Finite Group Databasebeta

← #26217874

Subgroups — #26217874

Order 12032.

1710 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
1C2×#15689697C211yesmaximal, characteristic
2#20256589C211yesmaximal, characteristic
3C2×#15689132C211yesmaximal, characteristic, complemented
4C2×#15689105C211yesmaximal, characteristic
5#20243778C214yesmaximal, complemented
6#20243773C214yesmaximal, complemented
7#20243099C211yesmaximal, characteristic, complemented
8#20243097C211yesmaximal, characteristic, complemented
9C2×C47×#419C211yesmaximal, characteristic, complemented
10C22×#10625350C2211yescharacteristic
11C22×#10625329C2211yescharacteristic
12#15689697—24no—
13#15689697C418yescomplemented
14C2×#13094022C2212yes—
15C2×#13094013C2212yes—
16C2×#13094007—22no—
17C2×#13094000—22no—
18#15689604—22no—
19#15689603—22no—
20#15689600C2212yes—
21#15689597C2212yes—
22#15689596—22no—
23C4×#10625350—22no—
24#15689591—22no—
25C2×#13093983C2211yescharacteristic
26C2×#13093983C2211yescharacteristic
27#117×D47—22no—
28#15689132—22no—
29#15689132C2214yes—
30C2×#13093948—22no—
31#15689105—24no—
32C2×#13093942C2212yes—
33C2×#13093940C2212yes—
34#15688884C2214yes—
35#15688882C2214yes—
36C23×Q8×C47C2211yescharacteristic
37C22×M16×C47C2211yescharacteristic
38C2×#117×C47C2211yescharacteristic
39C47×#419—22no—
40C47×#419C2214yes—
41C2×#103×C47—22no—
42C2×#10625350—21no—
43C2×#10625350—21no—
44C2×#10625350—21no—
45C2×#10625350—21no—
46C2×#10625350—22no—
47C2×#10625350—22no—
48C2×#10625350C2×C414yes—
49C2×#10625350D414yes—
50C22×Dic94C2311yescharacteristic
51C22×D188C2311yescharacteristic
52C22×C22⋊D47D412yes—
53C22×C4×D47D412yes—
54C2×#10625329—21no—
55C2×#10625329—22no—
56C2×#10625329—22no—
57C2×#10625329C2312yes—
58C22×C47⋊C8—21no—
59#13094022—24no—
60#13094022C2×C418yescomplemented
61#13094013—24no—
62#13094013C2×C418yescomplemented
63#13094007—216no—
64#13094000—216no—
65C4×Dic94—24no—
66#13093989—24no—
67C4×D188—24no—
68#13093986—24no—
69C4×C22⋊D47—28no—
70(C22⋊D47)⋊C4—28no—
71#13093983—21no—
72#13093983—21no—
73#13093983—22no—
74#13093983C2×C414yescomplemented
75#13093983D412yes—
76#13093983C2312yes—
77#13093982—24no—
78#13093981—24no—
79#13093980—24no—
80C2×C4⋊Dic47—21no—
81C2×C4⋊Dic47D412yes—
82C2×Dic47⋊C4—24no—
83C4⋊C4×D47—24no—
84C2×C22⋊Dic47—21no—
85C2×C22⋊Dic47—21no—
86C2×(C2×D47)⋊C4—24no—
87C22⋊C4×D47—24no—
88C2×C4×Dic47—21no—
89C2×C4×Dic47C2312yes—
90C42×D47—24no—
91#13093948—28no—
92#13093942—24no—
93#13093940—24no—
94C22×Q8×C47—21no—
95C22×Q8×C47—22no—
96C22×Q8×C47—21no—
97C22×Q8×C47—21no—
98C22×Q8×C47—21no—
99C22×Q8×C47—21no—
100C22×Q8×C47—22no—
101C22×Q8×C47—22no—
102C22×Q8×C47C2×C414yescomplemented
103C22×Q8×C47C2312yes—
104C23×C4×C47—21no—
105C23×C4×C47C2311yescharacteristic
106C2×M16×C47—21no—
107C2×M16×C47—22no—
108C2×M16×C47—22no—
109C2×M16×C47C2312yes—
110C22×C8×C47—21no—
111#117×C47—21no—
112#117×C47—21no—
113#117×C47D412yes—
114#117×C47C2312yes—
115C2×C4⋊C4×C47D412yes—
116C2×C22⋊C4×C47—21no—
117C2×C42×C47—21no—
118#103×C47—28no—
119C24×C47C2×D411yescharacteristic
120C23×D47C2×D412yes—
121C2×Q8×C47—24no—
122C2×Q8×C47—22no—
123C2×Q8×C47—24no—
124C2×Q8×C47—24no—
125C2×Q8×C47—24no—
126C2×Q8×C47—24no—
127C2×Q8×C47—22no—
128C2×Q8×C47—22no—
129C2×Q8×C47—22no—
130C2×Q8×C47—22no—
131C2×Q8×C47—41no—
132C2×Q8×C47—41no—
133C2×Q8×C47—42no—
134C2×Q8×C47—42no—
135C2×Q8×C47—42no—
136C2×Q8×C47—42no—
137C2×Q8×C47—42no—
138C2×Q8×C47C22×C414yes—
139C22×C4×C47—24no—
140C22×C4×C47—22no—
141C22×C4×C47—22no—
142C22×C4×C47—41no—
143C22×C4×C47—41no—
144C22×C4×C47—42no—
145C22×C4×C47C22×C412yes—
146C22×C4×C47C2×D411yescharacteristic
147C22×C4×C47C2×D412yes—
148C22×C4×C47C2×D411yescharacteristic
149C22×C4×C47C2×D411yescharacteristic
150C22×C4×C47C2×D411yescharacteristic
151C22×C4×C47C2×D411yescharacteristic
152C22×C4×C47#4112yes—
153C22×C4×C47#4112yes—
154C22×C4×C47C2411yescharacteristic
155C2×C22⋊D47—22no—
156C2×C22⋊D47—22no—
157C2×C22⋊D47—24no—
158C2×C22⋊D47C22⋊C418yes—
159C22×Dic47—22no—
160C22×Dic47—22no—
161C22×Dic47C2×D412yes—
162#10625350—24no—
163#10625350—24no—
164#10625350—24no—
165#10625350—24no—
166#10625350—24no—
167#10625350—24no—
168#10625350—24no—
169#10625350—24no—
170C2×D188—21no—
171C2×D188—21no—
172C2×D188—21no—
173C2×D188—21no—
174C2×D188C22×C412yes—
175C2×D188C2×D412yes—
176C2×C4×D47—22no—
177C2×C4×D47—22no—
178C2×C4×D47—24no—
179C2×C4×D47—28no—
180C2×C4×D47C22⋊C418yes—
181C2×Dic94—21no—
182C2×Dic94—21no—
183C2×Dic94—21no—
184C2×Dic94—21no—
185C2×Dic94C22×C412yes—
186C2×Dic94C2×D412yes—
187M16×C47—22no—
188M16×C47—22no—
189M16×C47—42no—
190C2×C8×C47—22no—
191C2×C8×C47—42no—
192C4⋊C4×C47—22no—
193C4⋊C4×C47C2×D414yes—
194C22⋊C4×C47—22no—
195C22⋊C4×C47—22no—
196C42×C47—22no—
197C42×C47—22no—
198C22⋊Dic47—24no—
199C22⋊Dic47—22no—
200C22⋊Dic47—22no—
201(C2×D47)⋊C4—28no—
202(C2×D47)⋊C4—216no—
203C4⋊Dic47—24no—
204C4⋊Dic47—22no—
205C4⋊Dic47C2×D414yes—
206Dic47⋊C4—28no—
207Dic47⋊C4—216no—
208C4×Dic47—28no—
209C4×Dic47—22no—
210C4×Dic47—22no—
211C4×Dic47—22no—
212C4×Dic47C22×C414yes—
213#10625329—22no—
214#10625329—22no—
215#10625329—42no—
216C2×C47⋊C8—22no—
217C2×C47⋊C8—42no—
218C23×C47—42no—
219C23×C47C2×C22⋊C412yes—
220C23×C47#12011yescharacteristic
221C23×C47#12011yescharacteristic
222C23×C47#12312yes—
223C23×C47C22×D411yescharacteristic
224C22×D47—22no—
225C22×D47—22no—
226C22×D47—44no—
227C22×D47C2×C22⋊C414yes—
228Q8×C47—24no—
229Q8×C47—24no—
230Q8×C47—42no—
231Q8×C47—42no—
232Q8×C47—44no—
233Q8×C47—44no—
234C2×C4×C47—24no—
235C2×C4×C47—24no—
236C2×C4×C47—42no—
237C2×C4×C47—42no—
238C2×C4×C47—44no—
239C2×C4×C47—44no—
240C2×C4×C47—82no—
241C2×C4×C47C2×C22⋊C412yes—
242C2×C4×C47C4×D412yes—
243C2×C4×C47C4×D412yes—
244C2×C4×C47C4×D412yes—
245C2×C4×C47C4×D412yes—
246C2×C4×C47#12011yescharacteristic
247C2×C4×C47#12011yescharacteristic
248C2×C4×C47#12112yes—
249C2×C4×C47#12112yes—
250C2×C4×C47#12112yes—
251C2×C4×C47#12112yes—
252C2×C4×C47#12312yes—
253C2×C4×C47C23×C411yescharacteristic
254C2×C4×C47C22×D411yescharacteristic
255C2×C4×C47C22×D411yescharacteristic
256C2×C4×C47C22×D411yescharacteristic
257C2×C4×C47C2×#4111yescharacteristic
258C2×C4×C47C2×#4111yescharacteristic
259C22⋊D47—28no—
260C22⋊D47—28no—
261C2×Dic47—22no—
262C2×Dic47—22no—
263C2×Dic47—24no—
264C2×Dic47—24no—
265C2×Dic47—44no—
266C2×Dic47—82no—
267C2×Dic47C2×C22⋊C414yes—
268D188—22no—
269D188—22no—
270D188—22no—
271D188—22no—
272C4×D47—28no—
273C4×D47—28no—
274C4×D47—88no—
275Dic94—22no—
276Dic94—22no—
277Dic94—22no—
278Dic94—22no—
279C8×C47—42no—
280C47⋊C8—42no—
281#20955—471nomaximal, Sylow
282C22×C47—22no—
283C22×C47—22no—
284C22×C47—22no—
285C22×C47—42no—
286C22×C47—42no—
287C22×C47#38612yes—
288C22×C47#38612yes—
289C22×C47C22×C22⋊C411yescharacteristic
290C22×C47C2×#12011yescharacteristic
291C22×C47C2×#12311yescharacteristic
292C2×D47—24no—
293C2×D47—44no—
294C2×D47—44no—
295C2×D47—82no—
296C4×C47—44no—
297C4×C47—44no—
298C4×C47#38612yes—
299C4×C47#38612yes—
300C4×C47C2×C4×D411yescharacteristic
301C4×C47C2×C4×D411yescharacteristic
302C4×C47C2×#12111yescharacteristic
303C4×C47C2×#12111yescharacteristic
304Dic47—24no—
305Dic47—44no—
306Dic47—44no—
307C2×#536—471no—
308#3428—471no—
309C2×#419—471no—
310C2×#419D4711yescharacteristic, complemented
311C2×#413—471no—
312#1886—474no—
313#1885—474no—
314#1733—471no—
315#1733—471no—
316C2×C47—21no—
317C2×C47—21no—
318C2×C47—22no—
319C2×C47—22no—
320C2×C47C2×#38611yescharacteristic
321C2×C47#302212yes—
322D47—44no—
323C22×#41—471no—
324C23×Q8C2×D4711yescharacteristic
325C22×M16—471no—
326C22×M16C2×D4711yescharacteristic
327#536—478no—
328#536—944no—
329C2×C4⋊Q8—472no—
330C2×#124—472no—
331C2×#123—942no—
332C2×C22⋊Q8—942no—
333#520—942no—
334#520—942no—
335#519—472no—
336#518—472no—
337#518—942no—
338C4×#41—942no—
339C4×#41—942no—
340C2×#117—471no—
341C2×#117—471no—
342C2×#117—942no—
343C2×#117C2×D4711yescharacteristic
344#419—22no—
345#419—474no—
346#419—942no—
347#419C2×D4714yes—
348C2×#103—22no—
349C2×#103—942no—
350#413—944no—
351C2×#101—472no—
352C2×#100—472no—
353#339—474no—
354#339—474no—
355C47#2095511yescharacteristic, complemented, Sylow
356C2×#41—474no—
357C2×#41—474no—
358C2×#41—942no—
359C2×#41—941no—
360C2×#41—941no—
361C2×#41—942no—
362C2×#41—941no—
363C2×#41—941no—
364C22×Q8—21no—
365C22×Q8—22no—
366C22×Q8—22no—
367C22×Q8—21no—
368C22×Q8—21no—
369C22×Q8—22no—
370C22×Q8—21no—
371C22×Q8—21no—
372C22×Q8—471no—
373C22×Q8C4×D4714yescomplemented
374C22×Q8C22×D4712yes—
375C22×D4—472no—
376C22×D4—471no—
377C23×C4—21no—
378C23×C4—472no—
379C23×C4C22×D4711yescharacteristic
380C2×M16—21no—
381C2×M16—22no—
382C2×M16—22no—
383C2×M16—472no—
384C2×M16—941no—
385C2×M16—942no—
386C2×M16—942no—
387C2×M16C22×D4712yes—
388C22×C8—21no—
389C22×C8—941no—
390C4⋊Q8—478no—
391C4⋊Q8—944no—
392#124—478no—
393#124—944no—
394#123—9416no—
395C22⋊Q8—9416no—
396C4×Q8—944no—
397C4×Q8—944no—
398C4×D4—944no—
399C4×D4—948no—
400C4×D4—948no—
401C4×D4—944no—
402#117—21no—
403#117—21no—
404#117—474no—
405#117—472no—
406#117—472no—
407#117—944no—
408#117—944no—
409#117—944no—
410#117—941no—
411#117—942no—
412#117—941no—
413#117C22⋊D4712yes—
414#117C22×D4712yes—
415C2×C4⋊C4—472no—
416C2×C4⋊C4—944no—
417C2×C4⋊C4—944no—
418C2×C4⋊C4—941no—
419C2×C4⋊C4C22⋊D4712yes—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—944no—
422C2×C22⋊C4—944no—
423C2×C22⋊C4—941no—
424C2×C22⋊C4—941no—
425C2×C42—21no—
426C2×C42—472no—
427C2×C42—944no—
428C2×C42—941no—
429#103—28no—
430#103—948no—
431#101—944no—
432#100—944no—
433C24—472no—
434C24D4×D4711yescharacteristic
435#41—944no—
436#41—944no—
437#41—944no—
438#41—944no—
439#41—944no—
440#41—944no—
441#41—944no—
442#41—944no—
443C2×Q8—24no—
444C2×Q8—22no—
445C2×Q8—24no—
446C2×Q8—24no—
447C2×Q8—24no—
448C2×Q8—24no—
449C2×Q8—22no—
450C2×Q8—22no—
451C2×Q8—22no—
452C2×Q8—22no—
453C2×Q8—41no—
454C2×Q8—41no—
455C2×Q8—42no—
456C2×Q8—42no—
457C2×Q8—42no—
458C2×Q8—42no—
459C2×Q8—42no—
460C2×Q8—472no—
461C2×Q8—472no—
462C2×Q8—941no—
463C2×Q8—941no—
464C2×Q8—941no—
465C2×Q8—941no—
466C2×Q8C2×C4×D4714yes—
467C2×D4—478no—
468C2×D4—472no—
469C2×D4—472no—
470C2×D4—942no—
471C2×D4—942no—
472C2×D4—944no—
473C2×D4—941no—
474C2×D4—941no—
475C2×D4—941no—
476C2×D4—941no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—42no—
483C22×C4—472no—
484C22×C4—478no—
485C22×C4—948no—
486C22×C4—942no—
487C22×C4—942no—
488C22×C4—944no—
489C22×C4—942no—
490C22×C4—942no—
491C22×C4C2×C4×D4712yes—
492C22×C4#1062535012yes—
493C22×C4D4×D4711yescharacteristic
494C22×C4D4×D4712yes—
495C22×C4D4×D4711yescharacteristic
496C22×C4D4×D4711yescharacteristic
497C22×C4#1062535212yes—
498C22×C4C2×C22⋊D4711yescharacteristic
499C22×C4C2×C22⋊D4711yescharacteristic
500C22×C4C23×D4711yescharacteristic
501M16—22no—
502M16—22no—
503M16—42no—
504M16—942no—
505M16—942no—
506M16—1882no—
507C2×C8—22no—
508C2×C8—42no—
509C2×C8—942no—
510C2×C8—1882no—
511C4⋊C4—22no—
512C4⋊C4—474no—
513C4⋊C4—9416no—
514C4⋊C4—948no—
515C4⋊C4—944no—
516C4⋊C4—942no—
517C4⋊C4C2×C22⋊D4714yes—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—9416no—
521C22⋊C4—948no—
522C22⋊C4—944no—
523C22⋊C4—942no—
524C22⋊C4—942no—
525C42—22no—
526C42—22no—
527C42—474no—
528C42—948no—
529C42—942no—
530C42—942no—
531C42—942no—
532C23—42no—
533C23—474no—
534C23—942no—
535C23—942no—
536C23—1884no—
537C23C22⋊C4×D4712yes—
538C23#1309399211yescharacteristic
539C23#1309399211yescharacteristic
540C23#1309400612yes—
541C23C2×D4×D4711yescharacteristic
542Q8—24no—
543Q8—24no—
544Q8—44no—
545Q8—44no—
546Q8—42no—
547Q8—42no—
548Q8—942no—
549Q8—942no—
550Q8—942no—
551Q8—942no—
552D4—948no—
553D4—948no—
554D4—942no—
555D4—942no—
556D4—942no—
557D4—942no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—44no—
561C2×C4—44no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—82no—
565C2×C4—474no—
566C2×C4—942no—
567C2×C4—942no—
568C2×C4—948no—
569C2×C4—948no—
570C2×C4—944no—
571C2×C4—944no—
572C2×C4—3768no—
573C2×C4—3762no—
574C2×C4—1884no—
575C2×C4C22⋊C4×D4712yes—
576C2×C4(C22⋊D47)⋊C412yes—
577C2×C4(C22⋊D47)⋊C412yes—
578C2×C4C4×C22⋊D4712yes—
579C2×C4C4×C22⋊D4712yes—
580C2×C4#1309399211yescharacteristic
581C2×C4#1309399211yescharacteristic
582C2×C4#1309399512yes—
583C2×C4#1309399512yes—
584C2×C4#1309399712yes—
585C2×C4#1309399712yes—
586C2×C4#1309400612yes—
587C2×C4C22×C4×D4711yescharacteristic
588C2×C4C2×D4×D4711yescharacteristic
589C2×C4C2×D4×D4711yescharacteristic
590C2×C4C22×C22⋊D4711yescharacteristic
591C2×C4C2×#1062535211yescharacteristic
592C2×C4C2×#1062535011yescharacteristic
593C8—42no—
594C8—1882no—
595C22—22no—
596C22—22no—
597C22—22no—
598C22—42no—
599C22—42no—
600C22—944no—
601C22—3762no—
602C22—1884no—
603C22—1884no—
604C22#1568899912yes—
605C22#1568899912yes—
606C22C2×C22⋊C4×D4711yescharacteristic
607C22C2×#1309399211yescharacteristic
608C22C2×#1309400611yescharacteristic
609C4—44no—
610C4—44no—
611C4—944no—
612C4—1884no—
613C4—1884no—
614C4#1568899912yes—
615C4#1568899912yes—
616C4C2×(C22⋊D47)⋊C411yescharacteristic
617C4C2×C4×C22⋊D4711yescharacteristic
618C4C2×#1309399511yescharacteristic
619C4C2×#1309399711yescharacteristic
620C2—21no—
621C2—21no—
622C2—22no—
623C2—22no—
624C2—1884no—
625C2C2×#1568899911yescharacteristic
626C2#2025276412yes—
subgroupG/H
centerC22C2×#13093992
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#419C2
socleC22×C47C2×#120
prime radicalC22×#10625350C22
cosocleC22×C4×C47C24
hypercenterC2×#419D47
hypocenterC47#20955
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#419

Complements

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

NH ≅ G/Ntype
3. C2×#15689132C2semidirect
5. #20243778C2semidirect
6. #20243773C2semidirect
7. #20243099C2semidirect
8. #20243097C2semidirect
9. C2×C47×#419C2semidirect
13. #15689697C4semidirect
60. #13094022C2×C4semidirect
62. #13094013C2×C4semidirect
74. #13093983C2×C4semidirect
102. C22×Q8×C47C2×C4semidirect
310. C2×#419D47semidirect
355. C47#20955semidirect
373. C22×Q8C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156896972
#202565892
C2×#156891322
C2×#156891052
#202437782
#202437732
#202430992
#202430972
C2×C47×#4192
#2095547