Finite Group Databasebeta

← #26246074

Subgroups — #26246074

Order 12032.

1126 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689161C211yesmaximal, characteristic, complemented
2C2×#15689159C211yesmaximal, characteristic, complemented
3C2×#15689119C211yesmaximal, characteristic
4#20245879C211yesmaximal, characteristic
5#20245791C211yesmaximal, characteristic, complemented
6#20244938C211yesmaximal, characteristic, complemented
7#20244934C211yesmaximal, characteristic, complemented
8#20244929C211yesmaximal, characteristic, complemented
9#20244924C211yesmaximal, characteristic, complemented
10#20244919C211yesmaximal, characteristic, complemented
11#20244914C211yesmaximal, characteristic, complemented
12#20244911C211yesmaximal, characteristic, complemented
13#20244907C211yesmaximal, characteristic, complemented
14C2×#15688877C211yesmaximal, characteristic, complemented
15C2×C47×#416C211yesmaximal, characteristic
16C23×C47⋊C8C2211yescharacteristic
17C2×#13093983C2211yescharacteristic
18C2×#13093983C2211yescharacteristic
19C22×C4×Dic47C2211yescharacteristic
20#15689161—24no—
21#15689159—24no—
22C2×#13093958C2211yescharacteristic
23C2×#13093958C2211yescharacteristic
24C2×#13093957C2211yescharacteristic
25C2×#13093957C2211yescharacteristic
26C2×#13093956C2211yescharacteristic
27C2×#13093956C2211yescharacteristic
28C2×#13093955C2211yescharacteristic
29C2×#13093955C2211yescharacteristic
30#15689119—24no—
31C2×#13093948C2211yescharacteristic
32C2×#13093948C2211yescharacteristic
33C2×#13093945C2211yescharacteristic
34C2×#13093945C2211yescharacteristic
35#15689030C2211yescharacteristic
36#15689030C2211yescharacteristic
37#15689026C2211yescharacteristic
38#15689026C2211yescharacteristic
39#15689003—22no—
40#15688992C2211yescharacteristic
41#15688992C2211yescharacteristic
42#15688988C2211yescharacteristic
43#15688988C2211yescharacteristic
44#15688981—22no—
45C4×Dic47⋊C4—22no—
46C4×C22⋊Dic47—22no—
47#15688877C2211yescharacteristic
48#15688877C2211yescharacteristic
49#15688877C2211yescharacteristic
50#15688877C2211yescharacteristic
51C22×#41×C47C2211yescharacteristic
52C23×C8×C47C2211yescharacteristic
53C2×#117×C47C2211yescharacteristic
54C47×#416—24no—
55C2×#103×C47C2211yescharacteristic
56C2×#103×C47C2211yescharacteristic
57C2×#102×C47C2211yescharacteristic
58C2×#102×C47C2211yescharacteristic
59C23×Dic47D412yes—
60C22×C47⋊C8—22no—
61C22×C47⋊C8—22no—
62C22×C47⋊C8D414yes—
63C22×C47⋊C8C2311yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65#13093983—22no—
66#13093983—22no—
67#13093983—22no—
68#13093983—22no—
69C2×C4⋊Dic47C2311yescharacteristic
70C2×C4⋊Dic47C2311yescharacteristic
71C2×C4⋊Dic47C2311yescharacteristic
72C2×C4⋊Dic47C2311yescharacteristic
73C2×Dic47⋊C4—22no—
74C2×Dic47⋊C4—22no—
75C2×C22⋊Dic47—21no—
76C2×C22⋊Dic47—21no—
77C2×C22⋊Dic47—22no—
78C2×C22⋊Dic47—22no—
79C2×C4×Dic47—22no—
80C2×C4×Dic47—22no—
81C2×C4×Dic47—21no—
82C2×C4×Dic47—21no—
83C2×C4×Dic47D412yes—
84C2×C4×Dic47C2311yescharacteristic
85C2×C4×Dic47C2311yescharacteristic
86#13093958—22no—
87#13093958—22no—
88#13093957—22no—
89#13093957—22no—
90#13093956—22no—
91#13093956—22no—
92#13093955—22no—
93#13093955—22no—
94#13093948—22no—
95#13093948—22no—
96#13093945—22no—
97#13093945—22no—
98C47⋊#95—22no—
99C47⋊#95—22no—
100C47⋊#95—22no—
101C47⋊#95—22no—
102C2×#41×C47—22no—
103C2×#41×C47—22no—
104C2×#41×C47—22no—
105C2×#41×C47—22no—
106C2×#41×C47—22no—
107C2×#41×C47Q814yes—
108C22×Q8×C47C2311yescharacteristic
109C22×D4×C47—21no—
110C22×D4×C47C2311yescharacteristic
111C23×C4×C47—21no—
112C23×C4×C47C2311yescharacteristic
113C22×C8×C47—22no—
114C22×C8×C47—22no—
115C22×C8×C47D414yes—
116C22×C8×C47C2311yescharacteristic
117C22×C8×C47C2311yescharacteristic
118#117×C47—22no—
119#117×C47—22no—
120C2×C4⋊C4×C47C2311yescharacteristic
121C2×C4⋊C4×C47C2311yescharacteristic
122C2×C22⋊C4×C47—21no—
123C2×C42×C47—21no—
124#103×C47—22no—
125#103×C47—22no—
126#102×C47—22no—
127#102×C47—22no—
128C24×C47—21no—
129C24×C47C2×D411yescharacteristic
130#41×C47—28no—
131#41×C47—28no—
132#41×C47—44no—
133#41×C47—44no—
134C2×Q8×C47—21no—
135C2×Q8×C47—21no—
136C2×Q8×C47—21no—
137C2×Q8×C47—21no—
138C2×Q8×C47—21no—
139C2×Q8×C47C2×Q812yes—
140C2×D4×C47—24no—
141C2×D4×C47—21no—
142C2×D4×C47—21no—
143C2×D4×C47—21no—
144C2×D4×C47—21no—
145C2×D4×C47—21no—
146C2×D4×C47—42no—
147C2×D4×C47—42no—
148C2×D4×C47C2×Q812yes—
149C22×C4×C47—21no—
150C22×C4×C47—24no—
151C22×C4×C47—21no—
152C22×C4×C47—21no—
153C22×C4×C47—42no—
154C22×C4×C47—42no—
155C22×C4×C47C2×D411yescharacteristic
156C22×C4×C47C2×D412yes—
157C22×C4×C47C2×D412yes—
158C22×C4×C47C2×Q812yes—
159C22×C4×C47#4112yes—
160C22×C4×C47#4112yes—
161C22×C4×C47#4112yes—
162C22×C4×C47C2411yescharacteristic
163C22×Dic47—24no—
164C22×Dic47—24no—
165C22×Dic47—21no—
166C22×Dic47—21no—
167C22×Dic47—21no—
168C22×Dic47—21no—
169C22×Dic47—42no—
170C22×Dic47C2×D412yes—
171C22×Dic47C2×D412yes—
172C2×C8×C47—28no—
173C2×C8×C47—21no—
174C2×C8×C47—21no—
175C2×C8×C47—21no—
176C2×C8×C47—21no—
177C2×C8×C47C2×D412yes—
178C2×C8×C47C2×D412yes—
179C4⋊C4×C47—21no—
180C4⋊C4×C47—21no—
181C4⋊C4×C47—21no—
182C4⋊C4×C47—21no—
183C22⋊C4×C47—42no—
184C42×C47—42no—
185C22⋊Dic47—44no—
186C22⋊Dic47—42no—
187C22⋊Dic47—42no—
188C22⋊Dic47—44no—
189C4⋊Dic47—21no—
190C4⋊Dic47—21no—
191C4⋊Dic47—21no—
192C4⋊Dic47—21no—
193C4⋊Dic47—21no—
194C4⋊Dic47—21no—
195C4⋊Dic47—21no—
196C4⋊Dic47—21no—
197Dic47⋊C4—44no—
198Dic47⋊C4—44no—
199C4×Dic47—24no—
200C4×Dic47—21no—
201C4×Dic47—21no—
202C4×Dic47—21no—
203C4×Dic47—21no—
204C4×Dic47—42no—
205C4×Dic47—42no—
206C2×C47⋊C8—28no—
207C2×C47⋊C8—21no—
208C2×C47⋊C8—21no—
209C2×C47⋊C8—21no—
210C2×C47⋊C8—21no—
211C2×C47⋊C8C2×D412yes—
212C2×C47⋊C8C2×D412yes—
213C23×C47—22no—
214C23×C47—22no—
215C23×C47—22no—
216C23×C47—41no—
217C23×C47—41no—
218C23×C47—42no—
219C23×C47—42no—
220C23×C47C22⋊Q812yes—
221C23×C47#12312yes—
222C23×C47#12712yes—
223C23×C47C22×D411yescharacteristic
224Q8×C47—22no—
225Q8×C47—22no—
226Q8×C47—41no—
227Q8×C47—41no—
228D4×C47—22no—
229D4×C47—22no—
230D4×C47—48no—
231D4×C47—41no—
232D4×C47—41no—
233C2×C4×C47—22no—
234C2×C4×C47—41no—
235C2×C4×C47—41no—
236C2×C4×C47—48no—
237C2×C4×C47—41no—
238C2×C4×C47—41no—
239C2×C4×C47—42no—
240C2×C4×C47—42no—
241C2×C4×C47C22⋊Q814yes—
242C2×C4×C47C22⋊Q812yes—
243C2×C4×C47C22⋊Q814yes—
244C2×C4×C47#12314yes—
245C2×C4×C47#12314yes—
246C2×C4×C47#12312yes—
247C2×C4×C47#12712yes—
248C2×C4×C47C22×D411yescharacteristic
249C2×C4×C47C22×D411yescharacteristic
250C2×C4×C47C22×Q811yescharacteristic
251C2×C4×C47C2×#4111yescharacteristic
252C2×C4×C47C2×#4111yescharacteristic
253C2×C4×C47C2×#4111yescharacteristic
254C2×Dic47—22no—
255C2×Dic47—22no—
256C2×Dic47—22no—
257C2×Dic47—22no—
258C2×Dic47—22no—
259C2×Dic47—48no—
260C2×Dic47—41no—
261C2×Dic47—41no—
262C2×Dic47—41no—
263C2×Dic47—41no—
264C2×Dic47—42no—
265C2×Dic47—42no—
266C2×Dic47—42no—
267C2×Dic47—42no—
268C2×Dic47#13514yes—
269C8×C47—22no—
270C8×C47—22no—
271C47⋊C8—22no—
272C47⋊C8—22no—
273#23730—471nomaximal, Sylow
274C22×C47—24no—
275C22×C47—24no—
276C22×C47—22no—
277C22×C47—22no—
278C22×C47—44no—
279C22×C47—42no—
280C22×C47—82no—
281C22×C47—81no—
282C22×C47—81no—
283C22×C47#39914yes—
284C22×C47C2×C22⋊Q811yescharacteristic
285C22×C47C2×#12311yescharacteristic
286C22×C47C2×#12711yescharacteristic
287C22×C47C2×#13512yes—
288C22×C47#57512yes—
289C4×C47—42no—
290C4×C47—81no—
291C4×C47—81no—
292C4×C47#39914yes—
293C4×C47C2×C22⋊Q811yescharacteristic
294C4×C47C2×C22⋊Q811yescharacteristic
295C4×C47C2×#12311yescharacteristic
296C4×C47C2×#12311yescharacteristic
297Dic47—24no—
298Dic47—42no—
299Dic47—81no—
300Dic47—81no—
301Dic47—81no—
302Dic47—81no—
303C2×#427—471no—
304C2×#427—471no—
305C2×#416—471no—
306C2×#416D4711yescharacteristic
307#2297—471no—
308#2285—471no—
309#2097—471no—
310#2097—471no—
311#2096—471no—
312#2095—471no—
313#2094—471no—
314#2093—471no—
315#2092—471no—
316#2092—471no—
317C2×#336—471no—
318C2×C47—24no—
319C2×C47—82no—
320C2×C47C2×#39911yescharacteristic
321C2×C47#307612yes—
322C2×C47#309112yes—
323C2×C47#314711yescharacteristic
324C2×C47#315011yescharacteristic
325C22×#41C2×D4711yescharacteristic
326C23×C8—471no—
327C23×C8C2×D4711yescharacteristic
328C2×#117—471no—
329C2×#117—471no—
330C2×#117C2×D4711yescharacteristic
331C22×C42—471no—
332#427—944no—
333#427—944no—
334C2×#107—471no—
335C2×#107—471no—
336C2×#107—471no—
337C2×#107—471no—
338C2×#106—471no—
339C2×#106—471no—
340C2×#106—471no—
341C2×#106—471no—
342#416—24no—
343#416—944no—
344C2×#103—471no—
345C2×#103—471no—
346C2×#103C2×D4711yescharacteristic
347C2×#103C2×D4711yescharacteristic
348C2×#102—471no—
349C2×#102—471no—
350C2×#102C2×D4711yescharacteristic
351C2×#102C2×D4711yescharacteristic
352#391—471no—
353#391—471no—
354#390—471no—
355#390—471no—
356#386—942no—
357#384—471no—
358#384—471no—
359#382—471no—
360#382—471no—
361#380—942no—
362C4×C4⋊C4—942no—
363C4×C22⋊C4—942no—
364#336—471no—
365#336—471no—
366#336—471no—
367#336—471no—
368C47#2373011yescharacteristic, complemented, Sylow
369C2×#41—22no—
370C2×#41—22no—
371C2×#41—22no—
372C2×#41—22no—
373C2×#41—22no—
374C2×#41Dic9414yes—
375C22×Q8C22×D4711yescharacteristic
376C22×D4—21no—
377C22×D4C22×D4711yescharacteristic
378C23×C4—21no—
379C23×C4—472no—
380C23×C4C22×D4711yescharacteristic
381C22×C8—22no—
382C22×C8—22no—
383C22×C8—474no—
384C22×C8—471no—
385C22×C8—471no—
386C22×C8—942no—
387C22×C8—942no—
388C22×C8C22⋊D4714yes—
389C22×C8C22×D4711yescharacteristic
390C22×C8C22×D4711yescharacteristic
391#117—22no—
392#117—22no—
393#117—942no—
394#117—942no—
395#117—942no—
396#117—942no—
397C2×C4⋊C4—471no—
398C2×C4⋊C4—471no—
399C2×C4⋊C4—471no—
400C2×C4⋊C4—471no—
401C2×C4⋊C4—942no—
402C2×C4⋊C4—942no—
403C2×C4⋊C4C22×D4711yescharacteristic
404C2×C4⋊C4C22×D4711yescharacteristic
405C2×C22⋊C4—21no—
406C2×C22⋊C4—942no—
407C2×C22⋊C4—942no—
408C2×C22⋊C4—941no—
409C2×C22⋊C4—941no—
410C2×C42—21no—
411C2×C42—472no—
412C2×C42—471no—
413C2×C42—471no—
414C2×C42—942no—
415C2×C42—942no—
416C2×C42—941no—
417C2×C42—941no—
418#107—942no—
419#107—942no—
420#107—942no—
421#107—942no—
422#106—942no—
423#106—942no—
424#106—942no—
425#106—942no—
426#103—22no—
427#103—22no—
428#103—942no—
429#103—942no—
430#102—22no—
431#102—22no—
432#102—942no—
433#102—942no—
434#95—942no—
435#95—942no—
436#95—942no—
437#95—942no—
438C24—21no—
439C24D4×D4711yescharacteristic
440#41—28no—
441#41—28no—
442#41—44no—
443#41—44no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8C2×Dic9412yes—
450C2×D4—24no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—42no—
457C2×D4—42no—
458C2×D4C2×Dic9412yes—
459C22×C4—21no—
460C22×C4—24no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—472no—
466C22×C4—472no—
467C22×C4—944no—
468C22×C4—944no—
469C22×C4—941no—
470C22×C4—941no—
471C22×C4—941no—
472C22×C4—941no—
473C22×C4—1882no—
474C22×C4C2×Dic9412yes—
475C22×C4#1062535012yes—
476C22×C4D4×D4712yes—
477C22×C4D4×D4711yescharacteristic
478C22×C4#1062535212yes—
479C22×C4#1062535212yes—
480C22×C4C2×C22⋊D4712yes—
481C22×C4C23×D4711yescharacteristic
482C2×C8—28no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—472no—
488C2×C8—472no—
489C2×C8—948no—
490C2×C8—941no—
491C2×C8—941no—
492C2×C8—941no—
493C2×C8—941no—
494C2×C8C2×C22⋊D4712yes—
495C2×C8C2×C22⋊D4712yes—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—941no—
501C4⋊C4—941no—
502C4⋊C4—941no—
503C4⋊C4—941no—
504C4⋊C4—941no—
505C4⋊C4—941no—
506C4⋊C4—941no—
507C4⋊C4—941no—
508C4⋊C4—1884no—
509C4⋊C4—1884no—
510C22⋊C4—42no—
511C22⋊C4—1884no—
512C22⋊C4—1884no—
513C22⋊C4—1882no—
514C22⋊C4—1882no—
515C42—42no—
516C42—944no—
517C42—941no—
518C42—941no—
519C42—941no—
520C42—941no—
521C42—1882no—
522C42—1882no—
523C23—22no—
524C23—22no—
525C23—22no—
526C23—41no—
527C23—42no—
528C23—41no—
529C23—42no—
530C23#1309400112yes—
531C23#1309400612yes—
532C23#1309402012yes—
533C23C2×D4×D4711yescharacteristic
534Q8—22no—
535Q8—22no—
536Q8—41no—
537Q8—41no—
538D4—22no—
539D4—22no—
540D4—48no—
541D4—41no—
542D4—41no—
543C2×C4—22no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—48no—
547C2×C4—42no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—42no—
551C2×C4—474no—
552C2×C4—942no—
553C2×C4—942no—
554C2×C4—942no—
555C2×C4—942no—
556C2×C4—942no—
557C2×C4—1888no—
558C2×C4—1882no—
559C2×C4—1882no—
560C2×C4—1881no—
561C2×C4—1881no—
562C2×C4—1881no—
563C2×C4—1881no—
564C2×C4—1882no—
565C2×C4—1882no—
566C2×C4#1309400112yes—
567C2×C4#1309400114yes—
568C2×C4#1309400314yes—
569C2×C4#1309400514yes—
570C2×C4#1309400612yes—
571C2×C4#1309400614yes—
572C2×C4#1309402012yes—
573C2×C4C2×D4×D4711yescharacteristic
574C2×C4C22×C22⋊D4711yescharacteristic
575C2×C4C22×Dic9411yescharacteristic
576C2×C4C2×#1062535211yescharacteristic
577C2×C4C2×#1062535211yescharacteristic
578C2×C4C2×#1062535011yescharacteristic
579C8—22no—
580C8—22no—
581C8—942no—
582C8—942no—
583C22—24no—
584C22—22no—
585C22—22no—
586C22—24no—
587C22—42no—
588C22—44no—
589C22—82no—
590C22—81no—
591C22—81no—
592C22#1568905914yes—
593C22C2×#1309400111yescharacteristic
594C22C2×#1309400611yescharacteristic
595C22C2×#1309402011yescharacteristic
596C22#135×D4712yes—
597C22#1568992012yes—
598C4—42no—
599C4—81no—
600C4—81no—
601C4—944no—
602C4—3761no—
603C4—3761no—
604C4—3761no—
605C4—3761no—
606C4—1882no—
607C4#1568905914yes—
608C4C2×#1309400111yescharacteristic
609C4C2×#1309400311yescharacteristic
610C4C2×#1309400511yescharacteristic
611C4C2×#1309400611yescharacteristic
612C2—24no—
613C2—82no—
614C2C2×#1568905911yescharacteristic
615C2#2025317212yes—
616C2#2025329912yes—
617C2#2025381211yescharacteristic
618C2#2025383111yescharacteristic
subgroupG/H
centerC22×C4D4×D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC2×C47×#416C2
socleC23×C47C22×D4
prime radicalC22×#41×C47C22
hypercenterC2×#416D47
hypocenterC47#23730
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. C2×#15689161C2semidirect
2. C2×#15689159C2semidirect
5. #20245791C2semidirect
6. #20244938C2semidirect
7. #20244934C2semidirect
8. #20244929C2semidirect
9. #20244924C2semidirect
10. #20244919C2semidirect
11. #20244914C2semidirect
12. #20244911C2semidirect
13. #20244907C2semidirect
14. C2×#15688877C2semidirect
368. C47#23730semidirect

Maximal subgroups

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

subgroupindex
C2×#156891612
C2×#156891592
C2×#156891192
#202458792
#202457912
#202449382
#202449342
#202449292
#202449242
#202449192
#202449142
#202449112
#202449072
C2×#156888772
C2×C47×#4162
#2373047