Finite Group Databasebeta

← D47×#1762 #26214033

Subgroups — D47×#1762 #26214033

Order 12032.

2118 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D47C211yesmaximal, characteristic
2C2×#102×D47C212yesmaximal
3C2×#97×D47C211yesmaximal, characteristic, complemented
4C4×C4⋊C4×D47C211yesmaximal, characteristic, complemented
5#20243216C211yesmaximal, characteristic, complemented
6#20243215C212yesmaximal, complemented
7#20243214C211yesmaximal, characteristic, complemented
8#20243213C211yesmaximal, characteristic, complemented
9#20243212C212yesmaximal, complemented
10#340×D47C212yesmaximal, complemented
11C47×#1762C211yesmaximal, characteristic, complemented
12C22×D4×D47C2211yescharacteristic
13C23×C4×D47—21no—
14C22×C8×D47C2212yes—
15C2×C4×D188C2211yescharacteristic
16C2×D4×Dic47C2211yescharacteristic
17C2×#13093986C2211yescharacteristic
18C2×C4×C22⋊D47—21no—
19C2×(C22⋊D47)⋊C4—21no—
20C4×D4×D47—24no—
21C4×D4×D47C418yescomplemented
22C2×C4⋊C4×D47C2211yescharacteristic
23C2×C4⋊C4×D47C2212yes—
24C2×C22⋊C4×D47—21no—
25C2×C42×D47—21no—
26C2×C42×D47C2211yescharacteristic
27C2×#13093946C2212yes—
28C2×#13093945C2212yes—
29C2×#13093944C2212yes—
30#102×D47C4116yescomplemented
31C2×#13093935C2211yescharacteristic, complemented
32C2×#13093934C2212yescomplemented
33#97×D47—24no—
34C4⋊C4×Dic47C2212yescomplemented
35C4×Dic47⋊C4—21no—
36C4×C4⋊Dic47C2211yescharacteristic, complemented
37#15688974—21no—
38#95×D47—21no—
39#15688886C2212yescomplemented
40#15688885C2212yescomplemented
41#15688885C2212yescomplemented
42C2×C4×D4×C47C2211yescharacteristic
43C2×#102×C47C2212yes—
44C2×#97×C47C2211yescharacteristic, complemented
45C4×C4⋊C4×C47C2211yescharacteristic, complemented
46C47×#340C2212yescomplemented
47C24×D47—21no—
48C22×D188C2311yescharacteristic
49C22×C22⋊D47—21no—
50C2×D4×D47—22no—
51C2×D4×D47—24no—
52C2×D4×D47C2×C414yes—
53C2×D4×D47C2×C418yes—
54C23×Dic47—21no—
55C22×C4×D47—22no—
56C22×C4×D47—21no—
57C22×C4×D47—21no—
58C22×C4×D47—21no—
59C22×C4×D47—28no—
60C22×C4×D47—48no—
61C22×C4×D47D411yescharacteristic
62C22×C4×D47D411yescharacteristic
63C22×C4×D47C2311yescharacteristic
64C22×C47⋊C8C2312yes—
65C2×C8×D47—24no—
66C2×C8×D47—24no—
67C2×C8×D47C2×C418yescomplemented
68C4×D188—22no—
69C4×D188C2×C414yescomplemented
70D4×Dic47—22no—
71D4×Dic47C2×C414yescomplemented
72#13093986—22no—
73#13093986C2×C414yescomplemented
74C4×C22⋊D47—28no—
75(C22⋊D47)⋊C4—28no—
76C2×C4⋊Dic47C2311yescharacteristic
77C2×C4⋊Dic47C2312yes—
78C2×Dic47⋊C4—22no—
79C2×Dic47⋊C4—21no—
80C4⋊C4×D47—22no—
81C4⋊C4×D47—24no—
82C4⋊C4×D47C2×C414yes—
83C4⋊C4×D47C2×C418yescomplemented
84C2×C22⋊Dic47—21no—
85C2×(C2×D47)⋊C4—21no—
86C2×(C2×D47)⋊C4—21no—
87C22⋊C4×D47—28no—
88C2×C4×Dic47—21no—
89C2×C4×Dic47—22no—
90C2×C4×Dic47D411yescharacteristic
91C2×C4×Dic47D411yescharacteristic
92C2×C4×Dic47C2311yescharacteristic
93C42×D47—44no—
94C42×D47C2×C414yes—
95C42×D47D414yes—
96#13093946C2×C418yescomplemented
97#13093945C2×C418yescomplemented
98#13093944C2×C418yescomplemented
99#13093935—22no—
100#13093934—24no—
101C47⋊#95—21no—
102C47⋊#95—22no—
103C22×D4×C47C2311yescharacteristic
104C23×C4×C47—21no—
105C22×C8×C47C2312yes—
106C4×D4×C47—22no—
107C4×D4×C47C2×C414yescomplemented
108C2×C4⋊C4×C47C2311yescharacteristic
109C2×C4⋊C4×C47C2312yes—
110C2×C22⋊C4×C47—21no—
111C2×C42×C47—21no—
112C2×C42×C47C2311yescharacteristic
113#102×C47C2×C418yescomplemented
114#97×C47—22no—
115#95×C47—21no—
116C24×C47—21no—
117C23×D47—21no—
118C23×D47—24no—
119C23×D47—28no—
120C23×D47—44no—
121C23×D47—42no—
122C23×D47—42no—
123C23×D47C2×D411yescharacteristic
124C2×D4×C47—21no—
125C2×D4×C47—22no—
126C2×D4×C47C22×C412yes—
127C2×D4×C47C22×C414yes—
128C22×C4×C47—22no—
129C22×C4×C47—21no—
130C22×C4×C47—24no—
131C22×C4×C47—44no—
132C22×C4×C47C2×D411yescharacteristic
133C22×C4×C47C2×D411yescharacteristic
134C22×C4×C47C2411yescharacteristic
135C2×C22⋊D47—24no—
136C2×C22⋊D47—28no—
137C22×Dic47—22no—
138C22×Dic47—21no—
139C22×Dic47—24no—
140C22×Dic47—44no—
141C22×Dic47C2×D411yescharacteristic
142C22×Dic47C2×D411yescharacteristic
143C22×Dic47C2×D411yescharacteristic
144D4×D47—28no—
145D4×D47—216no—
146D4×D47C42116yescomplemented
147C2×D188—21no—
148C2×D188—22no—
149C2×D188C22×C414yes—
150C2×D188C22×C412yes—
151C2×C4×D47—22no—
152C2×C4×D47—24no—
153C2×C4×D47—22no—
154C2×C4×D47—24no—
155C2×C4×D47—28no—
156C2×C4×D47—24no—
157C2×C4×D47—24no—
158C2×C4×D47—432no—
159C2×C4×D47—44no—
160C2×C4×D47—44no—
161C2×C4×D47—44no—
162C2×C4×D47—44no—
163C2×C4×D47—44no—
164C2×C4×D47C22⋊C414yes—
165C2×C4×D47C22⋊C414yes—
166C2×C4×D47C22×C412yes—
167C2×C4×D47C22×C414yes—
168C2×C4×D47C2×D412yes—
169C2×C4×D47#4114yes—
170C2×C8×C47—22no—
171C2×C8×C47—22no—
172C2×C8×C47C22×C414yescomplemented
173C4⋊C4×C47—21no—
174C4⋊C4×C47—22no—
175C4⋊C4×C47C22×C412yes—
176C4⋊C4×C47C22×C414yescomplemented
177C22⋊C4×C47—24no—
178C42×C47—42no—
179C42×C47C22×C412yes—
180C42×C47C2×D412yes—
181C22⋊Dic47—24no—
182(C2×D47)⋊C4—24no—
183(C2×D47)⋊C4—24no—
184C4⋊Dic47—21no—
185C4⋊Dic47—22no—
186C4⋊Dic47C22×C412yes—
187C4⋊Dic47C22×C414yescomplemented
188Dic47⋊C4—24no—
189Dic47⋊C4—28no—
190C4×Dic47—44no—
191C4×Dic47—42no—
192C4×Dic47C22⋊C414yes—
193C4×Dic47C22⋊C414yes—
194C4×Dic47C22×C412yes—
195C4×Dic47C2×D412yes—
196C2×C47⋊C8—22no—
197C2×C47⋊C8—22no—
198C2×C47⋊C8C22×C414yescomplemented
199C8×D47—216no—
200C23×C47—22no—
201C23×C47—24no—
202C23×C47—42no—
203C23×C47—41no—
204C23×C47—41no—
205C23×C47C22×D411yescharacteristic
206C22×D47—22no—
207C22×D47—24no—
208C22×D47—216no—
209C22×D47—42no—
210C22×D47—41no—
211C22×D47—41no—
212C22×D47—48no—
213C22×D47—48no—
214C22×D47—416no—
215C22×D47—416no—
216C22×D47C2×C22⋊C412yes—
217C22×D47C4×D414yes—
218C22×D47AGL(1,ℤ/8)12yes—
219C22×D47AGL(1,ℤ/8)14yes—
220C22×D47#13712yes—
221D4×C47—22no—
222D4×C47—24no—
223D4×C47C2×C4214yescomplemented
224C2×C4×C47—21no—
225C2×C4×C47—22no—
226C2×C4×C47—21no—
227C2×C4×C47—22no—
228C2×C4×C47—24no—
229C2×C4×C47—48no—
230C2×C4×C47—42no—
231C2×C4×C47—42no—
232C2×C4×C47—42no—
233C2×C4×C47C2×C22⋊C412yes—
234C2×C4×C47C2×C22⋊C412yes—
235C2×C4×C47C23×C411yescharacteristic
236C2×C4×C47C23×C412yes—
237C2×C4×C47C22×D411yescharacteristic
238C2×C4×C47C2×#4112yes—
239C22⋊D47—216no—
240C2×Dic47—21no—
241C2×Dic47—22no—
242C2×Dic47—21no—
243C2×Dic47—22no—
244C2×Dic47—24no—
245C2×Dic47—48no—
246C2×Dic47—42no—
247C2×Dic47—42no—
248C2×Dic47—42no—
249C2×Dic47C2×C22⋊C412yes—
250C2×Dic47C2×C22⋊C412yes—
251C2×Dic47C2×C22⋊C412yes—
252C2×Dic47C4×D414yes—
253D188—22no—
254D188—24no—
255D188C2×C4214yescomplemented
256C4×D47—28no—
257C4×D47—28no—
258C4×D47—48no—
259C4×D47—48no—
260C4×D47—48no—
261C4×D47—416no—
262C4×D47C2×C4214yes—
263C4×D47#11714yes—
264C4×D47C4×D418yes—
265C8×C47—24no—
266C47⋊C8—24no—
267C2×#1762—471nomaximal, Sylow
268C22×C47—24no—
269C22×C47—42no—
270C22×C47—42no—
271C22×C47—44no—
272C22×C47—44no—
273C22×C47C22×C22⋊C411yescharacteristic
274C22×C47C2×C4×D412yes—
275C22×C47C2×AGL(1,ℤ/8)12yes—
276C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
277C22×C47C2×#13711yescharacteristic
278C2×D47—24no—
279C2×D47—42no—
280C2×D47—42no—
281C2×D47—44no—
282C2×D47—44no—
283C2×D47—432no—
284C2×D47C4×C22⋊C414yes—
285C2×D47#41714yes—
286C2×D47#41814yes—
287C2×D47#44018yes—
288C2×D47#44218yes—
289C4×C47—22no—
290C4×C47—22no—
291C4×C47—42no—
292C4×C47—44no—
293C4×C47C22×C4211yescharacteristic
294C4×C47C2×#11711yescharacteristic
295C4×C47C2×C4×D412yes—
296Dic47—22no—
297Dic47—22no—
298Dic47—42no—
299Dic47—44no—
300Dic47C4×C22⋊C414yes—
301C22×C4×D4—471no—
302C22×#102—472no—
303C22×#97—471no—
304C2×C4×C4⋊C4—471no—
305#1762—472no—
306#1762—471no—
307#1762—471no—
308#1762—472no—
309#1762—471no—
310#1762D4711yescharacteristic, direct product factor
311C2×#340—472no—
312C2×C47—44no—
313C2×C47C2×C4×C22⋊C411yescharacteristic
314C2×C47C2×#41811yescharacteristic
315C2×C47C2×#41711yescharacteristic
316C2×C47C2×#44012yes—
317C2×C47C2×#44212yes—
318D47—44no—
319D47#176218yesdirect product factor
320C23×D4—471no—
321C24×C4—941no—
322C23×C8—472no—
323C2×C4×D4—471no—
324C2×C4×D4—478no—
325C2×C4×D4—471no—
326C2×C4×D4—471no—
327C2×C4×D4—941no—
328C2×C4×D4—944no—
329C2×C4×D4—941no—
330C2×C4×D4C2×D4711yescharacteristic
331C22×C4⋊C4—472no—
332C22×C4⋊C4—471no—
333C22×C22⋊C4—941no—
334C22×C42—471no—
335C22×C42—941no—
336C2×#102—472no—
337C2×#102—472no—
338C2×#102—472no—
339C2×#102—4716no—
340C2×#102C2×D4712yes—
341C2×#97—472no—
342C2×#97—471no—
343C2×#97—944no—
344C2×#97C2×D4711yescharacteristic, complemented
345C4×C4⋊C4—472no—
346C4×C4⋊C4—471no—
347C4×C4⋊C4—941no—
348C4×C4⋊C4—941no—
349C4×C4⋊C4C2×D4711yescharacteristic, complemented
350C2×#95—941no—
351#340—472no—
352#340—472no—
353#340—472no—
354#340C2×D4712yescomplemented
355C47C2×#176211yescharacteristic, complemented, Sylow
356C25—941no—
357C22×D4—474no—
358C22×D4—478no—
359C22×D4—471no—
360C22×D4—942no—
361C22×D4—944no—
362C22×D4—941no—
363C22×D4C22×D4711yescharacteristic
364C23×C4—21no—
365C23×C4—471no—
366C23×C4—471no—
367C23×C4—471no—
368C23×C4—941no—
369C23×C4—948no—
370C23×C4—941no—
371C23×C4—942no—
372C23×C4—941no—
373C23×C4—941no—
374C23×C4—1888no—
375C22×C8—472no—
376C22×C8—478no—
377C22×C8—944no—
378C22×C8—944no—
379C22×C8C22×D4712yes—
380C4×D4—22no—
381C4×D4—474no—
382C4×D4—474no—
383C4×D4—474no—
384C4×D4—948no—
385C4×D4—942no—
386C4×D4—948no—
387C4×D4—942no—
388C4×D4—942no—
389C4×D4C4×D4714yescomplemented
390C2×C4⋊C4—471no—
391C2×C4⋊C4—472no—
392C2×C4⋊C4—474no—
393C2×C4⋊C4—478no—
394C2×C4⋊C4—942no—
395C2×C4⋊C4—944no—
396C2×C4⋊C4—941no—
397C2×C4⋊C4—942no—
398C2×C4⋊C4C22×D4711yescharacteristic
399C2×C4⋊C4C22×D4712yes—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—948no—
402C2×C22⋊C4—941no—
403C2×C22⋊C4—941no—
404C2×C22⋊C4—941no—
405C2×C42—21no—
406C2×C42—471no—
407C2×C42—471no—
408C2×C42—471no—
409C2×C42—474no—
410C2×C42—474no—
411C2×C42—942no—
412C2×C42—941no—
413C2×C42—1884no—
414C2×C42C22×D4711yescharacteristic
415#102—478no—
416#102—478no—
417#102—478no—
418#102C4×D4718yescomplemented
419#97—22no—
420#97—944no—
421#97—942no—
422#95—21no—
423#95—942no—
424#95—941no—
425C24—21no—
426C24—471no—
427C24—944no—
428C24—948no—
429C24—941no—
430C24—1884no—
431C24—1882no—
432C24—1882no—
433C2×D4—21no—
434C2×D4—22no—
435C2×D4—4716no—
436C2×D4—474no—
437C2×D4—472no—
438C2×D4—948no—
439C2×D4—9416no—
440C2×D4—944no—
441C2×D4—948no—
442C2×D4—941no—
443C2×D4—942no—
444C2×D4C2×C4×D4714yes—
445C2×D4C2×C4×D4712yes—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—24no—
449C22×C4—44no—
450C22×C4—471no—
451C22×C4—472no—
452C22×C4—474no—
453C22×C4—472no—
454C22×C4—474no—
455C22×C4—471no—
456C22×C4—471no—
457C22×C4—474no—
458C22×C4—474no—
459C22×C4—944no—
460C22×C4—942no—
461C22×C4—942no—
462C22×C4—944no—
463C22×C4—944no—
464C22×C4—948no—
465C22×C4—944no—
466C22×C4—942no—
467C22×C4—941no—
468C22×C4—944no—
469C22×C4—1884no—
470C22×C4—18832no—
471C22×C4—1884no—
472C22×C4—1884no—
473C22×C4—1884no—
474C22×C4—1884no—
475C22×C4—1884no—
476C22×C4D4×D4711yescharacteristic
477C22×C4D4×D4711yescharacteristic
478C22×C4C23×D4711yescharacteristic
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—474no—
482C2×C8—9416no—
483C2×C8—942no—
484C2×C8—942no—
485C2×C8C2×C4×D4714yescomplemented
486C4⋊C4—21no—
487C4⋊C4—22no—
488C4⋊C4—472no—
489C4⋊C4—474no—
490C4⋊C4—948no—
491C4⋊C4—944no—
492C4⋊C4—941no—
493C4⋊C4—942no—
494C4⋊C4C2×C4×D4712yes—
495C4⋊C4C2×C4×D4714yescomplemented
496C22⋊C4—24no—
497C22⋊C4—944no—
498C22⋊C4—944no—
499C22⋊C4—944no—
500C42—42no—
501C42—474no—
502C42—474no—
503C42—472no—
504C42—472no—
505C42—1882no—
506C42—1884no—
507C42C2×C4×D4712yes—
508C42D4×D4712yes—
509C23—22no—
510C23—24no—
511C23—42no—
512C23—41no—
513C23—41no—
514C23—472no—
515C23—474no—
516C23—474no—
517C23—472no—
518C23—472no—
519C23—9416no—
520C23—942no—
521C23—944no—
522C23—1888no—
523C23—18816no—
524C23—18816no—
525C23—1888no—
526C23—1882no—
527C23—1881no—
528C23—1881no—
529C23C2×D4×D4711yescharacteristic
530D4—22no—
531D4—24no—
532D4—474no—
533D4—9416no—
534D4—942no—
535D4—944no—
536D4C42×D4714yescomplemented
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—48no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—472no—
547C2×C4—474no—
548C2×C4—474no—
549C2×C4—474no—
550C2×C4—478no—
551C2×C4—472no—
552C2×C4—472no—
553C2×C4—948no—
554C2×C4—948no—
555C2×C4—941no—
556C2×C4—942no—
557C2×C4—941no—
558C2×C4—942no—
559C2×C4—944no—
560C2×C4—1888no—
561C2×C4—1888no—
562C2×C4—18816no—
563C2×C4—1888no—
564C2×C4—1888no—
565C2×C4—1882no—
566C2×C4—1882no—
567C2×C4—1882no—
568C2×C4C22⋊C4×D4712yes—
569C2×C4C22⋊C4×D4712yes—
570C2×C4C22×C4×D4711yescharacteristic
571C2×C4C22×C4×D4712yes—
572C2×C4C2×D4×D4711yescharacteristic
573C2×C4#41×D4712yes—
574C8—24no—
575C8—944no—
576C22—24no—
577C22—44no—
578C22—44no—
579C22—42no—
580C22—42no—
581C22—478no—
582C22—478no—
583C22—474no—
584C22—474no—
585C22—474no—
586C22—944no—
587C22—18832no—
588C22—1884no—
589C22—1884no—
590C22—1882no—
591C22—1882no—
592C22C2×C22⋊C4×D4711yescharacteristic
593C22C4×D4×D4712yes—
594C22AGL(1,ℤ/8)×D4712yes—
595C22AGL(1,ℤ/8)×D4711yescharacteristic
596C22#137×D4711yescharacteristic
597C4—22no—
598C4—22no—
599C4—44no—
600C4—42no—
601C4—474no—
602C4—942no—
603C4—942no—
604C4—1884no—
605C4—1882no—
606C4C2×C42×D4711yescharacteristic
607C4#117×D4711yescharacteristic
608C4C4×D4×D4712yes—
609C2—44no—
610C2—478no—
611C2—1884no—
612C2C4×C22⋊C4×D4711yescharacteristic
613C2#418×D4711yescharacteristic
614C2#417×D4711yescharacteristic
615C2#440×D4712yes—
616C2#442×D4712yes—
subgroupG/H
centerC23C2×D4×D47
commutatorC4×C47C22×C42
FrattiniC22×C4C23×D47
FittingC47×#1762C2
socleC23×C47C22×D4
prime radicalC22×D4×D47C22
cosocleC22×C4×C47C24
hypercenter#1762D47
hypocenterC47C2×#1762
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
3. C2×#97×D47C2semidirect
4. C4×C4⋊C4×D47C2semidirect
5. #20243216C2semidirect
6. #20243215C2semidirect
7. #20243214C2semidirect
8. #20243213C2semidirect
9. #20243212C2semidirect
10. #340×D47C2semidirect
11. C47×#1762C2semidirect
21. C4×D4×D47C4semidirect
30. #102×D47C4semidirect
31. C2×#13093935C22semidirect
32. C2×#13093934C22semidirect
34. C4⋊C4×Dic47C22semidirect
36. C4×C4⋊Dic47C22semidirect
39. #15688886C22semidirect
40. #15688885C22semidirect
41. #15688885C22semidirect
44. C2×#97×C47C22semidirect
45. C4×C4⋊C4×C47C22semidirect
46. C47×#340C22semidirect
67. C2×C8×D47C2×C4semidirect
69. C4×D188C2×C4semidirect
71. D4×Dic47C2×C4semidirect
73. #13093986C2×C4semidirect
83. C4⋊C4×D47C2×C4semidirect
96. #13093946C2×C4semidirect
97. #13093945C2×C4semidirect
98. #13093944C2×C4semidirect
107. C4×D4×C47C2×C4semidirect
113. #102×C47C2×C4semidirect
146. D4×D47C42semidirect
172. C2×C8×C47C22×C4semidirect
176. C4⋊C4×C47C22×C4semidirect
187. C4⋊Dic47C22×C4semidirect
198. C2×C47⋊C8C22×C4semidirect
223. D4×C47C2×C42semidirect
255. D188C2×C42semidirect
310. #1762D47direct (N × H)
319. D47#1762direct (N × H)
344. C2×#97C2×D47semidirect
349. C4×C4⋊C4C2×D47semidirect
354. #340C2×D47semidirect
355. C47C2×#1762semidirect
389. C4×D4C4×D47semidirect
418. #102C4×D47semidirect
485. C2×C8C2×C4×D47semidirect
495. C4⋊C4C2×C4×D47semidirect
536. D4C42×D47semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D472
C2×#102×D472
C2×#97×D472
C4×C4⋊C4×D472
#202432162
#202432152
#202432142
#202432132
#202432122
#340×D472
C47×#17622
C2×#176247