharacteristic
211C2×C4×C47#12011yescharacteristic
212C2×C4×C47#13512yes—
213C2×C4×C47#13712yes—
214C2×C4×C47C22×D411yescharacteristic
215C2×C4×C47C22×D411yescharacteristic
216C2×C4×C47C22×D411yescharacteristic
217C8×C47—42no—
218C8×C47—42no—
219C8×C47—42no—
220#18927C4711yesmaximal, characteristic, direct product factor, Sylow
221C22×C47—21no—
222C22×C47—21no—
223C22×C47—42no—
224C22×C47—42no—
225C22×C47—42no—
226C22×C47—42no—
227C22×C47—42no—
228C22×C47—42no—
229C22×C47—84no—
230C22×C47#45212yes—
231C22×C47C2×#12011yescharacteristic
232C4×C47—21no—
233C4×C47—21no—
234C4×C47—21no—
235C4×C47—42no—
236C4×C47—42no—
237C4×C47—42no—
238C4×C47—42no—
239C4×C47—82no—
240C4×C47#45212yes—
241C4×C47C2×#13511yescharacteristic
242C4×C47C2×#13711yescharacteristic
243C4×C47#57612yes—
244#3506C2×C4711yescharacteristic
245#3227C2×C4711yescharacteristic, complemented
246#3209C2×C4711yescharacteristic, complemented
247C2×#474C2×C4711yescharacteristic, complemented
248#1652C2×C4714yescomplemented
249#1641C2×C4714yescomplemented
250#1540C2×C4711yescharacteristic, complemented
251#1481C2×C4711yescharacteristic, complemented
252#1478C2×C4711yescharacteristic, complemented
253C2×C47—22no—
254C2×C47—82no—
255C2×C47—82no—
256C2×C47C2×#45211yescharacteristic
257C2×C47#300811yescharacteristic
258C2×C47#302211yescharacteristic
259#559—22no—
260#556C22×C4712yes—
261#555—21no—
262#553—22no—
263#550C22×C4712yes—
264#547—21no—
265#538—22no—
266#535—21no—
267#533C22×C4711yescharacteristic
268#532C22×C4711yescharacteristic
269C2×C4⋊Q8C22×C4711yescharacteristic
270#525—22no—
271#520—21no—
272C2×C4×D4C22×C4711yescharacteristic
273#498C22×C4712yescomplemented
274#494—21no—
275#487—21no—
276#486C22×C4712yescomplemented
277#481—22no—
278#476—22no—
279#474—22no—
280#474C22×C4714yes—
281#462C22×C4714yescomplemented
282#451—22no—
283#431C22×C4711yescharacteristic
284#431C22×C4711yescharacteristic
285C2×#107—21no—
286C2×C4⋊C8C22×C4711yescharacteristic
287C2×#102—21no—
288#332C22×C4712yescomplemented
289#331C22×C4712yescomplemented
290Q8⋊C8C22×C4714yescomplemented
291D4⋊C8C22×C4714yes—
292C47#1892711yescharacteristic, direct product factor, Sylow
293C2×#41—22no—
294C2×#41—21no—
295C22×Q8—21no—
296C22×D4D4×C4711yescharacteristic
297C23×C4—21no—
298C2×Q16—24no—
299C22×C8—21no—
300C4⋊Q8—21no—
301C4⋊Q8—21no—
302C4⋊Q8—21no—
303C4⋊Q8D4×C4711yescharacteristic
304C4⋊Q8D4×C4711yescharacteristic
305C4⋊Q8C23×C4712yes—
306C4⋊Q8C23×C4711yescharacteristic
307#127—22no—
308#127C23×C4711yescharacteristic
309#126—24no—
310#125—21no—
311#124—24no—
312#124—22no—
313#124—21no—
314#123—24no—
315#123—24no—
316C22⋊Q8—22no—
317C22⋊Q8—21no—
318C22⋊Q8D4×C4712yes—
319#121—22no—
320#121—22no—
321#121—24no—
322#121—21no—
323#121—22no—
324#121D4×C4712yes—
325#120—24no—
326C4×Q8—22no—
327C4×Q8—21no—
328C4×Q8C23×C4712yes—
329C4×D4—24no—
330C4×D4—24no—
331C4×D4—22no—
332C4×D4—21no—
333C4×D4—21no—
334C4×D4—21no—
335C4×D4D4×C4712yes—
336C4×D4D4×C4712yes—
337C4×D4C23×C4712yes—
338#117—22no—
339#117—21no—
340#117—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4D4×C4711yescharacteristic
345C2×C22⋊C4—21no—
346C2×C42C23×C4711yescharacteristic
347#107—24no—
348#106—24no—
349C4⋊C8—21no—
350C4⋊C8—21no—
351C4⋊C8C23×C4712yes—
352C4⋊C8C23×C4712yes—
353#103—24no—
354#102—24no—
355#102—24no—
356C22⋊C8—21no—
357C22⋊C8—21no—
358C4×C8—21no—
359C4×C8C23×C4712yes—
360C24—21no—
361#41—42no—
362#41—42no—
363#41—84no—
364C2×Q8—21no—
365C2×Q8—21no—
366C2×Q8—22no—
367C2×Q8—41no—
368C2×Q8—82no—
369C2×Q8C2×D4×C4712yes—
370C2×D4—22no—
371C2×D4—24no—
372C2×D4—24no—
373C2×D4—21no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4C2×D4×C4712yes—
379C2×D4C2×D4×C4712yes—
380C22×C4—24no—
381C22×C4—21no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—41no—
386C22×C4—82no—
387C22×C4C2×D4×C4711yescharacteristic
388C22×C4C2×D4×C4711yescharacteristic
389C22×C4C2×D4×C4711yescharacteristic
390Q16—84no—
391C2×C8—22no—
392C2×C8—22no—
393C2×C8—22no—
394C2×C8—42no—
395C4⋊C4—24no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—22no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—41no—
406C4⋊C4—41no—
407C4⋊C4C2×D4×C4712yes—
408C4⋊C4C2×D4×C4712yes—
409C4⋊C4C2×D4×C4712yes—
410C22⋊C4—24no—
411C22⋊C4—24no—
412C22⋊C4—24no—
413C22⋊C4—22no—
414C22⋊C4—22no—
415C22⋊C4—22no—
416C22⋊C4—22no—
417C22⋊C4—22no—
418C42—24no—
419C42—22no—
420C42C2×D4×C4711yescharacteristic
421C42C2×D4×C4711yescharacteristic
422C42C2×D4×C4711yescharacteristic
423C42C24×C4711yescharacteristic
424C23—22no—
425C23—22no—
426C23—42no—
427C23—81no—
428C23—81no—
429C23#120×C4711yescharacteristic
430Q8—24no—
431Q8—41no—
432Q8—41no—
433Q8—44no—
434Q8—81no—
435Q8—82no—
436D4—22no—
437D4—22no—
438D4—42no—
439D4—44no—
440D4—42no—
441D4—41no—
442D4—41no—
443D4—42no—
444D4—84no—
445D4—84no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—41no—
452C2×C4—44no—
453C2×C4—44no—
454C2×C4—42no—
455C2×C4—82no—
456C2×C4—81no—
457C2×C4—84no—
458C2×C4—82no—
459C2×C4#120×C4711yescharacteristic
460C2×C4#120×C4711yescharacteristic
461C2×C4#120×C4711yescharacteristic
462C2×C4#135×C4712yes—
463C2×C4#137×C4712yes—
464C2×C4C22×D4×C4711yescharacteristic
465C2×C4C22×D4×C4711yescharacteristic
466C2×C4C22×D4×C4711yescharacteristic
467C8—42no—
468C8—42no—
469C8—42no—
470C22—21no—
471C22—21no—
472C22—42no—
473C22—42no—
474C22—42no—
475C22—42no—
476C22—42no—
477C22—42no—
478C22—84no—
479C22C47×#45212yes—
480C22C2×#120×C4711yescharacteristic
481C4—21no—
482C4—21no—
483C4—21no—
484C4—42no—
485C4—42no—
486C4—42no—
487C4—42no—
488C4—82no—
489C4C47×#45212yes—
490C4C2×#135×C4711yescharacteristic
491C4C2×#137×C4711yescharacteristic
492C4C47×#57612yes—
493C2—22no—
494C2—82no—
495C2—82no—
496C2C2×C47×#45211yescharacteristic
497C2C47×#300811yescharacteristic
498C2C47×#302211yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#3506C2
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×#3227C2semidirect
3. C47×#3209C2semidirect
4. C2×C47×#474C2semidirect
5. C47×#1652C2semidirect
6. C47×#1641C2semidirect
7. C47×#1540C2semidirect
8. C47×#1481C2semidirect
9. C47×#1478C2semidirect
24. C47×#498C22semidirect
27. C47×#486C22semidirect
32. C47×#462C22semidirect
39. C47×#332C22semidirect
40. C47×#331C22semidirect
41. C47×Q8⋊C8C22semidirect
220. #18927C47direct (N × H)
245. #3227C2×C47semidirect
246. #3209C2×C47semidirect
247. C2×#474C2×C47semidirect
248. #1652C2×C47semidirect
249. #1641C2×C47semidirect
250. #1540C2×C47semidirect
251. #1481C2×C47semidirect
252. #1478C2×C47semidirect
273. #498C22×C47semidirect
276. #486C22×C47semidirect
281. #462C22×C47semidirect
288. #332C22×C47semidirect
289. #331C22×C47semidirect
290. Q8⋊C8C22×C47semidirect
292. C47#18927direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35062
C47×#32272
C47×#32092
C2×C47×#4742
C47×#16522
C47×#16412
C47×#15402
C47×#14812
C47×#14782
#1892747