Finite Group Databasebeta

← #26243707

Subgroups — #26243707

Order 12032.

1148 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689141C211yesmaximal, characteristic
2C2×#15689141C211yesmaximal, characteristic
3C2×#15689096C211yesmaximal, characteristic
4#20244557C218yesmaximal, complemented
5C2×#15688893C211yesmaximal, characteristic, complemented
6#20243098C211yesmaximal, characteristic, complemented
7C2×#15688879C211yesmaximal, characteristic, complemented
8C47×#3458C211yesmaximal, characteristic, complemented
9C22×#10625350C2211yescharacteristic
10C22×#10625329C2211yescharacteristic
11C22×#10625329C2211yescharacteristic
12C2×#13093983C2211yescharacteristic
13#15689141—22no—
14#15689141—22no—
15#15689141—22no—
16#15689141C2214yes—
17C2×#13093952—22no—
18C2×#13093952C2214yes—
19#15689096—22no—
20#15689096C2214yes—
21C2×#13093938—22no—
22#15688893C2214yescomplemented
23#15688883C2214yescomplemented
24#15688879C2214yescomplemented
25C47×#544—22no—
26C47×#544—22no—
27C47×#544—22no—
28C47×#543—22no—
29C47×#533—22no—
30C47×#533—22no—
31C47×#533C2214yescomplemented
32C2×#117×C47C2211yescharacteristic
33C2×#117×C47C2211yescharacteristic
34C2×#117×C47C2211yescharacteristic
35C2×#10625350—21no—
36C2×#10625350—21no—
37C2×#10625350—21no—
38C2×#10625350—21no—
39C2×#10625350—21no—
40C2×#10625350—21no—
41C2×#10625350—21no—
42C2×#10625350—21no—
43C2×#10625350—21no—
44C2×#10625350—21no—
45C2×#10625350Q812yescomplemented
46C2×#10625350C2312yes—
47C22×Dic94Q811yescharacteristic, complemented
48C22×D188Q811yescharacteristic, complemented
49C22×C22⋊D47—21no—
50C22×C4×D47—21no—
51C2×#10625329—21no—
52C2×#10625329—21no—
53C2×#10625329—21no—
54C2×#10625329—21no—
55C2×#10625329—21no—
56C2×#10625329—21no—
57C2×#10625329—21no—
58C2×#10625329—21no—
59C2×#10625329—21no—
60C2×#10625329—21no—
61C2×#10625329C2312yes—
62C2×#10625329C2312yes—
63C22×C47⋊C8—21no—
64C22×C47⋊C8—21no—
65#13093983—21no—
66#13093983—21no—
67#13093983—21no—
68#13093983C2312yes—
69C2×C4⋊Dic47—21no—
70C2×C22⋊Dic47—21no—
71C2×C4×Dic47—21no—
72#13093952—28no—
73#13093952—28no—
74#13093938—28no—
75C23×C4×C47C2311yescharacteristic
76C4⋊Q8×C47—24no—
77C4⋊Q8×C47—24no—
78C4⋊Q8×C47—24no—
79#125×C47—24no—
80#125×C47—24no—
81#125×C47—24no—
82C22⋊Q8×C47—28no—
83C22⋊Q8×C47—28no—
84C22⋊Q8×C47—28no—
85C4×Q8×C47—28no—
86#117×C47—21no—
87#117×C47—21no—
88#117×C47—21no—
89#117×C47—21no—
90#117×C47—21no—
91#117×C47—21no—
92#117×C47D412yes—
93#117×C47D412yes—
94#117×C47D412yes—
95#117×C47D412yes—
96#117×C47C2312yes—
97#117×C47C2312yes—
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47—21no—
100C2×C4⋊C4×C47—21no—
101C2×C22⋊C4×C47—21no—
102C2×C22⋊C4×C47—21no—
103C2×C22⋊C4×C47D412yes—
104C2×C42×C47—21no—
105C2×C42×C47D412yes—
106C2×C42×C47C2312yes—
107C24×C47C2×D411yescharacteristic
108C23×D47—21no—
109C2×Q8×C47—28no—
110C22×C4×C47—22no—
111C22×C4×C47—22no—
112C22×C4×C47—22no—
113C22×C4×C47C2×D411yescharacteristic
114C22×C4×C47C2×D411yescharacteristic
115C22×C4×C47C2×D411yescharacteristic
116C22×C4×C47C2×D411yescharacteristic
117C22×C4×C47C2×D411yescharacteristic
118C22×C4×C47C2×Q811yescharacteristic
119C22×C4×C47C2×Q811yescharacteristic
120C22×C4×C47#4111yescharacteristic
121C22×C4×C47#4111yescharacteristic
122C22×C4×C47#4111yescharacteristic
123C22×C4×C47#4111yescharacteristic
124C22×C4×C47#4111yescharacteristic
125C22×C4×C47#4111yescharacteristic
126C22×C4×C47C2411yescharacteristic
127C2×C22⋊D47—22no—
128C2×C22⋊D47—22no—
129C2×C22⋊D47—41no—
130C2×C22⋊D47—41no—
131C2×C22⋊D47—41no—
132C2×C22⋊D47—41no—
133C22×Dic47—21no—
134C22×Dic47—41no—
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—41no—
144#10625350—41no—
145#10625350—41no—
146#10625350—41no—
147#10625350—41no—
148#10625350—41no—
149#10625350—41no—
150#10625350—41no—
151C2×D188—21no—
152C2×D188—21no—
153C2×D188—21no—
154C2×D188—21no—
155C2×D188—21no—
156C2×D188C2×Q812yes—
157C2×C4×D47—22no—
158C2×C4×D47—22no—
159C2×C4×D47—41no—
160C2×C4×D47—41no—
161C2×C4×D47—41no—
162C2×C4×D47—41no—
163C2×Dic94—21no—
164C2×Dic94—21no—
165C2×Dic94—21no—
166C2×Dic94—21no—
167C2×Dic94—21no—
168C2×Dic94C2×Q812yes—
169C4⋊C4×C47—28no—
170C4⋊C4×C47—28no—
171C4⋊C4×C47—28no—
172C4⋊C4×C47—22no—
173C4⋊C4×C47—22no—
174C4⋊C4×C47—22no—
175C4⋊C4×C47—22no—
176C4⋊C4×C47—22no—
177C4⋊C4×C47—22no—
178C22⋊C4×C47—22no—
179C22⋊C4×C47—22no—
180C22⋊C4×C47—22no—
181C22⋊C4×C47—22no—
182C22⋊C4×C47—22no—
183C22⋊C4×C47C2×D414yes—
184C42×C47—22no—
185C42×C47—22no—
186C42×C47—22no—
187C42×C47—22no—
188C42×C47C2×D414yes—
189C42×C47C2×D414yes—
190C22⋊Dic47—22no—
191C22⋊Dic47—41no—
192C4⋊Dic47—22no—
193C4⋊Dic47—41no—
194C4×Dic47—22no—
195C4×Dic47—41no—
196#10625329—22no—
197#10625329—22no—
198#10625329—22no—
199#10625329—22no—
200#10625329—41no—
201#10625329—41no—
202#10625329—41no—
203#10625329—41no—
204C2×C47⋊C8—22no—
205C2×C47⋊C8—22no—
206C2×C47⋊C8—41no—
207C2×C47⋊C8—41no—
208C2×C47⋊C8—41no—
209C2×C47⋊C8—41no—
210C23×C47—81no—
211C23×C47#12011yescharacteristic
212C23×C47#12011yescharacteristic
213C23×C47C22⋊Q811yescharacteristic
214C23×C47C22⋊Q811yescharacteristic
215C23×C47#12411yescharacteristic
216C23×C47#12411yescharacteristic
217C23×C47C22×D411yescharacteristic
218C22×D47—22no—
219C22×D47—41no—
220C22×D47—41no—
221C22×D47—82no—
222Q8×C47—88no—
223C2×C4×C47—24no—
224C2×C4×C47—24no—
225C2×C4×C47—24no—
226C2×C4×C47—82no—
227C2×C4×C47—82no—
228C2×C4×C47—82no—
229C2×C4×C47#12011yescharacteristic
230C2×C4×C47#12011yescharacteristic
231C2×C4×C47C22⋊Q811yescharacteristic
232C2×C4×C47C22⋊Q811yescharacteristic
233C2×C4×C47C22⋊Q811yescharacteristic
234C2×C4×C47C22⋊Q811yescharacteristic
235C2×C4×C47C22⋊Q811yescharacteristic
236C2×C4×C47C22⋊Q811yescharacteristic
237C2×C4×C47C22⋊Q811yescharacteristic
238C2×C4×C47C22⋊Q811yescharacteristic
239C2×C4×C47C22⋊Q811yescharacteristic
240C2×C4×C47C22⋊Q811yescharacteristic
241C2×C4×C47#12411yescharacteristic
242C2×C4×C47#12411yescharacteristic
243C2×C4×C47#12411yescharacteristic
244C2×C4×C47#12411yescharacteristic
245C2×C4×C47#12411yescharacteristic
246C2×C4×C47#12411yescharacteristic
247C2×C4×C47#12411yescharacteristic
248C2×C4×C47#12411yescharacteristic
249C2×C4×C47#12411yescharacteristic
250C2×C4×C47#12411yescharacteristic
251C2×C4×C47C22×D411yescharacteristic
252C2×C4×C47C22×D411yescharacteristic
253C2×C4×C47C22×Q811yescharacteristic
254C2×C4×C47C2×#4111yescharacteristic
255C2×C4×C47C2×#4111yescharacteristic
256C2×C4×C47C2×#4111yescharacteristic
257C22⋊D47—42no—
258C22⋊D47—42no—
259C22⋊D47—42no—
260C22⋊D47—42no—
261C2×Dic47—22no—
262C2×Dic47—41no—
263C2×Dic47—41no—
264C2×Dic47—42no—
265C2×Dic47—82no—
266D188—22no—
267D188—22no—
268D188—41no—
269D188—41no—
270C4×D47—42no—
271C4×D47—42no—
272C4×D47—42no—
273C4×D47—42no—
274Dic94—22no—
275Dic94—22no—
276Dic94—41no—
277Dic94—41no—
278C47⋊C8—42no—
279C47⋊C8—42no—
280#23472—471nomaximal, Sylow
281C22×C47—41no—
282C22×C47—41no—
283C22×C47—41no—
284C22×C47—41no—
285C22×C47—41no—
286C22×C47—41no—
287C22×C47—41no—
288C22×C47#39311yescharacteristic
289C22×C47#39311yescharacteristic
290C22×C47#39311yescharacteristic
291C22×C47#39311yescharacteristic
292C22×C47C2×#12011yescharacteristic
293C22×C47C2×C22⋊Q811yescharacteristic
294C22×C47C2×#12411yescharacteristic
295C2×D47—42no—
296C2×D47—82no—
297C2×D47—82no—
298C2×D47—82no—
299C4×C47—44no—
300C4×C47—44no—
301C4×C47—44no—
302C4×C47#39311yescharacteristic
303C4×C47#39311yescharacteristic
304C4×C47#39311yescharacteristic
305C4×C47#39311yescharacteristic
306C4×C47C2×C22⋊Q811yescharacteristic
307C4×C47C2×C22⋊Q811yescharacteristic
308C4×C47C2×#12411yescharacteristic
309C4×C47C2×#12411yescharacteristic
310Dic47—42no—
311Dic47—82no—
312#3458D4711yescharacteristic, complemented
313C2×#421—471no—
314C2×#421—471no—
315C2×#410—471no—
316#2031—478no—
317C2×#344—471no—
318#1733—471no—
319C2×H(3,ℤ/4)—471no—
320C2×C47—21no—
321C2×C47—21no—
322C2×C47—21no—
323C2×C47—21no—
324C2×C47—21no—
325C2×C47—21no—
326C2×C47—21no—
327C2×C47C2×#39311yescharacteristic
328D47—82no—
329C22×#41—471no—
330C22×M16—471no—
331C22×M16—471no—
332#544—22no—
333#544—22no—
334#544—22no—
335#543—22no—
336#533—22no—
337#533—22no—
338#533C2×D4714yescomplemented
339C2×#117—471no—
340C2×#117C2×D4711yescharacteristic
341C2×#117C2×D4711yescharacteristic
342C2×#117C2×D4711yescharacteristic
343#421—474no—
344#421—942no—
345#421—942no—
346#421—942no—
347C2×#104—474no—
348C2×#104—942no—
349#410—474no—
350#410—942no—
351C2×#99—942no—
352#344—474no—
353#339—474no—
354H(3,ℤ/4)—474no—
355C47#2347211yescharacteristic, complemented, Sylow
356C2×#41—472no—
357C2×#41—472no—
358C2×#41—941no—
359C2×#41—941no—
360C2×#41—941no—
361C2×#41—941no—
362C2×#41—941no—
363C2×#41—941no—
364C2×#41—941no—
365C2×#41—941no—
366C2×#41—941no—
367C2×#41—941no—
368C22×Q8—471no—
369C22×D4—471no—
370C22×D4—941no—
371C23×C4—941no—
372C23×C4C22×D4711yescharacteristic
373C2×M16—472no—
374C2×M16—472no—
375C2×M16—941no—
376C2×M16—941no—
377C2×M16—941no—
378C2×M16—941no—
379C2×M16—941no—
380C2×M16—941no—
381C2×M16—941no—
382C2×M16—941no—
383C2×M16—941no—
384C2×M16—941no—
385C22×C8—941no—
386C22×C8—941no—
387C4⋊Q8—24no—
388C4⋊Q8—24no—
389C4⋊Q8—24no—
390#125—24no—
391#125—24no—
392#125—24no—
393C22⋊Q8—28no—
394C22⋊Q8—28no—
395C22⋊Q8—28no—
396C4×Q8—28no—
397#117—21no—
398#117—21no—
399#117—21no—
400#117—21no—
401#117—21no—
402#117—21no—
403#117—472no—
404#117—941no—
405#117—941no—
406#117—941no—
407#117C22⋊D4712yes—
408#117C22⋊D4712yes—
409#117C22⋊D4712yes—
410#117C22⋊D4712yes—
411#117C22×D4712yes—
412#117C22×D4712yes—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—941no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—941no—
420C2×C22⋊C4C22⋊D4712yes—
421C2×C42—21no—
422C2×C42—941no—
423C2×C42C22⋊D4712yes—
424C2×C42C22×D4712yes—
425#104—948no—
426#104—948no—
427#99—948no—
428C24—941no—
429C24C2×C22⋊D4711yescharacteristic
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—1881no—
439#41—1881no—
440#41—1881no—
441#41—1881no—
442#41—1881no—
443#41—1881no—
444#41—1881no—
445#41—1881no—
446C2×Q8—28no—
447C2×Q8—472no—
448C2×Q8—941no—
449C2×Q8—941no—
450C2×Q8—941no—
451C2×Q8—941no—
452C2×Q8—941no—
453C2×D4—472no—
454C2×D4—942no—
455C2×D4—942no—
456C2×D4—941no—
457C2×D4—941no—
458C2×D4—941no—
459C2×D4—941no—
460C2×D4—941no—
461C2×D4—1881no—
462C2×D4—1881no—
463C2×D4—1881no—
464C2×D4—1881no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—941no—
469C22×C4—942no—
470C22×C4—942no—
471C22×C4—1881no—
472C22×C4—1881no—
473C22×C4—1881no—
474C22×C4—1881no—
475C22×C4—1881no—
476C22×C4Q8×D4711yescharacteristic
477C22×C4Q8×D4711yescharacteristic
478C22×C4#1062535411yescharacteristic
479C22×C4#1062535411yescharacteristic
480C22×C4#1062535411yescharacteristic
481C22×C4#1062535411yescharacteristic
482C22×C4#1062535411yescharacteristic
483C22×C4#1062535411yescharacteristic
484C22×C4C2×C22⋊D4711yescharacteristic
485C22×C4C2×C22⋊D4711yescharacteristic
486C22×C4C2×C22⋊D4711yescharacteristic
487C22×C4C2×C22⋊D4711yescharacteristic
488C22×C4C2×C22⋊D4711yescharacteristic
489C22×C4C23×D4711yescharacteristic
490M16—942no—
491M16—942no—
492M16—942no—
493M16—942no—
494M16—1881no—
495M16—1881no—
496M16—1881no—
497M16—1881no—
498C2×C8—942no—
499C2×C8—942no—
500C2×C8—1881no—
501C2×C8—1881no—
502C2×C8—1881no—
503C2×C8—1881no—
504C4⋊C4—28no—
505C4⋊C4—28no—
506C4⋊C4—28no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—942no—
514C4⋊C4—1881no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—942no—
521C22⋊C4—1881no—
522C22⋊C4C2×C22⋊D4714yes—
523C42—22no—
524C42—22no—
525C42—22no—
526C42—22no—
527C42—942no—
528C42—1881no—
529C42C2×C22⋊D4714yes—
530C42C2×C22⋊D4714yes—
531C23—81no—
532C23—942no—
533C23—3762no—
534C23—1881no—
535C23—1881no—
536C23#1309399311yescharacteristic
537C23#1309399311yescharacteristic
538C23#1309400011yescharacteristic
539C23#1309400011yescharacteristic
540C23#1309401311yescharacteristic
541C23#1309401311yescharacteristic
542C23C22×C22⋊D4711yescharacteristic
543Q8—88no—
544Q8—942no—
545Q8—942no—
546Q8—1881no—
547Q8—1881no—
548D4—942no—
549D4—942no—
550D4—1882no—
551D4—1882no—
552D4—1882no—
553D4—1882no—
554D4—1881no—
555D4—1881no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—82no—
560C2×C4—82no—
561C2×C4—82no—
562C2×C4—942no—
563C2×C4—3762no—
564C2×C4—1882no—
565C2×C4—1881no—
566C2×C4—1881no—
567C2×C4—1882no—
568C2×C4—1882no—
569C2×C4—1882no—
570C2×C4—1882no—
571C2×C4#1309399311yescharacteristic
572C2×C4#1309399311yescharacteristic
573C2×C4#1309400011yescharacteristic
574C2×C4#1309400011yescharacteristic
575C2×C4#1309400011yescharacteristic
576C2×C4#1309400011yescharacteristic
577C2×C4#1309400011yescharacteristic
578C2×C4#1309400011yescharacteristic
579C2×C4#1309400011yescharacteristic
580C2×C4#1309400011yescharacteristic
581C2×C4#1309400011yescharacteristic
582C2×C4#1309400011yescharacteristic
583C2×C4#1309401311yescharacteristic
584C2×C4#1309401311yescharacteristic
585C2×C4#1309401311yescharacteristic
586C2×C4#1309401311yescharacteristic
587C2×C4#1309401311yescharacteristic
588C2×C4#1309401311yescharacteristic
589C2×C4#1309401311yescharacteristic
590C2×C4#1309401311yescharacteristic
591C2×C4#1309401311yescharacteristic
592C2×C4#1309401311yescharacteristic
593C2×C4C22×C22⋊D4711yescharacteristic
594C2×C4C22×C22⋊D4711yescharacteristic
595C2×C4C2×Q8×D4711yescharacteristic
596C2×C4C2×#1062535411yescharacteristic
597C2×C4C2×#1062535411yescharacteristic
598C2×C4C2×#1062535411yescharacteristic
599C8—1882no—
600C8—1882no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—3762no—
609C22—3762no—
610C22—3762no—
611C22—1882no—
612C22#1568903411yescharacteristic
613C22#1568903411yescharacteristic
614C22#1568903411yescharacteristic
615C22#1568903411yescharacteristic
616C22C2×#1309399311yescharacteristic
617C22C2×#1309400011yescharacteristic
618C22C2×#1309401311yescharacteristic
619C4—44no—
620C4—44no—
621C4—44no—
622C4—3762no—
623C4—1882no—
624C4#1568903411yescharacteristic
625C4#1568903411yescharacteristic
626C4#1568903411yescharacteristic
627C4#1568903411yescharacteristic
628C4C2×#1309400011yescharacteristic
629C4C2×#1309400011yescharacteristic
630C4C2×#1309401311yescharacteristic
631C4C2×#1309401311yescharacteristic
632C2—21no—
633C2—21no—
634C2—21no—
635C2—21no—
636C2—21no—
637C2—21no—
638C2—21no—
639C2—3762no—
640C2C2×#1568903411yescharacteristic
subgroupG/H
centerC4C2×#13094013
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#3458C2
socleC2×C47C2×#393
prime radicalC22×#10625350C22
hypercenter#3458D47
hypocenterC47#23472
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C23×C4 ◁ #3458

Complements

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

NH ≅ G/Ntype
4. #20244557C2semidirect
5. C2×#15688893C2semidirect
6. #20243098C2semidirect
7. C2×#15688879C2semidirect
8. C47×#3458C2semidirect
22. #15688893C22semidirect
23. #15688883C22semidirect
24. #15688879C22semidirect
31. C47×#533C22semidirect
45. C2×#10625350Q8semidirect
47. C22×Dic94Q8semidirect
48. C22×D188Q8semidirect
312. #3458D47semidirect
338. #533C2×D47semidirect
355. C47#23472semidirect

Maximal subgroups

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

subgroupindex
C2×#156891412
C2×#156890962
#202445572
C2×#156888932
#202430982
C2×#156888792
C47×#34582
#2347247