Finite Group Databasebeta

← #26217170

Subgroups — #26217170

Order 12032.

1394 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256589C211yesmaximal, characteristic
2C2×#15689165C211yesmaximal, characteristic, complemented
3C2×#15689139C211yesmaximal, characteristic
4C2×#15689125C211yesmaximal, characteristic
5#20246008C211yesmaximal, characteristic, complemented
6#20243624C214yesmaximal, complemented
7#20243617C214yesmaximal, complemented
8#20243099C211yesmaximal, characteristic, complemented
9C47×#1742C211yesmaximal, characteristic, complemented
10C22×#10625350C2211yescharacteristic
11#15689604C2212yes—
12#15689604C2212yes—
13#15689603—21no—
14#15689603—21no—
15#15689600—21no—
16#15689597—21no—
17#15689596—22no—
18C4×#10625350—22no—
19#15689591—22no—
20C2×#13093983C2211yescharacteristic
21C2×#13093983C2211yescharacteristic
22#117×D47—22no—
23C22×C4⋊Dic47C2211yescharacteristic
24#15689165—22no—
25#15689165C2214yescomplemented
26C2×#13093958—21no—
27C2×#13093956—21no—
28#15689139C418yescomplemented
29C2×#13093950C2214yes—
30#15689125—22no—
31#15689125C2214yes—
32C2×#13093949—21no—
33C2×#13093946—21no—
34#15689021—22no—
35#15688995—22no—
36#15688992C2212yescomplemented
37#15688988C2212yescomplemented
38#15688884C2214yescomplemented
39C22×M16×C47C2211yescharacteristic
40C22×M16×C47C2211yescharacteristic
41C2×#117×C47C2211yescharacteristic
42C47×#343C2212yescomplemented
43C47×#343C2212yescomplemented
44C2×#10625350—21no—
45C2×#10625350—21no—
46C2×#10625350—22no—
47C2×#10625350—22no—
48C2×#10625350C2×C414yes—
49C2×#10625350D412yes—
50C2×#10625350Q814yes—
51C2×#10625350C2312yes—
52C22×Dic94D411yescharacteristic
53C22×D188D411yescharacteristic
54C22×C22⋊D47—21no—
55C23×Dic47—21no—
56C22×C4×D47—21no—
57C4×Dic94—22no—
58C4×Dic94—22no—
59#13093989—22no—
60#13093989—22no—
61C4×D188—22no—
62C4×D188—22no—
63#13093986—22no—
64#13093986—22no—
65C4×C22⋊D47—24no—
66C4×C22⋊D47—24no—
67(C22⋊D47)⋊C4—24no—
68(C22⋊D47)⋊C4—24no—
69#13093983—21no—
70#13093983—21no—
71#13093983—22no—
72#13093983C2×C414yescomplemented
73#13093983D412yes—
74#13093983C2312yes—
75#13093982—22no—
76#13093982—22no—
77#13093981—24no—
78#13093980—24no—
79C2×C4⋊Dic47—21no—
80C2×C4⋊Dic47—21no—
81C2×C4⋊Dic47—21no—
82C2×C4⋊Dic47—21no—
83C2×C4⋊Dic47—21no—
84C2×C4⋊Dic47—21no—
85C2×C4⋊Dic47D411yescharacteristic
86C2×C4⋊Dic47D411yescharacteristic
87C2×C4⋊Dic47C2312yes—
88C2×Dic47⋊C4—24no—
89C4⋊C4×D47—22no—
90C4⋊C4×D47—22no—
91C2×C22⋊Dic47—21no—
92C2×C22⋊Dic47—21no—
93C22⋊C4×D47—24no—
94C2×C4×Dic47—21no—
95C2×C4×Dic47C2312yes—
96C42×D47—24no—
97#13093958—24no—
98#13093956—24no—
99#13093950C2×C4116yescomplemented
100#13093949—24no—
101#13093946—24no—
102C47⋊#95—24no—
103C23×C4×C47C2311yescharacteristic
104C2×M16×C47—21no—
105C2×M16×C47—22no—
106C2×M16×C47—21no—
107C2×M16×C47—22no—
108C2×M16×C47—22no—
109C2×M16×C47C2×C414yescomplemented
110C2×M16×C47C2312yes—
111C2×M16×C47C2312yes—
112C22×C8×C47—21no—
113C22×C8×C47—21no—
114#117×C47—21no—
115#117×C47—21no—
116#117×C47—21no—
117#117×C47—21no—
118C2×C4⋊C4×C47C2311yescharacteristic
119C2×C4⋊C4×C47C2311yescharacteristic
120C2×C22⋊C4×C47D412yes—
121C2×C42×C47D412yes—
122C24×C47C2×D411yescharacteristic
123C23×D47—21no—
124C22×C4×C47C22×C412yes—
125C22×C4×C47C2×D412yes—
126C22×C4×C47C2×D412yes—
127C22×C4×C47C2×D411yescharacteristic
128C22×C4×C47C2×D411yescharacteristic
129C22×C4×C47C2×D411yescharacteristic
130C22×C4×C47C2×D411yescharacteristic
131C22×C4×C47C2×D411yescharacteristic
132C22×C4×C47C2×Q812yes—
133C22×C4×C47#4112yes—
134C22×C4×C47#4112yes—
135C22×C4×C47C2411yescharacteristic
136C2×C22⋊D47—24no—
137C2×C22⋊D47—22no—
138C2×C22⋊D47—24no—
139C2×C22⋊D47—22no—
140C22×Dic47—21no—
141C22×Dic47—22no—
142C22×Dic47—21no—
143C22×Dic47—21no—
144C22×Dic47—22no—
145C22×Dic47—41no—
146C22×Dic47—41no—
147C22×Dic47—82no—
148#10625350—24no—
149#10625350—24no—
150#10625350—24no—
151#10625350—24no—
152#10625350—24no—
153#10625350—22no—
154#10625350—22no—
155#10625350C4⋊C418yescomplemented
156#10625350C22×C414yes—
157#10625350C2×Q814yes—
158C2×D188—21no—
159C2×D188—22no—
160C2×D188C4⋊C414yescomplemented
161C2×D188C2×D412yes—
162C2×C4×D47—24no—
163C2×C4×D47—22no—
164C2×C4×D47—24no—
165C2×C4×D47—22no—
166C2×C4×D47—24no—
167C2×C4×D47—24no—
168C2×Dic94—21no—
169C2×Dic94—22no—
170C2×Dic94C4⋊C414yescomplemented
171C2×Dic94C2×D412yes—
172M16×C47—24no—
173M16×C47—22no—
174M16×C47—22no—
175M16×C47—22no—
176M16×C47—42no—
177M16×C47C22×C414yes—
178C2×C8×C47—24no—
179C2×C8×C47—22no—
180C2×C8×C47—22no—
181C2×C8×C47—42no—
182C4⋊C4×C47—21no—
183C4⋊C4×C47—21no—
184C4⋊C4×C47—21no—
185C4⋊C4×C47—21no—
186C22⋊C4×C47—22no—
187C22⋊C4×C47—22no—
188C42×C47—22no—
189C42×C47—22no—
190C22⋊Dic47—24no—
191C22⋊Dic47—22no—
192C22⋊Dic47—22no—
193(C2×D47)⋊C4—24no—
194(C2×D47)⋊C4—24no—
195C4⋊Dic47—24no—
196C4⋊Dic47—21no—
197C4⋊Dic47—21no—
198C4⋊Dic47—22no—
199C4⋊Dic47—22no—
200C4⋊Dic47—41no—
201C4⋊Dic47—41no—
202C4⋊Dic47C2×D412yes—
203C4⋊Dic47C2×D412yes—
204Dic47⋊C4—24no—
205Dic47⋊C4—24no—
206Dic47⋊C4—84no—
207C4×Dic47—24no—
208C4×Dic47—24no—
209C4×Dic47—22no—
210C4×Dic47—22no—
211C4×Dic47—22no—
212C4×Dic47C22×C414yes—
213C23×C47—41no—
214C23×C47—41no—
215C23×C47C4×D412yes—
216C23×C47#12011yescharacteristic
217C23×C47#12011yescharacteristic
218C23×C47C22⋊Q812yes—
219C23×C47C22×D411yescharacteristic
220C22×D47—22no—
221C22×D47—24no—
222C22×D47—81no—
223C22×D47—81no—
224C2×C4×C47—22no—
225C2×C4×C47—22no—
226C2×C4×C47—42no—
227C2×C4×C47—42no—
228C2×C4×C47C2×C4⋊C412yes—
229C2×C4×C47C2×C4⋊C412yes—
230C2×C4×C47C4×D412yes—
231C2×C4×C47C4×D412yes—
232C2×C4×C47C4×D412yes—
233C2×C4×C47#12011yescharacteristic
234C2×C4×C47#12011yescharacteristic
235C2×C4×C47C22⋊Q812yes—
236C2×C4×C47C22⋊Q812yes—
237C2×C4×C47C22⋊Q812yes—
238C2×C4×C47#12312yes—
239C2×C4×C47#12312yes—
240C2×C4×C47C23×C411yescharacteristic
241C2×C4×C47C22×D411yescharacteristic
242C2×C4×C47C22×D411yescharacteristic
243C2×C4×C47C22×Q811yescharacteristic
244C2×C4×C47C2×#4111yescharacteristic
245C2×C4×C47C2×#4111yescharacteristic
246C22⋊D47—24no—
247C22⋊D47—24no—
248C22⋊D47—28no—
249C2×Dic47—22no—
250C2×Dic47—24no—
251C2×Dic47—24no—
252C2×Dic47—22no—
253C2×Dic47—22no—
254C2×Dic47—42no—
255C2×Dic47—42no—
256C2×Dic47—44no—
257C2×Dic47—42no—
258C2×Dic47—81no—
259C2×Dic47—81no—
260C2×Dic47—82no—
261C2×Dic47—82no—
262D188—22no—
263D188—24no—
264D188C2×C4⋊C414yes—
265C4×D47—24no—
266C4×D47—24no—
267C4×D47—28no—
268C4×D47—84no—
269C4×D47—84no—
270Dic94—22no—
271Dic94—24no—
272Dic94C2×C4⋊C414yes—
273C8×C47—24no—
274C8×C47—42no—
275#20865—471nomaximal, Sylow
276C22×C47—21no—
277C22×C47—21no—
278C22×C47—21no—
279C22×C47—21no—
280C22×C47—21no—
281C22×C47—21no—
282C22×C47—42no—
283C22×C47—42no—
284C22×C47#38512yes—
285C22×C47#38512yes—
286C22×C47C2×C4×D411yescharacteristic
287C22×C47C2×#12011yescharacteristic
288C22×C47C2×C22⋊Q811yescharacteristic
289C2×D47—24no—
290C2×D47—42no—
291C2×D47—42no—
292C2×D47—84no—
293C4×C47—42no—
294C4×C47—42no—
295C4×C47#38512yes—
296C4×C47#38512yes—
297C4×C47C22×C4⋊C411yescharacteristic
298C4×C47C2×C4×D411yescharacteristic
299C4×C47C2×C22⋊Q811yescharacteristic
300C4×C47C2×#12311yescharacteristic
301Dic47—24no—
302Dic47—44no—
303Dic47—42no—
304Dic47—42no—
305Dic47—82no—
306#3428—471no—
307C2×#428—471no—
308C2×#421—471no—
309C2×#417—471no—
310#2317—471no—
311#1860—474no—
312#1859—474no—
313#1742D4711yescharacteristic, complemented
314#1733—471no—
315C2×C47—21no—
316C2×C47—22no—
317C2×C47—21no—
318C2×C47—22no—
319C2×C47C2×#38511yescharacteristic
320C2×C47#302111yescharacteristic
321C2×C47#302211yescharacteristic
322D47—44no—
323C22×#41—471no—
324C22×M16C2×D4711yescharacteristic
325C22×M16C2×D4711yescharacteristic
326#520—472no—
327#520—472no—
328#520—941no—
329#520—941no—
330#519—941no—
331#518—941no—
332#518—942no—
333C4×#41—942no—
334C4×#41—942no—
335C2×#117—471no—
336C2×#117—471no—
337C2×#117—942no—
338C2×#117C2×D4711yescharacteristic
339C22×C4⋊C4—471no—
340#428—474no—
341#428—942no—
342C2×#107—941no—
343C2×#106—941no—
344#421—478no—
345C2×#104—474no—
346#417—474no—
347#417—942no—
348C2×#103—941no—
349C2×#102—941no—
350#389—942no—
351#385—942no—
352#384—472no—
353#382—472no—
354#343C2×D4712yescomplemented
355#343C2×D4712yescomplemented
356#339—474no—
357C47#2086511yescharacteristic, complemented, Sylow
358C2×#41—474no—
359C2×#41—472no—
360C2×#41—474no—
361C2×#41—472no—
362C2×#41—941no—
363C2×#41—942no—
364C2×#41—941no—
365C2×#41—942no—
366C22×Q8—471no—
367C22×D4—471no—
368C22×D4—941no—
369C23×C4—941no—
370C23×C4—941no—
371C23×C4C22×D4711yescharacteristic
372C2×M16—21no—
373C2×M16—22no—
374C2×M16—21no—
375C2×M16—22no—
376C2×M16—22no—
377C2×M16C4×D4714yescomplemented
378C2×M16C22×D4712yes—
379C2×M16C22×D4712yes—
380C22×C8—21no—
381C22×C8—21no—
382C4×Q8—942no—
383C4×Q8—942no—
384C4×Q8—942no—
385C4×Q8—942no—
386C4×D4—942no—
387C4×D4—942no—
388C4×D4—944no—
389C4×D4—944no—
390C4×D4—942no—
391C4×D4—942no—
392C4×D4—944no—
393C4×D4—944no—
394#117—21no—
395#117—21no—
396#117—21no—
397#117—21no—
398#117—474no—
399#117—472no—
400#117—472no—
401#117—944no—
402#117—944no—
403#117—942no—
404#117—942no—
405#117—941no—
406#117—942no—
407#117—941no—
408C2×C4⋊C4—471no—
409C2×C4⋊C4—471no—
410C2×C4⋊C4—472no—
411C2×C4⋊C4—942no—
412C2×C4⋊C4—942no—
413C2×C4⋊C4—941no—
414C2×C4⋊C4—941no—
415C2×C4⋊C4—941no—
416C2×C4⋊C4—941no—
417C2×C4⋊C4—941no—
418C2×C4⋊C4—944no—
419C2×C4⋊C4—941no—
420C2×C4⋊C4C22×D4711yescharacteristic
421C2×C4⋊C4C22×D4711yescharacteristic
422C2×C22⋊C4—944no—
423C2×C22⋊C4—941no—
424C2×C22⋊C4—941no—
425C2×C22⋊C4D18812yes—
426C2×C42—472no—
427C2×C42—944no—
428C2×C42—941no—
429C2×C42D18812yes—
430#107—944no—
431#106—944no—
432#104—4716no—
433#103—944no—
434#102—944no—
435#95—944no—
436C24—941no—
437C24C2×D18811yescharacteristic
438#41—478no—
439#41—474no—
440#41—474no—
441#41—944no—
442#41—944no—
443#41—944no—
444#41—944no—
445#41—944no—
446#41—942no—
447#41—942no—
448C2×Q8—474no—
449C2×Q8—472no—
450C2×Q8—941no—
451C2×Q8—942no—
452C2×D4—474no—
453C2×D4—472no—
454C2×D4—944no—
455C2×D4—942no—
456C2×D4—944no—
457C2×D4—942no—
458C2×D4—941no—
459C2×D4—942no—
460C22×C4—944no—
461C22×C4—944no—
462C22×C4—941no—
463C22×C4—944no—
464C22×C4—942no—
465C22×C4—944no—
466C22×C4—942no—
467C22×C4—941no—
468C22×C4—941no—
469C22×C4—942no—
470C22×C4—942no—
471C22×C4—3762no—
472C22×C4—1881no—
473C22×C4—1881no—
474C22×C4C2×C4×D4712yes—
475C22×C4C2×D18812yes—
476C22×C4C2×D18812yes—
477C22×C4C2×D18811yescharacteristic
478C22×C4#1062535012yes—
479C22×C4D4×D4711yescharacteristic
480C22×C4D4×D4711yescharacteristic
481C22×C4D4×D4711yescharacteristic
482C22×C4D4×D4711yescharacteristic
483C22×C4#1062535212yes—
484C22×C4Q8×D4712yes—
485C22×C4C23×D4711yescharacteristic
486M16—24no—
487M16—22no—
488M16—22no—
489M16—22no—
490M16—42no—
491M16C2×C4×D4714yes—
492C2×C8—24no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—42no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—472no—
501C4⋊C4—472no—
502C4⋊C4—944no—
503C4⋊C4—944no—
504C4⋊C4—944no—
505C4⋊C4—941no—
506C4⋊C4—941no—
507C4⋊C4—942no—
508C4⋊C4—942no—
509C4⋊C4—3764no—
510C4⋊C4—1881no—
511C4⋊C4—1881no—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—944no—
515C22⋊C4—944no—
516C22⋊C4—944no—
517C22⋊C4—942no—
518C22⋊C4—942no—
519C42—22no—
520C42—22no—
521C42—474no—
522C42—944no—
523C42—944no—
524C42—942no—
525C42—942no—
526C42—942no—
527C23—41no—
528C23—41no—
529C23—944no—
530C23—942no—
531C23—3761no—
532C23—3761no—
533C23C4×D18812yes—
534C23#1309399411yescharacteristic
535C23#1309399411yescharacteristic
536C23#1309400412yes—
537C23C22×D18811yescharacteristic
538Q8—474no—
539Q8—944no—
540Q8—942no—
541D4—474no—
542D4—948no—
543D4—944no—
544D4—944no—
545D4—944no—
546D4—942no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—944no—
552C2×C4—942no—
553C2×C4—948no—
554C2×C4—944no—
555C2×C4—944no—
556C2×C4—944no—
557C2×C4—942no—
558C2×C4—942no—
559C2×C4—3764no—
560C2×C4—3764no—
561C2×C4—3762no—
562C2×C4—3762no—
563C2×C4—3761no—
564C2×C4—3761no—
565C2×C4—1884no—
566C2×C4—1882no—
567C2×C4—1882no—
568C2×C4—1882no—
569C2×C4C4⋊C4×D4712yes—
570C2×C4C4⋊C4×D4712yes—
571C2×C4(C22⋊D47)⋊C412yes—
572C2×C4(C22⋊D47)⋊C412yes—
573C2×C4C4×D18812yes—
574C2×C4#1309399411yescharacteristic
575C2×C4#1309399411yescharacteristic
576C2×C4#1309400212yes—
577C2×C4#1309400212yes—
578C2×C4#1309400412yes—
579C2×C4#1309400612yes—
580C2×C4#1309400612yes—
581C2×C4C22×C4×D4711yescharacteristic
582C2×C4C2×D4×D4711yescharacteristic
583C2×C4C2×D4×D4711yescharacteristic
584C2×C4C2×Q8×D4711yescharacteristic
585C2×C4C2×#1062535211yescharacteristic
586C2×C4C2×#1062535011yescharacteristic
587C8—24no—
588C8—42no—
589C22—21no—
590C22—21no—
591C22—21no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—42no—
596C22—42no—
597C22—944no—
598C22—3764no—
599C22—1882no—
600C22—1882no—
601C22#1568899712yes—
602C22#1568899712yes—
603C22C2×C4×D18811yescharacteristic
604C22C2×#1309399411yescharacteristic
605C22C2×#1309400411yescharacteristic
606C4—42no—
607C4—42no—
608C4—944no—
609C4—3762no—
610C4—1884no—
611C4—1882no—
612C4—1882no—
613C4#1568899712yes—
614C4#1568899712yes—
615C4C2×C4⋊C4×D4711yescharacteristic
616C4C2×(C22⋊D47)⋊C411yescharacteristic
617C4C2×#1309400211yescharacteristic
618C4C2×#1309400611yescharacteristic
619C2—21no—
620C2—22no—
621C2—22no—
622C2—21no—
623C2—1884no—
624C2C2×#1568899711yescharacteristic
625C2#2025276211yescharacteristic
626C2#2025276911yescharacteristic
subgroupG/H
centerC22C2×#13093994
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1742C2
socleC22×C47C2×#120
prime radicalC22×#10625350C22
cosocleC22×C4×C47C24
hypercenter#1742D47
hypocenterC47#20865
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1742

Complements

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

NH ≅ G/Ntype
2. C2×#15689165C2semidirect
5. #20246008C2semidirect
6. #20243624C2semidirect
7. #20243617C2semidirect
8. #20243099C2semidirect
9. C47×#1742C2semidirect
25. #15689165C22semidirect
28. #15689139C4semidirect
36. #15688992C22semidirect
37. #15688988C22semidirect
38. #15688884C22semidirect
42. C47×#343C22semidirect
43. C47×#343C22semidirect
72. #13093983C2×C4semidirect
99. #13093950C2×C4semidirect
109. C2×M16×C47C2×C4semidirect
155. #10625350C4⋊C4semidirect
160. C2×D188C4⋊C4semidirect
170. C2×Dic94C4⋊C4semidirect
313. #1742D47semidirect
354. #343C2×D47semidirect
355. #343C2×D47semidirect
357. C47#20865semidirect
377. C2×M16C4×D47semidirect

Maximal subgroups

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

subgroupindex
#202565892
C2×#156891652
C2×#156891392
C2×#156891252
#202460082
#202436242
#202436172
#202430992
C47×#17422
#2086547