Finite Group Databasebeta

← #26220648

Subgroups — #26220648

Order 12032.

814 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689221C211yesmaximal, characteristic
2#20246032C211yesmaximal, characteristic
3#20244272C211yesmaximal, characteristic
4#20244245C211yesmaximal, characteristic
5#20244123C211yesmaximal, characteristic, complemented
6#20244118C211yesmaximal, characteristic, complemented
7#20244084C211yesmaximal, characteristic
8#20244081C211yesmaximal, characteristic, complemented
9#20244070C211yesmaximal, characteristic
10#20244067C211yesmaximal, characteristic, complemented
11#20243286C211yesmaximal, characteristic, complemented
12C4×#13093948C211yesmaximal, characteristic, complemented
13C4×#13093944C211yesmaximal, characteristic
14#20243075C211yesmaximal, characteristic, complemented
15C47×#2320C211yesmaximal, characteristic, complemented
16C22×#10625336C2211yescharacteristic
17C2×C4×D188C2211yescharacteristic
18#15689221C418yescomplemented
19C2×#13093957C2211yescharacteristic
20C2×#13093957C2211yescharacteristic
21C2×#13093955C2211yescharacteristic
22C2×#13093948C2211yescharacteristic
23C2×#13093948C2211yescharacteristic
24C2×#13093948C2211yescharacteristic
25C2×#13093944C2211yescharacteristic
26C2×#13093944C2211yescharacteristic
27C2×#13093944C2211yescharacteristic
28C2×#13093935C2211yescharacteristic
29C2×#13093935C2211yescharacteristic
30C2×#13093935C2211yescharacteristic
31C2×C4×C47⋊C8C2211yescharacteristic
32C2×C4×C47⋊C8C2211yescharacteristic
33C2×C4×C47⋊C8C2211yescharacteristic
34#15689025C2211yescharacteristic
35#15689025C2211yescharacteristic
36#15689021C2211yescharacteristic
37#15689021C2211yescharacteristic
38#15689012—21no—
39#15689012—21no—
40#15688985—21no—
41#15688982—21no—
42C4×C4⋊Dic47C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49C2×C4×Q8×C47C2211yescharacteristic
50C47×#391C2211yescharacteristic
51C47×#391C2211yescharacteristic
52C47×#389C2211yescharacteristic
53C47×#389C2211yescharacteristic
54C47×#387—21no—
55C47×#387—21no—
56C47×#383—21no—
57C47×#382—21no—
58C4×C4⋊C4×C47C2211yescharacteristic
59C47×#376C2211yescharacteristic
60C22×D188C2311yescharacteristic
61C22×C4×D47—21no—
62C2×#10625336—22no—
63C2×#10625336—22no—
64C2×#10625336C2×C414yes—
65C22×C47⋊C8C2311yescharacteristic
66C22×C47⋊C8C2311yescharacteristic
67C22×C47⋊C8C2311yescharacteristic
68C22×C47⋊C8C2311yescharacteristic
69C4×D188—22no—
70C4×D188C2×C414yes—
71C2×C4⋊Dic47C2311yescharacteristic
72C2×C4⋊Dic47C2311yescharacteristic
73C2×C4⋊Dic47C2311yescharacteristic
74C2×Dic47⋊C4—21no—
75C2×Dic47⋊C4—21no—
76C2×(C2×D47)⋊C4—21no—
77C2×(C2×D47)⋊C4—21no—
78C2×(C2×D47)⋊C4—21no—
79C2×(C2×D47)⋊C4—21no—
80C2×(C2×D47)⋊C4—21no—
81C2×C4×Dic47—21no—
82#13093957—22no—
83#13093957C2×C414yes—
84#13093955—22no—
85#13093948—22no—
86#13093948—22no—
87#13093948C2×C414yes—
88#13093944—22no—
89#13093944—22no—
90#13093944C2×C414yes—
91#13093935—22no—
92#13093935—22no—
93#13093935C2×C414yes—
94C4×C47⋊C8—22no—
95C4×C47⋊C8—22no—
96C4×C47⋊C8—22no—
97C47⋊#95—21no—
98C47⋊#95—21no—
99C47⋊#95—21no—
100C22×Q8×C47C2311yescharacteristic
101C4×Q8×C47—22no—
102C4×Q8×C47C2×C414yes—
103C2×C4⋊C4×C47—21no—
104C2×C4⋊C4×C47—21no—
105C2×C4⋊C4×C47—21no—
106C2×C4⋊C4×C47C2311yescharacteristic
107C2×C4⋊C4×C47C2311yescharacteristic
108C2×C4⋊C4×C47C2311yescharacteristic
109C2×C42×C47—21no—
110C2×C42×C47—21no—
111C2×C42×C47C2311yescharacteristic
112C2×C42×C47C2311yescharacteristic
113C2×C42×C47C2311yescharacteristic
114#95×C47—21no—
115#95×C47—21no—
116#95×C47—21no—
117#95×C47—21no—
118#95×C47—21no—
119#95×C47—21no—
120#95×C47—21no—
121#95×C47D411yescharacteristic
122#95×C47D411yescharacteristic
123#95×C47D411yescharacteristic
124#95×C47D411yescharacteristic
125C23×D47—21no—
126C2×Q8×C47—21no—
127C2×Q8×C47—21no—
128C2×Q8×C47—21no—
129C2×Q8×C47—21no—
130C2×Q8×C47—21no—
131C2×Q8×C47C22×C412yes—
132C22×C4×C47—21no—
133C22×C4×C47—21no—
134C22×C4×C47—21no—
135C22×C4×C47—21no—
136C22×C4×C47C2×D411yescharacteristic
137C22×C4×C47C2×D411yescharacteristic
138C22×C4×C47C2×D411yescharacteristic
139C22×C4×C47C2×D411yescharacteristic
140C22×C4×C47C2×D411yescharacteristic
141C22×C4×C47C2×D411yescharacteristic
142C22×C4×C47C2411yescharacteristic
143C22×Dic47—21no—
144C22×Dic47—21no—
145C22×Dic47—21no—
146C2×D188—21no—
147C2×D188—21no—
148C2×D188—21no—
149C2×D188—21no—
150C2×D188—21no—
151C2×D188C22×C412yes—
152C2×C4×D47—24no—
153C2×C4×D47—81no—
154C2×C4×D47—81no—
155C4⋊C4×C47—24no—
156C4⋊C4×C47—21no—
157C4⋊C4×C47—21no—
158C4⋊C4×C47—21no—
159C4⋊C4×C47—21no—
160C4⋊C4×C47—21no—
161C4⋊C4×C47—81no—
162C4⋊C4×C47—81no—
163C4⋊C4×C47C22×C412yes—
164C42×C47—24no—
165C42×C47—21no—
166C42×C47—21no—
167C42×C47—21no—
168C42×C47—21no—
169C42×C47—81no—
170C42×C47C22×C412yes—
171C42×C47#4112yes—
172#10625336—28no—
173(C2×D47)⋊C4—24no—
174(C2×D47)⋊C4—81no—
175(C2×D47)⋊C4—81no—
176(C2×D47)⋊C4—81no—
177(C2×D47)⋊C4—81no—
178C4⋊Dic47—21no—
179C4⋊Dic47—21no—
180C4⋊Dic47—21no—
181C4⋊Dic47—21no—
182C4⋊Dic47—21no—
183C4⋊Dic47C22×C412yes—
184Dic47⋊C4—81no—
185Dic47⋊C4—81no—
186C4×Dic47—81no—
187C2×C47⋊C8—21no—
188C2×C47⋊C8—21no—
189C2×C47⋊C8—21no—
190C2×C47⋊C8—21no—
191C2×C47⋊C8—21no—
192C2×C47⋊C8—21no—
193C2×C47⋊C8C22×C412yes—
194C2×C47⋊C8C22×C412yes—
195C2×C47⋊C8#4112yes—
196C2×C47⋊C8#4112yes—
197C2×C47⋊C8#4112yes—
198C2×C47⋊C8#4112yes—
199C23×C47C22×D411yescharacteristic
200C22×D47—22no—
201C22×D47—41no—
202C22×D47—41no—
203C22×D47—41no—
204C22×D47—41no—
205C22×D47—41no—
206C22×D47—41no—
207Q8×C47—22no—
208Q8×C47—22no—
209Q8×C47—41no—
210Q8×C47—41no—
211C2×C4×C47—21no—
212C2×C4×C47—21no—
213C2×C4×C47—21no—
214C2×C4×C47—21no—
215C2×C4×C47—22no—
216C2×C4×C47—22no—
217C2×C4×C47—21no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—21no—
228C2×C4×C47—21no—
229C2×C4×C47—41no—
230C2×C4×C47—41no—
231C2×C4×C47—41no—
232C2×C4×C47—41no—
233C2×C4×C47—41no—
234C2×C4×C47—41no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47—41no—
238C2×C4×C47—41no—
239C2×C4×C47C4×D412yes—
240C2×C4×C47C4×D412yes—
241C2×C4×C47C23×C411yescharacteristic
242C2×C4×C47C2×#4111yescharacteristic
243C2×C4×C47C2×#4111yescharacteristic
244C2×C4×C47C2×#4111yescharacteristic
245C2×C4×C47C2×#4111yescharacteristic
246C2×C4×C47C2×#4111yescharacteristic
247C2×Dic47—22no—
248C2×Dic47—41no—
249C2×Dic47—41no—
250C2×Dic47—41no—
251C2×Dic47—41no—
252C2×Dic47—41no—
253C2×Dic47—41no—
254C2×Dic47—41no—
255C2×Dic47—41no—
256D188—22no—
257D188—22no—
258D188—41no—
259D188—41no—
260C4×D47—84no—
261C47⋊C8—22no—
262C47⋊C8—22no—
263C47⋊C8—22no—
264C47⋊C8#11714yes—
265#21291—471nomaximal, Sylow
266C22×C47C2×C4×D411yescharacteristic
267C22×C47#53211yescharacteristic
268C22×C47#53211yescharacteristic
269C22×C47#57611yescharacteristic
270C22×C47#57711yescharacteristic
271C22×C47#57711yescharacteristic
272C22×C47#57811yescharacteristic
273C2×D47—42no—
274C2×D47—42no—
275C2×D47—42no—
276C2×D47—81no—
277C2×D47—81no—
278C2×D47—81no—
279C2×D47—81no—
280C4×C47—22no—
281C4×C47—22no—
282C4×C47—41no—
283C4×C47—41no—
284C4×C47—41no—
285C4×C47—41no—
286C4×C47—42no—
287C4×C47—42no—
288C4×C47—81no—
289C4×C47—81no—
290C4×C47C2×#11711yescharacteristic
291C4×C47C4×#4111yescharacteristic
292C4×C47#52911yescharacteristic
293C4×C47#52911yescharacteristic
294Dic47—42no—
295Dic47—81no—
296Dic47—81no—
297C2×#440—471no—
298#2320D4711yescharacteristic, complemented
299#2319—471no—
300#1973—471no—
301#1968—471no—
302#1943—471no—
303#1942—471no—
304#1936—471no—
305#1935—471no—
306#1934—471no—
307#1933—471no—
308#1776—471no—
309C4×#103—471no—
310C4×#102—471no—
311#1726—471no—
312C2×C47#229311yescharacteristic
313C2×C47#294611yescharacteristic
314C2×C47#294711yescharacteristic
315C2×C47#317411yescharacteristic
316C2×C47#317511yescharacteristic
317C2×C47#317811yescharacteristic
318C2×C47#317911yescharacteristic
319D47—82no—
320C22×SD16—471no—
321C2×C4×Q8C2×D4711yescharacteristic
322C2×C4×D4—471no—
323#440—478no—
324C2×#107—471no—
325C2×#107—471no—
326C2×#106—471no—
327C2×#103—471no—
328C2×#103—471no—
329C2×#103—471no—
330C2×#102—471no—
331C2×#102—471no—
332C2×#102—471no—
333C2×#97—471no—
334C2×#97—471no—
335C2×#97—471no—
336C2×C4×C8—471no—
337C2×C4×C8—471no—
338C2×C4×C8—471no—
339#391C2×D4711yescharacteristic
340#391C2×D4711yescharacteristic
341#390—471no—
342#390—471no—
343#389—471no—
344#389—471no—
345#389C2×D4711yescharacteristic
346#389C2×D4711yescharacteristic
347#388—941no—
348#388—941no—
349#387—21no—
350#387—21no—
351#383—21no—
352#382—21no—
353#381—941no—
354#380—941no—
355C4×C4⋊C4—471no—
356C4×C4⋊C4C2×D4711yescharacteristic
357#376C2×D4711yescharacteristic
358#340—471no—
359#340—471no—
360#340—471no—
361#340—471no—
362#340—471no—
363#340—471no—
364C47#2129111yescharacteristic, complemented, Sylow
365C22×Q8C22×D4711yescharacteristic
366C22×D4—471no—
367C23×C4—941no—
368C2×SD16—474no—
369C2×SD16—942no—
370C2×SD16—942no—
371C22×C8—471no—
372C22×C8—471no—
373C22×C8—471no—
374C22×C8—471no—
375C4×Q8—22no—
376C4×Q8C4×D4714yes—
377C4×D4—474no—
378C4×D4—942no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—471no—
383C2×C4⋊C4—471no—
384C2×C4⋊C4—471no—
385C2×C4⋊C4—941no—
386C2×C4⋊C4—941no—
387C2×C4⋊C4C22×D4711yescharacteristic
388C2×C4⋊C4C22×D4711yescharacteristic
389C2×C4⋊C4C22×D4711yescharacteristic
390C2×C22⋊C4—941no—
391C2×C22⋊C4—941no—
392C2×C22⋊C4—941no—
393C2×C22⋊C4—941no—
394C2×C22⋊C4—941no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—941no—
398C2×C42C22×D4711yescharacteristic
399C2×C42C22×D4711yescharacteristic
400C2×C42C22×D4711yescharacteristic
401#107—474no—
402#107—942no—
403#106—942no—
404#103—474no—
405#103—942no—
406#103—942no—
407#102—474no—
408#102—942no—
409#102—942no—
410#97—474no—
411#97—942no—
412#97—942no—
413C4×C8—942no—
414C4×C8—942no—
415C4×C8—942no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—941no—
424#95—941no—
425#95—941no—
426#95C22⋊D4711yescharacteristic
427#95C22⋊D4711yescharacteristic
428#95C22⋊D4711yescharacteristic
429#95C22⋊D4711yescharacteristic
430C24—941no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8C2×C4×D4712yes—
437C2×D4—472no—
438C2×D4—941no—
439C2×D4—941no—
440C2×D4—941no—
441C2×D4—941no—
442C2×D4—941no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—941no—
448C22×C4—944no—
449C22×C4—941no—
450C22×C4—941no—
451C22×C4—3761no—
452C22×C4—3761no—
453C22×C4C2×C22⋊D4711yescharacteristic
454C22×C4C2×C22⋊D4711yescharacteristic
455C22×C4C2×C22⋊D4711yescharacteristic
456C22×C4C2×C22⋊D4711yescharacteristic
457C22×C4C2×C22⋊D4711yescharacteristic
458C22×C4C2×C22⋊D4711yescharacteristic
459C22×C4C23×D4711yescharacteristic
460SD16—948no—
461C2×C8—472no—
462C2×C8—472no—
463C2×C8—472no—
464C2×C8—472no—
465C2×C8—472no—
466C2×C8—472no—
467C2×C8—941no—
468C2×C8—941no—
469C2×C8—941no—
470C2×C8—941no—
471C2×C8—941no—
472C2×C8—941no—
473C4⋊C4—24no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—81no—
480C4⋊C4—81no—
481C4⋊C4—472no—
482C4⋊C4—941no—
483C4⋊C4—941no—
484C4⋊C4—941no—
485C4⋊C4—941no—
486C4⋊C4—941no—
487C4⋊C4—3761no—
488C4⋊C4—3761no—
489C4⋊C4C2×C4×D4712yes—
490C22⋊C4—944no—
491C22⋊C4—3761no—
492C22⋊C4—3761no—
493C22⋊C4—3761no—
494C22⋊C4—3761no—
495C42—24no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—21no—
500C42—81no—
501C42—3761no—
502C42C2×C4×D4712yes—
503C42#1062535012yes—
504C23—942no—
505C23—1881no—
506C23—1881no—
507C23—1881no—
508C23—1881no—
509C23—1881no—
510C23—1881no—
511C23C22×C22⋊D4711yescharacteristic
512Q8—22no—
513Q8—22no—
514Q8—41no—
515Q8—41no—
516D4—942no—
517D4—942no—
518D4—1881no—
519D4—1881no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—942no—
549C2×C4—3764no—
550C2×C4—1881no—
551C2×C4—1881no—
552C2×C4—1881no—
553C2×C4—1881no—
554C2×C4—1881no—
555C2×C4—1881no—
556C2×C4—1881no—
557C2×C4—1881no—
558C2×C4C4×C22⋊D4712yes—
559C2×C4C4×C22⋊D4712yes—
560C2×C4C22×C4×D4711yescharacteristic
561C2×C4#41×D4711yescharacteristic
562C2×C4#41×D4711yescharacteristic
563C2×C4#41×D4711yescharacteristic
564C2×C4#41×D4711yescharacteristic
565C2×C4C2×#1062535011yescharacteristic
566C8—474no—
567C8—942no—
568C8—942no—
569C8—942no—
570C22—3761no—
571C22—3761no—
572C22—3761no—
573C22—3761no—
574C22—1882no—
575C22—1882no—
576C22—1882no—
577C22C2×C4×C22⋊D4711yescharacteristic
578C22#1568966911yescharacteristic
579C22#1568966911yescharacteristic
580C22#1568992611yescharacteristic
581C22#1568993111yescharacteristic
582C22#1568993111yescharacteristic
583C22#1568993811yescharacteristic
584C4—22no—
585C4—22no—
586C4—42no—
587C4—41no—
588C4—41no—
589C4—42no—
590C4—41no—
591C4—41no—
592C4—81no—
593C4—81no—
594C4—3761no—
595C4—3761no—
596C4—1882no—
597C4#117×D4711yescharacteristic
598C4#1568959111yescharacteristic
599C4#1568965111yescharacteristic
600C4#1568965111yescharacteristic
601C2—3762no—
602C2#2024584711yescharacteristic
603C2#2025221611yescharacteristic
604C2#2025223111yescharacteristic
605C2#2025401711yescharacteristic
606C2#2025402111yescharacteristic
607C2#2025405811yescharacteristic
608C2#2025406511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2320C2
socleC23×C47C22×D4
prime radicalC22×D188C23
cosocleC22×C4×C47C24
hypercenter#2320D47
hypocenterC47#21291
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ #376 ◁ #2320

Complements

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

NH ≅ G/Ntype
5. #20244123C2semidirect
6. #20244118C2semidirect
8. #20244081C2semidirect
10. #20244067C2semidirect
11. #20243286C2semidirect
12. C4×#13093948C2semidirect
14. #20243075C2semidirect
15. C47×#2320C2semidirect
18. #15689221C4semidirect
298. #2320D47semidirect
364. C47#21291semidirect

Maximal subgroups

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

subgroupindex
C2×#156892212
#202460322
#202442722
#202442452
#202441232
#202441182
#202440842
#202440812
#202440702
#202440672
#202432862
C4×#130939482
C4×#130939442
#202430752
C47×#23202
#2129147