Finite Group Databasebeta

← #26216069

Subgroups — #26216069

Order 12032.

1502 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D47C211yesmaximal, characteristic
2C22×(C2×D47)⋊C8C211yesmaximal, characteristic
3#20245767C211yesmaximal, characteristic
4#20243482C212yesmaximal, complemented
5#20243481C212yesmaximal, complemented
6#20243477C212yesmaximal, complemented
7#20243473C212yesmaximal, complemented
8#20243105C211yesmaximal, characteristic, complemented
9#20243104C211yesmaximal, characteristic, complemented
10#20243104C211yesmaximal, characteristic, complemented
11C47×#1735C211yesmaximal, characteristic, complemented
12C23×C4×D47C2211yescharacteristic
13C23×C47⋊C8C2211yescharacteristic
14C2×#13093983C2211yescharacteristic
15C2×#13093983C2211yescharacteristic
16C2×#13093982C2211yescharacteristic
17C2×#13093982C2211yescharacteristic
18C2×#13093981—21no—
19C2×#13093980—21no—
20#117×D47—24no—
21#117×D47C418yescomplemented
22C2×C4⋊C4×D47C2211yescharacteristic
23C2×C4⋊C4×D47C2211yescharacteristic
24C2×C22⋊C4×D47—21no—
25C2×C42×D47—21no—
26C2×(C2×D47)⋊C8—24no—
27C2×(C2×D47)⋊C8C2212yes—
28C2×(C2×D47)⋊C8C2212yes—
29#15688984—21no—
30#15688980C2212yes—
31#15688980C2212yes—
32#15688978—21no—
33C4×(C2×D47)⋊C4—21no—
34C4×(C2×D47)⋊C4—21no—
35#15688886C2212yescomplemented
36#15688886C2212yescomplemented
37#15688885C2212yescomplemented
38#15688885C2212yescomplemented
39#15688885C2212yescomplemented
40#15688885C2212yescomplemented
41C23×C8×C47C2211yescharacteristic
42C2×#117×C47C2211yescharacteristic
43C2×#117×C47C2211yescharacteristic
44C47×#340C2212yescomplemented
45C47×#340C2212yescomplemented
46C24×D47D411yescharacteristic
47C23×Dic47D411yescharacteristic
48C22×C4×D47—22no—
49C22×C4×D47—22no—
50C22×C4×D47—22no—
51C22×C4×D47—22no—
52C22×C4×D47—21no—
53C22×C4×D47—21no—
54C22×C4×D47C2×C414yes—
55C22×C4×D47D411yescharacteristic
56C22×C4×D47D411yescharacteristic
57C22×C4×D47D414yes—
58C22×C4×D47C2311yescharacteristic
59C22×C4×D47C2311yescharacteristic
60C22×C47⋊C8—22no—
61C22×C47⋊C8—22no—
62C22×C47⋊C8—22no—
63C22×C47⋊C8C2312yes—
64#13093983—22no—
65#13093983—22no—
66#13093983—22no—
67#13093983C2×C414yes—
68#13093982—22no—
69#13093982—22no—
70#13093982C2×C414yes—
71#13093982C2×C414yes—
72#13093981—28no—
73#13093980—28no—
74C2×C4⋊Dic47C2312yes—
75C2×C4⋊Dic47C2311yescharacteristic
76C2×C4⋊Dic47C2311yescharacteristic
77C2×Dic47⋊C4—21no—
78C2×Dic47⋊C4—21no—
79C4⋊C4×D47—22no—
80C4⋊C4×D47—22no—
81C4⋊C4×D47C2×C414yes—
82C4⋊C4×D47C2×C414yes—
83C2×C22⋊Dic47—21no—
84C2×C22⋊Dic47—21no—
85C2×(C2×D47)⋊C4—21no—
86C2×(C2×D47)⋊C4—21no—
87C2×(C2×D47)⋊C4—22no—
88C2×(C2×D47)⋊C4—22no—
89C22⋊C4×D47—28no—
90C2×C4×Dic47—21no—
91C2×C4×Dic47—21no—
92C2×C4×Dic47—21no—
93C2×C4×Dic47—21no—
94C42×D47—28no—
95(C2×D47)⋊C8—24no—
96(C2×D47)⋊C8—24no—
97C47⋊#95—22no—
98C47⋊#95—22no—
99C23×C4×C47C2311yescharacteristic
100C22×C8×C47—22no—
101C22×C8×C47—22no—
102C22×C8×C47—22no—
103C22×C8×C47C2312yes—
104#117×C47—22no—
105#117×C47—22no—
106#117×C47—22no—
107#117×C47C2×C414yes—
108C2×C4⋊C4×C47C2312yes—
109C2×C4⋊C4×C47C2311yescharacteristic
110C2×C4⋊C4×C47C2311yescharacteristic
111C2×C22⋊C4×C47—21no—
112C2×C22⋊C4×C47—21no—
113C2×C42×C47—21no—
114C2×C42×C47—21no—
115C24×C47C2×D411yescharacteristic
116C23×D47—22no—
117C23×D47—22no—
118C23×D47—24no—
119C23×D47—42no—
120C23×D47C22⋊C414yes—
121C23×D47C2×D411yescharacteristic
122C23×D47C2×D411yescharacteristic
123C22×C4×C47—21no—
124C22×C4×C47—21no—
125C22×C4×C47—22no—
126C22×C4×C47C22×C412yes—
127C22×C4×C47C2×D411yescharacteristic
128C22×C4×C47C2×D412yes—
129C22×C4×C47#4112yes—
130C22×C4×C47#4112yes—
131C22×C4×C47#4112yes—
132C22×C4×C47#4112yes—
133C22×C4×C47C2411yescharacteristic
134C22×Dic47—22no—
135C22×Dic47—22no—
136C22×Dic47—21no—
137C22×Dic47—21no—
138C22×Dic47—22no—
139C22×Dic47C22⋊C414yes—
140C22×Dic47C2×D411yescharacteristic
141C22×Dic47C2×D411yescharacteristic
142C2×C4×D47—28no—
143C2×C4×D47—28no—
144C2×C4×D47—28no—
145C2×C4×D47—28no—
146C2×C4×D47—22no—
147C2×C4×D47—22no—
148C2×C4×D47—22no—
149C2×C4×D47—22no—
150C2×C4×D47—21no—
151C2×C4×D47—21no—
152C2×C4×D47—21no—
153C2×C4×D47—21no—
154C2×C4×D47—21no—
155C2×C4×D47—21no—
156C2×C4×D47—21no—
157C2×C4×D47—21no—
158C2×C4×D47—24no—
159C2×C4×D47—24no—
160C2×C4×D47—44no—
161C2×C4×D47—44no—
162C2×C4×D47C22⋊C414yes—
163C2×C4×D47C22⋊C414yes—
164C2×C4×D47C22×C412yes—
165C2×C4×D47C22×C412yes—
166C2×C4×D47C2×D412yes—
167C2×C4×D47C2×D412yes—
168C2×C8×C47—22no—
169C2×C8×C47—22no—
170C2×C8×C47—22no—
171C2×C8×C47—44no—
172C4⋊C4×C47—21no—
173C4⋊C4×C47—21no—
174C4⋊C4×C47—22no—
175C4⋊C4×C47—22no—
176C4⋊C4×C47C22×C412yes—
177C4⋊C4×C47C22×C412yes—
178C22⋊C4×C47—24no—
179C22⋊C4×C47—42no—
180C42×C47—24no—
181C42×C47—42no—
182C22⋊Dic47—24no—
183C22⋊Dic47—42no—
184(C2×D47)⋊C4—24no—
185(C2×D47)⋊C4—24no—
186(C2×D47)⋊C4—44no—
187(C2×D47)⋊C4—44no—
188C4⋊Dic47—21no—
189C4⋊Dic47—21no—
190C4⋊Dic47—22no—
191C4⋊Dic47—22no—
192C4⋊Dic47C22×C412yes—
193C4⋊Dic47C22×C412yes—
194Dic47⋊C4—24no—
195Dic47⋊C4—24no—
196C4×Dic47—24no—
197C4×Dic47—24no—
198C4×Dic47—24no—
199C4×Dic47—42no—
200C2×C47⋊C8—22no—
201C2×C47⋊C8—22no—
202C2×C47⋊C8—22no—
203C2×C47⋊C8—44no—
204C23×C47—22no—
205C23×C47—22no—
206C23×C47C2×C22⋊C412yes—
207C23×C47#12312yes—
208C23×C47#12312yes—
209C23×C47C22×D411yescharacteristic
210C22×D47—21no—
211C22×D47—21no—
212C22×D47—22no—
213C22×D47—21no—
214C22×D47—21no—
215C22×D47—22no—
216C22×D47—22no—
217C22×D47—28no—
218C22×D47—28no—
219C22×D47—44no—
220C22×D47—48no—
221C22×D47—48no—
222C22×D47C2×C22⋊C412yes—
223C22×D47C2×C22⋊C412yes—
224C22×D47#13514yes—
225C2×C4×C47—22no—
226C2×C4×C47—22no—
227C2×C4×C47—42no—
228C2×C4×C47—42no—
229C2×C4×C47—42no—
230C2×C4×C47—42no—
231C2×C4×C47—42no—
232C2×C4×C47C2×C22⋊C412yes—
233C2×C4×C47#11714yes—
234C2×C4×C47#11714yes—
235C2×C4×C47#12314yes—
236C2×C4×C47#12312yes—
237C2×C4×C47#12314yes—
238C2×C4×C47#12312yes—
239C2×C4×C47C23×C411yescharacteristic
240C2×C4×C47C22×D411yescharacteristic
241C2×C4×C47C2×#4111yescharacteristic
242C2×C4×C47C2×#4111yescharacteristic
243C2×C4×C47C2×#4111yescharacteristic
244C2×C4×C47C2×#4111yescharacteristic
245C2×Dic47—21no—
246C2×Dic47—21no—
247C2×Dic47—21no—
248C2×Dic47—21no—
249C2×Dic47—28no—
250C2×Dic47—22no—
251C2×Dic47—22no—
252C2×Dic47—42no—
253C2×Dic47—42no—
254C2×Dic47—42no—
255C2×Dic47—42no—
256C2×Dic47—42no—
257C2×Dic47C2×C22⋊C412yes—
258C2×Dic47C2×C22⋊C412yes—
259C4×D47—22no—
260C4×D47—22no—
261C4×D47—22no—
262C4×D47—22no—
263C4×D47—22no—
264C4×D47—22no—
265C4×D47—22no—
266C4×D47—22no—
267C4×D47—28no—
268C4×D47—28no—
269C4×D47—48no—
270C4×D47—48no—
271C8×C47—42no—
272C47⋊C8—42no—
273#20699—471nomaximal, Sylow
274C22×C47—24no—
275C22×C47—24no—
276C22×C47—22no—
277C22×C47—22no—
278C22×C47#38114yes—
279C22×C47C22×C22⋊C411yescharacteristic
280C22×C47C2×#12311yescharacteristic
281C22×C47C2×#12311yescharacteristic
282C22×C47C2×#13512yes—
283C22×C47#57512yes—
284C2×D47—24no—
285C2×D47—24no—
286C2×D47—22no—
287C2×D47—22no—
288C2×D47—22no—
289C2×D47—22no—
290C2×D47—22no—
291C2×D47—416no—
292C2×D47—42no—
293C2×D47—42no—
294C2×D47#41614yes—
295C4×C47—42no—
296C4×C47—42no—
297C4×C47—82no—
298C4×C47#38114yes—
299C4×C47C2×#11711yescharacteristic
300C4×C47C2×#11711yescharacteristic
301C4×C47C2×#12311yescharacteristic
302C4×C47C2×#12311yescharacteristic
303Dic47—22no—
304Dic47—22no—
305Dic47—42no—
306Dic47—42no—
307Dic47—82no—
308C22×#117—471no—
309C22×C22⋊C8—471no—
310#2280—471no—
311#1825—472no—
312#1825—472no—
313#1824—472no—
314#1823—472no—
315#1735—471no—
316#1735—471no—
317#1735—471no—
318#1735D4711yescharacteristic, complemented
319C2×C47—24no—
320C2×C47C2×#38111yescharacteristic
321C2×C47C2×#41611yescharacteristic
322C2×C47#289611yescharacteristic
323C2×C47#309112yes—
324C2×C47#309112yes—
325D47—24no—
326D47—42no—
327C24×C4—471no—
328C23×C8—471no—
329C23×C8C2×D4711yescharacteristic
330C2×#117—471no—
331C2×#117—478no—
332C2×#117—471no—
333C2×#117—471no—
334C2×#117—471no—
335C2×#117—941no—
336C2×#117—941no—
337C2×#117—944no—
338C2×#117C2×D4711yescharacteristic
339C2×#117C2×D4711yescharacteristic
340C22×C4⋊C4—471no—
341C22×C4⋊C4—471no—
342C22×C22⋊C4—941no—
343C22×C42—941no—
344C2×C22⋊C8—472no—
345C2×C22⋊C8—472no—
346C2×C22⋊C8—944no—
347#381—941no—
348#380—472no—
349#380—472no—
350#379—941no—
351C4×C22⋊C4—941no—
352C4×C22⋊C4—941no—
353#340—472no—
354#340—472no—
355#340—472no—
356#340—472no—
357#340—472no—
358#340—472no—
359#340C2×D4712yescomplemented
360#340C2×D4712yescomplemented
361C47#2069911yescharacteristic, complemented, Sylow
362C25—471no—
363C23×C4—471no—
364C23×C4—474no—
365C23×C4—474no—
366C23×C4—471no—
367C23×C4—471no—
368C23×C4—471no—
369C23×C4—471no—
370C23×C4—941no—
371C23×C4—941no—
372C23×C4—942no—
373C23×C4—942no—
374C23×C4—942no—
375C23×C4—942no—
376C23×C4C22×D4711yescharacteristic
377C22×C8—22no—
378C22×C8—22no—
379C22×C8—22no—
380C22×C8—472no—
381C22×C8—942no—
382C22×C8—942no—
383C22×C8—942no—
384C22×C8C22×D4712yes—
385#117—22no—
386#117—22no—
387#117—22no—
388#117—474no—
389#117—474no—
390#117—474no—
391#117—948no—
392#117—948no—
393#117—942no—
394#117—942no—
395#117—942no—
396#117—942no—
397#117—942no—
398#117C4×D4714yes—
399C2×C4⋊C4—471no—
400C2×C4⋊C4—471no—
401C2×C4⋊C4—474no—
402C2×C4⋊C4—474no—
403C2×C4⋊C4—472no—
404C2×C4⋊C4—942no—
405C2×C4⋊C4—942no—
406C2×C4⋊C4—941no—
407C2×C4⋊C4—941no—
408C2×C4⋊C4C22×D4712yes—
409C2×C4⋊C4C22×D4711yescharacteristic
410C2×C4⋊C4C22×D4711yescharacteristic
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—948no—
414C2×C22⋊C4—941no—
415C2×C22⋊C4—941no—
416C2×C22⋊C4—941no—
417C2×C22⋊C4—942no—
418C2×C22⋊C4—942no—
419C2×C22⋊C4—941no—
420C2×C42—21no—
421C2×C42—21no—
422C2×C42—948no—
423C2×C42—941no—
424C2×C42—941no—
425C2×C42—941no—
426C2×C42—941no—
427C22⋊C8—944no—
428C22⋊C8—944no—
429#95—942no—
430#95—942no—
431C24—471no—
432C24—471no—
433C24—474no—
434C24—944no—
435C24—942no—
436C24—942no—
437C24—1882no—
438C24D4×D4711yescharacteristic
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—474no—
443C22×C4—471no—
444C22×C4—471no—
445C22×C4—474no—
446C22×C4—474no—
447C22×C4—472no—
448C22×C4—472no—
449C22×C4—472no—
450C22×C4—472no—
451C22×C4—944no—
452C22×C4—944no—
453C22×C4—942no—
454C22×C4—942no—
455C22×C4—948no—
456C22×C4—948no—
457C22×C4—948no—
458C22×C4—942no—
459C22×C4—942no—
460C22×C4—948no—
461C22×C4—942no—
462C22×C4—942no—
463C22×C4—941no—
464C22×C4—941no—
465C22×C4—941no—
466C22×C4—941no—
467C22×C4—941no—
468C22×C4—941no—
469C22×C4—941no—
470C22×C4—941no—
471C22×C4—941no—
472C22×C4—941no—
473C22×C4—942no—
474C22×C4—1884no—
475C22×C4—1884no—
476C22×C4C2×C4×D4712yes—
477C22×C4#1062535012yes—
478C22×C4#1062535012yes—
479C22×C4D4×D4712yes—
480C22×C4D4×D4711yescharacteristic
481C22×C4#1062535212yes—
482C22×C4#1062535412yes—
483C22×C4C23×D4711yescharacteristic
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—22no—
487C2×C8—44no—
488C2×C8—942no—
489C2×C8—942no—
490C2×C8—942no—
491C2×C8—1884no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—472no—
497C4⋊C4—472no—
498C4⋊C4—944no—
499C4⋊C4—944no—
500C4⋊C4—941no—
501C4⋊C4—941no—
502C4⋊C4—942no—
503C4⋊C4—942no—
504C4⋊C4C2×C4×D4712yes—
505C4⋊C4C2×C4×D4712yes—
506C22⋊C4—24no—
507C22⋊C4—42no—
508C22⋊C4—944no—
509C22⋊C4—944no—
510C22⋊C4—944no—
511C22⋊C4—1884no—
512C22⋊C4—1884no—
513C22⋊C4—1882no—
514C42—24no—
515C42—42no—
516C42—944no—
517C42—944no—
518C42—944no—
519C42—1882no—
520C23—22no—
521C23—22no—
522C23—472no—
523C23—474no—
524C23—472no—
525C23—948no—
526C23—941no—
527C23—941no—
528C23—942no—
529C23—948no—
530C23—941no—
531C23—941no—
532C23—942no—
533C23—942no—
534C23—1884no—
535C23—1888no—
536C23—1888no—
537C23C22⋊C4×D4712yes—
538C23#1309400612yes—
539C23#1309400912yes—
540C23C2×D4×D4711yescharacteristic
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—472no—
549C2×C4—472no—
550C2×C4—948no—
551C2×C4—941no—
552C2×C4—941no—
553C2×C4—941no—
554C2×C4—941no—
555C2×C4—948no—
556C2×C4—948no—
557C2×C4—942no—
558C2×C4—942no—
559C2×C4—942no—
560C2×C4—942no—
561C2×C4—942no—
562C2×C4—942no—
563C2×C4—942no—
564C2×C4—942no—
565C2×C4—942no—
566C2×C4—942no—
567C2×C4—1888no—
568C2×C4—1888no—
569C2×C4—1882no—
570C2×C4—1882no—
571C2×C4—1882no—
572C2×C4—1882no—
573C2×C4—1882no—
574C2×C4C22⋊C4×D4712yes—
575C2×C4#1309398114yes—
576C2×C4#1309398214yes—
577C2×C4#1309400612yes—
578C2×C4#1309400614yes—
579C2×C4#1309400912yes—
580C2×C4#1309400914yes—
581C2×C4C22×C4×D4711yescharacteristic
582C2×C4C2×D4×D4711yescharacteristic
583C2×C4C2×#1062535211yescharacteristic
584C2×C4C2×#1062535011yescharacteristic
585C2×C4C2×#1062535011yescharacteristic
586C2×C4C2×#1062535411yescharacteristic
587C8—42no—
588C8—1882no—
589C22—24no—
590C22—24no—
591C22—22no—
592C22—22no—
593C22—474no—
594C22—942no—
595C22—944no—
596C22—944no—
597C22—942no—
598C22—942no—
599C22—942no—
600C22—942no—
601C22—18816no—
602C22—1882no—
603C22—1882no—
604C22#1568898514yes—
605C22C2×C22⋊C4×D4711yescharacteristic
606C22C2×#1309400611yescharacteristic
607C22C2×#1309400911yescharacteristic
608C22#135×D4712yes—
609C22#1568992012yes—
610C4—42no—
611C4—42no—
612C4—82no—
613C4—942no—
614C4—942no—
615C4—3762no—
616C4—1882no—
617C4—1882no—
618C4#1568898514yes—
619C4C2×#1309398111yescharacteristic
620C4C2×#1309398211yescharacteristic
621C4C2×#1309400611yescharacteristic
622C4C2×#1309400911yescharacteristic
623C2—24no—
624C2—944no—
625C2—1882no—
626C2C2×#1568898511yescharacteristic
627C2#416×D4711yescharacteristic
628C2#2025190311yescharacteristic
629C2#2025329912yes—
630C2#2025330512yes—
subgroupG/H
centerC22×C4D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1735C2
socleC23×C47C22×D4
prime radicalC24×D47D4
cosocleC22×C4×C47C24
hypercenter#1735D47
hypocenterC47#20699
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ #1735

Complements

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

NH ≅ G/Ntype
4. #20243482C2semidirect
5. #20243481C2semidirect
6. #20243477C2semidirect
7. #20243473C2semidirect
8. #20243105C2semidirect
9. #20243104C2semidirect
10. #20243104C2semidirect
11. C47×#1735C2semidirect
21. #117×D47C4semidirect
35. #15688886C22semidirect
36. #15688886C22semidirect
37. #15688885C22semidirect
38. #15688885C22semidirect
39. #15688885C22semidirect
40. #15688885C22semidirect
44. C47×#340C22semidirect
45. C47×#340C22semidirect
318. #1735D47semidirect
359. #340C2×D47semidirect
360. #340C2×D47semidirect
361. C47#20699semidirect

Maximal subgroups

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

subgroupindex
C2×#117×D472
C22×(C2×D47)⋊C82
#202457672
#202434822
#202434812
#202434772
#202434732
#202431052
#202431042
C47×#17352
#2069947