Finite Group Databasebeta

← #26224282

Subgroups — #26224282

Order 12032.

818 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689480C211yesmaximal, characteristic
2#20246099C211yesmaximal, characteristic
3#20244358C211yesmaximal, characteristic, complemented
4#20244202C211yesmaximal, characteristic
5#20244084C211yesmaximal, characteristic
6#20244077C211yesmaximal, characteristic, complemented
7#20244070C211yesmaximal, characteristic
8#20244063C211yesmaximal, characteristic, complemented
9#20243515C211yesmaximal, characteristic, complemented
10#20243221C211yesmaximal, characteristic, complemented
11#20243216C211yesmaximal, characteristic
12C4×#13093947C211yesmaximal, characteristic, complemented
13C4×#13093944C211yesmaximal, characteristic
14#20243075C211yesmaximal, characteristic, complemented
15C47×#2330C211yesmaximal, characteristic, complemented
16C2×#13094012C2211yescharacteristic
17C2×C4×Dic94C2211yescharacteristic
18C2×C4×D188C2211yescharacteristic
19#15689480C418yescomplemented
20C2×#13093947C2211yescharacteristic
21C2×#13093947C2211yescharacteristic
22C2×#13093947C2211yescharacteristic
23C2×#13093947C2211yescharacteristic
24C2×#13093944C2211yescharacteristic
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#15689029C2211yescharacteristic
35#15689025C2211yescharacteristic
36#15689015—21no—
37#15689015—21no—
38#15688997—21no—
39#15688997—21no—
40#15688993C2211yescharacteristic
41#15688885C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49C2×#125×C47C2211yescharacteristic
50C47×#389—21no—
51C47×#389—21no—
52C47×#389C2211yescharacteristic
53C47×#389C2211yescharacteristic
54C47×#387—21no—
55C47×#387—21no—
56C47×#384C2211yescharacteristic
57C4×C4⋊C4×C47C2211yescharacteristic
58C4×C4⋊C4×C47C2211yescharacteristic
59C47×#376C2211yescharacteristic
60C22×Dic94C2311yescharacteristic
61C22×D188C2311yescharacteristic
62C22×C4×D47—21no—
63C22×C47⋊C8C2311yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66C22×C47⋊C8C2311yescharacteristic
67#13094012—22no—
68#13094012C2×C414yes—
69C4×Dic94—22no—
70C4×Dic94—22no—
71C4×D188—22no—
72C4×D188—22no—
73C2×C4⋊Dic47—21no—
74C2×C4⋊Dic47—21no—
75C2×C4⋊Dic47C2311yescharacteristic
76C2×C4⋊Dic47C2311yescharacteristic
77C2×Dic47⋊C4—21no—
78C2×(C2×D47)⋊C4—21no—
79C2×(C2×D47)⋊C4—21no—
80C2×(C2×D47)⋊C4—21no—
81C2×(C2×D47)⋊C4—21no—
82C2×(C2×D47)⋊C4—21no—
83C2×C4×Dic47—21no—
84#13093947—22no—
85#13093947—22no—
86#13093947C2×C414yescomplemented
87#13093947C2×C414yescomplemented
88#13093944—22no—
89#13093944—22no—
90#13093944C2×C414yes—
91#13093944C2×C414yes—
92#13093935—22no—
93#13093935—22no—
94#13093935—22no—
95C4×C47⋊C8—22no—
96C4×C47⋊C8—22no—
97C4×C47⋊C8C2×C414yescomplemented
98C47⋊#95—21no—
99C47⋊#95—21no—
100#125×C47—22no—
101#125×C47C2×C414yescomplemented
102C2×C4⋊C4×C47—21no—
103C2×C4⋊C4×C47—21no—
104C2×C4⋊C4×C47—21no—
105C2×C4⋊C4×C47—21no—
106C2×C4⋊C4×C47—21no—
107C2×C4⋊C4×C47—21no—
108C2×C4⋊C4×C47C2311yescharacteristic
109C2×C4⋊C4×C47C2311yescharacteristic
110C2×C4⋊C4×C47C2311yescharacteristic
111C2×C4⋊C4×C47C2311yescharacteristic
112C2×C42×C47—21no—
113C2×C42×C47—21no—
114C2×C42×C47C2311yescharacteristic
115C2×C42×C47C2311yescharacteristic
116C2×C42×C47C2311yescharacteristic
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—
126C22×C4×C47—21no—
127C22×C4×C47—21no—
128C22×C4×C47—21no—
129C22×C4×C47—21no—
130C22×C4×C47C2×D411yescharacteristic
131C22×C4×C47C2×D411yescharacteristic
132C22×C4×C47C2×D411yescharacteristic
133C22×C4×C47C2×D411yescharacteristic
134C22×C4×C47C2×D411yescharacteristic
135C22×C4×C47C2×D411yescharacteristic
136C22×C4×C47C2411yescharacteristic
137C22×Dic47—21no—
138C22×Dic47—21no—
139C22×Dic47—21no—
140C2×D188—21no—
141C2×D188—21no—
142C2×D188—21no—
143C2×D188—21no—
144C2×D188—21no—
145C2×D188C22×C412yes—
146C2×C4×D47—42no—
147C2×C4×D47—81no—
148C2×C4×D47—81no—
149C2×Dic94—21no—
150C2×Dic94—21no—
151C2×Dic94—21no—
152C2×Dic94—21no—
153C2×Dic94—21no—
154C2×Dic94C22×C412yes—
155C4⋊C4×C47—24no—
156C4⋊C4×C47—24no—
157C4⋊C4×C47—21no—
158C4⋊C4×C47—21no—
159C4⋊C4×C47—21no—
160C4⋊C4×C47—21no—
161C4⋊C4×C47—21no—
162C4⋊C4×C47—21no—
163C4⋊C4×C47—81no—
164C4⋊C4×C47—81no—
165C4⋊C4×C47—81no—
166C4⋊C4×C47—81no—
167C4⋊C4×C47C22×C412yes—
168C4⋊C4×C47C22×C412yes—
169C42×C47—21no—
170C42×C47—21no—
171C42×C47—81no—
172C42×C47—81no—
173C42×C47C22×C412yes—
174C42×C47#4112yes—
175C42×C47#4112yes—
176C42×C47#4112yes—
177(C2×D47)⋊C4—24no—
178(C2×D47)⋊C4—24no—
179(C2×D47)⋊C4—42no—
180(C2×D47)⋊C4—81no—
181(C2×D47)⋊C4—81no—
182C4⋊Dic47—21no—
183C4⋊Dic47—21no—
184C4⋊Dic47—21no—
185C4⋊Dic47—21no—
186C4⋊Dic47—81no—
187C4⋊Dic47—81no—
188Dic47⋊C4—42no—
189C4×Dic47—42no—
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—21no—
198C2×C47⋊C8C22×C412yes—
199C2×C47⋊C8C22×C412yes—
200C2×C47⋊C8#4112yes—
201C2×C47⋊C8#4112yes—
202C23×C47C22×D411yescharacteristic
203C22×D47—22no—
204C22×D47—41no—
205C22×D47—41no—
206C22×D47—41no—
207C22×D47—41no—
208C22×D47—41no—
209C22×D47—41no—
210C2×C4×C47—21no—
211C2×C4×C47—21no—
212C2×C4×C47—21no—
213C2×C4×C47—21no—
214C2×C4×C47—21no—
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—22no—
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—41no—
227C2×C4×C47—41no—
228C2×C4×C47—41no—
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×C47C4×D412yes—
237C2×C4×C47C4×D412yes—
238C2×C4×C47#12412yes—
239C2×C4×C47#12412yes—
240C2×C4×C47C23×C411yescharacteristic
241C2×C4×C47C2×#4111yescharacteristic
242C2×C4×C47C2×#4111yescharacteristic
243C2×C4×C47C2×#4111yescharacteristic
244C2×C4×C47C2×#4111yescharacteristic
245C2×C4×C47C2×#4111yescharacteristic
246C2×Dic47—22no—
247C2×Dic47—41no—
248C2×Dic47—41no—
249C2×Dic47—41no—
250C2×Dic47—41no—
251C2×Dic47—41no—
252C2×Dic47—41no—
253C2×Dic47—41no—
254C2×Dic47—41no—
255D188—22no—
256D188—22no—
257D188—41no—
258D188—41no—
259C4×D47—84no—
260Dic94—22no—
261Dic94—22no—
262Dic94—41no—
263Dic94—41no—
264C47⋊C8—22no—
265C47⋊C8—22no—
266C47⋊C8—22no—
267C47⋊C8—22no—
268#21643—471nomaximal, Sylow
269C22×C47C2×C4×D411yescharacteristic
270C22×C47C2×#12411yescharacteristic
271C22×C47#53211yescharacteristic
272C22×C47#57611yescharacteristic
273C22×C47#57711yescharacteristic
274C22×C47#57711yescharacteristic
275C22×C47#57811yescharacteristic
276C2×D47—42no—
277C2×D47—42no—
278C2×D47—42no—
279C2×D47—81no—
280C2×D47—81no—
281C2×D47—81no—
282C2×D47—81no—
283C4×C47—22no—
284C4×C47—22no—
285C4×C47—22no—
286C4×C47—22no—
287C4×C47—41no—
288C4×C47—41no—
289C4×C47—42no—
290C4×C47—42no—
291C4×C47—81no—
292C4×C47—81no—
293C4×C47C4×#4111yescharacteristic
294C4×C47C4×#4111yescharacteristic
295C4×C47#52911yescharacteristic
296C4×C47#52911yescharacteristic
297Dic47—42no—
298Dic47—81no—
299Dic47—81no—
300C2×#488—471no—
301#2330D4711yescharacteristic, complemented
302#2326—471no—
303#1992—471no—
304#1959—471no—
305#1936—471no—
306#1935—471no—
307#1934—471no—
308#1933—471no—
309#1834—471no—
310#1763—471no—
311#1762—471no—
312C4×#103—471no—
313C4×#102—471no—
314#1726—471no—
315C2×C47C4×#12411yescharacteristic
316C2×C47#295111yescharacteristic
317C2×C47#295211yescharacteristic
318C2×C47#313611yescharacteristic
319C2×C47#313711yescharacteristic
320C2×C47#317811yescharacteristic
321C2×C47#317911yescharacteristic
322D47—82no—
323C2×#125C2×D4711yescharacteristic
324C2×#124—471no—
325C2×C4×Q8—471no—
326C2×C4×D4—471no—
327#488—478no—
328C2×#103—471no—
329C2×#103—471no—
330C2×#103—471no—
331C2×#103—471no—
332C2×#102—471no—
333C2×#102—471no—
334C2×#102—471no—
335C2×#102—471no—
336C2×#97—471no—
337C2×#97—471no—
338C2×#97—471no—
339C2×C4×C8—471no—
340C2×C4×C8—471no—
341C2×C4×C8—471no—
342#391—471no—
343#390—471no—
344#389—21no—
345#389—21no—
346#389C2×D4711yescharacteristic
347#389C2×D4711yescharacteristic
348#388—941no—
349#388—941no—
350#387—21no—
351#387—21no—
352#385—941no—
353#385—941no—
354#384—471no—
355#384C2×D4711yescharacteristic
356C4×C4⋊C4C2×D4711yescharacteristic
357C4×C4⋊C4C2×D4711yescharacteristic
358#376C2×D4711yescharacteristic
359#340—471no—
360#340—471no—
361#340—471no—
362#340—471no—
363#340—471no—
364#340—471no—
365#340—471no—
366#340—471no—
367C47#2164311yescharacteristic, complemented, Sylow
368C22×Q8—471no—
369C22×D4—471no—
370C23×C4—941no—
371C22×C8—471no—
372C22×C8—471no—
373C22×C8—471no—
374C22×C8—471no—
375#125—22no—
376#125C4×D4714yescomplemented
377#124—474no—
378#124—942no—
379C4×Q8—942no—
380C4×Q8—942no—
381C4×D4—942no—
382C4×D4—942no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—471no—
390C2×C4⋊C4—471no—
391C2×C4⋊C4—941no—
392C2×C4⋊C4—941no—
393C2×C4⋊C4—941no—
394C2×C4⋊C4C22×D4711yescharacteristic
395C2×C4⋊C4C22×D4711yescharacteristic
396C2×C4⋊C4C22×D4711yescharacteristic
397C2×C4⋊C4C22×D4711yescharacteristic
398C2×C22⋊C4—941no—
399C2×C22⋊C4—941no—
400C2×C22⋊C4—941no—
401C2×C22⋊C4—941no—
402C2×C22⋊C4—941no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—941no—
406C2×C42C22×D4711yescharacteristic
407C2×C42C22×D4711yescharacteristic
408C2×C42C22×D4711yescharacteristic
409#103—474no—
410#103—474no—
411#103—942no—
412#103—942no—
413#102—474no—
414#102—474no—
415#102—942no—
416#102—942no—
417#97—942no—
418#97—942no—
419#97—942no—
420C4×C8—474no—
421C4×C8—942no—
422C4×C8—942no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—941no—
428#95—941no—
429#95C22⋊D4711yescharacteristic
430#95C22⋊D4711yescharacteristic
431#95C22⋊D4711yescharacteristic
432#95C22⋊D4711yescharacteristic
433C24—941no—
434C2×Q8—472no—
435C2×Q8—941no—
436C2×Q8—941no—
437C2×Q8—941no—
438C2×Q8—941no—
439C2×Q8—941no—
440C2×D4—472no—
441C2×D4—941no—
442C2×D4—941no—
443C2×D4—941no—
444C2×D4—941no—
445C2×D4—941no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—941no—
451C22×C4—941no—
452C22×C4—941no—
453C22×C4—3761no—
454C22×C4—3761no—
455C22×C4—1882no—
456C22×C4C2×C22⋊D4711yescharacteristic
457C22×C4C2×C22⋊D4711yescharacteristic
458C22×C4C2×C22⋊D4711yescharacteristic
459C22×C4C2×C22⋊D4711yescharacteristic
460C22×C4C2×C22⋊D4711yescharacteristic
461C22×C4C2×C22⋊D4711yescharacteristic
462C22×C4C23×D4711yescharacteristic
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—
473C2×C8—941no—
474C2×C8—941no—
475C4⋊C4—24no—
476C4⋊C4—24no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—81no—
484C4⋊C4—81no—
485C4⋊C4—81no—
486C4⋊C4—81no—
487C4⋊C4—941no—
488C4⋊C4—941no—
489C4⋊C4—941no—
490C4⋊C4—941no—
491C4⋊C4—3761no—
492C4⋊C4—3761no—
493C4⋊C4—1882no—
494C4⋊C4C2×C4×D4712yes—
495C4⋊C4C2×C4×D4712yes—
496C22⋊C4—944no—
497C22⋊C4—944no—
498C22⋊C4—3761no—
499C22⋊C4—3761no—
500C22⋊C4—1882no—
501C42—21no—
502C42—21no—
503C42—81no—
504C42—81no—
505C42—1882no—
506C42C2×C4×D4712yes—
507C42#1062535012yes—
508C42#1062535412yes—
509C42#1062535412yes—
510C23—942no—
511C23—1881no—
512C23—1881no—
513C23—1881no—
514C23—1881no—
515C23—1881no—
516C23—1881no—
517C23C22×C22⋊D4711yescharacteristic
518Q8—942no—
519Q8—942no—
520Q8—1881no—
521Q8—1881no—
522D4—942no—
523D4—942no—
524D4—1881no—
525D4—1881no—
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—22no—
535C2×C4—22no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—942no—
553C2×C4—3764no—
554C2×C4—1881no—
555C2×C4—1881no—
556C2×C4—1881no—
557C2×C4—1881no—
558C2×C4—1881no—
559C2×C4—1881no—
560C2×C4—1881no—
561C2×C4—1881no—
562C2×C4C4×C22⋊D4712yes—
563C2×C4C4×C22⋊D4712yes—
564C2×C4#1309401312yes—
565C2×C4#1309401312yes—
566C2×C4C22×C4×D4711yescharacteristic
567C2×C4#41×D4711yescharacteristic
568C2×C4#41×D4711yescharacteristic
569C2×C4C2×#1062535011yescharacteristic
570C2×C4C2×#1062535411yescharacteristic
571C2×C4C2×#1062535411yescharacteristic
572C8—942no—
573C8—942no—
574C8—942no—
575C8—942no—
576C22—3761no—
577C22—3761no—
578C22—3761no—
579C22—3761no—
580C22—1882no—
581C22—1882no—
582C22—1882no—
583C22C2×C4×C22⋊D4711yescharacteristic
584C22C2×#1309401311yescharacteristic
585C22#1568966911yescharacteristic
586C22#1568992611yescharacteristic
587C22#1568993111yescharacteristic
588C22#1568993411yescharacteristic
589C22#1568993811yescharacteristic
590C4—22no—
591C4—22no—
592C4—22no—
593C4—22no—
594C4—42no—
595C4—41no—
596C4—42no—
597C4—41no—
598C4—81no—
599C4—81no—
600C4—3761no—
601C4—3761no—
602C4—1882no—
603C4C4×#1062535411yescharacteristic
604C4C4×#1062535411yescharacteristic
605C4#1568966011yescharacteristic
606C4#1568966011yescharacteristic
607C2—3762no—
608C2C4×#1309401311yescharacteristic
609C2#2025226111yescharacteristic
610C2#2025226911yescharacteristic
611C2#2025374711yescharacteristic
612C2#2025375811yescharacteristic
613C2#2025405811yescharacteristic
614C2#2025407311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2330C2
socleC23×C47C22×D4
prime radicalC22×D188C23
cosocleC22×C4×C47C24
hypercenter#2330D47
hypocenterC47#21643
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ #376 ◁ #2330

Complements

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

NH ≅ G/Ntype
3. #20244358C2semidirect
6. #20244077C2semidirect
8. #20244063C2semidirect
9. #20243515C2semidirect
10. #20243221C2semidirect
12. C4×#13093947C2semidirect
14. #20243075C2semidirect
15. C47×#2330C2semidirect
19. #15689480C4semidirect
86. #13093947C2×C4semidirect
87. #13093947C2×C4semidirect
97. C4×C47⋊C8C2×C4semidirect
101. #125×C47C2×C4semidirect
301. #2330D47semidirect
367. C47#21643semidirect
376. #125C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156894802
#202460992
#202443582
#202442022
#202440842
#202440772
#202440702
#202440632
#202435152
#202432212
#202432162
C4×#130939472
C4×#130939442
#202430752
C47×#23302
#2164347