Finite Group Databasebeta

← #26216303

Subgroups — #26216303

Order 12032.

1358 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#10625352C211yesmaximal, characteristic
2C2×#15689175C211yesmaximal, characteristic, complemented
3#20245781C211yesmaximal, characteristic, complemented
4#20243482C212yesmaximal, complemented
5#20243404C211yesmaximal, characteristic, complemented
6#20243400C211yesmaximal, characteristic, complemented
7#20243398C211yesmaximal, characteristic, complemented
8#20243325C212yesmaximal
9#20243207C212yesmaximal, complemented
10#102×Dic47C212yesmaximal, complemented
11C47×#1804C211yesmaximal, characteristic, complemented
12C22×#10625352C2211yescharacteristic
13C4×#10625352—24no—
14C4×#10625352C418yescomplemented
15C2×C4×Dic94C2211yescharacteristic
16C2×#13093989C2211yescharacteristic
17C2×D4×Dic47C2211yescharacteristic
18C2×C4×C22⋊D47—21no—
19C2×(C22⋊D47)⋊C4—21no—
20C2×#13093982C2211yescharacteristic
21C2×#13093980—21no—
22C22×C4×Dic47—21no—
23C2×C42×D47C2211yescharacteristic
24#15689175—24no—
25C2×C4⋊(C47⋊C8)C2211yescharacteristic
26C2×#13093949C2212yes—
27C2×#13093947C2212yes—
28C2×#13093945C2212yes—
29C2×(C2×D47)⋊C8C2212yes—
30C2×C8×Dic47C2212yes—
31#15688990—21no—
32#15688989C2211yescharacteristic
33#15688985—21no—
34#15688980C2212yes—
35C4⋊C4×Dic47C2212yes—
36#15688970—21no—
37#15688968—21no—
38#15688886C2212yes—
39#15688885C2212yes—
40#15688885C2212yes—
41C2×C4×D4×C47C2211yescharacteristic
42C2×C4⋊C8×C47C2211yescharacteristic
43C2×#102×C47C2212yes—
44C47×#382C2211yescharacteristic
45C47×#340C2212yes—
46C2×#10625352—22no—
47C2×#10625352—22no—
48C2×#10625352—22no—
49C2×#10625352—22no—
50C2×#10625352—22no—
51C2×#10625352C2×C414yes—
52C22×Dic94C2311yescharacteristic
53C22×C22⋊D47—21no—
54C23×Dic47—21no—
55C23×Dic47—21no—
56C22×C4×D47D411yescharacteristic
57C22×C4×D47D411yescharacteristic
58C22×C4×D47C2311yescharacteristic
59C22×C47⋊C8C2312yes—
60C4×Dic94—22no—
61C4×Dic94C2×C414yes—
62#13093989—22no—
63#13093989C2×C414yes—
64D4×Dic47—22no—
65D4×Dic47C2×C414yes—
66C4×C22⋊D47—28no—
67(C22⋊D47)⋊C4—28no—
68#13093982—22no—
69#13093982C2×C414yes—
70#13093980—28no—
71C2×C4⋊Dic47C2312yes—
72C2×C4⋊Dic47C2311yescharacteristic
73C2×Dic47⋊C4—21no—
74C2×Dic47⋊C4—21no—
75C2×C22⋊Dic47—21no—
76C2×(C2×D47)⋊C4—21no—
77C2×(C2×D47)⋊C4—22no—
78C2×C4×Dic47—21no—
79C2×C4×Dic47—21no—
80C2×C4×Dic47—21no—
81C2×C4×Dic47—28no—
82C2×C4×Dic47—22no—
83C2×C4×Dic47D411yescharacteristic
84C2×C4×Dic47D411yescharacteristic
85C2×C4×Dic47C2311yescharacteristic
86C42×D47C2×C414yes—
87C42×D47D414yes—
88C4⋊(C47⋊C8)—22no—
89#13093949—24no—
90#13093947—24no—
91#13093945—24no—
92(C2×D47)⋊C8—24no—
93C8×Dic47—24no—
94C47⋊#95—21no—
95C47⋊#95—21no—
96C47⋊#95—22no—
97C47⋊#95—22no—
98C22×D4×C47C2311yescharacteristic
99C23×C4×C47—21no—
100C22×C8×C47C2312yes—
101C4×D4×C47—22no—
102C4×D4×C47C2×C414yes—
103C2×C4⋊C4×C47C2312yes—
104C2×C4⋊C4×C47C2311yescharacteristic
105C2×C22⋊C4×C47—21no—
106C2×C42×C47C2311yescharacteristic
107C4⋊C8×C47—22no—
108#102×C47—24no—
109#95×C47—21no—
110#95×C47—21no—
111C24×C47—21no—
112C23×D47C2×D411yescharacteristic
113C2×D4×C47—21no—
114C2×D4×C47—21no—
115C2×D4×C47—21no—
116C2×D4×C47C22×C412yes—
117C2×D4×C47#4112yes—
118C2×D4×C47#4112yes—
119C22×C4×C47—21no—
120C22×C4×C47—24no—
121C22×C4×C47—22no—
122C22×C4×C47—44no—
123C22×C4×C47C2×D411yescharacteristic
124C22×C4×C47C2×D411yescharacteristic
125C22×C4×C47C2411yescharacteristic
126C2×C22⋊D47—24no—
127C2×C22⋊D47—24no—
128C2×C22⋊D47—24no—
129C22×Dic47—24no—
130C22×Dic47—24no—
131C22×Dic47—21no—
132C22×Dic47—24no—
133C22×Dic47—21no—
134C22×Dic47—24no—
135C22×Dic47—22no—
136C22×Dic47—44no—
137C22×Dic47C2×D411yescharacteristic
138C22×Dic47C2×D411yescharacteristic
139C22×Dic47C2×D411yescharacteristic
140#10625352—28no—
141#10625352—28no—
142#10625352—28no—
143#10625352—28no—
144C2×C4×D47—21no—
145C2×C4×D47—21no—
146C2×C4×D47—21no—
147C2×C4×D47—21no—
148C2×C4×D47—24no—
149C2×C4×D47—42no—
150C2×C4×D47C22⋊C414yes—
151C2×C4×D47C22⋊C414yes—
152C2×C4×D47C22×C412yes—
153C2×C4×D47C2×D412yes—
154C2×Dic94—21no—
155C2×Dic94—21no—
156C2×Dic94—21no—
157C2×Dic94C22×C412yes—
158C2×Dic94#4112yes—
159C2×Dic94#4112yes—
160C2×C8×C47—22no—
161C2×C8×C47—22no—
162C2×C8×C47—22no—
163C4⋊C4×C47—21no—
164C4⋊C4×C47—22no—
165C4⋊C4×C47—22no—
166C4⋊C4×C47C22×C412yes—
167C22⋊C4×C47—24no—
168C42×C47C22×C412yes—
169C42×C47C2×D412yes—
170C22⋊Dic47—24no—
171(C2×D47)⋊C4—24no—
172(C2×D47)⋊C4—44no—
173C4⋊Dic47—21no—
174C4⋊Dic47—22no—
175C4⋊Dic47—22no—
176C4⋊Dic47C22×C412yes—
177Dic47⋊C4—24no—
178Dic47⋊C4—24no—
179C4×Dic47—24no—
180C4×Dic47—24no—
181C4×Dic47—24no—
182C4×Dic47—44no—
183C4×Dic47C22⋊C414yes—
184C4×Dic47C22⋊C414yes—
185C4×Dic47C22×C412yes—
186C4×Dic47C2×D412yes—
187C2×C47⋊C8—22no—
188C2×C47⋊C8—22no—
189C2×C47⋊C8—22no—
190C23×C47—22no—
191C23×C47—22no—
192C23×C47—22no—
193C23×C47—42no—
194C23×C47—42no—
195C23×C47C22×D411yescharacteristic
196C22×D47—21no—
197C22×D47—21no—
198C22×D47—22no—
199C22×D47—22no—
200C22×D47C2×C22⋊C412yes—
201D4×C47—22no—
202D4×C47—22no—
203D4×C47—22no—
204D4×C47#11714yes—
205C2×C4×C47—22no—
206C2×C4×C47—22no—
207C2×C4×C47—22no—
208C2×C4×C47—48no—
209C2×C4×C47—42no—
210C2×C4×C47—42no—
211C2×C4×C47—42no—
212C2×C4×C47—42no—
213C2×C4×C47C2×C22⋊C412yes—
214C2×C4×C47C2×C22⋊C412yes—
215C2×C4×C47C23×C411yescharacteristic
216C2×C4×C47C22×D411yescharacteristic
217C2×C4×C47C2×#4111yescharacteristic
218C2×C4×C47C2×#4111yescharacteristic
219C2×C4×C47C2×#4111yescharacteristic
220C2×C4×C47C2×#4111yescharacteristic
221C22⋊D47—216no—
222C2×Dic47—216no—
223C2×Dic47—22no—
224C2×Dic47—22no—
225C2×Dic47—22no—
226C2×Dic47—21no—
227C2×Dic47—21no—
228C2×Dic47—22no—
229C2×Dic47—22no—
230C2×Dic47—42no—
231C2×Dic47—48no—
232C2×Dic47—42no—
233C2×Dic47—42no—
234C2×Dic47—42no—
235C2×Dic47C2×C22⋊C412yes—
236C2×Dic47C2×C22⋊C412yes—
237C2×Dic47C2×C22⋊C412yes—
238C2×Dic47#13514yes—
239C4×D47—22no—
240C4×D47—22no—
241C4×D47—22no—
242C4×D47—22no—
243C4×D47—28no—
244C4×D47—44no—
245Dic94—22no—
246Dic94—22no—
247Dic94—22no—
248Dic94#11714yes—
249C8×C47—42no—
250C47⋊C8—42no—
251#20736—471nomaximal, Sylow
252C22×C47—24no—
253C22×C47—44no—
254C22×C47—44no—
255C22×C47—42no—
256C22×C47—42no—
257C22×C47C22×C22⋊C411yescharacteristic
258C22×C47#52511yescharacteristic
259C22×C47#52511yescharacteristic
260C22×C47C2×#13512yes—
261C22×C47#57512yes—
262C2×D47—22no—
263C2×D47—22no—
264C2×D47—22no—
265C2×D47—42no—
266C2×D47—42no—
267C4×C47—22no—
268C4×C47—22no—
269C4×C47—42no—
270C4×C47—82no—
271C4×C47C2×#11711yescharacteristic
272C4×C47C2×#11711yescharacteristic
273C4×C47#52511yescharacteristic
274C4×C47#52511yescharacteristic
275Dic47—22no—
276Dic47—24no—
277Dic47—22no—
278Dic47—42no—
279Dic47—82no—
280Dic47#41614yes—
281C2×C4×#41—471no—
282C2×#431—471no—
283#2283—471no—
284#1825—472no—
285#1805—471no—
286#1805—471no—
287#1804—471no—
288#1804D4711yescharacteristic, complemented
289#1788—472no—
290C4×#103—472no—
291C4×#102—472no—
292C2×C47—44no—
293C2×C47#228011yescharacteristic
294C2×C47C2×#41611yescharacteristic
295C2×C47#289611yescharacteristic
296C2×C47#310212yes—
297C2×C47#310212yes—
298D47—42no—
299C22×#41—471no—
300C4×#41—478no—
301C4×#41—944no—
302C2×C4×Q8—471no—
303C2×C4×Q8—471no—
304C2×C4×D4—471no—
305C2×C4×D4—941no—
306C2×C4×D4—941no—
307C2×C4×D4C2×D4711yescharacteristic
308C2×#117—471no—
309C2×#117—941no—
310C22×C42—471no—
311C22×C42—941no—
312#431—944no—
313C2×C4⋊C8—471no—
314C2×C4⋊C8C2×D4711yescharacteristic
315C2×#103—472no—
316C2×#103—472no—
317C2×#102—472no—
318C2×#102C2×D4712yes—
319C2×C22⋊C8—472no—
320C2×C4×C8—472no—
321#383—941no—
322#382—471no—
323#382C2×D4711yescharacteristic
324#381—941no—
325#380—472no—
326C4×C4⋊C4—472no—
327C4×C22⋊C4—941no—
328#376—941no—
329#340—472no—
330#340—472no—
331#340—472no—
332#340C2×D4712yes—
333C47#2073611yescharacteristic, complemented, Sylow
334C2×#41—474no—
335C2×#41—942no—
336C2×#41—942no—
337C2×#41—942no—
338C2×#41—942no—
339C2×#41—942no—
340C22×Q8—471no—
341C22×D4—941no—
342C22×D4C22×D4711yescharacteristic
343C23×C4—21no—
344C23×C4—471no—
345C23×C4—471no—
346C23×C4—471no—
347C23×C4—941no—
348C23×C4—941no—
349C22×C8—472no—
350C22×C8C22×D4712yes—
351C4×Q8—474no—
352C4×Q8—474no—
353C4×Q8—942no—
354C4×Q8—942no—
355C4×D4—22no—
356C4×D4—474no—
357C4×D4—942no—
358C4×D4—948no—
359C4×D4—948no—
360C4×D4C4×D4714yes—
361#117—474no—
362#117—948no—
363#117—942no—
364C2×C4⋊C4—471no—
365C2×C4⋊C4—472no—
366C2×C4⋊C4—941no—
367C2×C4⋊C4—941no—
368C2×C4⋊C4C22×D4712yes—
369C2×C4⋊C4C22×D4711yescharacteristic
370C2×C22⋊C4—21no—
371C2×C22⋊C4—941no—
372C2×C22⋊C4—941no—
373C2×C22⋊C4—942no—
374C2×C42—471no—
375C2×C42—471no—
376C2×C42—471no—
377C2×C42—474no—
378C2×C42—474no—
379C2×C42—948no—
380C2×C42—941no—
381C2×C42—941no—
382C2×C42—941no—
383C2×C42—942no—
384C2×C42C22×D4711yescharacteristic
385C4⋊C8—22no—
386C4⋊C8—942no—
387#103—944no—
388#103—944no—
389#102—24no—
390#102—944no—
391C22⋊C8—944no—
392C4×C8—944no—
393#95—21no—
394#95—21no—
395#95—942no—
396#95—942no—
397#95—941no—
398#95—941no—
399C24—21no—
400C24—471no—
401#41—948no—
402#41—948no—
403#41—948no—
404#41—948no—
405C2×Q8—472no—
406C2×Q8—472no—
407C2×Q8—472no—
408C2×Q8—941no—
409C2×Q8—941no—
410C2×Q8—941no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—944no—
415C2×D4—944no—
416C2×D4—944no—
417C2×D4C2×C4×D4712yes—
418C2×D4#1062535212yes—
419C2×D4#1062535412yes—
420C22×C4—21no—
421C22×C4—24no—
422C22×C4—22no—
423C22×C4—44no—
424C22×C4—471no—
425C22×C4—471no—
426C22×C4—471no—
427C22×C4—474no—
428C22×C4—472no—
429C22×C4—472no—
430C22×C4—474no—
431C22×C4—944no—
432C22×C4—944no—
433C22×C4—944no—
434C22×C4—944no—
435C22×C4—944no—
436C22×C4—941no—
437C22×C4—941no—
438C22×C4—941no—
439C22×C4—941no—
440C22×C4—941no—
441C22×C4—941no—
442C22×C4—942no—
443C22×C4—1882no—
444C22×C4—1884no—
445C22×C4D4×D4711yescharacteristic
446C22×C4D4×D4711yescharacteristic
447C22×C4C23×D4711yescharacteristic
448C2×C8—22no—
449C2×C8—22no—
450C2×C8—22no—
451C2×C8—942no—
452C2×C8—942no—
453C2×C8—942no—
454C4⋊C4—21no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—472no—
458C4⋊C4—944no—
459C4⋊C4—944no—
460C4⋊C4—941no—
461C4⋊C4—942no—
462C4⋊C4—942no—
463C4⋊C4C2×C4×D4712yes—
464C22⋊C4—24no—
465C22⋊C4—944no—
466C22⋊C4—944no—
467C22⋊C4—1884no—
468C42—474no—
469C42—474no—
470C42—472no—
471C42—472no—
472C42—944no—
473C42—944no—
474C42—944no—
475C42—1884no—
476C42C2×C4×D4712yes—
477C42D4×D4712yes—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—42no—
482C23—42no—
483C23—472no—
484C23—941no—
485C23—941no—
486C23—942no—
487C23—942no—
488C23C2×D4×D4711yescharacteristic
489Q8—474no—
490Q8—942no—
491Q8—942no—
492Q8—942no—
493D4—22no—
494D4—22no—
495D4—22no—
496D4—9416no—
497D4#1309398214yes—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—48no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—472no—
507C2×C4—474no—
508C2×C4—472no—
509C2×C4—472no—
510C2×C4—948no—
511C2×C4—9416no—
512C2×C4—942no—
513C2×C4—941no—
514C2×C4—942no—
515C2×C4—941no—
516C2×C4—942no—
517C2×C4—942no—
518C2×C4—942no—
519C2×C4—942no—
520C2×C4—942no—
521C2×C4—942no—
522C2×C4—942no—
523C2×C4—1884no—
524C2×C4—1888no—
525C2×C4—1882no—
526C2×C4—1882no—
527C2×C4—1882no—
528C2×C4—1882no—
529C2×C4C22⋊C4×D4712yes—
530C2×C4C22⋊C4×D4712yes—
531C2×C4C22×C4×D4711yescharacteristic
532C2×C4C2×D4×D4711yescharacteristic
533C2×C4#41×D4711yescharacteristic
534C2×C4#41×D4711yescharacteristic
535C2×C4C2×#1062535211yescharacteristic
536C2×C4C2×#1062535411yescharacteristic
537C8—42no—
538C8—1882no—
539C22—24no—
540C22—44no—
541C22—44no—
542C22—42no—
543C22—42no—
544C22—942no—
545C22—942no—
546C22—942no—
547C22—1882no—
548C22—1882no—
549C22C2×C22⋊C4×D4711yescharacteristic
550C22#1568963311yescharacteristic
551C22#1568963611yescharacteristic
552C22#135×D4712yes—
553C22#1568991912yes—
554C4—22no—
555C4—22no—
556C4—42no—
557C4—82no—
558C4—474no—
559C4—942no—
560C4—944no—
561C4—942no—
562C4—3762no—
563C4—1882no—
564C4#117×D4711yescharacteristic
565C4C2×#1309398211yescharacteristic
566C4#1568963311yescharacteristic
567C4#1568963611yescharacteristic
568C2—44no—
569C2—1882no—
570C2#2024577011yescharacteristic
571C2#416×D4711yescharacteristic
572C2#2025190211yescharacteristic
573C2#2025340312yes—
574C2#2025341112yes—
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1804C2
socleC23×C47C22×D4
prime radicalC22×#10625352C22
cosocleC22×C4×C47C24
hypercenter#1804D47
hypocenterC47#20736
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
2. C2×#15689175C2semidirect
3. #20245781C2semidirect
4. #20243482C2semidirect
5. #20243404C2semidirect
6. #20243400C2semidirect
7. #20243398C2semidirect
9. #20243207C2semidirect
10. #102×Dic47C2semidirect
11. C47×#1804C2semidirect
14. C4×#10625352C4semidirect
288. #1804D47semidirect
333. C47#20736semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#106253522
C2×#156891752
#202457812
#202434822
#202434042
#202434002
#202433982
#202433252
#202432072
#102×Dic472
C47×#18042
#2073647