Finite Group Databasebeta

← #26123698

Subgroups — #26123698

Order 12032.

878 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×#15689141C211yesmaximal, characteristic
2C2×#15689120C211yesmaximal, characteristic
3C2×#15689096C211yesmaximal, characteristic
4#20243120C211yesmaximal, characteristic, complemented
5#20243098C211yesmaximal, characteristic, complemented
6#20243084C211yesmaximal, characteristic, complemented
7C2×C47×#427C211yesmaximal, characteristic, complemented
8C22×#10625350C2211yescharacteristic
9C22×#10625329C2211yescharacteristic
10C2×#13093983C2211yescharacteristic
11C2×#13093983C2211yescharacteristic
12#15689141—22no—
13#15689141—22no—
14C2×#13093952—22no—
15#15689120—22no—
16#15689120—21no—
17#15689120—21no—
18C2×#13093949C412yescomplemented
19C2×#13093946C412yescomplemented
20#15689096—22no—
21#15689096—22no—
22C2×#13093938—22no—
23#15688889—22no—
24#15688883—22no—
25#15688877—22no—
26C23×C8×C47C2211yescharacteristic
27C2×#117×C47C2211yescharacteristic
28C2×#117×C47C2211yescharacteristic
29C47×#427—22no—
30C47×#427—22no—
31C2×#107×C47—21no—
32C2×#106×C47—21no—
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×#10625350—21no—
42C2×#10625350—21no—
43C2×#10625350D412yes—
44C2×#10625350Q812yes—
45C22×Dic94C2×C411yescharacteristic
46C22×D188C2×C411yescharacteristic
47C22×C22⋊D47—21no—
48C22×C4×D47—21no—
49C2×#10625329—21no—
50C2×#10625329—21no—
51C2×#10625329—21no—
52C2×#10625329—21no—
53C2×#10625329—21no—
54C2×#10625329D412yes—
55C22×C47⋊C8—21no—
56#13093983—21no—
57#13093983—21no—
58#13093983—21no—
59#13093983—21no—
60#13093983—21no—
61#13093983—21no—
62#13093983—21no—
63#13093983—21no—
64C2×C4⋊Dic47—21no—
65C2×C4⋊Dic47C2×C412yes—
66C2×C22⋊Dic47—21no—
67C2×C22⋊Dic47D412yes—
68C2×C4×Dic47—21no—
69C2×C4×Dic47—21no—
70#13093952—28no—
71#13093949—22no—
72#13093949—22no—
73#13093946—22no—
74#13093946—22no—
75#13093938—28no—
76C23×C4×C47C2311yescharacteristic
77C22×C8×C47—21no—
78C22×C8×C47—21no—
79C22×C8×C47—21no—
80C22×C8×C47—21no—
81C22×C8×C47C2×C412yes—
82C22×C8×C47D412yes—
83C22×C8×C47D411yescharacteristic
84C22×C8×C47D411yescharacteristic
85#117×C47—21no—
86#117×C47—21no—
87#117×C47—21no—
88#117×C47—21no—
89#117×C47—21no—
90#117×C47—21no—
91#117×C47D412yes—
92#117×C47D412yes—
93C2×C4⋊C4×C47—21no—
94C2×C4⋊C4×C47—21no—
95C2×C22⋊C4×C47—21no—
96C2×C22⋊C4×C47—21no—
97C2×C42×C47—21no—
98C2×C42×C47—21no—
99#107×C47—24no—
100#106×C47—24no—
101C24×C47C2×D411yescharacteristic
102C23×D47—21no—
103C22×C4×C47—41no—
104C22×C4×C47—41no—
105C22×C4×C47C22×C411yescharacteristic
106C22×C4×C47C2×D411yescharacteristic
107C22×C4×C47C2×D411yescharacteristic
108C22×C4×C47C2×D411yescharacteristic
109C22×C4×C47C2×D411yescharacteristic
110C22×C4×C47C2×D411yescharacteristic
111C22×C4×C47C2×D411yescharacteristic
112C22×C4×C47C2×Q811yescharacteristic
113C22×C4×C47#4111yescharacteristic
114C22×C4×C47#4111yescharacteristic
115C22×C4×C47#4111yescharacteristic
116C22×C4×C47#4111yescharacteristic
117C22×C4×C47#4111yescharacteristic
118C22×C4×C47#4111yescharacteristic
119C2×C22⋊D47—22no—
120C2×C22⋊D47—22no—
121C2×C22⋊D47—41no—
122C2×C22⋊D47—41no—
123C2×C22⋊D47—41no—
124C2×C22⋊D47—41no—
125C22×Dic47—21no—
126C22×Dic47—22no—
127C22×Dic47—22no—
128#10625350—22no—
129#10625350—22no—
130#10625350—22no—
131#10625350—22no—
132#10625350—22no—
133#10625350—22no—
134#10625350—22no—
135#10625350—22no—
136#10625350—41no—
137#10625350—41no—
138#10625350—41no—
139#10625350—41no—
140#10625350—41no—
141#10625350—41no—
142#10625350—41no—
143#10625350—41no—
144C2×D188—21no—
145C2×D188—21no—
146C2×D188—21no—
147C2×D188—21no—
148C2×D188—21no—
149C2×D188C4⋊C412yes—
150C2×C4×D47—22no—
151C2×C4×D47—22no—
152C2×C4×D47—41no—
153C2×C4×D47—41no—
154C2×C4×D47—41no—
155C2×C4×D47—41no—
156C2×Dic94—21no—
157C2×Dic94—21no—
158C2×Dic94—21no—
159C2×Dic94—21no—
160C2×Dic94—21no—
161C2×Dic94C4⋊C412yes—
162C2×C8×C47—22no—
163C2×C8×C47—22no—
164C2×C8×C47—21no—
165C2×C8×C47—21no—
166C2×C8×C47—22no—
167C2×C8×C47—22no—
168C2×C8×C47—21no—
169C2×C8×C47—21no—
170C2×C8×C47C22⋊C412yes—
171C2×C8×C47C22⋊C412yes—
172C4⋊C4×C47—22no—
173C4⋊C4×C47—22no—
174C4⋊C4×C47—41no—
175C4⋊C4×C47—41no—
176C22⋊C4×C47—22no—
177C22⋊C4×C47—22no—
178C22⋊C4×C47—41no—
179C22⋊C4×C47—41no—
180C42×C47—22no—
181C42×C47—22no—
182C42×C47—41no—
183C42×C47—41no—
184C22⋊Dic47—22no—
185C22⋊Dic47—22no—
186C22⋊Dic47—41no—
187C22⋊Dic47—41no—
188C4⋊Dic47—22no—
189C4⋊Dic47—22no—
190C4⋊Dic47—41no—
191C4⋊Dic47—41no—
192C4×Dic47—41no—
193C4×Dic47—41no—
194C4×Dic47—41no—
195C4×Dic47—41no—
196#10625329—22no—
197#10625329—22no—
198#10625329—41no—
199#10625329—41no—
200C2×C47⋊C8—22no—
201C2×C47⋊C8—41no—
202C2×C47⋊C8—41no—
203C23×C47—42no—
204C23×C47C4×D411yescharacteristic
205C23×C47#12011yescharacteristic
206C23×C47#12111yescharacteristic
207C23×C47#12111yescharacteristic
208C23×C47C22⋊Q811yescharacteristic
209C23×C47#12311yescharacteristic
210C23×C47#12711yescharacteristic
211C22×D47—22no—
212C22×D47—41no—
213C22×D47—41no—
214C22×D47—82no—
215C2×C4×C47—42no—
216C2×C4×C47—42no—
217C2×C4×C47—82no—
218C2×C4×C47—82no—
219C2×C4×C47C2×C22⋊C411yescharacteristic
220C2×C4×C47C2×C4⋊C411yescharacteristic
221C2×C4×C47#11711yescharacteristic
222C2×C4×C47C4×D411yescharacteristic
223C2×C4×C47C4×D411yescharacteristic
224C2×C4×C47C4×D411yescharacteristic
225C2×C4×C47#12011yescharacteristic
226C2×C4×C47#12011yescharacteristic
227C2×C4×C47#12111yescharacteristic
228C2×C4×C47#12111yescharacteristic
229C2×C4×C47#12111yescharacteristic
230C2×C4×C47#12111yescharacteristic
231C2×C4×C47#12111yescharacteristic
232C2×C4×C47#12111yescharacteristic
233C2×C4×C47C22⋊Q811yescharacteristic
234C2×C4×C47C22⋊Q811yescharacteristic
235C2×C4×C47C22⋊Q811yescharacteristic
236C2×C4×C47C22⋊Q811yescharacteristic
237C2×C4×C47C22⋊Q811yescharacteristic
238C2×C4×C47#12311yescharacteristic
239C2×C4×C47#12311yescharacteristic
240C2×C4×C47#12311yescharacteristic
241C2×C4×C47#12311yescharacteristic
242C2×C4×C47#12411yescharacteristic
243C2×C4×C47#12411yescharacteristic
244C2×C4×C47#12411yescharacteristic
245C2×C4×C47#12611yescharacteristic
246C2×C4×C47#12611yescharacteristic
247C22⋊D47—42no—
248C22⋊D47—42no—
249C22⋊D47—42no—
250C22⋊D47—42no—
251C2×Dic47—22no—
252C2×Dic47—41no—
253C2×Dic47—41no—
254C2×Dic47—44no—
255C2×Dic47—42no—
256C2×Dic47—42no—
257C2×Dic47—82no—
258D188—22no—
259D188—22no—
260D188—41no—
261D188—41no—
262C4×D47—42no—
263C4×D47—42no—
264C4×D47—42no—
265C4×D47—42no—
266Dic94—22no—
267Dic94—22no—
268Dic94—41no—
269Dic94—41no—
270C8×C47—22no—
271C8×C47—22no—
272C47⋊C8—42no—
273#11126—471nomaximal, Sylow
274C22×C47—22no—
275C22×C47—22no—
276C22×C47—22no—
277C22×C47—41no—
278C22×C47—41no—
279C22×C47—41no—
280C22×C47—41no—
281C22×C47#38511yescharacteristic
282C22×C47#38811yescharacteristic
283C22×C47#39011yescharacteristic
284C22×C47#39211yescharacteristic
285C22×C47#39411yescharacteristic
286C22×C47#39611yescharacteristic
287C22×C47#39911yescharacteristic
288C2×D47—42no—
289C2×D47—82no—
290C2×D47—82no—
291C2×D47—82no—
292C4×C47—82no—
293C4×C47—82no—
294C4×C47#38011yescharacteristic
295C4×C47#38511yescharacteristic
296C4×C47#38611yescharacteristic
297C4×C47#38811yescharacteristic
298C4×C47#39311yescharacteristic
299C4×C47#39411yescharacteristic
300C4×C47#39611yescharacteristic
301C4×C47#39711yescharacteristic
302Dic47—42no—
303Dic47—82no—
304Dic47—82no—
305C2×#427D4711yescharacteristic, complemented
306C2×#421—471no—
307C2×#416—471no—
308C2×#410—471no—
309#1740—471no—
310#1733—471no—
311#1729—471no—
312C2×C47—21no—
313C2×C47—21no—
314C2×C47—21no—
315C2×C47—21no—
316C2×C47—21no—
317C2×C47—21no—
318C2×C47#143911yescharacteristic
319C2×C47#197612yes—
320D47—82no—
321C22×#41—471no—
322C22×M16—471no—
323C23×C8C2×D4711yescharacteristic
324C2×#117—471no—
325C2×#117—471no—
326C2×#117C2×D4711yescharacteristic
327C2×#117C2×D4711yescharacteristic
328#427—22no—
329#427—22no—
330C2×#107—21no—
331C2×#106—21no—
332#421—942no—
333#421—942no—
334C2×#104—942no—
335#416—942no—
336#416—941no—
337#416—941no—
338C2×#103—472no—
339C2×#102—472no—
340#410—942no—
341#410—942no—
342C2×#99—942no—
343#342—942no—
344#339—942no—
345#336—942no—
346C47#1112611yescharacteristic, complemented, Sylow
347C2×#41—472no—
348C2×#41—472no—
349C2×#41—941no—
350C2×#41—941no—
351C2×#41—941no—
352C2×#41—941no—
353C2×#41—941no—
354C2×#41—941no—
355C2×#41—941no—
356C2×#41—941no—
357C2×#41—941no—
358C2×#41—941no—
359C22×Q8—471no—
360C22×D4—471no—
361C22×D4—941no—
362C23×C4—941no—
363C23×C4C22×D4711yescharacteristic
364C2×M16—472no—
365C2×M16—941no—
366C2×M16—941no—
367C2×M16—941no—
368C2×M16—941no—
369C2×M16—941no—
370C22×C8—21no—
371C22×C8—21no—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8—941no—
375C22×C8C4×D4712yes—
376C22×C8D18812yes—
377C22×C8C22⋊D4711yescharacteristic
378C22×C8C22⋊D4711yescharacteristic
379#117—21no—
380#117—21no—
381#117—21no—
382#117—21no—
383#117—21no—
384#117—21no—
385#117—941no—
386#117—941no—
387#117—941no—
388#117—941no—
389#117—941no—
390#117—941no—
391#117—941no—
392#117—941no—
393#117C22⋊D4712yes—
394#117C22⋊D4712yes—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—472no—
398C2×C4⋊C4—941no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—472no—
402C2×C22⋊C4—941no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—941no—
406C2×C42—941no—
407#107—24no—
408#106—24no—
409#104—948no—
410#103—942no—
411#103—942no—
412#102—942no—
413#102—942no—
414#99—948no—
415C24—941no—
416C24D4×D4711yescharacteristic
417#41—942no—
418#41—942no—
419#41—942no—
420#41—942no—
421#41—942no—
422#41—942no—
423#41—942no—
424#41—942no—
425#41—1881no—
426#41—1881no—
427#41—1881no—
428#41—1881no—
429#41—1881no—
430#41—1881no—
431#41—1881no—
432#41—1881no—
433C2×Q8—472no—
434C2×Q8—941no—
435C2×Q8—941no—
436C2×Q8—941no—
437C2×Q8—941no—
438C2×Q8—941no—
439C2×D4—472no—
440C2×D4—942no—
441C2×D4—942no—
442C2×D4—941no—
443C2×D4—941no—
444C2×D4—941no—
445C2×D4—941no—
446C2×D4—941no—
447C2×D4—1881no—
448C2×D4—1881no—
449C2×D4—1881no—
450C2×D4—1881no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—941no—
454C22×C4—942no—
455C22×C4—942no—
456C22×C4—942no—
457C22×C4—942no—
458C22×C4—1881no—
459C22×C4—1881no—
460C22×C4—1881no—
461C22×C4—1881no—
462C22×C4C2×C4×D4711yescharacteristic
463C22×C4C2×D18811yescharacteristic
464C22×C4#1062535011yescharacteristic
465C22×C4#1062535011yescharacteristic
466C22×C4D4×D4711yescharacteristic
467C22×C4D4×D4711yescharacteristic
468C22×C4#1062535211yescharacteristic
469C22×C4Q8×D4711yescharacteristic
470C22×C4#1062535411yescharacteristic
471C22×C4#1062535411yescharacteristic
472C22×C4#1062535411yescharacteristic
473C22×C4C2×C22⋊D4711yescharacteristic
474C22×C4C2×C22⋊D4711yescharacteristic
475C22×C4C2×C22⋊D4711yescharacteristic
476M16—942no—
477M16—942no—
478M16—1881no—
479M16—1881no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—942no—
489C2×C8—1881no—
490C2×C8—1881no—
491C2×C8(C2×D47)⋊C412yes—
492C2×C8(C2×D47)⋊C412yes—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C4⋊C4—942no—
498C4⋊C4—942no—
499C4⋊C4—1881no—
500C4⋊C4—1881no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C22⋊C4—942no—
506C22⋊C4—942no—
507C22⋊C4—1881no—
508C22⋊C4—1881no—
509C42—22no—
510C42—22no—
511C42—41no—
512C42—41no—
513C42—1881no—
514C42—1881no—
515C42—1881no—
516C42—1881no—
517C23—42no—
518C23—942no—
519C23—3762no—
520C23—1881no—
521C23—1881no—
522C23#1309398611yescharacteristic
523C23#1309399211yescharacteristic
524C23#1309399611yescharacteristic
525C23#1309399911yescharacteristic
526C23#1309400211yescharacteristic
527C23#1309400911yescharacteristic
528C23#1309402011yescharacteristic
529Q8—942no—
530Q8—942no—
531Q8—1881no—
532Q8—1881no—
533D4—942no—
534D4—942no—
535D4—1882no—
536D4—1882no—
537D4—1882no—
538D4—1882no—
539D4—1881no—
540D4—1881no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—82no—
544C2×C4—82no—
545C2×C4—942no—
546C2×C4—3762no—
547C2×C4—1884no—
548C2×C4—1882no—
549C2×C4—1882no—
550C2×C4—1881no—
551C2×C4—1881no—
552C2×C4—1882no—
553C2×C4—1882no—
554C2×C4—1882no—
555C2×C4—1882no—
556C2×C4C2×(C2×D47)⋊C411yescharacteristic
557C2×C4C4⋊C4×D4711yescharacteristic
558C2×C4#1309398211yescharacteristic
559C2×C4C4×C22⋊D4711yescharacteristic
560C2×C4C4×C22⋊D4711yescharacteristic
561C2×C4#1309398611yescharacteristic
562C2×C4#1309399211yescharacteristic
563C2×C4#1309399311yescharacteristic
564C2×C4#1309399511yescharacteristic
565C2×C4#1309399611yescharacteristic
566C2×C4#1309399811yescharacteristic
567C2×C4#1309399811yescharacteristic
568C2×C4#1309399911yescharacteristic
569C2×C4#1309399911yescharacteristic
570C2×C4#1309400011yescharacteristic
571C2×C4#1309400011yescharacteristic
572C2×C4#1309400011yescharacteristic
573C2×C4#1309400211yescharacteristic
574C2×C4#1309400411yescharacteristic
575C2×C4#1309400711yescharacteristic
576C2×C4#1309400911yescharacteristic
577C2×C4#1309400911yescharacteristic
578C2×C4#1309400911yescharacteristic
579C2×C4#1309401311yescharacteristic
580C2×C4#1309401311yescharacteristic
581C2×C4#1309401311yescharacteristic
582C2×C4#1309401911yescharacteristic
583C2×C4#1309401911yescharacteristic
584C8—22no—
585C8—22no—
586C8—1882no—
587C22—22no—
588C22—22no—
589C22—22no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—3762no—
595C22—3762no—
596C22—3762no—
597C22—1882no—
598C22#1568899411yescharacteristic
599C22#1568901311yescharacteristic
600C22#1568902411yescharacteristic
601C22#1568903111yescharacteristic
602C22#1568904011yescharacteristic
603C22#1568904511yescharacteristic
604C22#1568905811yescharacteristic
605C4—82no—
606C4—82no—
607C4—3762no—
608C4—3762no—
609C4—1882no—
610C4#1568898011yescharacteristic
611C4#1568899411yescharacteristic
612C4#1568900211yescharacteristic
613C4#1568901311yescharacteristic
614C4#1568903411yescharacteristic
615C4#1568904011yescharacteristic
616C4#1568904511yescharacteristic
617C4#1568904911yescharacteristic
618C2—21no—
619C2—21no—
620C2—21no—
621C2—21no—
622C2—21no—
623C2—21no—
624C2—3762no—
625C2#2024163011yescharacteristic
626C2#2024428412yes—
subgroupG/H
centerC2×C4#13093999
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC2×C47×#427C2
socleC22×C47#390
prime radicalC22×#10625350C22
cosocleC23×C4×C47C23
hypercenterC2×#427D47
hypocenterC47#11126
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#427

Complements

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

NH ≅ G/Ntype
4. #20243120C2semidirect
5. #20243098C2semidirect
6. #20243084C2semidirect
7. C2×C47×#427C2semidirect
18. C2×#13093949C4semidirect
19. C2×#13093946C4semidirect
305. C2×#427D47semidirect
346. C47#11126semidirect

Maximal subgroups

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

subgroupindex
C2×#156891412
C2×#156891202
C2×#156890962
#202431202
#202430982
#202430842
C2×C47×#4272
#1112647