Finite Group Databasebeta

← D47×#1506 #26183425

Subgroups — D47×#1506 #26183425

Order 12032.

1130 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D47C211yesmaximal, characteristic
2#432×D47C211yesmaximal, characteristic
3#376×D47C211yesmaximal, characteristic
4#20241901C211yesmaximal, characteristic, complemented
5#20241900C211yesmaximal, characteristic, complemented
6#20241899C211yesmaximal, characteristic, complemented
7#20241898C214yesmaximal, complemented
8#328×D47C214yesmaximal
9C47×#1506C211yesmaximal, characteristic, complemented
10#15689680C2211yescharacteristic
11#15689679—21no—
12#15689678C411yescharacteristic, complemented
13#15689678C411yescharacteristic, complemented
14#15689677—21no—
15#15689677C412yescomplemented
16#15689676—21no—
17#15689675—21no—
18#15689675C2212yes—
19C4⋊Q8×D47C411yescharacteristic, complemented
20C4⋊Q8×D47C411yescharacteristic, complemented
21#125×D47—21no—
22C22⋊Q8×D47—21no—
23C22⋊Q8×D47C2212yes—
24C4×Q8×D47—21no—
25C4×Q8×D47C412yescomplemented
26#117×D47—21no—
27C2×C42×D47—21no—
28C2×C42×D47C2211yescharacteristic
29#15689180C2211yescharacteristic
30#15689179—21no—
31#15689178—21no—
32#15689177C2212yes—
33C4⋊C8×D47—21no—
34C22⋊C8×D47C2212yes—
35#97×D47—21no—
36#15688969—21no—
37#15688969C2211yescharacteristic
38#15688968—21no—
39#15688968C2212yes—
40#95×D47—21no—
41#95×D47C2212yes—
42#15688861C2214yes—
43#15688860C2214yes—
44#15688859C2214yes—
45C47×#533C2211yescharacteristic
46C47×#432C2211yescharacteristic
47C47×#376C2211yescharacteristic
48C47×#328C2214yes—
49C2×Q8×D47—21no—
50C2×Q8×D47C2×C412yes—
51C22×C4×D47—22no—
52C22×C4×D47D411yescharacteristic
53C22×C4×D47D411yescharacteristic
54C22×C4×D47C2311yescharacteristic
55C2×C8×D47—22no—
56#13094024C2×C411yescharacteristic, complemented
57#13094024C2×C411yescharacteristic, complemented
58#13094023—21no—
59#13094023—21no—
60#13094023—21no—
61#13094023C2×C412yescomplemented
62#13094022—21no—
63#13094022C2×C412yescomplemented
64#13094016—21no—
65#13094015—21no—
66#13094015—21no—
67#13094014—22no—
68#13094014—22no—
69#13094004—21no—
70#13094004C2×C412yes—
71#13094003—21no—
72#13094003C2312yes—
73#13094002—22no—
74#13094002—22no—
75#13094001—22no—
76#13094001—22no—
77#13094000—21no—
78#13094000C2×C412yes—
79Q8×Dic47—21no—
80Q8×Dic47C2×C412yescomplemented
81C4×Dic94—21no—
82C4×Dic94—22no—
83C4×Dic94—22no—
84C4×Dic94C2×C412yescomplemented
85#13093989—21no—
86#13093989—22no—
87#13093989—22no—
88#13093989C2×C412yescomplemented
89#13093983—21no—
90#13093982—21no—
91#13093982—21no—
92#13093981—22no—
93#13093980—22no—
94C4⋊C4×D47—21no—
95C4⋊C4×D47—21no—
96C4⋊C4×D47—21no—
97C4⋊C4×D47—22no—
98C4⋊C4×D47—22no—
99C4⋊C4×D47C2×C412yes—
100C22⋊C4×D47—22no—
101C2×C4×Dic47—21no—
102C2×C4×Dic47—22no—
103C2×C4×Dic47D411yescharacteristic
104C2×C4×Dic47D411yescharacteristic
105C2×C4×Dic47C2311yescharacteristic
106C42×D47—28no—
107C42×D47—22no—
108C42×D47C2×C411yescharacteristic
109C42×D47C2×C411yescharacteristic
110C42×D47C2×C411yescharacteristic
111C42×D47C2×C411yescharacteristic
112C42×D47D411yescharacteristic
113C42×D47D411yescharacteristic
114C42×D47D411yescharacteristic
115C42×D47D411yescharacteristic
116C4⋊(C47⋊C8)—21no—
117Dic47⋊C8—22no—
118C22⋊(C47⋊C8)C2312yes—
119(C2×D47)⋊C8—22no—
120#13093935—21no—
121#13093934—22no—
122C47⋊#95—21no—
123C47⋊#95—22no—
124C47⋊#95—22no—
125C47⋊#95C2312yes—
126C4⋊Q8×C47C2×C411yescharacteristic, complemented
127C4⋊Q8×C47C2×C411yescharacteristic, complemented
128#125×C47—21no—
129C22⋊Q8×C47—21no—
130C22⋊Q8×C47C2312yes—
131C4×Q8×C47—21no—
132C4×Q8×C47C2×C412yescomplemented
133#117×C47—21no—
134C2×C42×C47—21no—
135C2×C42×C47C2311yescharacteristic
136C4⋊C8×C47—21no—
137C22⋊C8×C47C2312yes—
138#97×C47—21no—
139#95×C47—21no—
140#95×C47C2312yes—
141C23×D47C2×D411yescharacteristic
142C2×Q8×C47—21no—
143C2×Q8×C47C22×C412yes—
144C22×C4×C47—22no—
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47C2×D411yescharacteristic
147C22×C4×C47C2411yescharacteristic
148C22×Dic47—22no—
149C22×Dic47C2×D411yescharacteristic
150C22×Dic47C2×D411yescharacteristic
151C22×Dic47C2×D411yescharacteristic
152Q8×D47—44no—
153Q8×D47—44no—
154C2×C4×D47—24no—
155C2×C4×D47—24no—
156C2×C4×D47—28no—
157C2×C4×D47—22no—
158C2×C4×D47—22no—
159C2×C4×D47—42no—
160C2×C4×D47—44no—
161C2×C4×D47—44no—
162C2×C4×D47C22⋊C411yescharacteristic
163C2×C4×D47C22⋊C411yescharacteristic
164C2×C4×D47C22⋊C411yescharacteristic
165C2×C4×D47C22⋊C411yescharacteristic
166C2×C4×D47C22⋊C411yescharacteristic
167C2×C4×D47C22⋊C411yescharacteristic
168C2×C4×D47C22⋊C411yescharacteristic
169C2×C4×D47C22⋊C411yescharacteristic
170C2×C4×D47C22×C411yescharacteristic
171C2×C4×D47C22×C411yescharacteristic
172C2×C4×D47C2×D411yescharacteristic
173C2×C4×D47C2×D411yescharacteristic
174C2×Dic94—21no—
175C2×Dic94—22no—
176C2×Dic94—22no—
177C2×Dic94C22×C412yes—
178C2×C8×C47—22no—
179C4⋊C4×C47—21no—
180C4⋊C4×C47—21no—
181C4⋊C4×C47—21no—
182C4⋊C4×C47—22no—
183C4⋊C4×C47—22no—
184C4⋊C4×C47C22×C412yes—
185C22⋊C4×C47—22no—
186C42×C47—24no—
187C42×C47—22no—
188C42×C47C22×C411yescharacteristic
189C42×C47C22×C411yescharacteristic
190C42×C47C2×D411yescharacteristic
191C42×C47C2×D411yescharacteristic
192C22⋊Dic47—22no—
193(C2×D47)⋊C4—22no—
194(C2×D47)⋊C4—22no—
195C4⋊Dic47—21no—
196C4⋊Dic47—21no—
197C4⋊Dic47—21no—
198C4⋊Dic47—22no—
199C4⋊Dic47—22no—
200C4⋊Dic47C22×C412yes—
201Dic47⋊C4—22no—
202Dic47⋊C4—22no—
203Dic47⋊C4—22no—
204Dic47⋊C4—22no—
205Dic47⋊C4—22no—
206Dic47⋊C4—22no—
207Dic47⋊C4—22no—
208Dic47⋊C4—22no—
209C4×Dic47—28no—
210C4×Dic47—24no—
211C4×Dic47—22no—
212C4×Dic47—22no—
213C4×Dic47—22no—
214C4×Dic47C22⋊C411yescharacteristic
215C4×Dic47C22⋊C411yescharacteristic
216C4×Dic47C22⋊C411yescharacteristic
217C4×Dic47C22⋊C411yescharacteristic
218C4×Dic47C22⋊C411yescharacteristic
219C4×Dic47C22⋊C411yescharacteristic
220C4×Dic47C22⋊C411yescharacteristic
221C4×Dic47C22⋊C411yescharacteristic
222C4×Dic47C22×C411yescharacteristic
223C4×Dic47C22×C411yescharacteristic
224C4×Dic47C2×D411yescharacteristic
225C4×Dic47C2×D411yescharacteristic
226C2×C47⋊C8—22no—
227C8×D47—44no—
228C23×C47C22×D411yescharacteristic
229C22×D47—22no—
230C22×D47—22no—
231C22×D47C2×C22⋊C411yescharacteristic
232C22×D47C2×C22⋊C411yescharacteristic
233C22×D47#13714yes—
234Q8×C47—42no—
235Q8×C47—42no—
236C2×C4×C47—22no—
237C2×C4×C47—22no—
238C2×C4×C47—24no—
239C2×C4×C47—22no—
240C2×C4×C47—22no—
241C2×C4×C47—41no—
242C2×C4×C47—42no—
243C2×C4×C47—42no—
244C2×C4×C47C2×C22⋊C411yescharacteristic
245C2×C4×C47C2×C22⋊C411yescharacteristic
246C2×C4×C47C2×C22⋊C411yescharacteristic
247C2×C4×C47C2×C22⋊C411yescharacteristic
248C2×C4×C47C23×C411yescharacteristic
249C2×C4×C47C22×D411yescharacteristic
250C2×Dic47—22no—
251C2×Dic47—22no—
252C2×Dic47—24no—
253C2×Dic47—22no—
254C2×Dic47—22no—
255C2×Dic47—41no—
256C2×Dic47—42no—
257C2×Dic47—42no—
258C2×Dic47C2×C22⋊C411yescharacteristic
259C2×Dic47C2×C22⋊C411yescharacteristic
260C2×Dic47C2×C22⋊C411yescharacteristic
261C2×Dic47C2×C22⋊C411yescharacteristic
262C2×Dic47C2×C22⋊C411yescharacteristic
263C2×Dic47C2×C22⋊C411yescharacteristic
264C4×D47—22no—
265C4×D47—22no—
266C4×D47—22no—
267C4×D47—22no—
268C4×D47—22no—
269C4×D47—22no—
270C4×D47—22no—
271C4×D47—22no—
272C4×D47—22no—
273C4×D47—41no—
274C4×D47—41no—
275C4×D47—416no—
276C4×D47—44no—
277C4×D47—44no—
278C4×D47#10414yes—
279Dic94—44no—
280Dic94—42no—
281Dic94—44no—
282Dic94—42no—
283C8×C47—42no—
284C47⋊C8—42no—
285C2×#1506—471nomaximal, Sylow
286C22×C47—21no—
287C22×C47—21no—
288C22×C47C22×C22⋊C411yescharacteristic
289C22×C47C2×#13712yes—
290C2×D47—21no—
291C2×D47—21no—
292C2×D47—28no—
293C2×D47#41012yes—
294C2×D47#41912yes—
295C2×D47#41912yes—
296C2×D47C2×#10412yes—
297C4×C47—21no—
298C4×C47—21no—
299C4×C47—21no—
300C4×C47—21no—
301C4×C47—21no—
302C4×C47—44no—
303C4×C47—42no—
304C4×C47—42no—
305C4×C47C2×#10412yes—
306Dic47—21no—
307Dic47—21no—
308Dic47—21no—
309Dic47—21no—
310Dic47—21no—
311Dic47—44no—
312Dic47—42no—
313Dic47—42no—
314Dic47C2×#10412yes—
315C2×#533—471no—
316C2×#432—471no—
317C2×#376—471no—
318#1506—471no—
319#1506—471no—
320#1506—474no—
321#1506—471no—
322#1506D4711yescharacteristic, direct product factor
323C2×#328—474no—
324C2×C47—22no—
325C2×C47C2×#41011yescharacteristic
326C2×C47C2×#41911yescharacteristic
327C2×C47C22×#10411yescharacteristic
328D47—22no—
329D47#150614yesdirect product factor
330#533—471no—
331#533—471no—
332#533—472no—
333#533—472no—
334#533—471no—
335#533—941no—
336#533—941no—
337#533—941no—
338#533—941no—
339#533C2×D4711yescharacteristic
340C2×C4⋊Q8—471no—
341C2×C4⋊Q8—471no—
342C2×#125—941no—
343C2×C22⋊Q8—472no—
344C2×C22⋊Q8—941no—
345C2×C4×Q8—472no—
346C2×C4×Q8—941no—
347C2×#117—941no—
348C22×C42—471no—
349C22×C42—941no—
350#432—471no—
351#432—472no—
352#432—941no—
353#432—941no—
354#432C2×D4711yescharacteristic
355C2×C4⋊C8—941no—
356C2×C22⋊C8—472no—
357C2×#97—941no—
358#376—471no—
359#376—472no—
360#376—941no—
361#376—941no—
362#376C2×D4711yescharacteristic
363C2×#95—472no—
364C2×#95—941no—
365#328—474no—
366#328—474no—
367#328—474no—
368#328C2×D4714yes—
369C47C2×#150611yescharacteristic, complemented, Sylow
370C22×Q8—472no—
371C22×Q8—941no—
372C23×C4—471no—
373C23×C4—471no—
374C23×C4—471no—
375C23×C4—942no—
376C22×C8—942no—
377C4⋊Q8—472no—
378C4⋊Q8—472no—
379C4⋊Q8—471no—
380C4⋊Q8—471no—
381C4⋊Q8—941no—
382C4⋊Q8—941no—
383C4⋊Q8—941no—
384C4⋊Q8—941no—
385C4⋊Q8C4×D4711yescharacteristic, complemented
386C4⋊Q8C4×D4711yescharacteristic, complemented
387#125—21no—
388#125—942no—
389#125—942no—
390#125—941no—
391#125—941no—
392#125—941no—
393C22⋊Q8—21no—
394C22⋊Q8—472no—
395C22⋊Q8—472no—
396C22⋊Q8—472no—
397C22⋊Q8—942no—
398C22⋊Q8—942no—
399C22⋊Q8—942no—
400C22⋊Q8—942no—
401C22⋊Q8—941no—
402C22⋊Q8—941no—
403C22⋊Q8—941no—
404C22⋊Q8C22×D4712yes—
405C4×Q8—21no—
406C4×Q8—472no—
407C4×Q8—472no—
408C4×Q8—472no—
409C4×Q8—942no—
410C4×Q8—942no—
411C4×Q8—942no—
412C4×Q8—941no—
413C4×Q8—942no—
414C4×Q8—941no—
415C4×Q8—941no—
416C4×Q8C4×D4712yescomplemented
417#117—21no—
418#117—942no—
419#117—942no—
420#117—941no—
421#117—941no—
422#117—941no—
423C2×C4⋊C4—472no—
424C2×C4⋊C4—941no—
425C2×C4⋊C4—941no—
426C2×C4⋊C4—942no—
427C2×C4⋊C4—942no—
428C2×C4⋊C4—941no—
429C2×C22⋊C4—942no—
430C2×C42—21no—
431C2×C42—471no—
432C2×C42—471no—
433C2×C42—471no—
434C2×C42—471no—
435C2×C42—471no—
436C2×C42—471no—
437C2×C42—471no—
438C2×C42—471no—
439C2×C42—471no—
440C2×C42—471no—
441C2×C42—471no—
442C2×C42—942no—
443C2×C42—948no—
444C2×C42—942no—
445C2×C42—941no—
446C2×C42C22×D4711yescharacteristic
447C4⋊C8—21no—
448C4⋊C8—942no—
449C4⋊C8—941no—
450C22⋊C8—472no—
451C22⋊C8—942no—
452C22⋊C8C22×D4712yes—
453#97—21no—
454#97—942no—
455#97—941no—
456#95—21no—
457#95—472no—
458#95—942no—
459#95—942no—
460#95—941no—
461#95C22×D4712yes—
462C24—471no—
463C2×Q8—21no—
464C2×Q8—472no—
465C2×Q8—942no—
466C2×Q8—942no—
467C2×Q8—941no—
468C2×Q8—1884no—
469C2×Q8—1884no—
470C2×Q8C2×C4×D4712yes—
471C22×C4—22no—
472C22×C4—471no—
473C22×C4—471no—
474C22×C4—471no—
475C22×C4—471no—
476C22×C4—471no—
477C22×C4—471no—
478C22×C4—471no—
479C22×C4—471no—
480C22×C4—471no—
481C22×C4—471no—
482C22×C4—471no—
483C22×C4—471no—
484C22×C4—471no—
485C22×C4—471no—
486C22×C4—471no—
487C22×C4—944no—
488C22×C4—944no—
489C22×C4—942no—
490C22×C4—942no—
491C22×C4—948no—
492C22×C4—942no—
493C22×C4—1882no—
494C22×C4—1884no—
495C22×C4—1884no—
496C22×C4D4×D4711yescharacteristic
497C22×C4D4×D4711yescharacteristic
498C22×C4C23×D4711yescharacteristic
499C2×C8—22no—
500C2×C8—942no—
501C2×C8—1884no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—472no—
508C4⋊C4—942no—
509C4⋊C4—942no—
510C4⋊C4—942no—
511C4⋊C4—942no—
512C4⋊C4—942no—
513C4⋊C4—942no—
514C4⋊C4—942no—
515C4⋊C4—942no—
516C4⋊C4—942no—
517C4⋊C4—941no—
518C4⋊C4—941no—
519C4⋊C4—941no—
520C4⋊C4—942no—
521C4⋊C4C2×C4×D4712yes—
522C22⋊C4—22no—
523C22⋊C4—942no—
524C22⋊C4—942no—
525C22⋊C4—942no—
526C42—24no—
527C42—22no—
528C42—471no—
529C42—471no—
530C42—471no—
531C42—471no—
532C42—471no—
533C42—471no—
534C42—471no—
535C42—471no—
536C42—471no—
537C42—471no—
538C42—471no—
539C42—471no—
540C42—942no—
541C42—942no—
542C42—944no—
543C42—948no—
544C42—942no—
545C42C2×C4×D4711yescharacteristic
546C42C2×C4×D4711yescharacteristic
547C42D4×D4711yescharacteristic
548C42D4×D4711yescharacteristic
549C23—471no—
550C23—471no—
551C23—474no—
552C23—942no—
553C23—942no—
554C23C2×D4×D4711yescharacteristic
555Q8—42no—
556Q8—42no—
557Q8—1882no—
558Q8—1884no—
559Q8—1884no—
560Q8—1882no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—24no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—471no—
570C2×C4—474no—
571C2×C4—471no—
572C2×C4—471no—
573C2×C4—471no—
574C2×C4—471no—
575C2×C4—471no—
576C2×C4—942no—
577C2×C4—942no—
578C2×C4—942no—
579C2×C4—942no—
580C2×C4—942no—
581C2×C4—942no—
582C2×C4—942no—
583C2×C4—942no—
584C2×C4—942no—
585C2×C4—942no—
586C2×C4—942no—
587C2×C4—944no—
588C2×C4—942no—
589C2×C4—942no—
590C2×C4—1881no—
591C2×C4—1881no—
592C2×C4—1884no—
593C2×C4—1884no—
594C2×C4—18816no—
595C2×C4—1881no—
596C2×C4—1882no—
597C2×C4—1882no—
598C2×C4C22⋊C4×D4711yescharacteristic
599C2×C4C22⋊C4×D4711yescharacteristic
600C2×C4C22⋊C4×D4711yescharacteristic
601C2×C4C22⋊C4×D4711yescharacteristic
602C2×C4C22×C4×D4711yescharacteristic
603C2×C4C2×D4×D4711yescharacteristic
604C8—42no—
605C8—1882no—
606C22—21no—
607C22—21no—
608C22—472no—
609C22—472no—
610C22—472no—
611C22—472no—
612C22—948no—
613C22—941no—
614C22—941no—
615C22C2×C22⋊C4×D4711yescharacteristic
616C22#137×D4712yes—
617C4—21no—
618C4—21no—
619C4—21no—
620C4—21no—
621C4—21no—
622C4—44no—
623C4—42no—
624C4—42no—
625C4—472no—
626C4—941no—
627C4—941no—
628C4—941no—
629C4—941no—
630C4—941no—
631C4—1884no—
632C4—1882no—
633C4—1882no—
634C4#104×D4712yes—
635C2—22no—
636C2—474no—
637C2—942no—
638C2#410×D4711yescharacteristic
639C2#419×D4711yescharacteristic
640C2C2×#104×D4711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1506C2
socleC22×C47C22×C22⋊C4
prime radicalC23×D47C2×D4
cosocleC22×C4×C47C24
hypercenter#1506D47
hypocenterC47C2×#1506
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1506

Complements

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

NH ≅ G/Ntype
4. #20241901C2semidirect
5. #20241900C2semidirect
6. #20241899C2semidirect
7. #20241898C2semidirect
9. C47×#1506C2semidirect
12. #15689678C4semidirect
13. #15689678C4semidirect
15. #15689677C4semidirect
19. C4⋊Q8×D47C4semidirect
20. C4⋊Q8×D47C4semidirect
25. C4×Q8×D47C4semidirect
56. #13094024C2×C4semidirect
57. #13094024C2×C4semidirect
61. #13094023C2×C4semidirect
63. #13094022C2×C4semidirect
80. Q8×Dic47C2×C4semidirect
84. C4×Dic94C2×C4semidirect
88. #13093989C2×C4semidirect
126. C4⋊Q8×C47C2×C4semidirect
127. C4⋊Q8×C47C2×C4semidirect
132. C4×Q8×C47C2×C4semidirect
322. #1506D47direct (N × H)
329. D47#1506direct (N × H)
369. C47C2×#1506semidirect
385. C4⋊Q8C4×D47semidirect
386. C4⋊Q8C4×D47semidirect
416. C4×Q8C4×D47semidirect

Maximal subgroups

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

subgroupindex
#533×D472
#432×D472
#376×D472
#202419012
#202419002
#202418992
#202418982
#328×D472
C47×#15062
C2×#150647