Finite Group Databasebeta

← #26316814

Subgroups — #26316814

Order 12032.

706 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
1#20249363C211yesmaximal, characteristic, complemented
2#20244783C211yesmaximal, characteristic, complemented
3#20244776C211yesmaximal, characteristic
4#20244769C211yesmaximal, characteristic, complemented
5#20244762C211yesmaximal, characteristic
6#20244205C211yesmaximal, characteristic
7#20244200C211yesmaximal, characteristic
8#20243656C211yesmaximal, characteristic, complemented
9#20243649C211yesmaximal, characteristic
10#20243642C211yesmaximal, characteristic, complemented
11#20243635C211yesmaximal, characteristic
12#20243554C211yesmaximal, characteristic, complemented
13#20243515C211yesmaximal, characteristic, complemented
14#20243245C211yesmaximal, characteristic, complemented
15C47×#2326C211yesmaximal, characteristic
16C2×#13093957C2211yescharacteristic
17C2×#13093957C2211yescharacteristic
18C2×#13093955C2211yescharacteristic
19C2×#13093955C2211yescharacteristic
20C2×C4⋊(C47⋊C8)C2211yescharacteristic
21C2×C4⋊(C47⋊C8)C2211yescharacteristic
22C2×#13093948C2211yescharacteristic
23C2×#13093948C2211yescharacteristic
24C2×#13093948C2211yescharacteristic
25C2×#13093948C2211yescharacteristic
26C2×#13093945C2211yescharacteristic
27C2×#13093945C2211yescharacteristic
28C2×#13093945C2211yescharacteristic
29C2×#13093945C2211yescharacteristic
30C2×#13093935C2211yescharacteristic
31C2×C4×C47⋊C8C2211yescharacteristic
32#15689065—21no—
33#15689065—21no—
34#15689057—21no—
35#15689057—21no—
36#15689021C2211yescharacteristic
37#15689021C2211yescharacteristic
38#15689021C2211yescharacteristic
39#15689021C2211yescharacteristic
40#15688993C2211yescharacteristic
41#15688989C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688878C2211yescharacteristic
47#15688878C2211yescharacteristic
48C2×#124×C47C2211yescharacteristic
49C2×C4×Q8×C47C2211yescharacteristic
50C2×C4×D4×C47C2211yescharacteristic
51C47×#391C2211yescharacteristic
52C47×#390C2211yescharacteristic
53C47×#388—21no—
54C47×#388—21no—
55C47×#385—21no—
56C47×#385—21no—
57C47×#384C2211yescharacteristic
58C47×#376C2211yescharacteristic
59C22×C47⋊C8C2311yescharacteristic
60C22×C47⋊C8C2311yescharacteristic
61C22×C47⋊C8C2311yescharacteristic
62C22×C47⋊C8C2311yescharacteristic
63C2×C4⋊Dic47—21no—
64C2×C4⋊Dic47—21no—
65C2×C4⋊Dic47C2311yescharacteristic
66C2×C4⋊Dic47C2311yescharacteristic
67C2×C4⋊Dic47C2311yescharacteristic
68C2×C4⋊Dic47C2311yescharacteristic
69C2×Dic47⋊C4—21no—
70C2×Dic47⋊C4—21no—
71C2×Dic47⋊C4—21no—
72C2×Dic47⋊C4—21no—
73#13093957—41no—
74#13093957—41no—
75#13093955—41no—
76#13093955—41no—
77C4⋊(C47⋊C8)—22no—
78C4⋊(C47⋊C8)—22no—
79#13093948—22no—
80#13093948—22no—
81#13093948—41no—
82#13093948—41no—
83#13093945—22no—
84#13093945—22no—
85#13093945—41no—
86#13093945—41no—
87#13093935—22no—
88C4×C47⋊C8—22no—
89C47⋊#95—21no—
90C47⋊#95—21no—
91C47⋊#95—21no—
92C47⋊#95—21no—
93C47⋊#95—21no—
94C47⋊#95—21no—
95C22×Q8×C47C2311yescharacteristic
96C22×D4×C47C2311yescharacteristic
97C23×C4×C47—21no—
98#124×C47—22no—
99#124×C47Q814yes—
100C4×Q8×C47—41no—
101C4×Q8×C47—41no—
102C4×D4×C47—41no—
103C4×D4×C47—41no—
104C2×C4⋊C4×C47—21no—
105C2×C4⋊C4×C47—21no—
106C2×C4⋊C4×C47—21no—
107C2×C4⋊C4×C47C2311yescharacteristic
108C2×C4⋊C4×C47C2311yescharacteristic
109C2×C22⋊C4×C47—21no—
110C2×C22⋊C4×C47—21no—
111C2×C22⋊C4×C47—21no—
112C2×C22⋊C4×C47—21no—
113C2×C22⋊C4×C47—21no—
114C2×C42×C47—21no—
115C2×C42×C47C2311yescharacteristic
116C2×C42×C47C2311yescharacteristic
117C2×C42×C47C2311yescharacteristic
118#95×C47—21no—
119#95×C47—21no—
120#95×C47D411yescharacteristic
121#95×C47D411yescharacteristic
122#95×C47D411yescharacteristic
123#95×C47D411yescharacteristic
124C24×C47—21no—
125C2×Q8×C47—21no—
126C2×Q8×C47—21no—
127C2×Q8×C47—21no—
128C2×Q8×C47—21no—
129C2×Q8×C47—21no—
130C2×Q8×C47C2×Q812yes—
131C2×D4×C47—21no—
132C2×D4×C47—21no—
133C2×D4×C47—21no—
134C2×D4×C47—21no—
135C2×D4×C47—21no—
136C2×D4×C47C2×Q812yes—
137C22×C4×C47—21no—
138C22×C4×C47—21no—
139C22×C4×C47—21no—
140C22×C4×C47—42no—
141C22×C4×C47—81no—
142C22×C4×C47—81no—
143C22×C4×C47C2×D411yescharacteristic
144C22×C4×C47C2×D411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47C2×D411yescharacteristic
147C22×C4×C47C2×D411yescharacteristic
148C22×C4×C47C2×D411yescharacteristic
149C22×C4×C47C2411yescharacteristic
150C22×Dic47—21no—
151C22×Dic47—21no—
152C22×Dic47—21no—
153C22×Dic47—21no—
154C4⋊C4×C47—21no—
155C4⋊C4×C47—21no—
156C4⋊C4×C47—21no—
157C4⋊C4×C47—21no—
158C4⋊C4×C47—42no—
159C4⋊C4×C47—81no—
160C4⋊C4×C47—81no—
161C22⋊C4×C47—24no—
162C22⋊C4×C47—24no—
163C22⋊C4×C47—42no—
164C22⋊C4×C47—81no—
165C22⋊C4×C47—81no—
166C42×C47—21no—
167C42×C47—21no—
168C42×C47—21no—
169C42×C47—21no—
170C42×C47—42no—
171C42×C47C2×Q812yes—
172C42×C47#4112yes—
173C4⋊Dic47—21no—
174C4⋊Dic47—21no—
175C4⋊Dic47—21no—
176C4⋊Dic47—21no—
177C4⋊Dic47—21no—
178C4⋊Dic47—21no—
179C4⋊Dic47—21no—
180C4⋊Dic47—21no—
181C4⋊Dic47—81no—
182C4⋊Dic47—81no—
183Dic47⋊C4—81no—
184Dic47⋊C4—81no—
185Dic47⋊C4—81no—
186Dic47⋊C4—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⋊C8—21no—
194C2×C47⋊C8—21no—
195C2×C47⋊C8—21no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8#4112yes—
198C2×C47⋊C8#4112yes—
199C23×C47—22no—
200C23×C47—41no—
201C23×C47—41no—
202C23×C47—41no—
203C23×C47—41no—
204C23×C47—41no—
205C23×C47—41no—
206C23×C47C22×D411yescharacteristic
207Q8×C47—22no—
208Q8×C47—22no—
209Q8×C47—41no—
210Q8×C47—41no—
211D4×C47—22no—
212D4×C47—22no—
213D4×C47—41no—
214D4×C47—41no—
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—21no—
219C2×C4×C47—22no—
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—21no—
230C2×C4×C47—21no—
231C2×C4×C47—21no—
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×C47—41no—
240C2×C4×C47—84no—
241C2×C4×C47C22⋊Q812yes—
242C2×C4×C47C22⋊Q812yes—
243C2×C4×C47C22×Q811yescharacteristic
244C2×C4×C47C2×#4111yescharacteristic
245C2×C4×C47C2×#4111yescharacteristic
246C2×C4×C47C2×#4111yescharacteristic
247C2×C4×C47H(5,𝔽2)11yescharacteristic
248C2×C4×C47H(5,𝔽2)11yescharacteristic
249C2×Dic47—41no—
250C2×Dic47—41no—
251C2×Dic47—41no—
252C2×Dic47—41no—
253C2×Dic47—41no—
254C2×Dic47—41no—
255C2×Dic47—41no—
256C2×Dic47—41no—
257C2×Dic47—41no—
258C2×Dic47—41no—
259C2×Dic47—41no—
260C2×Dic47—41no—
261C47⋊C8—22no—
262C47⋊C8—22no—
263C47⋊C8—41no—
264C47⋊C8—41no—
265#29203—471nomaximal, Sylow
266C22×C47—42no—
267C22×C47—42no—
268C22×C47—42no—
269C22×C47—81no—
270C22×C47—81no—
271C22×C47—81no—
272C22×C47—81no—
273C22×C47C2×C22⋊Q811yescharacteristic
274C22×C47#53211yescharacteristic
275C22×C47#53511yescharacteristic
276C22×C47#57611yescharacteristic
277C22×C47#57711yescharacteristic
278C22×C47#57711yescharacteristic
279C22×C47#57811yescharacteristic
280C4×C47—22no—
281C4×C47—22no—
282C4×C47—42no—
283C4×C47—41no—
284C4×C47—41no—
285C4×C47—41no—
286C4×C47—41no—
287C4×C47—81no—
288C4×C47—81no—
289C4×C47#55311yescharacteristic
290C4×C47#55311yescharacteristic
291C4×C47#55411yescharacteristic
292C4×C47#55411yescharacteristic
293Dic47—81no—
294Dic47—81no—
295Dic47—81no—
296Dic47—81no—
297#2647—471no—
298#2326D4711yescharacteristic
299#2068—471no—
300#2067—471no—
301#2066—471no—
302#2065—471no—
303#1959—471no—
304#1958—471no—
305#1865—471no—
306#1864—471no—
307#1863—471no—
308#1862—471no—
309#1847—471no—
310#1834—471no—
311#1768—471no—
312C2×C47—82no—
313C2×C47#256611yescharacteristic
314C2×C47#308311yescharacteristic
315C2×C47#308411yescharacteristic
316C2×C47#317811yescharacteristic
317C2×C47#317911yescharacteristic
318C2×C47#322411yescharacteristic
319C2×C47#322511yescharacteristic
320C2×#124C2×D4711yescharacteristic
321C2×C4×Q8C2×D4711yescharacteristic
322C2×C4×D4C2×D4711yescharacteristic
323C2×#107—471no—
324C2×#107—471no—
325C2×#106—471no—
326C2×#106—471no—
327C2×C4⋊C8—471no—
328C2×C4⋊C8—471no—
329C2×#103—471no—
330C2×#103—471no—
331C2×#103—471no—
332C2×#103—471no—
333C2×#102—471no—
334C2×#102—471no—
335C2×#102—471no—
336C2×#102—471no—
337C2×#97—471no—
338C2×C4×C8—471no—
339#400—941no—
340#400—941no—
341#398—941no—
342#398—941no—
343#391C2×D4711yescharacteristic
344#390C2×D4711yescharacteristic
345#389—471no—
346#389—471no—
347#389—471no—
348#389—471no—
349#388—21no—
350#388—21no—
351#385—21no—
352#385—21no—
353#384—471no—
354#384C2×D4711yescharacteristic
355#382—471no—
356#376C2×D4711yescharacteristic
357#340—471no—
358#340—471no—
359#340—471no—
360#340—471no—
361#336—471no—
362#336—471no—
363C47#2920311yescharacteristic, complemented, Sylow
364C22×Q8C22×D4711yescharacteristic
365C22×D4C22×D4711yescharacteristic
366C23×C4—21no—
367C22×C8—471no—
368C22×C8—471no—
369C22×C8—471no—
370C22×C8—471no—
371#124—22no—
372#124Dic9414yes—
373C4×Q8—41no—
374C4×Q8—41no—
375C4×D4—41no—
376C4×D4—41no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—471no—
381C2×C4⋊C4—471no—
382C2×C4⋊C4—471no—
383C2×C4⋊C4—471no—
384C2×C4⋊C4—941no—
385C2×C4⋊C4—941no—
386C2×C4⋊C4—941no—
387C2×C4⋊C4—941no—
388C2×C4⋊C4—941no—
389C2×C4⋊C4—941no—
390C2×C4⋊C4C22×D4711yescharacteristic
391C2×C4⋊C4C22×D4711yescharacteristic
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C42—21no—
398C2×C42C22×D4711yescharacteristic
399C2×C42C22×D4711yescharacteristic
400C2×C42C22×D4711yescharacteristic
401#107—1881no—
402#107—1881no—
403#106—1881no—
404#106—1881no—
405C4⋊C8—942no—
406C4⋊C8—942no—
407#103—942no—
408#103—942no—
409#103—1881no—
410#103—1881no—
411#102—942no—
412#102—942no—
413#102—1881no—
414#102—1881no—
415#97—942no—
416C4×C8—942no—
417#95—21no—
418#95—21no—
419#95—941no—
420#95—941no—
421#95—941no—
422#95—941no—
423#95—941no—
424#95—941no—
425#95C22⋊D4711yescharacteristic
426#95C22⋊D4711yescharacteristic
427#95C22⋊D4711yescharacteristic
428#95C22⋊D4711yescharacteristic
429C24—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8C2×Dic9412yes—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4C2×Dic9412yes—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—42no—
446C22×C4—81no—
447C22×C4—81no—
448C22×C4—941no—
449C22×C4—941no—
450C22×C4—941no—
451C22×C4—941no—
452C22×C4C2×C22⋊D4711yescharacteristic
453C22×C4C2×C22⋊D4711yescharacteristic
454C22×C4C2×C22⋊D4711yescharacteristic
455C22×C4C2×C22⋊D4711yescharacteristic
456C22×C4C2×C22⋊D4711yescharacteristic
457C22×C4C2×C22⋊D4711yescharacteristic
458C22×C4C23×D4711yescharacteristic
459C2×C8—472no—
460C2×C8—472no—
461C2×C8—941no—
462C2×C8—941no—
463C2×C8—941no—
464C2×C8—941no—
465C2×C8—941no—
466C2×C8—941no—
467C2×C8—941no—
468C2×C8—941no—
469C2×C8—941no—
470C2×C8—941no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—42no—
476C4⋊C4—81no—
477C4⋊C4—81no—
478C4⋊C4—941no—
479C4⋊C4—941no—
480C4⋊C4—941no—
481C4⋊C4—941no—
482C4⋊C4—941no—
483C4⋊C4—941no—
484C4⋊C4—941no—
485C4⋊C4—941no—
486C4⋊C4—3761no—
487C4⋊C4—3761no—
488C4⋊C4—3761no—
489C4⋊C4—3761no—
490C4⋊C4—3761no—
491C4⋊C4—3761no—
492C22⋊C4—24no—
493C22⋊C4—24no—
494C22⋊C4—42no—
495C22⋊C4—81no—
496C22⋊C4—81no—
497C42—21no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—42no—
502C42C2×Dic9412yes—
503C42#1062535012yes—
504C23—22no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23C22×C22⋊D4711yescharacteristic
512Q8—22no—
513Q8—22no—
514Q8—41no—
515Q8—41no—
516D4—22no—
517D4—22no—
518D4—41no—
519D4—41no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—21no—
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—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—84no—
546C2×C4—1881no—
547C2×C4—1881no—
548C2×C4—1881no—
549C2×C4—1881no—
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×C4#1309400312yes—
559C2×C4#1309400312yes—
560C2×C4C22×Dic9411yescharacteristic
561C2×C4#41×D4711yescharacteristic
562C2×C4#41×D4711yescharacteristic
563C2×C4C2×#1062535011yescharacteristic
564C2×C4#1309406911yescharacteristic
565C2×C4#1309406911yescharacteristic
566C8—942no—
567C8—942no—
568C8—1881no—
569C8—1881no—
570C22—42no—
571C22—42no—
572C22—42no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22C2×#1309400311yescharacteristic
578C22#1568966911yescharacteristic
579C22#1568969011yescharacteristic
580C22#1568992611yescharacteristic
581C22#1568993111yescharacteristic
582C22#1568993411yescharacteristic
583C22#1568993811yescharacteristic
584C4—22no—
585C4—22no—
586C4—42no—
587C4—41no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—81no—
592C4—81no—
593C4—3761no—
594C4—3761no—
595C4—3761no—
596C4—3761no—
597C4#1568982311yescharacteristic
598C4#1568982311yescharacteristic
599C4#1568983211yescharacteristic
600C4#1568983211yescharacteristic
601C2—82no—
602C2#2024858411yescharacteristic
603C2#2025323911yescharacteristic
604C2#2025325011yescharacteristic
605C2#2025405011yescharacteristic
606C2#2025406511yescharacteristic
607C2#2025448211yescharacteristic
608C2#2025449711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2326C2
socleC23×C47C22×D4
prime radicalC22×D4×C47C23
hypercenter#2326D47
hypocenterC47#29203
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ #376 ◁ #2326

Complements

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

NH ≅ G/Ntype
1. #20249363C2semidirect
2. #20244783C2semidirect
4. #20244769C2semidirect
8. #20243656C2semidirect
10. #20243642C2semidirect
12. #20243554C2semidirect
13. #20243515C2semidirect
14. #20243245C2semidirect
363. C47#29203semidirect

Maximal subgroups

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

subgroupindex
#202493632
#202447832
#202447762
#202447692
#202447622
#202442052
#202442002
#202436562
#202436492
#202436422
#202436352
#202435542
#202435152
#202432452
C47×#23262
#2920347