Finite Group Databasebeta

← #26216109

Subgroups — #26216109

Order 12032.

1470 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D47C211yesmaximal, characteristic
2C2×#15689086C211yesmaximal, characteristic
3#20245767C211yesmaximal, characteristic
4#20243486C218yesmaximal, complemented
5#20243099C211yesmaximal, characteristic, complemented
6#20243098C211yesmaximal, characteristic, complemented
7#20243097C211yesmaximal, characteristic, complemented
8C47×#1733C211yesmaximal, characteristic, complemented
9C23×C4×D47C2211yescharacteristic
10C22×#10625329C2211yescharacteristic
11C2×#13093983C2211yescharacteristic
12C2×#13093983C2211yescharacteristic
13C2×#13093982C412yescomplemented
14C2×#13093981—21no—
15C2×#13093980—21no—
16#117×D47—22no—
17#117×D47—22no—
18#117×D47C414yescomplemented
19#117×D47C2214yes—
20C2×C4⋊C4×D47C412yescomplemented
21C2×C22⋊C4×D47—21no—
22C2×C42×D47—21no—
23#15689086—21no—
24#15689086—21no—
25#15689086C2214yes—
26C2×(C2×D47)⋊C8—22no—
27#15688984—21no—
28#15688980—22no—
29#15688978—21no—
30C4×(C2×D47)⋊C4C2214yes—
31#15688884C2214yescomplemented
32#15688883C2214yescomplemented
33#15688882C2214yescomplemented
34C22×M16×C47C2211yescharacteristic
35C2×#117×C47C2211yescharacteristic
36C2×#117×C47C2211yescharacteristic
37C47×#339C2214yescomplemented
38C24×D47D411yescharacteristic
39C23×Dic47D411yescharacteristic
40C22×C4×D47—22no—
41C22×C4×D47—22no—
42C22×C4×D47—22no—
43C22×C4×D47—22no—
44C22×C4×D47—22no—
45C22×C4×D47C2×C411yescharacteristic
46C22×C4×D47C2×C412yes—
47C22×C4×D47C2×C411yescharacteristic
48C22×C4×D47D412yes—
49C22×C4×D47D411yescharacteristic
50C22×C4×D47D412yes—
51C22×C4×D47D411yescharacteristic
52C22×C4×D47C2312yes—
53C2×#10625329—21no—
54C2×#10625329—22no—
55C2×#10625329—22no—
56C2×#10625329C2312yes—
57C22×C47⋊C8—21no—
58#13093983—21no—
59#13093983—21no—
60#13093983—22no—
61#13093983—22no—
62#13093983C2×C412yes—
63#13093983C2312yes—
64#13093982—24no—
65#13093982C2×C418yes—
66#13093981—24no—
67#13093981—24no—
68#13093980—24no—
69#13093980—24no—
70C2×C4⋊Dic47—21no—
71C2×C4⋊Dic47C2×C412yes—
72C2×Dic47⋊C4—22no—
73C4⋊C4×D47—22no—
74C4⋊C4×D47—22no—
75C4⋊C4×D47C2×C414yes—
76C4⋊C4×D47C2×C414yes—
77C2×C22⋊Dic47—21no—
78C2×C22⋊Dic47—21no—
79C2×(C2×D47)⋊C4—22no—
80C2×(C2×D47)⋊C4—24no—
81C22⋊C4×D47—24no—
82C22⋊C4×D47—24no—
83C2×C4×Dic47—21no—
84C2×C4×Dic47—22no—
85C2×C4×Dic47C2312yes—
86C42×D47—24no—
87C42×D47—24no—
88(C2×D47)⋊C8—24no—
89(C2×D47)⋊C8—24no—
90C47⋊#95—24no—
91C23×C4×C47C2311yescharacteristic
92C2×M16×C47—21no—
93C2×M16×C47—22no—
94C2×M16×C47—22no—
95C2×M16×C47C2312yes—
96C22×C8×C47—21no—
97#117×C47—21no—
98#117×C47—21no—
99#117×C47—22no—
100#117×C47—22no—
101#117×C47C2×C412yes—
102#117×C47C2312yes—
103C2×C4⋊C4×C47—21no—
104C2×C4⋊C4×C47C2×C412yes—
105C2×C22⋊C4×C47—21no—
106C2×C22⋊C4×C47—21no—
107C2×C42×C47—21no—
108C2×C42×C47C2312yes—
109C24×C47C2×D411yescharacteristic
110C23×D47—22no—
111C23×D47—22no—
112C23×D47—44no—
113C23×D47C22⋊C411yescharacteristic
114C23×D47C22⋊C412yes—
115C23×D47C22⋊C411yescharacteristic
116C23×D47C2×D412yes—
117C22×C4×C47—22no—
118C22×C4×C47—22no—
119C22×C4×C47C22×C411yescharacteristic
120C22×C4×C47C22×C411yescharacteristic
121C22×C4×C47C2×D411yescharacteristic
122C22×C4×C47C2×D411yescharacteristic
123C22×C4×C47C2×D411yescharacteristic
124C22×C4×C47#4112yes—
125C22×C4×C47#4112yes—
126C22×C4×C47#4112yes—
127C22×C4×C47#4112yes—
128C22×C4×C47C2411yescharacteristic
129C22×Dic47—22no—
130C22×Dic47—22no—
131C22×Dic47—22no—
132C22×Dic47—22no—
133C22×Dic47C22⋊C411yescharacteristic
134C22×Dic47C22⋊C411yescharacteristic
135C22×Dic47C22⋊C412yes—
136C22×Dic47C2×D412yes—
137C2×C4×D47—22no—
138C2×C4×D47—24no—
139C2×C4×D47—22no—
140C2×C4×D47—22no—
141C2×C4×D47—24no—
142C2×C4×D47—22no—
143C2×C4×D47—24no—
144C2×C4×D47—22no—
145C2×C4×D47—22no—
146C2×C4×D47—24no—
147C2×C4×D47—22no—
148C2×C4×D47—22no—
149C2×C4×D47—24no—
150C2×C4×D47—24no—
151C2×C4×D47—22no—
152C2×C4×D47—22no—
153C2×C4×D47—22no—
154C2×C4×D47—22no—
155C2×C4×D47—24no—
156C2×C4×D47—24no—
157C2×C4×D47—48no—
158C2×C4×D47C22⋊C412yes—
159C2×C4×D47C22⋊C412yes—
160C2×C4×D47C22⋊C412yes—
161C2×C4×D47C22⋊C412yes—
162C2×C4×D47C22×C412yes—
163C2×C4×D47C22×C412yes—
164C2×C4×D47C2×D412yes—
165C2×C4×D47C2×D412yes—
166M16×C47—22no—
167M16×C47—22no—
168M16×C47—42no—
169C2×C8×C47—22no—
170C2×C8×C47—42no—
171C4⋊C4×C47—22no—
172C4⋊C4×C47—42no—
173C4⋊C4×C47C22×C414yes—
174C22⋊C4×C47—22no—
175C22⋊C4×C47—22no—
176C22⋊C4×C47—42no—
177C42×C47—22no—
178C42×C47—22no—
179C42×C47—22no—
180C42×C47—22no—
181C22⋊Dic47—22no—
182C22⋊Dic47—22no—
183C22⋊Dic47—42no—
184(C2×D47)⋊C4—28no—
185(C2×D47)⋊C4—48no—
186C4⋊Dic47—22no—
187C4⋊Dic47—42no—
188C4⋊Dic47C22×C414yes—
189Dic47⋊C4—24no—
190Dic47⋊C4—24no—
191C4×Dic47—22no—
192C4×Dic47—22no—
193C4×Dic47—28no—
194C4×Dic47—22no—
195C4×Dic47—22no—
196#10625329—22no—
197#10625329—22no—
198#10625329—42no—
199C2×C47⋊C8—22no—
200C2×C47⋊C8—42no—
201C23×C47—42no—
202C23×C47C2×C22⋊C411yescharacteristic
203C23×C47C2×C22⋊C411yescharacteristic
204C23×C47#12312yes—
205C23×C47#12312yes—
206C23×C47C22×D411yescharacteristic
207C22×D47—22no—
208C22×D47—24no—
209C22×D47—22no—
210C22×D47—22no—
211C22×D47—24no—
212C22×D47—22no—
213C22×D47—24no—
214C22×D47—24no—
215C22×D47—42no—
216C22×D47—42no—
217C22×D47—42no—
218C22×D47—48no—
219C22×D47—48no—
220C22×D47C2×C22⋊C412yes—
221C22×D47C2×C22⋊C412yes—
222C2×C4×C47—24no—
223C2×C4×C47—44no—
224C2×C4×C47—44no—
225C2×C4×C47—42no—
226C2×C4×C47C2×C22⋊C411yescharacteristic
227C2×C4×C47C2×C22⋊C411yescharacteristic
228C2×C4×C47#11712yes—
229C2×C4×C47#11712yes—
230C2×C4×C47#11712yes—
231C2×C4×C47#11712yes—
232C2×C4×C47#12312yes—
233C2×C4×C47#12312yes—
234C2×C4×C47#12312yes—
235C2×C4×C47#12312yes—
236C2×C4×C47#12312yes—
237C2×C4×C47#12312yes—
238C2×C4×C47C23×C411yescharacteristic
239C2×C4×C47C22×D411yescharacteristic
240C2×C4×C47C2×#4111yescharacteristic
241C2×C4×C47C2×#4111yescharacteristic
242C2×C4×C47C2×#4111yescharacteristic
243C2×C4×C47C2×#4111yescharacteristic
244C2×Dic47—22no—
245C2×Dic47—22no—
246C2×Dic47—22no—
247C2×Dic47—22no—
248C2×Dic47—24no—
249C2×Dic47—24no—
250C2×Dic47—44no—
251C2×Dic47—44no—
252C2×Dic47—42no—
253C2×Dic47C2×C22⋊C412yes—
254C2×Dic47C2×C22⋊C412yes—
255C4×D47—22no—
256C4×D47—22no—
257C4×D47—22no—
258C4×D47—22no—
259C4×D47—22no—
260C4×D47—22no—
261C4×D47—22no—
262C4×D47—22no—
263C4×D47—24no—
264C4×D47—24no—
265C4×D47—24no—
266C4×D47—24no—
267C4×D47—48no—
268C4×D47—48no—
269C8×C47—42no—
270C47⋊C8—42no—
271#20705—471nomaximal, Sylow
272C22×C47—22no—
273C22×C47—22no—
274C22×C47—22no—
275C22×C47—42no—
276C22×C47—42no—
277C22×C47#38112yes—
278C22×C47#38112yes—
279C22×C47C22×C22⋊C411yescharacteristic
280C22×C47C2×#12311yescharacteristic
281C22×C47C2×#12311yescharacteristic
282C2×D47—28no—
283C2×D47—22no—
284C2×D47—22no—
285C2×D47—22no—
286C2×D47—22no—
287C2×D47—22no—
288C2×D47—44no—
289C2×D47—44no—
290C2×D47—48no—
291C2×D47—44no—
292C2×D47#42114yes—
293C4×C47—44no—
294C4×C47—82no—
295C4×C47#38112yes—
296C4×C47#38112yes—
297C4×C47C2×#11711yescharacteristic
298C4×C47C2×#11711yescharacteristic
299C4×C47C2×#12311yescharacteristic
300C4×C47C2×#12311yescharacteristic
301Dic47—22no—
302Dic47—22no—
303Dic47—44no—
304Dic47—82no—
305C22×#117—471no—
306C2×#407—471no—
307#2280—471no—
308#1826—478no—
309#1733—471no—
310#1733—471no—
311#1733—471no—
312#1733D4711yescharacteristic, complemented
313C2×C47—21no—
314C2×C47—21no—
315C2×C47—22no—
316C2×C47—22no—
317C2×C47C2×#38111yescharacteristic
318C2×C47C2×#42112yes—
319D47—24no—
320D47—42no—
321C24×C4—471no—
322C22×M16—471no—
323C22×M16C2×D4711yescharacteristic
324C2×#117—471no—
325C2×#117—471no—
326C2×#117—474no—
327C2×#117—474no—
328C2×#117—472no—
329C2×#117—941no—
330C2×#117—941no—
331C2×#117—942no—
332C2×#117—942no—
333C2×#117C2×D4711yescharacteristic
334C2×#117C2×D4711yescharacteristic
335C22×C4⋊C4—472no—
336C22×C22⋊C4—941no—
337C22×C42—941no—
338#407—474no—
339#407—941no—
340#407—941no—
341C2×C22⋊C8—942no—
342#381—941no—
343#380—942no—
344#379—941no—
345C4×C22⋊C4—474no—
346#339—474no—
347#339—474no—
348#339—474no—
349#339C2×D4714yescomplemented
350C47#2070511yescharacteristic, complemented, Sylow
351C25—471no—
352C23×C4—471no—
353C23×C4—471no—
354C23×C4—471no—
355C23×C4—472no—
356C23×C4—472no—
357C23×C4—472no—
358C23×C4—471no—
359C23×C4—471no—
360C23×C4—472no—
361C23×C4—942no—
362C23×C4—942no—
363C23×C4—942no—
364C23×C4—942no—
365C23×C4—942no—
366C23×C4C22×D4711yescharacteristic
367C2×M16—21no—
368C2×M16—22no—
369C2×M16—22no—
370C2×M16—472no—
371C2×M16—941no—
372C2×M16—942no—
373C2×M16—942no—
374C2×M16C22×D4712yes—
375C22×C8—21no—
376C22×C8—941no—
377#117—21no—
378#117—21no—
379#117—22no—
380#117—22no—
381#117—472no—
382#117—472no—
383#117—478no—
384#117—944no—
385#117—944no—
386#117—944no—
387#117—944no—
388#117—944no—
389#117—941no—
390#117—941no—
391#117—942no—
392#117—942no—
393#117C4×D4712yes—
394#117C22×D4712yes—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—472no—
397C2×C4⋊C4—474no—
398C2×C4⋊C4—474no—
399C2×C4⋊C4—942no—
400C2×C4⋊C4—942no—
401C2×C4⋊C4—942no—
402C2×C4⋊C4—941no—
403C2×C4⋊C4C4×D4712yes—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—944no—
407C2×C22⋊C4—944no—
408C2×C22⋊C4—942no—
409C2×C22⋊C4—941no—
410C2×C22⋊C4—944no—
411C2×C22⋊C4—941no—
412C2×C42—21no—
413C2×C42—472no—
414C2×C42—944no—
415C2×C42—944no—
416C2×C42—942no—
417C2×C42—941no—
418C2×C42C22×D4712yes—
419C22⋊C8—944no—
420C22⋊C8—944no—
421#95—944no—
422C24—471no—
423C24—472no—
424C24—472no—
425C24—471no—
426C24—942no—
427C24—942no—
428C24—1884no—
429C24D4×D4711yescharacteristic
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—471no—
433C22×C4—471no—
434C22×C4—472no—
435C22×C4—472no—
436C22×C4—472no—
437C22×C4—472no—
438C22×C4—472no—
439C22×C4—472no—
440C22×C4—472no—
441C22×C4—472no—
442C22×C4—472no—
443C22×C4—472no—
444C22×C4—944no—
445C22×C4—944no—
446C22×C4—942no—
447C22×C4—942no—
448C22×C4—942no—
449C22×C4—942no—
450C22×C4—944no—
451C22×C4—942no—
452C22×C4—942no—
453C22×C4—944no—
454C22×C4—944no—
455C22×C4—942no—
456C22×C4—942no—
457C22×C4—944no—
458C22×C4—944no—
459C22×C4—942no—
460C22×C4—942no—
461C22×C4—944no—
462C22×C4—942no—
463C22×C4—942no—
464C22×C4—942no—
465C22×C4—942no—
466C22×C4—942no—
467C22×C4—942no—
468C22×C4—1888no—
469C22×C4C2×C4×D4711yescharacteristic
470C22×C4C2×C4×D4711yescharacteristic
471C22×C4#1062535012yes—
472C22×C4#1062535012yes—
473C22×C4D4×D4711yescharacteristic
474C22×C4D4×D4711yescharacteristic
475C22×C4D4×D4711yescharacteristic
476C22×C4#1062535212yes—
477C22×C4#1062535412yes—
478C22×C4C23×D4711yescharacteristic
479M16—22no—
480M16—22no—
481M16—42no—
482M16—942no—
483M16—942no—
484M16—1882no—
485C2×C8—22no—
486C2×C8—42no—
487C2×C8—942no—
488C2×C8—1882no—
489C4⋊C4—22no—
490C4⋊C4—42no—
491C4⋊C4—474no—
492C4⋊C4—944no—
493C4⋊C4—944no—
494C4⋊C4—942no—
495C4⋊C4—1882no—
496C4⋊C4C2×C4×D4714yes—
497C22⋊C4—22no—
498C22⋊C4—22no—
499C22⋊C4—42no—
500C22⋊C4—948no—
501C22⋊C4—942no—
502C22⋊C4—942no—
503C22⋊C4—1888no—
504C22⋊C4—1882no—
505C42—22no—
506C42—22no—
507C42—22no—
508C42—22no—
509C42—948no—
510C42—942no—
511C42—942no—
512C42—942no—
513C42—942no—
514C23—42no—
515C23—472no—
516C23—472no—
517C23—944no—
518C23—944no—
519C23—944no—
520C23—942no—
521C23—944no—
522C23—942no—
523C23—942no—
524C23—942no—
525C23—1882no—
526C23—1882no—
527C23—1882no—
528C23—1888no—
529C23—1888no—
530C23C22⋊C4×D4711yescharacteristic
531C23C22⋊C4×D4711yescharacteristic
532C23#1309400612yes—
533C23#1309400912yes—
534C23C2×D4×D4711yescharacteristic
535C2×C4—24no—
536C2×C4—44no—
537C2×C4—44no—
538C2×C4—42no—
539C2×C4—472no—
540C2×C4—472no—
541C2×C4—942no—
542C2×C4—942no—
543C2×C4—944no—
544C2×C4—942no—
545C2×C4—942no—
546C2×C4—944no—
547C2×C4—944no—
548C2×C4—944no—
549C2×C4—944no—
550C2×C4—942no—
551C2×C4—942no—
552C2×C4—942no—
553C2×C4—942no—
554C2×C4—942no—
555C2×C4—942no—
556C2×C4—942no—
557C2×C4—942no—
558C2×C4—944no—
559C2×C4—1888no—
560C2×C4—1888no—
561C2×C4—1884no—
562C2×C4—1882no—
563C2×C4—1884no—
564C2×C4C22⋊C4×D4711yescharacteristic
565C2×C4C22⋊C4×D4711yescharacteristic
566C2×C4#1309398112yes—
567C2×C4#1309398112yes—
568C2×C4#1309398212yes—
569C2×C4#1309398212yes—
570C2×C4#1309400612yes—
571C2×C4#1309400612yes—
572C2×C4#1309400612yes—
573C2×C4#1309400912yes—
574C2×C4#1309400912yes—
575C2×C4#1309400912yes—
576C2×C4C22×C4×D4711yescharacteristic
577C2×C4C2×D4×D4711yescharacteristic
578C2×C4C2×#1062535211yescharacteristic
579C2×C4C2×#1062535011yescharacteristic
580C2×C4C2×#1062535011yescharacteristic
581C2×C4C2×#1062535411yescharacteristic
582C8—42no—
583C8—1882no—
584C22—22no—
585C22—22no—
586C22—22no—
587C22—42no—
588C22—42no—
589C22—474no—
590C22—948no—
591C22—942no—
592C22—942no—
593C22—942no—
594C22—942no—
595C22—942no—
596C22—1884no—
597C22—1884no—
598C22—1888no—
599C22—1884no—
600C22#1568898512yes—
601C22#1568898512yes—
602C22C2×C22⋊C4×D4711yescharacteristic
603C22C2×#1309400611yescharacteristic
604C22C2×#1309400911yescharacteristic
605C4—44no—
606C4—82no—
607C4—942no—
608C4—942no—
609C4—3762no—
610C4—1884no—
611C4#1568898512yes—
612C4#1568898512yes—
613C4C2×#1309398111yescharacteristic
614C4C2×#1309398211yescharacteristic
615C4C2×#1309400611yescharacteristic
616C4C2×#1309400911yescharacteristic
617C2—21no—
618C2—21no—
619C2—22no—
620C2—22no—
621C2—944no—
622C2—1882no—
623C2C2×#1568898511yescharacteristic
624C2#421×D4712yes—
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1733C2
socleC22×C47C22×C22⋊C4
prime radicalC24×D47D4
cosocleC22×C4×C47C24
hypercenter#1733D47
hypocenterC47#20705
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1733

Complements

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

NH ≅ G/Ntype
4. #20243486C2semidirect
5. #20243099C2semidirect
6. #20243098C2semidirect
7. #20243097C2semidirect
8. C47×#1733C2semidirect
13. C2×#13093982C4semidirect
18. #117×D47C4semidirect
20. C2×C4⋊C4×D47C4semidirect
31. #15688884C22semidirect
32. #15688883C22semidirect
33. #15688882C22semidirect
37. C47×#339C22semidirect
312. #1733D47semidirect
349. #339C2×D47semidirect
350. C47#20705semidirect

Maximal subgroups

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

subgroupindex
C2×#117×D472
C2×#156890862
#202457672
#202434862
#202430992
#202430982
#202430972
C47×#17332
#2070547