Finite Group Databasebeta

← #26220762

Subgroups — #26220762

Order 12032.

1154 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D47C211yesmaximal, characteristic
2C4×M16×D47C211yesmaximal, characteristic
3#20245792C211yesmaximal, characteristic
4#20244333C211yesmaximal, characteristic, complemented
5#20244332C211yesmaximal, characteristic, complemented
6#20244331C211yesmaximal, characteristic, complemented
7#20244330C214yesmaximal, complemented
8#20243096C214yesmaximal
9C47×#1986C211yesmaximal, characteristic, complemented
10C2×M16×D47C2212yes—
11#15689680C2211yescharacteristic
12#15689679C412yescomplemented
13#15689678C411yescharacteristic, complemented
14#15689678C411yescharacteristic, complemented
15#15689677—21no—
16#15689677—21no—
17#15689676C2212yes—
18#15689675—21no—
19#15689675—21no—
20C4⋊Q8×D47C411yescharacteristic, complemented
21C4⋊Q8×D47C411yescharacteristic, complemented
22#125×D47C412yescomplemented
23C22⋊Q8×D47—21no—
24C22⋊Q8×D47—21no—
25C4×Q8×D47—21no—
26C4×Q8×D47—21no—
27C2×#13093981C2212yes—
28#117×D47C2212yes—
29C2×C42×D47C2211yescharacteristic
30C4×#10625329C2211yescharacteristic
31#15689075—21no—
32M16×Dic47C2212yes—
33C4×#10625324—21no—
34#97×D47—21no—
35C4×C8×D47—21no—
36#15688992—21no—
37#15688987—21no—
38#15688982—21no—
39#15688980—21no—
40C4×Dic47⋊C4C2212yes—
41C4×C4⋊Dic47C2211yescharacteristic
42#15688884C2214yes—
43#15688883C2214yes—
44#15688882C2214yes—
45C47×#533C2211yescharacteristic
46C4×M16×C47C2211yescharacteristic
47C4×C4⋊C4×C47C2211yescharacteristic
48C47×#339C2214yes—
49C2×Q8×D47—21no—
50C2×Q8×D47—21no—
51C22×C4×D47D411yescharacteristic
52C22×C4×D47D411yescharacteristic
53C22×C4×D47C2311yescharacteristic
54C2×#10625329C2312yes—
55C2×#10625324—22no—
56M16×D47—24no—
57M16×D47Q818yescomplemented
58C2×C8×D47—22no—
59#13094024C2×C411yescharacteristic
60#13094024C2×C411yescharacteristic
61#13094023—21no—
62#13094023—21no—
63#13094023C2×C412yes—
64#13094023C2×C412yes—
65#13094022—21no—
66#13094022—21no—
67#13094016C2×C412yes—
68#13094015C2×C412yes—
69#13094015C2×C412yes—
70#13094014—22no—
71#13094014—22no—
72#13094004—21no—
73#13094004—21no—
74#13094003—21no—
75#13094003—21no—
76#13094002—22no—
77#13094002—22no—
78#13094001—22no—
79#13094001—22no—
80#13094000—21no—
81#13094000—21no—
82Q8×Dic47—21no—
83Q8×Dic47—21no—
84C4×Dic94—21no—
85C4×Dic94—21no—
86C4×Dic94—22no—
87C4×Dic94—22no—
88#13093989—21no—
89#13093989—21no—
90#13093989—22no—
91#13093989—22no—
92#13093983C2312yes—
93#13093982C2×C412yes—
94#13093982C2×C412yes—
95#13093981—22no—
96#13093981—28no—
97#13093980—22no—
98C2×C4⋊Dic47—21no—
99C2×Dic47⋊C4—22no—
100C2×Dic47⋊C4—22no—
101C4⋊C4×D47—22no—
102C4⋊C4×D47—22no—
103C4⋊C4×D47—21no—
104C4⋊C4×D47—21no—
105C4⋊C4×D47C2×C412yes—
106C4⋊C4×D47C2×C412yes—
107C2×(C2×D47)⋊C4—22no—
108C22⋊C4×D47—22no—
109C2×C4×Dic47D411yescharacteristic
110C2×C4×Dic47D411yescharacteristic
111C2×C4×Dic47C2312yes—
112C2×C4×Dic47C2311yescharacteristic
113C42×D47—22no—
114C42×D47C2×C411yescharacteristic
115C42×D47C2×C411yescharacteristic
116C42×D47C2×C411yescharacteristic
117C42×D47C2×C411yescharacteristic
118C42×D47D411yescharacteristic
119C42×D47D411yescharacteristic
120C42×D47D411yescharacteristic
121C42×D47D411yescharacteristic
122#13093935—21no—
123#13093934—22no—
124C4×C47⋊C8—21no—
125C8×Dic47—22no—
126C47⋊#95—21no—
127C47⋊#95—22no—
128C2×M16×C47C2312yes—
129C4⋊Q8×C47C2×C411yescharacteristic
130C4⋊Q8×C47C2×C411yescharacteristic
131#125×C47C2×C412yes—
132C22⋊Q8×C47—21no—
133C22⋊Q8×C47—21no—
134C4×Q8×C47—21no—
135C4×Q8×C47—21no—
136#117×C47C2312yes—
137C2×C4⋊C4×C47—21no—
138C2×C42×C47C2312yes—
139C2×C42×C47C2311yescharacteristic
140#97×C47—21no—
141C4×C8×C47—21no—
142#95×C47—21no—
143C23×D47C2×D411yescharacteristic
144C2×Q8×C47—21no—
145C2×Q8×C47—21no—
146C22×C4×C47—22no—
147C22×C4×C47C2×D411yescharacteristic
148C22×C4×C47C2×D411yescharacteristic
149C22×C4×C47C2411yescharacteristic
150C22×Dic47—22no—
151C22×Dic47C2×D411yescharacteristic
152C22×Dic47C2×D411yescharacteristic
153C22×Dic47C2×D411yescharacteristic
154Q8×D47—44no—
155Q8×D47—44no—
156C2×C4×D47—22no—
157C2×C4×D47—22no—
158C2×C4×D47—42no—
159C2×C4×D47—42no—
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×D47C22⋊C411yescharacteristic
167C2×C4×D47C22⋊C411yescharacteristic
168C2×C4×D47C22×C411yescharacteristic
169C2×C4×D47C22×C411yescharacteristic
170C2×C4×D47C2×D411yescharacteristic
171C2×C4×D47C2×D411yescharacteristic
172C2×C4×D47C2×Q814yes—
173C2×C4×D47#4114yes—
174C2×Dic94—21no—
175C2×Dic94—21no—
176C2×Dic94—22no—
177C2×Dic94—22no—
178M16×C47—22no—
179M16×C47C2×Q814yescomplemented
180C2×C8×C47—22no—
181C4⋊C4×C47—22no—
182C4⋊C4×C47—22no—
183C4⋊C4×C47—21no—
184C4⋊C4×C47—21no—
185C4⋊C4×C47—42no—
186C4⋊C4×C47C22×C412yes—
187C4⋊C4×C47C22×C412yes—
188C22⋊C4×C47—22no—
189C42×C47—22no—
190C42×C47—24no—
191C42×C47C22×C411yescharacteristic
192C42×C47C22×C411yescharacteristic
193C42×C47C2×D411yescharacteristic
194C42×C47C2×D411yescharacteristic
195C22⋊Dic47—22no—
196(C2×D47)⋊C4—22no—
197(C2×D47)⋊C4—22no—
198(C2×D47)⋊C4—44no—
199C4⋊Dic47—21no—
200C4⋊Dic47—21no—
201C4⋊Dic47—22no—
202C4⋊Dic47—22no—
203C4⋊Dic47—42no—
204C4⋊Dic47C22×C412yes—
205C4⋊Dic47C22×C412yes—
206Dic47⋊C4—22no—
207Dic47⋊C4—22no—
208Dic47⋊C4—22no—
209Dic47⋊C4—22no—
210Dic47⋊C4—22no—
211Dic47⋊C4—22no—
212Dic47⋊C4—22no—
213Dic47⋊C4—22no—
214Dic47⋊C4—44no—
215Dic47⋊C4—44no—
216C4×Dic47—22no—
217C4×Dic47—22no—
218C4×Dic47—22no—
219C4×Dic47—24no—
220C4×Dic47C22⋊C411yescharacteristic
221C4×Dic47C22⋊C411yescharacteristic
222C4×Dic47C22⋊C411yescharacteristic
223C4×Dic47C22⋊C411yescharacteristic
224C4×Dic47C22⋊C411yescharacteristic
225C4×Dic47C22⋊C411yescharacteristic
226C4×Dic47C22⋊C411yescharacteristic
227C4×Dic47C22⋊C411yescharacteristic
228C4×Dic47C22×C411yescharacteristic
229C4×Dic47C22×C411yescharacteristic
230C4×Dic47C2×D411yescharacteristic
231C4×Dic47C2×D411yescharacteristic
232#10625329—22no—
233#10625329C2×Q814yescomplemented
234C2×C47⋊C8—22no—
235#10625324—28no—
236C8×D47—28no—
237C23×C47C22×D411yescharacteristic
238C22×D47—41no—
239C22×D47—41no—
240C22×D47C2×C22⋊C411yescharacteristic
241C22×D47C2×C22⋊C411yescharacteristic
242C22×D47#12412yes—
243C22×D47C4⋊Q812yes—
244Q8×C47—42no—
245Q8×C47—42no—
246C2×C4×C47—22no—
247C2×C4×C47—22no—
248C2×C4×C47—22no—
249C2×C4×C47—41no—
250C2×C4×C47—42no—
251C2×C4×C47—42no—
252C2×C4×C47—42no—
253C2×C4×C47C2×C22⋊C411yescharacteristic
254C2×C4×C47C2×C22⋊C411yescharacteristic
255C2×C4×C47C2×C22⋊C411yescharacteristic
256C2×C4×C47C2×C22⋊C411yescharacteristic
257C2×C4×C47C23×C411yescharacteristic
258C2×C4×C47C22×D411yescharacteristic
259C2×C4×C47C22×Q812yes—
260C2×C4×C47C2×#4112yes—
261C2×Dic47—22no—
262C2×Dic47—22no—
263C2×Dic47—22no—
264C2×Dic47—41no—
265C2×Dic47—42no—
266C2×Dic47—42no—
267C2×Dic47—42no—
268C2×Dic47C2×C22⋊C411yescharacteristic
269C2×Dic47C2×C22⋊C411yescharacteristic
270C2×Dic47C2×C22⋊C411yescharacteristic
271C2×Dic47C2×C22⋊C411yescharacteristic
272C2×Dic47C2×C22⋊C411yescharacteristic
273C2×Dic47C2×C22⋊C411yescharacteristic
274C2×Dic47#12412yes—
275C2×Dic47C4⋊Q812yes—
276C4×D47—22no—
277C4×D47—22no—
278C4×D47—22no—
279C4×D47—22no—
280C4×D47—41no—
281C4×D47—41no—
282C4×D47—41no—
283C4×D47—41no—
284C4×D47—44no—
285C4×D47—44no—
286C4×D47C4×Q814yes—
287C4×D47C4×Q814yes—
288C4×D47C22⋊Q814yes—
289C4×D47C22⋊Q814yes—
290Dic94—44no—
291Dic94—42no—
292Dic94—42no—
293Dic94—44no—
294C8×C47—24no—
295C47⋊C8—24no—
296#21306—471nomaximal, Sylow
297C22×C47—21no—
298C22×C47—21no—
299C22×C47C22×C22⋊C411yescharacteristic
300C22×C47C2×#12411yescharacteristic
301C22×C47C2×C4⋊Q811yescharacteristic
302C2×D47—21no—
303C2×D47—21no—
304C2×D47—21no—
305C2×D47—21no—
306C2×D47—42no—
307C2×D47—42no—
308C2×D47#39112yes—
309C2×D47#39112yes—
310C4×C47—21no—
311C4×C47—21no—
312C4×C47—21no—
313C4×C47—42no—
314C4×C47—42no—
315C4×C47—82no—
316C4×C47#42112yes—
317C4×C47C2×C4×Q812yes—
318C4×C47C2×C22⋊Q812yes—
319Dic47—21no—
320Dic47—21no—
321Dic47—21no—
322Dic47—42no—
323Dic47—42no—
324Dic47—82no—
325Dic47#39112yes—
326Dic47#39112yes—
327Dic47#42112yes—
328C2×#533—471no—
329C2×C4×M16—471no—
330#2285—471no—
331#1986—471no—
332#1986—471no—
333#1986—474no—
334#1986—471no—
335#1986D4711yescharacteristic, complemented
336#1733—474no—
337C2×C47—21no—
338C2×C47—21no—
339C2×C47C2×#39111yescharacteristic
340C2×C47C2×#42111yescharacteristic
341C2×C47C2×#42111yescharacteristic
342D47—22no—
343D47—22no—
344C22×M16—472no—
345#533—471no—
346#533—471no—
347#533—472no—
348#533—472no—
349#533—471no—
350#533—941no—
351#533—941no—
352#533—941no—
353#533—941no—
354#533C2×D4711yescharacteristic
355C2×C4⋊Q8—471no—
356C2×C4⋊Q8—471no—
357C2×#125—472no—
358C2×C22⋊Q8—941no—
359C2×C22⋊Q8—941no—
360C2×C4×Q8—941no—
361C2×C4×Q8—941no—
362C2×#117—472no—
363C2×#117—472no—
364C22×C42—471no—
365C4×M16—472no—
366C4×M16—471no—
367C4×M16—941no—
368C4×M16—941no—
369C4×M16C2×D4711yescharacteristic
370C2×#97—941no—
371C2×C4×C8—941no—
372#384—941no—
373#382—941no—
374#380—941no—
375#380—941no—
376C4×C4⋊C4—472no—
377C4×C4⋊C4—471no—
378C4×C4⋊C4C2×D4711yescharacteristic
379#339—474no—
380#339—474no—
381#339—474no—
382#339C2×D4714yes—
383C47#2130611yescharacteristic, complemented, Sylow
384C22×Q8—941no—
385C22×Q8—941no—
386C23×C4—471no—
387C23×C4—471no—
388C23×C4—471no—
389C2×M16—472no—
390C2×M16—478no—
391C2×M16—942no—
392C2×M16—944no—
393C2×M16C22×D4712yes—
394C22×C8—942no—
395C4⋊Q8—472no—
396C4⋊Q8—472no—
397C4⋊Q8—471no—
398C4⋊Q8—471no—
399C4⋊Q8—941no—
400C4⋊Q8—941no—
401C4⋊Q8—941no—
402C4⋊Q8—941no—
403C4⋊Q8C4×D4711yescharacteristic
404C4⋊Q8C4×D4711yescharacteristic
405#125—472no—
406#125—472no—
407#125—472no—
408#125—942no—
409#125—942no—
410#125C4×D4712yes—
411C22⋊Q8—21no—
412C22⋊Q8—21no—
413C22⋊Q8—942no—
414C22⋊Q8—942no—
415C22⋊Q8—942no—
416C22⋊Q8—942no—
417C22⋊Q8—941no—
418C22⋊Q8—941no—
419C22⋊Q8—941no—
420C22⋊Q8—941no—
421C22⋊Q8—941no—
422C22⋊Q8—941no—
423C4×Q8—21no—
424C4×Q8—21no—
425C4×Q8—942no—
426C4×Q8—942no—
427C4×Q8—942no—
428C4×Q8—942no—
429C4×Q8—941no—
430C4×Q8—941no—
431C4×Q8—941no—
432C4×Q8—941no—
433C4×Q8—941no—
434C4×Q8—941no—
435#117—472no—
436#117—472no—
437#117—472no—
438#117—942no—
439#117—948no—
440#117—942no—
441#117C22×D4712yes—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—472no—
444C2×C4⋊C4—472no—
445C2×C4⋊C4—942no—
446C2×C4⋊C4—942no—
447C2×C4⋊C4—941no—
448C2×C4⋊C4—941no—
449C2×C4⋊C4—942no—
450C2×C4⋊C4—942no—
451C2×C4⋊C4—941no—
452C2×C22⋊C4—942no—
453C2×C22⋊C4—942no—
454C2×C42—471no—
455C2×C42—471no—
456C2×C42—471no—
457C2×C42—471no—
458C2×C42—471no—
459C2×C42—471no—
460C2×C42—471no—
461C2×C42—471no—
462C2×C42—471no—
463C2×C42—471no—
464C2×C42—471no—
465C2×C42—472no—
466C2×C42—942no—
467C2×C42C22×D4712yes—
468C2×C42C22×D4711yescharacteristic
469#97—21no—
470#97—942no—
471#97—941no—
472C4×C8—21no—
473C4×C8—942no—
474C4×C8—941no—
475#95—21no—
476#95—942no—
477#95—941no—
478C24—471no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—942no—
482C2×Q8—942no—
483C2×Q8—941no—
484C2×Q8—941no—
485C2×Q8—1884no—
486C2×Q8—1884no—
487C22×C4—22no—
488C22×C4—471no—
489C22×C4—471no—
490C22×C4—471no—
491C22×C4—471no—
492C22×C4—471no—
493C22×C4—474no—
494C22×C4—474no—
495C22×C4—471no—
496C22×C4—471no—
497C22×C4—471no—
498C22×C4—471no—
499C22×C4—471no—
500C22×C4—471no—
501C22×C4—471no—
502C22×C4—471no—
503C22×C4—471no—
504C22×C4—471no—
505C22×C4—942no—
506C22×C4—942no—
507C22×C4—942no—
508C22×C4—1882no—
509C22×C4—1882no—
510C22×C4D4×D4711yescharacteristic
511C22×C4D4×D4711yescharacteristic
512C22×C4C23×D4711yescharacteristic
513M16—22no—
514M16—474no—
515M16—948no—
516M16—942no—
517M16Q8×D4714yescomplemented
518C2×C8—22no—
519C2×C8—948no—
520C2×C8—942no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—42no—
526C4⋊C4—472no—
527C4⋊C4—472no—
528C4⋊C4—942no—
529C4⋊C4—942no—
530C4⋊C4—942no—
531C4⋊C4—942no—
532C4⋊C4—942no—
533C4⋊C4—942no—
534C4⋊C4—942no—
535C4⋊C4—942no—
536C4⋊C4—942no—
537C4⋊C4—942no—
538C4⋊C4—941no—
539C4⋊C4—941no—
540C4⋊C4—1882no—
541C4⋊C4—1884no—
542C4⋊C4—1884no—
543C4⋊C4C2×C4×D4712yes—
544C4⋊C4C2×C4×D4712yes—
545C22⋊C4—22no—
546C22⋊C4—942no—
547C22⋊C4—942no—
548C22⋊C4—942no—
549C22⋊C4—1884no—
550C42—22no—
551C42—24no—
552C42—471no—
553C42—471no—
554C42—471no—
555C42—471no—
556C42—471no—
557C42—471no—
558C42—471no—
559C42—471no—
560C42—471no—
561C42—471no—
562C42—471no—
563C42—471no—
564C42—942no—
565C42—942no—
566C42—942no—
567C42—944no—
568C42C2×C4×D4711yescharacteristic
569C42C2×C4×D4711yescharacteristic
570C42D4×D4711yescharacteristic
571C42D4×D4711yescharacteristic
572C23—471no—
573C23—471no—
574C23—472no—
575C23—472no—
576C23—1881no—
577C23—1881no—
578C23C2×D4×D4711yescharacteristic
579Q8—42no—
580Q8—42no—
581Q8—1882no—
582Q8—1884no—
583Q8—1884no—
584Q8—1882no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—471no—
593C2×C4—471no—
594C2×C4—471no—
595C2×C4—472no—
596C2×C4—472no—
597C2×C4—474no—
598C2×C4—474no—
599C2×C4—474no—
600C2×C4—474no—
601C2×C4—471no—
602C2×C4—471no—
603C2×C4—471no—
604C2×C4—942no—
605C2×C4—942no—
606C2×C4—942no—
607C2×C4—942no—
608C2×C4—942no—
609C2×C4—942no—
610C2×C4—942no—
611C2×C4—1881no—
612C2×C4—1881no—
613C2×C4—1881no—
614C2×C4—1881no—
615C2×C4—1884no—
616C2×C4—1884no—
617C2×C4—1881no—
618C2×C4—1882no—
619C2×C4—1882no—
620C2×C4—1882no—
621C2×C4C22⋊C4×D4711yescharacteristic
622C2×C4C22⋊C4×D4711yescharacteristic
623C2×C4C22⋊C4×D4711yescharacteristic
624C2×C4C22⋊C4×D4711yescharacteristic
625C2×C4C22×C4×D4711yescharacteristic
626C2×C4C2×D4×D4711yescharacteristic
627C2×C4C2×Q8×D4712yes—
628C2×C4#41×D4712yes—
629C8—24no—
630C8—944no—
631C22—21no—
632C22—21no—
633C22—472no—
634C22—472no—
635C22—941no—
636C22—941no—
637C22—941no—
638C22—941no—
639C22—1882no—
640C22—1882no—
641C22C2×C22⋊C4×D4711yescharacteristic
642C22#124×D4711yescharacteristic
643C22C4⋊Q8×D4711yescharacteristic
644C4—21no—
645C4—21no—
646C4—21no—
647C4—42no—
648C4—42no—
649C4—82no—
650C4—472no—
651C4—472no—
652C4—472no—
653C4—941no—
654C4—941no—
655C4—941no—
656C4—3762no—
657C4—1882no—
658C4—1882no—
659C4#1568913812yes—
660C4C4×Q8×D4712yes—
661C4C22⋊Q8×D4712yes—
662C2—21no—
663C2—21no—
664C2—942no—
665C2—942no—
666C2#391×D4711yescharacteristic
667C2#421×D4711yescharacteristic
668C2C2×#1568913811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1986C2
socleC22×C47C22×C22⋊C4
prime radicalC23×D47C2×D4
cosocleC22×C4×C47C24
hypercenter#1986D47
hypocenterC47#21306
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1986

Complements

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

NH ≅ G/Ntype
4. #20244333C2semidirect
5. #20244332C2semidirect
6. #20244331C2semidirect
7. #20244330C2semidirect
9. C47×#1986C2semidirect
12. #15689679C4semidirect
13. #15689678C4semidirect
14. #15689678C4semidirect
20. C4⋊Q8×D47C4semidirect
21. C4⋊Q8×D47C4semidirect
22. #125×D47C4semidirect
57. M16×D47Q8semidirect
179. M16×C47C2×Q8semidirect
233. #10625329C2×Q8semidirect
335. #1986D47semidirect
383. C47#21306semidirect
517. M16Q8×D47semidirect

Maximal subgroups

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

subgroupindex
#533×D472
C4×M16×D472
#202457922
#202443332
#202443322
#202443312
#202443302
#202430962
C47×#19862
#2130647