Finite Group Databasebeta

← D47×#3195 #27086884

Subgroups — D47×#3195 #27086884

Order 12032.

2322 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D47C212yesmaximal
2#20254212C211yesmaximal, characteristic, complemented
3#20254211C214yesmaximal, complemented
4#20254210C214yesmaximal, complemented
5#20254209C212yesmaximal, complemented
6#20254208C214yesmaximal, complemented
7#483×D47C214yesmaximal, complemented
8#470×D47C214yesmaximal, complemented
9#451×D47C214yesmaximal, complemented
10#407×D47C211yesmaximal, characteristic
11C47×#3195C211yesmaximal, characteristic, complemented
12C22×Q8×D47C2212yes—
13C23×C4×D47C2211yescharacteristic
14C2×Q16×D47C2214yescomplemented
15C2×M16×D47C2212yes—
16C2×#13094004C2212yes—
17C2×#13094003C2212yes—
18C2×#13094002—22no—
19C2×#13094001—22no—
20C2×#13094000C2212yes—
21C22⋊Q8×D47—22no—
22C22⋊Q8×D47—22no—
23C22⋊Q8×D47—22no—
24C22⋊Q8×D47—22no—
25C22⋊Q8×D47C2214yes—
26C22⋊Q8×D47C2214yes—
27C22⋊Q8×D47C2214yes—
28C22⋊Q8×D47C2214yes—
29C2×C4⋊C4×D47—22no—
30C2×C4⋊C4×D47C2212yes—
31C2×C22⋊C4×D47—22no—
32#15689455C2218yescomplemented
33#15689454C2214yescomplemented
34#15689453C2214yescomplemented
35#15689452C2218yescomplemented
36#15689451C2214yescomplemented
37#15689382C2214yescomplemented
38#15689381C2214yescomplemented
39#15689380C2218yescomplemented
40#15689379C2218yescomplemented
41#15689378C2214yescomplemented
42#15689281C2214yescomplemented
43#15689280C2218yescomplemented
44#15689279C2214yescomplemented
45#15689278C2214yescomplemented
46#15689277C2218yescomplemented
47#106×D47C2214yescomplemented
48#103×D47C2218yescomplemented
49#15689087C2211yescharacteristic
50#15689086C2212yes—
51#15689085C2214yes—
52C22⋊C8×D47C2214yes—
53C2×C22⋊Q8×C47C2212yes—
54C47×#483C2214yescomplemented
55C47×#470C2214yescomplemented
56C47×#451C2214yescomplemented
57C47×#407C2211yescharacteristic
58C24×D47D411yescharacteristic
59C22×Dic94—22no—
60C22×Dic94C2312yes—
61C2×Q8×D47—22no—
62C2×Q8×D47—22no—
63C2×Q8×D47—48no—
64C2×Q8×D47C2314yes—
65C2×Q8×D47C2314yes—
66C23×Dic47D411yescharacteristic
67C22×C4×D47—22no—
68C22×C4×D47—22no—
69C22×C4×D47—44no—
70C22×C4×D47D412yes—
71C22×C4×D47D411yescharacteristic
72C22×C4×D47D411yescharacteristic
73C22×C4×D47D412yes—
74C22×C4×D47C2312yes—
75C22×C4×D47C2311yescharacteristic
76C22×C4×D47C2312yes—
77C22×C4×D47C2311yescharacteristic
78C2×Dic188C2314yescomplemented
79C2×#10625337C2318yescomplemented
80Q16×D47—48no—
81C2×#10625329C2312yes—
82C2×#10625324C2314yes—
83M16×D47—44no—
84C2×C8×D47C2314yes—
85#13094004—22no—
86#13094004—22no—
87#13094004C2314yes—
88#13094004C2314yes—
89#13094003—22no—
90#13094003—22no—
91#13094003C2314yes—
92#13094003C2314yes—
93#13094002—24no—
94#13094002—24no—
95#13094002—24no—
96#13094002—24no—
97#13094001—24no—
98#13094001—24no—
99#13094001—24no—
100#13094001—24no—
101#13094000—22no—
102#13094000—22no—
103#13094000C2314yes—
104#13094000C2314yes—
105C2×C4⋊Dic47—22no—
106C2×C4⋊Dic47C2312yes—
107C2×Dic47⋊C4—22no—
108C2×Dic47⋊C4—22no—
109C2×Dic47⋊C4—22no—
110C4⋊C4×D47—24no—
111C4⋊C4×D47—24no—
112C4⋊C4×D47—24no—
113C4⋊C4×D47—24no—
114C4⋊C4×D47—22no—
115C4⋊C4×D47—22no—
116C4⋊C4×D47C2314yes—
117C4⋊C4×D47C2314yes—
118C2×C22⋊Dic47—22no—
119C2×(C2×D47)⋊C4—22no—
120C2×(C2×D47)⋊C4—22no—
121C22⋊C4×D47—24no—
122C22⋊C4×D47—24no—
123C22⋊C4×D47—24no—
124C22⋊C4×D47—24no—
125#13093956C2314yescomplemented
126#13093955C2318yescomplemented
127#13093949C2318yescomplemented
128#13093948C2318yescomplemented
129#13093947C2318yescomplemented
130C22⋊(C47⋊C8)C2314yes—
131(C2×D47)⋊C8C2318yes—
132C22×Q8×C47C2312yes—
133C23×C4×C47C2311yescharacteristic
134C2×Q16×C47C2314yescomplemented
135C2×M16×C47C2312yes—
136C22⋊Q8×C47—22no—
137C22⋊Q8×C47—22no—
138C22⋊Q8×C47C2314yes—
139C22⋊Q8×C47C2314yes—
140C2×C4⋊C4×C47—22no—
141C2×C4⋊C4×C47C2312yes—
142C2×C22⋊C4×C47—22no—
143#106×C47C2314yescomplemented
144#103×C47C2318yescomplemented
145C22⋊C8×C47C2314yes—
146C24×C47C2×D411yescharacteristic
147C23×D47—28no—
148C23×D47—42no—
149C23×D47C2×D411yescharacteristic
150C23×D47C2×D411yescharacteristic
151C23×D47C2×D412yes—
152C23×D47C2×D412yes—
153C2×Q8×C47—22no—
154C2×Q8×C47—44no—
155C2×Q8×C47C2414yes—
156C22×C4×C47—22no—
157C22×C4×C47—22no—
158C22×C4×C47—42no—
159C22×C4×C47C2×D412yes—
160C22×C4×C47C2×D411yescharacteristic
161C22×C4×C47C2412yes—
162C22×C4×C47C2411yescharacteristic
163C22×Dic47—22no—
164C22×Dic47—22no—
165C22×Dic47—42no—
166C22×Dic47C2×D412yes—
167C22×Dic47C2×D411yescharacteristic
168C22×Dic47C2×D412yes—
169C22×Dic47C2×D411yescharacteristic
170Q8×D47—216no—
171Q8×D47—48no—
172Q8×D47—48no—
173Q8×D47—48no—
174C2×C4×D47—24no—
175C2×C4×D47—28no—
176C2×C4×D47—24no—
177C2×C4×D47—24no—
178C2×C4×D47—24no—
179C2×C4×D47—24no—
180C2×C4×D47—44no—
181C2×C4×D47—42no—
182C2×C4×D47—44no—
183C2×C4×D47—42no—
184C2×C4×D47—44no—
185C2×C4×D47—42no—
186C2×C4×D47—48no—
187C2×C4×D47—48no—
188C2×C4×D47C2×D411yescharacteristic
189C2×C4×D47C2×D412yes—
190C2×C4×D47C2×D412yes—
191C2×C4×D47C2×D411yescharacteristic
192C2×C4×D47C2×D412yes—
193C2×C4×D47C2×D412yes—
194C2×C4×D47C2×D412yes—
195C2×C4×D47C2412yes—
196C2×C4×D47C2411yescharacteristic
197C2×C4×D47C2411yescharacteristic
198C2×Dic94—22no—
199C2×Dic94—24no—
200C2×Dic94—24no—
201C2×Dic94—44no—
202C2×Dic94—48no—
203C2×Dic94C2414yes—
204Q16×C47—44no—
205M16×C47—42no—
206C2×C8×C47C2414yes—
207C4⋊C4×C47—24no—
208C4⋊C4×C47—24no—
209C4⋊C4×C47—22no—
210C4⋊C4×C47C2414yes—
211C22⋊C4×C47—24no—
212C22⋊C4×C47—24no—
213C22⋊Dic47—24no—
214C22⋊Dic47—24no—
215#10625337—48no—
216(C2×D47)⋊C4—24no—
217(C2×D47)⋊C4—24no—
218(C2×D47)⋊C4—24no—
219(C2×D47)⋊C4—24no—
220C4⋊Dic47—22no—
221C4⋊Dic47—24no—
222C4⋊Dic47—24no—
223C4⋊Dic47C2414yes—
224Dic47⋊C4—24no—
225Dic47⋊C4—24no—
226Dic47⋊C4—24no—
227Dic47⋊C4—24no—
228Dic47⋊C4—24no—
229Dic47⋊C4—24no—
230#10625329—42no—
231C2×C47⋊C8C2414yes—
232Dic188—44no—
233#10625324—44no—
234C8×D47—28no—
235C23×C47—24no—
236C23×C47—41no—
237C23×C47C22×D411yescharacteristic
238C23×C47C22×D412yes—
239C22×D47—24no—
240C22×D47—24no—
241C22×D47—24no—
242C22×D47—22no—
243C22×D47—24no—
244C22×D47—24no—
245C22×D47—24no—
246C22×D47—41no—
247C22×D47—42no—
248C22×D47—416no—
249C22×D47#13718yes—
250C22×D47C22×D411yescharacteristic
251C22×D47C22×D412yes—
252C22×D47C22×D411yescharacteristic
253Q8×C47—28no—
254Q8×C47—44no—
255C2×C4×C47—22no—
256C2×C4×C47—24no—
257C2×C4×C47—24no—
258C2×C4×C47—24no—
259C2×C4×C47—41no—
260C2×C4×C47—42no—
261C2×C4×C47—44no—
262C2×C4×C47—44no—
263C2×C4×C47C22×D411yescharacteristic
264C2×C4×C47C22×D412yes—
265C2×C4×C47C2511yescharacteristic
266C2×Dic47—24no—
267C2×Dic47—22no—
268C2×Dic47—24no—
269C2×Dic47—24no—
270C2×Dic47—41no—
271C2×Dic47—42no—
272C2×Dic47—44no—
273C2×Dic47—44no—
274C2×Dic47C22×D411yescharacteristic
275C2×Dic47C22×D412yes—
276C2×Dic47C22×D411yescharacteristic
277C4×D47—22no—
278C4×D47—24no—
279C4×D47—22no—
280C4×D47—24no—
281C4×D47—22no—
282C4×D47—24no—
283C4×D47—42no—
284C4×D47—42no—
285C4×D47—42no—
286C4×D47—48no—
287C4×D47—48no—
288C4×D47—48no—
289C4×D47—48no—
290C4×D47H(5,𝔽2)14yes—
291Dic94—28no—
292Dic94—48no—
293Dic94—44no—
294Dic94—48no—
295C8×C47—24no—
296C47⋊C8—24no—
297C2×#3195—471nomaximal, Sylow
298C22×C47—22no—
299C22×C47—22no—
300C22×C47—21no—
301C22×C47—22no—
302C22×C47—44no—
303C22×C47C2×#13714yes—
304C22×C47C23×D411yescharacteristic
305C2×D47—22no—
306C2×D47—22no—
307C2×D47—216no—
308C2×D47—21no—
309C2×D47—22no—
310C2×D47—44no—
311C2×D47—48no—
312C2×D47—44no—
313C2×D47#53412yes—
314C2×D47C2×#13714yes—
315C2×D47C2×#13714yes—
316C4×C47—22no—
317C4×C47—21no—
318C4×C47—44no—
319C4×C47—44no—
320C4×C47C2×H(5,𝔽2)12yes—
321Dic47—22no—
322Dic47—21no—
323Dic47—44no—
324Dic47—44no—
325Dic47#53412yes—
326C22×C22⋊Q8—472no—
327#3195—474no—
328#3195—474no—
329#3195—474no—
330#3195—471no—
331#3195—472no—
332#3195D4711yescharacteristic, direct product factor
333C2×#483—474no—
334C2×#470—474no—
335C2×#451—474no—
336C2×#407—471no—
337C2×C47—24no—
338C2×C47—41no—
339C2×C47C2×#53411yescharacteristic
340C2×C47C22×#13712yes—
341D47—24no—
342D47—41no—
343D47#319514yesdirect product factor
344C23×Q8—472no—
345C24×C4—471no—
346C22×Q16—474no—
347C22×M16—472no—
348C2×C22⋊Q8—472no—
349C2×C22⋊Q8—472no—
350C2×C22⋊Q8—474no—
351C2×C22⋊Q8—474no—
352C2×C22⋊Q8—474no—
353C2×C22⋊Q8—474no—
354C2×C22⋊Q8—472no—
355C2×C22⋊Q8—942no—
356C2×C22⋊Q8—942no—
357C2×C22⋊Q8—942no—
358C2×C22⋊Q8—942no—
359C2×C22⋊Q8—942no—
360C2×C22⋊Q8—942no—
361C2×C22⋊Q8C2×D4712yes—
362C22×C4⋊C4—472no—
363C22×C4⋊C4—942no—
364C22×C22⋊C4—942no—
365#483—474no—
366#483—474no—
367#483—478no—
368#483—478no—
369#483—474no—
370#483C2×D4714yescomplemented
371#470—474no—
372#470—474no—
373#470—478no—
374#470—474no—
375#470—478no—
376#470C2×D4714yescomplemented
377#451—474no—
378#451—478no—
379#451—474no—
380#451—478no—
381#451—474no—
382#451C2×D4714yescomplemented
383C2×#106—474no—
384C2×#103—478no—
385#407—471no—
386#407—472no—
387#407—474no—
388#407C2×D4711yescharacteristic
389C2×C22⋊C8—474no—
390C47C2×#319511yescharacteristic, complemented, Sylow
391C25—471no—
392C22×Q8—474no—
393C22×Q8—474no—
394C22×Q8—472no—
395C22×Q8—942no—
396C22×Q8—942no—
397C22×Q8—942no—
398C22×Q8—1888no—
399C22×Q8C22×D4712yes—
400C23×C4—471no—
401C23×C4—472no—
402C23×C4—471no—
403C23×C4—472no—
404C23×C4—472no—
405C23×C4—471no—
406C23×C4—471no—
407C23×C4—472no—
408C23×C4—471no—
409C23×C4—942no—
410C23×C4—942no—
411C23×C4—1884no—
412C23×C4C22×D4711yescharacteristic
413C2×Q16—478no—
414C2×Q16—474no—
415C2×Q16—1888no—
416C2×Q16C22×D4714yescomplemented
417C2×M16—472no—
418C2×M16—474no—
419C2×M16—1884no—
420C2×M16C22×D4712yes—
421C22×C8—474no—
422C22⋊Q8—22no—
423C22⋊Q8—22no—
424C22⋊Q8—474no—
425C22⋊Q8—474no—
426C22⋊Q8—474no—
427C22⋊Q8—474no—
428C22⋊Q8—474no—
429C22⋊Q8—474no—
430C22⋊Q8—944no—
431C22⋊Q8—944no—
432C22⋊Q8—944no—
433C22⋊Q8—944no—
434C22⋊Q8—944no—
435C22⋊Q8—944no—
436C22⋊Q8—944no—
437C22⋊Q8—944no—
438C22⋊Q8—942no—
439C22⋊Q8—942no—
440C22⋊Q8—942no—
441C22⋊Q8—942no—
442C22⋊Q8—942no—
443C22⋊Q8—942no—
444C22⋊Q8C22×D4714yes—
445C22⋊Q8C22×D4714yes—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—472no—
448C2×C4⋊C4—474no—
449C2×C4⋊C4—474no—
450C2×C4⋊C4—942no—
451C2×C4⋊C4—942no—
452C2×C4⋊C4—944no—
453C2×C4⋊C4—944no—
454C2×C4⋊C4—944no—
455C2×C4⋊C4—944no—
456C2×C4⋊C4—942no—
457C2×C4⋊C4—942no—
458C2×C4⋊C4—942no—
459C2×C4⋊C4—942no—
460C2×C4⋊C4C22×D4712yes—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—944no—
463C2×C22⋊C4—944no—
464C2×C22⋊C4—944no—
465C2×C22⋊C4—944no—
466C2×C22⋊C4—942no—
467C2×C22⋊C4—942no—
468C2×C22⋊C4—942no—
469#106—474no—
470#106—478no—
471#106C22×D4714yescomplemented
472#103—478no—
473#103—478no—
474#103—478no—
475#103C22×D4718yescomplemented
476C22⋊C8—474no—
477C22⋊C8—478no—
478C22⋊C8C22×D4714yes—
479C24—472no—
480C24—471no—
481C24—471no—
482C24—472no—
483C24—948no—
484C24—1882no—
485C24D4×D4711yescharacteristic
486C2×Q8—22no—
487C2×Q8—44no—
488C2×Q8—474no—
489C2×Q8—944no—
490C2×Q8—944no—
491C2×Q8—9416no—
492C2×Q8—942no—
493C2×Q8—1884no—
494C2×Q8—1888no—
495C2×Q8—1888no—
496C2×Q8—1888no—
497C2×Q8—1888no—
498C2×Q8C23×D4714yes—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—42no—
502C22×C4—471no—
503C22×C4—472no—
504C22×C4—471no—
505C22×C4—472no—
506C22×C4—471no—
507C22×C4—471no—
508C22×C4—472no—
509C22×C4—472no—
510C22×C4—471no—
511C22×C4—472no—
512C22×C4—471no—
513C22×C4—472no—
514C22×C4—472no—
515C22×C4—472no—
516C22×C4—944no—
517C22×C4—948no—
518C22×C4—944no—
519C22×C4—944no—
520C22×C4—944no—
521C22×C4—944no—
522C22×C4—942no—
523C22×C4—942no—
524C22×C4—1882no—
525C22×C4—1884no—
526C22×C4—1884no—
527C22×C4—1882no—
528C22×C4—1884no—
529C22×C4—1882no—
530C22×C4—1888no—
531C22×C4—1888no—
532C22×C4—1882no—
533C22×C4D4×D4712yes—
534C22×C4D4×D4711yescharacteristic
535C22×C4C23×D4712yes—
536C22×C4C23×D4711yescharacteristic
537Q16—44no—
538Q16—1884no—
539Q16—1888no—
540M16—42no—
541M16—1884no—
542M16—1882no—
543C2×C8—474no—
544C2×C8—948no—
545C2×C8C23×D4714yes—
546C4⋊C4—24no—
547C4⋊C4—24no—
548C4⋊C4—22no—
549C4⋊C4—474no—
550C4⋊C4—944no—
551C4⋊C4—944no—
552C4⋊C4—944no—
553C4⋊C4—944no—
554C4⋊C4—944no—
555C4⋊C4—944no—
556C4⋊C4—944no—
557C4⋊C4—944no—
558C4⋊C4—942no—
559C4⋊C4C23×D4714yes—
560C22⋊C4—24no—
561C22⋊C4—24no—
562C22⋊C4—944no—
563C22⋊C4—944no—
564C22⋊C4—944no—
565C22⋊C4—944no—
566C22⋊C4—944no—
567C22⋊C4—944no—
568C23—24no—
569C23—41no—
570C23—471no—
571C23—478no—
572C23—472no—
573C23—471no—
574C23—944no—
575C23—944no—
576C23—942no—
577C23—944no—
578C23—944no—
579C23—944no—
580C23—944no—
581C23—1882no—
582C23—1881no—
583C23—18816no—
584C23C2×D4×D4711yescharacteristic
585C23C2×D4×D4712yes—
586Q8—28no—
587Q8—44no—
588Q8—948no—
589Q8—1884no—
590Q8—1888no—
591Q8—1888no—
592C2×C4—22no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—41no—
597C2×C4—42no—
598C2×C4—44no—
599C2×C4—44no—
600C2×C4—471no—
601C2×C4—474no—
602C2×C4—471no—
603C2×C4—472no—
604C2×C4—942no—
605C2×C4—944no—
606C2×C4—942no—
607C2×C4—944no—
608C2×C4—942no—
609C2×C4—944no—
610C2×C4—942no—
611C2×C4—944no—
612C2×C4—944no—
613C2×C4—944no—
614C2×C4—1882no—
615C2×C4—1882no—
616C2×C4—1882no—
617C2×C4—1888no—
618C2×C4—1888no—
619C2×C4—1888no—
620C2×C4—1888no—
621C2×C4—1881no—
622C2×C4—1882no—
623C2×C4—1884no—
624C2×C4—1884no—
625C2×C4C2×D4×D4711yescharacteristic
626C2×C4C2×D4×D4712yes—
627C2×C4C24×D4711yescharacteristic
628C8—24no—
629C8—944no—
630C22—22no—
631C22—22no—
632C22—22no—
633C22—21no—
634C22—44no—
635C22—474no—
636C22—472no—
637C22—474no—
638C22—9416no—
639C22—942no—
640C22—942no—
641C22—942no—
642C22—941no—
643C22—1888no—
644C22—1884no—
645C22—1884no—
646C22#137×D4714yes—
647C22C22×D4×D4711yescharacteristic
648C4—22no—
649C4—21no—
650C4—44no—
651C4—44no—
652C4—472no—
653C4—942no—
654C4—941no—
655C4—1884no—
656C4—1884no—
657C4H(5,𝔽2)×D4712yes—
658C2—24no—
659C2—41no—
660C2—474no—
661C2—944no—
662C2—1881no—
663C2#534×D4711yescharacteristic
664C2C2×#137×D4712yes—
subgroupG/H
centerC22C22×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC47×#3195C2
socleC22×C47C23×D4
prime radicalC24×D47D4
hypercenter#3195D47
hypocenterC47C2×#3195
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3195

Complements

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

NH ≅ G/Ntype
2. #20254212C2semidirect
3. #20254211C2semidirect
4. #20254210C2semidirect
5. #20254209C2semidirect
6. #20254208C2semidirect
7. #483×D47C2semidirect
8. #470×D47C2semidirect
9. #451×D47C2semidirect
11. C47×#3195C2semidirect
14. C2×Q16×D47C22semidirect
32. #15689455C22semidirect
33. #15689454C22semidirect
34. #15689453C22semidirect
35. #15689452C22semidirect
36. #15689451C22semidirect
37. #15689382C22semidirect
38. #15689381C22semidirect
39. #15689380C22semidirect
40. #15689379C22semidirect
41. #15689378C22semidirect
42. #15689281C22semidirect
43. #15689280C22semidirect
44. #15689279C22semidirect
45. #15689278C22semidirect
46. #15689277C22semidirect
47. #106×D47C22semidirect
48. #103×D47C22semidirect
54. C47×#483C22semidirect
55. C47×#470C22semidirect
56. C47×#451C22semidirect
78. C2×Dic188C23semidirect
79. C2×#10625337C23semidirect
125. #13093956C23semidirect
126. #13093955C23semidirect
127. #13093949C23semidirect
128. #13093948C23semidirect
129. #13093947C23semidirect
134. C2×Q16×C47C23semidirect
143. #106×C47C23semidirect
144. #103×C47C23semidirect
332. #3195D47direct (N × H)
343. D47#3195direct (N × H)
370. #483C2×D47semidirect
376. #470C2×D47semidirect
382. #451C2×D47semidirect
390. C47C2×#3195semidirect
416. C2×Q16C22×D47semidirect
471. #106C22×D47semidirect
475. #103C22×D47semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D472
#202542122
#202542112
#202542102
#202542092
#202542082
#483×D472
#470×D472
#451×D472
#407×D472
C47×#31952
C2×#319547