Finite Group Databasebeta

← #26245262

Subgroups — #26245262

Order 12032.

898 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689160C211yesmaximal, characteristic
2C2×#15689158C211yesmaximal, characteristic
3#20245869C211yesmaximal, characteristic
4#20245794C211yesmaximal, characteristic
5#20244871C211yesmaximal, characteristic, complemented
6#20244870C211yesmaximal, characteristic, complemented
7#20244869C211yesmaximal, characteristic, complemented
8#20244868C211yesmaximal, characteristic, complemented
9#20244867C211yesmaximal, characteristic, complemented
10#20244863C211yesmaximal, characteristic, complemented
11#20244862C211yesmaximal, characteristic, complemented
12#20243103C211yesmaximal, characteristic
13#20243103C211yesmaximal, characteristic
14#336×D47C211yesmaximal, characteristic
15C47×#2085C211yesmaximal, characteristic, complemented
16C22×C8×D47C2211yescharacteristic
17C22×C8×D47C2211yescharacteristic
18C2×#13093982C2211yescharacteristic
19C2×#13093982C2211yescharacteristic
20C2×#13093982C2211yescharacteristic
21C2×#13093982C2211yescharacteristic
22C2×C42×D47C2211yescharacteristic
23#15689160—24no—
24#15689158—24no—
25C2×#13093958C2211yescharacteristic
26C2×#13093957C2211yescharacteristic
27C2×#13093957C2211yescharacteristic
28C2×#13093956C2211yescharacteristic
29C2×#13093955C2211yescharacteristic
30C2×#13093955C2211yescharacteristic
31#15689022C2211yescharacteristic
32#15689021C2211yescharacteristic
33#15689019C2211yescharacteristic
34#15688997—21no—
35#15688994—21no—
36#15688992C2211yescharacteristic
37#15688992C2211yescharacteristic
38#15688989C2211yescharacteristic
39#15688982—21no—
40#15688982—21no—
41C4⋊C4×Dic47—21no—
42#15688974—21no—
43#15688974—21no—
44#15688974—21no—
45#15688886C2211yescharacteristic
46#15688886C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688885C2211yescharacteristic
51#15688878C2211yescharacteristic
52#15688877C2211yescharacteristic
53#15688877C2211yescharacteristic
54C2×#107×C47C2211yescharacteristic
55C2×#106×C47C2211yescharacteristic
56C47×#389C2211yescharacteristic
57C47×#382C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#336C2211yescharacteristic
61C22×C4×D47D411yescharacteristic
62C22×C4×D47D411yescharacteristic
63C22×C4×D47C2311yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66C2×C8×D47—22no—
67C2×C8×D47—22no—
68C2×C8×D47—22no—
69C2×C8×D47—22no—
70C2×C8×D47Q814yes—
71C2×C8×D47Q814yes—
72#13093982—22no—
73#13093982—22no—
74#13093982—22no—
75#13093982—22no—
76#13093982—22no—
77#13093982—22no—
78#13093982—22no—
79#13093982D414yes—
80C2×C4⋊Dic47—21no—
81C2×C4⋊Dic47C2311yescharacteristic
82C2×C4⋊Dic47C2311yescharacteristic
83C2×C4⋊Dic47C2311yescharacteristic
84C2×C4⋊Dic47C2311yescharacteristic
85C2×Dic47⋊C4—21no—
86C2×Dic47⋊C4—21no—
87C2×Dic47⋊C4—21no—
88C2×Dic47⋊C4—21no—
89C2×Dic47⋊C4—21no—
90C2×Dic47⋊C4—21no—
91C2×(C2×D47)⋊C4—21no—
92C2×(C2×D47)⋊C4—21no—
93C2×(C2×D47)⋊C4—21no—
94C2×(C2×D47)⋊C4—21no—
95C2×C4×Dic47—21no—
96C2×C4×Dic47—21no—
97C2×C4×Dic47—21no—
98C2×C4×Dic47—21no—
99C2×C4×Dic47D411yescharacteristic
100C2×C4×Dic47D411yescharacteristic
101C2×C4×Dic47C2311yescharacteristic
102C42×D47—22no—
103C42×D47—22no—
104#13093958—22no—
105#13093957—22no—
106#13093957—22no—
107#13093956—22no—
108#13093955—22no—
109#13093955—22no—
110C47⋊#95—21no—
111C47⋊#95—21no—
112C47⋊#95—21no—
113C47⋊#95—21no—
114C47⋊#95—21no—
115C22×C8×C47C2311yescharacteristic
116C22×C8×C47C2311yescharacteristic
117C2×C4⋊C4×C47—21no—
118C2×C4⋊C4×C47C2311yescharacteristic
119C2×C4⋊C4×C47C2311yescharacteristic
120C2×C4⋊C4×C47C2311yescharacteristic
121C2×C4⋊C4×C47C2311yescharacteristic
122C2×C42×C47C2311yescharacteristic
123#107×C47—22no—
124#106×C47—22no—
125#95×C47—21no—
126#95×C47—21no—
127#95×C47—21no—
128C23×D47C2×D411yescharacteristic
129C22×C4×C47—21no—
130C22×C4×C47—21no—
131C22×C4×C47—21no—
132C22×C4×C47—21no—
133C22×C4×C47C2×D411yescharacteristic
134C22×C4×C47C2×D411yescharacteristic
135C22×C4×C47C2411yescharacteristic
136C22×Dic47—21no—
137C22×Dic47—21no—
138C22×Dic47—21no—
139C22×Dic47—21no—
140C22×Dic47C2×D411yescharacteristic
141C22×Dic47C2×D411yescharacteristic
142C22×Dic47C2×D411yescharacteristic
143C2×C4×D47—22no—
144C2×C4×D47—22no—
145C2×C4×D47—22no—
146C2×C4×D47—22no—
147C2×C4×D47—41no—
148C2×C4×D47—41no—
149C2×C4×D47C2×D412yes—
150C2×C4×D47C2×Q812yes—
151C2×C4×D47C2×Q812yes—
152C2×C4×D47#4112yes—
153C2×C4×D47#4112yes—
154C2×C4×D47#4112yes—
155C2×C8×C47—21no—
156C2×C8×C47—21no—
157C2×C8×C47—21no—
158C2×C8×C47—21no—
159C2×C8×C47C2×Q812yes—
160C2×C8×C47C2×Q812yes—
161C4⋊C4×C47—21no—
162C4⋊C4×C47—21no—
163C4⋊C4×C47—21no—
164C4⋊C4×C47—21no—
165C4⋊C4×C47—21no—
166C4⋊C4×C47—21no—
167C4⋊C4×C47—21no—
168C4⋊C4×C47—42no—
169C4⋊C4×C47C2×D412yes—
170C42×C47—21no—
171C42×C47—21no—
172(C2×D47)⋊C4—24no—
173(C2×D47)⋊C4—42no—
174(C2×D47)⋊C4—42no—
175(C2×D47)⋊C4—42no—
176C4⋊Dic47—21no—
177C4⋊Dic47—21no—
178C4⋊Dic47—21no—
179C4⋊Dic47—21no—
180C4⋊Dic47—21no—
181C4⋊Dic47—21no—
182C4⋊Dic47—21no—
183C4⋊Dic47—42no—
184C4⋊Dic47C2×D412yes—
185Dic47⋊C4—42no—
186Dic47⋊C4—42no—
187Dic47⋊C4—42no—
188Dic47⋊C4—42no—
189Dic47⋊C4—42no—
190Dic47⋊C4—42no—
191C4×Dic47—21no—
192C4×Dic47—21no—
193C4×Dic47—24no—
194C4×Dic47—22no—
195C4×Dic47—22no—
196C4×Dic47—42no—
197C4×Dic47—42no—
198C4×Dic47—42no—
199C2×C47⋊C8—21no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8—21no—
202C2×C47⋊C8—21no—
203C2×C47⋊C8C2×Q812yes—
204C2×C47⋊C8C2×Q812yes—
205C8×D47—28no—
206C8×D47—28no—
207C23×C47C22×D411yescharacteristic
208C22×D47—21no—
209C22×D47—21no—
210C22×D47—21no—
211C22×D47—21no—
212C22×D47#12112yes—
213C22×D47#12312yes—
214C22×D47C4⋊Q812yes—
215C2×C4×C47—22no—
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—41no—
223C2×C4×C47—41no—
224C2×C4×C47—41no—
225C2×C4×C47—41no—
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×C47C22×D411yescharacteristic
234C2×C4×C47C22×Q811yescharacteristic
235C2×C4×C47C22×Q811yescharacteristic
236C2×C4×C47C2×#4111yescharacteristic
237C2×C4×C47C2×#4111yescharacteristic
238C2×C4×C47C2×#4111yescharacteristic
239C2×Dic47—21no—
240C2×Dic47—21no—
241C2×Dic47—21no—
242C2×Dic47—21no—
243C2×Dic47—22no—
244C2×Dic47—41no—
245C2×Dic47—41no—
246C2×Dic47—41no—
247C2×Dic47—41no—
248C2×Dic47—41no—
249C2×Dic47—41no—
250C2×Dic47—41no—
251C2×Dic47—41no—
252C2×Dic47—41no—
253C2×Dic47—41no—
254C2×Dic47—41no—
255C2×Dic47#12112yes—
256C2×Dic47#12312yes—
257C2×Dic47C4⋊Q812yes—
258C2×Dic47#13512yes—
259C2×Dic47#13512yes—
260C4×D47—44no—
261C4×D47—44no—
262C4×D47C22⋊Q814yes—
263C4×D47C22⋊Q814yes—
264C4×D47#12514yes—
265C4×D47#12514yes—
266C8×C47—22no—
267C8×C47—22no—
268C47⋊C8—22no—
269C47⋊C8—22no—
270#23656—471nomaximal, Sylow
271C22×C47C2×#12111yescharacteristic
272C22×C47C2×#12311yescharacteristic
273C22×C47C2×C4⋊Q811yescharacteristic
274C22×C47C2×#13511yescharacteristic
275C22×C47C2×#13511yescharacteristic
276C22×C47#57511yescharacteristic
277C22×C47#57511yescharacteristic
278C2×D47—22no—
279C2×D47—22no—
280C2×D47—22no—
281C2×D47—22no—
282C2×D47—22no—
283C2×D47—22no—
284C2×D47#39814yes—
285C4×C47—41no—
286C4×C47—41no—
287C4×C47—42no—
288C4×C47—81no—
289C4×C47—81no—
290C4×C47—81no—
291C4×C47C2×C22⋊Q811yescharacteristic
292C4×C47C2×C22⋊Q811yescharacteristic
293C4×C47C2×#12511yescharacteristic
294C4×C47C2×#12511yescharacteristic
295Dic47—22no—
296Dic47—22no—
297Dic47—42no—
298Dic47—81no—
299Dic47—81no—
300Dic47—81no—
301Dic47#39814yes—
302C2×#427—471no—
303C2×#427—471no—
304#2296—471no—
305#2285—471no—
306#2085—471no—
307#2085—471no—
308#2085—471no—
309#2085D4711yescharacteristic, complemented
310#2084—471no—
311#2084—471no—
312#2083—471no—
313#2083—471no—
314#1735—471no—
315#1735—471no—
316C2×#336—471no—
317C2×C47C2×#39811yescharacteristic
318C2×C47#303511yescharacteristic
319C2×C47#303511yescharacteristic
320C2×C47#309111yescharacteristic
321C2×C47#309111yescharacteristic
322C2×C47#316011yescharacteristic
323C2×C47#316211yescharacteristic
324D47—24no—
325C23×C8—471no—
326C23×C8—471no—
327C2×#117—471no—
328C2×#117—471no—
329C2×#117—471no—
330C2×#117—471no—
331C22×C42—471no—
332#427—944no—
333#427—944no—
334C2×#107—471no—
335C2×#107—471no—
336C2×#107—471no—
337C2×#107C2×D4711yescharacteristic
338C2×#106—471no—
339C2×#106—471no—
340C2×#106—471no—
341C2×#106C2×D4711yescharacteristic
342#389—471no—
343#389—471no—
344#389—471no—
345#389C2×D4711yescharacteristic
346#385—941no—
347#385—941no—
348#384—471no—
349#384—471no—
350#382—471no—
351#382C2×D4711yescharacteristic
352#380—941no—
353#380—941no—
354C4×C4⋊C4—941no—
355C4×C4⋊C4—941no—
356C4×C4⋊C4—941no—
357C4×C4⋊C4—941no—
358#340—471no—
359#340—471no—
360#340—471no—
361#340—471no—
362#340—471no—
363#340—471no—
364#340C2×D4711yescharacteristic
365#340C2×D4711yescharacteristic
366#336—471no—
367#336—471no—
368#336—471no—
369#336C2×D4711yescharacteristic
370C47#2365611yescharacteristic, complemented, Sylow
371C23×C4—471no—
372C23×C4—471no—
373C23×C4—471no—
374C22×C8—471no—
375C22×C8—471no—
376C22×C8—474no—
377C22×C8—474no—
378C22×C8—942no—
379C22×C8—942no—
380C22×C8—942no—
381C22×C8—942no—
382C22×C8C22×D4711yescharacteristic
383C22×C8C22×D4711yescharacteristic
384#117—474no—
385#117—942no—
386#117—942no—
387#117—942no—
388#117—942no—
389#117—942no—
390#117—942no—
391#117—942no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—471no—
394C2×C4⋊C4—471no—
395C2×C4⋊C4—471no—
396C2×C4⋊C4—471no—
397C2×C4⋊C4—941no—
398C2×C4⋊C4—941no—
399C2×C4⋊C4—941no—
400C2×C4⋊C4—941no—
401C2×C4⋊C4—941no—
402C2×C4⋊C4—941no—
403C2×C4⋊C4—941no—
404C2×C4⋊C4C22×D4711yescharacteristic
405C2×C4⋊C4C22×D4711yescharacteristic
406C2×C4⋊C4C22×D4711yescharacteristic
407C2×C4⋊C4C22×D4711yescharacteristic
408C2×C22⋊C4—941no—
409C2×C22⋊C4—941no—
410C2×C22⋊C4—941no—
411C2×C22⋊C4—941no—
412C2×C42—471no—
413C2×C42—471no—
414C2×C42—471no—
415C2×C42—942no—
416C2×C42—942no—
417C2×C42—941no—
418C2×C42—941no—
419C2×C42—941no—
420C2×C42—941no—
421C2×C42C22×D4711yescharacteristic
422#107—22no—
423#107—942no—
424#107—942no—
425#107—942no—
426#106—22no—
427#106—942no—
428#106—942no—
429#106—942no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—941no—
434#95—941no—
435#95—941no—
436#95—941no—
437#95—941no—
438C24—471no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—471no—
444C22×C4—472no—
445C22×C4—472no—
446C22×C4—472no—
447C22×C4—472no—
448C22×C4—472no—
449C22×C4—472no—
450C22×C4—471no—
451C22×C4—471no—
452C22×C4—942no—
453C22×C4—942no—
454C22×C4—942no—
455C22×C4—942no—
456C22×C4—941no—
457C22×C4—941no—
458C22×C4—941no—
459C22×C4—941no—
460C22×C4—1881no—
461C22×C4—1881no—
462C22×C4D4×D4711yescharacteristic
463C22×C4D4×D4711yescharacteristic
464C22×C4C23×D4711yescharacteristic
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—472no—
470C2×C8—472no—
471C2×C8—948no—
472C2×C8—948no—
473C2×C8—941no—
474C2×C8—941no—
475C2×C8—941no—
476C2×C8—941no—
477C2×C8Q8×D4712yes—
478C2×C8Q8×D4712yes—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—42no—
487C4⋊C4—472no—
488C4⋊C4—941no—
489C4⋊C4—941no—
490C4⋊C4—941no—
491C4⋊C4—941no—
492C4⋊C4—941no—
493C4⋊C4—941no—
494C4⋊C4—941no—
495C4⋊C4—1882no—
496C4⋊C4—1882no—
497C4⋊C4—1882no—
498C4⋊C4—1882no—
499C4⋊C4—1882no—
500C4⋊C4—1882no—
501C4⋊C4—1882no—
502C4⋊C4D4×D4712yes—
503C22⋊C4—944no—
504C22⋊C4—1882no—
505C22⋊C4—1882no—
506C22⋊C4—1882no—
507C42—21no—
508C42—21no—
509C42—942no—
510C42—942no—
511C42—944no—
512C42—941no—
513C42—941no—
514C42—1882no—
515C42—1882no—
516C42—1882no—
517C23—472no—
518C23—472no—
519C23—472no—
520C23—941no—
521C23—941no—
522C23—941no—
523C23—941no—
524C23C2×D4×D4711yescharacteristic
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—472no—
544C2×C4—472no—
545C2×C4—472no—
546C2×C4—474no—
547C2×C4—474no—
548C2×C4—474no—
549C2×C4—474no—
550C2×C4—472no—
551C2×C4—472no—
552C2×C4—941no—
553C2×C4—941no—
554C2×C4—941no—
555C2×C4—941no—
556C2×C4—942no—
557C2×C4—1884no—
558C2×C4—1884no—
559C2×C4—1881no—
560C2×C4—1881no—
561C2×C4—1881no—
562C2×C4—1881no—
563C2×C4—1881no—
564C2×C4—1881no—
565C2×C4—1881no—
566C2×C4—1881no—
567C2×C4—1881no—
568C2×C4—1881no—
569C2×C4—1881no—
570C2×C4C2×D4×D4711yescharacteristic
571C2×C4C2×Q8×D4711yescharacteristic
572C2×C4C2×Q8×D4711yescharacteristic
573C2×C4#41×D4711yescharacteristic
574C2×C4#41×D4711yescharacteristic
575C2×C4#41×D4711yescharacteristic
576C8—22no—
577C8—22no—
578C8—942no—
579C8—942no—
580C22—474no—
581C22—942no—
582C22—942no—
583C22—942no—
584C22—942no—
585C22—942no—
586C22—942no—
587C22#121×D4711yescharacteristic
588C22#123×D4711yescharacteristic
589C22C4⋊Q8×D4711yescharacteristic
590C22#135×D4711yescharacteristic
591C22#135×D4711yescharacteristic
592C22#1568991911yescharacteristic
593C22#1568992211yescharacteristic
594C4—41no—
595C4—41no—
596C4—42no—
597C4—81no—
598C4—81no—
599C4—81no—
600C4—474no—
601C4—942no—
602C4—942no—
603C4—3761no—
604C4—3761no—
605C4—3761no—
606C4—1882no—
607C4C22⋊Q8×D4711yescharacteristic
608C4C22⋊Q8×D4711yescharacteristic
609C4#125×D4711yescharacteristic
610C4#125×D4711yescharacteristic
611C2—944no—
612C2#398×D4711yescharacteristic
613C2#2025284011yescharacteristic
614C2#2025284211yescharacteristic
615C2#2025330011yescharacteristic
616C2#2025330611yescharacteristic
617C2#2025390111yescharacteristic
618C2#2025390911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2085C2
socleC23×C47C22×D4
prime radicalC23×D47C2×D4
hypercenter#2085D47
hypocenterC47#23656
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2085

Complements

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

NH ≅ G/Ntype
5. #20244871C2semidirect
6. #20244870C2semidirect
7. #20244869C2semidirect
8. #20244868C2semidirect
9. #20244867C2semidirect
10. #20244863C2semidirect
11. #20244862C2semidirect
15. C47×#2085C2semidirect
309. #2085D47semidirect
370. C47#23656semidirect

Maximal subgroups

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

subgroupindex
C2×#156891602
C2×#156891582
#202458692
#202457942
#202448712
#202448702
#202448692
#202448682
#202448672
#202448632
#202448622
#202431032
#336×D472
C47×#20852
#2365647