Finite Group Databasebeta

← D47×#3335 #27094693

Subgroups — D47×#3335 #27094693

Order 12032.

2158 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#554×D47C211yesmaximal, characteristic, complemented
2#547×D47C211yesmaximal, characteristic
3#20255748C211yesmaximal, characteristic, complemented
4#20255747C211yesmaximal, characteristic, complemented
5#20255746C211yesmaximal, characteristic, complemented
6#20255745C211yesmaximal, characteristic, complemented
7#20255744C211yesmaximal, characteristic, complemented
8#20255743C212yesmaximal, complemented
9#20255742C211yesmaximal, characteristic, complemented
10#20255741C212yesmaximal, complemented
11#20255740C212yesmaximal, complemented
12#20255739C211yesmaximal, characteristic, complemented
13#20255738C212yesmaximal, complemented
14#498×D47C211yesmaximal, characteristic, complemented
15#481×D47C212yesmaximal, complemented
16#483×D47C212yesmaximal, complemented
17#475×D47C211yesmaximal, characteristic, complemented
18#476×D47C211yesmaximal, characteristic, complemented
19#465×D47C212yesmaximal, complemented
20C4×SD16×D47C211yesmaximal, characteristic, complemented
21C8×D4×D47C211yesmaximal, characteristic, complemented
22C2×#106×D47C212yesmaximal, complemented
23C47×#3335C211yesmaximal, characteristic, complemented
24C2×#41×D47—21no—
25C2×SD16×D47C2211yescharacteristic
26C22×C8×D47C2212yes—
27#15689834C2211yescharacteristic, complemented
28#15689833C2211yescharacteristic, complemented
29#15689832—21no—
30#15689831C2212yescomplemented
31#15689830C2211yescharacteristic, complemented
32#15689829—21no—
33#15689828C2212yescomplemented
34#15689827—22no—
35#15689778C2211yescharacteristic
36#15689777C2211yescharacteristic
37#15689776C2211yescharacteristic
38#15689775—21no—
39#15689774C2212yes—
40#15689773C2212yes—
41#15689772—21no—
42#15689771—22no—
43C4⋊Q8×D47C2211yescharacteristic
44C4⋊Q8×D47C2211yescharacteristic
45#125×D47—21no—
46#123×D47—22no—
47C22⋊Q8×D47—21no—
48C22⋊Q8×D47—22no—
49C22⋊Q8×D47C2212yes—
50#121×D47C2212yes—
51C4×Q8×D47C2211yescharacteristic
52C4×D4×D47—21no—
53C4×D4×D47C2211yescharacteristic
54C4×D4×D47C2211yescharacteristic
55C2×C4⋊C4×D47C2212yes—
56C2×C4⋊C4×D47C2212yes—
57#15689521C2211yescharacteristic, complemented
58#15689520C2212yescomplemented
59#15689520C2212yescomplemented
60#15689519C2211yescharacteristic, complemented
61#15689519C2211yescharacteristic, complemented
62#15689455C2212yescomplemented
63#15689455C2212yescomplemented
64#15689454C2212yescomplemented
65#15689453C2212yescomplemented
66#15689452C2212yescomplemented
67#15689452C2212yescomplemented
68#15689451C2212yescomplemented
69#15689443C2212yescomplemented
70#15689443C2212yescomplemented
71#15689442C2212yescomplemented
72#15689441C2212yescomplemented
73#15689440C2212yescomplemented
74#15689440C2212yescomplemented
75#15689439C2212yescomplemented
76#15689414C2211yescharacteristic, complemented
77#15689413C2211yescharacteristic, complemented
78#15689412C2212yescomplemented
79#15689411C2212yescomplemented
80#15689410C2211yescharacteristic, complemented
81#15689409C2211yescharacteristic, complemented
82#15689408C2211yescharacteristic, complemented
83#15689407C2212yescomplemented
84#15689406C2212yescomplemented
85#15689405C2211yescharacteristic, complemented
86#15689355C2212yescomplemented
87#15689354C2212yescomplemented
88#15689353C2212yescomplemented
89#15689352C2212yescomplemented
90#15689351C2212yescomplemented
91#15689350C2212yescomplemented
92#15689349C2212yescomplemented
93#15689214C2211yescharacteristic, complemented
94C4×#10625325C2211yescharacteristic, complemented
95SD16×Dic47C2211yescharacteristic, complemented
96C4×#10625336C2211yescharacteristic, complemented
97#15689210C2211yescharacteristic, complemented
98C4×#10625335C2211yescharacteristic, complemented
99#15689208C2211yescharacteristic, complemented
100C8×D188C2211yescharacteristic, complemented
101D4×C47⋊C8C2211yescharacteristic, complemented
102#15689188C2211yescharacteristic, complemented
103C8×C22⋊D47C2212yescomplemented
104(C22⋊D47)⋊C8C2212yescomplemented
105C2×#13093956C2212yescomplemented
106C2×#13093955C2212yescomplemented
107C2×#13093955C2212yescomplemented
108#106×D47C2212yes—
109#106×D47C2211yescharacteristic
110#106×D47C2212yes—
111#106×D47C2212yes—
112#106×D47C2212yes—
113#106×D47C2212yescomplemented
114#106×D47C2212yescomplemented
115#106×D47C2212yescomplemented
116#106×D47C2212yescomplemented
117C4⋊C8×D47C2211yescharacteristic
118#103×D47C2212yes—
119#103×D47C2211yescharacteristic
120#102×D47C2212yes—
121#102×D47C2211yescharacteristic
122C22⋊C8×D47C2212yes—
123C4×C8×D47C2211yescharacteristic
124C47×#554C2211yescharacteristic, complemented
125C47×#547C2211yescharacteristic
126C47×#498C2211yescharacteristic, complemented
127C47×#483C2212yescomplemented
128C47×#481C2212yescomplemented
129C47×#476C2211yescharacteristic, complemented
130C47×#475C2211yescharacteristic, complemented
131C47×#465C2212yescomplemented
132C4×SD16×C47C2211yescharacteristic, complemented
133C8×D4×C47C2211yescharacteristic, complemented
134C2×#106×C47C2212yescomplemented
135C2×#10625354—21no—
136C2×#10625350—22no—
137C2×#10625350—21no—
138C2×#10625352—21no—
139C2×#10625352—22no—
140#41×D47—48no—
141C2×Q8×D47—21no—
142C2×Q8×D47—21no—
143C2×Q8×D47C2311yescharacteristic
144C2×D4×D47—22no—
145C2×D4×D47D411yescharacteristic
146C2×D4×D47C2311yescharacteristic
147C22×C4×D47—22no—
148C22×C4×D47—22no—
149C22×C4×D47—21no—
150C22×C4×D47C2312yes—
151C2×#10625325C2311yescharacteristic
152C2×#10625335C2311yescharacteristic
153C2×#10625336C2311yescharacteristic
154SD16×D47—24no—
155C22×C47⋊C8C2312yes—
156C2×C8×D47—28no—
157C2×C8×D47C2311yescharacteristic
158C2×C8×D47C2312yes—
159C2×C8×D47C2312yes—
160C2×C8×D47C2312yes—
161C2×C8×D47C2311yescharacteristic
162#13094024C2311yescharacteristic
163#13094024C2311yescharacteristic
164#13094023—21no—
165#13094023—21no—
166#13094023C2312yes—
167#13094023C2312yes—
168#13094022—21no—
169#13094022—21no—
170#13094016—21no—
171#13094015—21no—
172#13094015—21no—
173#13094014—22no—
174#13094014—22no—
175#13094009—22no—
176#13094009—22no—
177#13094008—22no—
178#13094007—22no—
179#13094006—22no—
180#13094006—22no—
181#13094005—22no—
182#13094004—21no—
183#13094004—22no—
184#13094004C2312yes—
185#13094003—22no—
186#13094003—21no—
187#13094003C2312yes—
188#13094002—22no—
189#13094002—22no—
190#13094002—22no—
191#13094002—22no—
192#13094001—22no—
193#13094001—22no—
194#13094001—22no—
195#13094001—22no—
196#13094000—22no—
197#13094000—21no—
198#13094000C2312yes—
199#13093999C2312yes—
200#13093998C2312yes—
201#13093997—22no—
202#13093996—22no—
203#13093995C2312yes—
204Q8×Dic47C2311yescharacteristic
205C4×Dic94—21no—
206C4×Dic94C2311yescharacteristic
207#13093989—21no—
208#13093989C2311yescharacteristic
209C4×D188—21no—
210C4×D188C2311yescharacteristic
211C4×D188C2311yescharacteristic
212D4×Dic47—21no—
213D4×Dic47D411yescharacteristic
214D4×Dic47C2311yescharacteristic
215#13093986—21no—
216#13093986D411yescharacteristic
217#13093986C2311yescharacteristic
218C4×C22⋊D47—22no—
219C4×C22⋊D47—21no—
220C4×C22⋊D47C2312yes—
221(C22⋊D47)⋊C4—22no—
222(C22⋊D47)⋊C4—21no—
223(C22⋊D47)⋊C4D412yes—
224C2×C4⋊Dic47C2312yes—
225C2×C4⋊Dic47C2312yes—
226C2×Dic47⋊C4—22no—
227C2×Dic47⋊C4—22no—
228C4⋊C4×D47—22no—
229C4⋊C4×D47—22no—
230C4⋊C4×D47—22no—
231C4⋊C4×D47—22no—
232C4⋊C4×D47—21no—
233C4⋊C4×D47—21no—
234C4⋊C4×D47—22no—
235C4⋊C4×D47—21no—
236C4⋊C4×D47D411yescharacteristic
237C4⋊C4×D47C2312yes—
238C4⋊C4×D47C2312yes—
239C4⋊C4×D47C2311yescharacteristic
240C4⋊C4×D47C2311yescharacteristic
241C4⋊C4×D47C2312yes—
242C4⋊C4×D47C2312yes—
243C4⋊C4×D47C2312yes—
244C4⋊C4×D47C2312yes—
245C22⋊C4×D47—22no—
246C22⋊C4×D47—21no—
247C22⋊C4×D47—22no—
248C22⋊C4×D47D412yes—
249C42×D47—21no—
250C42×D47C2311yescharacteristic
251#13093956C2312yes—
252#13093956C2312yes—
253#13093956C2312yes—
254#13093956C2311yescharacteristic
255#13093956C2312yes—
256#13093955C2312yes—
257#13093955C2312yes—
258#13093955C2312yes—
259#13093955C2312yes—
260#13093955C2312yes—
261#13093955C2312yes—
262#13093955C2311yescharacteristic
263#13093955C2311yescharacteristic
264#13093955C2312yes—
265#13093955C2312yes—
266C4⋊(C47⋊C8)C2311yescharacteristic
267Dic47⋊C8C2312yes—
268#13093949C2312yes—
269#13093949C2311yescharacteristic
270#13093948C2312yes—
271#13093948C2311yescharacteristic
272#13093947C2312yes—
273#13093947C2311yescharacteristic
274#13093946C2312yes—
275#13093946C2311yescharacteristic
276#13093945C2312yes—
277#13093945C2311yescharacteristic
278#13093944C2312yes—
279#13093944C2311yescharacteristic
280C22⋊(C47⋊C8)C2312yes—
281(C2×D47)⋊C8C2312yes—
282(C2×D47)⋊C8C2312yes—
283C4×C47⋊C8C2311yescharacteristic
284C8×Dic47C2311yescharacteristic
285C8×Dic47C2311yescharacteristic
286C2×#41×C47—21no—
287C2×SD16×C47C2311yescharacteristic
288C22×C8×C47C2312yes—
289C4⋊Q8×C47C2311yescharacteristic
290C4⋊Q8×C47C2311yescharacteristic
291#125×C47—21no—
292#123×C47—22no—
293C22⋊Q8×C47—21no—
294C22⋊Q8×C47—22no—
295C22⋊Q8×C47C2312yes—
296#121×C47C2312yes—
297C4×Q8×C47C2311yescharacteristic
298C4×D4×C47—21no—
299C4×D4×C47C2311yescharacteristic
300C4×D4×C47C2311yescharacteristic
301C2×C4⋊C4×C47C2312yes—
302C2×C4⋊C4×C47C2312yes—
303#106×C47C2312yes—
304#106×C47C2312yes—
305#106×C47C2312yes—
306#106×C47C2312yes—
307#106×C47C2311yescharacteristic
308C4⋊C8×C47C2311yescharacteristic
309#103×C47C2312yes—
310#103×C47C2311yescharacteristic
311#102×C47C2312yes—
312#102×C47C2311yescharacteristic
313C22⋊C8×C47C2312yes—
314C4×C8×C47C2311yescharacteristic
315C23×D47—21no—
316C23×D47C2×D412yes—
317#41×C47—44no—
318C2×Q8×C47—21no—
319C2×Q8×C47—21no—
320C2×Q8×C47C2411yescharacteristic
321C2×D4×C47—22no—
322C2×D4×C47C2×D411yescharacteristic
323C2×D4×C47C2411yescharacteristic
324C22×C4×C47—22no—
325C22×C4×C47—22no—
326C22×C4×C47—21no—
327C22×C4×C47C2412yes—
328C2×C22⋊D47—22no—
329C2×C22⋊D47—22no—
330C2×C22⋊D47—21no—
331C2×C22⋊D47C2×D412yes—
332C22×Dic47—22no—
333C22×Dic47—22no—
334C22×Dic47—21no—
335C22×Dic47C2×D412yes—
336#10625354—44no—
337Q8×D47—22no—
338Q8×D47—22no—
339Q8×D47—44no—
340Q8×D47—82no—
341#10625352—44no—
342#10625352—48no—
343D4×D47—22no—
344D4×D47—22no—
345D4×D47—48no—
346D4×D47SD1618yescomplemented
347#10625350—48no—
348#10625350—44no—
349C2×D188—22no—
350C2×D188C2×D411yescharacteristic
351C2×D188C2411yescharacteristic
352C2×C4×D47—24no—
353C2×C4×D47—24no—
354C2×C4×D47—21no—
355C2×C4×D47—21no—
356C2×C4×D47—22no—
357C2×C4×D47—21no—
358C2×C4×D47—22no—
359C2×C4×D47—22no—
360C2×C4×D47—22no—
361C2×C4×D47—21no—
362C2×C4×D47—21no—
363C2×C4×D47—22no—
364C2×C4×D47—22no—
365C2×C4×D47—48no—
366C2×C4×D47—44no—
367C2×C4×D47—84no—
368C2×C4×D47C2×D411yescharacteristic
369C2×C4×D47C2×D412yes—
370C2×C4×D47C2×D412yes—
371C2×C4×D47C2×D411yescharacteristic
372C2×C4×D47C2412yes—
373C2×C4×D47C2411yescharacteristic
374C2×Dic94—21no—
375C2×Dic94—21no—
376C2×Dic94—22no—
377C2×Dic94—21no—
378C2×Dic94—22no—
379C2×Dic94C2411yescharacteristic
380SD16×C47—22no—
381C2×C8×C47—24no—
382C2×C8×C47C2412yes—
383C2×C8×C47C2411yescharacteristic
384C2×C8×C47C2411yescharacteristic
385C4⋊C4×C47—22no—
386C4⋊C4×C47—22no—
387C4⋊C4×C47—21no—
388C4⋊C4×C47—21no—
389C4⋊C4×C47—22no—
390C4⋊C4×C47—21no—
391C4⋊C4×C47C2×D411yescharacteristic
392C4⋊C4×C47C2411yescharacteristic
393C4⋊C4×C47C2412yes—
394C4⋊C4×C47C2411yescharacteristic
395C4⋊C4×C47C2412yes—
396C22⋊C4×C47—22no—
397C22⋊C4×C47—21no—
398C22⋊C4×C47—22no—
399C22⋊C4×C47C2×D412yes—
400C42×C47—21no—
401C42×C47C2411yescharacteristic
402C22⋊Dic47—22no—
403C22⋊Dic47—21no—
404C22⋊Dic47—22no—
405C22⋊Dic47C2×D412yes—
406#10625336—22no—
407#10625335—22no—
408(C2×D47)⋊C4—22no—
409(C2×D47)⋊C4—22no—
410(C2×D47)⋊C4—21no—
411(C2×D47)⋊C4—22no—
412(C2×D47)⋊C4—21no—
413(C2×D47)⋊C4—22no—
414(C2×D47)⋊C4C2×D412yes—
415(C2×D47)⋊C4C2×D412yes—
416C4⋊Dic47—22no—
417C4⋊Dic47—22no—
418C4⋊Dic47—21no—
419C4⋊Dic47—21no—
420C4⋊Dic47—21no—
421C4⋊Dic47—22no—
422C4⋊Dic47C2×D411yescharacteristic
423C4⋊Dic47C2411yescharacteristic
424C4⋊Dic47C2412yes—
425C4⋊Dic47C2411yescharacteristic
426C4⋊Dic47C2412yes—
427Dic47⋊C4—21no—
428Dic47⋊C4—22no—
429Dic47⋊C4—21no—
430Dic47⋊C4—21no—
431Dic47⋊C4—22no—
432Dic47⋊C4—22no—
433Dic47⋊C4—22no—
434Dic47⋊C4—22no—
435Dic47⋊C4—22no—
436Dic47⋊C4—22no—
437Dic47⋊C4—22no—
438Dic47⋊C4—21no—
439Dic47⋊C4—22no—
440Dic47⋊C4—22no—
441Dic47⋊C4C2×D412yes—
442C4×Dic47—21no—
443C4×Dic47—21no—
444C4×Dic47—21no—
445C4×Dic47C2×D411yescharacteristic
446C4×Dic47C2×D411yescharacteristic
447C4×Dic47C2411yescharacteristic
448C2×C47⋊C8—24no—
449C2×C47⋊C8C2411yescharacteristic
450C2×C47⋊C8C2412yes—
451C2×C47⋊C8C2411yescharacteristic
452#10625325—22no—
453C8×D47—24no—
454C8×D47—22no—
455C8×D47—24no—
456C8×D47—24no—
457C8×D47#4114yescomplemented
458C23×C47—21no—
459C23×C47C22×D412yes—
460C22×D47—24no—
461C22×D47—24no—
462C22×D47—21no—
463C22×D47—42no—
464C22×D47—42no—
465C22×D47—42no—
466C22×D47C2×SD1618yes—
467C22×D47C22×D412yes—
468C22×D47C22×D411yescharacteristic
469Q8×C47—21no—
470Q8×C47—21no—
471Q8×C47—42no—
472Q8×C47—81no—
473D4×C47—21no—
474D4×C47—21no—
475D4×C47—44no—
476D4×C47C2×SD1614yescomplemented
477C2×C4×C47—22no—
478C2×C4×C47—22no—
479C2×C4×C47—21no—
480C2×C4×C47—21no—
481C2×C4×C47—22no—
482C2×C4×C47—22no—
483C2×C4×C47—21no—
484C2×C4×C47—44no—
485C2×C4×C47—42no—
486C2×C4×C47—82no—
487C2×C4×C47C22×D411yescharacteristic
488C2×C4×C47C22×D412yes—
489C2×C4×C47C22×D411yescharacteristic
490C2×C4×C47C2511yescharacteristic
491C22⋊D47—44no—
492C22⋊D47—44no—
493C22⋊D47—42no—
494C22⋊D47C2×SD1618yescomplemented
495C2×Dic47—24no—
496C2×Dic47—21no—
497C2×Dic47—21no—
498C2×Dic47—22no—
499C2×Dic47—22no—
500C2×Dic47—21no—
501C2×Dic47—44no—
502C2×Dic47—42no—
503C2×Dic47—82no—
504C2×Dic47C22×D411yescharacteristic
505C2×Dic47C22×D412yes—
506C2×Dic47C22×D411yescharacteristic
507C2×Dic47C22×D411yescharacteristic
508D188—21no—
509D188—21no—
510D188—44no—
511D188C2×SD1614yescomplemented
512C4×D47—24no—
513C4×D47—22no—
514C4×D47—22no—
515C4×D47—22no—
516C4×D47—24no—
517C4×D47—42no—
518C4×D47—42no—
519C4×D47—44no—
520C4×D47—44no—
521C4×D47—44no—
522C4×D47—42no—
523C4×D47—44no—
524C4×D47—42no—
525C4×D47—42no—
526C4×D47—82no—
527C4×D47—82no—
528C4×D47C2×SD1614yes—
529C4×D47C2×#4112yes—
530C4×D472−1+412yes—
531Dic94—21no—
532Dic94—21no—
533Dic94—42no—
534Dic94—42no—
535Dic94—44no—
536Dic94—82no—
537Dic94—81no—
538C8×C47—22no—
539C8×C47—21no—
540C8×C47C2×#4112yescomplemented
541C47⋊C8—22no—
542C47⋊C8—21no—
543C47⋊C8C2×#4112yescomplemented
544C2×#3335—471nomaximal, Sylow
545C22×C47—22no—
546C22×C47—22no—
547C22×C47—41no—
548C22×C47—41no—
549C22×C47—41no—
550C22×C47C22×SD1614yes—
551C22×C47C23×D411yescharacteristic
552C2×D47—22no—
553C2×D47—22no—
554C2×D47—216no—
555C2×D47—41no—
556C2×D47—41no—
557C2×D47—41no—
558C2×D47—84no—
559C2×D47#54712yes—
560C2×D47C22×SD1614yes—
561C2×D47C22×SD1612yes—
562C2×D47#57712yes—
563C4×C47—22no—
564C4×C47—21no—
565C4×C47—41no—
566C4×C47—42no—
567C4×C47—41no—
568C4×C47—42no—
569C4×C47—41no—
570C4×C47C22×SD1612yes—
571C4×C47C22×#4111yescharacteristic
572C4×C47C2×2−1+411yescharacteristic
573Dic47—22no—
574Dic47—21no—
575Dic47—41no—
576Dic47—42no—
577Dic47—41no—
578Dic47—42no—
579Dic47—41no—
580Dic47#54712yes—
581Dic47C22×SD1612yes—
582C2×#554—471no—
583C2×#547—471no—
584#3335—471no—
585#3335—472no—
586#3335—472no—
587#3335—471no—
588#3335—471no—
589#3335—472no—
590#3335—471no—
591#3335—471no—
592#3335—472no—
593#3335—471no—
594#3335—471no—
595#3335D4711yescharacteristic, direct product factor
596C2×#498—471no—
597C2×#481—472no—
598C2×#483—472no—
599C2×#475—471no—
600C2×#476—471no—
601C2×#465—472no—
602C2×C4×SD16—471no—
603C2×C8×D4—471no—
604C22×#106—472no—
605C2×C47—24no—
606C2×C47—81no—
607C2×C47C2×#54711yescharacteristic
608C2×C47C23×SD1611yescharacteristic
609C2×C47C2×#57711yescharacteristic
610D47—24no—
611D47—81no—
612D47#333514yesdirect product factor
613C22×#41—941no—
614C22×SD16—471no—
615C23×C8—472no—
616#554—471no—
617#554—472no—
618#554—471no—
619#554—471no—
620#554—472no—
621#554—941no—
622#554—942no—
623#554—941no—
624#554C2×D4711yescharacteristic, complemented
625#547—471no—
626#547—472no—
627#547—471no—
628#547—471no—
629#547—472no—
630#547—941no—
631#547—942no—
632#547—941no—
633#547C2×D4711yescharacteristic
634C2×C4⋊Q8—471no—
635C2×C4⋊Q8—471no—
636C2×#125—941no—
637C2×#123—942no—
638C2×C22⋊Q8—472no—
639C2×C22⋊Q8—942no—
640C2×C22⋊Q8—941no—
641C2×#121—472no—
642C2×C4×Q8—471no—
643C2×C4×D4—471no—
644C2×C4×D4—471no—
645C2×C4×D4—941no—
646C22×C4⋊C4—472no—
647C22×C4⋊C4—472no—
648#498—471no—
649#498—471no—
650#498—472no—
651#498—472no—
652#498—471no—
653#498C2×D4711yescharacteristic, complemented
654#483—472no—
655#483—472no—
656#483—472no—
657#483—472no—
658#483—472no—
659#483—472no—
660#483—472no—
661#483C2×D4712yescomplemented
662#481—472no—
663#481—472no—
664#481—472no—
665#481—472no—
666#481—472no—
667#481—472no—
668#481—472no—
669#481C2×D4712yescomplemented
670#476—471no—
671#476—471no—
672#476—472no—
673#476—471no—
674#476—472no—
675#476C2×D4711yescharacteristic, complemented
676#475—471no—
677#475—471no—
678#475—472no—
679#475—471no—
680#475—472no—
681#475C2×D4711yescharacteristic, complemented
682#465—472no—
683#465—472no—
684#465—472no—
685#465—472no—
686#465—472no—
687#465—472no—
688#465—472no—
689#465C2×D4712yescomplemented
690C4×SD16—471no—
691C4×SD16—471no—
692C4×SD16—471no—
693C4×SD16—471no—
694C4×SD16—471no—
695C4×SD16—471no—
696C4×SD16—471no—
697C4×SD16C2×D4711yescharacteristic, complemented
698C8×D4—472no—
699C8×D4—471no—
700C8×D4—471no—
701C8×D4—472no—
702C8×D4—471no—
703C8×D4C2×D4711yescharacteristic, complemented
704C2×#106—472no—
705C2×#106—472no—
706C2×#106—472no—
707C2×#106—472no—
708C2×#106—472no—
709C2×#106—472no—
710C2×#106—472no—
711C2×#106—472no—
712C2×#106—472no—
713C2×#106—472no—
714C2×#106—472no—
715C2×#106—471no—
716C2×#106C2×D4712yescomplemented
717C2×C4⋊C8—471no—
718C2×#103—472no—
719C2×#103—471no—
720C2×#102—471no—
721C2×#102—472no—
722C2×C22⋊C8—472no—
723C2×C4×C8—471no—
724C47C2×#333511yescharacteristic, complemented, Sylow
725C2×#41—21no—
726C2×#41—942no—
727C2×#41—941no—
728C2×#41—942no—
729C2×#41—941no—
730C2×#41—941no—
731C2×#41—1888no—
732C22×Q8—471no—
733C22×Q8—941no—
734C22×Q8—941no—
735C22×D4—471no—
736C22×D4—471no—
737C22×D4—942no—
738C23×C4—472no—
739C23×C4—941no—
740C23×C4—942no—
741C23×C4—942no—
742C2×SD16—471no—
743C2×SD16—471no—
744C2×SD16—471no—
745C2×SD16—944no—
746C2×SD16C22×D4711yescharacteristic
747C22×C8—471no—
748C22×C8—472no—
749C22×C8—472no—
750C22×C8—472no—
751C22×C8—472no—
752C22×C8—471no—
753C22×C8—948no—
754C22×C8C22×D4712yes—
755C4⋊Q8—472no—
756C4⋊Q8—472no—
757C4⋊Q8—471no—
758C4⋊Q8—471no—
759C4⋊Q8—941no—
760C4⋊Q8—941no—
761C4⋊Q8—941no—
762C4⋊Q8—941no—
763C4⋊Q8C22×D4711yescharacteristic
764C4⋊Q8C22×D4711yescharacteristic
765#125—21no—
766#125—941no—
767#125—942no—
768#125—942no—
769#125—941no—
770#125—941no—
771#123—22no—
772#123—942no—
773#123—942no—
774#123—942no—
775#123—942no—
776#123—942no—
777#123—942no—
778#123—942no—
779C22⋊Q8—21no—
780C22⋊Q8—22no—
781C22⋊Q8—472no—
782C22⋊Q8—472no—
783C22⋊Q8—472no—
784C22⋊Q8—942no—
785C22⋊Q8—942no—
786C22⋊Q8—942no—
787C22⋊Q8—942no—
788C22⋊Q8—942no—
789C22⋊Q8—942no—
790C22⋊Q8—942no—
791C22⋊Q8—942no—
792C22⋊Q8—942no—
793C22⋊Q8—942no—
794C22⋊Q8—941no—
795C22⋊Q8—941no—
796C22⋊Q8—941no—
797C22⋊Q8—942no—
798C22⋊Q8C22×D4712yes—
799#121—472no—
800#121—472no—
801#121—472no—
802#121—942no—
803#121—942no—
804#121C22×D4712yes—
805C4×Q8—471no—
806C4×Q8—471no—
807C4×Q8—471no—
808C4×Q8—941no—
809C4×Q8—941no—
810C4×Q8C22×D4711yescharacteristic
811C4×D4—21no—
812C4×D4—471no—
813C4×D4—472no—
814C4×D4—471no—
815C4×D4—472no—
816C4×D4—471no—
817C4×D4—471no—
818C4×D4—471no—
819C4×D4—471no—
820C4×D4—941no—
821C4×D4—941no—
822C4×D4—941no—
823C4×D4—942no—
824C4×D4—941no—
825C4×D4—942no—
826C4×D4—941no—
827C4×D4C22×D4711yescharacteristic
828C4×D4C22×D4711yescharacteristic
829C2×C4⋊C4—471no—
830C2×C4⋊C4—472no—
831C2×C4⋊C4—472no—
832C2×C4⋊C4—471no—
833C2×C4⋊C4—471no—
834C2×C4⋊C4—472no—
835C2×C4⋊C4—472no—
836C2×C4⋊C4—472no—
837C2×C4⋊C4—472no—
838C2×C4⋊C4—472no—
839C2×C4⋊C4—472no—
840C2×C4⋊C4—942no—
841C2×C4⋊C4—942no—
842C2×C4⋊C4—942no—
843C2×C4⋊C4—942no—
844C2×C4⋊C4—941no—
845C2×C4⋊C4—941no—
846C2×C4⋊C4—942no—
847C2×C4⋊C4—941no—
848C2×C4⋊C4—942no—
849C2×C4⋊C4—942no—
850C2×C4⋊C4C22×D4712yes—
851C2×C4⋊C4C22×D4712yes—
852C2×C22⋊C4—472no—
853C2×C22⋊C4—941no—
854C2×C22⋊C4—942no—
855C2×C22⋊C4—942no—
856C2×C42—471no—
857C2×C42—941no—
858#106—471no—
859#106—472no—
860#106—472no—
861#106—472no—
862#106—472no—
863#106—471no—
864#106—471no—
865#106—472no—
866#106—472no—
867#106—472no—
868#106—472no—
869#106—472no—
870#106—472no—
871#106—472no—
872#106—472no—
873#106C22×D4711yescharacteristic
874#106C22×D4712yes—
875#106C22×D4712yes—
876#106C22×D4712yes—
877#106C22×D4712yes—
878C4⋊C8—472no—
879C4⋊C8—471no—
880C4⋊C8C22×D4711yescharacteristic
881#103—471no—
882#103—472no—
883#103—471no—
884#103—472no—
885#103—471no—
886#103—472no—
887#103C22×D4711yescharacteristic
888#103C22×D4712yes—
889#102—471no—
890#102—472no—
891#102—471no—
892#102—472no—
893#102—471no—
894#102—472no—
895#102C22×D4711yescharacteristic
896#102C22×D4712yes—
897C22⋊C8—472no—
898C22⋊C8—472no—
899C22⋊C8—472no—
900C22⋊C8C22×D4712yes—
901C4×C8—471no—
902C4×C8—471no—
903C4×C8—471no—
904C4×C8C22×D4711yescharacteristic
905C24—472no—
906C24—941no—
907#41—44no—
908#41—1888no—
909#41—1884no—
910#41—1888no—
911#41—1884no—
912#41—1884no—
913C2×Q8—21no—
914C2×Q8—21no—
915C2×Q8—471no—
916C2×Q8—942no—
917C2×Q8—941no—
918C2×Q8—942no—
919C2×Q8—942no—
920C2×Q8—942no—
921C2×Q8—941no—
922C2×Q8—941no—
923C2×Q8—3762no—
924C2×Q8—1884no—
925C2×Q8C23×D4711yescharacteristic
926C2×D4—22no—
927C2×D4—472no—
928C2×D4—478no—
929C2×D4—471no—
930C2×D4—471no—
931C2×D4—942no—
932C2×D4—942no—
933C2×D4—942no—
934C2×D4—941no—
935C2×D4—942no—
936C2×D4—942no—
937C2×D4—1888no—
938C2×D4D4×D4711yescharacteristic
939C2×D4C23×D4711yescharacteristic
940C22×C4—22no—
941C22×C4—22no—
942C22×C4—21no—
943C22×C4—471no—
944C22×C4—471no—
945C22×C4—472no—
946C22×C4—471no—
947C22×C4—472no—
948C22×C4—472no—
949C22×C4—472no—
950C22×C4—944no—
951C22×C4—944no—
952C22×C4—941no—
953C22×C4—942no—
954C22×C4—942no—
955C22×C4—941no—
956C22×C4—941no—
957C22×C4—942no—
958C22×C4—941no—
959C22×C4—942no—
960C22×C4—942no—
961C22×C4—942no—
962C22×C4—941no—
963C22×C4—942no—
964C22×C4—942no—
965C22×C4—941no—
966C22×C4—3764no—
967C22×C4—1884no—
968C22×C4—1888no—
969C22×C4C23×D4712yes—
970SD16—22no—
971SD16—942no—
972SD16—942no—
973SD16—942no—
974C2×C8—24no—
975C2×C8—471no—
976C2×C8—474no—
977C2×C8—471no—
978C2×C8—472no—
979C2×C8—944no—
980C2×C8—942no—
981C2×C8—944no—
982C2×C8—944no—
983C2×C8—944no—
984C2×C8C23×D4711yescharacteristic
985C2×C8C23×D4712yes—
986C2×C8C23×D4711yescharacteristic
987C4⋊C4—22no—
988C4⋊C4—22no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—22no—
992C4⋊C4—21no—
993C4⋊C4—472no—
994C4⋊C4—471no—
995C4⋊C4—471no—
996C4⋊C4—472no—
997C4⋊C4—471no—
998C4⋊C4—472no—
999C4⋊C4—941no—
1000C4⋊C4—941no—
1001C4⋊C4—942no—
1002C4⋊C4—942no—
1003C4⋊C4—942no—
1004C4⋊C4—942no—
1005C4⋊C4—942no—
1006C4⋊C4—942no—
1007C4⋊C4—942no—
1008C4⋊C4—941no—
1009C4⋊C4—942no—
1010C4⋊C4—942no—
1011C4⋊C4—941no—
1012C4⋊C4—942no—
1013C4⋊C4—941no—
1014C4⋊C4—942no—
1015C4⋊C4—942no—
1016C4⋊C4—942no—
1017C4⋊C4—941no—
1018C4⋊C4—941no—
1019C4⋊C4D4×D4711yescharacteristic
1020C4⋊C4C23×D4711yescharacteristic
1021C4⋊C4C23×D4712yes—
1022C4⋊C4C23×D4711yescharacteristic
1023C4⋊C4C23×D4712yes—
1024C22⋊C4—22no—
1025C22⋊C4—21no—
1026C22⋊C4—22no—
1027C22⋊C4—472no—
1028C22⋊C4—472no—
1029C22⋊C4—472no—
1030C22⋊C4—941no—
1031C22⋊C4—942no—
1032C22⋊C4—942no—
1033C22⋊C4—942no—
1034C22⋊C4—941no—
1035C22⋊C4—942no—
1036C22⋊C4—942no—
1037C22⋊C4—941no—
1038C22⋊C4—942no—
1039C22⋊C4D4×D4712yes—
1040C42—21no—
1041C42—471no—
1042C42—471no—
1043C42—471no—
1044C42—941no—
1045C42—941no—
1046C42—941no—
1047C42C23×D4711yescharacteristic
1048C23—21no—
1049C23—471no—
1050C23—478no—
1051C23—472no—
1052C23—944no—
1053C23—944no—
1054C23—941no—
1055C23—1882no—
1056C23—1882no—
1057C23—1882no—
1058C23C2×D4×D4712yes—
1059Q8—21no—
1060Q8—21no—
1061Q8—42no—
1062Q8—81no—
1063Q8—941no—
1064Q8—941no—
1065Q8—3761no—
1066Q8—3762no—
1067Q8—1882no—
1068Q8—1884no—
1069Q8—1882no—
1070D4—21no—
1071D4—21no—
1072D4—44no—
1073D4—478no—
1074D4—474no—
1075D4—941no—
1076D4—941no—
1077D4—1884no—
1078D4—1882no—
1079D4—1884no—
1080D4—1884no—
1081D4SD16×D4714yescomplemented
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—22no—
1087C2×C4—21no—
1088C2×C4—22no—
1089C2×C4—44no—
1090C2×C4—42no—
1091C2×C4—82no—
1092C2×C4—471no—
1093C2×C4—471no—
1094C2×C4—474no—
1095C2×C4—472no—
1096C2×C4—472no—
1097C2×C4—471no—
1098C2×C4—472no—
1099C2×C4—944no—
1100C2×C4—944no—
1101C2×C4—942no—
1102C2×C4—944no—
1103C2×C4—942no—
1104C2×C4—942no—
1105C2×C4—941no—
1106C2×C4—941no—
1107C2×C4—942no—
1108C2×C4—941no—
1109C2×C4—942no—
1110C2×C4—3762no—
1111C2×C4—3762no—
1112C2×C4—3762no—
1113C2×C4—1882no—
1114C2×C4—1882no—
1115C2×C4—1884no—
1116C2×C4—1882no—
1117C2×C4—1884no—
1118C2×C4—1884no—
1119C2×C4—1884no—
1120C2×C4—1882no—
1121C2×C4—1882no—
1122C2×C4—1884no—
1123C2×C4—1882no—
1124C2×C4C2×D4×D4711yescharacteristic
1125C2×C4C2×D4×D4712yes—
1126C2×C4C2×D4×D4711yescharacteristic
1127C2×C4C24×D4711yescharacteristic
1128C8—22no—
1129C8—21no—
1130C8—472no—
1131C8—942no—
1132C8—941no—
1133C8#41×D4712yescomplemented
1134C22—22no—
1135C22—22no—
1136C22—41no—
1137C22—41no—
1138C22—41no—
1139C22—472no—
1140C22—472no—
1141C22—472no—
1142C22—474no—
1143C22—9416no—
1144C22—942no—
1145C22—942no—
1146C22—3764no—
1147C22—1881no—
1148C22—1881no—
1149C22—1881no—
1150C22C2×SD16×D4714yes—
1151C22C22×D4×D4711yescharacteristic
1152C4—22no—
1153C4—21no—
1154C4—41no—
1155C4—42no—
1156C4—41no—
1157C4—41no—
1158C4—42no—
1159C4—472no—
1160C4—472no—
1161C4—942no—
1162C4—941no—
1163C4—1881no—
1164C4—1882no—
1165C4—1881no—
1166C4—1881no—
1167C4—1882no—
1168C4C2×SD16×D4712yes—
1169C4C2×#41×D4711yescharacteristic
1170C42−1+4×D4711yescharacteristic
1171C2—24no—
1172C2—81no—
1173C2—474no—
1174C2—944no—
1175C2—3761no—
1176C2#547×D4711yescharacteristic
1177C2C22×SD16×D4711yescharacteristic
1178C2#577×D4711yescharacteristic
subgroupG/H
centerC22C22×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC47×#3335C2
socleC22×C47C23×D4
prime radical#547×D47C2
hypercenter#3335D47
hypocenterC47C2×#3335
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3335

Complements

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

NH ≅ G/Ntype
1. #554×D47C2semidirect
3. #20255748C2semidirect
4. #20255747C2semidirect
5. #20255746C2semidirect
6. #20255745C2semidirect
7. #20255744C2semidirect
8. #20255743C2semidirect
9. #20255742C2semidirect
10. #20255741C2semidirect
11. #20255740C2semidirect
12. #20255739C2semidirect
13. #20255738C2semidirect
14. #498×D47C2semidirect
15. #481×D47C2semidirect
16. #483×D47C2semidirect
17. #475×D47C2semidirect
18. #476×D47C2semidirect
19. #465×D47C2semidirect
20. C4×SD16×D47C2semidirect
21. C8×D4×D47C2semidirect
22. C2×#106×D47C2semidirect
23. C47×#3335C2semidirect
27. #15689834C22semidirect
28. #15689833C22semidirect
30. #15689831C22semidirect
31. #15689830C22semidirect
33. #15689828C22semidirect
57. #15689521C22semidirect
58. #15689520C22semidirect
59. #15689520C22semidirect
60. #15689519C22semidirect
61. #15689519C22semidirect
62. #15689455C22semidirect
63. #15689455C22semidirect
64. #15689454C22semidirect
65. #15689453C22semidirect
66. #15689452C22semidirect
67. #15689452C22semidirect
68. #15689451C22semidirect
69. #15689443C22semidirect
70. #15689443C22semidirect
71. #15689442C22semidirect
72. #15689441C22semidirect
73. #15689440C22semidirect
74. #15689440C22semidirect
75. #15689439C22semidirect
76. #15689414C22semidirect
77. #15689413C22semidirect
78. #15689412C22semidirect
79. #15689411C22semidirect
80. #15689410C22semidirect
81. #15689409C22semidirect
82. #15689408C22semidirect
83. #15689407C22semidirect
84. #15689406C22semidirect
85. #15689405C22semidirect
86. #15689355C22semidirect
87. #15689354C22semidirect
88. #15689353C22semidirect
89. #15689352C22semidirect
90. #15689351C22semidirect
91. #15689350C22semidirect
92. #15689349C22semidirect
93. #15689214C22semidirect
94. C4×#10625325C22semidirect
95. SD16×Dic47C22semidirect
96. C4×#10625336C22semidirect
97. #15689210C22semidirect
98. C4×#10625335C22semidirect
99. #15689208C22semidirect
100. C8×D188C22semidirect
101. D4×C47⋊C8C22semidirect
102. #15689188C22semidirect
103. C8×C22⋊D47C22semidirect
104. (C22⋊D47)⋊C8C22semidirect
105. C2×#13093956C22semidirect
106. C2×#13093955C22semidirect
107. C2×#13093955C22semidirect
113. #106×D47C22semidirect
114. #106×D47C22semidirect
115. #106×D47C22semidirect
116. #106×D47C22semidirect
124. C47×#554C22semidirect
126. C47×#498C22semidirect
127. C47×#483C22semidirect
128. C47×#481C22semidirect
129. C47×#476C22semidirect
130. C47×#475C22semidirect
131. C47×#465C22semidirect
132. C4×SD16×C47C22semidirect
133. C8×D4×C47C22semidirect
134. C2×#106×C47C22semidirect
346. D4×D47SD16semidirect
457. C8×D47#41semidirect
476. D4×C47C2×SD16semidirect
494. C22⋊D47C2×SD16semidirect
511. D188C2×SD16semidirect
540. C8×C47C2×#41semidirect
543. C47⋊C8C2×#41semidirect
595. #3335D47direct (N × H)
612. D47#3335direct (N × H)
624. #554C2×D47semidirect
653. #498C2×D47semidirect
661. #483C2×D47semidirect
669. #481C2×D47semidirect
675. #476C2×D47semidirect
681. #475C2×D47semidirect
689. #465C2×D47semidirect
697. C4×SD16C2×D47semidirect
703. C8×D4C2×D47semidirect
716. C2×#106C2×D47semidirect
724. C47C2×#3335semidirect
1081. D4SD16×D47semidirect
1133. C8#41×D47semidirect

Maximal subgroups

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

subgroupindex
#554×D472
#547×D472
#202557482
#202557472
#202557462
#202557452
#202557442
#202557432
#202557422
#202557412
#202557402
#202557392
#202557382
#498×D472
#481×D472
#483×D472
#475×D472
#476×D472
#465×D472
C4×SD16×D472
C8×D4×D472
C2×#106×D472
C47×#33352
C2×#333547