Finite Group Databasebeta

← #26264515

Subgroups — #26264515

Order 12032.

858 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689456C211yesmaximal, characteristic
2C2×#15689362C211yesmaximal, characteristic
3#20247866C211yesmaximal, characteristic
4#20244859C211yesmaximal, characteristic, complemented
5#20244796C211yesmaximal, characteristic, complemented
6#20244780C211yesmaximal, characteristic, complemented
7#20244710C211yesmaximal, characteristic, complemented
8#20244146C211yesmaximal, characteristic, complemented
9#20244029C211yesmaximal, characteristic, complemented
10#20243729C211yesmaximal, characteristic, complemented
11#20243695C211yesmaximal, characteristic
12#20243568C211yesmaximal, characteristic
13#20243393C211yesmaximal, characteristic, complemented
14C2×#15688885C211yesmaximal, characteristic
15C47×#2360C211yesmaximal, characteristic
16C22×#10625337C2211yescharacteristic
17C23×C47⋊C8C2211yescharacteristic
18C2×#13094003C2211yescharacteristic
19C22×C4⋊Dic47C2211yescharacteristic
20#15689456—24no—
21#15689362—24no—
22C2×#13093957C2211yescharacteristic
23C2×#13093957C2211yescharacteristic
24C2×#13093957C2211yescharacteristic
25C2×C4⋊(C47⋊C8)C2211yescharacteristic
26C2×C4⋊(C47⋊C8)C2211yescharacteristic
27C2×#13093948C2211yescharacteristic
28C2×#13093948C2211yescharacteristic
29C2×#13093948C2211yescharacteristic
30C2×#13093947C2211yescharacteristic
31C2×#13093947C2211yescharacteristic
32C2×#13093947C2211yescharacteristic
33C2×C22⋊(C47⋊C8)C2211yescharacteristic
34#15689055—21no—
35#15689055—21no—
36#15689029C2211yescharacteristic
37#15689029C2211yescharacteristic
38#15688998—21no—
39#15688998—21no—
40#15688993C2211yescharacteristic
41#15688993C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688878C2211yescharacteristic
49#15688878C2211yescharacteristic
50C2×C22⋊Q8×C47C2211yescharacteristic
51C2×C4×Q8×C47C2211yescharacteristic
52C22×C4⋊C4×C47C2211yescharacteristic
53C47×#391C2211yescharacteristic
54C47×#389—21no—
55C47×#389C2211yescharacteristic
56C47×#387—21no—
57C47×#385—21no—
58C4×C4⋊C4×C47C2211yescharacteristic
59C4×C22⋊C4×C47—21no—
60C4×C22⋊C4×C47C2211yescharacteristic
61C22×Dic94C2311yescharacteristic
62C23×Dic47—21no—
63C2×#10625337—22no—
64C2×#10625337—22no—
65C2×#10625337—41no—
66C22×C47⋊C8—22no—
67C22×C47⋊C8—22no—
68C22×C47⋊C8—41no—
69C22×C47⋊C8C2311yescharacteristic
70C22×C47⋊C8C2311yescharacteristic
71C22×C47⋊C8C2311yescharacteristic
72C22×C47⋊C8C2311yescharacteristic
73#13094003—22no—
74#13094003—22no—
75C2×C4⋊Dic47—22no—
76C2×C4⋊Dic47—22no—
77C2×C4⋊Dic47—21no—
78C2×C4⋊Dic47—21no—
79C2×C4⋊Dic47—21no—
80C2×C4⋊Dic47—21no—
81C2×C4⋊Dic47—21no—
82C2×C4⋊Dic47C2311yescharacteristic
83C2×C4⋊Dic47C2311yescharacteristic
84C2×C4⋊Dic47C2311yescharacteristic
85C2×Dic47⋊C4—21no—
86C2×C22⋊Dic47—21no—
87#13093957—22no—
88#13093957—22no—
89#13093957—22no—
90C4⋊(C47⋊C8)—22no—
91C4⋊(C47⋊C8)—41no—
92#13093948—22no—
93#13093948—22no—
94#13093948—22no—
95#13093947—22no—
96#13093947—22no—
97#13093947—41no—
98C22⋊(C47⋊C8)—22no—
99C47⋊#95—21no—
100C47⋊#95—21no—
101C47⋊#95—21no—
102C47⋊#95—21no—
103C22×Q8×C47C2311yescharacteristic
104C23×C4×C47—21no—
105C23×C4×C47C2311yescharacteristic
106C22⋊Q8×C47—22no—
107C22⋊Q8×C47D414yes—
108C4×Q8×C47—22no—
109C4×Q8×C47—41no—
110C2×C4⋊C4×C47—21no—
111C2×C4⋊C4×C47—22no—
112C2×C4⋊C4×C47—21no—
113C2×C4⋊C4×C47—21no—
114C2×C4⋊C4×C47—21no—
115C2×C4⋊C4×C47—41no—
116C2×C4⋊C4×C47C2311yescharacteristic
117C2×C4⋊C4×C47C2311yescharacteristic
118C2×C4⋊C4×C47C2311yescharacteristic
119C2×C22⋊C4×C47—21no—
120C2×C22⋊C4×C47D411yescharacteristic
121C2×C22⋊C4×C47D411yescharacteristic
122C2×C42×C47—21no—
123C2×C42×C47—21no—
124C2×C42×C47C2311yescharacteristic
125C2×C42×C47C2311yescharacteristic
126#95×C47—21no—
127#95×C47—21no—
128#95×C47—21no—
129#95×C47—21no—
130#95×C47D411yescharacteristic
131#95×C47D411yescharacteristic
132C24×C47C2×D411yescharacteristic
133C2×Q8×C47—21no—
134C2×Q8×C47—21no—
135C2×Q8×C47—21no—
136C2×Q8×C47—21no—
137C2×Q8×C47—21no—
138C2×Q8×C47C2×D412yes—
139C22×C4×C47—21no—
140C22×C4×C47—21no—
141C22×C4×C47—21no—
142C22×C4×C47—21no—
143C22×C4×C47—21no—
144C22×C4×C47—21no—
145C22×C4×C47—21no—
146C22×C4×C47—21no—
147C22×C4×C47—42no—
148C22×C4×C47—42no—
149C22×C4×C47—81no—
150C22×C4×C47C2×D411yescharacteristic
151C22×C4×C47C2×D411yescharacteristic
152C22×C4×C47C2×D411yescharacteristic
153C22×C4×C47C2×D412yes—
154C22×C4×C47C2×D411yescharacteristic
155C22×C4×C47C2×D411yescharacteristic
156C22×C4×C47#4112yes—
157C22×C4×C47C2411yescharacteristic
158C22×Dic47—21no—
159C22×Dic47—21no—
160C22×Dic47—21no—
161C22×Dic47—21no—
162C22×Dic47—42no—
163C22×Dic47—81no—
164C22×Dic47—81no—
165C2×Dic94—21no—
166C2×Dic94—21no—
167C2×Dic94—21no—
168C2×Dic94—21no—
169C2×Dic94—21no—
170C2×Dic94—21no—
171C4⋊C4×C47—24no—
172C4⋊C4×C47—21no—
173C4⋊C4×C47—21no—
174C4⋊C4×C47—21no—
175C4⋊C4×C47—21no—
176C4⋊C4×C47—42no—
177C4⋊C4×C47—42no—
178C4⋊C4×C47—81no—
179C4⋊C4×C47C2×D412yes—
180C4⋊C4×C47#4112yes—
181C22⋊C4×C47—24no—
182C22⋊C4×C47—22no—
183C22⋊C4×C47Q1614yescomplemented
184C42×C47—21no—
185C42×C47—21no—
186C42×C47—21no—
187C42×C47—21no—
188C42×C47—42no—
189C42×C47—81no—
190C22⋊Dic47—42no—
191#10625337—44no—
192C4⋊Dic47—21no—
193C4⋊Dic47—21no—
194C4⋊Dic47—21no—
195C4⋊Dic47—21no—
196C4⋊Dic47—21no—
197C4⋊Dic47—21no—
198C4⋊Dic47—42no—
199C4⋊Dic47—81no—
200C4⋊Dic47—81no—
201C4⋊Dic47—81no—
202C4⋊Dic47—81no—
203Dic47⋊C4—42no—
204C2×C47⋊C8—21no—
205C2×C47⋊C8—21no—
206C2×C47⋊C8—21no—
207C2×C47⋊C8—21no—
208C2×C47⋊C8—21no—
209C2×C47⋊C8—21no—
210C2×C47⋊C8—21no—
211C2×C47⋊C8—21no—
212C2×C47⋊C8—21no—
213C2×C47⋊C8—21no—
214C2×C47⋊C8—21no—
215C2×C47⋊C8—44no—
216C2×C47⋊C8#4112yes—
217C23×C47—21no—
218C23×C47—21no—
219C23×C47—21no—
220C23×C47—21no—
221C23×C47#12112yes—
222C23×C47C2×Q1612yes—
223C23×C47#13712yes—
224C23×C47C22×D411yescharacteristic
225Q8×C47—22no—
226Q8×C47—22no—
227Q8×C47—41no—
228Q8×C47—41no—
229C2×C4×C47—21no—
230C2×C4×C47—21no—
231C2×C4×C47—21no—
232C2×C4×C47—21no—
233C2×C4×C47—21no—
234C2×C4×C47—21no—
235C2×C4×C47—22no—
236C2×C4×C47—22no—
237C2×C4×C47—22no—
238C2×C4×C47—22no—
239C2×C4×C47—22no—
240C2×C4×C47—22no—
241C2×C4×C47—21no—
242C2×C4×C47—22no—
243C2×C4×C47—21no—
244C2×C4×C47—21no—
245C2×C4×C47—21no—
246C2×C4×C47—21no—
247C2×C4×C47—21no—
248C2×C4×C47—41no—
249C2×C4×C47—41no—
250C2×C4×C47—41no—
251C2×C4×C47—41no—
252C2×C4×C47—41no—
253C2×C4×C47—41no—
254C2×C4×C47—41no—
255C2×C4×C47—41no—
256C2×C4×C47—41no—
257C2×C4×C47—84no—
258C2×C4×C47#12112yes—
259C2×C4×C47C2×Q1612yes—
260C2×C4×C47C2×Q1612yes—
261C2×C4×C47C22×D411yescharacteristic
262C2×C4×C47C2×#4111yescharacteristic
263C2×C4×C47C2×#4111yescharacteristic
264C2×C4×C47C2×#4111yescharacteristic
265C2×C4×C47H(5,𝔽2)11yescharacteristic
266C2×C4×C472−1+411yescharacteristic
267C2×Dic47—41no—
268C2×Dic47—41no—
269C2×Dic47—41no—
270C2×Dic47—41no—
271C2×Dic47—41no—
272C2×Dic47—41no—
273C2×Dic47—41no—
274C2×Dic47—41no—
275C2×Dic47—41no—
276C2×Dic47—41no—
277C2×Dic47—41no—
278C2×Dic47—41no—
279C2×Dic47—84no—
280Dic94—41no—
281Dic94—41no—
282Dic94—41no—
283Dic94—41no—
284C47⋊C8—22no—
285C47⋊C8—41no—
286C47⋊C8—41no—
287C47⋊C8—41no—
288#25206—471nomaximal, Sylow
289C22×C47—22no—
290C22×C47—22no—
291C22×C47—22no—
292C22×C47—22no—
293C22×C47—22no—
294C22×C47—22no—
295C22×C47#46214yes—
296C22×C47C2×#12111yescharacteristic
297C22×C47#54611yescharacteristic
298C22×C47#54711yescharacteristic
299C22×C47C22×Q1611yescharacteristic
300C22×C47C2×#13711yescharacteristic
301C22×C47#57611yescharacteristic
302C22×C47#57711yescharacteristic
303C4×C47—22no—
304C4×C47—22no—
305C4×C47—22no—
306C4×C47—41no—
307C4×C47—42no—
308C4×C47—42no—
309C4×C47—41no—
310C4×C47—42no—
311C4×C47—81no—
312C4×C47#52911yescharacteristic
313C4×C47#53911yescharacteristic
314C4×C47#54611yescharacteristic
315C4×C47#54711yescharacteristic
316Dic47—81no—
317Dic47—81no—
318Dic47—81no—
319Dic47—81no—
320C2×#484—471no—
321C2×#467—471no—
322#2502—471no—
323#2360D4711yescharacteristic
324#2083—471no—
325#2072—471no—
326#2068—471no—
327#2056—471no—
328#1947—471no—
329#1928—471no—
330#1878—471no—
331#1872—471no—
332#1850—471no—
333#1803—471no—
334C2×#340—471no—
335C2×C47—24no—
336C2×C47#242511yescharacteristic
337C2×C47C2×#46211yescharacteristic
338C2×C47#304511yescharacteristic
339C2×C47#329911yescharacteristic
340C2×C47#331411yescharacteristic
341C2×C47#333811yescharacteristic
342C2×C47#334411yescharacteristic
343C22×Q16—471no—
344C23×C8—471no—
345C2×C22⋊Q8—471no—
346C2×C22⋊Q8C2×D4711yescharacteristic
347C2×C4×Q8C2×D4711yescharacteristic
348C22×C4⋊C4—471no—
349C22×C4⋊C4C2×D4711yescharacteristic
350#484—944no—
351#467—944no—
352C2×#107—471no—
353C2×#107—471no—
354C2×#107—471no—
355C2×C4⋊C8—471no—
356C2×C4⋊C8—471no—
357C2×#103—471no—
358C2×#103—471no—
359C2×#103—471no—
360C2×#103—471no—
361C2×#103—471no—
362C2×#103—471no—
363C2×C22⋊C8—471no—
364#398—941no—
365#398—941no—
366#391—471no—
367#391—471no—
368#391C2×D4711yescharacteristic
369#389—21no—
370#389C2×D4711yescharacteristic
371#387—21no—
372#385—21no—
373#385—941no—
374#385—941no—
375#384—471no—
376#384—471no—
377C4×C4⋊C4C2×D4711yescharacteristic
378C4×C22⋊C4—21no—
379C4×C22⋊C4C2×D4711yescharacteristic
380#340—471no—
381#340—471no—
382#340—471no—
383#340—471no—
384#340—471no—
385#340—471no—
386#336—471no—
387#336—471no—
388C47#2520611yescharacteristic, complemented, Sylow
389C22×Q8—471no—
390C22×Q8C22×D4711yescharacteristic
391C23×C4—21no—
392C23×C4—941no—
393C23×C4C22×D4711yescharacteristic
394C2×Q16—942no—
395C2×Q16—942no—
396C2×Q16—1881no—
397C22×C8—471no—
398C22×C8—471no—
399C22×C8—471no—
400C22×C8—471no—
401C22×C8—942no—
402C22×C8—942no—
403C22×C8—1881no—
404C22⋊Q8—22no—
405C22⋊Q8—942no—
406C22⋊Q8—942no—
407C22⋊Q8D18814yes—
408C4×Q8—22no—
409C4×Q8—41no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—41no—
416C2×C4⋊C4—471no—
417C2×C4⋊C4—471no—
418C2×C4⋊C4—471no—
419C2×C4⋊C4—942no—
420C2×C4⋊C4—942no—
421C2×C4⋊C4—941no—
422C2×C4⋊C4—941no—
423C2×C4⋊C4—941no—
424C2×C4⋊C4—941no—
425C2×C4⋊C4—941no—
426C2×C4⋊C4—941no—
427C2×C4⋊C4C22×D4711yescharacteristic
428C2×C4⋊C4C22×D4711yescharacteristic
429C2×C4⋊C4C22×D4711yescharacteristic
430C2×C22⋊C4—21no—
431C2×C22⋊C4—941no—
432C2×C22⋊C4C22⋊D4711yescharacteristic
433C2×C22⋊C4C22⋊D4711yescharacteristic
434C2×C42—21no—
435C2×C42—21no—
436C2×C42C22×D4711yescharacteristic
437C2×C42C22×D4711yescharacteristic
438#107—942no—
439#107—942no—
440#107—942no—
441C4⋊C8—942no—
442C4⋊C8—1881no—
443#103—942no—
444#103—942no—
445#103—942no—
446#103—942no—
447#103—942no—
448#103—1881no—
449C22⋊C8—942no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—941no—
455#95—941no—
456#95—941no—
457#95—941no—
458#95C22⋊D4711yescharacteristic
459#95C22⋊D4711yescharacteristic
460C24C2×C22⋊D4711yescharacteristic
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—941no—
467C2×Q8—941no—
468C2×Q8—941no—
469C2×Q8—941no—
470C2×Q8—941no—
471C2×Q8—941no—
472C2×Q8C2×D18812yes—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—81no—
484C22×C4—941no—
485C22×C4—941no—
486C22×C4—941no—
487C22×C4—941no—
488C22×C4—3761no—
489C22×C4—3761no—
490C22×C4—1882no—
491C22×C4C2×D18812yes—
492C22×C4#1062535012yes—
493C22×C4C2×C22⋊D4711yescharacteristic
494C22×C4C2×C22⋊D4711yescharacteristic
495C22×C4C2×C22⋊D4711yescharacteristic
496C22×C4C2×C22⋊D4711yescharacteristic
497C22×C4C2×C22⋊D4711yescharacteristic
498C22×C4C23×D4711yescharacteristic
499Q16—1884no—
500C2×C8—472no—
501C2×C8—941no—
502C2×C8—941no—
503C2×C8—941no—
504C2×C8—941no—
505C2×C8—941no—
506C2×C8—941no—
507C2×C8—941no—
508C2×C8—941no—
509C2×C8—941no—
510C2×C8—941no—
511C2×C8—941no—
512C2×C8—1884no—
513C4⋊C4—24no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—42no—
519C4⋊C4—42no—
520C4⋊C4—81no—
521C4⋊C4—941no—
522C4⋊C4—941no—
523C4⋊C4—941no—
524C4⋊C4—941no—
525C4⋊C4—941no—
526C4⋊C4—941no—
527C4⋊C4—3761no—
528C4⋊C4—3761no—
529C4⋊C4—3761no—
530C4⋊C4—3761no—
531C4⋊C4—1882no—
532C4⋊C4—1882no—
533C4⋊C4C2×D18812yes—
534C4⋊C4#1062535212yes—
535C22⋊C4—24no—
536C22⋊C4—22no—
537C22⋊C4—1882no—
538C22⋊C4#1062533714yescomplemented
539C42—21no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—42no—
544C42—81no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23#1309399812yes—
550C23C2×#1062533712yes—
551C23#1309405412yes—
552C23C22×C22⋊D4711yescharacteristic
553Q8—22no—
554Q8—22no—
555Q8—41no—
556Q8—41no—
557Q8—1881no—
558Q8—1881no—
559Q8—1881no—
560Q8—1881no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—21no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—84no—
590C2×C4—3764no—
591C2×C4—1881no—
592C2×C4—1881no—
593C2×C4—1881no—
594C2×C4—1881no—
595C2×C4—1881no—
596C2×C4—1881no—
597C2×C4—1881no—
598C2×C4—1881no—
599C2×C4—1881no—
600C2×C4—1881no—
601C2×C4—1881no—
602C2×C4—1881no—
603C2×C4#1309399812yes—
604C2×C4C2×#1062533712yes—
605C2×C4C2×#1062533712yes—
606C2×C4C22×D18811yescharacteristic
607C2×C4#41×D4711yescharacteristic
608C2×C4C2×#1062535211yescharacteristic
609C2×C4C2×#1062535011yescharacteristic
610C2×C4#1309406911yescharacteristic
611C2×C4#1309407111yescharacteristic
612C8—942no—
613C8—1881no—
614C8—1881no—
615C8—1881no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—22no—
621C22—22no—
622C22#1568933314yes—
623C22C2×#1309399811yescharacteristic
624C22#1568976711yescharacteristic
625C22#1568977211yescharacteristic
626C22C22×#1062533711yescharacteristic
627C22C2×#1309405411yescharacteristic
628C22#1568992611yescharacteristic
629C22#1568993111yescharacteristic
630C4—22no—
631C4—22no—
632C4—22no—
633C4—41no—
634C4—42no—
635C4—41no—
636C4—42no—
637C4—42no—
638C4—81no—
639C4—3761no—
640C4—3761no—
641C4—3761no—
642C4—3761no—
643C4#1568965311yescharacteristic
644C4#1568971511yescharacteristic
645C4#1568976811yescharacteristic
646C4#1568977711yescharacteristic
647C2—24no—
648C2#2024693311yescharacteristic
649C2C2×#1568933311yescharacteristic
650C2#2025292711yescharacteristic
651C2#2025526411yescharacteristic
652C2#2025546911yescharacteristic
653C2#2025577611yescharacteristic
654C2#2025584311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2360C2
socleC23×C47C22×D4
prime radicalC24×C47C2×D4
hypercenter#2360D47
hypocenterC47#25206
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2360

Complements

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

NH ≅ G/Ntype
4. #20244859C2semidirect
5. #20244796C2semidirect
6. #20244780C2semidirect
7. #20244710C2semidirect
8. #20244146C2semidirect
9. #20244029C2semidirect
10. #20243729C2semidirect
13. #20243393C2semidirect
183. C22⋊C4×C47Q16semidirect
388. C47#25206semidirect
538. C22⋊C4#10625337semidirect

Maximal subgroups

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

subgroupindex
C2×#156894562
C2×#156893622
#202478662
#202448592
#202447962
#202447802
#202447102
#202441462
#202440292
#202437292
#202436952
#202435682
#202433932
C2×#156888852
C47×#23602
#2520647