Finite Group Databasebeta

← #26268336

Subgroups — #26268336

Order 12032.

790 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689410C211yesmaximal, characteristic
2C2×#15689254C211yesmaximal, characteristic, complemented
3#20248746C211yesmaximal, characteristic
4#20244890C211yesmaximal, characteristic, complemented
5#20244889C211yesmaximal, characteristic, complemented
6#20244773C211yesmaximal, characteristic
7#20244759C211yesmaximal, characteristic
8#20244362C211yesmaximal, characteristic, complemented
9#20244156C211yesmaximal, characteristic, complemented
10#20244123C211yesmaximal, characteristic, complemented
11#20244113C211yesmaximal, characteristic, complemented
12#20244084C211yesmaximal, characteristic
13#20244070C211yesmaximal, characteristic
14#20243216C211yesmaximal, characteristic
15C47×#2546C211yesmaximal, characteristic, complemented
16C2×C4×D188C2211yescharacteristic
17#15689410—24no—
18#15689254—24no—
19C2×#13093957C2211yescharacteristic
20C2×#13093955C2211yescharacteristic
21C2×#13093955C2211yescharacteristic
22C2×#13093955C2211yescharacteristic
23C2×C4⋊(C47⋊C8)C2211yescharacteristic
24C2×C4⋊(C47⋊C8)C2211yescharacteristic
25C2×C4⋊(C47⋊C8)C2211yescharacteristic
26C2×#13093944C2211yescharacteristic
27C2×#13093944C2211yescharacteristic
28C2×#13093944C2211yescharacteristic
29C2×#13093944C2211yescharacteristic
30C2×#13093935C2211yescharacteristic
31C2×#13093935C2211yescharacteristic
32C2×C4×C47⋊C8C2211yescharacteristic
33#15689058—21no—
34#15689034—21no—
35#15689025C2211yescharacteristic
36#15689025C2211yescharacteristic
37#15689021C2211yescharacteristic
38#15689021C2211yescharacteristic
39#15688994—21no—
40#15688994—21no—
41#15688989C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688885C2211yescharacteristic
50C2×C4⋊Q8×C47—21no—
51C2×C4⋊Q8×C47C2211yescharacteristic
52C2×C4×Q8×C47C2211yescharacteristic
53C47×#398—21no—
54C47×#398—21no—
55C47×#391—21no—
56C47×#389C2211yescharacteristic
57C47×#389C2211yescharacteristic
58C47×#389C2211yescharacteristic
59C47×#389C2211yescharacteristic
60C4×C4⋊C4×C47C2211yescharacteristic
61C22×D188C2311yescharacteristic
62C22×C4×D47—21no—
63C22×C47⋊C8C2311yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66C22×C47⋊C8C2311yescharacteristic
67C4×D188—22no—
68C4×D188—22no—
69C2×C4⋊Dic47C2311yescharacteristic
70C2×C4⋊Dic47C2311yescharacteristic
71C2×C4⋊Dic47C2311yescharacteristic
72C2×Dic47⋊C4—21no—
73C2×Dic47⋊C4—21no—
74C2×(C2×D47)⋊C4—21no—
75C2×(C2×D47)⋊C4—21no—
76C2×(C2×D47)⋊C4—21no—
77C2×(C2×D47)⋊C4—21no—
78C2×(C2×D47)⋊C4—21no—
79#13093957—22no—
80#13093955—22no—
81#13093955—22no—
82#13093955—22no—
83C4⋊(C47⋊C8)—22no—
84C4⋊(C47⋊C8)—22no—
85C4⋊(C47⋊C8)D414yes—
86#13093944—22no—
87#13093944—22no—
88#13093944—22no—
89#13093944Q814yescomplemented
90#13093935—22no—
91#13093935—22no—
92C4×C47⋊C8—22no—
93C47⋊#95—21no—
94C47⋊#95—21no—
95C47⋊#95—21no—
96C47⋊#95—21no—
97C22×Q8×C47—21no—
98C22×Q8×C47D411yescharacteristic
99C4⋊Q8×C47—22no—
100C4⋊Q8×C47—22no—
101C4⋊Q8×C47—44no—
102C4×Q8×C47—22no—
103C4×Q8×C47—22no—
104C2×C4⋊C4×C47—21no—
105C2×C4⋊C4×C47—21no—
106C2×C4⋊C4×C47—21no—
107C2×C4⋊C4×C47—21no—
108C2×C4⋊C4×C47—21no—
109C2×C4⋊C4×C47D411yescharacteristic
110C2×C4⋊C4×C47D411yescharacteristic
111C2×C4⋊C4×C47D411yescharacteristic
112C2×C4⋊C4×C47C2311yescharacteristic
113C2×C4⋊C4×C47C2311yescharacteristic
114C2×C4⋊C4×C47C2311yescharacteristic
115C2×C4⋊C4×C47C2311yescharacteristic
116C2×C42×C47—21no—
117C2×C42×C47C2311yescharacteristic
118C2×C42×C47C2311yescharacteristic
119C2×C42×C47C2311yescharacteristic
120#95×C47—21no—
121#95×C47—21no—
122#95×C47—21no—
123#95×C47—21no—
124#95×C47—21no—
125C23×D47—21no—
126C2×Q8×C47—22no—
127C2×Q8×C47—22no—
128C2×Q8×C47—41no—
129C2×Q8×C47—42no—
130C2×Q8×C47—42no—
131C2×Q8×C47—42no—
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×D188C2×Q812yes—
152C2×C4×D47—42no—
153C2×C4×D47—81no—
154C2×C4×D47—81no—
155C4⋊C4×C47—22no—
156C4⋊C4×C47—22no—
157C4⋊C4×C47—22no—
158C4⋊C4×C47—21no—
159C4⋊C4×C47—21no—
160C4⋊C4×C47—21no—
161C4⋊C4×C47—21no—
162C4⋊C4×C47—21no—
163C4⋊C4×C47—21no—
164C4⋊C4×C47—42no—
165C4⋊C4×C47—42no—
166C4⋊C4×C47—42no—
167C4⋊C4×C47—42no—
168C4⋊C4×C47—42no—
169C4⋊C4×C47C2×Q812yes—
170C4⋊C4×C47#4112yes—
171C42×C47—21no—
172C42×C47—21no—
173C42×C47—21no—
174C42×C47—21no—
175C42×C47—42no—
176C42×C47C2×D412yes—
177C42×C47#4112yes—
178(C2×D47)⋊C4—42no—
179(C2×D47)⋊C4—42no—
180(C2×D47)⋊C4—42no—
181(C2×D47)⋊C4—81no—
182(C2×D47)⋊C4—81no—
183C4⋊Dic47—21no—
184C4⋊Dic47—21no—
185C4⋊Dic47—21no—
186C4⋊Dic47—21no—
187C4⋊Dic47—21no—
188C4⋊Dic47—21no—
189Dic47⋊C4—81no—
190Dic47⋊C4—81no—
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⋊C8—21no—
199C2×C47⋊C8—21no—
200C2×C47⋊C8C2×D412yes—
201C2×C47⋊C8C2×D412yes—
202C2×C47⋊C8C2×Q812yes—
203C23×C47C22×D411yescharacteristic
204C22×D47—22no—
205C22×D47—41no—
206C22×D47—41no—
207C22×D47—41no—
208C22×D47—41no—
209C22×D47—41no—
210C22×D47—41no—
211Q8×C47—44no—
212Q8×C47—84no—
213C2×C4×C47—21no—
214C2×C4×C47—21no—
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—22no—
223C2×C4×C47—22no—
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—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×C47—41no—
240C2×C4×C47#12112yes—
241C2×C4×C47#12112yes—
242C2×C4×C47AGL(1,ℤ/8)12yes—
243C2×C4×C47C22×D411yescharacteristic
244C2×C4×C47C22×Q811yescharacteristic
245C2×C4×C47C2×#4111yescharacteristic
246C2×C4×C47C2×#4111yescharacteristic
247C2×C4×C472−1+411yescharacteristic
248C2×C4×C472−1+411yescharacteristic
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—
258D188—22no—
259D188—22no—
260D188—41no—
261D188—41no—
262C4×D47—84no—
263C47⋊C8—22no—
264C47⋊C8—22no—
265C47⋊C8—22no—
266C47⋊C8—41no—
267#25485—471nomaximal, Sylow
268C22×C47C2×#12111yescharacteristic
269C22×C47#54811yescharacteristic
270C22×C47D4×Q811yescharacteristic
271C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
272C22×C47#57511yescharacteristic
273C22×C47#57711yescharacteristic
274C22×C47#57711yescharacteristic
275C2×D47—42no—
276C2×D47—42no—
277C2×D47—42no—
278C2×D47—81no—
279C2×D47—81no—
280C2×D47—81no—
281C2×D47—81no—
282C4×C47—22no—
283C4×C47—22no—
284C4×C47—22no—
285C4×C47—42no—
286C4×C47—42no—
287C4×C47—41no—
288C4×C47—41no—
289C4×C47—41no—
290C4×C47—81no—
291C4×C47—81no—
292C4×C47#53311yescharacteristic
293C4×C47#54111yescharacteristic
294C4×C47#54711yescharacteristic
295C4×C47D4×Q811yescharacteristic
296Dic47—81no—
297Dic47—81no—
298Dic47—81no—
299C2×#476—471no—
300C2×#446—471no—
301#2580—471no—
302#2546D4711yescharacteristic, complemented
303#2088—471no—
304#2088—471no—
305#2067—471no—
306#2065—471no—
307#1993—471no—
308#1949—471no—
309#1943—471no—
310#1941—471no—
311#1936—471no—
312#1934—471no—
313#1762—471no—
314C2×C47#242911yescharacteristic
315C2×C47#305511yescharacteristic
316C2×C47#305711yescharacteristic
317C2×C47#337111yescharacteristic
318C2×C47#337311yescharacteristic
319C2×C47#338411yescharacteristic
320C2×C47#338811yescharacteristic
321D47—82no—
322C2×C4⋊Q8—21no—
323C2×C4⋊Q8C2×D4711yescharacteristic
324C2×C4×Q8C2×D4711yescharacteristic
325C2×C4×D4—471no—
326#476—944no—
327#446—944no—
328C2×#107—471no—
329C2×#106—471no—
330C2×#106—471no—
331C2×#106—471no—
332C2×C4⋊C8—471no—
333C2×C4⋊C8—471no—
334C2×C4⋊C8—471no—
335C2×#102—471no—
336C2×#102—471no—
337C2×#102—471no—
338C2×#102—471no—
339C2×#97—471no—
340C2×#97—471no—
341C2×C4×C8—471no—
342#399—941no—
343#398—21no—
344#398—21no—
345#393—941no—
346#391—21no—
347#390—471no—
348#390—471no—
349#389—471no—
350#389—471no—
351#389C2×D4711yescharacteristic
352#389C2×D4711yescharacteristic
353#389C2×D4711yescharacteristic
354#389C2×D4711yescharacteristic
355#385—941no—
356#385—941no—
357#382—471no—
358C4×C4⋊C4C2×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#2548511yescharacteristic, complemented, Sylow
368C22×Q8—21no—
369C22×Q8C22⋊D4711yescharacteristic
370C22×D4—471no—
371C23×C4—941no—
372C22×C8—471no—
373C22×C8—471no—
374C22×C8—471no—
375C22×C8—471no—
376C4⋊Q8—22no—
377C4⋊Q8—22no—
378C4⋊Q8—44no—
379C4×Q8—22no—
380C4×Q8—22no—
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—471no—
389C2×C4⋊C4—471no—
390C2×C4⋊C4—471no—
391C2×C4⋊C4—941no—
392C2×C4⋊C4—941no—
393C2×C4⋊C4C22⋊D4711yescharacteristic
394C2×C4⋊C4C22⋊D4711yescharacteristic
395C2×C4⋊C4C22⋊D4711yescharacteristic
396C2×C4⋊C4C22×D4711yescharacteristic
397C2×C4⋊C4C22×D4711yescharacteristic
398C2×C4⋊C4C22×D4711yescharacteristic
399C2×C4⋊C4C22×D4711yescharacteristic
400C2×C22⋊C4—941no—
401C2×C22⋊C4—941no—
402C2×C22⋊C4—941no—
403C2×C22⋊C4—941no—
404C2×C22⋊C4—941no—
405C2×C42—21no—
406C2×C42C22×D4711yescharacteristic
407C2×C42C22×D4711yescharacteristic
408C2×C42C22×D4711yescharacteristic
409#107—942no—
410#106—942no—
411#106—942no—
412#106—942no—
413C4⋊C8—474no—
414C4⋊C8—942no—
415C4⋊C8—942no—
416#102—474no—
417#102—942no—
418#102—942no—
419#102—942no—
420#97—942no—
421#97—942no—
422C4×C8—942no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—941no—
429#95—941no—
430#95—941no—
431#95—941no—
432C24—941no—
433C2×Q8—22no—
434C2×Q8—22no—
435C2×Q8—41no—
436C2×Q8—42no—
437C2×Q8—42no—
438C2×Q8—42no—
439C2×D4—472no—
440C2×D4—941no—
441C2×D4—941no—
442C2×D4—941no—
443C2×D4—941no—
444C2×D4—941no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—941no—
450C22×C4—941no—
451C22×C4—941no—
452C22×C4—3761no—
453C22×C4—3761no—
454C22×C4—1882no—
455C22×C4C2×C22⋊D4711yescharacteristic
456C22×C4C2×C22⋊D4711yescharacteristic
457C22×C4C2×C22⋊D4711yescharacteristic
458C22×C4C2×C22⋊D4711yescharacteristic
459C22×C4C2×C22⋊D4711yescharacteristic
460C22×C4C2×C22⋊D4711yescharacteristic
461C22×C4C23×D4711yescharacteristic
462C2×C8—472no—
463C2×C8—472no—
464C2×C8—472no—
465C2×C8—941no—
466C2×C8—941no—
467C2×C8—941no—
468C2×C8—941no—
469C2×C8—941no—
470C2×C8—941no—
471C2×C8—941no—
472C2×C8—941no—
473C2×C8—941no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—42no—
484C4⋊C4—42no—
485C4⋊C4—42no—
486C4⋊C4—42no—
487C4⋊C4—42no—
488C4⋊C4—941no—
489C4⋊C4—941no—
490C4⋊C4—941no—
491C4⋊C4—941no—
492C4⋊C4—941no—
493C4⋊C4—941no—
494C4⋊C4—3761no—
495C4⋊C4—3761no—
496C4⋊C4Q8×D4712yes—
497C4⋊C4#1062535412yes—
498C22⋊C4—3761no—
499C22⋊C4—3761no—
500C22⋊C4—1882no—
501C22⋊C4—1882no—
502C22⋊C4—1882no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—42no—
508C42D4×D4712yes—
509C42#1062535212yes—
510C23—942no—
511C23—1881no—
512C23—1881no—
513C23—1881no—
514C23—1881no—
515C23—1881no—
516C23—1881no—
517C23C22×C22⋊D4711yescharacteristic
518Q8—44no—
519Q8—84no—
520D4—942no—
521D4—942no—
522D4—1881no—
523D4—1881no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—41no—
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—3764no—
552C2×C4—1881no—
553C2×C4—1881no—
554C2×C4—1881no—
555C2×C4—1881no—
556C2×C4—1881no—
557C2×C4—1881no—
558C2×C4—1881no—
559C2×C4—1881no—
560C2×C4—1881no—
561C2×C4#1309399612yes—
562C2×C4#1309399612yes—
563C2×C4#1309405012yes—
564C2×C4C2×D4×D4711yescharacteristic
565C2×C4C2×Q8×D4711yescharacteristic
566C2×C4C2×#1062535211yescharacteristic
567C2×C4C2×#1062535411yescharacteristic
568C2×C4#1309407211yescharacteristic
569C2×C4#1309407211yescharacteristic
570C8—942no—
571C8—942no—
572C8—942no—
573C8—1881no—
574C22—3761no—
575C22—3761no—
576C22—3761no—
577C22—3761no—
578C22—1882no—
579C22—1882no—
580C22—1882no—
581C22C2×#1309399611yescharacteristic
582C22#1568978411yescharacteristic
583C22Q8×C22⋊D4711yescharacteristic
584C22C2×#1309405011yescharacteristic
585C22#1568992111yescharacteristic
586C22#1568993111yescharacteristic
587C22#1568993111yescharacteristic
588C4—22no—
589C4—22no—
590C4—22no—
591C4—42no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—42no—
596C4—81no—
597C4—81no—
598C4—3761no—
599C4—3761no—
600C4—3761no—
601C4#1568967811yescharacteristic
602C4#1568973411yescharacteristic
603C4#1568977611yescharacteristic
604C4#1568978811yescharacteristic
605C2—3762no—
606C2#2024699011yescharacteristic
607C2#2025300311yescharacteristic
608C2#2025302911yescharacteristic
609C2#2025615611yescharacteristic
610C2#2025618011yescharacteristic
611C2#2025628311yescharacteristic
612C2#2025632711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2546C2
socleC23×C47C22×D4
prime radicalC22×D188C23
hypercenter#2546D47
hypocenterC47#25485
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2546

Complements

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

NH ≅ G/Ntype
2. C2×#15689254C2semidirect
4. #20244890C2semidirect
5. #20244889C2semidirect
8. #20244362C2semidirect
9. #20244156C2semidirect
10. #20244123C2semidirect
11. #20244113C2semidirect
15. C47×#2546C2semidirect
89. #13093944Q8semidirect
302. #2546D47semidirect
367. C47#25485semidirect

Maximal subgroups

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

subgroupindex
C2×#156894102
C2×#156892542
#202487462
#202448902
#202448892
#202447732
#202447592
#202443622
#202441562
#202441232
#202441132
#202440842
#202440702
#202432162
C47×#25462
#2548547