Finite Group Databasebeta

← D47×#2298 #26374670

Subgroups — D47×#2298 #26374670

Order 12032.

2902 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D47C211yesmaximal, characteristic
2#20245886C211yesmaximal, characteristic, complemented
3#20245885C211yesmaximal, characteristic, complemented
4#20245884C212yesmaximal, complemented
5#20245883C211yesmaximal, characteristic, complemented
6#20245882C214yesmaximal, complemented
7#20245881C212yesmaximal, complemented
8#20245880C214yesmaximal, complemented
9#388×D47C214yesmaximal
10#387×D47C214yesmaximal, complemented
11C4×C4⋊C4×D47C212yesmaximal, complemented
12C4×C22⋊C4×D47C212yesmaximal
13#376×D47C211yesmaximal, characteristic, complemented
14C43×D47C211yesmaximal, characteristic, complemented
15C47×#2298C211yesmaximal, characteristic, complemented
16C23×C4×D47C2211yescharacteristic
17C2×#13093983C2211yescharacteristic
18C2×#13093982C2212yes—
19C2×#13093981C2211yescharacteristic
20C2×#13093981C2211yescharacteristic
21C2×#13093980C2212yes—
22#117×D47C4116yescomplemented
23C2×C4⋊C4×D47C2214yes—
24C2×C4⋊C4×D47C2212yes—
25C2×C22⋊C4×D47C2214yes—
26C2×C22⋊C4×D47C2212yes—
27C2×C42×D47C2214yes—
28C2×C42×D47C2212yes—
29C2×C42×D47C2212yes—
30C2×C42×D47C2211yescharacteristic
31C2×C42×D47C2211yescharacteristic
32#15689017C2214yes—
33#15689016C2214yes—
34#15689015C2214yes—
35#15689014C2214yes—
36#15689013C2214yes—
37#15689012C2214yes—
38#15689011C2214yes—
39#15689010C2214yescomplemented
40#15689009C2214yescomplemented
41#15689008C2214yescomplemented
42#15689007C2214yescomplemented
43#15689006C2214yescomplemented
44#15689005C2214yescomplemented
45#15689004C2214yescomplemented
46C4⋊C4×Dic47C2214yescomplemented
47C4×Dic47⋊C4C2212yescomplemented
48C4×Dic47⋊C4C2212yescomplemented
49C4×C4⋊Dic47C2212yescomplemented
50#15688974C2214yescomplemented
51C22⋊C4×Dic47C2214yes—
52C4×(C2×D47)⋊C4C2212yes—
53C4×(C2×D47)⋊C4C2212yes—
54C4×C22⋊Dic47C2212yes—
55#15688970C2214yes—
56#15688969C2212yescomplemented
57#15688969C2211yescharacteristic, complemented
58#15688968C2214yescomplemented
59#95×D47C2214yes—
60#95×D47C2214yes—
61#95×D47C2214yes—
62C42×Dic47C2214yescomplemented
63C42×Dic47C2212yescomplemented
64C42×Dic47C2211yescharacteristic, complemented
65C2×#117×C47C2211yescharacteristic
66C47×#388C2214yes—
67C47×#387C2214yescomplemented
68C4×C4⋊C4×C47C2212yescomplemented
69C4×C22⋊C4×C47C2212yes—
70C47×#376C2211yescharacteristic, complemented
71C43×C47C2211yescharacteristic, complemented
72C24×D47C2311yescharacteristic
73C23×Dic47C2311yescharacteristic
74C22×C4×D47—28no—
75C22×C4×D47C2×C418yes—
76C22×C4×D47C2314yes—
77C22×C4×D47C2311yescharacteristic
78C22×C4×D47C2312yes—
79C22×C4×D47C2312yes—
80C22×C4×D47C2311yescharacteristic
81C22×C4×D47C2311yescharacteristic
82C22×C4×D47C2314yes—
83C22×C4×D47C2311yescharacteristic
84#13093983C2×C418yescomplemented
85#13093982C2×C4116yescomplemented
86#13093981C2×C418yescomplemented
87#13093981C2×C418yescomplemented
88#13093980C2×C4116yescomplemented
89C2×C4⋊Dic47C2314yes—
90C2×C4⋊Dic47C2312yes—
91C2×Dic47⋊C4C2314yes—
92C2×Dic47⋊C4C2314yes—
93C2×Dic47⋊C4C2312yes—
94C2×Dic47⋊C4C2312yes—
95C4⋊C4×D47—216no—
96C4⋊C4×D47C2×C4116yes—
97C2×C22⋊Dic47C2314yes—
98C2×C22⋊Dic47C2312yes—
99C2×(C2×D47)⋊C4C2314yes—
100C2×(C2×D47)⋊C4C2314yes—
101C2×(C2×D47)⋊C4C2312yes—
102C2×(C2×D47)⋊C4C2312yes—
103C22⋊C4×D47—216no—
104C22⋊C4×D47C2×C4116yes—
105C2×C4×Dic47C2314yes—
106C2×C4×Dic47C2312yes—
107C2×C4×Dic47C2314yes—
108C2×C4×Dic47C2314yes—
109C2×C4×Dic47C2314yes—
110C2×C4×Dic47C2314yes—
111C2×C4×Dic47C2312yes—
112C2×C4×Dic47C2312yes—
113C2×C4×Dic47C2311yescharacteristic
114C2×C4×Dic47C2312yes—
115C2×C4×Dic47C2311yescharacteristic
116C42×D47—216no—
117C42×D47—28no—
118C42×D47—28no—
119C42×D47C2×C418yes—
120C42×D47C2×C418yes—
121C47⋊#95C2314yes—
122C47⋊#95C2314yes—
123C47⋊#95C2314yes—
124C47⋊#95C2314yes—
125C47⋊#95C2314yes—
126C47⋊#95C2314yes—
127C47⋊#95C2314yes—
128C47⋊#95C2314yes—
129C47⋊#95C2314yes—
130C23×C4×C47C2311yescharacteristic
131#117×C47C2×C418yescomplemented
132C2×C4⋊C4×C47C2314yes—
133C2×C4⋊C4×C47C2312yes—
134C2×C22⋊C4×C47C2314yes—
135C2×C22⋊C4×C47C2312yes—
136C2×C42×C47C2312yes—
137C2×C42×C47C2314yes—
138C2×C42×C47C2312yes—
139C2×C42×C47C2311yescharacteristic
140C2×C42×C47C2311yescharacteristic
141#95×C47C2314yes—
142#95×C47C2314yes—
143#95×C47C2314yes—
144C24×C47C2411yescharacteristic
145C23×D47—28no—
146C23×D47—24no—
147C23×D47C22×C414yes—
148C23×D47C2411yescharacteristic
149C23×D47C2411yescharacteristic
150C22×C4×C47—24no—
151C22×C4×C47C22×C414yes—
152C22×C4×C47C2414yes—
153C22×C4×C47C2412yes—
154C22×C4×C47C2412yes—
155C22×C4×C47C2411yescharacteristic
156C22×C4×C47C2414yes—
157C22×C4×C47C2411yescharacteristic
158C22×Dic47—24no—
159C22×Dic47C22×C414yes—
160C22×Dic47C2414yes—
161C22×Dic47C2411yescharacteristic
162C22×Dic47C2412yes—
163C22×Dic47C2412yes—
164C22×Dic47C2414yes—
165C22×Dic47C2411yescharacteristic
166C2×C4×D47—28no—
167C2×C4×D47—28no—
168C2×C4×D47—28no—
169C2×C4×D47—28no—
170C2×C4×D47—24no—
171C2×C4×D47—24no—
172C2×C4×D47—24no—
173C2×C4×D47—232no—
174C2×C4×D47—28no—
175C2×C4×D47—28no—
176C2×C4×D47—28no—
177C2×C4×D47C22×C418yes—
178C2×C4×D47C22×C418yes—
179C2×C4×D47C22×C414yes—
180C2×C4×D47C22×C414yes—
181C2×C4×D47C22×C414yes—
182C2×C4×D47C22×C414yes—
183C2×C4×D47#41116yes—
184C2×C4×D47#4118yes—
185C4⋊C4×C47—28no—
186C4⋊C4×C47C22×C418yes—
187C22⋊C4×C47—28no—
188C22⋊C4×C47C22×C418yes—
189C42×C47—28no—
190C42×C47—24no—
191C42×C47—24no—
192C42×C47C22×C414yes—
193C42×C47C22×C414yes—
194C22⋊Dic47—28no—
195C22⋊Dic47C22×C418yes—
196(C2×D47)⋊C4—28no—
197(C2×D47)⋊C4—28no—
198(C2×D47)⋊C4C22×C418yes—
199(C2×D47)⋊C4C22×C418yes—
200C4⋊Dic47—28no—
201C4⋊Dic47C22×C418yes—
202Dic47⋊C4—28no—
203Dic47⋊C4—28no—
204Dic47⋊C4C22×C418yes—
205Dic47⋊C4C22×C418yes—
206C4×Dic47—28no—
207C4×Dic47—24no—
208C4×Dic47—24no—
209C4×Dic47—28no—
210C4×Dic47—28no—
211C4×Dic47—28no—
212C4×Dic47—28no—
213C4×Dic47C22×C418yes—
214C4×Dic47C22×C418yes—
215C4×Dic47C22×C414yes—
216C4×Dic47C22×C414yes—
217C23×C47—24no—
218C23×C47—22no—
219C23×C47C23×C412yes—
220C23×C47C2511yescharacteristic
221C22×D47—24no—
222C22×D47—22no—
223C22×D47—28no—
224C22×D47—216no—
225C22×D47—416no—
226C22×D47C23×C412yes—
227C22×D47C23×C412yes—
228C22×D47C2×#4114yes—
229C22×D47C2×#4118yes—
230C2×C4×C47—24no—
231C2×C4×C47—24no—
232C2×C4×C47—24no—
233C2×C4×C47—24no—
234C2×C4×C47—22no—
235C2×C4×C47—28no—
236C2×C4×C47—24no—
237C2×C4×C47—24no—
238C2×C4×C47—24no—
239C2×C4×C47C23×C414yes—
240C2×C4×C47C23×C414yes—
241C2×C4×C47C23×C412yes—
242C2×C4×C47C23×C412yes—
243C2×C4×C47C2×#4118yes—
244C2×C4×C47C2×#4114yes—
245C2×Dic47—24no—
246C2×Dic47—24no—
247C2×Dic47—24no—
248C2×Dic47—24no—
249C2×Dic47—22no—
250C2×Dic47—28no—
251C2×Dic47—24no—
252C2×Dic47—24no—
253C2×Dic47—24no—
254C2×Dic47C23×C414yes—
255C2×Dic47C23×C414yes—
256C2×Dic47C23×C412yes—
257C2×Dic47C23×C412yes—
258C2×Dic47C2×#4118yes—
259C2×Dic47C2×#4114yes—
260C4×D47—28no—
261C4×D47—216no—
262C4×D47—216no—
263C4×D47—232no—
264C4×D47—28no—
265C4×D47—28no—
266C4×D47—416no—
267C4×D47#117116yes—
268C2×#2298—471nomaximal, Sylow
269C22×C47—22no—
270C22×C47—24no—
271C22×C47—44no—
272C22×C47C24×C411yescharacteristic
273C22×C47C22×#4112yes—
274C22×C47C22×#4114yes—
275C2×D47—22no—
276C2×D47—24no—
277C2×D47—44no—
278C2×D47—416no—
279C2×D47C2×#11714yes—
280C2×D47C4×#4118yes—
281C2×D47#529116yes—
282C4×C47—22no—
283C4×C47—24no—
284C4×C47—24no—
285C4×C47—28no—
286C4×C47—44no—
287C4×C47C2×#11714yes—
288Dic47—22no—
289Dic47—24no—
290Dic47—24no—
291Dic47—28no—
292Dic47—44no—
293Dic47C2×#11714yes—
294C22×#117—471no—
295#2298—474no—
296#2298—474no—
297#2298—472no—
298#2298—472no—
299#2298—471no—
300#2298—471no—
301#2298—471no—
302#2298D4711yescharacteristic, direct product factor
303C2×#388—474no—
304C2×#387—474no—
305C2×C4×C4⋊C4—472no—
306C2×C4×C22⋊C4—472no—
307C2×#376—471no—
308C2×C43—471no—
309C2×C47—42no—
310C2×C47C22×#11711yescharacteristic
311C2×C47C2×C4×#4112yes—
312C2×C47C2×#52914yes—
313D47—42no—
314D47#229818yesdirect product factor
315C24×C4—471no—
316C2×#117—471no—
317C2×#117—4716no—
318C2×#117—472no—
319C2×#117—472no—
320C2×#117—471no—
321C2×#117—471no—
322C2×#117C2×D4711yescharacteristic
323C22×C4⋊C4—472no—
324C22×C4⋊C4—474no—
325C22×C22⋊C4—472no—
326C22×C22⋊C4—474no—
327C22×C42—471no—
328C22×C42—471no—
329C22×C42—472no—
330C22×C42—474no—
331C22×C42—472no—
332#388—474no—
333#388—474no—
334#388—474no—
335#388—474no—
336#388—474no—
337#388—474no—
338#388—474no—
339#388C2×D4714yes—
340#387—474no—
341#387—474no—
342#387—474no—
343#387—474no—
344#387—474no—
345#387—474no—
346#387—474no—
347#387C2×D4714yescomplemented
348C4×C4⋊C4—474no—
349C4×C4⋊C4—472no—
350C4×C4⋊C4—472no—
351C4×C4⋊C4—472no—
352C4×C4⋊C4—474no—
353C4×C4⋊C4C2×D4712yescomplemented
354C4×C22⋊C4—472no—
355C4×C22⋊C4—474no—
356C4×C22⋊C4—472no—
357C4×C22⋊C4—472no—
358C4×C22⋊C4—474no—
359C4×C22⋊C4C2×D4712yes—
360#376—472no—
361#376—471no—
362#376—474no—
363#376C2×D4711yescharacteristic, complemented
364C2×#95—474no—
365C2×#95—474no—
366C2×#95—474no—
367C43—474no—
368C43—472no—
369C43—471no—
370C43C2×D4711yescharacteristic, complemented
371C47C2×#229811yescharacteristic, complemented, Sylow
372C25—471no—
373C23×C4—471no—
374C23×C4—471no—
375C23×C4—478no—
376C23×C4—472no—
377C23×C4—472no—
378C23×C4—474no—
379C23×C4—471no—
380C23×C4—471no—
381C23×C4—471no—
382C23×C4—474no—
383C23×C4—948no—
384C23×C4C22×D4711yescharacteristic
385#117—478no—
386#117—4716no—
387#117—4716no—
388#117—478no—
389#117—478no—
390#117C4×D4718yescomplemented
391C2×C4⋊C4—472no—
392C2×C4⋊C4—472no—
393C2×C4⋊C4—472no—
394C2×C4⋊C4—4716no—
395C2×C4⋊C4—474no—
396C2×C4⋊C4—474no—
397C2×C4⋊C4—474no—
398C2×C4⋊C4—9416no—
399C2×C4⋊C4C22×D4714yes—
400C2×C4⋊C4C22×D4712yes—
401C2×C22⋊C4—472no—
402C2×C22⋊C4—472no—
403C2×C22⋊C4—472no—
404C2×C22⋊C4—4716no—
405C2×C22⋊C4—474no—
406C2×C22⋊C4—474no—
407C2×C22⋊C4—474no—
408C2×C22⋊C4—9416no—
409C2×C22⋊C4C22×D4714yes—
410C2×C22⋊C4C22×D4712yes—
411C2×C42—472no—
412C2×C42—472no—
413C2×C42—471no—
414C2×C42—471no—
415C2×C42—478no—
416C2×C42—478no—
417C2×C42—474no—
418C2×C42—474no—
419C2×C42—474no—
420C2×C42—474no—
421C2×C42—474no—
422C2×C42—472no—
423C2×C42—472no—
424C2×C42—948no—
425C2×C42—948no—
426C2×C42—9416no—
427C2×C42C22×D4714yes—
428C2×C42C22×D4712yes—
429C2×C42C22×D4712yes—
430C2×C42C22×D4711yescharacteristic
431C2×C42C22×D4711yescharacteristic
432#95—474no—
433#95—474no—
434#95—474no—
435#95—474no—
436#95—474no—
437#95—474no—
438#95—474no—
439#95—474no—
440#95—474no—
441#95C22×D4714yes—
442#95C22×D4714yes—
443#95C22×D4714yes—
444C24—471no—
445C24—474no—
446C24—471no—
447C24—948no—
448C24—944no—
449C24C23×D4711yescharacteristic
450C22×C4—24no—
451C22×C4—471no—
452C22×C4—474no—
453C22×C4—478no—
454C22×C4—474no—
455C22×C4—471no—
456C22×C4—472no—
457C22×C4—474no—
458C22×C4—472no—
459C22×C4—478no—
460C22×C4—478no—
461C22×C4—474no—
462C22×C4—474no—
463C22×C4—474no—
464C22×C4—4716no—
465C22×C4—474no—
466C22×C4—944no—
467C22×C4—9432no—
468C22×C4—948no—
469C22×C4—948no—
470C22×C4—948no—
471C22×C4—948no—
472C22×C4—944no—
473C22×C4—948no—
474C22×C4—948no—
475C22×C4—948no—
476C22×C4—944no—
477C22×C4—944no—
478C22×C4C2×C4×D4714yes—
479C22×C4C23×D4714yes—
480C22×C4C23×D4711yescharacteristic
481C22×C4C23×D4712yes—
482C22×C4C23×D4712yes—
483C22×C4C23×D4714yes—
484C22×C4C23×D4711yescharacteristic
485C4⋊C4—28no—
486C4⋊C4—478no—
487C4⋊C4—478no—
488C4⋊C4—478no—
489C4⋊C4—948no—
490C4⋊C4—948no—
491C4⋊C4—948no—
492C4⋊C4C2×C4×D4718yes—
493C22⋊C4—28no—
494C22⋊C4—478no—
495C22⋊C4—478no—
496C22⋊C4—478no—
497C22⋊C4—948no—
498C22⋊C4—948no—
499C22⋊C4—948no—
500C22⋊C4C2×C4×D4718yes—
501C42—28no—
502C42—24no—
503C42—24no—
504C42—478no—
505C42—478no—
506C42—474no—
507C42—474no—
508C42—948no—
509C42—948no—
510C42—948no—
511C42—948no—
512C42—948no—
513C42—944no—
514C42—944no—
515C42C2×C4×D4714yes—
516C42C2×C4×D4714yes—
517C23—24no—
518C23—22no—
519C23—472no—
520C23—474no—
521C23—478no—
522C23—472no—
523C23—948no—
524C23—9416no—
525C23—944no—
526C23—942no—
527C23—18816no—
528C23C22×C4×D4712yes—
529C23C24×D4711yescharacteristic
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—28no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—472no—
540C2×C4—474no—
541C2×C4—4716no—
542C2×C4—474no—
543C2×C4—474no—
544C2×C4—472no—
545C2×C4—478no—
546C2×C4—948no—
547C2×C4—9416no—
548C2×C4—9416no—
549C2×C4—9432no—
550C2×C4—948no—
551C2×C4—948no—
552C2×C4—944no—
553C2×C4—944no—
554C2×C4—944no—
555C2×C4—944no—
556C2×C4—942no—
557C2×C4—948no—
558C2×C4—944no—
559C2×C4—944no—
560C2×C4—944no—
561C2×C4—18816no—
562C2×C4C22×C4×D4714yes—
563C2×C4C22×C4×D4714yes—
564C2×C4C22×C4×D4712yes—
565C2×C4C22×C4×D4712yes—
566C2×C4#41×D4718yes—
567C2×C4#41×D4714yes—
568C22—22no—
569C22—24no—
570C22—44no—
571C22—474no—
572C22—478no—
573C22—4716no—
574C22—942no—
575C22—944no—
576C22—18816no—
577C22—1884no—
578C22C23×C4×D4711yescharacteristic
579C22C2×#41×D4712yes—
580C22C2×#41×D4714yes—
581C4—22no—
582C4—24no—
583C4—24no—
584C4—28no—
585C4—44no—
586C4—474no—
587C4—942no—
588C4—944no—
589C4—944no—
590C4—948no—
591C4—1884no—
592C4#117×D4714yes—
593C2—42no—
594C2—478no—
595C2—1882no—
596C2C2×#117×D4711yescharacteristic
597C2C4×#41×D4712yes—
598C2#529×D4714yes—
subgroupG/H
centerC22×C4C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC47×#2298C2
socle, cosocleC23×C47C25
prime radicalC24×D47C23
hypercenter#2298D47
hypocenterC47C2×#2298
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #2298

Complements

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

NH ≅ G/Ntype
2. #20245886C2semidirect
3. #20245885C2semidirect
4. #20245884C2semidirect
5. #20245883C2semidirect
6. #20245882C2semidirect
7. #20245881C2semidirect
8. #20245880C2semidirect
10. #387×D47C2semidirect
11. C4×C4⋊C4×D47C2semidirect
13. #376×D47C2semidirect
14. C43×D47C2semidirect
15. C47×#2298C2semidirect
22. #117×D47C4semidirect
39. #15689010C22semidirect
40. #15689009C22semidirect
41. #15689008C22semidirect
42. #15689007C22semidirect
43. #15689006C22semidirect
44. #15689005C22semidirect
45. #15689004C22semidirect
46. C4⋊C4×Dic47C22semidirect
47. C4×Dic47⋊C4C22semidirect
48. C4×Dic47⋊C4C22semidirect
49. C4×C4⋊Dic47C22semidirect
50. #15688974C22semidirect
56. #15688969C22semidirect
57. #15688969C22semidirect
58. #15688968C22semidirect
62. C42×Dic47C22semidirect
63. C42×Dic47C22semidirect
64. C42×Dic47C22semidirect
67. C47×#387C22semidirect
68. C4×C4⋊C4×C47C22semidirect
70. C47×#376C22semidirect
71. C43×C47C22semidirect
84. #13093983C2×C4semidirect
85. #13093982C2×C4semidirect
86. #13093981C2×C4semidirect
87. #13093981C2×C4semidirect
88. #13093980C2×C4semidirect
131. #117×C47C2×C4semidirect
302. #2298D47direct (N × H)
314. D47#2298direct (N × H)
347. #387C2×D47semidirect
353. C4×C4⋊C4C2×D47semidirect
363. #376C2×D47semidirect
370. C43C2×D47semidirect
371. C47C2×#2298semidirect
390. #117C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#117×D472
#202458862
#202458852
#202458842
#202458832
#202458822
#202458812
#202458802
#388×D472
#387×D472
C4×C4⋊C4×D472
C4×C22⋊C4×D472
#376×D472
C43×D472
C47×#22982
C2×#229847