Finite Group Databasebeta

← D47×#2961 #27080645

Subgroups — D47×#2961 #27080645

Order 12032.

1894 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D47C211yesmaximal, characteristic
2#20252329C211yesmaximal, characteristic, complemented
3#20252328C211yesmaximal, characteristic, complemented
4#20252327C212yesmaximal, complemented
5#20252326C212yesmaximal, complemented
6#20252325C211yesmaximal, characteristic, complemented
7#20252324C218yesmaximal, complemented
8#446×D47C218yesmaximal, complemented
9#424×D47C212yesmaximal
10#423×D47C211yesmaximal, characteristic
11#405×D47C212yesmaximal
12C2×#97×D47C211yesmaximal, characteristic
13C47×#2961C211yesmaximal, characteristic, complemented
14C2×M16×D47C2212yes—
15C22×C8×D47C2211yescharacteristic
16C22×C8×D47C2211yescharacteristic
17#15689680C2211yescharacteristic
18#15689679C412yes—
19#15689678C412yes—
20#15689677C2214yes—
21#15689676C2212yes—
22#15689675C414yes—
23C4⋊Q8×D47C412yes—
24#125×D47C412yes—
25C22⋊Q8×D47C414yes—
26C4×Q8×D47C2214yes—
27#117×D47C2212yes—
28C2×C42×D47C2211yescharacteristic
29#15689254C2218yescomplemented
30#15689253C2218yescomplemented
31#15689252C2218yescomplemented
32#15689252C2218yescomplemented
33#15689251C2218yescomplemented
34#15689251C2218yescomplemented
35#15689250C2218yescomplemented
36#15689151C2212yes—
37#15689150C2212yes—
38#15689149C2212yes—
39#15689148C2218yes—
40#15689147C2211yescharacteristic
41#15689146C2212yes—
42#15689145C2214yes—
43C4⋊C8×D47C2214yes—
44C4⋊C8×D47C2218yes—
45#15689081C2212yes—
46#15689080C2214yes—
47#15689079C2212yes—
48#15689078C2212yes—
49#15689077C2214yes—
50C2×#13093935C2211yescharacteristic
51C2×#13093934C2211yescharacteristic
52C2×#13093934C2211yescharacteristic
53#97×D47C2214yes—
54#97×D47C2214yes—
55#97×D47C2214yes—
56C4×C8×D47C2214yes—
57C47×#533C2211yescharacteristic
58C47×#446C2218yescomplemented
59C47×#424C2212yes—
60C47×#423C2211yescharacteristic
61C47×#405C2212yes—
62C2×#97×C47C2211yescharacteristic
63C2×Q8×D47C2×C414yes—
64C22×C4×D47C2×C412yes—
65C22×C4×D47C2311yescharacteristic
66C2×#10625329C2312yes—
67C2×#10625324C2314yes—
68M16×D47—28no—
69C22×C47⋊C8C2311yescharacteristic
70C22×C47⋊C8C2311yescharacteristic
71C2×C8×D47—24no—
72C2×C8×D47Q818yescomplemented
73C2×C8×D47C2314yes—
74C2×C8×D47C2312yes—
75C2×C8×D47C2312yes—
76C2×C8×D47C2312yes—
77C2×C8×D47C2312yes—
78#13094024C2×C412yes—
79#13094023C2×C414yes—
80#13094023C2×C414yes—
81#13094022C2×C414yes—
82#13094016C2×C412yes—
83#13094015C2×C414yes—
84#13094014C2×C418yes—
85#13094004C2×C414yes—
86#13094003C2×C414yes—
87#13094002C2×C418yes—
88#13094001C2×C418yes—
89#13094000C2×C414yes—
90Q8×Dic47C2×C414yes—
91C4×Dic94C2318yes—
92C4×Dic94C2314yes—
93#13093989C2×C414yes—
94#13093989C2×C418yes—
95#13093983C2312yes—
96#13093982C2×C414yes—
97#13093981C2314yes—
98#13093980C2×C414yes—
99C4⋊C4×D47C2×C414yes—
100C4⋊C4×D47C2×C418yes—
101C4⋊C4×D47C2×C414yes—
102C22⋊C4×D47C2×C414yes—
103C2×C4×Dic47C2×C412yes—
104C2×C4×Dic47C2311yescharacteristic
105C42×D47C2×C411yescharacteristic
106C42×D47C2×C411yescharacteristic
107C42×D47C2×C411yescharacteristic
108C42×D47C2×C411yescharacteristic
109C42×D47C2312yes—
110C42×D47C2312yes—
111C42×D47C2314yes—
112C4⋊(C47⋊C8)C2314yes—
113C4⋊(C47⋊C8)C2318yes—
114Dic47⋊C8C2318yes—
115Dic47⋊C8C2318yes—
116Dic47⋊C8C2318yes—
117#13093935C2314yes—
118#13093935C2314yes—
119#13093934C2314yes—
120#13093934C2314yes—
121#13093934C2314yes—
122#13093934C2314yes—
123C4×C47⋊C8C2314yes—
124C8×Dic47C2314yes—
125C8×Dic47C2314yes—
126C2×M16×C47C2312yes—
127C22×C8×C47C2311yescharacteristic
128C22×C8×C47C2311yescharacteristic
129C4⋊Q8×C47C2×C412yes—
130#125×C47C2×C412yes—
131C22⋊Q8×C47C2×C414yes—
132C4×Q8×C47C2314yes—
133#117×C47C2312yes—
134C2×C42×C47C2311yescharacteristic
135C4⋊C8×C47C2318yes—
136C4⋊C8×C47C2314yes—
137#97×C47C2314yes—
138#97×C47C2314yes—
139C4×C8×C47C2314yes—
140C23×D47C22×C411yescharacteristic
141C2×Q8×C47C22×C414yes—
142C22×C4×C47C22×C412yes—
143C22×C4×C47C2411yescharacteristic
144C22×Dic47C22×C412yes—
145C22×Dic47C22×C411yescharacteristic
146Q8×D47—48no—
147C2×C4×D47—44no—
148C2×C4×D47C22×C412yes—
149C2×C4×D47C22×C412yes—
150C2×C4×D47C22×C418yes—
151C2×C4×D47C22×C412yes—
152C2×C4×D47C22×C412yes—
153C2×C4×D47C22×C411yescharacteristic
154C2×C4×D47C22×C411yescharacteristic
155C2×C4×D47C2×Q814yes—
156C2×C4×D47#4114yes—
157C2×C4×D47C2411yescharacteristic
158C2×C4×D47C2411yescharacteristic
159C2×Dic94C22×C418yes—
160C2×Dic94C22×C414yes—
161M16×C47—24no—
162C2×C8×C47—22no—
163C2×C8×C47C2×Q814yescomplemented
164C2×C8×C47C2412yes—
165C2×C8×C47C2414yes—
166C2×C8×C47C2412yes—
167C4⋊C4×C47C22×C414yes—
168C4⋊C4×C47C22×C418yes—
169C4⋊C4×C47C22×C414yes—
170C22⋊C4×C47C22×C414yes—
171C42×C47C22×C411yescharacteristic
172C42×C47C22×C411yescharacteristic
173C42×C47C2412yes—
174C42×C47C2414yes—
175C22⋊Dic47C22×C414yes—
176(C2×D47)⋊C4C22×C418yes—
177C4⋊Dic47C22×C414yes—
178C4⋊Dic47C22×C414yes—
179C4⋊Dic47C22×C418yes—
180Dic47⋊C4C22×C418yes—
181Dic47⋊C4C22×C418yes—
182Dic47⋊C4C22×C418yes—
183Dic47⋊C4C22×C418yes—
184C4×Dic47C22×C411yescharacteristic
185C4×Dic47C22×C411yescharacteristic
186C4×Dic47C22×C412yes—
187C4×Dic47C22×C412yes—
188C4×Dic47C22×C412yes—
189C4×Dic47C22×C412yes—
190C4×Dic47C22×C418yes—
191C4×Dic47C2414yes—
192C4×Dic47C2412yes—
193#10625329—24no—
194C2×C47⋊C8—22no—
195C2×C47⋊C8C2×Q814yescomplemented
196C2×C47⋊C8C2414yes—
197C2×C47⋊C8C2412yes—
198C2×C47⋊C8C2412yes—
199#10625324—28no—
200C8×D47—24no—
201C8×D47—24no—
202C8×D47—28no—
203C8×D47C2×Q818yes—
204C8×D47C2×Q818yescomplemented
205C23×C47C23×C411yescharacteristic
206C22×D47—24no—
207C22×D47C4×Q814yes—
208C22×D47C23×C411yescharacteristic
209C22×D47C23×C411yescharacteristic
210Q8×C47—44no—
211C2×C4×C47—42no—
212C2×C4×C47C23×C412yes—
213C2×C4×C47C23×C412yes—
214C2×C4×C47C23×C418yes—
215C2×C4×C47C23×C411yescharacteristic
216C2×C4×C47C22×Q812yes—
217C2×C4×C47C2×#4112yes—
218C2×C4×C47C2511yescharacteristic
219C2×Dic47—42no—
220C2×Dic47C4×Q814yes—
221C2×Dic47C23×C412yes—
222C2×Dic47C23×C412yes—
223C2×Dic47C23×C418yes—
224C2×Dic47C23×C411yescharacteristic
225C2×Dic47C23×C411yescharacteristic
226C4×D47—24no—
227C4×D47—24no—
228C4×D47—216no—
229C4×D47—42no—
230C4×D47—42no—
231C4×D47C4×Q814yes—
232C4×D47C4×Q814yes—
233C4×D47C22×Q812yes—
234C4×D47C22×Q812yes—
235C4×D47C2×#4112yes—
236C4×D47C2×#4112yes—
237Dic94—48no—
238Dic94—44no—
239C8×C47—22no—
240C8×C47—24no—
241C8×C47C22×Q814yes—
242C47⋊C8—22no—
243C47⋊C8—24no—
244C47⋊C8C22×Q814yes—
245C2×#2961—471nomaximal, Sylow
246C22×C47—22no—
247C22×C47C2×C4×Q812yes—
248C22×C47C24×C411yescharacteristic
249C2×D47—22no—
250C2×D47—28no—
251C2×D47C2×C4×Q812yes—
252C2×D47C2×C4×Q812yes—
253C2×D47#56814yes—
254C4×C47—22no—
255C4×C47—28no—
256C4×C47—22no—
257C4×C47C2×C4×Q812yes—
258C4×C47C23×Q811yescharacteristic
259C4×C47C22×#4111yescharacteristic
260Dic47—22no—
261Dic47—28no—
262Dic47—22no—
263Dic47C2×C4×Q812yes—
264Dic47C2×C4×Q812yes—
265C2×#533—471no—
266#2961—478no—
267#2961—472no—
268#2961—471no—
269#2961—472no—
270#2961—471no—
271#2961—471no—
272#2961D4711yescharacteristic, direct product factor
273C2×#446—478no—
274C2×#424—472no—
275C2×#423—471no—
276C2×#405—472no—
277C22×#97—471no—
278C2×C47—22no—
279C2×C47C22×C4×Q811yescharacteristic
280C2×C47C2×#56812yes—
281D47—22no—
282D47#296114yesdirect product factor
283C22×M16—472no—
284C23×C8—471no—
285C23×C8—471no—
286#533—472no—
287#533—472no—
288#533—474no—
289#533—474no—
290#533—472no—
291#533—471no—
292#533C2×D4711yescharacteristic
293C2×C4⋊Q8—472no—
294C2×#125—472no—
295C2×C22⋊Q8—474no—
296C2×C4×Q8—474no—
297C2×#117—472no—
298C22×C42—471no—
299#446—478no—
300#446—478no—
301#446—478no—
302#446—478no—
303#446—478no—
304#446—478no—
305#446—478no—
306#446C2×D4718yescomplemented
307#424—472no—
308#424—472no—
309#424—472no—
310#424—478no—
311#424C2×D4712yes—
312#423—472no—
313#423—471no—
314#423—474no—
315#423C2×D4711yescharacteristic
316C2×C4⋊C8—474no—
317C2×C4⋊C8—478no—
318#405—472no—
319#405—472no—
320#405—472no—
321#405—474no—
322#405—474no—
323#405C2×D4712yes—
324C2×#97—471no—
325C2×#97—471no—
326C2×#97—471no—
327C2×#97—474no—
328C2×#97—474no—
329C2×#97—474no—
330C2×#97C2×D4711yescharacteristic
331C2×C4×C8—474no—
332C47C2×#296111yescharacteristic, complemented, Sylow
333C22×Q8—474no—
334C23×C4—471no—
335C23×C4—472no—
336C2×M16—472no—
337C2×M16—474no—
338C2×M16—948no—
339C2×M16C22×D4712yes—
340C22×C8—471no—
341C22×C8—478no—
342C22×C8—472no—
343C22×C8—472no—
344C22×C8—471no—
345C22×C8—472no—
346C22×C8—472no—
347C22×C8—474no—
348C22×C8—944no—
349C22×C8C22×D4711yescharacteristic
350C22×C8C22×D4711yescharacteristic
351C4⋊Q8—474no—
352C4⋊Q8—474no—
353C4⋊Q8—474no—
354C4⋊Q8—472no—
355C4⋊Q8C4×D4712yes—
356#125—478no—
357#125—474no—
358#125—472no—
359#125C4×D4712yes—
360C22⋊Q8—474no—
361C22⋊Q8—474no—
362C22⋊Q8—478no—
363C22⋊Q8—474no—
364C22⋊Q8—478no—
365C22⋊Q8C4×D4714yes—
366C4×Q8—474no—
367C4×Q8—474no—
368C4×Q8—478no—
369C4×Q8—474no—
370C4×Q8—478no—
371C4×Q8C22×D4714yes—
372#117—472no—
373#117—474no—
374#117—474no—
375#117—474no—
376#117C22×D4712yes—
377C2×C4⋊C4—474no—
378C2×C4⋊C4—478no—
379C2×C4⋊C4—474no—
380C2×C22⋊C4—474no—
381C2×C42—472no—
382C2×C42—471no—
383C2×C42—471no—
384C2×C42—471no—
385C2×C42—471no—
386C2×C42—471no—
387C2×C42—474no—
388C2×C42—472no—
389C2×C42—472no—
390C2×C42C22×D4711yescharacteristic
391C4⋊C8—478no—
392C4⋊C8—478no—
393C4⋊C8—478no—
394C4⋊C8—474no—
395C4⋊C8—478no—
396C4⋊C8C22×D4714yes—
397C4⋊C8C22×D4718yes—
398#97—474no—
399#97—474no—
400#97—474no—
401#97—474no—
402#97—474no—
403#97—474no—
404#97C22×D4714yes—
405#97C22×D4714yes—
406C4×C8—474no—
407C4×C8—474no—
408C4×C8—474no—
409C4×C8C22×D4714yes—
410C24—471no—
411C2×Q8—478no—
412C2×Q8—474no—
413C2×Q8—1888no—
414C2×Q8C2×C4×D4714yes—
415C22×C4—471no—
416C22×C4—471no—
417C22×C4—471no—
418C22×C4—474no—
419C22×C4—474no—
420C22×C4—471no—
421C22×C4—471no—
422C22×C4—472no—
423C22×C4—472no—
424C22×C4—472no—
425C22×C4—478no—
426C22×C4—472no—
427C22×C4—472no—
428C22×C4—1884no—
429C22×C4C2×C4×D4712yes—
430C22×C4C23×D4711yescharacteristic
431M16—24no—
432M16—948no—
433M16—944no—
434C2×C8—22no—
435C2×C8—474no—
436C2×C8—472no—
437C2×C8—478no—
438C2×C8—478no—
439C2×C8—474no—
440C2×C8—472no—
441C2×C8—944no—
442C2×C8—944no—
443C2×C8—948no—
444C2×C8—942no—
445C2×C8Q8×D4714yescomplemented
446C2×C8C23×D4714yes—
447C2×C8C23×D4712yes—
448C2×C8C23×D4712yes—
449C4⋊C4—478no—
450C4⋊C4—478no—
451C4⋊C4—478no—
452C4⋊C4—478no—
453C4⋊C4—474no—
454C4⋊C4—478no—
455C4⋊C4—474no—
456C4⋊C4C2×C4×D4714yes—
457C4⋊C4C2×C4×D4718yes—
458C4⋊C4C2×C4×D4714yes—
459C22⋊C4—474no—
460C22⋊C4—478no—
461C22⋊C4C2×C4×D4714yes—
462C42—472no—
463C42—472no—
464C42—472no—
465C42—471no—
466C42—472no—
467C42—471no—
468C42—478no—
469C42—474no—
470C42—472no—
471C42C2×C4×D4711yescharacteristic
472C42C2×C4×D4711yescharacteristic
473C42C23×D4714yes—
474C42C23×D4712yes—
475C23—471no—
476C23—474no—
477C23—471no—
478C23—944no—
479C23C22×C4×D4711yescharacteristic
480Q8—44no—
481Q8—1884no—
482Q8—1888no—
483C2×C4—42no—
484C2×C4—474no—
485C2×C4—471no—
486C2×C4—471no—
487C2×C4—474no—
488C2×C4—474no—
489C2×C4—472no—
490C2×C4—472no—
491C2×C4—472no—
492C2×C4—472no—
493C2×C4—472no—
494C2×C4—472no—
495C2×C4—478no—
496C2×C4—944no—
497C2×C4—944no—
498C2×C4—9416no—
499C2×C4—1882no—
500C2×C4—1882no—
501C2×C4—1882no—
502C2×C4C22×C4×D4712yes—
503C2×C4C22×C4×D4712yes—
504C2×C4C22×C4×D4718yes—
505C2×C4C22×C4×D4711yescharacteristic
506C2×C4C2×Q8×D4712yes—
507C2×C4#41×D4712yes—
508C2×C4C24×D4711yescharacteristic
509C8—22no—
510C8—24no—
511C8—474no—
512C8—942no—
513C8—944no—
514C8C2×Q8×D4714yes—
515C22—22no—
516C22—474no—
517C22—472no—
518C22—472no—
519C22—948no—
520C22—942no—
521C22C4×Q8×D4712yes—
522C22C23×C4×D4711yescharacteristic
523C4—22no—
524C4—22no—
525C4—28no—
526C4—472no—
527C4—472no—
528C4—942no—
529C4—942no—
530C4—948no—
531C4C4×Q8×D4712yes—
532C4C22×Q8×D4711yescharacteristic
533C4C2×#41×D4711yescharacteristic
534C2—22no—
535C2—474no—
536C2—942no—
537C2C2×C4×Q8×D4711yescharacteristic
538C2#568×D4712yes—
subgroupG/H
center, FrattiniC2×C4C24×D47
commutator, socleC22×C47C24×C4
FittingC47×#2961C2
prime radicalC23×D47C22×C4
cosocleC2×C4×C47C25
hypercenter#2961D47
hypocenterC47C2×#2961
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #2961

Complements

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

NH ≅ G/Ntype
2. #20252329C2semidirect
3. #20252328C2semidirect
4. #20252327C2semidirect
5. #20252326C2semidirect
6. #20252325C2semidirect
7. #20252324C2semidirect
8. #446×D47C2semidirect
13. C47×#2961C2semidirect
29. #15689254C22semidirect
30. #15689253C22semidirect
31. #15689252C22semidirect
32. #15689252C22semidirect
33. #15689251C22semidirect
34. #15689251C22semidirect
35. #15689250C22semidirect
58. C47×#446C22semidirect
72. C2×C8×D47Q8semidirect
163. C2×C8×C47C2×Q8semidirect
195. C2×C47⋊C8C2×Q8semidirect
204. C8×D47C2×Q8semidirect
272. #2961D47direct (N × H)
282. D47#2961direct (N × H)
306. #446C2×D47semidirect
332. C47C2×#2961semidirect
445. C2×C8Q8×D47semidirect

Maximal subgroups

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

subgroupindex
#533×D472
#202523292
#202523282
#202523272
#202523262
#202523252
#202523242
#446×D472
#424×D472
#423×D472
#405×D472
C2×#97×D472
C47×#29612
C2×#296147