Finite Group Databasebeta

← #26216358

Subgroups — #26216358

Order 12032.

1382 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#10625352C211yesmaximal, characteristic
2C2×#15689179C211yesmaximal, characteristic, complemented
3#20245793C211yesmaximal, characteristic, complemented
4#20243482C212yesmaximal, complemented
5#20243394C211yesmaximal, characteristic, complemented
6#20243390C211yesmaximal, characteristic, complemented
7#20243388C211yesmaximal, characteristic, complemented
8#20243325C212yesmaximal
9#20243217C212yesmaximal, complemented
10#20243215C212yesmaximal, complemented
11C47×#1802C211yesmaximal, characteristic, complemented
12C22×#10625352C2211yescharacteristic
13C4×#10625352—24no—
14C4×#10625352C418yescomplemented
15C2×C4×Dic94C2211yescharacteristic
16C2×#13093989C2211yescharacteristic
17C2×D4×Dic47C2211yescharacteristic
18C2×C4×C22⋊D47—21no—
19C2×(C22⋊D47)⋊C4—21no—
20C2×#13093982—21no—
21C2×#13093982C2211yescharacteristic
22C2×#13093980—21no—
23C22×C4×Dic47—21no—
24C2×C42×D47C2211yescharacteristic
25#15689179—24no—
26C2×C4⋊(C47⋊C8)C2211yescharacteristic
27C2×#13093949C2212yes—
28C2×#13093947C2212yes—
29C2×#13093945C2212yes—
30C2×(C2×D47)⋊C8C2212yes—
31C2×#13093934C2212yes—
32#15688993C2211yescharacteristic
33#15688988—21no—
34#15688980—21no—
35#15688980C2212yes—
36C4⋊C4×Dic47—21no—
37C4⋊C4×Dic47C2212yes—
38#15688886C2212yes—
39#15688885C2212yes—
40#15688885C2212yes—
41C2×C4×D4×C47C2211yescharacteristic
42C2×C4⋊C8×C47C2211yescharacteristic
43C2×#102×C47C2212yes—
44C47×#384C2211yescharacteristic
45C47×#340C2212yes—
46C2×#10625352—22no—
47C2×#10625352—22no—
48C2×#10625352—22no—
49C2×#10625352—22no—
50C2×#10625352—22no—
51C2×#10625352C2×C414yes—
52C22×Dic94C2311yescharacteristic
53C22×C22⋊D47—21no—
54C23×Dic47—21no—
55C23×Dic47—21no—
56C22×C4×D47D411yescharacteristic
57C22×C4×D47D411yescharacteristic
58C22×C4×D47C2311yescharacteristic
59C22×C47⋊C8C2312yes—
60C4×Dic94—22no—
61C4×Dic94C2×C414yes—
62#13093989—22no—
63#13093989C2×C414yes—
64D4×Dic47—22no—
65D4×Dic47C2×C414yes—
66C4×C22⋊D47—28no—
67(C22⋊D47)⋊C4—28no—
68#13093982—22no—
69#13093982—44no—
70#13093982C2×C414yes—
71#13093980—28no—
72C2×C4⋊Dic47—21no—
73C2×C4⋊Dic47—21no—
74C2×C4⋊Dic47C2312yes—
75C2×C4⋊Dic47C2311yescharacteristic
76C2×Dic47⋊C4—21no—
77C2×Dic47⋊C4—21no—
78C2×C22⋊Dic47—21no—
79C2×(C2×D47)⋊C4—21no—
80C2×(C2×D47)⋊C4—22no—
81C2×C4×Dic47—21no—
82C2×C4×Dic47—21no—
83C2×C4×Dic47—21no—
84C2×C4×Dic47—28no—
85C2×C4×Dic47—22no—
86C2×C4×Dic47D411yescharacteristic
87C2×C4×Dic47D411yescharacteristic
88C2×C4×Dic47C2311yescharacteristic
89C42×D47C2×C414yes—
90C42×D47D414yes—
91C4⋊(C47⋊C8)—22no—
92#13093949—24no—
93#13093947—24no—
94#13093945—24no—
95(C2×D47)⋊C8—24no—
96#13093934—24no—
97C47⋊#95—22no—
98C47⋊#95—22no—
99C22×D4×C47C2311yescharacteristic
100C23×C4×C47—21no—
101C22×C8×C47C2312yes—
102C4×D4×C47—22no—
103C4×D4×C47C2×C414yes—
104C2×C4⋊C4×C47—21no—
105C2×C4⋊C4×C47—21no—
106C2×C4⋊C4×C47C2312yes—
107C2×C4⋊C4×C47C2311yescharacteristic
108C2×C22⋊C4×C47—21no—
109C2×C42×C47C2311yescharacteristic
110C4⋊C8×C47—22no—
111#102×C47—24no—
112C24×C47—21no—
113C23×D47C2×D411yescharacteristic
114C2×D4×C47—21no—
115C2×D4×C47—21no—
116C2×D4×C47—21no—
117C2×D4×C47C22×C412yes—
118C2×D4×C47#4112yes—
119C2×D4×C47#4112yes—
120C22×C4×C47—21no—
121C22×C4×C47—24no—
122C22×C4×C47—22no—
123C22×C4×C47—42no—
124C22×C4×C47—42no—
125C22×C4×C47C2×D411yescharacteristic
126C22×C4×C47C2×D411yescharacteristic
127C22×C4×C47C2411yescharacteristic
128C2×C22⋊D47—24no—
129C2×C22⋊D47—24no—
130C2×C22⋊D47—24no—
131C22×Dic47—24no—
132C22×Dic47—24no—
133C22×Dic47—21no—
134C22×Dic47—24no—
135C22×Dic47—21no—
136C22×Dic47—24no—
137C22×Dic47—22no—
138C22×Dic47—42no—
139C22×Dic47—42no—
140C22×Dic47C2×D411yescharacteristic
141C22×Dic47C2×D411yescharacteristic
142C22×Dic47C2×D411yescharacteristic
143#10625352—28no—
144#10625352—28no—
145#10625352—28no—
146#10625352—28no—
147C2×C4×D47—22no—
148C2×C4×D47—22no—
149C2×C4×D47—21no—
150C2×C4×D47—21no—
151C2×C4×D47—21no—
152C2×C4×D47—21no—
153C2×C4×D47—41no—
154C2×C4×D47—41no—
155C2×C4×D47C22⋊C414yes—
156C2×C4×D47C22⋊C414yes—
157C2×C4×D47C22×C412yes—
158C2×C4×D47C2×D412yes—
159C2×Dic94—21no—
160C2×Dic94—21no—
161C2×Dic94—21no—
162C2×Dic94C22×C412yes—
163C2×Dic94#4112yes—
164C2×Dic94#4112yes—
165C2×C8×C47—22no—
166C2×C8×C47—22no—
167C2×C8×C47—22no—
168C4⋊C4×C47—21no—
169C4⋊C4×C47—22no—
170C4⋊C4×C47—22no—
171C4⋊C4×C47—42no—
172C4⋊C4×C47—42no—
173C4⋊C4×C47C22×C412yes—
174C22⋊C4×C47—24no—
175C42×C47C22×C412yes—
176C42×C47C2×D412yes—
177C22⋊Dic47—24no—
178(C2×D47)⋊C4—24no—
179(C2×D47)⋊C4—44no—
180C4⋊Dic47—21no—
181C4⋊Dic47—22no—
182C4⋊Dic47—22no—
183C4⋊Dic47—42no—
184C4⋊Dic47—42no—
185C4⋊Dic47C22×C412yes—
186Dic47⋊C4—24no—
187Dic47⋊C4—24no—
188C4×Dic47—24no—
189C4×Dic47—24no—
190C4×Dic47—24no—
191C4×Dic47—44no—
192C4×Dic47C22⋊C414yes—
193C4×Dic47C22⋊C414yes—
194C4×Dic47C22×C412yes—
195C4×Dic47C2×D412yes—
196C2×C47⋊C8—22no—
197C2×C47⋊C8—22no—
198C2×C47⋊C8—22no—
199C23×C47—22no—
200C23×C47—22no—
201C23×C47—22no—
202C23×C47—41no—
203C23×C47—41no—
204C23×C47—41no—
205C23×C47—41no—
206C23×C47C22×D411yescharacteristic
207C22×D47—21no—
208C22×D47—21no—
209C22×D47—21no—
210C22×D47—21no—
211C22×D47—21no—
212C22×D47—21no—
213C22×D47C2×C22⋊C412yes—
214D4×C47—22no—
215D4×C47—22no—
216D4×C47—22no—
217D4×C47#11714yescomplemented
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—22no—
221C2×C4×C47—41no—
222C2×C4×C47—41no—
223C2×C4×C47—48no—
224C2×C4×C47—42no—
225C2×C4×C47—42no—
226C2×C4×C47—42no—
227C2×C4×C47C2×C22⋊C412yes—
228C2×C4×C47C2×C22⋊C412yes—
229C2×C4×C47AGL(1,ℤ/8)12yes—
230C2×C4×C47#13712yes—
231C2×C4×C47C23×C411yescharacteristic
232C2×C4×C47C22×D411yescharacteristic
233C2×C4×C47C2×#4111yescharacteristic
234C2×C4×C47C2×#4111yescharacteristic
235C2×C4×C47C2×#4111yescharacteristic
236C2×C4×C47C2×#4111yescharacteristic
237C22⋊D47—216no—
238C2×Dic47—216no—
239C2×Dic47—22no—
240C2×Dic47—22no—
241C2×Dic47—22no—
242C2×Dic47—21no—
243C2×Dic47—21no—
244C2×Dic47—21no—
245C2×Dic47—21no—
246C2×Dic47—21no—
247C2×Dic47—21no—
248C2×Dic47—22no—
249C2×Dic47—48no—
250C2×Dic47—41no—
251C2×Dic47—41no—
252C2×Dic47—42no—
253C2×Dic47—42no—
254C2×Dic47—42no—
255C2×Dic47C2×C22⋊C412yes—
256C2×Dic47C2×C22⋊C412yes—
257C2×Dic47C2×C22⋊C412yes—
258C4×D47—22no—
259C4×D47—22no—
260C4×D47—22no—
261C4×D47—22no—
262C4×D47—28no—
263C4×D47—44no—
264Dic94—22no—
265Dic94—22no—
266Dic94—22no—
267Dic94#11714yescomplemented
268C8×C47—42no—
269C47⋊C8—42no—
270#20743—471nomaximal, Sylow
271C22×C47—24no—
272C22×C47—42no—
273C22×C47—42no—
274C22×C47—42no—
275C22×C47—42no—
276C22×C47—42no—
277C22×C47—42no—
278C22×C47C22×C22⋊C411yescharacteristic
279C22×C47#52511yescharacteristic
280C22×C47#52511yescharacteristic
281C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
282C22×C47C2×#13711yescharacteristic
283C22×C47#57511yescharacteristic
284C22×C47#57511yescharacteristic
285C2×D47—22no—
286C2×D47—22no—
287C2×D47—22no—
288C2×D47—41no—
289C2×D47—41no—
290C2×D47—41no—
291C2×D47—41no—
292C4×C47—22no—
293C4×C47—42no—
294C4×C47—82no—
295C4×C47#41714yes—
296C4×C47C2×#11711yescharacteristic
297C4×C47C2×#11711yescharacteristic
298C4×C47#52511yescharacteristic
299C4×C47#52511yescharacteristic
300Dic47—22no—
301Dic47—22no—
302Dic47—24no—
303Dic47—22no—
304Dic47—42no—
305Dic47—82no—
306C2×C4×#41—471no—
307C2×#432—471no—
308#2285—471no—
309#1825—472no—
310#1803—471no—
311#1803—471no—
312#1802—471no—
313#1802D4711yescharacteristic, complemented
314#1788—472no—
315#1763—472no—
316#1762—472no—
317C2×C47—44no—
318C2×C47#228011yescharacteristic
319C2×C47C2×#41711yescharacteristic
320C2×C47#289611yescharacteristic
321C2×C47#311511yescharacteristic
322C2×C47#311511yescharacteristic
323C2×C47#311611yescharacteristic
324C2×C47#311611yescharacteristic
325D47—42no—
326C22×#41—471no—
327C4×#41—478no—
328C4×#41—944no—
329C2×C4×Q8—471no—
330C2×C4×Q8—471no—
331C2×C4×D4—471no—
332C2×C4×D4—941no—
333C2×C4×D4—941no—
334C2×C4×D4C2×D4711yescharacteristic
335C2×#117—471no—
336C2×#117—941no—
337C2×#117—941no—
338C22×C42—471no—
339C22×C42—941no—
340#432—944no—
341C2×C4⋊C8—471no—
342C2×C4⋊C8C2×D4711yescharacteristic
343C2×#103—472no—
344C2×#103—472no—
345C2×#102—472no—
346C2×#102C2×D4712yes—
347C2×C22⋊C8—472no—
348C2×#97—472no—
349#384—471no—
350#384C2×D4711yescharacteristic
351#382—941no—
352#380—472no—
353#380—941no—
354C4×C4⋊C4—472no—
355C4×C4⋊C4—941no—
356#340—472no—
357#340—472no—
358#340—472no—
359#340C2×D4712yes—
360C47#2074311yescharacteristic, complemented, Sylow
361C2×#41—474no—
362C2×#41—942no—
363C2×#41—942no—
364C2×#41—942no—
365C2×#41—942no—
366C2×#41—942no—
367C22×Q8—471no—
368C22×D4—941no—
369C22×D4C22×D4711yescharacteristic
370C23×C4—21no—
371C23×C4—471no—
372C23×C4—471no—
373C23×C4—471no—
374C23×C4—941no—
375C23×C4—941no—
376C22×C8—472no—
377C22×C8C22×D4712yes—
378C4×Q8—474no—
379C4×Q8—474no—
380C4×Q8—942no—
381C4×Q8—942no—
382C4×D4—22no—
383C4×D4—474no—
384C4×D4—942no—
385C4×D4—948no—
386C4×D4—948no—
387C4×D4C4×D4714yes—
388#117—474no—
389#117—948no—
390#117—942no—
391#117—1884no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—471no—
395C2×C4⋊C4—472no—
396C2×C4⋊C4—941no—
397C2×C4⋊C4—941no—
398C2×C4⋊C4—941no—
399C2×C4⋊C4—941no—
400C2×C4⋊C4C22×D4712yes—
401C2×C4⋊C4C22×D4711yescharacteristic
402C2×C22⋊C4—21no—
403C2×C22⋊C4—941no—
404C2×C22⋊C4—941no—
405C2×C22⋊C4—942no—
406C2×C42—471no—
407C2×C42—471no—
408C2×C42—471no—
409C2×C42—474no—
410C2×C42—474no—
411C2×C42—948no—
412C2×C42—941no—
413C2×C42—941no—
414C2×C42—941no—
415C2×C42—942no—
416C2×C42C22×D4711yescharacteristic
417C4⋊C8—22no—
418C4⋊C8—942no—
419#103—944no—
420#103—944no—
421#102—24no—
422#102—944no—
423C22⋊C8—944no—
424#97—944no—
425#95—942no—
426#95—942no—
427C24—21no—
428C24—471no—
429#41—948no—
430#41—948no—
431#41—948no—
432#41—948no—
433C2×Q8—472no—
434C2×Q8—472no—
435C2×Q8—472no—
436C2×Q8—941no—
437C2×Q8—941no—
438C2×Q8—941no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—944no—
443C2×D4—944no—
444C2×D4—944no—
445C2×D4C2×C4×D4712yes—
446C2×D4#1062535212yes—
447C2×D4#1062535412yes—
448C22×C4—21no—
449C22×C4—24no—
450C22×C4—22no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—471no—
454C22×C4—471no—
455C22×C4—471no—
456C22×C4—474no—
457C22×C4—472no—
458C22×C4—472no—
459C22×C4—474no—
460C22×C4—944no—
461C22×C4—944no—
462C22×C4—944no—
463C22×C4—944no—
464C22×C4—941no—
465C22×C4—942no—
466C22×C4—942no—
467C22×C4—941no—
468C22×C4—941no—
469C22×C4—941no—
470C22×C4—941no—
471C22×C4—941no—
472C22×C4—942no—
473C22×C4—1881no—
474C22×C4—1881no—
475C22×C4—1882no—
476C22×C4—1882no—
477C22×C4D4×D4711yescharacteristic
478C22×C4D4×D4711yescharacteristic
479C22×C4C23×D4711yescharacteristic
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—942no—
484C2×C8—942no—
485C2×C8—942no—
486C4⋊C4—21no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—42no—
490C4⋊C4—42no—
491C4⋊C4—472no—
492C4⋊C4—944no—
493C4⋊C4—944no—
494C4⋊C4—941no—
495C4⋊C4—942no—
496C4⋊C4—942no—
497C4⋊C4—1882no—
498C4⋊C4—1882no—
499C4⋊C4C2×C4×D4712yes—
500C22⋊C4—24no—
501C22⋊C4—944no—
502C22⋊C4—944no—
503C22⋊C4—1884no—
504C42—474no—
505C42—474no—
506C42—472no—
507C42—472no—
508C42—944no—
509C42—944no—
510C42—944no—
511C42—1884no—
512C42C2×C4×D4712yes—
513C42D4×D4712yes—
514C23—22no—
515C23—22no—
516C23—22no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23—472no—
522C23—941no—
523C23—941no—
524C23—941no—
525C23—941no—
526C23—941no—
527C23—941no—
528C23C2×D4×D4711yescharacteristic
529Q8—474no—
530Q8—942no—
531Q8—942no—
532Q8—942no—
533D4—22no—
534D4—22no—
535D4—22no—
536D4—9416no—
537D4#1309398214yescomplemented
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—48no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—472no—
548C2×C4—472no—
549C2×C4—472no—
550C2×C4—9416no—
551C2×C4—942no—
552C2×C4—941no—
553C2×C4—942no—
554C2×C4—941no—
555C2×C4—942no—
556C2×C4—941no—
557C2×C4—941no—
558C2×C4—941no—
559C2×C4—941no—
560C2×C4—942no—
561C2×C4—942no—
562C2×C4—948no—
563C2×C4—942no—
564C2×C4—942no—
565C2×C4—942no—
566C2×C4—1884no—
567C2×C4—1888no—
568C2×C4—1882no—
569C2×C4—1882no—
570C2×C4—1882no—
571C2×C4—1881no—
572C2×C4—1881no—
573C2×C4C22⋊C4×D4712yes—
574C2×C4C22⋊C4×D4712yes—
575C2×C4#1309404812yes—
576C2×C4#1309405312yes—
577C2×C4C22×C4×D4711yescharacteristic
578C2×C4C2×D4×D4711yescharacteristic
579C2×C4#41×D4711yescharacteristic
580C2×C4#41×D4711yescharacteristic
581C2×C4C2×#1062535211yescharacteristic
582C2×C4C2×#1062535411yescharacteristic
583C8—42no—
584C8—1882no—
585C22—24no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—942no—
593C22—942no—
594C22—942no—
595C22—1881no—
596C22—1881no—
597C22—1881no—
598C22—1881no—
599C22C2×C22⋊C4×D4711yescharacteristic
600C22#1568963311yescharacteristic
601C22#1568963611yescharacteristic
602C22C2×#1309404811yescharacteristic
603C22C2×#1309405311yescharacteristic
604C22#1568991911yescharacteristic
605C22#1568992211yescharacteristic
606C4—22no—
607C4—42no—
608C4—82no—
609C4—942no—
610C4—942no—
611C4—944no—
612C4—942no—
613C4—3762no—
614C4—1882no—
615C4#1568912114yes—
616C4#117×D4711yescharacteristic
617C4C2×#1309398211yescharacteristic
618C4#1568963311yescharacteristic
619C4#1568963611yescharacteristic
620C2—44no—
621C2—1882no—
622C2#2024577011yescharacteristic
623C2C2×#1568912111yescharacteristic
624C2#2025190411yescharacteristic
625C2#2025353611yescharacteristic
626C2#2025354111yescharacteristic
627C2#2025354711yescharacteristic
628C2#2025355211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1802C2
socleC23×C47C22×D4
prime radicalC22×#10625352C22
cosocleC22×C4×C47C24
hypercenter#1802D47
hypocenterC47#20743
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
2. C2×#15689179C2semidirect
3. #20245793C2semidirect
4. #20243482C2semidirect
5. #20243394C2semidirect
6. #20243390C2semidirect
7. #20243388C2semidirect
9. #20243217C2semidirect
10. #20243215C2semidirect
11. C47×#1802C2semidirect
14. C4×#10625352C4semidirect
217. D4×C47#117semidirect
267. Dic94#117semidirect
313. #1802D47semidirect
360. C47#20743semidirect
537. D4#13093982semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#106253522
C2×#156891792
#202457932
#202434822
#202433942
#202433902
#202433882
#202433252
#202432172
#202432152
C47×#18022
#2074347