Finite Group Databasebeta

← D47×#1952 #26219820

Subgroups — D47×#1952 #26219820

Order 12032.

918 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#108×D47C211yesmaximal, characteristic
2#428×D47C212yesmaximal
3C2×#107×D47C211yesmaximal, characteristic
4#405×D47C211yesmaximal, characteristic
5#20244174C211yesmaximal, characteristic, complemented
6#20244173C211yesmaximal, characteristic, complemented
7#20244172C212yesmaximal, complemented
8#20244171C211yesmaximal, characteristic, complemented
9#20244170C212yesmaximal, complemented
10#343×D47C212yesmaximal
11C47×#1952C211yesmaximal, characteristic, complemented
12C2×M16×D47C2212yes—
13C2×M16×D47C2211yescharacteristic
14C22×C8×D47C2211yescharacteristic
15#117×D47C2211yescharacteristic
16C2×C4⋊C4×D47C2212yes—
17C2×#13093960C2211yescharacteristic
18C2×#13093959C2212yes—
19#108×D47C418yescomplemented
20#15689166C2212yes—
21#15689165C2212yes—
22#15689164—22no—
23#15689163C2212yes—
24#15689162—22no—
25C2×#13093958C2211yescharacteristic
26C2×#13093957C2212yes—
27#107×D47—21no—
28#107×D47—21no—
29#107×D47—21no—
30#107×D47—21no—
31#107×D47—22no—
32#106×D47—22no—
33#15689081C2211yescharacteristic
34#15689080—21no—
35#15689079C2211yescharacteristic
36#15689078C2211yescharacteristic
37#15689077—21no—
38#97×D47—21no—
39C4×C8×D47—21no—
40#15688892C2212yes—
41#15688891C2212yes—
42#15688891C2212yes—
43C2×#108×C47C2211yescharacteristic
44C47×#428C2212yes—
45C2×#107×C47C2211yescharacteristic
46C47×#405C2211yescharacteristic
47C47×#343C2212yes—
48C22×C4×D47—22no—
49C22×C4×D47C2311yescharacteristic
50C2×#10625329C2312yes—
51C2×#10625329C2311yescharacteristic
52C2×#10625324—21no—
53C2×#10625324—22no—
54M16×D47—24no—
55M16×D47—22no—
56M16×D47C2×C418yes—
57M16×D47Q814yes—
58C22×C47⋊C8C2311yescharacteristic
59C2×C8×D47—21no—
60C2×C8×D47—22no—
61C2×C8×D47C2×C414yes—
62C2×C8×D47D411yescharacteristic
63C2×C8×D47D411yescharacteristic
64C2×C8×D47D411yescharacteristic
65C2×C8×D47D411yescharacteristic
66C2×C8×D47Q814yes—
67#13093983C2311yescharacteristic
68#13093982D411yescharacteristic
69#13093982D411yescharacteristic
70#13093981—21no—
71#13093980—21no—
72C2×C4⋊Dic47C2312yes—
73C2×Dic47⋊C4—22no—
74C4⋊C4×D47—22no—
75C4⋊C4×D47—22no—
76C4⋊C4×D47—22no—
77C4⋊C4×D47—22no—
78C4⋊C4×D47D411yescharacteristic
79C4⋊C4×D47D411yescharacteristic
80C22⋊C4×D47—21no—
81C42×D47—21no—
82#13093960C2×C414yescomplemented
83#13093959C2×C418yescomplemented
84#13093958—21no—
85#13093958—21no—
86#13093958—22no—
87#13093957—22no—
88#13093957—22no—
89#13093957—22no—
90#13093957—22no—
91#13093956—22no—
92#13093955—22no—
93#13093955—22no—
94#13093935—21no—
95#13093934—21no—
96#13093934—21no—
97C4×C47⋊C8—21no—
98C8×Dic47—21no—
99C8×Dic47—21no—
100C2×M16×C47C2312yes—
101C2×M16×C47C2311yescharacteristic
102C22×C8×C47C2311yescharacteristic
103#117×C47C2311yescharacteristic
104C2×C4⋊C4×C47C2312yes—
105#108×C47C2×C414yescomplemented
106#107×C47—21no—
107#107×C47—21no—
108#107×C47—22no—
109#106×C47—22no—
110#97×C47—21no—
111C4×C8×C47—21no—
112C23×D47#4111yescharacteristic
113C22×C4×C47—22no—
114C22×C4×C47C2411yescharacteristic
115C22×Dic47—22no—
116C22×Dic47#4111yescharacteristic
117C2×C4×D47—21no—
118C2×C4×D47—21no—
119C2×C4×D47—42no—
120C2×C4×D47—42no—
121C2×C4×D47—84no—
122C2×C4×D47C22×C412yes—
123C2×C4×D47C2×D411yescharacteristic
124C2×C4×D47C2×D411yescharacteristic
125C2×C4×D47C2×D411yescharacteristic
126C2×C4×D47C2×D411yescharacteristic
127C2×C4×D47C2×Q812yes—
128C2×C4×D47C2×Q812yes—
129C2×C4×D47#4112yes—
130M16×C47—22no—
131M16×C47—21no—
132M16×C47C22×C414yes—
133M16×C47C2×Q812yes—
134C2×C8×C47—22no—
135C2×C8×C47—21no—
136C2×C8×C47C22×C412yes—
137C2×C8×C47C2×D411yescharacteristic
138C2×C8×C47C2×D411yescharacteristic
139C2×C8×C47C2×Q812yes—
140C4⋊C4×C47—22no—
141C4⋊C4×C47—22no—
142C4⋊C4×C47C2×D411yescharacteristic
143C4⋊C4×C47C2×D411yescharacteristic
144C22⋊C4×C47—21no—
145C42×C47—21no—
146C22⋊Dic47—21no—
147(C2×D47)⋊C4—21no—
148(C2×D47)⋊C4—21no—
149C4⋊Dic47—22no—
150C4⋊Dic47—22no—
151C4⋊Dic47C2×D411yescharacteristic
152C4⋊Dic47C2×D411yescharacteristic
153Dic47⋊C4—21no—
154Dic47⋊C4—21no—
155Dic47⋊C4—42no—
156Dic47⋊C4—42no—
157C4×Dic47—21no—
158C4×Dic47—21no—
159C4×Dic47—21no—
160#10625329—22no—
161#10625329—21no—
162#10625329C22×C414yes—
163#10625329C2×Q812yes—
164C2×C47⋊C8—21no—
165C2×C47⋊C8—22no—
166C2×C47⋊C8C22×C412yes—
167C2×C47⋊C8C2×D411yescharacteristic
168C2×C47⋊C8C2×D411yescharacteristic
169C2×C47⋊C8C2×Q812yes—
170#10625324—28no—
171#10625324—24no—
172C8×D47—28no—
173C8×D47—24no—
174C8×D47C4⋊C414yes—
175C8×D47C4⋊C414yes—
176C8×D47C4⋊C414yes—
177C8×D47C4⋊C414yes—
178C23×C47C2×#4111yescharacteristic
179C22×D47—22no—
180C22×D47—22no—
181C22×D47C4×Q812yes—
182C22×D47#12111yescharacteristic
183C22×D47#12111yescharacteristic
184C22×D47#12512yes—
185C2×C4×C47—21no—
186C2×C4×C47—21no—
187C2×C4×C47—42no—
188C2×C4×C47—82no—
189C2×C4×C47C23×C411yescharacteristic
190C2×C4×C47C22×D411yescharacteristic
191C2×C4×C47C22×D411yescharacteristic
192C2×C4×C47C22×Q811yescharacteristic
193C2×C4×C47C22×Q811yescharacteristic
194C2×C4×C47C2×#4111yescharacteristic
195C2×Dic47—21no—
196C2×Dic47—21no—
197C2×Dic47—42no—
198C2×Dic47—82no—
199C2×Dic47C4×Q812yes—
200C2×Dic47#12111yescharacteristic
201C2×Dic47#12111yescharacteristic
202C2×Dic47#12512yes—
203C4×D47—42no—
204C4×D47—42no—
205C4×D47—84no—
206C4×D47—84no—
207C4×D47C2×C4⋊C412yes—
208C4×D47C2×C4⋊C412yes—
209C4×D47C4×D412yes—
210C4×D47C4×D412yes—
211C4×D47C22⋊Q812yes—
212C4×D47C22⋊Q812yes—
213C4×D47C4⋊Q812yes—
214C4×D47C4⋊Q812yes—
215C8×C47—24no—
216C8×C47—22no—
217C8×C47C2×C4⋊C412yes—
218C8×C47C2×C4⋊C412yes—
219C47⋊C8—24no—
220C47⋊C8—22no—
221C47⋊C8C2×C4⋊C412yes—
222C47⋊C8C2×C4⋊C412yes—
223C2×#1952—471nomaximal, Sylow
224C22×C47—21no—
225C22×C47—21no—
226C22×C47C2×C4×Q811yescharacteristic
227C22×C47C2×#12111yescharacteristic
228C22×C47C2×#12511yescharacteristic
229C2×D47—21no—
230C2×D47—21no—
231C2×D47—24no—
232C2×D47—24no—
233C2×D47#38912yes—
234C2×D47#38912yes—
235C2×D47#47212yes—
236C2×D47#47312yes—
237C4×C47—41no—
238C4×C47—41no—
239C4×C47—82no—
240C4×C47C22×C4⋊C411yescharacteristic
241C4×C47C2×C4×D411yescharacteristic
242C4×C47C2×C22⋊Q811yescharacteristic
243C4×C47C2×C4⋊Q811yescharacteristic
244Dic47—41no—
245Dic47—41no—
246Dic47—82no—
247Dic47#38912yes—
248Dic47#38912yes—
249C22×#108—471no—
250C2×#428—472no—
251C22×#107—471no—
252C2×#405—471no—
253#1952—471no—
254#1952—472no—
255#1952—471no—
256#1952—471no—
257#1952—472no—
258#1952D4711yescharacteristic, direct product factor
259C2×#343—472no—
260C2×C47—21no—
261C2×C47—21no—
262C2×C47C2×#38911yescharacteristic
263C2×C47C2×#47211yescharacteristic
264C2×C47C2×#47311yescharacteristic
265D47—22no—
266D47#195214yesdirect product factor
267C22×M16—471no—
268C22×M16—472no—
269C23×C8—471no—
270C2×#117—471no—
271C22×C4⋊C4—472no—
272C2×#108—472no—
273C2×#108—471no—
274C2×#108—478no—
275C2×#108C2×D4711yescharacteristic
276#428—472no—
277#428—472no—
278#428—472no—
279#428—942no—
280#428—942no—
281#428C2×D4712yes—
282C2×#107—471no—
283C2×#107—472no—
284C2×#107—942no—
285C2×#107—941no—
286C2×#107—941no—
287C2×#107—941no—
288C2×#107—941no—
289C2×#107C2×D4711yescharacteristic
290C2×#106—942no—
291#405—471no—
292#405—471no—
293#405—471no—
294#405—941no—
295#405—941no—
296#405C2×D4711yescharacteristic
297C2×#97—941no—
298C2×C4×C8—941no—
299#343—472no—
300#343—472no—
301#343—472no—
302#343C2×D4712yes—
303C47C2×#195211yescharacteristic, complemented, Sylow
304C23×C4—471no—
305C23×C4—942no—
306C2×M16—471no—
307C2×M16—472no—
308C2×M16—478no—
309C2×M16—474no—
310C2×M16—941no—
311C2×M16—942no—
312C2×M16—942no—
313C2×M16—944no—
314C2×M16C22×D4712yes—
315C2×M16C22×D4711yescharacteristic
316C22×C8—471no—
317C22×C8—474no—
318C22×C8—471no—
319C22×C8—471no—
320C22×C8—471no—
321C22×C8—471no—
322C22×C8—474no—
323C22×C8—941no—
324C22×C8—942no—
325C22×C8C22×D4711yescharacteristic
326#117—471no—
327#117—471no—
328#117—471no—
329#117—941no—
330#117—941no—
331#117C22×D4711yescharacteristic
332C2×C4⋊C4—471no—
333C2×C4⋊C4—471no—
334C2×C4⋊C4—472no—
335C2×C4⋊C4—942no—
336C2×C4⋊C4—942no—
337C2×C4⋊C4—942no—
338C2×C4⋊C4—942no—
339C2×C4⋊C4—942no—
340C2×C4⋊C4C22×D4712yes—
341C2×C22⋊C4—941no—
342C2×C42—941no—
343#108—478no—
344#108—474no—
345#108C4×D4714yescomplemented
346#107—21no—
347#107—21no—
348#107—22no—
349#107—942no—
350#107—942no—
351#107—942no—
352#107—942no—
353#107—941no—
354#107—941no—
355#107—942no—
356#106—22no—
357#106—942no—
358#106—942no—
359#106—942no—
360#97—21no—
361#97—941no—
362#97—941no—
363#97—941no—
364C4×C8—21no—
365C4×C8—941no—
366C4×C8—941no—
367C4×C8—941no—
368C24—471no—
369C22×C4—22no—
370C22×C4—471no—
371C22×C4—472no—
372C22×C4—471no—
373C22×C4—471no—
374C22×C4—471no—
375C22×C4—471no—
376C22×C4—472no—
377C22×C4—472no—
378C22×C4—472no—
379C22×C4—941no—
380C22×C4—941no—
381C22×C4—942no—
382C22×C4—3764no—
383C22×C4—1882no—
384C22×C4—1882no—
385C22×C4C23×D4711yescharacteristic
386M16—22no—
387M16—21no—
388M16—474no—
389M16—472no—
390M16—948no—
391M16—944no—
392M16—942no—
393M16—941no—
394M16C2×C4×D4714yes—
395M16Q8×D4712yes—
396C2×C8—21no—
397C2×C8—22no—
398C2×C8—472no—
399C2×C8—471no—
400C2×C8—471no—
401C2×C8—472no—
402C2×C8—474no—
403C2×C8—474no—
404C2×C8—474no—
405C2×C8—474no—
406C2×C8—948no—
407C2×C8—944no—
408C2×C8—941no—
409C2×C8—942no—
410C2×C8C2×C4×D4712yes—
411C2×C8D4×D4711yescharacteristic
412C2×C8D4×D4711yescharacteristic
413C2×C8Q8×D4712yes—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—471no—
417C4⋊C4—471no—
418C4⋊C4—941no—
419C4⋊C4—941no—
420C4⋊C4—942no—
421C4⋊C4—942no—
422C4⋊C4—1882no—
423C4⋊C4—1882no—
424C4⋊C4D4×D4711yescharacteristic
425C4⋊C4D4×D4711yescharacteristic
426C22⋊C4—21no—
427C22⋊C4—941no—
428C22⋊C4—941no—
429C22⋊C4—941no—
430C42—21no—
431C42—941no—
432C42—941no—
433C42—941no—
434C23—471no—
435C23—472no—
436C23—471no—
437C23—472no—
438C23—942no—
439C23—942no—
440C23#41×D4711yescharacteristic
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—42no—
444C2×C4—82no—
445C2×C4—472no—
446C2×C4—471no—
447C2×C4—471no—
448C2×C4—472no—
449C2×C4—472no—
450C2×C4—472no—
451C2×C4—472no—
452C2×C4—472no—
453C2×C4—472no—
454C2×C4—472no—
455C2×C4—472no—
456C2×C4—472no—
457C2×C4—941no—
458C2×C4—941no—
459C2×C4—3764no—
460C2×C4—3764no—
461C2×C4—3762no—
462C2×C4—1882no—
463C2×C4—1882no—
464C2×C4—1882no—
465C2×C4C22×C4×D4711yescharacteristic
466C2×C4C2×D4×D4711yescharacteristic
467C2×C4C2×D4×D4711yescharacteristic
468C2×C4C2×Q8×D4711yescharacteristic
469C2×C4C2×Q8×D4711yescharacteristic
470C2×C4#41×D4711yescharacteristic
471C8—24no—
472C8—22no—
473C8—472no—
474C8—472no—
475C8—944no—
476C8—942no—
477C8C4⋊C4×D4712yes—
478C8C4⋊C4×D4712yes—
479C22—21no—
480C22—21no—
481C22—472no—
482C22—472no—
483C22—472no—
484C22—472no—
485C22—944no—
486C22—944no—
487C22—941no—
488C22—941no—
489C22C4×Q8×D4711yescharacteristic
490C22#121×D4711yescharacteristic
491C22#125×D4711yescharacteristic
492C4—41no—
493C4—41no—
494C4—82no—
495C4—472no—
496C4—472no—
497C4—3762no—
498C4—1881no—
499C4—1881no—
500C4C2×C4⋊C4×D4711yescharacteristic
501C4C4×D4×D4711yescharacteristic
502C4C22⋊Q8×D4711yescharacteristic
503C4C4⋊Q8×D4711yescharacteristic
504C2—21no—
505C2—21no—
506C2—474no—
507C2—942no—
508C2#389×D4711yescharacteristic
509C2#472×D4711yescharacteristic
510C2#473×D4711yescharacteristic
subgroupG/H
centerC22#121×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1952C2
socleC22×C47C2×#121
prime radicalC23×D47#41
cosocleC22×C4×C47C24
hypercenter#1952D47
hypocenterC47C2×#1952
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1952

Complements

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

NH ≅ G/Ntype
5. #20244174C2semidirect
6. #20244173C2semidirect
7. #20244172C2semidirect
8. #20244171C2semidirect
9. #20244170C2semidirect
11. C47×#1952C2semidirect
19. #108×D47C4semidirect
82. #13093960C2×C4semidirect
83. #13093959C2×C4semidirect
105. #108×C47C2×C4semidirect
258. #1952D47direct (N × H)
266. D47#1952direct (N × H)
303. C47C2×#1952semidirect
345. #108C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#108×D472
#428×D472
C2×#107×D472
#405×D472
#202441742
#202441732
#202441722
#202441712
#202441702
#343×D472
C47×#19522
C2×#195247