Finite Group Databasebeta

← #26121609

Subgroups — #26121609

Order 12032.

1208 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256589C211yesmaximal, characteristic
2C2×#15689096C211yesmaximal, characteristic
3#20251832C211yesmaximal, characteristic
4#20243099C211yesmaximal, characteristic, complemented
5C2×#15688879C211yesmaximal, characteristic, complemented
6C2×#15688879C211yesmaximal, characteristic, complemented
7C47×#1733C211yesmaximal, characteristic, complemented
8C22×#10625350C2211yescharacteristic
9C22×#10625329C2211yescharacteristic
10#15689604—22no—
11#15689603—22no—
12#15689600C412yescomplemented
13#15689597C412yescomplemented
14#15689596—22no—
15C4×#10625350—22no—
16#15689591—22no—
17C2×#13093983C2211yescharacteristic
18C2×#13093983C2211yescharacteristic
19#117×D47—22no—
20#15689096—22no—
21#15689096C414yescomplemented
22C2×#13093938—22no—
23#15689091C414yescomplemented
24#15689089—22no—
25#15689086—22no—
26#15688884—22no—
27#15688879—22no—
28#15688879—22no—
29C22×M16×C47C2211yescharacteristic
30C2×#117×C47C2211yescharacteristic
31C2×#117×C47C2211yescharacteristic
32C47×#339—22no—
33C2×#10625350—21no—
34C2×#10625350—21no—
35C2×#10625350—21no—
36C2×#10625350—21no—
37C2×#10625350—21no—
38C2×#10625350—21no—
39C2×#10625350—21no—
40C2×#10625350—21no—
41C2×#10625350C2×C412yes—
42C2×#10625350C2×C412yes—
43C2×#10625350D412yes—
44C2×#10625350Q812yes—
45C22×Dic94C2×C411yescharacteristic
46C22×D188C2×C411yescharacteristic
47C22×C22⋊D47D412yes—
48C22×C4×D47D412yes—
49C2×#10625329—21no—
50C2×#10625329—21no—
51C2×#10625329—21no—
52C2×#10625329—21no—
53C2×#10625329—21no—
54C2×#10625329—21no—
55C22×C47⋊C8C2×C412yescomplemented
56C4×Dic94—24no—
57#13093989—24no—
58C4×D188—24no—
59#13093986—24no—
60C4×C22⋊D47—28no—
61(C22⋊D47)⋊C4—28no—
62#13093983—21no—
63#13093983—21no—
64#13093983—21no—
65#13093983—21no—
66#13093983—21no—
67#13093983C2×C412yes—
68#13093983C2×C412yescomplemented
69#13093983D412yes—
70#13093982—24no—
71#13093981—24no—
72#13093980—24no—
73C2×C4⋊Dic47—21no—
74C2×C4⋊Dic47—21no—
75C4⋊C4×D47—24no—
76C2×C22⋊Dic47—21no—
77C2×C22⋊Dic47—21no—
78C22⋊C4×D47—24no—
79C2×C4×Dic47—21no—
80C2×C4×Dic47D412yes—
81C42×D47—24no—
82#13093938—28no—
83(C2×D47)⋊C8—28no—
84C23×C4×C47C2311yescharacteristic
85C2×M16×C47—21no—
86C2×M16×C47—21no—
87C2×M16×C47—21no—
88C2×M16×C47—21no—
89C2×M16×C47—21no—
90C2×M16×C47C2×C412yescomplemented
91C22×C8×C47—21no—
92#117×C47—21no—
93#117×C47—21no—
94#117×C47—21no—
95#117×C47—21no—
96#117×C47—21no—
97#117×C47C2×C412yes—
98#117×C47C2×C412yescomplemented
99#117×C47D412yes—
100C2×C4⋊C4×C47—21no—
101C2×C4⋊C4×C47—21no—
102C2×C22⋊C4×C47—21no—
103C2×C22⋊C4×C47—21no—
104C2×C42×C47—21no—
105C2×C42×C47D412yes—
106C24×C47C2×D411yescharacteristic
107C23×D47C22⋊C412yes—
108C22×C4×C47—22no—
109C22×C4×C47—41no—
110C22×C4×C47C22×C411yescharacteristic
111C22×C4×C47C22×C411yescharacteristic
112C22×C4×C47C22×C411yescharacteristic
113C22×C4×C47C2×D411yescharacteristic
114C22×C4×C47C2×D411yescharacteristic
115C22×C4×C47C2×D411yescharacteristic
116C22×C4×C47C2×D411yescharacteristic
117C22×C4×C47C2×D411yescharacteristic
118C22×C4×C47C2×D411yescharacteristic
119C22×C4×C47C2×Q811yescharacteristic
120C22×C4×C47#4111yescharacteristic
121C22×C4×C47#4111yescharacteristic
122C22×C4×C47#4111yescharacteristic
123C22×C4×C47#4111yescharacteristic
124C2×C22⋊D47—22no—
125C2×C22⋊D47—22no—
126C2×C22⋊D47—22no—
127C2×C22⋊D47—22no—
128C2×C22⋊D47C22⋊C414yes—
129C2×C22⋊D47C4⋊C414yes—
130C22×Dic47—22no—
131C22×Dic47—41no—
132C22×Dic47C22⋊C412yes—
133#10625350—22no—
134#10625350—22no—
135#10625350—22no—
136#10625350—22no—
137#10625350—22no—
138#10625350—22no—
139#10625350—22no—
140#10625350—22no—
141#10625350—22no—
142#10625350—22no—
143#10625350—22no—
144#10625350—22no—
145#10625350—22no—
146#10625350—22no—
147#10625350—22no—
148#10625350—22no—
149C2×D188—21no—
150C2×D188—21no—
151C2×D188—21no—
152C2×D188—21no—
153C2×D188C4212yes—
154C2×D188C4⋊C412yes—
155C2×C4×D47—22no—
156C2×C4×D47—22no—
157C2×C4×D47—22no—
158C2×C4×D47—22no—
159C2×C4×D47—28no—
160C2×C4×D47C22⋊C414yes—
161C2×C4×D47C4⋊C414yes—
162C2×Dic94—21no—
163C2×Dic94—21no—
164C2×Dic94—21no—
165C2×Dic94—21no—
166C2×Dic94C4212yes—
167C2×Dic94C4⋊C412yes—
168M16×C47—22no—
169M16×C47—22no—
170M16×C47—41no—
171M16×C47—41no—
172C2×C8×C47—22no—
173C2×C8×C47—41no—
174C2×C8×C47—41no—
175C4⋊C4×C47—22no—
176C4⋊C4×C47—22no—
177C4⋊C4×C47—22no—
178C4⋊C4×C47—41no—
179C22⋊C4×C47—22no—
180C22⋊C4×C47—22no—
181C22⋊C4×C47—22no—
182C22⋊C4×C47—41no—
183C42×C47—22no—
184C42×C47—22no—
185C42×C47—41no—
186C42×C47C22⋊C414yes—
187C22⋊Dic47—22no—
188C22⋊Dic47—22no—
189C22⋊Dic47—22no—
190C22⋊Dic47—41no—
191(C2×D47)⋊C4—28no—
192C4⋊Dic47—22no—
193C4⋊Dic47—22no—
194C4⋊Dic47—22no—
195C4⋊Dic47—41no—
196Dic47⋊C4—28no—
197C4×Dic47—28no—
198C4×Dic47—22no—
199C4×Dic47—22no—
200C4×Dic47—41no—
201C4×Dic47C22⋊C414yes—
202#10625329—41no—
203#10625329—41no—
204#10625329—41no—
205#10625329—41no—
206C2×C47⋊C8—22no—
207C2×C47⋊C8—22no—
208C2×C47⋊C8—22no—
209C23×C47—81no—
210C23×C47C2×C22⋊C411yescharacteristic
211C23×C47C2×C22⋊C411yescharacteristic
212C23×C47C2×C4⋊C411yescharacteristic
213C23×C47#12011yescharacteristic
214C23×C47#12011yescharacteristic
215C23×C47#12311yescharacteristic
216C23×C47#12311yescharacteristic
217C22×D47—22no—
218C22×D47—22no—
219C22×D47—82no—
220C22×D47#9514yes—
221C2×C4×C47—24no—
222C2×C4×C47—42no—
223C2×C4×C47—82no—
224C2×C4×C47—82no—
225C2×C4×C47C2×C4211yescharacteristic
226C2×C4×C47C2×C22⋊C411yescharacteristic
227C2×C4×C47C2×C22⋊C411yescharacteristic
228C2×C4×C47C2×C22⋊C411yescharacteristic
229C2×C4×C47C2×C4⋊C411yescharacteristic
230C2×C4×C47C2×C4⋊C411yescharacteristic
231C2×C4×C47#11711yescharacteristic
232C2×C4×C47#11711yescharacteristic
233C2×C4×C47C4×D411yescharacteristic
234C2×C4×C47C4×D411yescharacteristic
235C2×C4×C47C4×D411yescharacteristic
236C2×C4×C47C4×D411yescharacteristic
237C2×C4×C47C4×D411yescharacteristic
238C2×C4×C47C4×D411yescharacteristic
239C2×C4×C47C4×D411yescharacteristic
240C2×C4×C47C4×D411yescharacteristic
241C2×C4×C47#12011yescharacteristic
242C2×C4×C47#12011yescharacteristic
243C2×C4×C47#12111yescharacteristic
244C2×C4×C47#12111yescharacteristic
245C2×C4×C47#12111yescharacteristic
246C2×C4×C47#12111yescharacteristic
247C2×C4×C47C22⋊Q811yescharacteristic
248C2×C4×C47C22⋊Q811yescharacteristic
249C2×C4×C47C22⋊Q811yescharacteristic
250C2×C4×C47C22⋊Q811yescharacteristic
251C2×C4×C47#12311yescharacteristic
252C2×C4×C47#12311yescharacteristic
253C22⋊D47—24no—
254C22⋊D47—24no—
255C22⋊D47—24no—
256C22⋊D47—24no—
257C2×Dic47—22no—
258C2×Dic47—22no—
259C2×Dic47—24no—
260C2×Dic47—42no—
261C2×Dic47—82no—
262C2×Dic47—82no—
263C2×Dic47#9514yes—
264D188—22no—
265D188—22no—
266D188—22no—
267D188—22no—
268C4×D47—24no—
269C4×D47—24no—
270C4×D47—24no—
271C4×D47—24no—
272C4×D47—88no—
273Dic94—22no—
274Dic94—22no—
275Dic94—22no—
276Dic94—22no—
277C8×C47—42no—
278C47⋊C8—42no—
279#10743—471nomaximal, Sylow
280C22×C47—41no—
281C22×C47—41no—
282C22×C47—41no—
283C22×C47—41no—
284C22×C47—41no—
285C22×C47—41no—
286C22×C47—41no—
287C22×C47C2×#9511yescharacteristic
288C22×C47#37911yescharacteristic
289C22×C47#38111yescharacteristic
290C22×C47#38511yescharacteristic
291C22×C47#38511yescharacteristic
292C22×C47#38611yescharacteristic
293C22×C47#38611yescharacteristic
294C2×D47—24no—
295C2×D47—44no—
296C2×D47—44no—
297C2×D47—82no—
298C4×C47—44no—
299C4×C47—82no—
300C4×C47C4×C22⋊C411yescharacteristic
301C4×C47C4×C22⋊C411yescharacteristic
302C4×C47#38011yescharacteristic
303C4×C47#38011yescharacteristic
304C4×C47#38511yescharacteristic
305C4×C47#38511yescharacteristic
306C4×C47#38611yescharacteristic
307C4×C47#38611yescharacteristic
308Dic47—24no—
309Dic47—44no—
310Dic47—82no—
311#3428—471no—
312C2×#410—471no—
313#2879—471no—
314#1733—471no—
315#1733D4711yescharacteristic, complemented
316C2×H(3,ℤ/4)—471no—
317C2×H(3,ℤ/4)—471no—
318C2×C47—21no—
319C2×C47—21no—
320C2×C47—21no—
321C2×C47—21no—
322C2×C47—21no—
323C2×C47—21no—
324C2×C47—21no—
325C2×C47C22⋊#9511yescharacteristic
326D47—44no—
327C22×#41—471no—
328C22×M16—471no—
329C22×M16C2×D4711yescharacteristic
330#520—942no—
331#520—942no—
332#519—472no—
333#518—472no—
334#518—942no—
335C4×#41—942no—
336C4×#41—942no—
337C2×#117—471no—
338C2×#117—471no—
339C2×#117—942no—
340C2×#117C2×D4711yescharacteristic
341C2×#117C2×D4711yescharacteristic
342#410—474no—
343#410—942no—
344C2×#99—942no—
345#408—474no—
346#408—942no—
347#407—942no—
348#339—22no—
349#339—942no—
350H(3,ℤ/4)—942no—
351H(3,ℤ/4)—942no—
352C47#1074311yescharacteristic, complemented, Sylow
353C2×#41—472no—
354C2×#41—472no—
355C2×#41—472no—
356C2×#41—472no—
357C2×#41—941no—
358C2×#41—941no—
359C2×#41—941no—
360C2×#41—941no—
361C2×#41—941no—
362C2×#41—941no—
363C2×#41—941no—
364C2×#41—941no—
365C22×Q8—471no—
366C22×D4—472no—
367C22×D4—471no—
368C23×C4—472no—
369C23×C4C22×D4711yescharacteristic
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—941no—
376C2×M16—941no—
377C2×M16—941no—
378C2×M16—941no—
379C2×M16—941no—
380C2×M16—941no—
381C2×M16C4×D4712yescomplemented
382C22×C8—21no—
383C22×C8—472no—
384C4×Q8—944no—
385C4×Q8—944no—
386C4×D4—944no—
387C4×D4—948no—
388C4×D4—948no—
389C4×D4—944no—
390#117—21no—
391#117—21no—
392#117—21no—
393#117—21no—
394#117—21no—
395#117—472no—
396#117—472no—
397#117—472no—
398#117—944no—
399#117—944no—
400#117—944no—
401#117—941no—
402#117—941no—
403#117—941no—
404#117—941no—
405#117—941no—
406#117C4×D4712yes—
407#117C4×D4712yescomplemented
408#117D18812yes—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—944no—
412C2×C4⋊C4—941no—
413C2×C4⋊C4—941no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—944no—
417C2×C22⋊C4—941no—
418C2×C22⋊C4—941no—
419C2×C42—21no—
420C2×C42—472no—
421C2×C42—944no—
422C2×C42—941no—
423C2×C42C22⋊D4712yes—
424#99—948no—
425C22⋊C8—948no—
426C24—472no—
427C24D4×D4711yescharacteristic
428#41—942no—
429#41—942no—
430#41—942no—
431#41—942no—
432#41—942no—
433#41—942no—
434#41—942no—
435#41—942no—
436#41—942no—
437#41—942no—
438#41—942no—
439#41—942no—
440#41—942no—
441#41—942no—
442#41—942no—
443#41—942no—
444C2×Q8—472no—
445C2×Q8—472no—
446C2×Q8—941no—
447C2×Q8—941no—
448C2×Q8—941no—
449C2×Q8—941no—
450C2×D4—474no—
451C2×D4—474no—
452C2×D4—472no—
453C2×D4—472no—
454C2×D4—942no—
455C2×D4—942no—
456C2×D4—942no—
457C2×D4—942no—
458C2×D4—941no—
459C2×D4—941no—
460C2×D4—941no—
461C2×D4—941no—
462C22×C4—22no—
463C22×C4—41no—
464C22×C4—472no—
465C22×C4—474no—
466C22×C4—474no—
467C22×C4—948no—
468C22×C4—942no—
469C22×C4—942no—
470C22×C4—942no—
471C22×C4—942no—
472C22×C4—942no—
473C22×C4—1881no—
474C22×C4C2×C4×D4711yescharacteristic
475C22×C4C2×C4×D4711yescharacteristic
476C22×C4C2×C4×D4711yescharacteristic
477C22×C4C2×D18811yescharacteristic
478C22×C4#1062535011yescharacteristic
479C22×C4#1062535011yescharacteristic
480C22×C4D4×D4711yescharacteristic
481C22×C4D4×D4711yescharacteristic
482C22×C4D4×D4711yescharacteristic
483C22×C4D4×D4711yescharacteristic
484C22×C4#1062535211yescharacteristic
485C22×C4Q8×D4711yescharacteristic
486C22×C4#1062535411yescharacteristic
487C22×C4C2×C22⋊D4711yescharacteristic
488M16—22no—
489M16—22no—
490M16—41no—
491M16—41no—
492M16—1881no—
493M16—1881no—
494M16—1881no—
495M16—1881no—
496C2×C8—22no—
497C2×C8—41no—
498C2×C8—41no—
499C2×C8—942no—
500C2×C8—942no—
501C2×C8—942no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—41no—
506C4⋊C4—948no—
507C4⋊C4—942no—
508C4⋊C4—942no—
509C4⋊C4—942no—
510C4⋊C4—1881no—
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—41no—
515C22⋊C4—948no—
516C22⋊C4—942no—
517C22⋊C4—942no—
518C22⋊C4—942no—
519C22⋊C4—1881no—
520C42—22no—
521C42—22no—
522C42—41no—
523C42—474no—
524C42—948no—
525C42—942no—
526C42—942no—
527C42—1881no—
528C42(C2×D47)⋊C414yes—
529C23—81no—
530C23—474no—
531C23—942no—
532C23—942no—
533C23—3762no—
534C23C22⋊C4×D4711yescharacteristic
535C23C22⋊C4×D4711yescharacteristic
536C23C4⋊C4×D4711yescharacteristic
537C23#1309399211yescharacteristic
538C23#1309399411yescharacteristic
539C23#1309400611yescharacteristic
540C23#1309400911yescharacteristic
541Q8—942no—
542Q8—942no—
543Q8—942no—
544Q8—942no—
545D4—944no—
546D4—944no—
547D4—944no—
548D4—944no—
549D4—942no—
550D4—942no—
551D4—942no—
552D4—942no—
553C2×C4—24no—
554C2×C4—42no—
555C2×C4—82no—
556C2×C4—82no—
557C2×C4—474no—
558C2×C4—942no—
559C2×C4—942no—
560C2×C4—944no—
561C2×C4—944no—
562C2×C4—944no—
563C2×C4—944no—
564C2×C4—944no—
565C2×C4—3768no—
566C2×C4—3762no—
567C2×C4—3762no—
568C2×C4—1882no—
569C2×C4C42×D4711yescharacteristic
570C2×C4C22⋊C4×D4711yescharacteristic
571C2×C4C22⋊C4×D4711yescharacteristic
572C2×C4C2×(C2×D47)⋊C411yescharacteristic
573C2×C4C4⋊C4×D4711yescharacteristic
574C2×C4C4⋊C4×D4711yescharacteristic
575C2×C4#1309398111yescharacteristic
576C2×C4#1309398211yescharacteristic
577C2×C4(C22⋊D47)⋊C411yescharacteristic
578C2×C4(C22⋊D47)⋊C411yescharacteristic
579C2×C4C4×C22⋊D4711yescharacteristic
580C2×C4C4×C22⋊D4711yescharacteristic
581C2×C4#1309398611yescharacteristic
582C2×C4#1309398611yescharacteristic
583C2×C4C4×D18811yescharacteristic
584C2×C4C4×D18811yescharacteristic
585C2×C4#1309399211yescharacteristic
586C2×C4#1309399411yescharacteristic
587C2×C4#1309399511yescharacteristic
588C2×C4#1309399711yescharacteristic
589C2×C4#1309399711yescharacteristic
590C2×C4#1309399911yescharacteristic
591C2×C4#1309400011yescharacteristic
592C2×C4#1309400211yescharacteristic
593C2×C4#1309400211yescharacteristic
594C2×C4#1309400411yescharacteristic
595C2×C4#1309400611yescharacteristic
596C2×C4#1309400911yescharacteristic
597C8—42no—
598C8—1882no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—944no—
607C22—3762no—
608C22—1884no—
609C22—1884no—
610C22#95×D4711yescharacteristic
611C22#1568897811yescharacteristic
612C22#1568898511yescharacteristic
613C22#1568899411yescharacteristic
614C22#1568899711yescharacteristic
615C22#1568899911yescharacteristic
616C22#1568900111yescharacteristic
617C4—44no—
618C4—82no—
619C4—944no—
620C4—3762no—
621C4—1884no—
622C4#1568897011yescharacteristic
623C4C4×(C2×D47)⋊C411yescharacteristic
624C4#1568898011yescharacteristic
625C4#1568898211yescharacteristic
626C4#1568899411yescharacteristic
627C4#1568899711yescharacteristic
628C4#1568899911yescharacteristic
629C4#1568900111yescharacteristic
630C2—21no—
631C2—21no—
632C2—21no—
633C2—21no—
634C2—21no—
635C2—21no—
636C2—21no—
637C2—1884no—
638C2(C2×D47)⋊#9511yescharacteristic
subgroupG/H
centerC4#15688999
commutatorC2×C4×C47C2×C42
FrattiniC23×C4C22×D47
FittingC47×#1733C2
socleC2×C47C22⋊#95
prime radicalC22×#10625350C22
cosocleC23×C4×C47C23
hypercenter#1733D47
hypocenterC47#10743
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C23×C4 ◁ #1733

Complements

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

NH ≅ G/Ntype
4. #20243099C2semidirect
5. C2×#15688879C2semidirect
6. C2×#15688879C2semidirect
7. C47×#1733C2semidirect
12. #15689600C4semidirect
13. #15689597C4semidirect
21. #15689096C4semidirect
23. #15689091C4semidirect
55. C22×C47⋊C8C2×C4semidirect
68. #13093983C2×C4semidirect
90. C2×M16×C47C2×C4semidirect
98. #117×C47C2×C4semidirect
315. #1733D47semidirect
352. C47#10743semidirect
381. C2×M16C4×D47semidirect
407. #117C4×D47semidirect

Maximal subgroups

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

subgroupindex
#202565892
C2×#156890962
#202518322
#202430992
C2×#156888792
C47×#17332
#1074347