Finite Group Databasebeta

← #26183012

Subgroups — #26183012

Order 12032.

958 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689677C211yesmaximal, characteristic
2#20252020C211yesmaximal, characteristic
3#20252016C211yesmaximal, characteristic
4#20241859C214yesmaximal, complemented
5#20241818C211yesmaximal, characteristic, complemented
6#20241817C211yesmaximal, characteristic, complemented
7#20241816C211yesmaximal, characteristic, complemented
8#20241807C214yesmaximal, complemented
9C47×#1487C211yesmaximal, characteristic, complemented
10#15689677—21no—
11#15689677—21no—
12#15689677—21no—
13#15689677—21no—
14#15689677C412yes—
15#15689677C412yes—
16#15689677C2212yes—
17#15689677C2212yes—
18C2×#13094023C411yescharacteristic
19C2×#13094022C411yescharacteristic
20C2×#13094014—21no—
21C2×#13094004C411yescharacteristic
22C2×#13094002—21no—
23C2×#13094000C411yescharacteristic
24C2×C4×Dic94—21no—
25C2×C4×Dic94C2211yescharacteristic
26C2×#13093981—21no—
27C2×C42×D47C2211yescharacteristic
28#15689179—21no—
29#15689179—21no—
30#15689179C2212yes—
31#15689177—21no—
32#15689176C2211yescharacteristic
33#15689175—21no—
34#15689175C2212yes—
35#15689174C2212yes—
36#15689147C2211yescharacteristic
37#15689145—21no—
38#15689086—21no—
39#15689085—21no—
40M16×Dic47—21no—
41C4×#10625324C2212yes—
42#15688855C2214yescomplemented
43Q8⋊(C47⋊C8)C2214yescomplemented
44#15688853C2214yescomplemented
45C2×C4×Q8×C47C2211yescharacteristic
46C47×#431C2211yescharacteristic
47C47×#423C2211yescharacteristic
48C47×Q8⋊C8C2214yescomplemented
49C22×Dic94—21no—
50C22×Dic94C2×C411yescharacteristic
51C22×C4×D47C2×C411yescharacteristic
52C22×C4×D47D411yescharacteristic
53C22×C4×D47D411yescharacteristic
54C2×#10625329—21no—
55C2×#10625324—22no—
56#13094023—21no—
57#13094023—21no—
58#13094023C2×C412yes—
59#13094023C2×C412yes—
60#13094022—21no—
61#13094022—21no—
62#13094022C2×C412yes—
63#13094022C2×C412yes—
64#13094014—22no—
65#13094014—22no—
66#13094014—22no—
67#13094014—22no—
68#13094004—21no—
69#13094004—21no—
70#13094004C2×C412yes—
71#13094004C2×C412yes—
72#13094002—22no—
73#13094002—22no—
74#13094002—22no—
75#13094002—22no—
76#13094000—21no—
77#13094000—21no—
78#13094000C2×C412yes—
79#13094000C2×C412yes—
80C4×Dic94—21no—
81C4×Dic94—21no—
82C4×Dic94—22no—
83C4×Dic94—22no—
84C4×Dic94—22no—
85C4×Dic94—22no—
86C4×Dic94C2×C412yes—
87C4×Dic94C2312yes—
88#13093981—22no—
89#13093981—22no—
90#13093981—22no—
91#13093981—22no—
92C2×C4⋊Dic47—21no—
93C2×C4⋊Dic47C2×C411yescharacteristic
94C2×Dic47⋊C4—21no—
95C2×Dic47⋊C4—21no—
96C2×Dic47⋊C4—21no—
97C2×Dic47⋊C4—21no—
98C2×Dic47⋊C4—21no—
99C2×(C2×D47)⋊C4—21no—
100C2×(C2×D47)⋊C4—21no—
101C2×C4×Dic47—21no—
102C2×C4×Dic47C2×C411yescharacteristic
103C2×C4×Dic47D411yescharacteristic
104C2×C4×Dic47D411yescharacteristic
105C42×D47C2×C411yescharacteristic
106C42×D47C2×C411yescharacteristic
107C42×D47D411yescharacteristic
108C42×D47D411yescharacteristic
109C42×D47D411yescharacteristic
110C42×D47D411yescharacteristic
111C42×D47C2311yescharacteristic
112C42×D47C2311yescharacteristic
113C4⋊(C47⋊C8)—21no—
114C4⋊(C47⋊C8)—21no—
115C4⋊(C47⋊C8)C2312yes—
116Dic47⋊C8—22no—
117C22⋊(C47⋊C8)—21no—
118(C2×D47)⋊C8—22no—
119(C2×D47)⋊C8—22no—
120(C2×D47)⋊C8—22no—
121#13093934—22no—
122#13093934—22no—
123C4×C47⋊C8C2312yes—
124C8×Dic47—22no—
125C22×Q8×C47C2×C411yescharacteristic
126C2×M16×C47—21no—
127C4×Q8×C47—21no—
128C4×Q8×C47—21no—
129C4×Q8×C47C2×C412yes—
130C4×Q8×C47C2312yes—
131C2×C4⋊C4×C47—21no—
132C2×C4⋊C4×C47C2×C411yescharacteristic
133C2×C42×C47—21no—
134C2×C42×C47C2311yescharacteristic
135C4⋊C8×C47—21no—
136C4⋊C8×C47—21no—
137C4⋊C8×C47C2312yes—
138C22⋊C8×C47—21no—
139C4×C8×C47C2312yes—
140C23×D47C22⋊C411yescharacteristic
141C2×Q8×C47—21no—
142C2×Q8×C47—42no—
143C2×Q8×C47C22×C412yes—
144C22×C4×C47—21no—
145C22×C4×C47—21no—
146C22×C4×C47C22×C411yescharacteristic
147C22×C4×C47C2×D411yescharacteristic
148C22×C4×C47C2×D411yescharacteristic
149C22×Dic47—21no—
150C22×Dic47—21no—
151C22×Dic47C22⋊C411yescharacteristic
152C22×Dic47C22⋊C411yescharacteristic
153C22×Dic47C22⋊C411yescharacteristic
154C2×C4×D47—22no—
155C2×C4×D47—22no—
156C2×C4×D47—42no—
157C2×C4×D47—42no—
158C2×C4×D47C22⋊C411yescharacteristic
159C2×C4×D47C22⋊C411yescharacteristic
160C2×C4×D47C22⋊C411yescharacteristic
161C2×C4×D47C22⋊C411yescharacteristic
162C2×C4×D47C22⋊C411yescharacteristic
163C2×C4×D47C22⋊C411yescharacteristic
164C2×C4×D47C22×C411yescharacteristic
165C2×C4×D47C22×C411yescharacteristic
166C2×C4×D47C2×D411yescharacteristic
167C2×C4×D47C2×D411yescharacteristic
168C2×C4×D47C2×D411yescharacteristic
169C2×C4×D47C2×D411yescharacteristic
170C2×Dic94—21no—
171C2×Dic94—22no—
172C2×Dic94—22no—
173C2×Dic94—42no—
174C2×Dic94—44no—
175C2×Dic94C22×C412yes—
176M16×C47—42no—
177C2×C8×C47—22no—
178C2×C8×C47—22no—
179C4⋊C4×C47—22no—
180C4⋊C4×C47—21no—
181C4⋊C4×C47—22no—
182C4⋊C4×C47C22×C412yes—
183C42×C47—22no—
184C42×C47—22no—
185C42×C47C22×C411yescharacteristic
186C42×C47C2×D411yescharacteristic
187C42×C47C2×D411yescharacteristic
188C42×C47C2411yescharacteristic
189(C2×D47)⋊C4—22no—
190(C2×D47)⋊C4—22no—
191(C2×D47)⋊C4—22no—
192(C2×D47)⋊C4—22no—
193C4⋊Dic47—21no—
194C4⋊Dic47—22no—
195C4⋊Dic47—22no—
196C4⋊Dic47C22×C412yes—
197Dic47⋊C4—22no—
198Dic47⋊C4—22no—
199Dic47⋊C4—22no—
200Dic47⋊C4—22no—
201Dic47⋊C4—22no—
202Dic47⋊C4—22no—
203Dic47⋊C4—22no—
204Dic47⋊C4—22no—
205Dic47⋊C4—22no—
206Dic47⋊C4—22no—
207C4×Dic47—22no—
208C4×Dic47—22no—
209C4×Dic47C22⋊C411yescharacteristic
210C4×Dic47C22⋊C411yescharacteristic
211C4×Dic47C22⋊C411yescharacteristic
212C4×Dic47C22⋊C411yescharacteristic
213C4×Dic47C22⋊C411yescharacteristic
214C4×Dic47C22⋊C411yescharacteristic
215C4×Dic47C22×C411yescharacteristic
216C4×Dic47C22×C411yescharacteristic
217C4×Dic47C2×D411yescharacteristic
218C4×Dic47C2×D411yescharacteristic
219C4×Dic47C2×D411yescharacteristic
220C4×Dic47C2×D411yescharacteristic
221#10625329—42no—
222C2×C47⋊C8—22no—
223C2×C47⋊C8—22no—
224#10625324—44no—
225C23×C47C2×C22⋊C411yescharacteristic
226C22×D47—22no—
227C22×D47—41no—
228C22×D47—41no—
229C22×D47C2×C22⋊C411yescharacteristic
230C22×D47C2×C22⋊C411yescharacteristic
231Q8×C47—24no—
232Q8×C47—42no—
233C2×C4×C47—22no—
234C2×C4×C47—22no—
235C2×C4×C47—22no—
236C2×C4×C47—41no—
237C2×C4×C47—42no—
238C2×C4×C47—42no—
239C2×C4×C47C2×C22⋊C411yescharacteristic
240C2×C4×C47C2×C22⋊C411yescharacteristic
241C2×C4×C47C2×C22⋊C411yescharacteristic
242C2×C4×C47#13712yes—
243C2×C4×C47#13712yes—
244C2×C4×C47C23×C411yescharacteristic
245C2×C4×C47C22×D411yescharacteristic
246C2×C4×C47C22×D411yescharacteristic
247C2×Dic47—22no—
248C2×Dic47—22no—
249C2×Dic47—22no—
250C2×Dic47—22no—
251C2×Dic47—41no—
252C2×Dic47—42no—
253C2×Dic47—42no—
254C2×Dic47C2×C22⋊C411yescharacteristic
255C2×Dic47C2×C22⋊C411yescharacteristic
256C2×Dic47C2×C22⋊C411yescharacteristic
257C2×Dic47C2×C22⋊C411yescharacteristic
258C2×Dic47C2×C22⋊C411yescharacteristic
259C2×Dic47C2×C22⋊C411yescharacteristic
260C4×D47—22no—
261C4×D47—22no—
262C4×D47—21no—
263C4×D47—21no—
264C4×D47—21no—
265C4×D47—21no—
266C4×D47—22no—
267C4×D47—22no—
268C4×D47—22no—
269C4×D47—22no—
270C4×D47—41no—
271C4×D47—41no—
272C4×D47—41no—
273C4×D47—41no—
274Dic94—24no—
275Dic94—44no—
276Dic94—42no—
277Dic94—44no—
278C8×C47—42no—
279C8×C47—42no—
280C47⋊C8—42no—
281C47⋊C8—42no—
282#17491—471nomaximal, Sylow
283C22×C47—21no—
284C22×C47—21no—
285C22×C47#41912yes—
286C22×C47C22×C22⋊C411yescharacteristic
287C2×D47—21no—
288C2×D47—21no—
289C2×D47—21no—
290C2×D47—21no—
291C2×D47—21no—
292C2×D47—21no—
293C2×D47—44no—
294C4×C47—21no—
295C4×C47—21no—
296C4×C47—21no—
297C4×C47—42no—
298C4×C47—42no—
299C4×C47#41912yes—
300C4×C47#56812yes—
301C4×C47C2×#13711yescharacteristic
302C4×C47C2×#13711yescharacteristic
303Dic47—21no—
304Dic47—21no—
305Dic47—21no—
306Dic47—21no—
307Dic47—21no—
308Dic47—42no—
309Dic47—42no—
310Dic47#42112yes—
311C2×#533—471no—
312#2920—471no—
313#2920—471no—
314#1497—474no—
315#1487—471no—
316#1487—471no—
317#1487—471no—
318#1487D4711yescharacteristic, complemented
319#1485—474no—
320C2×C47—22no—
321C2×C47#287911yescharacteristic
322C2×C47C2×#41911yescharacteristic
323C2×C47C2×#42111yescharacteristic
324D47—41no—
325D47—41no—
326#533—472no—
327#533—472no—
328#533—472no—
329#533—472no—
330#533—941no—
331#533—941no—
332#533—941no—
333#533—941no—
334C2×C4⋊Q8—471no—
335C2×C4⋊Q8—471no—
336C2×#125—941no—
337C2×C22⋊Q8—471no—
338C2×C22⋊Q8—471no—
339C2×C22⋊Q8—941no—
340C2×C4×Q8—471no—
341C2×C4×Q8—941no—
342C2×C4×Q8C2×D4711yescharacteristic
343C2×#117—941no—
344C22×C42—471no—
345#432—472no—
346#432—941no—
347#432—941no—
348#432—941no—
349#431—471no—
350#431—472no—
351#431—472no—
352#431—941no—
353#431C2×D4711yescharacteristic
354#423—471no—
355#423—941no—
356#423C2×D4711yescharacteristic
357#407—941no—
358#407—941no—
359C4×M16—472no—
360C4×M16—941no—
361Q8⋊C8—474no—
362Q8⋊C8—474no—
363Q8⋊C8—474no—
364Q8⋊C8C2×D4714yescomplemented
365C47#1749111yescharacteristic, complemented, Sylow
366C22×Q8—471no—
367C22×Q8—941no—
368C22×Q8C4×D4711yescharacteristic
369C23×C4—471no—
370C23×C4—471no—
371C23×C4—471no—
372C2×M16—21no—
373C2×M16—942no—
374C2×M16—941no—
375C4⋊Q8—472no—
376C4⋊Q8—472no—
377C4⋊Q8—472no—
378C4⋊Q8—472no—
379C4⋊Q8—941no—
380C4⋊Q8—941no—
381C4⋊Q8—941no—
382C4⋊Q8—941no—
383#125—942no—
384#125—942no—
385#125—942no—
386#125—942no—
387C22⋊Q8—472no—
388C22⋊Q8—472no—
389C22⋊Q8—472no—
390C22⋊Q8—472no—
391C22⋊Q8—941no—
392C22⋊Q8—941no—
393C22⋊Q8—942no—
394C22⋊Q8—942no—
395C22⋊Q8—942no—
396C22⋊Q8—942no—
397C22⋊Q8—941no—
398C22⋊Q8—941no—
399C4×Q8—21no—
400C4×Q8—21no—
401C4×Q8—472no—
402C4×Q8—472no—
403C4×Q8—942no—
404C4×Q8—942no—
405C4×Q8—942no—
406C4×Q8—942no—
407C4×Q8—941no—
408C4×Q8—941no—
409C4×Q8C4×D4712yes—
410C4×Q8C22×D4712yes—
411#117—942no—
412#117—942no—
413#117—942no—
414#117—942no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—471no—
417C2×C4⋊C4—941no—
418C2×C4⋊C4—941no—
419C2×C4⋊C4—941no—
420C2×C4⋊C4—941no—
421C2×C4⋊C4—941no—
422C2×C4⋊C4—941no—
423C2×C4⋊C4C4×D4711yescharacteristic
424C2×C22⋊C4—941no—
425C2×C22⋊C4—941no—
426C2×C42—21no—
427C2×C42—471no—
428C2×C42—471no—
429C2×C42—471no—
430C2×C42—471no—
431C2×C42—471no—
432C2×C42—471no—
433C2×C42—471no—
434C2×C42—471no—
435C2×C42—471no—
436C2×C42—471no—
437C2×C42—471no—
438C2×C42—941no—
439C2×C42C22×D4711yescharacteristic
440C4⋊C8—21no—
441C4⋊C8—21no—
442C4⋊C8—472no—
443C4⋊C8—942no—
444C4⋊C8—941no—
445C4⋊C8—941no—
446C4⋊C8C22×D4712yes—
447C22⋊C8—21no—
448C22⋊C8—942no—
449C22⋊C8—942no—
450C22⋊C8—942no—
451C22⋊C8—941no—
452#97—942no—
453#97—942no—
454C4×C8—472no—
455C4×C8—942no—
456C4×C8C22×D4712yes—
457C24—471no—
458C2×Q8—21no—
459C2×Q8—42no—
460C2×Q8—472no—
461C2×Q8—942no—
462C2×Q8—942no—
463C2×Q8—941no—
464C2×Q8—1882no—
465C2×Q8—1884no—
466C2×Q8C2×C4×D4712yes—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—471no—
470C22×C4—471no—
471C22×C4—471no—
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—942no—
485C22×C4—942no—
486C22×C4—941no—
487C22×C4—941no—
488C22×C4—1882no—
489C22×C4—1882no—
490C22×C4C2×C4×D4711yescharacteristic
491C22×C4D4×D4711yescharacteristic
492C22×C4D4×D4711yescharacteristic
493M16—42no—
494M16—1884no—
495M16—1882no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—942no—
499C2×C8—942no—
500C4⋊C4—22no—
501C4⋊C4—21no—
502C4⋊C4—22no—
503C4⋊C4—472no—
504C4⋊C4—942no—
505C4⋊C4—942no—
506C4⋊C4—942no—
507C4⋊C4—942no—
508C4⋊C4—942no—
509C4⋊C4—942no—
510C4⋊C4—942no—
511C4⋊C4—942no—
512C4⋊C4—942no—
513C4⋊C4—942no—
514C4⋊C4—942no—
515C4⋊C4—941no—
516C4⋊C4—942no—
517C4⋊C4C2×C4×D4712yes—
518C22⋊C4—942no—
519C22⋊C4—942no—
520C22⋊C4—942no—
521C22⋊C4—942no—
522C42—22no—
523C42—22no—
524C42—471no—
525C42—471no—
526C42—471no—
527C42—471no—
528C42—471no—
529C42—471no—
530C42—471no—
531C42—471no—
532C42—471no—
533C42—471no—
534C42—471no—
535C42—471no—
536C42—942no—
537C42—942no—
538C42C2×C4×D4711yescharacteristic
539C42D4×D4711yescharacteristic
540C42D4×D4711yescharacteristic
541C42C23×D4711yescharacteristic
542C23—471no—
543C23—471no—
544C23—942no—
545C23—1881no—
546C23—1881no—
547C23C22⋊C4×D4711yescharacteristic
548Q8—24no—
549Q8—42no—
550Q8—944no—
551Q8—1882no—
552Q8—1884no—
553Q8—1884no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—41no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—471no—
561C2×C4—471no—
562C2×C4—471no—
563C2×C4—471no—
564C2×C4—471no—
565C2×C4—471no—
566C2×C4—942no—
567C2×C4—942no—
568C2×C4—942no—
569C2×C4—942no—
570C2×C4—942no—
571C2×C4—942no—
572C2×C4—942no—
573C2×C4—942no—
574C2×C4—941no—
575C2×C4—941no—
576C2×C4—941no—
577C2×C4—941no—
578C2×C4—942no—
579C2×C4—942no—
580C2×C4—1881no—
581C2×C4—1881no—
582C2×C4—1881no—
583C2×C4—1881no—
584C2×C4—1881no—
585C2×C4—1882no—
586C2×C4—1882no—
587C2×C4C22⋊C4×D4711yescharacteristic
588C2×C4C22⋊C4×D4711yescharacteristic
589C2×C4C22⋊C4×D4711yescharacteristic
590C2×C4#1309405312yes—
591C2×C4#1309405612yes—
592C2×C4C22×C4×D4711yescharacteristic
593C2×C4C2×D4×D4711yescharacteristic
594C2×C4C2×D4×D4711yescharacteristic
595C8—42no—
596C8—42no—
597C8—1882no—
598C8—1882no—
599C22—21no—
600C22—21no—
601C22—941no—
602C22—941no—
603C22—941no—
604C22—941no—
605C22—941no—
606C22—941no—
607C22—1884no—
608C22#1568913012yes—
609C22C2×C22⋊C4×D4711yescharacteristic
610C4—21no—
611C4—21no—
612C4—21no—
613C4—42no—
614C4—42no—
615C4—472no—
616C4—941no—
617C4—941no—
618C4—941no—
619C4—941no—
620C4—941no—
621C4—1882no—
622C4—1882no—
623C4#1568913012yes—
624C4#1568988912yes—
625C4C2×#1309405311yescharacteristic
626C4C2×#1309405611yescharacteristic
627C2—22no—
628C2—1881no—
629C2—1881no—
630C2#2025183111yescharacteristic
631C2C2×#1568913011yescharacteristic
632C2#421×D4711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1487C2
socleC22×C47C22×C22⋊C4
prime radicalC23×D47C22⋊C4
cosocleC42×C47C24
hypercenter#1487D47
hypocenterC47#17491
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1487

Complements

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

NH ≅ G/Ntype
4. #20241859C2semidirect
5. #20241818C2semidirect
6. #20241817C2semidirect
7. #20241816C2semidirect
8. #20241807C2semidirect
9. C47×#1487C2semidirect
42. #15688855C22semidirect
43. Q8⋊(C47⋊C8)C22semidirect
44. #15688853C22semidirect
48. C47×Q8⋊C8C22semidirect
318. #1487D47semidirect
364. Q8⋊C8C2×D47semidirect
365. C47#17491semidirect

Maximal subgroups

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

subgroupindex
C2×#156896772
#202520202
#202520162
#202418592
#202418182
#202418172
#202418162
#202418072
C47×#14872
#1749147