Finite Group Databasebeta

← #26257615

Subgroups — #26257615

Order 12032.

802 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689403C211yesmaximal, characteristic, complemented
2C2×#15689184C211yesmaximal, characteristic, complemented
3#20249209C211yesmaximal, characteristic, complemented
4#20244819C211yesmaximal, characteristic, complemented
5#20244814C211yesmaximal, characteristic, complemented
6#20244574C211yesmaximal, characteristic
7#20244567C211yesmaximal, characteristic
8#20244336C211yesmaximal, characteristic, complemented
9#20244156C211yesmaximal, characteristic, complemented
10#20244128C211yesmaximal, characteristic, complemented
11#20244118C211yesmaximal, characteristic, complemented
12#20244088C211yesmaximal, characteristic, complemented
13#20244074C211yesmaximal, characteristic, complemented
14#20243398C211yesmaximal, characteristic, complemented
15C47×#2324C211yesmaximal, characteristic
16C2×#13094024C2211yescharacteristic
17#15689403—24no—
18#15689184—24no—
19C2×#13093957C2211yescharacteristic
20C2×#13093957C2211yescharacteristic
21C2×#13093957C2211yescharacteristic
22C2×#13093955C2211yescharacteristic
23C2×C4⋊(C47⋊C8)C2211yescharacteristic
24C2×C4⋊(C47⋊C8)C2211yescharacteristic
25C2×#13093945C2211yescharacteristic
26C2×#13093945C2211yescharacteristic
27C2×#13093945C2211yescharacteristic
28C2×#13093945C2211yescharacteristic
29C2×C22⋊(C47⋊C8)C2211yescharacteristic
30C2×C22⋊(C47⋊C8)C2211yescharacteristic
31C2×#13093935C2211yescharacteristic
32C2×C4×C47⋊C8C2211yescharacteristic
33#15689062—21no—
34#15689059—21no—
35#15689043—21no—
36#15689035—21no—
37#15689021C2211yescharacteristic
38#15689021C2211yescharacteristic
39#15688989C2211yescharacteristic
40#15688983C2211yescharacteristic
41#15688983C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688885C2211yescharacteristic
50C2×#121×C47C2211yescharacteristic
51C2×C4×D4×C47C2211yescharacteristic
52C2×#117×C47C2211yescharacteristic
53C47×#390—21no—
54C47×#390C2211yescharacteristic
55C47×#389C2211yescharacteristic
56C47×#388—21no—
57C47×#386—21no—
58C47×#385—21no—
59C47×#380C2211yescharacteristic
60C4×C4⋊C4×C47C2211yescharacteristic
61C22×Dic94—21no—
62C22×C47⋊C8C2311yescharacteristic
63C22×C47⋊C8C2311yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66#13094024—22no—
67#13094024—22no—
68C2×C4⋊Dic47—21no—
69C2×C4⋊Dic47C2311yescharacteristic
70C2×C4⋊Dic47C2311yescharacteristic
71C2×C4⋊Dic47C2311yescharacteristic
72C2×C4⋊Dic47C2311yescharacteristic
73C2×Dic47⋊C4—21no—
74C2×Dic47⋊C4—21no—
75C2×C22⋊Dic47—21no—
76C2×C22⋊Dic47—21no—
77#13093957—22no—
78#13093957—22no—
79#13093957—22no—
80#13093955—22no—
81C4⋊(C47⋊C8)—22no—
82C4⋊(C47⋊C8)D414yescomplemented
83#13093945—22no—
84#13093945—22no—
85#13093945—22no—
86#13093945—22no—
87C22⋊(C47⋊C8)—22no—
88C22⋊(C47⋊C8)—22no—
89#13093935—22no—
90C4×C47⋊C8—22no—
91C47⋊#95—21no—
92C47⋊#95—21no—
93C47⋊#95—21no—
94C47⋊#95—21no—
95C47⋊#95—21no—
96C47⋊#95—21no—
97C22×D4×C47—21no—
98C22×D4×C47C2311yescharacteristic
99C23×C4×C47—21no—
100C23×C4×C47C2311yescharacteristic
101#121×C47—22no—
102#121×C47—22no—
103C4×D4×C47—22no—
104C4×D4×C47—22no—
105#117×C47—22no—
106#117×C47—22no—
107C2×C4⋊C4×C47—21no—
108C2×C4⋊C4×C47D411yescharacteristic
109C2×C4⋊C4×C47D411yescharacteristic
110C2×C4⋊C4×C47C2311yescharacteristic
111C2×C4⋊C4×C47C2311yescharacteristic
112C2×C4⋊C4×C47C2311yescharacteristic
113C2×C22⋊C4×C47—21no—
114C2×C22⋊C4×C47—21no—
115C2×C22⋊C4×C47—21no—
116C2×C22⋊C4×C47—21no—
117C2×C22⋊C4×C47—21no—
118C2×C22⋊C4×C47D411yescharacteristic
119C2×C22⋊C4×C47D411yescharacteristic
120C2×C42×C47—21no—
121C2×C42×C47C2311yescharacteristic
122C2×C42×C47C2311yescharacteristic
123#95×C47—21no—
124#95×C47—21no—
125#95×C47—21no—
126C24×C47—21no—
127C24×C47C2×D411yescharacteristic
128C2×D4×C47—24no—
129C2×D4×C47—21no—
130C2×D4×C47—21no—
131C2×D4×C47—21no—
132C2×D4×C47—21no—
133C2×D4×C47—21no—
134C2×D4×C47—81no—
135C2×D4×C47—81no—
136C2×D4×C47#4112yes—
137C22×C4×C47—21no—
138C22×C4×C47—21no—
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—42no—
147C22×C4×C47—81no—
148C22×C4×C47—81no—
149C22×C4×C47C2×D411yescharacteristic
150C22×C4×C47C2×D411yescharacteristic
151C22×C4×C47C2×D411yescharacteristic
152C22×C4×C47C2×D411yescharacteristic
153C22×C4×C47C2×D411yescharacteristic
154C22×C4×C47C2411yescharacteristic
155C22×Dic47—21no—
156C22×Dic47—21no—
157C22×Dic47—21no—
158C22×Dic47—21no—
159C2×Dic94—42no—
160C2×Dic94—81no—
161C2×Dic94—81no—
162C4⋊C4×C47—22no—
163C4⋊C4×C47—22no—
164C4⋊C4×C47—21no—
165C4⋊C4×C47—21no—
166C4⋊C4×C47—21no—
167C4⋊C4×C47—21no—
168C4⋊C4×C47—21no—
169C4⋊C4×C47—81no—
170C4⋊C4×C47#4112yes—
171C22⋊C4×C47—24no—
172C22⋊C4×C47—22no—
173C22⋊C4×C47—22no—
174C22⋊C4×C47—42no—
175C22⋊C4×C47—81no—
176C22⋊C4×C47—81no—
177C22⋊C4×C47—81no—
178C42×C47—21no—
179C42×C47—21no—
180C42×C47—81no—
181C42×C47C2×D412yes—
182C42×C47#4112yes—
183C22⋊Dic47—81no—
184C22⋊Dic47—81no—
185C4⋊Dic47—21no—
186C4⋊Dic47—21no—
187C4⋊Dic47—21no—
188C4⋊Dic47—21no—
189C4⋊Dic47—21no—
190C4⋊Dic47—21no—
191C4⋊Dic47—21no—
192C4⋊Dic47—21no—
193C4⋊Dic47—42no—
194Dic47⋊C4—81no—
195Dic47⋊C4—81no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8—21no—
199C2×C47⋊C8—21no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8—21no—
202C2×C47⋊C8—21no—
203C2×C47⋊C8—21no—
204C2×C47⋊C8—21no—
205C2×C47⋊C8—21no—
206C2×C47⋊C8C2×D412yes—
207C2×C47⋊C8C2×D412yes—
208C23×C47—21no—
209C23×C47—22no—
210C23×C47—21no—
211C23×C47—21no—
212C23×C47—21no—
213C23×C47—21no—
214C23×C47—21no—
215C23×C47—21no—
216C23×C47—41no—
217C23×C47—41no—
218C23×C47—41no—
219C23×C47—41no—
220C23×C47—41no—
221C23×C47—41no—
222C23×C47C22×D411yescharacteristic
223D4×C47—22no—
224D4×C47—22no—
225D4×C47—41no—
226D4×C47—41no—
227D4×C47—84no—
228C2×C4×C47—21no—
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—21no—
236C2×C4×C47—22no—
237C2×C4×C47—21no—
238C2×C4×C47—21no—
239C2×C4×C47—21no—
240C2×C4×C47—21no—
241C2×C4×C47—21no—
242C2×C4×C47—41no—
243C2×C4×C47—41no—
244C2×C4×C47—41no—
245C2×C4×C47—41no—
246C2×C4×C47—41no—
247C2×C4×C47—41no—
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—84no—
255C2×C4×C47#12112yes—
256C2×C4×C47#12112yes—
257C2×C4×C47C22×D411yescharacteristic
258C2×C4×C47C2×#4111yescharacteristic
259C2×C4×C47C2×#4111yescharacteristic
260C2×C4×C47C2×#4111yescharacteristic
261C2×C4×C472−1+411yescharacteristic
262C2×C4×C472−1+411yescharacteristic
263C2×Dic47—41no—
264C2×Dic47—41no—
265C2×Dic47—41no—
266C2×Dic47—41no—
267C2×Dic47—41no—
268C2×Dic47—41no—
269C2×Dic47—41no—
270C2×Dic47—41no—
271C2×Dic47—41no—
272C2×Dic47—41no—
273C2×Dic47—41no—
274C2×Dic47—41no—
275Dic94—84no—
276C47⋊C8—22no—
277C47⋊C8—22no—
278C47⋊C8—41no—
279C47⋊C8—41no—
280#24712—471nomaximal, Sylow
281C22×C47—41no—
282C22×C47—42no—
283C22×C47—41no—
284C22×C47—42no—
285C22×C47—41no—
286C22×C47—42no—
287C22×C47—41no—
288C22×C47—41no—
289C22×C47—41no—
290C22×C47—41no—
291C22×C47—81no—
292C22×C47—81no—
293C22×C47—81no—
294C22×C47—81no—
295C22×C47C2×#12111yescharacteristic
296C22×C47#52511yescharacteristic
297C22×C47#53611yescharacteristic
298C22×C47#57611yescharacteristic
299C22×C47#57611yescharacteristic
300C22×C47#57711yescharacteristic
301C22×C47#57811yescharacteristic
302C4×C47—22no—
303C4×C47—22no—
304C4×C47—42no—
305C4×C47—41no—
306C4×C47—41no—
307C4×C47—41no—
308C4×C47—81no—
309C4×C47—81no—
310C4×C47#54711yescharacteristic
311C4×C47#54811yescharacteristic
312C4×C47#55211yescharacteristic
313C4×C47#55611yescharacteristic
314Dic47—81no—
315Dic47—81no—
316Dic47—81no—
317Dic47—81no—
318C2×#474—471no—
319C2×#433—471no—
320#2628—471no—
321#2324D4711yescharacteristic
322#2076—471no—
323#2075—471no—
324#2034—471no—
325#2033—471no—
326#1987—471no—
327#1949—471no—
328#1944—471no—
329#1942—471no—
330#1936—471no—
331#1934—471no—
332#1804—471no—
333C2×C47—81no—
334C2×C47—82no—
335C2×C47#241511yescharacteristic
336C2×C47#305811yescharacteristic
337C2×C47#306311yescharacteristic
338C2×C47#311811yescharacteristic
339C2×C47#312411yescharacteristic
340C2×C47#324111yescharacteristic
341C2×C47#324311yescharacteristic
342C2×C4⋊Q8—471no—
343C2×#121C2×D4711yescharacteristic
344C2×C4×D4C2×D4711yescharacteristic
345C2×#117C2×D4711yescharacteristic
346#474—944no—
347#433—944no—
348C2×#107—471no—
349C2×#107—471no—
350C2×#107—471no—
351C2×#106—471no—
352C2×C4⋊C8—471no—
353C2×C4⋊C8—471no—
354C2×#102—471no—
355C2×#102—471no—
356C2×#102—471no—
357C2×#102—471no—
358C2×C22⋊C8—471no—
359C2×C22⋊C8—471no—
360C2×#97—471no—
361C2×C4×C8—471no—
362#400—941no—
363#399—941no—
364#395—941no—
365#393—941no—
366#390—21no—
367#390C2×D4711yescharacteristic
368#389—471no—
369#389—471no—
370#389C2×D4711yescharacteristic
371#388—21no—
372#386—21no—
373#385—21no—
374#382—471no—
375#380—471no—
376#380—471no—
377#380C2×D4711yescharacteristic
378C4×C4⋊C4C2×D4711yescharacteristic
379#340—471no—
380#340—471no—
381#340—471no—
382#340—471no—
383#340—471no—
384#340—471no—
385#340—471no—
386#340—471no—
387C47#2471211yescharacteristic, complemented, Sylow
388C22×Q8—941no—
389C22×D4—21no—
390C22×D4C22×D4711yescharacteristic
391C23×C4—21no—
392C23×C4C22×D4711yescharacteristic
393C22×C8—471no—
394C22×C8—471no—
395C22×C8—471no—
396C22×C8—471no—
397C4⋊Q8—942no—
398C4⋊Q8—942no—
399#121—22no—
400#121—22no—
401C4×D4—22no—
402C4×D4—22no—
403#117—22no—
404#117—22no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—471no—
407C2×C4⋊C4—471no—
408C2×C4⋊C4—471no—
409C2×C4⋊C4—471no—
410C2×C4⋊C4—941no—
411C2×C4⋊C4—941no—
412C2×C4⋊C4—941no—
413C2×C4⋊C4C22⋊D4711yescharacteristic
414C2×C4⋊C4C22⋊D4711yescharacteristic
415C2×C4⋊C4C22×D4711yescharacteristic
416C2×C4⋊C4C22×D4711yescharacteristic
417C2×C4⋊C4C22×D4711yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—941no—
424C2×C22⋊C4—941no—
425C2×C22⋊C4C22⋊D4711yescharacteristic
426C2×C22⋊C4C22⋊D4711yescharacteristic
427C2×C42—21no—
428C2×C42C22×D4711yescharacteristic
429C2×C42C22×D4711yescharacteristic
430#107—942no—
431#107—942no—
432#107—942no—
433#106—942no—
434C4⋊C8—474no—
435C4⋊C8—942no—
436#102—942no—
437#102—942no—
438#102—942no—
439#102—942no—
440C22⋊C8—942no—
441C22⋊C8—942no—
442#97—942no—
443C4×C8—942no—
444#95—21no—
445#95—21no—
446#95—21no—
447#95—941no—
448#95—941no—
449#95—941no—
450#95—941no—
451#95—941no—
452#95—941no—
453C24—21no—
454C24C2×C22⋊D4711yescharacteristic
455C2×Q8—3761no—
456C2×Q8—3761no—
457C2×Q8—1882no—
458C2×D4—24no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—81no—
465C2×D4—81no—
466C2×D4#1062535012yes—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—42no—
477C22×C4—81no—
478C22×C4—81no—
479C22×C4—941no—
480C22×C4—941no—
481C22×C4—941no—
482C22×C4—941no—
483C22×C4C2×C22⋊D4711yescharacteristic
484C22×C4C2×C22⋊D4711yescharacteristic
485C22×C4C2×C22⋊D4711yescharacteristic
486C22×C4C2×C22⋊D4711yescharacteristic
487C22×C4C2×C22⋊D4711yescharacteristic
488C22×C4C23×D4711yescharacteristic
489C2×C8—472no—
490C2×C8—472no—
491C2×C8—941no—
492C2×C8—941no—
493C2×C8—941no—
494C2×C8—941no—
495C2×C8—941no—
496C2×C8—941no—
497C2×C8—941no—
498C2×C8—941no—
499C2×C8—941no—
500C2×C8—941no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—81no—
509C4⋊C4—941no—
510C4⋊C4—941no—
511C4⋊C4—941no—
512C4⋊C4—941no—
513C4⋊C4—941no—
514C4⋊C4—941no—
515C4⋊C4—941no—
516C4⋊C4—941no—
517C4⋊C4—3761no—
518C4⋊C4—3761no—
519C4⋊C4—1882no—
520C4⋊C4#1062535012yes—
521C22⋊C4—24no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—42no—
525C22⋊C4—81no—
526C22⋊C4—81no—
527C22⋊C4—81no—
528C22⋊C4—3761no—
529C22⋊C4—3761no—
530C42—21no—
531C42—21no—
532C42—81no—
533C42D4×D4712yes—
534C42#1062535212yes—
535C23—21no—
536C23—22no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—21no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23C22×C22⋊D4711yescharacteristic
550Q8—3764no—
551D4—22no—
552D4—22no—
553D4—41no—
554D4—41no—
555D4—84no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—84no—
583C2×C4—1881no—
584C2×C4—1881no—
585C2×C4—1881no—
586C2×C4—1881no—
587C2×C4—1881no—
588C2×C4—1881no—
589C2×C4—1881no—
590C2×C4—1881no—
591C2×C4—1881no—
592C2×C4—1881no—
593C2×C4—1881no—
594C2×C4—1881no—
595C2×C4#1309399612yes—
596C2×C4#1309399612yes—
597C2×C4C2×D4×D4711yescharacteristic
598C2×C4C2×#1062535211yescharacteristic
599C2×C4C2×#1062535011yescharacteristic
600C2×C4C2×#1062535011yescharacteristic
601C2×C4#1309407111yescharacteristic
602C2×C4#1309407111yescharacteristic
603C8—942no—
604C8—942no—
605C8—1881no—
606C8—1881no—
607C22—41no—
608C22—42no—
609C22—41no—
610C22—41no—
611C22—42no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22—42no—
617C22—81no—
618C22—81no—
619C22—81no—
620C22—81no—
621C22C2×#1309399611yescharacteristic
622C22#1568963411yescharacteristic
623C22#1568969411yescharacteristic
624C22#1568992611yescharacteristic
625C22#1568992611yescharacteristic
626C22#1568993411yescharacteristic
627C22#1568993811yescharacteristic
628C4—22no—
629C4—22no—
630C4—41no—
631C4—41no—
632C4—42no—
633C4—41no—
634C4—81no—
635C4—81no—
636C4—3761no—
637C4—3761no—
638C4—3761no—
639C4—3761no—
640C4#1568977811yescharacteristic
641C4#1568978211yescharacteristic
642C4#1568981311yescharacteristic
643C4#1568984311yescharacteristic
644C2—81no—
645C2—82no—
646C2#2024681711yescharacteristic
647C2#2025303311yescharacteristic
648C2#2025308111yescharacteristic
649C2#2025357211yescharacteristic
650C2#2025365011yescharacteristic
651C2#2025463511yescharacteristic
652C2#2025466511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2324C2
socleC23×C47C22×D4
prime radicalC2×#121×C47C22
hypercenter#2324D47
hypocenterC47#24712
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2324

Complements

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

NH ≅ G/Ntype
1. C2×#15689403C2semidirect
2. C2×#15689184C2semidirect
3. #20249209C2semidirect
4. #20244819C2semidirect
5. #20244814C2semidirect
8. #20244336C2semidirect
9. #20244156C2semidirect
10. #20244128C2semidirect
11. #20244118C2semidirect
12. #20244088C2semidirect
13. #20244074C2semidirect
14. #20243398C2semidirect
82. C4⋊(C47⋊C8)D4semidirect
387. C47#24712semidirect

Maximal subgroups

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

subgroupindex
C2×#156894032
C2×#156891842
#202492092
#202448192
#202448142
#202445742
#202445672
#202443362
#202441562
#202441282
#202441182
#202440882
#202440742
#202433982
C47×#23242
#2471247